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<!DOCTYPE PROOF SYSTEM "http://a3pat.ensiie.fr/pub/a3pat.dtd">
<PROOF><SIGNATURE><SYMBOLLIST><SYMBOL arity="1" unmarked=""><NAME>isNatKind</NAME></SYMBOL><SYMBOL arity="2" unmarked="U21"><NAME>Marked_U21</NAME></SYMBOL><SYMBOL arity="1" unmarked=""><NAME>U22</NAME></SYMBOL><SYMBOL arity="3" unmarked="U11"><NAME>Marked_U11</NAME></SYMBOL><SYMBOL arity="2" unmarked=""><NAME>plus</NAME></SYMBOL><SYMBOL arity="1" unmarked="s"><NAME>Marked_s</NAME></SYMBOL><SYMBOL arity="1" unmarked=""><NAME>active</NAME></SYMBOL><SYMBOL arity="1" unmarked="active"><NAME>Marked_active</NAME></SYMBOL><SYMBOL arity="2" unmarked=""><NAME>and</NAME></SYMBOL><SYMBOL arity="2" unmarked="U31"><NAME>Marked_U31</NAME></SYMBOL><SYMBOL arity="0" unmarked=""><NAME>tt</NAME></SYMBOL><SYMBOL arity="1" unmarked="isNat"><NAME>Marked_isNat</NAME></SYMBOL><SYMBOL arity="2" unmarked=""><NAME>U31</NAME></SYMBOL><SYMBOL arity="2" unmarked="and"><NAME>Marked_and</NAME></SYMBOL><SYMBOL arity="2" unmarked=""><NAME>U12</NAME></SYMBOL><SYMBOL arity="0" unmarked=""><NAME>0</NAME></SYMBOL><SYMBOL arity="1" unmarked="U22"><NAME>Marked_U22</NAME></SYMBOL><SYMBOL arity="1" unmarked=""><NAME>U13</NAME></SYMBOL><SYMBOL arity="2" unmarked="U12"><NAME>Marked_U12</NAME></SYMBOL><SYMBOL arity="1" unmarked=""><NAME>s</NAME></SYMBOL><SYMBOL arity="2" unmarked="plus"><NAME>Marked_plus</NAME></SYMBOL><SYMBOL arity="1" unmarked=""><NAME>isNat</NAME></SYMBOL><SYMBOL arity="1" unmarked="mark"><NAME>Marked_mark</NAME></SYMBOL><SYMBOL arity="3" unmarked=""><NAME>U41</NAME></SYMBOL><SYMBOL arity="3" unmarked="U41"><NAME>Marked_U41</NAME></SYMBOL><SYMBOL arity="3" unmarked=""><NAME>U11</NAME></SYMBOL><SYMBOL arity="1" unmarked="U13"><NAME>Marked_U13</NAME></SYMBOL><SYMBOL arity="2" unmarked=""><NAME>U21</NAME></SYMBOL><SYMBOL arity="1" unmarked="isNatKind"><NAME>Marked_isNatKind</NAME></SYMBOL><SYMBOL arity="1" unmarked=""><NAME>mark</NAME></SYMBOL></SYMBOLLIST><VARLIST><VAR>X3</VAR><VAR>X2</VAR><VAR>X1</VAR><VAR>X</VAR><VAR>M</VAR><VAR>N</VAR><VAR>V2</VAR><VAR>V1</VAR></VARLIST></SIGNATURE><PROPERTY criterion="dp" prop="sntrs"><SYSTEM><REWSYS><RULE><LHS>active(U11(tt,V1,V2))</LHS><RHS>mark(U12(isNat(V1),V2))</RHS></RULE><RULE><LHS>active(U12(tt,V2))</LHS><RHS>mark(U13(isNat(V2)))</RHS></RULE><RULE><LHS>active(U13(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U21(tt,V1))</LHS><RHS>mark(U22(isNat(V1)))</RHS></RULE><RULE><LHS>active(U22(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U31(tt,N))</LHS><RHS>mark(N)</RHS></RULE><RULE><LHS>active(U41(tt,M,N))</LHS><RHS>mark(s(plus(N,M)))</RHS></RULE><RULE><LHS>active(and(tt,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(isNat(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNat(plus(V1,V2)))</LHS><RHS>mark(U11(and(isNatKind(V1),isNatKind(V2)),V1,V2))</RHS></RULE><RULE><LHS>active(isNat(s(V1)))</LHS><RHS>mark(U21(isNatKind(V1),V1))</RHS></RULE><RULE><LHS>active(isNatKind(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNatKind(plus(V1,V2)))</LHS><RHS>mark(and(isNatKind(V1),isNatKind(V2)))</RHS></RULE><RULE><LHS>active(isNatKind(s(V1)))</LHS><RHS>mark(isNatKind(V1))</RHS></RULE><RULE><LHS>active(plus(N,0))</LHS><RHS>mark(U31(and(isNat(N),isNatKind(N)),N))</RHS></RULE><RULE><LHS>active(plus(N,s(M)))</LHS><RHS>mark(U41(and(and(isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),M,N))</RHS></RULE><RULE><LHS>mark(U11(X1,X2,X3))</LHS><RHS>active(U11(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(tt)</LHS><RHS>active(tt)</RHS></RULE><RULE><LHS>mark(U12(X1,X2))</LHS><RHS>active(U12(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(isNat(X))</LHS><RHS>active(isNat(X))</RHS></RULE><RULE><LHS>mark(U13(X))</LHS><RHS>active(U13(mark(X)))</RHS></RULE><RULE><LHS>mark(U21(X1,X2))</LHS><RHS>active(U21(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U22(X))</LHS><RHS>active(U22(mark(X)))</RHS></RULE><RULE><LHS>mark(U31(X1,X2))</LHS><RHS>active(U31(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U41(X1,X2,X3))</LHS><RHS>active(U41(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(mark(X)))</RHS></RULE><RULE><LHS>mark(plus(X1,X2))</LHS><RHS>active(plus(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(isNatKind(X))</LHS><RHS>active(isNatKind(X))</RHS></RULE><RULE><LHS>U11(mark(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,mark(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,mark(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(active(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,active(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,active(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U12(mark(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,mark(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(active(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,active(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>isNat(mark(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>isNat(active(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>U13(mark(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U13(active(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U21(mark(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,mark(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(active(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,active(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U22(mark(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U22(active(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U31(mark(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,mark(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(active(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,active(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U41(mark(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,mark(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,mark(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(active(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,active(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,active(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>s(mark(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>s(active(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>plus(mark(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,mark(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(active(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,active(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>and(mark(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,mark(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(active(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,active(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>isNatKind(mark(X))</LHS><RHS>isNatKind(X)</RHS></RULE><RULE><LHS>isNatKind(active(X))</LHS><RHS>isNatKind(X)</RHS></RULE></REWSYS></SYSTEM><CRITERION/><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(U11(tt,V1,V2))</LHS><RHS>mark(U12(isNat(V1),V2))</RHS></RULE><RULE><LHS>active(U12(tt,V2))</LHS><RHS>mark(U13(isNat(V2)))</RHS></RULE><RULE><LHS>active(U13(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U21(tt,V1))</LHS><RHS>mark(U22(isNat(V1)))</RHS></RULE><RULE><LHS>active(U22(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U31(tt,N))</LHS><RHS>mark(N)</RHS></RULE><RULE><LHS>active(U41(tt,M,N))</LHS><RHS>mark(s(plus(N,M)))</RHS></RULE><RULE><LHS>active(and(tt,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(isNat(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNat(plus(V1,V2)))</LHS><RHS>mark(U11(and(isNatKind(V1),isNatKind(V2)),V1,V2))</RHS></RULE><RULE><LHS>active(isNat(s(V1)))</LHS><RHS>mark(U21(isNatKind(V1),V1))</RHS></RULE><RULE><LHS>active(isNatKind(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNatKind(plus(V1,V2)))</LHS><RHS>mark(and(isNatKind(V1),isNatKind(V2)))</RHS></RULE><RULE><LHS>active(isNatKind(s(V1)))</LHS><RHS>mark(isNatKind(V1))</RHS></RULE><RULE><LHS>active(plus(N,0))</LHS><RHS>mark(U31(and(isNat(N),isNatKind(N)),N))</RHS></RULE><RULE><LHS>active(plus(N,s(M)))</LHS><RHS>mark(U41(and(and(isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),M,N))</RHS></RULE><RULE><LHS>mark(U11(X1,X2,X3))</LHS><RHS>active(U11(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(tt)</LHS><RHS>active(tt)</RHS></RULE><RULE><LHS>mark(U12(X1,X2))</LHS><RHS>active(U12(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(isNat(X))</LHS><RHS>active(isNat(X))</RHS></RULE><RULE><LHS>mark(U13(X))</LHS><RHS>active(U13(mark(X)))</RHS></RULE><RULE><LHS>mark(U21(X1,X2))</LHS><RHS>active(U21(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U22(X))</LHS><RHS>active(U22(mark(X)))</RHS></RULE><RULE><LHS>mark(U31(X1,X2))</LHS><RHS>active(U31(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U41(X1,X2,X3))</LHS><RHS>active(U41(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(mark(X)))</RHS></RULE><RULE><LHS>mark(plus(X1,X2))</LHS><RHS>active(plus(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(isNatKind(X))</LHS><RHS>active(isNatKind(X))</RHS></RULE><RULE><LHS>U11(mark(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,mark(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,mark(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(active(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,active(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,active(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U12(mark(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,mark(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(active(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,active(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>isNat(mark(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>isNat(active(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>U13(mark(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U13(active(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U21(mark(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,mark(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(active(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,active(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U22(mark(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U22(active(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U31(mark(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,mark(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(active(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,active(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U41(mark(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,mark(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,mark(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(active(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,active(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,active(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>s(mark(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>s(active(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>plus(mark(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,mark(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(active(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,active(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>and(mark(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,mark(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(active(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,active(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>isNatKind(mark(X))</LHS><RHS>isNatKind(X)</RHS></RULE><RULE><LHS>isNatKind(active(X))</LHS><RHS>isNatKind(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_active(U11(tt,V1,V2))</LHS><RHS>Marked_mark(U12(isNat(V1),V2))</RHS></DPRULE><DPRULE num="1"><LHS>Marked_active(U11(tt,V1,V2))</LHS><RHS>Marked_U12(isNat(V1),V2)</RHS></DPRULE><DPRULE num="2"><LHS>Marked_active(U11(tt,V1,V2))</LHS><RHS>Marked_isNat(V1)</RHS></DPRULE><DPRULE num="3"><LHS>Marked_active(U12(tt,V2))</LHS><RHS>Marked_mark(U13(isNat(V2)))</RHS></DPRULE><DPRULE num="4"><LHS>Marked_active(U12(tt,V2))</LHS><RHS>Marked_U13(isNat(V2))</RHS></DPRULE><DPRULE num="5"><LHS>Marked_active(U12(tt,V2))</LHS><RHS>Marked_isNat(V2)</RHS></DPRULE><DPRULE num="6"><LHS>Marked_active(U13(tt))</LHS><RHS>Marked_mark(tt)</RHS></DPRULE><DPRULE num="7"><LHS>Marked_active(U21(tt,V1))</LHS><RHS>Marked_mark(U22(isNat(V1)))</RHS></DPRULE><DPRULE num="8"><LHS>Marked_active(U21(tt,V1))</LHS><RHS>Marked_U22(isNat(V1))</RHS></DPRULE><DPRULE num="9"><LHS>Marked_active(U21(tt,V1))</LHS><RHS>Marked_isNat(V1)</RHS></DPRULE><DPRULE num="10"><LHS>Marked_active(U22(tt))</LHS><RHS>Marked_mark(tt)</RHS></DPRULE><DPRULE num="11"><LHS>Marked_active(U31(tt,N))</LHS><RHS>Marked_mark(N)</RHS></DPRULE><DPRULE num="12"><LHS>Marked_active(U41(tt,M,N))</LHS><RHS>Marked_mark(s(plus(N,M)))</RHS></DPRULE><DPRULE num="13"><LHS>Marked_active(U41(tt,M,N))</LHS><RHS>Marked_s(plus(N,M))</RHS></DPRULE><DPRULE num="14"><LHS>Marked_active(U41(tt,M,N))</LHS><RHS>Marked_plus(N,M)</RHS></DPRULE><DPRULE num="15"><LHS>Marked_active(and(tt,X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="16"><LHS>Marked_active(isNat(0))</LHS><RHS>Marked_mark(tt)</RHS></DPRULE><DPRULE num="17"><LHS>Marked_active(isNat(plus(V1,V2)))</LHS><RHS>Marked_mark(U11(and(isNatKind(V1),isNatKind(V2)),V1,V2))</RHS></DPRULE><DPRULE num="18"><LHS>Marked_active(isNat(plus(V1,V2)))</LHS><RHS>Marked_U11(and(isNatKind(V1),isNatKind(V2)),V1,V2)</RHS></DPRULE><DPRULE num="19"><LHS>Marked_active(isNat(plus(V1,V2)))</LHS><RHS>Marked_and(isNatKind(V1),isNatKind(V2))</RHS></DPRULE><DPRULE num="20"><LHS>Marked_active(isNat(plus(V1,V2)))</LHS><RHS>Marked_isNatKind(V1)</RHS></DPRULE><DPRULE num="21"><LHS>Marked_active(isNat(plus(V1,V2)))</LHS><RHS>Marked_isNatKind(V2)</RHS></DPRULE><DPRULE num="22"><LHS>Marked_active(isNat(s(V1)))</LHS><RHS>Marked_mark(U21(isNatKind(V1),V1))</RHS></DPRULE><DPRULE num="23"><LHS>Marked_active(isNat(s(V1)))</LHS><RHS>Marked_U21(isNatKind(V1),V1)</RHS></DPRULE><DPRULE num="24"><LHS>Marked_active(isNat(s(V1)))</LHS><RHS>Marked_isNatKind(V1)</RHS></DPRULE><DPRULE num="25"><LHS>Marked_active(isNatKind(0))</LHS><RHS>Marked_mark(tt)</RHS></DPRULE><DPRULE num="26"><LHS>Marked_active(isNatKind(plus(V1,V2)))</LHS><RHS>Marked_mark(and(isNatKind(V1),isNatKind(V2)))</RHS></DPRULE><DPRULE num="27"><LHS>Marked_active(isNatKind(plus(V1,V2)))</LHS><RHS>Marked_and(isNatKind(V1),isNatKind(V2))</RHS></DPRULE><DPRULE num="28"><LHS>Marked_active(isNatKind(plus(V1,V2)))</LHS><RHS>Marked_isNatKind(V1)</RHS></DPRULE><DPRULE num="29"><LHS>Marked_active(isNatKind(plus(V1,V2)))</LHS><RHS>Marked_isNatKind(V2)</RHS></DPRULE><DPRULE num="30"><LHS>Marked_active(isNatKind(s(V1)))</LHS><RHS>Marked_mark(isNatKind(V1))</RHS></DPRULE><DPRULE num="31"><LHS>Marked_active(isNatKind(s(V1)))</LHS><RHS>Marked_isNatKind(V1)</RHS></DPRULE><DPRULE num="32"><LHS>Marked_active(plus(N,0))</LHS><RHS>Marked_mark(U31(and(isNat(N),isNatKind(N)),N))</RHS></DPRULE><DPRULE num="33"><LHS>Marked_active(plus(N,0))</LHS><RHS>Marked_U31(and(isNat(N),isNatKind(N)),N)</RHS></DPRULE><DPRULE num="34"><LHS>Marked_active(plus(N,0))</LHS><RHS>Marked_and(isNat(N),isNatKind(N))</RHS></DPRULE><DPRULE num="35"><LHS>Marked_active(plus(N,0))</LHS><RHS>Marked_isNat(N)</RHS></DPRULE><DPRULE num="36"><LHS>Marked_active(plus(N,0))</LHS><RHS>Marked_isNatKind(N)</RHS></DPRULE><DPRULE num="37"><LHS>Marked_active(plus(N,s(M)))</LHS><RHS>Marked_mark(U41(and(and(isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),
             M,N))</RHS></DPRULE><DPRULE num="38"><LHS>Marked_active(plus(N,s(M)))</LHS><RHS>Marked_U41(and(and(isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),M,N)</RHS></DPRULE><DPRULE num="39"><LHS>Marked_active(plus(N,s(M)))</LHS><RHS>Marked_and(and(isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N)))</RHS></DPRULE><DPRULE num="40"><LHS>Marked_active(plus(N,s(M)))</LHS><RHS>Marked_and(isNat(M),isNatKind(M))</RHS></DPRULE><DPRULE num="41"><LHS>Marked_active(plus(N,s(M)))</LHS><RHS>Marked_isNat(M)</RHS></DPRULE><DPRULE num="42"><LHS>Marked_active(plus(N,s(M)))</LHS><RHS>Marked_isNatKind(M)</RHS></DPRULE><DPRULE num="43"><LHS>Marked_active(plus(N,s(M)))</LHS><RHS>Marked_and(isNat(N),isNatKind(N))</RHS></DPRULE><DPRULE num="44"><LHS>Marked_active(plus(N,s(M)))</LHS><RHS>Marked_isNat(N)</RHS></DPRULE><DPRULE num="45"><LHS>Marked_active(plus(N,s(M)))</LHS><RHS>Marked_isNatKind(N)</RHS></DPRULE><DPRULE num="46"><LHS>Marked_mark(U11(X1,X2,X3))</LHS><RHS>Marked_active(U11(mark(X1),X2,X3))</RHS></DPRULE><DPRULE num="47"><LHS>Marked_mark(U11(X1,X2,X3))</LHS><RHS>Marked_U11(mark(X1),X2,X3)</RHS></DPRULE><DPRULE num="48"><LHS>Marked_mark(U11(X1,X2,X3))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="49"><LHS>Marked_mark(tt)</LHS><RHS>Marked_active(tt)</RHS></DPRULE><DPRULE num="50"><LHS>Marked_mark(U12(X1,X2))</LHS><RHS>Marked_active(U12(mark(X1),X2))</RHS></DPRULE><DPRULE num="51"><LHS>Marked_mark(U12(X1,X2))</LHS><RHS>Marked_U12(mark(X1),X2)</RHS></DPRULE><DPRULE num="52"><LHS>Marked_mark(U12(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="53"><LHS>Marked_mark(isNat(X))</LHS><RHS>Marked_active(isNat(X))</RHS></DPRULE><DPRULE num="54"><LHS>Marked_mark(U13(X))</LHS><RHS>Marked_active(U13(mark(X)))</RHS></DPRULE><DPRULE num="55"><LHS>Marked_mark(U13(X))</LHS><RHS>Marked_U13(mark(X))</RHS></DPRULE><DPRULE num="56"><LHS>Marked_mark(U13(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="57"><LHS>Marked_mark(U21(X1,X2))</LHS><RHS>Marked_active(U21(mark(X1),X2))</RHS></DPRULE><DPRULE num="58"><LHS>Marked_mark(U21(X1,X2))</LHS><RHS>Marked_U21(mark(X1),X2)</RHS></DPRULE><DPRULE num="59"><LHS>Marked_mark(U21(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="60"><LHS>Marked_mark(U22(X))</LHS><RHS>Marked_active(U22(mark(X)))</RHS></DPRULE><DPRULE num="61"><LHS>Marked_mark(U22(X))</LHS><RHS>Marked_U22(mark(X))</RHS></DPRULE><DPRULE num="62"><LHS>Marked_mark(U22(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="63"><LHS>Marked_mark(U31(X1,X2))</LHS><RHS>Marked_active(U31(mark(X1),X2))</RHS></DPRULE><DPRULE num="64"><LHS>Marked_mark(U31(X1,X2))</LHS><RHS>Marked_U31(mark(X1),X2)</RHS></DPRULE><DPRULE num="65"><LHS>Marked_mark(U31(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="66"><LHS>Marked_mark(U41(X1,X2,X3))</LHS><RHS>Marked_active(U41(mark(X1),X2,X3))</RHS></DPRULE><DPRULE num="67"><LHS>Marked_mark(U41(X1,X2,X3))</LHS><RHS>Marked_U41(mark(X1),X2,X3)</RHS></DPRULE><DPRULE num="68"><LHS>Marked_mark(U41(X1,X2,X3))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="69"><LHS>Marked_mark(s(X))</LHS><RHS>Marked_active(s(mark(X)))</RHS></DPRULE><DPRULE num="70"><LHS>Marked_mark(s(X))</LHS><RHS>Marked_s(mark(X))</RHS></DPRULE><DPRULE num="71"><LHS>Marked_mark(s(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="72"><LHS>Marked_mark(plus(X1,X2))</LHS><RHS>Marked_active(plus(mark(X1),mark(X2)))</RHS></DPRULE><DPRULE num="73"><LHS>Marked_mark(plus(X1,X2))</LHS><RHS>Marked_plus(mark(X1),mark(X2))</RHS></DPRULE><DPRULE num="74"><LHS>Marked_mark(plus(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="75"><LHS>Marked_mark(plus(X1,X2))</LHS><RHS>Marked_mark(X2)</RHS></DPRULE><DPRULE num="76"><LHS>Marked_mark(and(X1,X2))</LHS><RHS>Marked_active(and(mark(X1),X2))</RHS></DPRULE><DPRULE num="77"><LHS>Marked_mark(and(X1,X2))</LHS><RHS>Marked_and(mark(X1),X2)</RHS></DPRULE><DPRULE num="78"><LHS>Marked_mark(and(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="79"><LHS>Marked_mark(0)</LHS><RHS>Marked_active(0)</RHS></DPRULE><DPRULE num="80"><LHS>Marked_mark(isNatKind(X))</LHS><RHS>Marked_active(isNatKind(X))</RHS></DPRULE><DPRULE num="81"><LHS>Marked_U11(mark(X1),X2,X3)</LHS><RHS>Marked_U11(X1,X2,X3)</RHS></DPRULE><DPRULE num="82"><LHS>Marked_U11(X1,mark(X2),X3)</LHS><RHS>Marked_U11(X1,X2,X3)</RHS></DPRULE><DPRULE num="83"><LHS>Marked_U11(X1,X2,mark(X3))</LHS><RHS>Marked_U11(X1,X2,X3)</RHS></DPRULE><DPRULE num="84"><LHS>Marked_U11(active(X1),X2,X3)</LHS><RHS>Marked_U11(X1,X2,X3)</RHS></DPRULE><DPRULE num="85"><LHS>Marked_U11(X1,active(X2),X3)</LHS><RHS>Marked_U11(X1,X2,X3)</RHS></DPRULE><DPRULE num="86"><LHS>Marked_U11(X1,X2,active(X3))</LHS><RHS>Marked_U11(X1,X2,X3)</RHS></DPRULE><DPRULE num="87"><LHS>Marked_U12(mark(X1),X2)</LHS><RHS>Marked_U12(X1,X2)</RHS></DPRULE><DPRULE num="88"><LHS>Marked_U12(X1,mark(X2))</LHS><RHS>Marked_U12(X1,X2)</RHS></DPRULE><DPRULE num="89"><LHS>Marked_U12(active(X1),X2)</LHS><RHS>Marked_U12(X1,X2)</RHS></DPRULE><DPRULE num="90"><LHS>Marked_U12(X1,active(X2))</LHS><RHS>Marked_U12(X1,X2)</RHS></DPRULE><DPRULE num="91"><LHS>Marked_isNat(mark(X))</LHS><RHS>Marked_isNat(X)</RHS></DPRULE><DPRULE num="92"><LHS>Marked_isNat(active(X))</LHS><RHS>Marked_isNat(X)</RHS></DPRULE><DPRULE num="93"><LHS>Marked_U13(mark(X))</LHS><RHS>Marked_U13(X)</RHS></DPRULE><DPRULE num="94"><LHS>Marked_U13(active(X))</LHS><RHS>Marked_U13(X)</RHS></DPRULE><DPRULE num="95"><LHS>Marked_U21(mark(X1),X2)</LHS><RHS>Marked_U21(X1,X2)</RHS></DPRULE><DPRULE num="96"><LHS>Marked_U21(X1,mark(X2))</LHS><RHS>Marked_U21(X1,X2)</RHS></DPRULE><DPRULE num="97"><LHS>Marked_U21(active(X1),X2)</LHS><RHS>Marked_U21(X1,X2)</RHS></DPRULE><DPRULE num="98"><LHS>Marked_U21(X1,active(X2))</LHS><RHS>Marked_U21(X1,X2)</RHS></DPRULE><DPRULE num="99"><LHS>Marked_U22(mark(X))</LHS><RHS>Marked_U22(X)</RHS></DPRULE><DPRULE num="100"><LHS>Marked_U22(active(X))</LHS><RHS>Marked_U22(X)</RHS></DPRULE><DPRULE num="101"><LHS>Marked_U31(mark(X1),X2)</LHS><RHS>Marked_U31(X1,X2)</RHS></DPRULE><DPRULE num="102"><LHS>Marked_U31(X1,mark(X2))</LHS><RHS>Marked_U31(X1,X2)</RHS></DPRULE><DPRULE num="103"><LHS>Marked_U31(active(X1),X2)</LHS><RHS>Marked_U31(X1,X2)</RHS></DPRULE><DPRULE num="104"><LHS>Marked_U31(X1,active(X2))</LHS><RHS>Marked_U31(X1,X2)</RHS></DPRULE><DPRULE num="105"><LHS>Marked_U41(mark(X1),X2,X3)</LHS><RHS>Marked_U41(X1,X2,X3)</RHS></DPRULE><DPRULE num="106"><LHS>Marked_U41(X1,mark(X2),X3)</LHS><RHS>Marked_U41(X1,X2,X3)</RHS></DPRULE><DPRULE num="107"><LHS>Marked_U41(X1,X2,mark(X3))</LHS><RHS>Marked_U41(X1,X2,X3)</RHS></DPRULE><DPRULE num="108"><LHS>Marked_U41(active(X1),X2,X3)</LHS><RHS>Marked_U41(X1,X2,X3)</RHS></DPRULE><DPRULE num="109"><LHS>Marked_U41(X1,active(X2),X3)</LHS><RHS>Marked_U41(X1,X2,X3)</RHS></DPRULE><DPRULE num="110"><LHS>Marked_U41(X1,X2,active(X3))</LHS><RHS>Marked_U41(X1,X2,X3)</RHS></DPRULE><DPRULE num="111"><LHS>Marked_s(mark(X))</LHS><RHS>Marked_s(X)</RHS></DPRULE><DPRULE num="112"><LHS>Marked_s(active(X))</LHS><RHS>Marked_s(X)</RHS></DPRULE><DPRULE num="113"><LHS>Marked_plus(mark(X1),X2)</LHS><RHS>Marked_plus(X1,X2)</RHS></DPRULE><DPRULE num="114"><LHS>Marked_plus(X1,mark(X2))</LHS><RHS>Marked_plus(X1,X2)</RHS></DPRULE><DPRULE num="115"><LHS>Marked_plus(active(X1),X2)</LHS><RHS>Marked_plus(X1,X2)</RHS></DPRULE><DPRULE num="116"><LHS>Marked_plus(X1,active(X2))</LHS><RHS>Marked_plus(X1,X2)</RHS></DPRULE><DPRULE num="117"><LHS>Marked_and(mark(X1),X2)</LHS><RHS>Marked_and(X1,X2)</RHS></DPRULE><DPRULE num="118"><LHS>Marked_and(X1,mark(X2))</LHS><RHS>Marked_and(X1,X2)</RHS></DPRULE><DPRULE num="119"><LHS>Marked_and(active(X1),X2)</LHS><RHS>Marked_and(X1,X2)</RHS></DPRULE><DPRULE num="120"><LHS>Marked_and(X1,active(X2))</LHS><RHS>Marked_and(X1,X2)</RHS></DPRULE><DPRULE num="121"><LHS>Marked_isNatKind(mark(X))</LHS><RHS>Marked_isNatKind(X)</RHS></DPRULE><DPRULE num="122"><LHS>Marked_isNatKind(active(X))</LHS><RHS>Marked_isNatKind(X)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><DAG approx="simpl"><CCLIST><SCC num="0"><NODE ref="121"/><NODE ref="122"/></SCC><SCC num="1"><NODE ref="117"/><NODE ref="118"/><NODE ref="119"/><NODE ref="120"/></SCC><SCC num="2"><NODE ref="113"/><NODE ref="114"/><NODE ref="115"/><NODE ref="116"/></SCC><SCC num="3"><NODE ref="111"/><NODE ref="112"/></SCC><SCC num="4"><NODE ref="105"/><NODE ref="106"/><NODE ref="107"/><NODE ref="108"/><NODE ref="109"/><NODE ref="110"/></SCC><SCC num="5"><NODE ref="101"/><NODE ref="102"/><NODE ref="103"/><NODE ref="104"/></SCC><SCC num="6"><NODE ref="99"/><NODE ref="100"/></SCC><SCC num="7"><NODE ref="95"/><NODE ref="96"/><NODE ref="97"/><NODE ref="98"/></SCC><SCC num="8"><NODE ref="93"/><NODE ref="94"/></SCC><SCC num="9"><NODE ref="91"/><NODE ref="92"/></SCC><SCC num="10"><NODE ref="87"/><NODE ref="88"/><NODE ref="89"/><NODE ref="90"/></SCC><SCC num="11"><NODE ref="81"/><NODE ref="82"/><NODE ref="83"/><NODE ref="84"/><NODE ref="85"/><NODE ref="86"/></SCC><SCC num="12"><NODE ref="0"/><NODE ref="3"/><NODE ref="7"/><NODE ref="11"/><NODE ref="12"/><NODE ref="15"/><NODE ref="17"/><NODE ref="22"/><NODE ref="26"/><NODE ref="30"/><NODE ref="32"/><NODE ref="37"/><NODE ref="46"/><NODE ref="48"/><NODE ref="50"/><NODE ref="52"/><NODE ref="53"/><NODE ref="54"/><NODE ref="56"/><NODE ref="57"/><NODE ref="59"/><NODE ref="60"/><NODE ref="62"/><NODE ref="63"/><NODE ref="65"/><NODE ref="66"/><NODE ref="68"/><NODE ref="69"/><NODE ref="71"/><NODE ref="72"/><NODE ref="74"/><NODE ref="75"/><NODE ref="76"/><NODE ref="78"/><NODE ref="80"/></SCC><NONSCC num="13"><NODE ref="45"/></NONSCC><NONSCC num="14"><NODE ref="44"/></NONSCC><NONSCC num="15"><NODE ref="43"/></NONSCC><NONSCC num="16"><NODE ref="42"/></NONSCC><NONSCC num="17"><NODE ref="41"/></NONSCC><NONSCC num="18"><NODE ref="40"/></NONSCC><NONSCC num="19"><NODE ref="39"/></NONSCC><NONSCC num="20"><NODE ref="38"/></NONSCC><NONSCC num="21"><NODE ref="36"/></NONSCC><NONSCC num="22"><NODE ref="35"/></NONSCC><NONSCC num="23"><NODE ref="34"/></NONSCC><NONSCC num="24"><NODE ref="33"/></NONSCC><NONSCC num="25"><NODE ref="31"/></NONSCC><NONSCC num="26"><NODE ref="29"/></NONSCC><NONSCC num="27"><NODE ref="28"/></NONSCC><NONSCC num="28"><NODE ref="27"/></NONSCC><NONSCC num="29"><NODE ref="25"/></NONSCC><NONSCC num="30"><NODE ref="24"/></NONSCC><NONSCC num="31"><NODE ref="23"/></NONSCC><NONSCC num="32"><NODE ref="21"/></NONSCC><NONSCC num="33"><NODE ref="20"/></NONSCC><NONSCC num="34"><NODE ref="19"/></NONSCC><NONSCC num="35"><NODE ref="18"/></NONSCC><NONSCC num="36"><NODE ref="16"/></NONSCC><NONSCC num="37"><NODE ref="14"/></NONSCC><NONSCC num="38"><NODE ref="13"/></NONSCC><NONSCC num="39"><NODE ref="10"/></NONSCC><NONSCC num="40"><NODE ref="9"/></NONSCC><NONSCC num="41"><NODE ref="8"/></NONSCC><NONSCC num="42"><NODE ref="6"/></NONSCC><NONSCC num="43"><NODE ref="5"/></NONSCC><NONSCC num="44"><NODE ref="4"/></NONSCC><NONSCC num="45"><NODE ref="2"/></NONSCC><NONSCC num="46"><NODE ref="1"/></NONSCC><NONSCC num="47"><NODE ref="79"/></NONSCC><NONSCC num="48"><NODE ref="77"/></NONSCC><NONSCC num="49"><NODE ref="73"/></NONSCC><NONSCC num="50"><NODE ref="70"/></NONSCC><NONSCC num="51"><NODE ref="67"/></NONSCC><NONSCC num="52"><NODE ref="64"/></NONSCC><NONSCC num="53"><NODE ref="61"/></NONSCC><NONSCC num="54"><NODE ref="58"/></NONSCC><NONSCC num="55"><NODE ref="55"/></NONSCC><NONSCC num="56"><NODE ref="51"/></NONSCC><NONSCC num="57"><NODE ref="49"/></NONSCC><NONSCC num="58"><NODE ref="47"/></NONSCC></CCLIST><EDGE end="58" start="12"/><EDGE end="57" start="12"/><EDGE end="56" start="12"/><EDGE end="55" start="12"/><EDGE end="54" start="12"/><EDGE end="53" start="12"/><EDGE end="52" start="12"/><EDGE end="51" start="12"/><EDGE end="50" start="12"/><EDGE end="49" start="12"/><EDGE end="48" start="12"/><EDGE end="47" start="12"/><EDGE end="46" start="12"/><EDGE end="45" start="12"/><EDGE end="44" start="12"/><EDGE end="43" start="12"/><EDGE end="42" start="12"/><EDGE end="41" start="12"/><EDGE end="40" start="12"/><EDGE end="39" start="12"/><EDGE end="38" start="12"/><EDGE end="37" start="12"/><EDGE end="36" start="12"/><EDGE end="35" start="12"/><EDGE end="34" start="12"/><EDGE end="33" start="12"/><EDGE end="32" start="12"/><EDGE end="31" start="12"/><EDGE end="30" start="12"/><EDGE end="29" start="12"/><EDGE end="28" start="12"/><EDGE end="27" start="12"/><EDGE end="26" start="12"/><EDGE end="25" start="12"/><EDGE end="24" start="12"/><EDGE end="23" start="12"/><EDGE end="22" start="12"/><EDGE end="21" start="12"/><EDGE end="20" start="12"/><EDGE end="19" start="12"/><EDGE end="18" start="12"/><EDGE end="17" start="12"/><EDGE end="16" start="12"/><EDGE end="15" start="12"/><EDGE end="14" start="12"/><EDGE end="13" start="12"/><EDGE end="0" start="13"/><EDGE end="9" start="14"/><EDGE end="1" start="15"/><EDGE end="0" start="16"/><EDGE end="9" start="17"/><EDGE end="1" start="18"/><EDGE end="1" start="19"/><EDGE end="4" start="20"/><EDGE end="0" start="21"/><EDGE end="9" start="22"/><EDGE end="1" start="23"/><EDGE end="5" start="24"/><EDGE end="0" start="25"/><EDGE end="0" start="26"/><EDGE end="0" start="27"/><EDGE end="1" start="28"/><EDGE end="57" start="29"/><EDGE end="0" start="30"/><EDGE end="7" start="31"/><EDGE end="0" start="32"/><EDGE end="0" start="33"/><EDGE end="1" start="34"/><EDGE end="11" start="35"/><EDGE end="57" start="36"/><EDGE end="2" start="37"/><EDGE end="3" start="38"/><EDGE end="57" start="39"/><EDGE end="9" start="40"/><EDGE end="6" start="41"/><EDGE end="57" start="42"/><EDGE end="9" start="43"/><EDGE end="8" start="44"/><EDGE end="9" start="45"/><EDGE end="10" start="46"/><EDGE end="1" start="48"/><EDGE end="2" start="49"/><EDGE end="3" start="50"/><EDGE end="4" start="51"/><EDGE end="5" start="52"/><EDGE end="6" start="53"/><EDGE end="7" start="54"/><EDGE end="8" start="55"/><EDGE end="10" start="56"/><EDGE end="11" start="58"/></DAG></CRITERION><PROPERTY criterion="stronggraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(U11(tt,V1,V2))</LHS><RHS>mark(U12(isNat(V1),V2))</RHS></RULE><RULE><LHS>active(U12(tt,V2))</LHS><RHS>mark(U13(isNat(V2)))</RHS></RULE><RULE><LHS>active(U13(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U21(tt,V1))</LHS><RHS>mark(U22(isNat(V1)))</RHS></RULE><RULE><LHS>active(U22(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U31(tt,N))</LHS><RHS>mark(N)</RHS></RULE><RULE><LHS>active(U41(tt,M,N))</LHS><RHS>mark(s(plus(N,M)))</RHS></RULE><RULE><LHS>active(and(tt,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(isNat(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNat(plus(V1,V2)))</LHS><RHS>mark(U11(and(isNatKind(V1),isNatKind(V2)),V1,V2))</RHS></RULE><RULE><LHS>active(isNat(s(V1)))</LHS><RHS>mark(U21(isNatKind(V1),V1))</RHS></RULE><RULE><LHS>active(isNatKind(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNatKind(plus(V1,V2)))</LHS><RHS>mark(and(isNatKind(V1),isNatKind(V2)))</RHS></RULE><RULE><LHS>active(isNatKind(s(V1)))</LHS><RHS>mark(isNatKind(V1))</RHS></RULE><RULE><LHS>active(plus(N,0))</LHS><RHS>mark(U31(and(isNat(N),isNatKind(N)),N))</RHS></RULE><RULE><LHS>active(plus(N,s(M)))</LHS><RHS>mark(U41(and(and(isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),M,N))</RHS></RULE><RULE><LHS>mark(U11(X1,X2,X3))</LHS><RHS>active(U11(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(tt)</LHS><RHS>active(tt)</RHS></RULE><RULE><LHS>mark(U12(X1,X2))</LHS><RHS>active(U12(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(isNat(X))</LHS><RHS>active(isNat(X))</RHS></RULE><RULE><LHS>mark(U13(X))</LHS><RHS>active(U13(mark(X)))</RHS></RULE><RULE><LHS>mark(U21(X1,X2))</LHS><RHS>active(U21(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U22(X))</LHS><RHS>active(U22(mark(X)))</RHS></RULE><RULE><LHS>mark(U31(X1,X2))</LHS><RHS>active(U31(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U41(X1,X2,X3))</LHS><RHS>active(U41(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(mark(X)))</RHS></RULE><RULE><LHS>mark(plus(X1,X2))</LHS><RHS>active(plus(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(isNatKind(X))</LHS><RHS>active(isNatKind(X))</RHS></RULE><RULE><LHS>U11(mark(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,mark(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,mark(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(active(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,active(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,active(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U12(mark(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,mark(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(active(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,active(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>isNat(mark(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>isNat(active(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>U13(mark(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U13(active(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U21(mark(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,mark(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(active(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,active(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U22(mark(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U22(active(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U31(mark(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,mark(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(active(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,active(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U41(mark(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,mark(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,mark(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(active(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,active(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,active(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>s(mark(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>s(active(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>plus(mark(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,mark(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(active(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,active(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>and(mark(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,mark(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(active(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,active(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>isNatKind(mark(X))</LHS><RHS>isNatKind(X)</RHS></RULE><RULE><LHS>isNatKind(active(X))</LHS><RHS>isNatKind(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_active(U11(tt,V1,V2))</LHS><RHS>Marked_mark(U12(isNat(V1),V2))</RHS></DPRULE><DPRULE num="1"><LHS>Marked_active(U12(tt,V2))</LHS><RHS>Marked_mark(U13(isNat(V2)))</RHS></DPRULE><DPRULE num="2"><LHS>Marked_active(U21(tt,V1))</LHS><RHS>Marked_mark(U22(isNat(V1)))</RHS></DPRULE><DPRULE num="3"><LHS>Marked_active(U31(tt,N))</LHS><RHS>Marked_mark(N)</RHS></DPRULE><DPRULE num="4"><LHS>Marked_active(U41(tt,M,N))</LHS><RHS>Marked_mark(s(plus(N,M)))</RHS></DPRULE><DPRULE num="5"><LHS>Marked_active(and(tt,X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="6"><LHS>Marked_active(isNat(plus(V1,V2)))</LHS><RHS>Marked_mark(U11(and(isNatKind(V1),isNatKind(V2)),V1,V2))</RHS></DPRULE><DPRULE num="7"><LHS>Marked_active(isNat(s(V1)))</LHS><RHS>Marked_mark(U21(isNatKind(V1),V1))</RHS></DPRULE><DPRULE num="8"><LHS>Marked_active(isNatKind(plus(V1,V2)))</LHS><RHS>Marked_mark(and(isNatKind(V1),isNatKind(V2)))</RHS></DPRULE><DPRULE num="9"><LHS>Marked_active(isNatKind(s(V1)))</LHS><RHS>Marked_mark(isNatKind(V1))</RHS></DPRULE><DPRULE num="10"><LHS>Marked_active(plus(N,0))</LHS><RHS>Marked_mark(U31(and(isNat(N),isNatKind(N)),N))</RHS></DPRULE><DPRULE num="11"><LHS>Marked_active(plus(N,s(M)))</LHS><RHS>Marked_mark(U41(and(and(isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),
             M,N))</RHS></DPRULE><DPRULE num="12"><LHS>Marked_mark(U11(X1,X2,X3))</LHS><RHS>Marked_active(U11(mark(X1),X2,X3))</RHS></DPRULE><DPRULE num="13"><LHS>Marked_mark(U11(X1,X2,X3))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="14"><LHS>Marked_mark(U12(X1,X2))</LHS><RHS>Marked_active(U12(mark(X1),X2))</RHS></DPRULE><DPRULE num="15"><LHS>Marked_mark(U12(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="16"><LHS>Marked_mark(isNat(X))</LHS><RHS>Marked_active(isNat(X))</RHS></DPRULE><DPRULE num="17"><LHS>Marked_mark(U13(X))</LHS><RHS>Marked_active(U13(mark(X)))</RHS></DPRULE><DPRULE num="18"><LHS>Marked_mark(U13(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="19"><LHS>Marked_mark(U21(X1,X2))</LHS><RHS>Marked_active(U21(mark(X1),X2))</RHS></DPRULE><DPRULE num="20"><LHS>Marked_mark(U21(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="21"><LHS>Marked_mark(U22(X))</LHS><RHS>Marked_active(U22(mark(X)))</RHS></DPRULE><DPRULE num="22"><LHS>Marked_mark(U22(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="23"><LHS>Marked_mark(U31(X1,X2))</LHS><RHS>Marked_active(U31(mark(X1),X2))</RHS></DPRULE><DPRULE num="24"><LHS>Marked_mark(U31(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="25"><LHS>Marked_mark(U41(X1,X2,X3))</LHS><RHS>Marked_active(U41(mark(X1),X2,X3))</RHS></DPRULE><DPRULE num="26"><LHS>Marked_mark(U41(X1,X2,X3))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="27"><LHS>Marked_mark(s(X))</LHS><RHS>Marked_active(s(mark(X)))</RHS></DPRULE><DPRULE num="28"><LHS>Marked_mark(s(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="29"><LHS>Marked_mark(plus(X1,X2))</LHS><RHS>Marked_active(plus(mark(X1),mark(X2)))</RHS></DPRULE><DPRULE num="30"><LHS>Marked_mark(plus(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="31"><LHS>Marked_mark(plus(X1,X2))</LHS><RHS>Marked_mark(X2)</RHS></DPRULE><DPRULE num="32"><LHS>Marked_mark(and(X1,X2))</LHS><RHS>Marked_active(and(mark(X1),X2))</RHS></DPRULE><DPRULE num="33"><LHS>Marked_mark(and(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="34"><LHS>Marked_mark(isNatKind(X))</LHS><RHS>Marked_active(isNatKind(X))</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><ORDERING type="poly"><POLYSYMB><SYMBOL><NAME>mark</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U21</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U11</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U41</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="2"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>Marked_mark</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>isNat</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>s</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U13</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>0</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U12</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U31</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>tt</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>and</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>Marked_active</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>active</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>plus</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U22</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>isNatKind</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB></ORDERING><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_active(plus(N,0))</LHS><RHS>Marked_mark(U31(and(isNat(N),isNatKind(N)),N))</RHS></DPRULE></DPLIST></STRICTPAIRS></CRITERION><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(U11(tt,V1,V2))</LHS><RHS>mark(U12(isNat(V1),V2))</RHS></RULE><RULE><LHS>active(U12(tt,V2))</LHS><RHS>mark(U13(isNat(V2)))</RHS></RULE><RULE><LHS>active(U13(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U21(tt,V1))</LHS><RHS>mark(U22(isNat(V1)))</RHS></RULE><RULE><LHS>active(U22(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U31(tt,N))</LHS><RHS>mark(N)</RHS></RULE><RULE><LHS>active(U41(tt,M,N))</LHS><RHS>mark(s(plus(N,M)))</RHS></RULE><RULE><LHS>active(and(tt,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(isNat(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNat(plus(V1,V2)))</LHS><RHS>mark(U11(and(isNatKind(V1),isNatKind(V2)),V1,V2))</RHS></RULE><RULE><LHS>active(isNat(s(V1)))</LHS><RHS>mark(U21(isNatKind(V1),V1))</RHS></RULE><RULE><LHS>active(isNatKind(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNatKind(plus(V1,V2)))</LHS><RHS>mark(and(isNatKind(V1),isNatKind(V2)))</RHS></RULE><RULE><LHS>active(isNatKind(s(V1)))</LHS><RHS>mark(isNatKind(V1))</RHS></RULE><RULE><LHS>active(plus(N,0))</LHS><RHS>mark(U31(and(isNat(N),isNatKind(N)),N))</RHS></RULE><RULE><LHS>active(plus(N,s(M)))</LHS><RHS>mark(U41(and(and(isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),M,N))</RHS></RULE><RULE><LHS>mark(U11(X1,X2,X3))</LHS><RHS>active(U11(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(tt)</LHS><RHS>active(tt)</RHS></RULE><RULE><LHS>mark(U12(X1,X2))</LHS><RHS>active(U12(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(isNat(X))</LHS><RHS>active(isNat(X))</RHS></RULE><RULE><LHS>mark(U13(X))</LHS><RHS>active(U13(mark(X)))</RHS></RULE><RULE><LHS>mark(U21(X1,X2))</LHS><RHS>active(U21(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U22(X))</LHS><RHS>active(U22(mark(X)))</RHS></RULE><RULE><LHS>mark(U31(X1,X2))</LHS><RHS>active(U31(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U41(X1,X2,X3))</LHS><RHS>active(U41(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(mark(X)))</RHS></RULE><RULE><LHS>mark(plus(X1,X2))</LHS><RHS>active(plus(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(isNatKind(X))</LHS><RHS>active(isNatKind(X))</RHS></RULE><RULE><LHS>U11(mark(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,mark(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,mark(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(active(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,active(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,active(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U12(mark(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,mark(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(active(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,active(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>isNat(mark(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>isNat(active(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>U13(mark(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U13(active(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U21(mark(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,mark(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(active(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,active(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U22(mark(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U22(active(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U31(mark(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,mark(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(active(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,active(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U41(mark(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,mark(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,mark(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(active(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,active(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,active(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>s(mark(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>s(active(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>plus(mark(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,mark(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(active(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,active(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>and(mark(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,mark(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(active(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,active(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>isNatKind(mark(X))</LHS><RHS>isNatKind(X)</RHS></RULE><RULE><LHS>isNatKind(active(X))</LHS><RHS>isNatKind(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_active(U11(tt,V1,V2))</LHS><RHS>Marked_mark(U12(isNat(V1),V2))</RHS></DPRULE><DPRULE num="1"><LHS>Marked_active(U12(tt,V2))</LHS><RHS>Marked_mark(U13(isNat(V2)))</RHS></DPRULE><DPRULE num="2"><LHS>Marked_active(U21(tt,V1))</LHS><RHS>Marked_mark(U22(isNat(V1)))</RHS></DPRULE><DPRULE num="3"><LHS>Marked_active(U31(tt,N))</LHS><RHS>Marked_mark(N)</RHS></DPRULE><DPRULE num="4"><LHS>Marked_active(U41(tt,M,N))</LHS><RHS>Marked_mark(s(plus(N,M)))</RHS></DPRULE><DPRULE num="5"><LHS>Marked_active(and(tt,X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="6"><LHS>Marked_active(isNat(plus(V1,V2)))</LHS><RHS>Marked_mark(U11(and(isNatKind(V1),isNatKind(V2)),V1,V2))</RHS></DPRULE><DPRULE num="7"><LHS>Marked_active(isNat(s(V1)))</LHS><RHS>Marked_mark(U21(isNatKind(V1),V1))</RHS></DPRULE><DPRULE num="8"><LHS>Marked_active(isNatKind(plus(V1,V2)))</LHS><RHS>Marked_mark(and(isNatKind(V1),isNatKind(V2)))</RHS></DPRULE><DPRULE num="9"><LHS>Marked_active(isNatKind(s(V1)))</LHS><RHS>Marked_mark(isNatKind(V1))</RHS></DPRULE><DPRULE num="10"><LHS>Marked_active(plus(N,s(M)))</LHS><RHS>Marked_mark(U41(and(and(isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),
             M,N))</RHS></DPRULE><DPRULE num="11"><LHS>Marked_mark(U11(X1,X2,X3))</LHS><RHS>Marked_active(U11(mark(X1),X2,X3))</RHS></DPRULE><DPRULE num="12"><LHS>Marked_mark(U11(X1,X2,X3))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="13"><LHS>Marked_mark(U12(X1,X2))</LHS><RHS>Marked_active(U12(mark(X1),X2))</RHS></DPRULE><DPRULE num="14"><LHS>Marked_mark(U12(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="15"><LHS>Marked_mark(isNat(X))</LHS><RHS>Marked_active(isNat(X))</RHS></DPRULE><DPRULE num="16"><LHS>Marked_mark(U13(X))</LHS><RHS>Marked_active(U13(mark(X)))</RHS></DPRULE><DPRULE num="17"><LHS>Marked_mark(U13(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="18"><LHS>Marked_mark(U21(X1,X2))</LHS><RHS>Marked_active(U21(mark(X1),X2))</RHS></DPRULE><DPRULE num="19"><LHS>Marked_mark(U21(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="20"><LHS>Marked_mark(U22(X))</LHS><RHS>Marked_active(U22(mark(X)))</RHS></DPRULE><DPRULE num="21"><LHS>Marked_mark(U22(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="22"><LHS>Marked_mark(U31(X1,X2))</LHS><RHS>Marked_active(U31(mark(X1),X2))</RHS></DPRULE><DPRULE num="23"><LHS>Marked_mark(U31(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="24"><LHS>Marked_mark(U41(X1,X2,X3))</LHS><RHS>Marked_active(U41(mark(X1),X2,X3))</RHS></DPRULE><DPRULE num="25"><LHS>Marked_mark(U41(X1,X2,X3))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="26"><LHS>Marked_mark(s(X))</LHS><RHS>Marked_active(s(mark(X)))</RHS></DPRULE><DPRULE num="27"><LHS>Marked_mark(s(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="28"><LHS>Marked_mark(plus(X1,X2))</LHS><RHS>Marked_active(plus(mark(X1),mark(X2)))</RHS></DPRULE><DPRULE num="29"><LHS>Marked_mark(plus(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="30"><LHS>Marked_mark(plus(X1,X2))</LHS><RHS>Marked_mark(X2)</RHS></DPRULE><DPRULE num="31"><LHS>Marked_mark(and(X1,X2))</LHS><RHS>Marked_active(and(mark(X1),X2))</RHS></DPRULE><DPRULE num="32"><LHS>Marked_mark(and(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="33"><LHS>Marked_mark(isNatKind(X))</LHS><RHS>Marked_active(isNatKind(X))</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><DAG approx="simpl"><CCLIST><SCC num="0"><NODE ref="0"/><NODE ref="1"/><NODE ref="2"/><NODE ref="3"/><NODE ref="4"/><NODE ref="5"/><NODE ref="6"/><NODE ref="7"/><NODE ref="8"/><NODE ref="9"/><NODE ref="10"/><NODE ref="11"/><NODE ref="12"/><NODE ref="13"/><NODE ref="14"/><NODE ref="15"/><NODE ref="16"/><NODE ref="17"/><NODE ref="18"/><NODE ref="19"/><NODE ref="20"/><NODE ref="21"/><NODE ref="22"/><NODE ref="23"/><NODE ref="24"/><NODE ref="25"/><NODE ref="26"/><NODE ref="27"/><NODE ref="28"/><NODE ref="29"/><NODE ref="30"/><NODE ref="31"/><NODE ref="32"/><NODE ref="33"/></SCC></CCLIST></DAG></CRITERION><PROPERTY criterion="stronggraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(U11(tt,V1,V2))</LHS><RHS>mark(U12(isNat(V1),V2))</RHS></RULE><RULE><LHS>active(U12(tt,V2))</LHS><RHS>mark(U13(isNat(V2)))</RHS></RULE><RULE><LHS>active(U13(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U21(tt,V1))</LHS><RHS>mark(U22(isNat(V1)))</RHS></RULE><RULE><LHS>active(U22(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U31(tt,N))</LHS><RHS>mark(N)</RHS></RULE><RULE><LHS>active(U41(tt,M,N))</LHS><RHS>mark(s(plus(N,M)))</RHS></RULE><RULE><LHS>active(and(tt,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(isNat(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNat(plus(V1,V2)))</LHS><RHS>mark(U11(and(isNatKind(V1),isNatKind(V2)),V1,V2))</RHS></RULE><RULE><LHS>active(isNat(s(V1)))</LHS><RHS>mark(U21(isNatKind(V1),V1))</RHS></RULE><RULE><LHS>active(isNatKind(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNatKind(plus(V1,V2)))</LHS><RHS>mark(and(isNatKind(V1),isNatKind(V2)))</RHS></RULE><RULE><LHS>active(isNatKind(s(V1)))</LHS><RHS>mark(isNatKind(V1))</RHS></RULE><RULE><LHS>active(plus(N,0))</LHS><RHS>mark(U31(and(isNat(N),isNatKind(N)),N))</RHS></RULE><RULE><LHS>active(plus(N,s(M)))</LHS><RHS>mark(U41(and(and(isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),M,N))</RHS></RULE><RULE><LHS>mark(U11(X1,X2,X3))</LHS><RHS>active(U11(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(tt)</LHS><RHS>active(tt)</RHS></RULE><RULE><LHS>mark(U12(X1,X2))</LHS><RHS>active(U12(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(isNat(X))</LHS><RHS>active(isNat(X))</RHS></RULE><RULE><LHS>mark(U13(X))</LHS><RHS>active(U13(mark(X)))</RHS></RULE><RULE><LHS>mark(U21(X1,X2))</LHS><RHS>active(U21(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U22(X))</LHS><RHS>active(U22(mark(X)))</RHS></RULE><RULE><LHS>mark(U31(X1,X2))</LHS><RHS>active(U31(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U41(X1,X2,X3))</LHS><RHS>active(U41(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(mark(X)))</RHS></RULE><RULE><LHS>mark(plus(X1,X2))</LHS><RHS>active(plus(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(isNatKind(X))</LHS><RHS>active(isNatKind(X))</RHS></RULE><RULE><LHS>U11(mark(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,mark(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,mark(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(active(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,active(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,active(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U12(mark(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,mark(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(active(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,active(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>isNat(mark(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>isNat(active(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>U13(mark(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U13(active(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U21(mark(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,mark(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(active(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,active(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U22(mark(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U22(active(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U31(mark(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,mark(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(active(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,active(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U41(mark(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,mark(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,mark(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(active(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,active(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,active(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>s(mark(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>s(active(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>plus(mark(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,mark(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(active(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,active(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>and(mark(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,mark(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(active(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,active(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>isNatKind(mark(X))</LHS><RHS>isNatKind(X)</RHS></RULE><RULE><LHS>isNatKind(active(X))</LHS><RHS>isNatKind(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_active(U11(tt,V1,V2))</LHS><RHS>Marked_mark(U12(isNat(V1),V2))</RHS></DPRULE><DPRULE num="1"><LHS>Marked_active(U12(tt,V2))</LHS><RHS>Marked_mark(U13(isNat(V2)))</RHS></DPRULE><DPRULE num="2"><LHS>Marked_active(U21(tt,V1))</LHS><RHS>Marked_mark(U22(isNat(V1)))</RHS></DPRULE><DPRULE num="3"><LHS>Marked_active(U31(tt,N))</LHS><RHS>Marked_mark(N)</RHS></DPRULE><DPRULE num="4"><LHS>Marked_active(U41(tt,M,N))</LHS><RHS>Marked_mark(s(plus(N,M)))</RHS></DPRULE><DPRULE num="5"><LHS>Marked_active(and(tt,X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="6"><LHS>Marked_active(isNat(plus(V1,V2)))</LHS><RHS>Marked_mark(U11(and(isNatKind(V1),isNatKind(V2)),V1,V2))</RHS></DPRULE><DPRULE num="7"><LHS>Marked_active(isNat(s(V1)))</LHS><RHS>Marked_mark(U21(isNatKind(V1),V1))</RHS></DPRULE><DPRULE num="8"><LHS>Marked_active(isNatKind(plus(V1,V2)))</LHS><RHS>Marked_mark(and(isNatKind(V1),isNatKind(V2)))</RHS></DPRULE><DPRULE num="9"><LHS>Marked_active(isNatKind(s(V1)))</LHS><RHS>Marked_mark(isNatKind(V1))</RHS></DPRULE><DPRULE num="10"><LHS>Marked_active(plus(N,s(M)))</LHS><RHS>Marked_mark(U41(and(and(isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),
             M,N))</RHS></DPRULE><DPRULE num="11"><LHS>Marked_mark(U11(X1,X2,X3))</LHS><RHS>Marked_active(U11(mark(X1),X2,X3))</RHS></DPRULE><DPRULE num="12"><LHS>Marked_mark(U11(X1,X2,X3))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="13"><LHS>Marked_mark(U12(X1,X2))</LHS><RHS>Marked_active(U12(mark(X1),X2))</RHS></DPRULE><DPRULE num="14"><LHS>Marked_mark(U12(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="15"><LHS>Marked_mark(isNat(X))</LHS><RHS>Marked_active(isNat(X))</RHS></DPRULE><DPRULE num="16"><LHS>Marked_mark(U13(X))</LHS><RHS>Marked_active(U13(mark(X)))</RHS></DPRULE><DPRULE num="17"><LHS>Marked_mark(U13(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="18"><LHS>Marked_mark(U21(X1,X2))</LHS><RHS>Marked_active(U21(mark(X1),X2))</RHS></DPRULE><DPRULE num="19"><LHS>Marked_mark(U21(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="20"><LHS>Marked_mark(U22(X))</LHS><RHS>Marked_active(U22(mark(X)))</RHS></DPRULE><DPRULE num="21"><LHS>Marked_mark(U22(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="22"><LHS>Marked_mark(U31(X1,X2))</LHS><RHS>Marked_active(U31(mark(X1),X2))</RHS></DPRULE><DPRULE num="23"><LHS>Marked_mark(U31(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="24"><LHS>Marked_mark(U41(X1,X2,X3))</LHS><RHS>Marked_active(U41(mark(X1),X2,X3))</RHS></DPRULE><DPRULE num="25"><LHS>Marked_mark(U41(X1,X2,X3))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="26"><LHS>Marked_mark(s(X))</LHS><RHS>Marked_active(s(mark(X)))</RHS></DPRULE><DPRULE num="27"><LHS>Marked_mark(s(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="28"><LHS>Marked_mark(plus(X1,X2))</LHS><RHS>Marked_active(plus(mark(X1),mark(X2)))</RHS></DPRULE><DPRULE num="29"><LHS>Marked_mark(plus(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="30"><LHS>Marked_mark(plus(X1,X2))</LHS><RHS>Marked_mark(X2)</RHS></DPRULE><DPRULE num="31"><LHS>Marked_mark(and(X1,X2))</LHS><RHS>Marked_active(and(mark(X1),X2))</RHS></DPRULE><DPRULE num="32"><LHS>Marked_mark(and(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="33"><LHS>Marked_mark(isNatKind(X))</LHS><RHS>Marked_active(isNatKind(X))</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><ORDERING type="poly"><POLYSYMB><SYMBOL><NAME>mark</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U21</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U11</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U41</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>Marked_mark</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>isNat</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>s</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U13</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>0</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U12</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U31</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>tt</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>and</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>Marked_active</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>active</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>plus</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U22</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>isNatKind</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB></ORDERING><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_mark(U13(X))</LHS><RHS>Marked_active(U13(mark(X)))</RHS></DPRULE><DPRULE num="1"><LHS>Marked_mark(U22(X))</LHS><RHS>Marked_active(U22(mark(X)))</RHS></DPRULE><DPRULE num="2"><LHS>Marked_mark(s(X))</LHS><RHS>Marked_active(s(mark(X)))</RHS></DPRULE></DPLIST></STRICTPAIRS></CRITERION><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(U11(tt,V1,V2))</LHS><RHS>mark(U12(isNat(V1),V2))</RHS></RULE><RULE><LHS>active(U12(tt,V2))</LHS><RHS>mark(U13(isNat(V2)))</RHS></RULE><RULE><LHS>active(U13(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U21(tt,V1))</LHS><RHS>mark(U22(isNat(V1)))</RHS></RULE><RULE><LHS>active(U22(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U31(tt,N))</LHS><RHS>mark(N)</RHS></RULE><RULE><LHS>active(U41(tt,M,N))</LHS><RHS>mark(s(plus(N,M)))</RHS></RULE><RULE><LHS>active(and(tt,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(isNat(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNat(plus(V1,V2)))</LHS><RHS>mark(U11(and(isNatKind(V1),isNatKind(V2)),V1,V2))</RHS></RULE><RULE><LHS>active(isNat(s(V1)))</LHS><RHS>mark(U21(isNatKind(V1),V1))</RHS></RULE><RULE><LHS>active(isNatKind(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNatKind(plus(V1,V2)))</LHS><RHS>mark(and(isNatKind(V1),isNatKind(V2)))</RHS></RULE><RULE><LHS>active(isNatKind(s(V1)))</LHS><RHS>mark(isNatKind(V1))</RHS></RULE><RULE><LHS>active(plus(N,0))</LHS><RHS>mark(U31(and(isNat(N),isNatKind(N)),N))</RHS></RULE><RULE><LHS>active(plus(N,s(M)))</LHS><RHS>mark(U41(and(and(isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),M,N))</RHS></RULE><RULE><LHS>mark(U11(X1,X2,X3))</LHS><RHS>active(U11(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(tt)</LHS><RHS>active(tt)</RHS></RULE><RULE><LHS>mark(U12(X1,X2))</LHS><RHS>active(U12(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(isNat(X))</LHS><RHS>active(isNat(X))</RHS></RULE><RULE><LHS>mark(U13(X))</LHS><RHS>active(U13(mark(X)))</RHS></RULE><RULE><LHS>mark(U21(X1,X2))</LHS><RHS>active(U21(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U22(X))</LHS><RHS>active(U22(mark(X)))</RHS></RULE><RULE><LHS>mark(U31(X1,X2))</LHS><RHS>active(U31(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U41(X1,X2,X3))</LHS><RHS>active(U41(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(mark(X)))</RHS></RULE><RULE><LHS>mark(plus(X1,X2))</LHS><RHS>active(plus(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(isNatKind(X))</LHS><RHS>active(isNatKind(X))</RHS></RULE><RULE><LHS>U11(mark(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,mark(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,mark(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(active(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,active(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,active(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U12(mark(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,mark(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(active(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,active(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>isNat(mark(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>isNat(active(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>U13(mark(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U13(active(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U21(mark(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,mark(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(active(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,active(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U22(mark(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U22(active(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U31(mark(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,mark(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(active(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,active(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U41(mark(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,mark(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,mark(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(active(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,active(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,active(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>s(mark(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>s(active(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>plus(mark(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,mark(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(active(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,active(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>and(mark(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,mark(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(active(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,active(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>isNatKind(mark(X))</LHS><RHS>isNatKind(X)</RHS></RULE><RULE><LHS>isNatKind(active(X))</LHS><RHS>isNatKind(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_active(U11(tt,V1,V2))</LHS><RHS>Marked_mark(U12(isNat(V1),V2))</RHS></DPRULE><DPRULE num="1"><LHS>Marked_active(U12(tt,V2))</LHS><RHS>Marked_mark(U13(isNat(V2)))</RHS></DPRULE><DPRULE num="2"><LHS>Marked_active(U21(tt,V1))</LHS><RHS>Marked_mark(U22(isNat(V1)))</RHS></DPRULE><DPRULE num="3"><LHS>Marked_active(U31(tt,N))</LHS><RHS>Marked_mark(N)</RHS></DPRULE><DPRULE num="4"><LHS>Marked_active(U41(tt,M,N))</LHS><RHS>Marked_mark(s(plus(N,M)))</RHS></DPRULE><DPRULE num="5"><LHS>Marked_active(and(tt,X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="6"><LHS>Marked_active(isNat(plus(V1,V2)))</LHS><RHS>Marked_mark(U11(and(isNatKind(V1),isNatKind(V2)),V1,V2))</RHS></DPRULE><DPRULE num="7"><LHS>Marked_active(isNat(s(V1)))</LHS><RHS>Marked_mark(U21(isNatKind(V1),V1))</RHS></DPRULE><DPRULE num="8"><LHS>Marked_active(isNatKind(plus(V1,V2)))</LHS><RHS>Marked_mark(and(isNatKind(V1),isNatKind(V2)))</RHS></DPRULE><DPRULE num="9"><LHS>Marked_active(isNatKind(s(V1)))</LHS><RHS>Marked_mark(isNatKind(V1))</RHS></DPRULE><DPRULE num="10"><LHS>Marked_active(plus(N,s(M)))</LHS><RHS>Marked_mark(U41(and(and(isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),
             M,N))</RHS></DPRULE><DPRULE num="11"><LHS>Marked_mark(U11(X1,X2,X3))</LHS><RHS>Marked_active(U11(mark(X1),X2,X3))</RHS></DPRULE><DPRULE num="12"><LHS>Marked_mark(U11(X1,X2,X3))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="13"><LHS>Marked_mark(U12(X1,X2))</LHS><RHS>Marked_active(U12(mark(X1),X2))</RHS></DPRULE><DPRULE num="14"><LHS>Marked_mark(U12(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="15"><LHS>Marked_mark(isNat(X))</LHS><RHS>Marked_active(isNat(X))</RHS></DPRULE><DPRULE num="16"><LHS>Marked_mark(U13(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="17"><LHS>Marked_mark(U21(X1,X2))</LHS><RHS>Marked_active(U21(mark(X1),X2))</RHS></DPRULE><DPRULE num="18"><LHS>Marked_mark(U21(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="19"><LHS>Marked_mark(U22(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="20"><LHS>Marked_mark(U31(X1,X2))</LHS><RHS>Marked_active(U31(mark(X1),X2))</RHS></DPRULE><DPRULE num="21"><LHS>Marked_mark(U31(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="22"><LHS>Marked_mark(U41(X1,X2,X3))</LHS><RHS>Marked_active(U41(mark(X1),X2,X3))</RHS></DPRULE><DPRULE num="23"><LHS>Marked_mark(U41(X1,X2,X3))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="24"><LHS>Marked_mark(s(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="25"><LHS>Marked_mark(plus(X1,X2))</LHS><RHS>Marked_active(plus(mark(X1),mark(X2)))</RHS></DPRULE><DPRULE num="26"><LHS>Marked_mark(plus(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="27"><LHS>Marked_mark(plus(X1,X2))</LHS><RHS>Marked_mark(X2)</RHS></DPRULE><DPRULE num="28"><LHS>Marked_mark(and(X1,X2))</LHS><RHS>Marked_active(and(mark(X1),X2))</RHS></DPRULE><DPRULE num="29"><LHS>Marked_mark(and(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="30"><LHS>Marked_mark(isNatKind(X))</LHS><RHS>Marked_active(isNatKind(X))</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><DAG approx="simpl"><CCLIST><SCC num="0"><NODE ref="0"/><NODE ref="1"/><NODE ref="2"/><NODE ref="3"/><NODE ref="4"/><NODE ref="5"/><NODE ref="6"/><NODE ref="7"/><NODE ref="8"/><NODE ref="9"/><NODE ref="10"/><NODE ref="11"/><NODE ref="12"/><NODE ref="13"/><NODE ref="14"/><NODE ref="15"/><NODE ref="16"/><NODE ref="17"/><NODE ref="18"/><NODE ref="19"/><NODE ref="20"/><NODE ref="21"/><NODE ref="22"/><NODE ref="23"/><NODE ref="24"/><NODE ref="25"/><NODE ref="26"/><NODE ref="27"/><NODE ref="28"/><NODE ref="29"/><NODE ref="30"/></SCC></CCLIST></DAG></CRITERION><PROPERTY criterion="stronggraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(U11(tt,V1,V2))</LHS><RHS>mark(U12(isNat(V1),V2))</RHS></RULE><RULE><LHS>active(U12(tt,V2))</LHS><RHS>mark(U13(isNat(V2)))</RHS></RULE><RULE><LHS>active(U13(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U21(tt,V1))</LHS><RHS>mark(U22(isNat(V1)))</RHS></RULE><RULE><LHS>active(U22(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U31(tt,N))</LHS><RHS>mark(N)</RHS></RULE><RULE><LHS>active(U41(tt,M,N))</LHS><RHS>mark(s(plus(N,M)))</RHS></RULE><RULE><LHS>active(and(tt,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(isNat(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNat(plus(V1,V2)))</LHS><RHS>mark(U11(and(isNatKind(V1),isNatKind(V2)),V1,V2))</RHS></RULE><RULE><LHS>active(isNat(s(V1)))</LHS><RHS>mark(U21(isNatKind(V1),V1))</RHS></RULE><RULE><LHS>active(isNatKind(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNatKind(plus(V1,V2)))</LHS><RHS>mark(and(isNatKind(V1),isNatKind(V2)))</RHS></RULE><RULE><LHS>active(isNatKind(s(V1)))</LHS><RHS>mark(isNatKind(V1))</RHS></RULE><RULE><LHS>active(plus(N,0))</LHS><RHS>mark(U31(and(isNat(N),isNatKind(N)),N))</RHS></RULE><RULE><LHS>active(plus(N,s(M)))</LHS><RHS>mark(U41(and(and(isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),M,N))</RHS></RULE><RULE><LHS>mark(U11(X1,X2,X3))</LHS><RHS>active(U11(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(tt)</LHS><RHS>active(tt)</RHS></RULE><RULE><LHS>mark(U12(X1,X2))</LHS><RHS>active(U12(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(isNat(X))</LHS><RHS>active(isNat(X))</RHS></RULE><RULE><LHS>mark(U13(X))</LHS><RHS>active(U13(mark(X)))</RHS></RULE><RULE><LHS>mark(U21(X1,X2))</LHS><RHS>active(U21(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U22(X))</LHS><RHS>active(U22(mark(X)))</RHS></RULE><RULE><LHS>mark(U31(X1,X2))</LHS><RHS>active(U31(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U41(X1,X2,X3))</LHS><RHS>active(U41(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(mark(X)))</RHS></RULE><RULE><LHS>mark(plus(X1,X2))</LHS><RHS>active(plus(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(isNatKind(X))</LHS><RHS>active(isNatKind(X))</RHS></RULE><RULE><LHS>U11(mark(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,mark(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,mark(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(active(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,active(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,active(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U12(mark(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,mark(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(active(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,active(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>isNat(mark(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>isNat(active(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>U13(mark(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U13(active(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U21(mark(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,mark(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(active(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,active(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U22(mark(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U22(active(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U31(mark(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,mark(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(active(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,active(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U41(mark(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,mark(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,mark(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(active(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,active(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,active(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>s(mark(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>s(active(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>plus(mark(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,mark(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(active(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,active(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>and(mark(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,mark(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(active(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,active(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>isNatKind(mark(X))</LHS><RHS>isNatKind(X)</RHS></RULE><RULE><LHS>isNatKind(active(X))</LHS><RHS>isNatKind(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_active(U11(tt,V1,V2))</LHS><RHS>Marked_mark(U12(isNat(V1),V2))</RHS></DPRULE><DPRULE num="1"><LHS>Marked_active(U12(tt,V2))</LHS><RHS>Marked_mark(U13(isNat(V2)))</RHS></DPRULE><DPRULE num="2"><LHS>Marked_active(U21(tt,V1))</LHS><RHS>Marked_mark(U22(isNat(V1)))</RHS></DPRULE><DPRULE num="3"><LHS>Marked_active(U31(tt,N))</LHS><RHS>Marked_mark(N)</RHS></DPRULE><DPRULE num="4"><LHS>Marked_active(U41(tt,M,N))</LHS><RHS>Marked_mark(s(plus(N,M)))</RHS></DPRULE><DPRULE num="5"><LHS>Marked_active(and(tt,X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="6"><LHS>Marked_active(isNat(plus(V1,V2)))</LHS><RHS>Marked_mark(U11(and(isNatKind(V1),isNatKind(V2)),V1,V2))</RHS></DPRULE><DPRULE num="7"><LHS>Marked_active(isNat(s(V1)))</LHS><RHS>Marked_mark(U21(isNatKind(V1),V1))</RHS></DPRULE><DPRULE num="8"><LHS>Marked_active(isNatKind(plus(V1,V2)))</LHS><RHS>Marked_mark(and(isNatKind(V1),isNatKind(V2)))</RHS></DPRULE><DPRULE num="9"><LHS>Marked_active(isNatKind(s(V1)))</LHS><RHS>Marked_mark(isNatKind(V1))</RHS></DPRULE><DPRULE num="10"><LHS>Marked_active(plus(N,s(M)))</LHS><RHS>Marked_mark(U41(and(and(isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),
             M,N))</RHS></DPRULE><DPRULE num="11"><LHS>Marked_mark(U11(X1,X2,X3))</LHS><RHS>Marked_active(U11(mark(X1),X2,X3))</RHS></DPRULE><DPRULE num="12"><LHS>Marked_mark(U11(X1,X2,X3))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="13"><LHS>Marked_mark(U12(X1,X2))</LHS><RHS>Marked_active(U12(mark(X1),X2))</RHS></DPRULE><DPRULE num="14"><LHS>Marked_mark(U12(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="15"><LHS>Marked_mark(isNat(X))</LHS><RHS>Marked_active(isNat(X))</RHS></DPRULE><DPRULE num="16"><LHS>Marked_mark(U13(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="17"><LHS>Marked_mark(U21(X1,X2))</LHS><RHS>Marked_active(U21(mark(X1),X2))</RHS></DPRULE><DPRULE num="18"><LHS>Marked_mark(U21(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="19"><LHS>Marked_mark(U22(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="20"><LHS>Marked_mark(U31(X1,X2))</LHS><RHS>Marked_active(U31(mark(X1),X2))</RHS></DPRULE><DPRULE num="21"><LHS>Marked_mark(U31(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="22"><LHS>Marked_mark(U41(X1,X2,X3))</LHS><RHS>Marked_active(U41(mark(X1),X2,X3))</RHS></DPRULE><DPRULE num="23"><LHS>Marked_mark(U41(X1,X2,X3))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="24"><LHS>Marked_mark(s(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="25"><LHS>Marked_mark(plus(X1,X2))</LHS><RHS>Marked_active(plus(mark(X1),mark(X2)))</RHS></DPRULE><DPRULE num="26"><LHS>Marked_mark(plus(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="27"><LHS>Marked_mark(plus(X1,X2))</LHS><RHS>Marked_mark(X2)</RHS></DPRULE><DPRULE num="28"><LHS>Marked_mark(and(X1,X2))</LHS><RHS>Marked_active(and(mark(X1),X2))</RHS></DPRULE><DPRULE num="29"><LHS>Marked_mark(and(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="30"><LHS>Marked_mark(isNatKind(X))</LHS><RHS>Marked_active(isNatKind(X))</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><ORDERING type="poly"><POLYSYMB><SYMBOL><NAME>mark</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U21</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U11</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U41</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="2"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>Marked_mark</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>isNat</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>s</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U13</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>0</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U12</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U31</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>tt</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>and</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>Marked_active</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>active</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>plus</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U22</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>isNatKind</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB></ORDERING><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_active(plus(N,s(M)))</LHS><RHS>Marked_mark(U41(and(and(isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),
             M,N))</RHS></DPRULE><DPRULE num="1"><LHS>Marked_mark(U41(X1,X2,X3))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="2"><LHS>Marked_mark(s(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE></DPLIST></STRICTPAIRS></CRITERION><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(U11(tt,V1,V2))</LHS><RHS>mark(U12(isNat(V1),V2))</RHS></RULE><RULE><LHS>active(U12(tt,V2))</LHS><RHS>mark(U13(isNat(V2)))</RHS></RULE><RULE><LHS>active(U13(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U21(tt,V1))</LHS><RHS>mark(U22(isNat(V1)))</RHS></RULE><RULE><LHS>active(U22(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U31(tt,N))</LHS><RHS>mark(N)</RHS></RULE><RULE><LHS>active(U41(tt,M,N))</LHS><RHS>mark(s(plus(N,M)))</RHS></RULE><RULE><LHS>active(and(tt,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(isNat(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNat(plus(V1,V2)))</LHS><RHS>mark(U11(and(isNatKind(V1),isNatKind(V2)),V1,V2))</RHS></RULE><RULE><LHS>active(isNat(s(V1)))</LHS><RHS>mark(U21(isNatKind(V1),V1))</RHS></RULE><RULE><LHS>active(isNatKind(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNatKind(plus(V1,V2)))</LHS><RHS>mark(and(isNatKind(V1),isNatKind(V2)))</RHS></RULE><RULE><LHS>active(isNatKind(s(V1)))</LHS><RHS>mark(isNatKind(V1))</RHS></RULE><RULE><LHS>active(plus(N,0))</LHS><RHS>mark(U31(and(isNat(N),isNatKind(N)),N))</RHS></RULE><RULE><LHS>active(plus(N,s(M)))</LHS><RHS>mark(U41(and(and(isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),M,N))</RHS></RULE><RULE><LHS>mark(U11(X1,X2,X3))</LHS><RHS>active(U11(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(tt)</LHS><RHS>active(tt)</RHS></RULE><RULE><LHS>mark(U12(X1,X2))</LHS><RHS>active(U12(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(isNat(X))</LHS><RHS>active(isNat(X))</RHS></RULE><RULE><LHS>mark(U13(X))</LHS><RHS>active(U13(mark(X)))</RHS></RULE><RULE><LHS>mark(U21(X1,X2))</LHS><RHS>active(U21(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U22(X))</LHS><RHS>active(U22(mark(X)))</RHS></RULE><RULE><LHS>mark(U31(X1,X2))</LHS><RHS>active(U31(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U41(X1,X2,X3))</LHS><RHS>active(U41(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(mark(X)))</RHS></RULE><RULE><LHS>mark(plus(X1,X2))</LHS><RHS>active(plus(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(isNatKind(X))</LHS><RHS>active(isNatKind(X))</RHS></RULE><RULE><LHS>U11(mark(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,mark(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,mark(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(active(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,active(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,active(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U12(mark(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,mark(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(active(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,active(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>isNat(mark(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>isNat(active(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>U13(mark(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U13(active(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U21(mark(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,mark(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(active(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,active(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U22(mark(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U22(active(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U31(mark(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,mark(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(active(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,active(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U41(mark(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,mark(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,mark(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(active(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,active(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,active(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>s(mark(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>s(active(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>plus(mark(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,mark(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(active(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,active(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>and(mark(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,mark(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(active(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,active(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>isNatKind(mark(X))</LHS><RHS>isNatKind(X)</RHS></RULE><RULE><LHS>isNatKind(active(X))</LHS><RHS>isNatKind(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_active(U11(tt,V1,V2))</LHS><RHS>Marked_mark(U12(isNat(V1),V2))</RHS></DPRULE><DPRULE num="1"><LHS>Marked_active(U12(tt,V2))</LHS><RHS>Marked_mark(U13(isNat(V2)))</RHS></DPRULE><DPRULE num="2"><LHS>Marked_active(U21(tt,V1))</LHS><RHS>Marked_mark(U22(isNat(V1)))</RHS></DPRULE><DPRULE num="3"><LHS>Marked_active(U31(tt,N))</LHS><RHS>Marked_mark(N)</RHS></DPRULE><DPRULE num="4"><LHS>Marked_active(U41(tt,M,N))</LHS><RHS>Marked_mark(s(plus(N,M)))</RHS></DPRULE><DPRULE num="5"><LHS>Marked_active(and(tt,X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="6"><LHS>Marked_active(isNat(plus(V1,V2)))</LHS><RHS>Marked_mark(U11(and(isNatKind(V1),isNatKind(V2)),V1,V2))</RHS></DPRULE><DPRULE num="7"><LHS>Marked_active(isNat(s(V1)))</LHS><RHS>Marked_mark(U21(isNatKind(V1),V1))</RHS></DPRULE><DPRULE num="8"><LHS>Marked_active(isNatKind(plus(V1,V2)))</LHS><RHS>Marked_mark(and(isNatKind(V1),isNatKind(V2)))</RHS></DPRULE><DPRULE num="9"><LHS>Marked_active(isNatKind(s(V1)))</LHS><RHS>Marked_mark(isNatKind(V1))</RHS></DPRULE><DPRULE num="10"><LHS>Marked_mark(U11(X1,X2,X3))</LHS><RHS>Marked_active(U11(mark(X1),X2,X3))</RHS></DPRULE><DPRULE num="11"><LHS>Marked_mark(U11(X1,X2,X3))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="12"><LHS>Marked_mark(U12(X1,X2))</LHS><RHS>Marked_active(U12(mark(X1),X2))</RHS></DPRULE><DPRULE num="13"><LHS>Marked_mark(U12(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="14"><LHS>Marked_mark(isNat(X))</LHS><RHS>Marked_active(isNat(X))</RHS></DPRULE><DPRULE num="15"><LHS>Marked_mark(U13(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="16"><LHS>Marked_mark(U21(X1,X2))</LHS><RHS>Marked_active(U21(mark(X1),X2))</RHS></DPRULE><DPRULE num="17"><LHS>Marked_mark(U21(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="18"><LHS>Marked_mark(U22(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="19"><LHS>Marked_mark(U31(X1,X2))</LHS><RHS>Marked_active(U31(mark(X1),X2))</RHS></DPRULE><DPRULE num="20"><LHS>Marked_mark(U31(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="21"><LHS>Marked_mark(U41(X1,X2,X3))</LHS><RHS>Marked_active(U41(mark(X1),X2,X3))</RHS></DPRULE><DPRULE num="22"><LHS>Marked_mark(plus(X1,X2))</LHS><RHS>Marked_active(plus(mark(X1),mark(X2)))</RHS></DPRULE><DPRULE num="23"><LHS>Marked_mark(plus(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="24"><LHS>Marked_mark(plus(X1,X2))</LHS><RHS>Marked_mark(X2)</RHS></DPRULE><DPRULE num="25"><LHS>Marked_mark(and(X1,X2))</LHS><RHS>Marked_active(and(mark(X1),X2))</RHS></DPRULE><DPRULE num="26"><LHS>Marked_mark(and(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="27"><LHS>Marked_mark(isNatKind(X))</LHS><RHS>Marked_active(isNatKind(X))</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><DAG approx="simpl"><CCLIST><SCC num="0"><NODE ref="0"/><NODE ref="1"/><NODE ref="2"/><NODE ref="3"/><NODE ref="4"/><NODE ref="5"/><NODE ref="6"/><NODE ref="7"/><NODE ref="8"/><NODE ref="9"/><NODE ref="10"/><NODE ref="11"/><NODE ref="12"/><NODE ref="13"/><NODE ref="14"/><NODE ref="15"/><NODE ref="16"/><NODE ref="17"/><NODE ref="18"/><NODE ref="19"/><NODE ref="20"/><NODE ref="21"/><NODE ref="22"/><NODE ref="23"/><NODE ref="24"/><NODE ref="25"/><NODE ref="26"/><NODE ref="27"/></SCC></CCLIST></DAG></CRITERION><PROPERTY criterion="stronggraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(U11(tt,V1,V2))</LHS><RHS>mark(U12(isNat(V1),V2))</RHS></RULE><RULE><LHS>active(U12(tt,V2))</LHS><RHS>mark(U13(isNat(V2)))</RHS></RULE><RULE><LHS>active(U13(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U21(tt,V1))</LHS><RHS>mark(U22(isNat(V1)))</RHS></RULE><RULE><LHS>active(U22(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U31(tt,N))</LHS><RHS>mark(N)</RHS></RULE><RULE><LHS>active(U41(tt,M,N))</LHS><RHS>mark(s(plus(N,M)))</RHS></RULE><RULE><LHS>active(and(tt,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(isNat(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNat(plus(V1,V2)))</LHS><RHS>mark(U11(and(isNatKind(V1),isNatKind(V2)),V1,V2))</RHS></RULE><RULE><LHS>active(isNat(s(V1)))</LHS><RHS>mark(U21(isNatKind(V1),V1))</RHS></RULE><RULE><LHS>active(isNatKind(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNatKind(plus(V1,V2)))</LHS><RHS>mark(and(isNatKind(V1),isNatKind(V2)))</RHS></RULE><RULE><LHS>active(isNatKind(s(V1)))</LHS><RHS>mark(isNatKind(V1))</RHS></RULE><RULE><LHS>active(plus(N,0))</LHS><RHS>mark(U31(and(isNat(N),isNatKind(N)),N))</RHS></RULE><RULE><LHS>active(plus(N,s(M)))</LHS><RHS>mark(U41(and(and(isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),M,N))</RHS></RULE><RULE><LHS>mark(U11(X1,X2,X3))</LHS><RHS>active(U11(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(tt)</LHS><RHS>active(tt)</RHS></RULE><RULE><LHS>mark(U12(X1,X2))</LHS><RHS>active(U12(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(isNat(X))</LHS><RHS>active(isNat(X))</RHS></RULE><RULE><LHS>mark(U13(X))</LHS><RHS>active(U13(mark(X)))</RHS></RULE><RULE><LHS>mark(U21(X1,X2))</LHS><RHS>active(U21(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U22(X))</LHS><RHS>active(U22(mark(X)))</RHS></RULE><RULE><LHS>mark(U31(X1,X2))</LHS><RHS>active(U31(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U41(X1,X2,X3))</LHS><RHS>active(U41(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(mark(X)))</RHS></RULE><RULE><LHS>mark(plus(X1,X2))</LHS><RHS>active(plus(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(isNatKind(X))</LHS><RHS>active(isNatKind(X))</RHS></RULE><RULE><LHS>U11(mark(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,mark(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,mark(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(active(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,active(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,active(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U12(mark(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,mark(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(active(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,active(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>isNat(mark(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>isNat(active(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>U13(mark(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U13(active(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U21(mark(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,mark(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(active(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,active(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U22(mark(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U22(active(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U31(mark(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,mark(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(active(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,active(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U41(mark(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,mark(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,mark(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(active(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,active(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,active(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>s(mark(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>s(active(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>plus(mark(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,mark(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(active(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,active(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>and(mark(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,mark(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(active(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,active(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>isNatKind(mark(X))</LHS><RHS>isNatKind(X)</RHS></RULE><RULE><LHS>isNatKind(active(X))</LHS><RHS>isNatKind(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_active(U11(tt,V1,V2))</LHS><RHS>Marked_mark(U12(isNat(V1),V2))</RHS></DPRULE><DPRULE num="1"><LHS>Marked_active(U12(tt,V2))</LHS><RHS>Marked_mark(U13(isNat(V2)))</RHS></DPRULE><DPRULE num="2"><LHS>Marked_active(U21(tt,V1))</LHS><RHS>Marked_mark(U22(isNat(V1)))</RHS></DPRULE><DPRULE num="3"><LHS>Marked_active(U31(tt,N))</LHS><RHS>Marked_mark(N)</RHS></DPRULE><DPRULE num="4"><LHS>Marked_active(U41(tt,M,N))</LHS><RHS>Marked_mark(s(plus(N,M)))</RHS></DPRULE><DPRULE num="5"><LHS>Marked_active(and(tt,X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="6"><LHS>Marked_active(isNat(plus(V1,V2)))</LHS><RHS>Marked_mark(U11(and(isNatKind(V1),isNatKind(V2)),V1,V2))</RHS></DPRULE><DPRULE num="7"><LHS>Marked_active(isNat(s(V1)))</LHS><RHS>Marked_mark(U21(isNatKind(V1),V1))</RHS></DPRULE><DPRULE num="8"><LHS>Marked_active(isNatKind(plus(V1,V2)))</LHS><RHS>Marked_mark(and(isNatKind(V1),isNatKind(V2)))</RHS></DPRULE><DPRULE num="9"><LHS>Marked_active(isNatKind(s(V1)))</LHS><RHS>Marked_mark(isNatKind(V1))</RHS></DPRULE><DPRULE num="10"><LHS>Marked_mark(U11(X1,X2,X3))</LHS><RHS>Marked_active(U11(mark(X1),X2,X3))</RHS></DPRULE><DPRULE num="11"><LHS>Marked_mark(U11(X1,X2,X3))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="12"><LHS>Marked_mark(U12(X1,X2))</LHS><RHS>Marked_active(U12(mark(X1),X2))</RHS></DPRULE><DPRULE num="13"><LHS>Marked_mark(U12(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="14"><LHS>Marked_mark(isNat(X))</LHS><RHS>Marked_active(isNat(X))</RHS></DPRULE><DPRULE num="15"><LHS>Marked_mark(U13(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="16"><LHS>Marked_mark(U21(X1,X2))</LHS><RHS>Marked_active(U21(mark(X1),X2))</RHS></DPRULE><DPRULE num="17"><LHS>Marked_mark(U21(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="18"><LHS>Marked_mark(U22(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="19"><LHS>Marked_mark(U31(X1,X2))</LHS><RHS>Marked_active(U31(mark(X1),X2))</RHS></DPRULE><DPRULE num="20"><LHS>Marked_mark(U31(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="21"><LHS>Marked_mark(U41(X1,X2,X3))</LHS><RHS>Marked_active(U41(mark(X1),X2,X3))</RHS></DPRULE><DPRULE num="22"><LHS>Marked_mark(plus(X1,X2))</LHS><RHS>Marked_active(plus(mark(X1),mark(X2)))</RHS></DPRULE><DPRULE num="23"><LHS>Marked_mark(plus(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="24"><LHS>Marked_mark(plus(X1,X2))</LHS><RHS>Marked_mark(X2)</RHS></DPRULE><DPRULE num="25"><LHS>Marked_mark(and(X1,X2))</LHS><RHS>Marked_active(and(mark(X1),X2))</RHS></DPRULE><DPRULE num="26"><LHS>Marked_mark(and(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="27"><LHS>Marked_mark(isNatKind(X))</LHS><RHS>Marked_active(isNatKind(X))</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><ORDERING type="poly"><POLYSYMB><SYMBOL><NAME>mark</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U21</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U11</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U41</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>Marked_mark</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>isNat</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>s</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U13</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>0</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U12</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U31</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>tt</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>and</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>Marked_active</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>active</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>plus</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U22</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>isNatKind</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB></ORDERING><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_mark(plus(X1,X2))</LHS><RHS>Marked_active(plus(mark(X1),mark(X2)))</RHS></DPRULE></DPLIST></STRICTPAIRS></CRITERION><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(U11(tt,V1,V2))</LHS><RHS>mark(U12(isNat(V1),V2))</RHS></RULE><RULE><LHS>active(U12(tt,V2))</LHS><RHS>mark(U13(isNat(V2)))</RHS></RULE><RULE><LHS>active(U13(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U21(tt,V1))</LHS><RHS>mark(U22(isNat(V1)))</RHS></RULE><RULE><LHS>active(U22(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U31(tt,N))</LHS><RHS>mark(N)</RHS></RULE><RULE><LHS>active(U41(tt,M,N))</LHS><RHS>mark(s(plus(N,M)))</RHS></RULE><RULE><LHS>active(and(tt,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(isNat(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNat(plus(V1,V2)))</LHS><RHS>mark(U11(and(isNatKind(V1),isNatKind(V2)),V1,V2))</RHS></RULE><RULE><LHS>active(isNat(s(V1)))</LHS><RHS>mark(U21(isNatKind(V1),V1))</RHS></RULE><RULE><LHS>active(isNatKind(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNatKind(plus(V1,V2)))</LHS><RHS>mark(and(isNatKind(V1),isNatKind(V2)))</RHS></RULE><RULE><LHS>active(isNatKind(s(V1)))</LHS><RHS>mark(isNatKind(V1))</RHS></RULE><RULE><LHS>active(plus(N,0))</LHS><RHS>mark(U31(and(isNat(N),isNatKind(N)),N))</RHS></RULE><RULE><LHS>active(plus(N,s(M)))</LHS><RHS>mark(U41(and(and(isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),M,N))</RHS></RULE><RULE><LHS>mark(U11(X1,X2,X3))</LHS><RHS>active(U11(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(tt)</LHS><RHS>active(tt)</RHS></RULE><RULE><LHS>mark(U12(X1,X2))</LHS><RHS>active(U12(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(isNat(X))</LHS><RHS>active(isNat(X))</RHS></RULE><RULE><LHS>mark(U13(X))</LHS><RHS>active(U13(mark(X)))</RHS></RULE><RULE><LHS>mark(U21(X1,X2))</LHS><RHS>active(U21(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U22(X))</LHS><RHS>active(U22(mark(X)))</RHS></RULE><RULE><LHS>mark(U31(X1,X2))</LHS><RHS>active(U31(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U41(X1,X2,X3))</LHS><RHS>active(U41(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(mark(X)))</RHS></RULE><RULE><LHS>mark(plus(X1,X2))</LHS><RHS>active(plus(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(isNatKind(X))</LHS><RHS>active(isNatKind(X))</RHS></RULE><RULE><LHS>U11(mark(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,mark(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,mark(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(active(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,active(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,active(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U12(mark(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,mark(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(active(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,active(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>isNat(mark(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>isNat(active(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>U13(mark(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U13(active(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U21(mark(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,mark(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(active(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,active(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U22(mark(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U22(active(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U31(mark(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,mark(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(active(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,active(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U41(mark(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,mark(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,mark(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(active(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,active(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,active(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>s(mark(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>s(active(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>plus(mark(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,mark(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(active(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,active(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>and(mark(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,mark(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(active(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,active(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>isNatKind(mark(X))</LHS><RHS>isNatKind(X)</RHS></RULE><RULE><LHS>isNatKind(active(X))</LHS><RHS>isNatKind(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_active(U11(tt,V1,V2))</LHS><RHS>Marked_mark(U12(isNat(V1),V2))</RHS></DPRULE><DPRULE num="1"><LHS>Marked_active(U12(tt,V2))</LHS><RHS>Marked_mark(U13(isNat(V2)))</RHS></DPRULE><DPRULE num="2"><LHS>Marked_active(U21(tt,V1))</LHS><RHS>Marked_mark(U22(isNat(V1)))</RHS></DPRULE><DPRULE num="3"><LHS>Marked_active(U31(tt,N))</LHS><RHS>Marked_mark(N)</RHS></DPRULE><DPRULE num="4"><LHS>Marked_active(U41(tt,M,N))</LHS><RHS>Marked_mark(s(plus(N,M)))</RHS></DPRULE><DPRULE num="5"><LHS>Marked_active(and(tt,X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="6"><LHS>Marked_active(isNat(plus(V1,V2)))</LHS><RHS>Marked_mark(U11(and(isNatKind(V1),isNatKind(V2)),V1,V2))</RHS></DPRULE><DPRULE num="7"><LHS>Marked_active(isNat(s(V1)))</LHS><RHS>Marked_mark(U21(isNatKind(V1),V1))</RHS></DPRULE><DPRULE num="8"><LHS>Marked_active(isNatKind(plus(V1,V2)))</LHS><RHS>Marked_mark(and(isNatKind(V1),isNatKind(V2)))</RHS></DPRULE><DPRULE num="9"><LHS>Marked_active(isNatKind(s(V1)))</LHS><RHS>Marked_mark(isNatKind(V1))</RHS></DPRULE><DPRULE num="10"><LHS>Marked_mark(U11(X1,X2,X3))</LHS><RHS>Marked_active(U11(mark(X1),X2,X3))</RHS></DPRULE><DPRULE num="11"><LHS>Marked_mark(U11(X1,X2,X3))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="12"><LHS>Marked_mark(U12(X1,X2))</LHS><RHS>Marked_active(U12(mark(X1),X2))</RHS></DPRULE><DPRULE num="13"><LHS>Marked_mark(U12(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="14"><LHS>Marked_mark(isNat(X))</LHS><RHS>Marked_active(isNat(X))</RHS></DPRULE><DPRULE num="15"><LHS>Marked_mark(U13(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="16"><LHS>Marked_mark(U21(X1,X2))</LHS><RHS>Marked_active(U21(mark(X1),X2))</RHS></DPRULE><DPRULE num="17"><LHS>Marked_mark(U21(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="18"><LHS>Marked_mark(U22(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="19"><LHS>Marked_mark(U31(X1,X2))</LHS><RHS>Marked_active(U31(mark(X1),X2))</RHS></DPRULE><DPRULE num="20"><LHS>Marked_mark(U31(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="21"><LHS>Marked_mark(U41(X1,X2,X3))</LHS><RHS>Marked_active(U41(mark(X1),X2,X3))</RHS></DPRULE><DPRULE num="22"><LHS>Marked_mark(plus(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="23"><LHS>Marked_mark(plus(X1,X2))</LHS><RHS>Marked_mark(X2)</RHS></DPRULE><DPRULE num="24"><LHS>Marked_mark(and(X1,X2))</LHS><RHS>Marked_active(and(mark(X1),X2))</RHS></DPRULE><DPRULE num="25"><LHS>Marked_mark(and(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="26"><LHS>Marked_mark(isNatKind(X))</LHS><RHS>Marked_active(isNatKind(X))</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><DAG approx="simpl"><CCLIST><SCC num="0"><NODE ref="0"/><NODE ref="1"/><NODE ref="2"/><NODE ref="3"/><NODE ref="4"/><NODE ref="5"/><NODE ref="6"/><NODE ref="7"/><NODE ref="8"/><NODE ref="9"/><NODE ref="10"/><NODE ref="11"/><NODE ref="12"/><NODE ref="13"/><NODE ref="14"/><NODE ref="15"/><NODE ref="16"/><NODE ref="17"/><NODE ref="18"/><NODE ref="19"/><NODE ref="20"/><NODE ref="21"/><NODE ref="22"/><NODE ref="23"/><NODE ref="24"/><NODE ref="25"/><NODE ref="26"/></SCC></CCLIST></DAG></CRITERION><PROPERTY criterion="stronggraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(U11(tt,V1,V2))</LHS><RHS>mark(U12(isNat(V1),V2))</RHS></RULE><RULE><LHS>active(U12(tt,V2))</LHS><RHS>mark(U13(isNat(V2)))</RHS></RULE><RULE><LHS>active(U13(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U21(tt,V1))</LHS><RHS>mark(U22(isNat(V1)))</RHS></RULE><RULE><LHS>active(U22(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U31(tt,N))</LHS><RHS>mark(N)</RHS></RULE><RULE><LHS>active(U41(tt,M,N))</LHS><RHS>mark(s(plus(N,M)))</RHS></RULE><RULE><LHS>active(and(tt,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(isNat(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNat(plus(V1,V2)))</LHS><RHS>mark(U11(and(isNatKind(V1),isNatKind(V2)),V1,V2))</RHS></RULE><RULE><LHS>active(isNat(s(V1)))</LHS><RHS>mark(U21(isNatKind(V1),V1))</RHS></RULE><RULE><LHS>active(isNatKind(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNatKind(plus(V1,V2)))</LHS><RHS>mark(and(isNatKind(V1),isNatKind(V2)))</RHS></RULE><RULE><LHS>active(isNatKind(s(V1)))</LHS><RHS>mark(isNatKind(V1))</RHS></RULE><RULE><LHS>active(plus(N,0))</LHS><RHS>mark(U31(and(isNat(N),isNatKind(N)),N))</RHS></RULE><RULE><LHS>active(plus(N,s(M)))</LHS><RHS>mark(U41(and(and(isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),M,N))</RHS></RULE><RULE><LHS>mark(U11(X1,X2,X3))</LHS><RHS>active(U11(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(tt)</LHS><RHS>active(tt)</RHS></RULE><RULE><LHS>mark(U12(X1,X2))</LHS><RHS>active(U12(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(isNat(X))</LHS><RHS>active(isNat(X))</RHS></RULE><RULE><LHS>mark(U13(X))</LHS><RHS>active(U13(mark(X)))</RHS></RULE><RULE><LHS>mark(U21(X1,X2))</LHS><RHS>active(U21(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U22(X))</LHS><RHS>active(U22(mark(X)))</RHS></RULE><RULE><LHS>mark(U31(X1,X2))</LHS><RHS>active(U31(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U41(X1,X2,X3))</LHS><RHS>active(U41(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(mark(X)))</RHS></RULE><RULE><LHS>mark(plus(X1,X2))</LHS><RHS>active(plus(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(isNatKind(X))</LHS><RHS>active(isNatKind(X))</RHS></RULE><RULE><LHS>U11(mark(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,mark(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,mark(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(active(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,active(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,active(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U12(mark(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,mark(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(active(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,active(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>isNat(mark(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>isNat(active(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>U13(mark(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U13(active(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U21(mark(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,mark(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(active(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,active(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U22(mark(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U22(active(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U31(mark(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,mark(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(active(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,active(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U41(mark(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,mark(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,mark(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(active(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,active(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,active(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>s(mark(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>s(active(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>plus(mark(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,mark(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(active(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,active(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>and(mark(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,mark(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(active(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,active(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>isNatKind(mark(X))</LHS><RHS>isNatKind(X)</RHS></RULE><RULE><LHS>isNatKind(active(X))</LHS><RHS>isNatKind(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_active(U11(tt,V1,V2))</LHS><RHS>Marked_mark(U12(isNat(V1),V2))</RHS></DPRULE><DPRULE num="1"><LHS>Marked_active(U12(tt,V2))</LHS><RHS>Marked_mark(U13(isNat(V2)))</RHS></DPRULE><DPRULE num="2"><LHS>Marked_active(U21(tt,V1))</LHS><RHS>Marked_mark(U22(isNat(V1)))</RHS></DPRULE><DPRULE num="3"><LHS>Marked_active(U31(tt,N))</LHS><RHS>Marked_mark(N)</RHS></DPRULE><DPRULE num="4"><LHS>Marked_active(U41(tt,M,N))</LHS><RHS>Marked_mark(s(plus(N,M)))</RHS></DPRULE><DPRULE num="5"><LHS>Marked_active(and(tt,X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="6"><LHS>Marked_active(isNat(plus(V1,V2)))</LHS><RHS>Marked_mark(U11(and(isNatKind(V1),isNatKind(V2)),V1,V2))</RHS></DPRULE><DPRULE num="7"><LHS>Marked_active(isNat(s(V1)))</LHS><RHS>Marked_mark(U21(isNatKind(V1),V1))</RHS></DPRULE><DPRULE num="8"><LHS>Marked_active(isNatKind(plus(V1,V2)))</LHS><RHS>Marked_mark(and(isNatKind(V1),isNatKind(V2)))</RHS></DPRULE><DPRULE num="9"><LHS>Marked_active(isNatKind(s(V1)))</LHS><RHS>Marked_mark(isNatKind(V1))</RHS></DPRULE><DPRULE num="10"><LHS>Marked_mark(U11(X1,X2,X3))</LHS><RHS>Marked_active(U11(mark(X1),X2,X3))</RHS></DPRULE><DPRULE num="11"><LHS>Marked_mark(U11(X1,X2,X3))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="12"><LHS>Marked_mark(U12(X1,X2))</LHS><RHS>Marked_active(U12(mark(X1),X2))</RHS></DPRULE><DPRULE num="13"><LHS>Marked_mark(U12(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="14"><LHS>Marked_mark(isNat(X))</LHS><RHS>Marked_active(isNat(X))</RHS></DPRULE><DPRULE num="15"><LHS>Marked_mark(U13(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="16"><LHS>Marked_mark(U21(X1,X2))</LHS><RHS>Marked_active(U21(mark(X1),X2))</RHS></DPRULE><DPRULE num="17"><LHS>Marked_mark(U21(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="18"><LHS>Marked_mark(U22(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="19"><LHS>Marked_mark(U31(X1,X2))</LHS><RHS>Marked_active(U31(mark(X1),X2))</RHS></DPRULE><DPRULE num="20"><LHS>Marked_mark(U31(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="21"><LHS>Marked_mark(U41(X1,X2,X3))</LHS><RHS>Marked_active(U41(mark(X1),X2,X3))</RHS></DPRULE><DPRULE num="22"><LHS>Marked_mark(plus(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="23"><LHS>Marked_mark(plus(X1,X2))</LHS><RHS>Marked_mark(X2)</RHS></DPRULE><DPRULE num="24"><LHS>Marked_mark(and(X1,X2))</LHS><RHS>Marked_active(and(mark(X1),X2))</RHS></DPRULE><DPRULE num="25"><LHS>Marked_mark(and(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="26"><LHS>Marked_mark(isNatKind(X))</LHS><RHS>Marked_active(isNatKind(X))</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><ORDERING type="poly"><POLYSYMB><SYMBOL><NAME>mark</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U21</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U11</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>3</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="2"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U41</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>3</INT></COEF><ARG degree="1" num="2"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>Marked_mark</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>isNat</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>s</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U13</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>0</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U12</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U31</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>tt</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>and</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>Marked_active</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>active</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>plus</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>3</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U22</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>isNatKind</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB></ORDERING><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_active(isNat(s(V1)))</LHS><RHS>Marked_mark(U21(isNatKind(V1),V1))</RHS></DPRULE></DPLIST></STRICTPAIRS></CRITERION><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(U11(tt,V1,V2))</LHS><RHS>mark(U12(isNat(V1),V2))</RHS></RULE><RULE><LHS>active(U12(tt,V2))</LHS><RHS>mark(U13(isNat(V2)))</RHS></RULE><RULE><LHS>active(U13(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U21(tt,V1))</LHS><RHS>mark(U22(isNat(V1)))</RHS></RULE><RULE><LHS>active(U22(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U31(tt,N))</LHS><RHS>mark(N)</RHS></RULE><RULE><LHS>active(U41(tt,M,N))</LHS><RHS>mark(s(plus(N,M)))</RHS></RULE><RULE><LHS>active(and(tt,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(isNat(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNat(plus(V1,V2)))</LHS><RHS>mark(U11(and(isNatKind(V1),isNatKind(V2)),V1,V2))</RHS></RULE><RULE><LHS>active(isNat(s(V1)))</LHS><RHS>mark(U21(isNatKind(V1),V1))</RHS></RULE><RULE><LHS>active(isNatKind(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNatKind(plus(V1,V2)))</LHS><RHS>mark(and(isNatKind(V1),isNatKind(V2)))</RHS></RULE><RULE><LHS>active(isNatKind(s(V1)))</LHS><RHS>mark(isNatKind(V1))</RHS></RULE><RULE><LHS>active(plus(N,0))</LHS><RHS>mark(U31(and(isNat(N),isNatKind(N)),N))</RHS></RULE><RULE><LHS>active(plus(N,s(M)))</LHS><RHS>mark(U41(and(and(isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),M,N))</RHS></RULE><RULE><LHS>mark(U11(X1,X2,X3))</LHS><RHS>active(U11(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(tt)</LHS><RHS>active(tt)</RHS></RULE><RULE><LHS>mark(U12(X1,X2))</LHS><RHS>active(U12(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(isNat(X))</LHS><RHS>active(isNat(X))</RHS></RULE><RULE><LHS>mark(U13(X))</LHS><RHS>active(U13(mark(X)))</RHS></RULE><RULE><LHS>mark(U21(X1,X2))</LHS><RHS>active(U21(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U22(X))</LHS><RHS>active(U22(mark(X)))</RHS></RULE><RULE><LHS>mark(U31(X1,X2))</LHS><RHS>active(U31(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U41(X1,X2,X3))</LHS><RHS>active(U41(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(mark(X)))</RHS></RULE><RULE><LHS>mark(plus(X1,X2))</LHS><RHS>active(plus(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(isNatKind(X))</LHS><RHS>active(isNatKind(X))</RHS></RULE><RULE><LHS>U11(mark(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,mark(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,mark(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(active(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,active(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,active(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U12(mark(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,mark(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(active(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,active(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>isNat(mark(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>isNat(active(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>U13(mark(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U13(active(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U21(mark(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,mark(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(active(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,active(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U22(mark(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U22(active(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U31(mark(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,mark(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(active(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,active(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U41(mark(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,mark(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,mark(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(active(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,active(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,active(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>s(mark(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>s(active(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>plus(mark(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,mark(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(active(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,active(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>and(mark(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,mark(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(active(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,active(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>isNatKind(mark(X))</LHS><RHS>isNatKind(X)</RHS></RULE><RULE><LHS>isNatKind(active(X))</LHS><RHS>isNatKind(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_active(U11(tt,V1,V2))</LHS><RHS>Marked_mark(U12(isNat(V1),V2))</RHS></DPRULE><DPRULE num="1"><LHS>Marked_active(U12(tt,V2))</LHS><RHS>Marked_mark(U13(isNat(V2)))</RHS></DPRULE><DPRULE num="2"><LHS>Marked_active(U21(tt,V1))</LHS><RHS>Marked_mark(U22(isNat(V1)))</RHS></DPRULE><DPRULE num="3"><LHS>Marked_active(U31(tt,N))</LHS><RHS>Marked_mark(N)</RHS></DPRULE><DPRULE num="4"><LHS>Marked_active(U41(tt,M,N))</LHS><RHS>Marked_mark(s(plus(N,M)))</RHS></DPRULE><DPRULE num="5"><LHS>Marked_active(and(tt,X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="6"><LHS>Marked_active(isNat(plus(V1,V2)))</LHS><RHS>Marked_mark(U11(and(isNatKind(V1),isNatKind(V2)),V1,V2))</RHS></DPRULE><DPRULE num="7"><LHS>Marked_active(isNatKind(plus(V1,V2)))</LHS><RHS>Marked_mark(and(isNatKind(V1),isNatKind(V2)))</RHS></DPRULE><DPRULE num="8"><LHS>Marked_active(isNatKind(s(V1)))</LHS><RHS>Marked_mark(isNatKind(V1))</RHS></DPRULE><DPRULE num="9"><LHS>Marked_mark(U11(X1,X2,X3))</LHS><RHS>Marked_active(U11(mark(X1),X2,X3))</RHS></DPRULE><DPRULE num="10"><LHS>Marked_mark(U11(X1,X2,X3))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="11"><LHS>Marked_mark(U12(X1,X2))</LHS><RHS>Marked_active(U12(mark(X1),X2))</RHS></DPRULE><DPRULE num="12"><LHS>Marked_mark(U12(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="13"><LHS>Marked_mark(isNat(X))</LHS><RHS>Marked_active(isNat(X))</RHS></DPRULE><DPRULE num="14"><LHS>Marked_mark(U13(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="15"><LHS>Marked_mark(U21(X1,X2))</LHS><RHS>Marked_active(U21(mark(X1),X2))</RHS></DPRULE><DPRULE num="16"><LHS>Marked_mark(U21(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="17"><LHS>Marked_mark(U22(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="18"><LHS>Marked_mark(U31(X1,X2))</LHS><RHS>Marked_active(U31(mark(X1),X2))</RHS></DPRULE><DPRULE num="19"><LHS>Marked_mark(U31(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="20"><LHS>Marked_mark(U41(X1,X2,X3))</LHS><RHS>Marked_active(U41(mark(X1),X2,X3))</RHS></DPRULE><DPRULE num="21"><LHS>Marked_mark(plus(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="22"><LHS>Marked_mark(plus(X1,X2))</LHS><RHS>Marked_mark(X2)</RHS></DPRULE><DPRULE num="23"><LHS>Marked_mark(and(X1,X2))</LHS><RHS>Marked_active(and(mark(X1),X2))</RHS></DPRULE><DPRULE num="24"><LHS>Marked_mark(and(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="25"><LHS>Marked_mark(isNatKind(X))</LHS><RHS>Marked_active(isNatKind(X))</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><DAG approx="simpl"><CCLIST><SCC num="0"><NODE ref="0"/><NODE ref="1"/><NODE ref="2"/><NODE ref="3"/><NODE ref="4"/><NODE ref="5"/><NODE ref="6"/><NODE ref="7"/><NODE ref="8"/><NODE ref="9"/><NODE ref="10"/><NODE ref="11"/><NODE ref="12"/><NODE ref="13"/><NODE ref="14"/><NODE ref="15"/><NODE ref="16"/><NODE ref="17"/><NODE ref="18"/><NODE ref="19"/><NODE ref="20"/><NODE ref="21"/><NODE ref="22"/><NODE ref="23"/><NODE ref="24"/><NODE ref="25"/></SCC></CCLIST></DAG></CRITERION><PROPERTY criterion="stronggraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(U11(tt,V1,V2))</LHS><RHS>mark(U12(isNat(V1),V2))</RHS></RULE><RULE><LHS>active(U12(tt,V2))</LHS><RHS>mark(U13(isNat(V2)))</RHS></RULE><RULE><LHS>active(U13(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U21(tt,V1))</LHS><RHS>mark(U22(isNat(V1)))</RHS></RULE><RULE><LHS>active(U22(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U31(tt,N))</LHS><RHS>mark(N)</RHS></RULE><RULE><LHS>active(U41(tt,M,N))</LHS><RHS>mark(s(plus(N,M)))</RHS></RULE><RULE><LHS>active(and(tt,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(isNat(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNat(plus(V1,V2)))</LHS><RHS>mark(U11(and(isNatKind(V1),isNatKind(V2)),V1,V2))</RHS></RULE><RULE><LHS>active(isNat(s(V1)))</LHS><RHS>mark(U21(isNatKind(V1),V1))</RHS></RULE><RULE><LHS>active(isNatKind(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNatKind(plus(V1,V2)))</LHS><RHS>mark(and(isNatKind(V1),isNatKind(V2)))</RHS></RULE><RULE><LHS>active(isNatKind(s(V1)))</LHS><RHS>mark(isNatKind(V1))</RHS></RULE><RULE><LHS>active(plus(N,0))</LHS><RHS>mark(U31(and(isNat(N),isNatKind(N)),N))</RHS></RULE><RULE><LHS>active(plus(N,s(M)))</LHS><RHS>mark(U41(and(and(isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),M,N))</RHS></RULE><RULE><LHS>mark(U11(X1,X2,X3))</LHS><RHS>active(U11(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(tt)</LHS><RHS>active(tt)</RHS></RULE><RULE><LHS>mark(U12(X1,X2))</LHS><RHS>active(U12(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(isNat(X))</LHS><RHS>active(isNat(X))</RHS></RULE><RULE><LHS>mark(U13(X))</LHS><RHS>active(U13(mark(X)))</RHS></RULE><RULE><LHS>mark(U21(X1,X2))</LHS><RHS>active(U21(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U22(X))</LHS><RHS>active(U22(mark(X)))</RHS></RULE><RULE><LHS>mark(U31(X1,X2))</LHS><RHS>active(U31(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U41(X1,X2,X3))</LHS><RHS>active(U41(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(mark(X)))</RHS></RULE><RULE><LHS>mark(plus(X1,X2))</LHS><RHS>active(plus(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(isNatKind(X))</LHS><RHS>active(isNatKind(X))</RHS></RULE><RULE><LHS>U11(mark(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,mark(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,mark(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(active(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,active(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,active(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U12(mark(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,mark(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(active(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,active(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>isNat(mark(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>isNat(active(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>U13(mark(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U13(active(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U21(mark(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,mark(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(active(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,active(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U22(mark(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U22(active(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U31(mark(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,mark(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(active(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,active(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U41(mark(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,mark(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,mark(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(active(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,active(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,active(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>s(mark(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>s(active(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>plus(mark(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,mark(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(active(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,active(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>and(mark(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,mark(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(active(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,active(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>isNatKind(mark(X))</LHS><RHS>isNatKind(X)</RHS></RULE><RULE><LHS>isNatKind(active(X))</LHS><RHS>isNatKind(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_active(U11(tt,V1,V2))</LHS><RHS>Marked_mark(U12(isNat(V1),V2))</RHS></DPRULE><DPRULE num="1"><LHS>Marked_active(U12(tt,V2))</LHS><RHS>Marked_mark(U13(isNat(V2)))</RHS></DPRULE><DPRULE num="2"><LHS>Marked_active(U21(tt,V1))</LHS><RHS>Marked_mark(U22(isNat(V1)))</RHS></DPRULE><DPRULE num="3"><LHS>Marked_active(U31(tt,N))</LHS><RHS>Marked_mark(N)</RHS></DPRULE><DPRULE num="4"><LHS>Marked_active(U41(tt,M,N))</LHS><RHS>Marked_mark(s(plus(N,M)))</RHS></DPRULE><DPRULE num="5"><LHS>Marked_active(and(tt,X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="6"><LHS>Marked_active(isNat(plus(V1,V2)))</LHS><RHS>Marked_mark(U11(and(isNatKind(V1),isNatKind(V2)),V1,V2))</RHS></DPRULE><DPRULE num="7"><LHS>Marked_active(isNatKind(plus(V1,V2)))</LHS><RHS>Marked_mark(and(isNatKind(V1),isNatKind(V2)))</RHS></DPRULE><DPRULE num="8"><LHS>Marked_active(isNatKind(s(V1)))</LHS><RHS>Marked_mark(isNatKind(V1))</RHS></DPRULE><DPRULE num="9"><LHS>Marked_mark(U11(X1,X2,X3))</LHS><RHS>Marked_active(U11(mark(X1),X2,X3))</RHS></DPRULE><DPRULE num="10"><LHS>Marked_mark(U11(X1,X2,X3))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="11"><LHS>Marked_mark(U12(X1,X2))</LHS><RHS>Marked_active(U12(mark(X1),X2))</RHS></DPRULE><DPRULE num="12"><LHS>Marked_mark(U12(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="13"><LHS>Marked_mark(isNat(X))</LHS><RHS>Marked_active(isNat(X))</RHS></DPRULE><DPRULE num="14"><LHS>Marked_mark(U13(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="15"><LHS>Marked_mark(U21(X1,X2))</LHS><RHS>Marked_active(U21(mark(X1),X2))</RHS></DPRULE><DPRULE num="16"><LHS>Marked_mark(U21(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="17"><LHS>Marked_mark(U22(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="18"><LHS>Marked_mark(U31(X1,X2))</LHS><RHS>Marked_active(U31(mark(X1),X2))</RHS></DPRULE><DPRULE num="19"><LHS>Marked_mark(U31(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="20"><LHS>Marked_mark(U41(X1,X2,X3))</LHS><RHS>Marked_active(U41(mark(X1),X2,X3))</RHS></DPRULE><DPRULE num="21"><LHS>Marked_mark(plus(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="22"><LHS>Marked_mark(plus(X1,X2))</LHS><RHS>Marked_mark(X2)</RHS></DPRULE><DPRULE num="23"><LHS>Marked_mark(and(X1,X2))</LHS><RHS>Marked_active(and(mark(X1),X2))</RHS></DPRULE><DPRULE num="24"><LHS>Marked_mark(and(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="25"><LHS>Marked_mark(isNatKind(X))</LHS><RHS>Marked_active(isNatKind(X))</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><ORDERING type="poly"><POLYSYMB><SYMBOL><NAME>mark</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U21</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U11</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U41</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>3</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>Marked_mark</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>isNat</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>s</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U13</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>0</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U12</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U31</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>tt</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>and</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>Marked_active</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>active</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>plus</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U22</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>isNatKind</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB></ORDERING><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_active(U41(tt,M,N))</LHS><RHS>Marked_mark(s(plus(N,M)))</RHS></DPRULE></DPLIST></STRICTPAIRS></CRITERION><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(U11(tt,V1,V2))</LHS><RHS>mark(U12(isNat(V1),V2))</RHS></RULE><RULE><LHS>active(U12(tt,V2))</LHS><RHS>mark(U13(isNat(V2)))</RHS></RULE><RULE><LHS>active(U13(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U21(tt,V1))</LHS><RHS>mark(U22(isNat(V1)))</RHS></RULE><RULE><LHS>active(U22(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U31(tt,N))</LHS><RHS>mark(N)</RHS></RULE><RULE><LHS>active(U41(tt,M,N))</LHS><RHS>mark(s(plus(N,M)))</RHS></RULE><RULE><LHS>active(and(tt,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(isNat(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNat(plus(V1,V2)))</LHS><RHS>mark(U11(and(isNatKind(V1),isNatKind(V2)),V1,V2))</RHS></RULE><RULE><LHS>active(isNat(s(V1)))</LHS><RHS>mark(U21(isNatKind(V1),V1))</RHS></RULE><RULE><LHS>active(isNatKind(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNatKind(plus(V1,V2)))</LHS><RHS>mark(and(isNatKind(V1),isNatKind(V2)))</RHS></RULE><RULE><LHS>active(isNatKind(s(V1)))</LHS><RHS>mark(isNatKind(V1))</RHS></RULE><RULE><LHS>active(plus(N,0))</LHS><RHS>mark(U31(and(isNat(N),isNatKind(N)),N))</RHS></RULE><RULE><LHS>active(plus(N,s(M)))</LHS><RHS>mark(U41(and(and(isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),M,N))</RHS></RULE><RULE><LHS>mark(U11(X1,X2,X3))</LHS><RHS>active(U11(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(tt)</LHS><RHS>active(tt)</RHS></RULE><RULE><LHS>mark(U12(X1,X2))</LHS><RHS>active(U12(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(isNat(X))</LHS><RHS>active(isNat(X))</RHS></RULE><RULE><LHS>mark(U13(X))</LHS><RHS>active(U13(mark(X)))</RHS></RULE><RULE><LHS>mark(U21(X1,X2))</LHS><RHS>active(U21(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U22(X))</LHS><RHS>active(U22(mark(X)))</RHS></RULE><RULE><LHS>mark(U31(X1,X2))</LHS><RHS>active(U31(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U41(X1,X2,X3))</LHS><RHS>active(U41(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(mark(X)))</RHS></RULE><RULE><LHS>mark(plus(X1,X2))</LHS><RHS>active(plus(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(isNatKind(X))</LHS><RHS>active(isNatKind(X))</RHS></RULE><RULE><LHS>U11(mark(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,mark(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,mark(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(active(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,active(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,active(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U12(mark(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,mark(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(active(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,active(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>isNat(mark(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>isNat(active(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>U13(mark(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U13(active(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U21(mark(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,mark(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(active(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,active(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U22(mark(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U22(active(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U31(mark(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,mark(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(active(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,active(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U41(mark(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,mark(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,mark(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(active(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,active(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,active(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>s(mark(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>s(active(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>plus(mark(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,mark(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(active(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,active(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>and(mark(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,mark(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(active(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,active(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>isNatKind(mark(X))</LHS><RHS>isNatKind(X)</RHS></RULE><RULE><LHS>isNatKind(active(X))</LHS><RHS>isNatKind(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_active(U11(tt,V1,V2))</LHS><RHS>Marked_mark(U12(isNat(V1),V2))</RHS></DPRULE><DPRULE num="1"><LHS>Marked_active(U12(tt,V2))</LHS><RHS>Marked_mark(U13(isNat(V2)))</RHS></DPRULE><DPRULE num="2"><LHS>Marked_active(U21(tt,V1))</LHS><RHS>Marked_mark(U22(isNat(V1)))</RHS></DPRULE><DPRULE num="3"><LHS>Marked_active(U31(tt,N))</LHS><RHS>Marked_mark(N)</RHS></DPRULE><DPRULE num="4"><LHS>Marked_active(and(tt,X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="5"><LHS>Marked_active(isNat(plus(V1,V2)))</LHS><RHS>Marked_mark(U11(and(isNatKind(V1),isNatKind(V2)),V1,V2))</RHS></DPRULE><DPRULE num="6"><LHS>Marked_active(isNatKind(plus(V1,V2)))</LHS><RHS>Marked_mark(and(isNatKind(V1),isNatKind(V2)))</RHS></DPRULE><DPRULE num="7"><LHS>Marked_active(isNatKind(s(V1)))</LHS><RHS>Marked_mark(isNatKind(V1))</RHS></DPRULE><DPRULE num="8"><LHS>Marked_mark(U11(X1,X2,X3))</LHS><RHS>Marked_active(U11(mark(X1),X2,X3))</RHS></DPRULE><DPRULE num="9"><LHS>Marked_mark(U11(X1,X2,X3))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="10"><LHS>Marked_mark(U12(X1,X2))</LHS><RHS>Marked_active(U12(mark(X1),X2))</RHS></DPRULE><DPRULE num="11"><LHS>Marked_mark(U12(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="12"><LHS>Marked_mark(isNat(X))</LHS><RHS>Marked_active(isNat(X))</RHS></DPRULE><DPRULE num="13"><LHS>Marked_mark(U13(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="14"><LHS>Marked_mark(U21(X1,X2))</LHS><RHS>Marked_active(U21(mark(X1),X2))</RHS></DPRULE><DPRULE num="15"><LHS>Marked_mark(U21(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="16"><LHS>Marked_mark(U22(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="17"><LHS>Marked_mark(U31(X1,X2))</LHS><RHS>Marked_active(U31(mark(X1),X2))</RHS></DPRULE><DPRULE num="18"><LHS>Marked_mark(U31(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="19"><LHS>Marked_mark(U41(X1,X2,X3))</LHS><RHS>Marked_active(U41(mark(X1),X2,X3))</RHS></DPRULE><DPRULE num="20"><LHS>Marked_mark(plus(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="21"><LHS>Marked_mark(plus(X1,X2))</LHS><RHS>Marked_mark(X2)</RHS></DPRULE><DPRULE num="22"><LHS>Marked_mark(and(X1,X2))</LHS><RHS>Marked_active(and(mark(X1),X2))</RHS></DPRULE><DPRULE num="23"><LHS>Marked_mark(and(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="24"><LHS>Marked_mark(isNatKind(X))</LHS><RHS>Marked_active(isNatKind(X))</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><DAG approx="simpl"><CCLIST><SCC num="0"><NODE ref="0"/><NODE ref="1"/><NODE ref="2"/><NODE ref="3"/><NODE ref="4"/><NODE ref="5"/><NODE ref="6"/><NODE ref="7"/><NODE ref="8"/><NODE ref="9"/><NODE ref="10"/><NODE ref="11"/><NODE ref="12"/><NODE ref="13"/><NODE ref="14"/><NODE ref="15"/><NODE ref="16"/><NODE ref="17"/><NODE ref="18"/><NODE ref="19"/><NODE ref="20"/><NODE ref="21"/><NODE ref="22"/><NODE ref="23"/><NODE ref="24"/></SCC></CCLIST></DAG></CRITERION><PROPERTY criterion="stronggraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(U11(tt,V1,V2))</LHS><RHS>mark(U12(isNat(V1),V2))</RHS></RULE><RULE><LHS>active(U12(tt,V2))</LHS><RHS>mark(U13(isNat(V2)))</RHS></RULE><RULE><LHS>active(U13(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U21(tt,V1))</LHS><RHS>mark(U22(isNat(V1)))</RHS></RULE><RULE><LHS>active(U22(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U31(tt,N))</LHS><RHS>mark(N)</RHS></RULE><RULE><LHS>active(U41(tt,M,N))</LHS><RHS>mark(s(plus(N,M)))</RHS></RULE><RULE><LHS>active(and(tt,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(isNat(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNat(plus(V1,V2)))</LHS><RHS>mark(U11(and(isNatKind(V1),isNatKind(V2)),V1,V2))</RHS></RULE><RULE><LHS>active(isNat(s(V1)))</LHS><RHS>mark(U21(isNatKind(V1),V1))</RHS></RULE><RULE><LHS>active(isNatKind(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNatKind(plus(V1,V2)))</LHS><RHS>mark(and(isNatKind(V1),isNatKind(V2)))</RHS></RULE><RULE><LHS>active(isNatKind(s(V1)))</LHS><RHS>mark(isNatKind(V1))</RHS></RULE><RULE><LHS>active(plus(N,0))</LHS><RHS>mark(U31(and(isNat(N),isNatKind(N)),N))</RHS></RULE><RULE><LHS>active(plus(N,s(M)))</LHS><RHS>mark(U41(and(and(isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),M,N))</RHS></RULE><RULE><LHS>mark(U11(X1,X2,X3))</LHS><RHS>active(U11(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(tt)</LHS><RHS>active(tt)</RHS></RULE><RULE><LHS>mark(U12(X1,X2))</LHS><RHS>active(U12(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(isNat(X))</LHS><RHS>active(isNat(X))</RHS></RULE><RULE><LHS>mark(U13(X))</LHS><RHS>active(U13(mark(X)))</RHS></RULE><RULE><LHS>mark(U21(X1,X2))</LHS><RHS>active(U21(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U22(X))</LHS><RHS>active(U22(mark(X)))</RHS></RULE><RULE><LHS>mark(U31(X1,X2))</LHS><RHS>active(U31(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U41(X1,X2,X3))</LHS><RHS>active(U41(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(mark(X)))</RHS></RULE><RULE><LHS>mark(plus(X1,X2))</LHS><RHS>active(plus(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(isNatKind(X))</LHS><RHS>active(isNatKind(X))</RHS></RULE><RULE><LHS>U11(mark(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,mark(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,mark(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(active(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,active(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,active(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U12(mark(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,mark(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(active(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,active(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>isNat(mark(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>isNat(active(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>U13(mark(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U13(active(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U21(mark(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,mark(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(active(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,active(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U22(mark(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U22(active(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U31(mark(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,mark(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(active(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,active(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U41(mark(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,mark(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,mark(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(active(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,active(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,active(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>s(mark(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>s(active(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>plus(mark(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,mark(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(active(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,active(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>and(mark(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,mark(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(active(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,active(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>isNatKind(mark(X))</LHS><RHS>isNatKind(X)</RHS></RULE><RULE><LHS>isNatKind(active(X))</LHS><RHS>isNatKind(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_active(U11(tt,V1,V2))</LHS><RHS>Marked_mark(U12(isNat(V1),V2))</RHS></DPRULE><DPRULE num="1"><LHS>Marked_active(U12(tt,V2))</LHS><RHS>Marked_mark(U13(isNat(V2)))</RHS></DPRULE><DPRULE num="2"><LHS>Marked_active(U21(tt,V1))</LHS><RHS>Marked_mark(U22(isNat(V1)))</RHS></DPRULE><DPRULE num="3"><LHS>Marked_active(U31(tt,N))</LHS><RHS>Marked_mark(N)</RHS></DPRULE><DPRULE num="4"><LHS>Marked_active(and(tt,X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="5"><LHS>Marked_active(isNat(plus(V1,V2)))</LHS><RHS>Marked_mark(U11(and(isNatKind(V1),isNatKind(V2)),V1,V2))</RHS></DPRULE><DPRULE num="6"><LHS>Marked_active(isNatKind(plus(V1,V2)))</LHS><RHS>Marked_mark(and(isNatKind(V1),isNatKind(V2)))</RHS></DPRULE><DPRULE num="7"><LHS>Marked_active(isNatKind(s(V1)))</LHS><RHS>Marked_mark(isNatKind(V1))</RHS></DPRULE><DPRULE num="8"><LHS>Marked_mark(U11(X1,X2,X3))</LHS><RHS>Marked_active(U11(mark(X1),X2,X3))</RHS></DPRULE><DPRULE num="9"><LHS>Marked_mark(U11(X1,X2,X3))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="10"><LHS>Marked_mark(U12(X1,X2))</LHS><RHS>Marked_active(U12(mark(X1),X2))</RHS></DPRULE><DPRULE num="11"><LHS>Marked_mark(U12(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="12"><LHS>Marked_mark(isNat(X))</LHS><RHS>Marked_active(isNat(X))</RHS></DPRULE><DPRULE num="13"><LHS>Marked_mark(U13(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="14"><LHS>Marked_mark(U21(X1,X2))</LHS><RHS>Marked_active(U21(mark(X1),X2))</RHS></DPRULE><DPRULE num="15"><LHS>Marked_mark(U21(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="16"><LHS>Marked_mark(U22(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="17"><LHS>Marked_mark(U31(X1,X2))</LHS><RHS>Marked_active(U31(mark(X1),X2))</RHS></DPRULE><DPRULE num="18"><LHS>Marked_mark(U31(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="19"><LHS>Marked_mark(U41(X1,X2,X3))</LHS><RHS>Marked_active(U41(mark(X1),X2,X3))</RHS></DPRULE><DPRULE num="20"><LHS>Marked_mark(plus(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="21"><LHS>Marked_mark(plus(X1,X2))</LHS><RHS>Marked_mark(X2)</RHS></DPRULE><DPRULE num="22"><LHS>Marked_mark(and(X1,X2))</LHS><RHS>Marked_active(and(mark(X1),X2))</RHS></DPRULE><DPRULE num="23"><LHS>Marked_mark(and(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="24"><LHS>Marked_mark(isNatKind(X))</LHS><RHS>Marked_active(isNatKind(X))</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><ORDERING type="poly"><POLYSYMB><SYMBOL><NAME>mark</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U21</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U11</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U41</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>Marked_mark</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>isNat</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>s</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U13</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>0</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U12</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U31</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>tt</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>and</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>Marked_active</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>active</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>plus</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U22</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>isNatKind</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB></ORDERING><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_mark(U41(X1,X2,X3))</LHS><RHS>Marked_active(U41(mark(X1),X2,X3))</RHS></DPRULE></DPLIST></STRICTPAIRS></CRITERION><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(U11(tt,V1,V2))</LHS><RHS>mark(U12(isNat(V1),V2))</RHS></RULE><RULE><LHS>active(U12(tt,V2))</LHS><RHS>mark(U13(isNat(V2)))</RHS></RULE><RULE><LHS>active(U13(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U21(tt,V1))</LHS><RHS>mark(U22(isNat(V1)))</RHS></RULE><RULE><LHS>active(U22(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U31(tt,N))</LHS><RHS>mark(N)</RHS></RULE><RULE><LHS>active(U41(tt,M,N))</LHS><RHS>mark(s(plus(N,M)))</RHS></RULE><RULE><LHS>active(and(tt,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(isNat(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNat(plus(V1,V2)))</LHS><RHS>mark(U11(and(isNatKind(V1),isNatKind(V2)),V1,V2))</RHS></RULE><RULE><LHS>active(isNat(s(V1)))</LHS><RHS>mark(U21(isNatKind(V1),V1))</RHS></RULE><RULE><LHS>active(isNatKind(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNatKind(plus(V1,V2)))</LHS><RHS>mark(and(isNatKind(V1),isNatKind(V2)))</RHS></RULE><RULE><LHS>active(isNatKind(s(V1)))</LHS><RHS>mark(isNatKind(V1))</RHS></RULE><RULE><LHS>active(plus(N,0))</LHS><RHS>mark(U31(and(isNat(N),isNatKind(N)),N))</RHS></RULE><RULE><LHS>active(plus(N,s(M)))</LHS><RHS>mark(U41(and(and(isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),M,N))</RHS></RULE><RULE><LHS>mark(U11(X1,X2,X3))</LHS><RHS>active(U11(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(tt)</LHS><RHS>active(tt)</RHS></RULE><RULE><LHS>mark(U12(X1,X2))</LHS><RHS>active(U12(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(isNat(X))</LHS><RHS>active(isNat(X))</RHS></RULE><RULE><LHS>mark(U13(X))</LHS><RHS>active(U13(mark(X)))</RHS></RULE><RULE><LHS>mark(U21(X1,X2))</LHS><RHS>active(U21(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U22(X))</LHS><RHS>active(U22(mark(X)))</RHS></RULE><RULE><LHS>mark(U31(X1,X2))</LHS><RHS>active(U31(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U41(X1,X2,X3))</LHS><RHS>active(U41(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(mark(X)))</RHS></RULE><RULE><LHS>mark(plus(X1,X2))</LHS><RHS>active(plus(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(isNatKind(X))</LHS><RHS>active(isNatKind(X))</RHS></RULE><RULE><LHS>U11(mark(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,mark(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,mark(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(active(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,active(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,active(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U12(mark(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,mark(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(active(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,active(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>isNat(mark(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>isNat(active(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>U13(mark(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U13(active(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U21(mark(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,mark(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(active(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,active(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U22(mark(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U22(active(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U31(mark(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,mark(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(active(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,active(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U41(mark(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,mark(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,mark(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(active(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,active(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,active(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>s(mark(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>s(active(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>plus(mark(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,mark(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(active(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,active(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>and(mark(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,mark(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(active(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,active(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>isNatKind(mark(X))</LHS><RHS>isNatKind(X)</RHS></RULE><RULE><LHS>isNatKind(active(X))</LHS><RHS>isNatKind(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_active(U11(tt,V1,V2))</LHS><RHS>Marked_mark(U12(isNat(V1),V2))</RHS></DPRULE><DPRULE num="1"><LHS>Marked_active(U12(tt,V2))</LHS><RHS>Marked_mark(U13(isNat(V2)))</RHS></DPRULE><DPRULE num="2"><LHS>Marked_active(U21(tt,V1))</LHS><RHS>Marked_mark(U22(isNat(V1)))</RHS></DPRULE><DPRULE num="3"><LHS>Marked_active(U31(tt,N))</LHS><RHS>Marked_mark(N)</RHS></DPRULE><DPRULE num="4"><LHS>Marked_active(and(tt,X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="5"><LHS>Marked_active(isNat(plus(V1,V2)))</LHS><RHS>Marked_mark(U11(and(isNatKind(V1),isNatKind(V2)),V1,V2))</RHS></DPRULE><DPRULE num="6"><LHS>Marked_active(isNatKind(plus(V1,V2)))</LHS><RHS>Marked_mark(and(isNatKind(V1),isNatKind(V2)))</RHS></DPRULE><DPRULE num="7"><LHS>Marked_active(isNatKind(s(V1)))</LHS><RHS>Marked_mark(isNatKind(V1))</RHS></DPRULE><DPRULE num="8"><LHS>Marked_mark(U11(X1,X2,X3))</LHS><RHS>Marked_active(U11(mark(X1),X2,X3))</RHS></DPRULE><DPRULE num="9"><LHS>Marked_mark(U11(X1,X2,X3))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="10"><LHS>Marked_mark(U12(X1,X2))</LHS><RHS>Marked_active(U12(mark(X1),X2))</RHS></DPRULE><DPRULE num="11"><LHS>Marked_mark(U12(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="12"><LHS>Marked_mark(isNat(X))</LHS><RHS>Marked_active(isNat(X))</RHS></DPRULE><DPRULE num="13"><LHS>Marked_mark(U13(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="14"><LHS>Marked_mark(U21(X1,X2))</LHS><RHS>Marked_active(U21(mark(X1),X2))</RHS></DPRULE><DPRULE num="15"><LHS>Marked_mark(U21(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="16"><LHS>Marked_mark(U22(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="17"><LHS>Marked_mark(U31(X1,X2))</LHS><RHS>Marked_active(U31(mark(X1),X2))</RHS></DPRULE><DPRULE num="18"><LHS>Marked_mark(U31(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="19"><LHS>Marked_mark(plus(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="20"><LHS>Marked_mark(plus(X1,X2))</LHS><RHS>Marked_mark(X2)</RHS></DPRULE><DPRULE num="21"><LHS>Marked_mark(and(X1,X2))</LHS><RHS>Marked_active(and(mark(X1),X2))</RHS></DPRULE><DPRULE num="22"><LHS>Marked_mark(and(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="23"><LHS>Marked_mark(isNatKind(X))</LHS><RHS>Marked_active(isNatKind(X))</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><DAG approx="simpl"><CCLIST><SCC num="0"><NODE ref="0"/><NODE ref="1"/><NODE ref="2"/><NODE ref="3"/><NODE ref="4"/><NODE ref="5"/><NODE ref="6"/><NODE ref="7"/><NODE ref="8"/><NODE ref="9"/><NODE ref="10"/><NODE ref="11"/><NODE ref="12"/><NODE ref="13"/><NODE ref="14"/><NODE ref="15"/><NODE ref="16"/><NODE ref="17"/><NODE ref="18"/><NODE ref="19"/><NODE ref="20"/><NODE ref="21"/><NODE ref="22"/><NODE ref="23"/></SCC></CCLIST></DAG></CRITERION><PROPERTY criterion="stronggraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(U11(tt,V1,V2))</LHS><RHS>mark(U12(isNat(V1),V2))</RHS></RULE><RULE><LHS>active(U12(tt,V2))</LHS><RHS>mark(U13(isNat(V2)))</RHS></RULE><RULE><LHS>active(U13(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U21(tt,V1))</LHS><RHS>mark(U22(isNat(V1)))</RHS></RULE><RULE><LHS>active(U22(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U31(tt,N))</LHS><RHS>mark(N)</RHS></RULE><RULE><LHS>active(U41(tt,M,N))</LHS><RHS>mark(s(plus(N,M)))</RHS></RULE><RULE><LHS>active(and(tt,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(isNat(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNat(plus(V1,V2)))</LHS><RHS>mark(U11(and(isNatKind(V1),isNatKind(V2)),V1,V2))</RHS></RULE><RULE><LHS>active(isNat(s(V1)))</LHS><RHS>mark(U21(isNatKind(V1),V1))</RHS></RULE><RULE><LHS>active(isNatKind(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNatKind(plus(V1,V2)))</LHS><RHS>mark(and(isNatKind(V1),isNatKind(V2)))</RHS></RULE><RULE><LHS>active(isNatKind(s(V1)))</LHS><RHS>mark(isNatKind(V1))</RHS></RULE><RULE><LHS>active(plus(N,0))</LHS><RHS>mark(U31(and(isNat(N),isNatKind(N)),N))</RHS></RULE><RULE><LHS>active(plus(N,s(M)))</LHS><RHS>mark(U41(and(and(isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),M,N))</RHS></RULE><RULE><LHS>mark(U11(X1,X2,X3))</LHS><RHS>active(U11(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(tt)</LHS><RHS>active(tt)</RHS></RULE><RULE><LHS>mark(U12(X1,X2))</LHS><RHS>active(U12(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(isNat(X))</LHS><RHS>active(isNat(X))</RHS></RULE><RULE><LHS>mark(U13(X))</LHS><RHS>active(U13(mark(X)))</RHS></RULE><RULE><LHS>mark(U21(X1,X2))</LHS><RHS>active(U21(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U22(X))</LHS><RHS>active(U22(mark(X)))</RHS></RULE><RULE><LHS>mark(U31(X1,X2))</LHS><RHS>active(U31(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U41(X1,X2,X3))</LHS><RHS>active(U41(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(mark(X)))</RHS></RULE><RULE><LHS>mark(plus(X1,X2))</LHS><RHS>active(plus(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(isNatKind(X))</LHS><RHS>active(isNatKind(X))</RHS></RULE><RULE><LHS>U11(mark(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,mark(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,mark(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(active(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,active(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,active(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U12(mark(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,mark(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(active(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,active(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>isNat(mark(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>isNat(active(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>U13(mark(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U13(active(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U21(mark(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,mark(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(active(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,active(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U22(mark(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U22(active(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U31(mark(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,mark(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(active(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,active(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U41(mark(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,mark(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,mark(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(active(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,active(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,active(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>s(mark(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>s(active(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>plus(mark(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,mark(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(active(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,active(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>and(mark(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,mark(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(active(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,active(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>isNatKind(mark(X))</LHS><RHS>isNatKind(X)</RHS></RULE><RULE><LHS>isNatKind(active(X))</LHS><RHS>isNatKind(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_active(U11(tt,V1,V2))</LHS><RHS>Marked_mark(U12(isNat(V1),V2))</RHS></DPRULE><DPRULE num="1"><LHS>Marked_active(U12(tt,V2))</LHS><RHS>Marked_mark(U13(isNat(V2)))</RHS></DPRULE><DPRULE num="2"><LHS>Marked_active(U21(tt,V1))</LHS><RHS>Marked_mark(U22(isNat(V1)))</RHS></DPRULE><DPRULE num="3"><LHS>Marked_active(U31(tt,N))</LHS><RHS>Marked_mark(N)</RHS></DPRULE><DPRULE num="4"><LHS>Marked_active(and(tt,X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="5"><LHS>Marked_active(isNat(plus(V1,V2)))</LHS><RHS>Marked_mark(U11(and(isNatKind(V1),isNatKind(V2)),V1,V2))</RHS></DPRULE><DPRULE num="6"><LHS>Marked_active(isNatKind(plus(V1,V2)))</LHS><RHS>Marked_mark(and(isNatKind(V1),isNatKind(V2)))</RHS></DPRULE><DPRULE num="7"><LHS>Marked_active(isNatKind(s(V1)))</LHS><RHS>Marked_mark(isNatKind(V1))</RHS></DPRULE><DPRULE num="8"><LHS>Marked_mark(U11(X1,X2,X3))</LHS><RHS>Marked_active(U11(mark(X1),X2,X3))</RHS></DPRULE><DPRULE num="9"><LHS>Marked_mark(U11(X1,X2,X3))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="10"><LHS>Marked_mark(U12(X1,X2))</LHS><RHS>Marked_active(U12(mark(X1),X2))</RHS></DPRULE><DPRULE num="11"><LHS>Marked_mark(U12(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="12"><LHS>Marked_mark(isNat(X))</LHS><RHS>Marked_active(isNat(X))</RHS></DPRULE><DPRULE num="13"><LHS>Marked_mark(U13(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="14"><LHS>Marked_mark(U21(X1,X2))</LHS><RHS>Marked_active(U21(mark(X1),X2))</RHS></DPRULE><DPRULE num="15"><LHS>Marked_mark(U21(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="16"><LHS>Marked_mark(U22(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="17"><LHS>Marked_mark(U31(X1,X2))</LHS><RHS>Marked_active(U31(mark(X1),X2))</RHS></DPRULE><DPRULE num="18"><LHS>Marked_mark(U31(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="19"><LHS>Marked_mark(plus(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="20"><LHS>Marked_mark(plus(X1,X2))</LHS><RHS>Marked_mark(X2)</RHS></DPRULE><DPRULE num="21"><LHS>Marked_mark(and(X1,X2))</LHS><RHS>Marked_active(and(mark(X1),X2))</RHS></DPRULE><DPRULE num="22"><LHS>Marked_mark(and(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="23"><LHS>Marked_mark(isNatKind(X))</LHS><RHS>Marked_active(isNatKind(X))</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><ORDERING type="poly"><POLYSYMB><SYMBOL><NAME>mark</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U21</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U11</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U41</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>Marked_mark</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>isNat</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>s</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U13</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>0</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U12</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U31</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>tt</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>and</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>Marked_active</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>active</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>plus</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U22</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>isNatKind</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB></ORDERING><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_mark(plus(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_mark(plus(X1,X2))</LHS><RHS>Marked_mark(X2)</RHS></DPRULE></DPLIST></STRICTPAIRS></CRITERION><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(U11(tt,V1,V2))</LHS><RHS>mark(U12(isNat(V1),V2))</RHS></RULE><RULE><LHS>active(U12(tt,V2))</LHS><RHS>mark(U13(isNat(V2)))</RHS></RULE><RULE><LHS>active(U13(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U21(tt,V1))</LHS><RHS>mark(U22(isNat(V1)))</RHS></RULE><RULE><LHS>active(U22(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U31(tt,N))</LHS><RHS>mark(N)</RHS></RULE><RULE><LHS>active(U41(tt,M,N))</LHS><RHS>mark(s(plus(N,M)))</RHS></RULE><RULE><LHS>active(and(tt,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(isNat(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNat(plus(V1,V2)))</LHS><RHS>mark(U11(and(isNatKind(V1),isNatKind(V2)),V1,V2))</RHS></RULE><RULE><LHS>active(isNat(s(V1)))</LHS><RHS>mark(U21(isNatKind(V1),V1))</RHS></RULE><RULE><LHS>active(isNatKind(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNatKind(plus(V1,V2)))</LHS><RHS>mark(and(isNatKind(V1),isNatKind(V2)))</RHS></RULE><RULE><LHS>active(isNatKind(s(V1)))</LHS><RHS>mark(isNatKind(V1))</RHS></RULE><RULE><LHS>active(plus(N,0))</LHS><RHS>mark(U31(and(isNat(N),isNatKind(N)),N))</RHS></RULE><RULE><LHS>active(plus(N,s(M)))</LHS><RHS>mark(U41(and(and(isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),M,N))</RHS></RULE><RULE><LHS>mark(U11(X1,X2,X3))</LHS><RHS>active(U11(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(tt)</LHS><RHS>active(tt)</RHS></RULE><RULE><LHS>mark(U12(X1,X2))</LHS><RHS>active(U12(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(isNat(X))</LHS><RHS>active(isNat(X))</RHS></RULE><RULE><LHS>mark(U13(X))</LHS><RHS>active(U13(mark(X)))</RHS></RULE><RULE><LHS>mark(U21(X1,X2))</LHS><RHS>active(U21(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U22(X))</LHS><RHS>active(U22(mark(X)))</RHS></RULE><RULE><LHS>mark(U31(X1,X2))</LHS><RHS>active(U31(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U41(X1,X2,X3))</LHS><RHS>active(U41(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(mark(X)))</RHS></RULE><RULE><LHS>mark(plus(X1,X2))</LHS><RHS>active(plus(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(isNatKind(X))</LHS><RHS>active(isNatKind(X))</RHS></RULE><RULE><LHS>U11(mark(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,mark(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,mark(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(active(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,active(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,active(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U12(mark(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,mark(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(active(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,active(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>isNat(mark(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>isNat(active(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>U13(mark(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U13(active(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U21(mark(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,mark(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(active(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,active(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U22(mark(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U22(active(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U31(mark(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,mark(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(active(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,active(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U41(mark(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,mark(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,mark(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(active(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,active(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,active(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>s(mark(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>s(active(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>plus(mark(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,mark(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(active(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,active(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>and(mark(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,mark(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(active(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,active(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>isNatKind(mark(X))</LHS><RHS>isNatKind(X)</RHS></RULE><RULE><LHS>isNatKind(active(X))</LHS><RHS>isNatKind(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_active(U11(tt,V1,V2))</LHS><RHS>Marked_mark(U12(isNat(V1),V2))</RHS></DPRULE><DPRULE num="1"><LHS>Marked_active(U12(tt,V2))</LHS><RHS>Marked_mark(U13(isNat(V2)))</RHS></DPRULE><DPRULE num="2"><LHS>Marked_active(U21(tt,V1))</LHS><RHS>Marked_mark(U22(isNat(V1)))</RHS></DPRULE><DPRULE num="3"><LHS>Marked_active(U31(tt,N))</LHS><RHS>Marked_mark(N)</RHS></DPRULE><DPRULE num="4"><LHS>Marked_active(and(tt,X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="5"><LHS>Marked_active(isNat(plus(V1,V2)))</LHS><RHS>Marked_mark(U11(and(isNatKind(V1),isNatKind(V2)),V1,V2))</RHS></DPRULE><DPRULE num="6"><LHS>Marked_active(isNatKind(plus(V1,V2)))</LHS><RHS>Marked_mark(and(isNatKind(V1),isNatKind(V2)))</RHS></DPRULE><DPRULE num="7"><LHS>Marked_active(isNatKind(s(V1)))</LHS><RHS>Marked_mark(isNatKind(V1))</RHS></DPRULE><DPRULE num="8"><LHS>Marked_mark(U11(X1,X2,X3))</LHS><RHS>Marked_active(U11(mark(X1),X2,X3))</RHS></DPRULE><DPRULE num="9"><LHS>Marked_mark(U11(X1,X2,X3))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="10"><LHS>Marked_mark(U12(X1,X2))</LHS><RHS>Marked_active(U12(mark(X1),X2))</RHS></DPRULE><DPRULE num="11"><LHS>Marked_mark(U12(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="12"><LHS>Marked_mark(isNat(X))</LHS><RHS>Marked_active(isNat(X))</RHS></DPRULE><DPRULE num="13"><LHS>Marked_mark(U13(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="14"><LHS>Marked_mark(U21(X1,X2))</LHS><RHS>Marked_active(U21(mark(X1),X2))</RHS></DPRULE><DPRULE num="15"><LHS>Marked_mark(U21(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="16"><LHS>Marked_mark(U22(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="17"><LHS>Marked_mark(U31(X1,X2))</LHS><RHS>Marked_active(U31(mark(X1),X2))</RHS></DPRULE><DPRULE num="18"><LHS>Marked_mark(U31(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="19"><LHS>Marked_mark(and(X1,X2))</LHS><RHS>Marked_active(and(mark(X1),X2))</RHS></DPRULE><DPRULE num="20"><LHS>Marked_mark(and(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="21"><LHS>Marked_mark(isNatKind(X))</LHS><RHS>Marked_active(isNatKind(X))</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><DAG approx="simpl"><CCLIST><SCC num="0"><NODE ref="0"/><NODE ref="1"/><NODE ref="2"/><NODE ref="3"/><NODE ref="4"/><NODE ref="5"/><NODE ref="6"/><NODE ref="7"/><NODE ref="8"/><NODE ref="9"/><NODE ref="10"/><NODE ref="11"/><NODE ref="12"/><NODE ref="13"/><NODE ref="14"/><NODE ref="15"/><NODE ref="16"/><NODE ref="17"/><NODE ref="18"/><NODE ref="19"/><NODE ref="20"/><NODE ref="21"/></SCC></CCLIST></DAG></CRITERION><PROPERTY criterion="stronggraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(U11(tt,V1,V2))</LHS><RHS>mark(U12(isNat(V1),V2))</RHS></RULE><RULE><LHS>active(U12(tt,V2))</LHS><RHS>mark(U13(isNat(V2)))</RHS></RULE><RULE><LHS>active(U13(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U21(tt,V1))</LHS><RHS>mark(U22(isNat(V1)))</RHS></RULE><RULE><LHS>active(U22(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U31(tt,N))</LHS><RHS>mark(N)</RHS></RULE><RULE><LHS>active(U41(tt,M,N))</LHS><RHS>mark(s(plus(N,M)))</RHS></RULE><RULE><LHS>active(and(tt,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(isNat(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNat(plus(V1,V2)))</LHS><RHS>mark(U11(and(isNatKind(V1),isNatKind(V2)),V1,V2))</RHS></RULE><RULE><LHS>active(isNat(s(V1)))</LHS><RHS>mark(U21(isNatKind(V1),V1))</RHS></RULE><RULE><LHS>active(isNatKind(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNatKind(plus(V1,V2)))</LHS><RHS>mark(and(isNatKind(V1),isNatKind(V2)))</RHS></RULE><RULE><LHS>active(isNatKind(s(V1)))</LHS><RHS>mark(isNatKind(V1))</RHS></RULE><RULE><LHS>active(plus(N,0))</LHS><RHS>mark(U31(and(isNat(N),isNatKind(N)),N))</RHS></RULE><RULE><LHS>active(plus(N,s(M)))</LHS><RHS>mark(U41(and(and(isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),M,N))</RHS></RULE><RULE><LHS>mark(U11(X1,X2,X3))</LHS><RHS>active(U11(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(tt)</LHS><RHS>active(tt)</RHS></RULE><RULE><LHS>mark(U12(X1,X2))</LHS><RHS>active(U12(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(isNat(X))</LHS><RHS>active(isNat(X))</RHS></RULE><RULE><LHS>mark(U13(X))</LHS><RHS>active(U13(mark(X)))</RHS></RULE><RULE><LHS>mark(U21(X1,X2))</LHS><RHS>active(U21(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U22(X))</LHS><RHS>active(U22(mark(X)))</RHS></RULE><RULE><LHS>mark(U31(X1,X2))</LHS><RHS>active(U31(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U41(X1,X2,X3))</LHS><RHS>active(U41(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(mark(X)))</RHS></RULE><RULE><LHS>mark(plus(X1,X2))</LHS><RHS>active(plus(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(isNatKind(X))</LHS><RHS>active(isNatKind(X))</RHS></RULE><RULE><LHS>U11(mark(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,mark(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,mark(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(active(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,active(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,active(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U12(mark(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,mark(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(active(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,active(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>isNat(mark(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>isNat(active(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>U13(mark(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U13(active(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U21(mark(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,mark(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(active(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,active(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U22(mark(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U22(active(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U31(mark(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,mark(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(active(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,active(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U41(mark(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,mark(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,mark(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(active(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,active(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,active(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>s(mark(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>s(active(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>plus(mark(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,mark(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(active(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,active(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>and(mark(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,mark(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(active(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,active(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>isNatKind(mark(X))</LHS><RHS>isNatKind(X)</RHS></RULE><RULE><LHS>isNatKind(active(X))</LHS><RHS>isNatKind(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_active(U11(tt,V1,V2))</LHS><RHS>Marked_mark(U12(isNat(V1),V2))</RHS></DPRULE><DPRULE num="1"><LHS>Marked_active(U12(tt,V2))</LHS><RHS>Marked_mark(U13(isNat(V2)))</RHS></DPRULE><DPRULE num="2"><LHS>Marked_active(U21(tt,V1))</LHS><RHS>Marked_mark(U22(isNat(V1)))</RHS></DPRULE><DPRULE num="3"><LHS>Marked_active(U31(tt,N))</LHS><RHS>Marked_mark(N)</RHS></DPRULE><DPRULE num="4"><LHS>Marked_active(and(tt,X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="5"><LHS>Marked_active(isNat(plus(V1,V2)))</LHS><RHS>Marked_mark(U11(and(isNatKind(V1),isNatKind(V2)),V1,V2))</RHS></DPRULE><DPRULE num="6"><LHS>Marked_active(isNatKind(plus(V1,V2)))</LHS><RHS>Marked_mark(and(isNatKind(V1),isNatKind(V2)))</RHS></DPRULE><DPRULE num="7"><LHS>Marked_active(isNatKind(s(V1)))</LHS><RHS>Marked_mark(isNatKind(V1))</RHS></DPRULE><DPRULE num="8"><LHS>Marked_mark(U11(X1,X2,X3))</LHS><RHS>Marked_active(U11(mark(X1),X2,X3))</RHS></DPRULE><DPRULE num="9"><LHS>Marked_mark(U11(X1,X2,X3))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="10"><LHS>Marked_mark(U12(X1,X2))</LHS><RHS>Marked_active(U12(mark(X1),X2))</RHS></DPRULE><DPRULE num="11"><LHS>Marked_mark(U12(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="12"><LHS>Marked_mark(isNat(X))</LHS><RHS>Marked_active(isNat(X))</RHS></DPRULE><DPRULE num="13"><LHS>Marked_mark(U13(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="14"><LHS>Marked_mark(U21(X1,X2))</LHS><RHS>Marked_active(U21(mark(X1),X2))</RHS></DPRULE><DPRULE num="15"><LHS>Marked_mark(U21(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="16"><LHS>Marked_mark(U22(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="17"><LHS>Marked_mark(U31(X1,X2))</LHS><RHS>Marked_active(U31(mark(X1),X2))</RHS></DPRULE><DPRULE num="18"><LHS>Marked_mark(U31(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="19"><LHS>Marked_mark(and(X1,X2))</LHS><RHS>Marked_active(and(mark(X1),X2))</RHS></DPRULE><DPRULE num="20"><LHS>Marked_mark(and(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="21"><LHS>Marked_mark(isNatKind(X))</LHS><RHS>Marked_active(isNatKind(X))</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><ORDERING type="poly"><POLYSYMB><SYMBOL><NAME>mark</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U21</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U11</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="2"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U41</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>3</INT></COEF><ARG degree="1" num="2"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>Marked_mark</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>isNat</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>s</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U13</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>0</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U12</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U31</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>tt</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>and</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>Marked_active</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>active</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>plus</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>3</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U22</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>isNatKind</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB></ORDERING><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_active(isNat(plus(V1,V2)))</LHS><RHS>Marked_mark(U11(and(isNatKind(V1),isNatKind(V2)),V1,V2))</RHS></DPRULE></DPLIST></STRICTPAIRS></CRITERION><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(U11(tt,V1,V2))</LHS><RHS>mark(U12(isNat(V1),V2))</RHS></RULE><RULE><LHS>active(U12(tt,V2))</LHS><RHS>mark(U13(isNat(V2)))</RHS></RULE><RULE><LHS>active(U13(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U21(tt,V1))</LHS><RHS>mark(U22(isNat(V1)))</RHS></RULE><RULE><LHS>active(U22(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U31(tt,N))</LHS><RHS>mark(N)</RHS></RULE><RULE><LHS>active(U41(tt,M,N))</LHS><RHS>mark(s(plus(N,M)))</RHS></RULE><RULE><LHS>active(and(tt,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(isNat(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNat(plus(V1,V2)))</LHS><RHS>mark(U11(and(isNatKind(V1),isNatKind(V2)),V1,V2))</RHS></RULE><RULE><LHS>active(isNat(s(V1)))</LHS><RHS>mark(U21(isNatKind(V1),V1))</RHS></RULE><RULE><LHS>active(isNatKind(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNatKind(plus(V1,V2)))</LHS><RHS>mark(and(isNatKind(V1),isNatKind(V2)))</RHS></RULE><RULE><LHS>active(isNatKind(s(V1)))</LHS><RHS>mark(isNatKind(V1))</RHS></RULE><RULE><LHS>active(plus(N,0))</LHS><RHS>mark(U31(and(isNat(N),isNatKind(N)),N))</RHS></RULE><RULE><LHS>active(plus(N,s(M)))</LHS><RHS>mark(U41(and(and(isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),M,N))</RHS></RULE><RULE><LHS>mark(U11(X1,X2,X3))</LHS><RHS>active(U11(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(tt)</LHS><RHS>active(tt)</RHS></RULE><RULE><LHS>mark(U12(X1,X2))</LHS><RHS>active(U12(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(isNat(X))</LHS><RHS>active(isNat(X))</RHS></RULE><RULE><LHS>mark(U13(X))</LHS><RHS>active(U13(mark(X)))</RHS></RULE><RULE><LHS>mark(U21(X1,X2))</LHS><RHS>active(U21(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U22(X))</LHS><RHS>active(U22(mark(X)))</RHS></RULE><RULE><LHS>mark(U31(X1,X2))</LHS><RHS>active(U31(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U41(X1,X2,X3))</LHS><RHS>active(U41(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(mark(X)))</RHS></RULE><RULE><LHS>mark(plus(X1,X2))</LHS><RHS>active(plus(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(isNatKind(X))</LHS><RHS>active(isNatKind(X))</RHS></RULE><RULE><LHS>U11(mark(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,mark(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,mark(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(active(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,active(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,active(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U12(mark(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,mark(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(active(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,active(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>isNat(mark(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>isNat(active(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>U13(mark(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U13(active(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U21(mark(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,mark(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(active(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,active(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U22(mark(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U22(active(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U31(mark(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,mark(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(active(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,active(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U41(mark(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,mark(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,mark(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(active(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,active(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,active(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>s(mark(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>s(active(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>plus(mark(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,mark(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(active(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,active(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>and(mark(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,mark(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(active(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,active(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>isNatKind(mark(X))</LHS><RHS>isNatKind(X)</RHS></RULE><RULE><LHS>isNatKind(active(X))</LHS><RHS>isNatKind(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_active(U11(tt,V1,V2))</LHS><RHS>Marked_mark(U12(isNat(V1),V2))</RHS></DPRULE><DPRULE num="1"><LHS>Marked_active(U12(tt,V2))</LHS><RHS>Marked_mark(U13(isNat(V2)))</RHS></DPRULE><DPRULE num="2"><LHS>Marked_active(U21(tt,V1))</LHS><RHS>Marked_mark(U22(isNat(V1)))</RHS></DPRULE><DPRULE num="3"><LHS>Marked_active(U31(tt,N))</LHS><RHS>Marked_mark(N)</RHS></DPRULE><DPRULE num="4"><LHS>Marked_active(and(tt,X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="5"><LHS>Marked_active(isNatKind(plus(V1,V2)))</LHS><RHS>Marked_mark(and(isNatKind(V1),isNatKind(V2)))</RHS></DPRULE><DPRULE num="6"><LHS>Marked_active(isNatKind(s(V1)))</LHS><RHS>Marked_mark(isNatKind(V1))</RHS></DPRULE><DPRULE num="7"><LHS>Marked_mark(U11(X1,X2,X3))</LHS><RHS>Marked_active(U11(mark(X1),X2,X3))</RHS></DPRULE><DPRULE num="8"><LHS>Marked_mark(U11(X1,X2,X3))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="9"><LHS>Marked_mark(U12(X1,X2))</LHS><RHS>Marked_active(U12(mark(X1),X2))</RHS></DPRULE><DPRULE num="10"><LHS>Marked_mark(U12(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="11"><LHS>Marked_mark(isNat(X))</LHS><RHS>Marked_active(isNat(X))</RHS></DPRULE><DPRULE num="12"><LHS>Marked_mark(U13(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="13"><LHS>Marked_mark(U21(X1,X2))</LHS><RHS>Marked_active(U21(mark(X1),X2))</RHS></DPRULE><DPRULE num="14"><LHS>Marked_mark(U21(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="15"><LHS>Marked_mark(U22(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="16"><LHS>Marked_mark(U31(X1,X2))</LHS><RHS>Marked_active(U31(mark(X1),X2))</RHS></DPRULE><DPRULE num="17"><LHS>Marked_mark(U31(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="18"><LHS>Marked_mark(and(X1,X2))</LHS><RHS>Marked_active(and(mark(X1),X2))</RHS></DPRULE><DPRULE num="19"><LHS>Marked_mark(and(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="20"><LHS>Marked_mark(isNatKind(X))</LHS><RHS>Marked_active(isNatKind(X))</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><DAG approx="simpl"><CCLIST><SCC num="0"><NODE ref="0"/><NODE ref="1"/><NODE ref="2"/><NODE ref="3"/><NODE ref="4"/><NODE ref="5"/><NODE ref="6"/><NODE ref="7"/><NODE ref="8"/><NODE ref="9"/><NODE ref="10"/><NODE ref="11"/><NODE ref="12"/><NODE ref="13"/><NODE ref="14"/><NODE ref="15"/><NODE ref="16"/><NODE ref="17"/><NODE ref="18"/><NODE ref="19"/><NODE ref="20"/></SCC></CCLIST></DAG></CRITERION><PROPERTY criterion="stronggraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(U11(tt,V1,V2))</LHS><RHS>mark(U12(isNat(V1),V2))</RHS></RULE><RULE><LHS>active(U12(tt,V2))</LHS><RHS>mark(U13(isNat(V2)))</RHS></RULE><RULE><LHS>active(U13(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U21(tt,V1))</LHS><RHS>mark(U22(isNat(V1)))</RHS></RULE><RULE><LHS>active(U22(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U31(tt,N))</LHS><RHS>mark(N)</RHS></RULE><RULE><LHS>active(U41(tt,M,N))</LHS><RHS>mark(s(plus(N,M)))</RHS></RULE><RULE><LHS>active(and(tt,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(isNat(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNat(plus(V1,V2)))</LHS><RHS>mark(U11(and(isNatKind(V1),isNatKind(V2)),V1,V2))</RHS></RULE><RULE><LHS>active(isNat(s(V1)))</LHS><RHS>mark(U21(isNatKind(V1),V1))</RHS></RULE><RULE><LHS>active(isNatKind(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNatKind(plus(V1,V2)))</LHS><RHS>mark(and(isNatKind(V1),isNatKind(V2)))</RHS></RULE><RULE><LHS>active(isNatKind(s(V1)))</LHS><RHS>mark(isNatKind(V1))</RHS></RULE><RULE><LHS>active(plus(N,0))</LHS><RHS>mark(U31(and(isNat(N),isNatKind(N)),N))</RHS></RULE><RULE><LHS>active(plus(N,s(M)))</LHS><RHS>mark(U41(and(and(isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),M,N))</RHS></RULE><RULE><LHS>mark(U11(X1,X2,X3))</LHS><RHS>active(U11(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(tt)</LHS><RHS>active(tt)</RHS></RULE><RULE><LHS>mark(U12(X1,X2))</LHS><RHS>active(U12(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(isNat(X))</LHS><RHS>active(isNat(X))</RHS></RULE><RULE><LHS>mark(U13(X))</LHS><RHS>active(U13(mark(X)))</RHS></RULE><RULE><LHS>mark(U21(X1,X2))</LHS><RHS>active(U21(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U22(X))</LHS><RHS>active(U22(mark(X)))</RHS></RULE><RULE><LHS>mark(U31(X1,X2))</LHS><RHS>active(U31(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U41(X1,X2,X3))</LHS><RHS>active(U41(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(mark(X)))</RHS></RULE><RULE><LHS>mark(plus(X1,X2))</LHS><RHS>active(plus(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(isNatKind(X))</LHS><RHS>active(isNatKind(X))</RHS></RULE><RULE><LHS>U11(mark(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,mark(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,mark(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(active(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,active(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,active(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U12(mark(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,mark(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(active(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,active(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>isNat(mark(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>isNat(active(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>U13(mark(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U13(active(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U21(mark(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,mark(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(active(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,active(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U22(mark(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U22(active(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U31(mark(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,mark(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(active(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,active(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U41(mark(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,mark(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,mark(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(active(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,active(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,active(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>s(mark(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>s(active(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>plus(mark(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,mark(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(active(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,active(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>and(mark(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,mark(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(active(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,active(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>isNatKind(mark(X))</LHS><RHS>isNatKind(X)</RHS></RULE><RULE><LHS>isNatKind(active(X))</LHS><RHS>isNatKind(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_active(U11(tt,V1,V2))</LHS><RHS>Marked_mark(U12(isNat(V1),V2))</RHS></DPRULE><DPRULE num="1"><LHS>Marked_active(U12(tt,V2))</LHS><RHS>Marked_mark(U13(isNat(V2)))</RHS></DPRULE><DPRULE num="2"><LHS>Marked_active(U21(tt,V1))</LHS><RHS>Marked_mark(U22(isNat(V1)))</RHS></DPRULE><DPRULE num="3"><LHS>Marked_active(U31(tt,N))</LHS><RHS>Marked_mark(N)</RHS></DPRULE><DPRULE num="4"><LHS>Marked_active(and(tt,X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="5"><LHS>Marked_active(isNatKind(plus(V1,V2)))</LHS><RHS>Marked_mark(and(isNatKind(V1),isNatKind(V2)))</RHS></DPRULE><DPRULE num="6"><LHS>Marked_active(isNatKind(s(V1)))</LHS><RHS>Marked_mark(isNatKind(V1))</RHS></DPRULE><DPRULE num="7"><LHS>Marked_mark(U11(X1,X2,X3))</LHS><RHS>Marked_active(U11(mark(X1),X2,X3))</RHS></DPRULE><DPRULE num="8"><LHS>Marked_mark(U11(X1,X2,X3))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="9"><LHS>Marked_mark(U12(X1,X2))</LHS><RHS>Marked_active(U12(mark(X1),X2))</RHS></DPRULE><DPRULE num="10"><LHS>Marked_mark(U12(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="11"><LHS>Marked_mark(isNat(X))</LHS><RHS>Marked_active(isNat(X))</RHS></DPRULE><DPRULE num="12"><LHS>Marked_mark(U13(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="13"><LHS>Marked_mark(U21(X1,X2))</LHS><RHS>Marked_active(U21(mark(X1),X2))</RHS></DPRULE><DPRULE num="14"><LHS>Marked_mark(U21(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="15"><LHS>Marked_mark(U22(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="16"><LHS>Marked_mark(U31(X1,X2))</LHS><RHS>Marked_active(U31(mark(X1),X2))</RHS></DPRULE><DPRULE num="17"><LHS>Marked_mark(U31(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="18"><LHS>Marked_mark(and(X1,X2))</LHS><RHS>Marked_active(and(mark(X1),X2))</RHS></DPRULE><DPRULE num="19"><LHS>Marked_mark(and(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="20"><LHS>Marked_mark(isNatKind(X))</LHS><RHS>Marked_active(isNatKind(X))</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><ORDERING type="poly"><POLYSYMB><SYMBOL><NAME>mark</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U21</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U11</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U41</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>Marked_mark</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>isNat</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>s</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U13</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>0</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U12</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U31</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>tt</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>and</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>Marked_active</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>active</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>plus</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U22</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>isNatKind</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB></ORDERING><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_mark(isNat(X))</LHS><RHS>Marked_active(isNat(X))</RHS></DPRULE></DPLIST></STRICTPAIRS></CRITERION><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(U11(tt,V1,V2))</LHS><RHS>mark(U12(isNat(V1),V2))</RHS></RULE><RULE><LHS>active(U12(tt,V2))</LHS><RHS>mark(U13(isNat(V2)))</RHS></RULE><RULE><LHS>active(U13(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U21(tt,V1))</LHS><RHS>mark(U22(isNat(V1)))</RHS></RULE><RULE><LHS>active(U22(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U31(tt,N))</LHS><RHS>mark(N)</RHS></RULE><RULE><LHS>active(U41(tt,M,N))</LHS><RHS>mark(s(plus(N,M)))</RHS></RULE><RULE><LHS>active(and(tt,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(isNat(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNat(plus(V1,V2)))</LHS><RHS>mark(U11(and(isNatKind(V1),isNatKind(V2)),V1,V2))</RHS></RULE><RULE><LHS>active(isNat(s(V1)))</LHS><RHS>mark(U21(isNatKind(V1),V1))</RHS></RULE><RULE><LHS>active(isNatKind(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNatKind(plus(V1,V2)))</LHS><RHS>mark(and(isNatKind(V1),isNatKind(V2)))</RHS></RULE><RULE><LHS>active(isNatKind(s(V1)))</LHS><RHS>mark(isNatKind(V1))</RHS></RULE><RULE><LHS>active(plus(N,0))</LHS><RHS>mark(U31(and(isNat(N),isNatKind(N)),N))</RHS></RULE><RULE><LHS>active(plus(N,s(M)))</LHS><RHS>mark(U41(and(and(isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),M,N))</RHS></RULE><RULE><LHS>mark(U11(X1,X2,X3))</LHS><RHS>active(U11(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(tt)</LHS><RHS>active(tt)</RHS></RULE><RULE><LHS>mark(U12(X1,X2))</LHS><RHS>active(U12(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(isNat(X))</LHS><RHS>active(isNat(X))</RHS></RULE><RULE><LHS>mark(U13(X))</LHS><RHS>active(U13(mark(X)))</RHS></RULE><RULE><LHS>mark(U21(X1,X2))</LHS><RHS>active(U21(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U22(X))</LHS><RHS>active(U22(mark(X)))</RHS></RULE><RULE><LHS>mark(U31(X1,X2))</LHS><RHS>active(U31(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U41(X1,X2,X3))</LHS><RHS>active(U41(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(mark(X)))</RHS></RULE><RULE><LHS>mark(plus(X1,X2))</LHS><RHS>active(plus(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(isNatKind(X))</LHS><RHS>active(isNatKind(X))</RHS></RULE><RULE><LHS>U11(mark(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,mark(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,mark(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(active(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,active(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,active(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U12(mark(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,mark(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(active(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,active(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>isNat(mark(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>isNat(active(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>U13(mark(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U13(active(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U21(mark(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,mark(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(active(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,active(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U22(mark(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U22(active(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U31(mark(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,mark(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(active(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,active(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U41(mark(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,mark(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,mark(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(active(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,active(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,active(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>s(mark(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>s(active(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>plus(mark(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,mark(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(active(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,active(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>and(mark(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,mark(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(active(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,active(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>isNatKind(mark(X))</LHS><RHS>isNatKind(X)</RHS></RULE><RULE><LHS>isNatKind(active(X))</LHS><RHS>isNatKind(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_active(U11(tt,V1,V2))</LHS><RHS>Marked_mark(U12(isNat(V1),V2))</RHS></DPRULE><DPRULE num="1"><LHS>Marked_active(U12(tt,V2))</LHS><RHS>Marked_mark(U13(isNat(V2)))</RHS></DPRULE><DPRULE num="2"><LHS>Marked_active(U21(tt,V1))</LHS><RHS>Marked_mark(U22(isNat(V1)))</RHS></DPRULE><DPRULE num="3"><LHS>Marked_active(U31(tt,N))</LHS><RHS>Marked_mark(N)</RHS></DPRULE><DPRULE num="4"><LHS>Marked_active(and(tt,X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="5"><LHS>Marked_active(isNatKind(plus(V1,V2)))</LHS><RHS>Marked_mark(and(isNatKind(V1),isNatKind(V2)))</RHS></DPRULE><DPRULE num="6"><LHS>Marked_active(isNatKind(s(V1)))</LHS><RHS>Marked_mark(isNatKind(V1))</RHS></DPRULE><DPRULE num="7"><LHS>Marked_mark(U11(X1,X2,X3))</LHS><RHS>Marked_active(U11(mark(X1),X2,X3))</RHS></DPRULE><DPRULE num="8"><LHS>Marked_mark(U11(X1,X2,X3))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="9"><LHS>Marked_mark(U12(X1,X2))</LHS><RHS>Marked_active(U12(mark(X1),X2))</RHS></DPRULE><DPRULE num="10"><LHS>Marked_mark(U12(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="11"><LHS>Marked_mark(U13(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="12"><LHS>Marked_mark(U21(X1,X2))</LHS><RHS>Marked_active(U21(mark(X1),X2))</RHS></DPRULE><DPRULE num="13"><LHS>Marked_mark(U21(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="14"><LHS>Marked_mark(U22(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="15"><LHS>Marked_mark(U31(X1,X2))</LHS><RHS>Marked_active(U31(mark(X1),X2))</RHS></DPRULE><DPRULE num="16"><LHS>Marked_mark(U31(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="17"><LHS>Marked_mark(and(X1,X2))</LHS><RHS>Marked_active(and(mark(X1),X2))</RHS></DPRULE><DPRULE num="18"><LHS>Marked_mark(and(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="19"><LHS>Marked_mark(isNatKind(X))</LHS><RHS>Marked_active(isNatKind(X))</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><DAG approx="simpl"><CCLIST><SCC num="0"><NODE ref="0"/><NODE ref="1"/><NODE ref="2"/><NODE ref="3"/><NODE ref="4"/><NODE ref="5"/><NODE ref="6"/><NODE ref="7"/><NODE ref="8"/><NODE ref="9"/><NODE ref="10"/><NODE ref="11"/><NODE ref="12"/><NODE ref="13"/><NODE ref="14"/><NODE ref="15"/><NODE ref="16"/><NODE ref="17"/><NODE ref="18"/><NODE ref="19"/></SCC></CCLIST></DAG></CRITERION><PROPERTY criterion="stronggraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(U11(tt,V1,V2))</LHS><RHS>mark(U12(isNat(V1),V2))</RHS></RULE><RULE><LHS>active(U12(tt,V2))</LHS><RHS>mark(U13(isNat(V2)))</RHS></RULE><RULE><LHS>active(U13(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U21(tt,V1))</LHS><RHS>mark(U22(isNat(V1)))</RHS></RULE><RULE><LHS>active(U22(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U31(tt,N))</LHS><RHS>mark(N)</RHS></RULE><RULE><LHS>active(U41(tt,M,N))</LHS><RHS>mark(s(plus(N,M)))</RHS></RULE><RULE><LHS>active(and(tt,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(isNat(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNat(plus(V1,V2)))</LHS><RHS>mark(U11(and(isNatKind(V1),isNatKind(V2)),V1,V2))</RHS></RULE><RULE><LHS>active(isNat(s(V1)))</LHS><RHS>mark(U21(isNatKind(V1),V1))</RHS></RULE><RULE><LHS>active(isNatKind(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNatKind(plus(V1,V2)))</LHS><RHS>mark(and(isNatKind(V1),isNatKind(V2)))</RHS></RULE><RULE><LHS>active(isNatKind(s(V1)))</LHS><RHS>mark(isNatKind(V1))</RHS></RULE><RULE><LHS>active(plus(N,0))</LHS><RHS>mark(U31(and(isNat(N),isNatKind(N)),N))</RHS></RULE><RULE><LHS>active(plus(N,s(M)))</LHS><RHS>mark(U41(and(and(isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),M,N))</RHS></RULE><RULE><LHS>mark(U11(X1,X2,X3))</LHS><RHS>active(U11(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(tt)</LHS><RHS>active(tt)</RHS></RULE><RULE><LHS>mark(U12(X1,X2))</LHS><RHS>active(U12(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(isNat(X))</LHS><RHS>active(isNat(X))</RHS></RULE><RULE><LHS>mark(U13(X))</LHS><RHS>active(U13(mark(X)))</RHS></RULE><RULE><LHS>mark(U21(X1,X2))</LHS><RHS>active(U21(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U22(X))</LHS><RHS>active(U22(mark(X)))</RHS></RULE><RULE><LHS>mark(U31(X1,X2))</LHS><RHS>active(U31(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U41(X1,X2,X3))</LHS><RHS>active(U41(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(mark(X)))</RHS></RULE><RULE><LHS>mark(plus(X1,X2))</LHS><RHS>active(plus(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(isNatKind(X))</LHS><RHS>active(isNatKind(X))</RHS></RULE><RULE><LHS>U11(mark(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,mark(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,mark(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(active(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,active(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,active(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U12(mark(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,mark(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(active(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,active(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>isNat(mark(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>isNat(active(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>U13(mark(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U13(active(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U21(mark(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,mark(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(active(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,active(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U22(mark(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U22(active(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U31(mark(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,mark(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(active(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,active(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U41(mark(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,mark(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,mark(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(active(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,active(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,active(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>s(mark(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>s(active(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>plus(mark(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,mark(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(active(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,active(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>and(mark(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,mark(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(active(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,active(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>isNatKind(mark(X))</LHS><RHS>isNatKind(X)</RHS></RULE><RULE><LHS>isNatKind(active(X))</LHS><RHS>isNatKind(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_active(U11(tt,V1,V2))</LHS><RHS>Marked_mark(U12(isNat(V1),V2))</RHS></DPRULE><DPRULE num="1"><LHS>Marked_active(U12(tt,V2))</LHS><RHS>Marked_mark(U13(isNat(V2)))</RHS></DPRULE><DPRULE num="2"><LHS>Marked_active(U21(tt,V1))</LHS><RHS>Marked_mark(U22(isNat(V1)))</RHS></DPRULE><DPRULE num="3"><LHS>Marked_active(U31(tt,N))</LHS><RHS>Marked_mark(N)</RHS></DPRULE><DPRULE num="4"><LHS>Marked_active(and(tt,X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="5"><LHS>Marked_active(isNatKind(plus(V1,V2)))</LHS><RHS>Marked_mark(and(isNatKind(V1),isNatKind(V2)))</RHS></DPRULE><DPRULE num="6"><LHS>Marked_active(isNatKind(s(V1)))</LHS><RHS>Marked_mark(isNatKind(V1))</RHS></DPRULE><DPRULE num="7"><LHS>Marked_mark(U11(X1,X2,X3))</LHS><RHS>Marked_active(U11(mark(X1),X2,X3))</RHS></DPRULE><DPRULE num="8"><LHS>Marked_mark(U11(X1,X2,X3))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="9"><LHS>Marked_mark(U12(X1,X2))</LHS><RHS>Marked_active(U12(mark(X1),X2))</RHS></DPRULE><DPRULE num="10"><LHS>Marked_mark(U12(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="11"><LHS>Marked_mark(U13(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="12"><LHS>Marked_mark(U21(X1,X2))</LHS><RHS>Marked_active(U21(mark(X1),X2))</RHS></DPRULE><DPRULE num="13"><LHS>Marked_mark(U21(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="14"><LHS>Marked_mark(U22(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="15"><LHS>Marked_mark(U31(X1,X2))</LHS><RHS>Marked_active(U31(mark(X1),X2))</RHS></DPRULE><DPRULE num="16"><LHS>Marked_mark(U31(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="17"><LHS>Marked_mark(and(X1,X2))</LHS><RHS>Marked_active(and(mark(X1),X2))</RHS></DPRULE><DPRULE num="18"><LHS>Marked_mark(and(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="19"><LHS>Marked_mark(isNatKind(X))</LHS><RHS>Marked_active(isNatKind(X))</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><ORDERING type="poly"><POLYSYMB><SYMBOL><NAME>mark</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U21</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U11</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>3</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="2"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U41</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>3</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>3</INT></COEF><ARG degree="1" num="2"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>Marked_mark</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>isNat</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>s</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U13</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>0</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U12</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U31</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>tt</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>and</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>Marked_active</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>active</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>plus</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>3</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U22</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>isNatKind</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB></ORDERING><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_mark(U21(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_mark(U22(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE></DPLIST></STRICTPAIRS></CRITERION><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(U11(tt,V1,V2))</LHS><RHS>mark(U12(isNat(V1),V2))</RHS></RULE><RULE><LHS>active(U12(tt,V2))</LHS><RHS>mark(U13(isNat(V2)))</RHS></RULE><RULE><LHS>active(U13(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U21(tt,V1))</LHS><RHS>mark(U22(isNat(V1)))</RHS></RULE><RULE><LHS>active(U22(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U31(tt,N))</LHS><RHS>mark(N)</RHS></RULE><RULE><LHS>active(U41(tt,M,N))</LHS><RHS>mark(s(plus(N,M)))</RHS></RULE><RULE><LHS>active(and(tt,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(isNat(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNat(plus(V1,V2)))</LHS><RHS>mark(U11(and(isNatKind(V1),isNatKind(V2)),V1,V2))</RHS></RULE><RULE><LHS>active(isNat(s(V1)))</LHS><RHS>mark(U21(isNatKind(V1),V1))</RHS></RULE><RULE><LHS>active(isNatKind(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNatKind(plus(V1,V2)))</LHS><RHS>mark(and(isNatKind(V1),isNatKind(V2)))</RHS></RULE><RULE><LHS>active(isNatKind(s(V1)))</LHS><RHS>mark(isNatKind(V1))</RHS></RULE><RULE><LHS>active(plus(N,0))</LHS><RHS>mark(U31(and(isNat(N),isNatKind(N)),N))</RHS></RULE><RULE><LHS>active(plus(N,s(M)))</LHS><RHS>mark(U41(and(and(isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),M,N))</RHS></RULE><RULE><LHS>mark(U11(X1,X2,X3))</LHS><RHS>active(U11(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(tt)</LHS><RHS>active(tt)</RHS></RULE><RULE><LHS>mark(U12(X1,X2))</LHS><RHS>active(U12(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(isNat(X))</LHS><RHS>active(isNat(X))</RHS></RULE><RULE><LHS>mark(U13(X))</LHS><RHS>active(U13(mark(X)))</RHS></RULE><RULE><LHS>mark(U21(X1,X2))</LHS><RHS>active(U21(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U22(X))</LHS><RHS>active(U22(mark(X)))</RHS></RULE><RULE><LHS>mark(U31(X1,X2))</LHS><RHS>active(U31(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U41(X1,X2,X3))</LHS><RHS>active(U41(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(mark(X)))</RHS></RULE><RULE><LHS>mark(plus(X1,X2))</LHS><RHS>active(plus(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(isNatKind(X))</LHS><RHS>active(isNatKind(X))</RHS></RULE><RULE><LHS>U11(mark(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,mark(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,mark(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(active(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,active(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,active(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U12(mark(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,mark(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(active(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,active(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>isNat(mark(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>isNat(active(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>U13(mark(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U13(active(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U21(mark(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,mark(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(active(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,active(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U22(mark(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U22(active(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U31(mark(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,mark(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(active(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,active(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U41(mark(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,mark(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,mark(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(active(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,active(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,active(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>s(mark(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>s(active(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>plus(mark(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,mark(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(active(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,active(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>and(mark(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,mark(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(active(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,active(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>isNatKind(mark(X))</LHS><RHS>isNatKind(X)</RHS></RULE><RULE><LHS>isNatKind(active(X))</LHS><RHS>isNatKind(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_active(U11(tt,V1,V2))</LHS><RHS>Marked_mark(U12(isNat(V1),V2))</RHS></DPRULE><DPRULE num="1"><LHS>Marked_active(U12(tt,V2))</LHS><RHS>Marked_mark(U13(isNat(V2)))</RHS></DPRULE><DPRULE num="2"><LHS>Marked_active(U21(tt,V1))</LHS><RHS>Marked_mark(U22(isNat(V1)))</RHS></DPRULE><DPRULE num="3"><LHS>Marked_active(U31(tt,N))</LHS><RHS>Marked_mark(N)</RHS></DPRULE><DPRULE num="4"><LHS>Marked_active(and(tt,X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="5"><LHS>Marked_active(isNatKind(plus(V1,V2)))</LHS><RHS>Marked_mark(and(isNatKind(V1),isNatKind(V2)))</RHS></DPRULE><DPRULE num="6"><LHS>Marked_active(isNatKind(s(V1)))</LHS><RHS>Marked_mark(isNatKind(V1))</RHS></DPRULE><DPRULE num="7"><LHS>Marked_mark(U11(X1,X2,X3))</LHS><RHS>Marked_active(U11(mark(X1),X2,X3))</RHS></DPRULE><DPRULE num="8"><LHS>Marked_mark(U11(X1,X2,X3))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="9"><LHS>Marked_mark(U12(X1,X2))</LHS><RHS>Marked_active(U12(mark(X1),X2))</RHS></DPRULE><DPRULE num="10"><LHS>Marked_mark(U12(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="11"><LHS>Marked_mark(U13(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="12"><LHS>Marked_mark(U21(X1,X2))</LHS><RHS>Marked_active(U21(mark(X1),X2))</RHS></DPRULE><DPRULE num="13"><LHS>Marked_mark(U31(X1,X2))</LHS><RHS>Marked_active(U31(mark(X1),X2))</RHS></DPRULE><DPRULE num="14"><LHS>Marked_mark(U31(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="15"><LHS>Marked_mark(and(X1,X2))</LHS><RHS>Marked_active(and(mark(X1),X2))</RHS></DPRULE><DPRULE num="16"><LHS>Marked_mark(and(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="17"><LHS>Marked_mark(isNatKind(X))</LHS><RHS>Marked_active(isNatKind(X))</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><DAG approx="simpl"><CCLIST><SCC num="0"><NODE ref="0"/><NODE ref="1"/><NODE ref="2"/><NODE ref="3"/><NODE ref="4"/><NODE ref="5"/><NODE ref="6"/><NODE ref="7"/><NODE ref="8"/><NODE ref="9"/><NODE ref="10"/><NODE ref="11"/><NODE ref="12"/><NODE ref="13"/><NODE ref="14"/><NODE ref="15"/><NODE ref="16"/><NODE ref="17"/></SCC></CCLIST></DAG></CRITERION><PROPERTY criterion="stronggraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(U11(tt,V1,V2))</LHS><RHS>mark(U12(isNat(V1),V2))</RHS></RULE><RULE><LHS>active(U12(tt,V2))</LHS><RHS>mark(U13(isNat(V2)))</RHS></RULE><RULE><LHS>active(U13(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U21(tt,V1))</LHS><RHS>mark(U22(isNat(V1)))</RHS></RULE><RULE><LHS>active(U22(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U31(tt,N))</LHS><RHS>mark(N)</RHS></RULE><RULE><LHS>active(U41(tt,M,N))</LHS><RHS>mark(s(plus(N,M)))</RHS></RULE><RULE><LHS>active(and(tt,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(isNat(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNat(plus(V1,V2)))</LHS><RHS>mark(U11(and(isNatKind(V1),isNatKind(V2)),V1,V2))</RHS></RULE><RULE><LHS>active(isNat(s(V1)))</LHS><RHS>mark(U21(isNatKind(V1),V1))</RHS></RULE><RULE><LHS>active(isNatKind(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNatKind(plus(V1,V2)))</LHS><RHS>mark(and(isNatKind(V1),isNatKind(V2)))</RHS></RULE><RULE><LHS>active(isNatKind(s(V1)))</LHS><RHS>mark(isNatKind(V1))</RHS></RULE><RULE><LHS>active(plus(N,0))</LHS><RHS>mark(U31(and(isNat(N),isNatKind(N)),N))</RHS></RULE><RULE><LHS>active(plus(N,s(M)))</LHS><RHS>mark(U41(and(and(isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),M,N))</RHS></RULE><RULE><LHS>mark(U11(X1,X2,X3))</LHS><RHS>active(U11(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(tt)</LHS><RHS>active(tt)</RHS></RULE><RULE><LHS>mark(U12(X1,X2))</LHS><RHS>active(U12(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(isNat(X))</LHS><RHS>active(isNat(X))</RHS></RULE><RULE><LHS>mark(U13(X))</LHS><RHS>active(U13(mark(X)))</RHS></RULE><RULE><LHS>mark(U21(X1,X2))</LHS><RHS>active(U21(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U22(X))</LHS><RHS>active(U22(mark(X)))</RHS></RULE><RULE><LHS>mark(U31(X1,X2))</LHS><RHS>active(U31(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U41(X1,X2,X3))</LHS><RHS>active(U41(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(mark(X)))</RHS></RULE><RULE><LHS>mark(plus(X1,X2))</LHS><RHS>active(plus(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(isNatKind(X))</LHS><RHS>active(isNatKind(X))</RHS></RULE><RULE><LHS>U11(mark(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,mark(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,mark(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(active(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,active(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,active(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U12(mark(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,mark(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(active(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,active(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>isNat(mark(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>isNat(active(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>U13(mark(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U13(active(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U21(mark(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,mark(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(active(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,active(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U22(mark(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U22(active(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U31(mark(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,mark(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(active(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,active(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U41(mark(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,mark(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,mark(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(active(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,active(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,active(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>s(mark(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>s(active(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>plus(mark(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,mark(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(active(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,active(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>and(mark(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,mark(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(active(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,active(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>isNatKind(mark(X))</LHS><RHS>isNatKind(X)</RHS></RULE><RULE><LHS>isNatKind(active(X))</LHS><RHS>isNatKind(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_active(U11(tt,V1,V2))</LHS><RHS>Marked_mark(U12(isNat(V1),V2))</RHS></DPRULE><DPRULE num="1"><LHS>Marked_active(U12(tt,V2))</LHS><RHS>Marked_mark(U13(isNat(V2)))</RHS></DPRULE><DPRULE num="2"><LHS>Marked_active(U21(tt,V1))</LHS><RHS>Marked_mark(U22(isNat(V1)))</RHS></DPRULE><DPRULE num="3"><LHS>Marked_active(U31(tt,N))</LHS><RHS>Marked_mark(N)</RHS></DPRULE><DPRULE num="4"><LHS>Marked_active(and(tt,X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="5"><LHS>Marked_active(isNatKind(plus(V1,V2)))</LHS><RHS>Marked_mark(and(isNatKind(V1),isNatKind(V2)))</RHS></DPRULE><DPRULE num="6"><LHS>Marked_active(isNatKind(s(V1)))</LHS><RHS>Marked_mark(isNatKind(V1))</RHS></DPRULE><DPRULE num="7"><LHS>Marked_mark(U11(X1,X2,X3))</LHS><RHS>Marked_active(U11(mark(X1),X2,X3))</RHS></DPRULE><DPRULE num="8"><LHS>Marked_mark(U11(X1,X2,X3))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="9"><LHS>Marked_mark(U12(X1,X2))</LHS><RHS>Marked_active(U12(mark(X1),X2))</RHS></DPRULE><DPRULE num="10"><LHS>Marked_mark(U12(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="11"><LHS>Marked_mark(U13(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="12"><LHS>Marked_mark(U21(X1,X2))</LHS><RHS>Marked_active(U21(mark(X1),X2))</RHS></DPRULE><DPRULE num="13"><LHS>Marked_mark(U31(X1,X2))</LHS><RHS>Marked_active(U31(mark(X1),X2))</RHS></DPRULE><DPRULE num="14"><LHS>Marked_mark(U31(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="15"><LHS>Marked_mark(and(X1,X2))</LHS><RHS>Marked_active(and(mark(X1),X2))</RHS></DPRULE><DPRULE num="16"><LHS>Marked_mark(and(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="17"><LHS>Marked_mark(isNatKind(X))</LHS><RHS>Marked_active(isNatKind(X))</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><ORDERING type="poly"><POLYSYMB><SYMBOL><NAME>mark</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U21</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U11</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="2"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U41</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>3</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>Marked_mark</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>isNat</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>s</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U13</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>0</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U12</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U31</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>tt</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>and</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>Marked_active</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>active</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>plus</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>3</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U22</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>isNatKind</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB></ORDERING><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_active(U21(tt,V1))</LHS><RHS>Marked_mark(U22(isNat(V1)))</RHS></DPRULE></DPLIST></STRICTPAIRS></CRITERION><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(U11(tt,V1,V2))</LHS><RHS>mark(U12(isNat(V1),V2))</RHS></RULE><RULE><LHS>active(U12(tt,V2))</LHS><RHS>mark(U13(isNat(V2)))</RHS></RULE><RULE><LHS>active(U13(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U21(tt,V1))</LHS><RHS>mark(U22(isNat(V1)))</RHS></RULE><RULE><LHS>active(U22(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U31(tt,N))</LHS><RHS>mark(N)</RHS></RULE><RULE><LHS>active(U41(tt,M,N))</LHS><RHS>mark(s(plus(N,M)))</RHS></RULE><RULE><LHS>active(and(tt,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(isNat(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNat(plus(V1,V2)))</LHS><RHS>mark(U11(and(isNatKind(V1),isNatKind(V2)),V1,V2))</RHS></RULE><RULE><LHS>active(isNat(s(V1)))</LHS><RHS>mark(U21(isNatKind(V1),V1))</RHS></RULE><RULE><LHS>active(isNatKind(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNatKind(plus(V1,V2)))</LHS><RHS>mark(and(isNatKind(V1),isNatKind(V2)))</RHS></RULE><RULE><LHS>active(isNatKind(s(V1)))</LHS><RHS>mark(isNatKind(V1))</RHS></RULE><RULE><LHS>active(plus(N,0))</LHS><RHS>mark(U31(and(isNat(N),isNatKind(N)),N))</RHS></RULE><RULE><LHS>active(plus(N,s(M)))</LHS><RHS>mark(U41(and(and(isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),M,N))</RHS></RULE><RULE><LHS>mark(U11(X1,X2,X3))</LHS><RHS>active(U11(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(tt)</LHS><RHS>active(tt)</RHS></RULE><RULE><LHS>mark(U12(X1,X2))</LHS><RHS>active(U12(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(isNat(X))</LHS><RHS>active(isNat(X))</RHS></RULE><RULE><LHS>mark(U13(X))</LHS><RHS>active(U13(mark(X)))</RHS></RULE><RULE><LHS>mark(U21(X1,X2))</LHS><RHS>active(U21(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U22(X))</LHS><RHS>active(U22(mark(X)))</RHS></RULE><RULE><LHS>mark(U31(X1,X2))</LHS><RHS>active(U31(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U41(X1,X2,X3))</LHS><RHS>active(U41(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(mark(X)))</RHS></RULE><RULE><LHS>mark(plus(X1,X2))</LHS><RHS>active(plus(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(isNatKind(X))</LHS><RHS>active(isNatKind(X))</RHS></RULE><RULE><LHS>U11(mark(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,mark(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,mark(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(active(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,active(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,active(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U12(mark(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,mark(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(active(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,active(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>isNat(mark(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>isNat(active(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>U13(mark(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U13(active(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U21(mark(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,mark(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(active(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,active(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U22(mark(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U22(active(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U31(mark(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,mark(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(active(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,active(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U41(mark(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,mark(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,mark(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(active(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,active(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,active(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>s(mark(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>s(active(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>plus(mark(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,mark(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(active(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,active(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>and(mark(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,mark(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(active(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,active(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>isNatKind(mark(X))</LHS><RHS>isNatKind(X)</RHS></RULE><RULE><LHS>isNatKind(active(X))</LHS><RHS>isNatKind(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_active(U11(tt,V1,V2))</LHS><RHS>Marked_mark(U12(isNat(V1),V2))</RHS></DPRULE><DPRULE num="1"><LHS>Marked_active(U12(tt,V2))</LHS><RHS>Marked_mark(U13(isNat(V2)))</RHS></DPRULE><DPRULE num="2"><LHS>Marked_active(U31(tt,N))</LHS><RHS>Marked_mark(N)</RHS></DPRULE><DPRULE num="3"><LHS>Marked_active(and(tt,X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="4"><LHS>Marked_active(isNatKind(plus(V1,V2)))</LHS><RHS>Marked_mark(and(isNatKind(V1),isNatKind(V2)))</RHS></DPRULE><DPRULE num="5"><LHS>Marked_active(isNatKind(s(V1)))</LHS><RHS>Marked_mark(isNatKind(V1))</RHS></DPRULE><DPRULE num="6"><LHS>Marked_mark(U11(X1,X2,X3))</LHS><RHS>Marked_active(U11(mark(X1),X2,X3))</RHS></DPRULE><DPRULE num="7"><LHS>Marked_mark(U11(X1,X2,X3))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="8"><LHS>Marked_mark(U12(X1,X2))</LHS><RHS>Marked_active(U12(mark(X1),X2))</RHS></DPRULE><DPRULE num="9"><LHS>Marked_mark(U12(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="10"><LHS>Marked_mark(U13(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="11"><LHS>Marked_mark(U21(X1,X2))</LHS><RHS>Marked_active(U21(mark(X1),X2))</RHS></DPRULE><DPRULE num="12"><LHS>Marked_mark(U31(X1,X2))</LHS><RHS>Marked_active(U31(mark(X1),X2))</RHS></DPRULE><DPRULE num="13"><LHS>Marked_mark(U31(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="14"><LHS>Marked_mark(and(X1,X2))</LHS><RHS>Marked_active(and(mark(X1),X2))</RHS></DPRULE><DPRULE num="15"><LHS>Marked_mark(and(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="16"><LHS>Marked_mark(isNatKind(X))</LHS><RHS>Marked_active(isNatKind(X))</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><DAG approx="simpl"><CCLIST><SCC num="0"><NODE ref="0"/><NODE ref="1"/><NODE ref="2"/><NODE ref="3"/><NODE ref="4"/><NODE ref="5"/><NODE ref="6"/><NODE ref="7"/><NODE ref="8"/><NODE ref="9"/><NODE ref="10"/><NODE ref="11"/><NODE ref="12"/><NODE ref="13"/><NODE ref="14"/><NODE ref="15"/><NODE ref="16"/></SCC></CCLIST></DAG></CRITERION><PROPERTY criterion="stronggraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(U11(tt,V1,V2))</LHS><RHS>mark(U12(isNat(V1),V2))</RHS></RULE><RULE><LHS>active(U12(tt,V2))</LHS><RHS>mark(U13(isNat(V2)))</RHS></RULE><RULE><LHS>active(U13(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U21(tt,V1))</LHS><RHS>mark(U22(isNat(V1)))</RHS></RULE><RULE><LHS>active(U22(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U31(tt,N))</LHS><RHS>mark(N)</RHS></RULE><RULE><LHS>active(U41(tt,M,N))</LHS><RHS>mark(s(plus(N,M)))</RHS></RULE><RULE><LHS>active(and(tt,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(isNat(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNat(plus(V1,V2)))</LHS><RHS>mark(U11(and(isNatKind(V1),isNatKind(V2)),V1,V2))</RHS></RULE><RULE><LHS>active(isNat(s(V1)))</LHS><RHS>mark(U21(isNatKind(V1),V1))</RHS></RULE><RULE><LHS>active(isNatKind(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNatKind(plus(V1,V2)))</LHS><RHS>mark(and(isNatKind(V1),isNatKind(V2)))</RHS></RULE><RULE><LHS>active(isNatKind(s(V1)))</LHS><RHS>mark(isNatKind(V1))</RHS></RULE><RULE><LHS>active(plus(N,0))</LHS><RHS>mark(U31(and(isNat(N),isNatKind(N)),N))</RHS></RULE><RULE><LHS>active(plus(N,s(M)))</LHS><RHS>mark(U41(and(and(isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),M,N))</RHS></RULE><RULE><LHS>mark(U11(X1,X2,X3))</LHS><RHS>active(U11(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(tt)</LHS><RHS>active(tt)</RHS></RULE><RULE><LHS>mark(U12(X1,X2))</LHS><RHS>active(U12(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(isNat(X))</LHS><RHS>active(isNat(X))</RHS></RULE><RULE><LHS>mark(U13(X))</LHS><RHS>active(U13(mark(X)))</RHS></RULE><RULE><LHS>mark(U21(X1,X2))</LHS><RHS>active(U21(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U22(X))</LHS><RHS>active(U22(mark(X)))</RHS></RULE><RULE><LHS>mark(U31(X1,X2))</LHS><RHS>active(U31(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U41(X1,X2,X3))</LHS><RHS>active(U41(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(mark(X)))</RHS></RULE><RULE><LHS>mark(plus(X1,X2))</LHS><RHS>active(plus(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(isNatKind(X))</LHS><RHS>active(isNatKind(X))</RHS></RULE><RULE><LHS>U11(mark(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,mark(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,mark(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(active(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,active(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,active(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U12(mark(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,mark(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(active(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,active(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>isNat(mark(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>isNat(active(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>U13(mark(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U13(active(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U21(mark(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,mark(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(active(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,active(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U22(mark(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U22(active(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U31(mark(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,mark(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(active(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,active(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U41(mark(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,mark(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,mark(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(active(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,active(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,active(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>s(mark(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>s(active(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>plus(mark(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,mark(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(active(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,active(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>and(mark(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,mark(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(active(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,active(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>isNatKind(mark(X))</LHS><RHS>isNatKind(X)</RHS></RULE><RULE><LHS>isNatKind(active(X))</LHS><RHS>isNatKind(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_active(U11(tt,V1,V2))</LHS><RHS>Marked_mark(U12(isNat(V1),V2))</RHS></DPRULE><DPRULE num="1"><LHS>Marked_active(U12(tt,V2))</LHS><RHS>Marked_mark(U13(isNat(V2)))</RHS></DPRULE><DPRULE num="2"><LHS>Marked_active(U31(tt,N))</LHS><RHS>Marked_mark(N)</RHS></DPRULE><DPRULE num="3"><LHS>Marked_active(and(tt,X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="4"><LHS>Marked_active(isNatKind(plus(V1,V2)))</LHS><RHS>Marked_mark(and(isNatKind(V1),isNatKind(V2)))</RHS></DPRULE><DPRULE num="5"><LHS>Marked_active(isNatKind(s(V1)))</LHS><RHS>Marked_mark(isNatKind(V1))</RHS></DPRULE><DPRULE num="6"><LHS>Marked_mark(U11(X1,X2,X3))</LHS><RHS>Marked_active(U11(mark(X1),X2,X3))</RHS></DPRULE><DPRULE num="7"><LHS>Marked_mark(U11(X1,X2,X3))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="8"><LHS>Marked_mark(U12(X1,X2))</LHS><RHS>Marked_active(U12(mark(X1),X2))</RHS></DPRULE><DPRULE num="9"><LHS>Marked_mark(U12(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="10"><LHS>Marked_mark(U13(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="11"><LHS>Marked_mark(U21(X1,X2))</LHS><RHS>Marked_active(U21(mark(X1),X2))</RHS></DPRULE><DPRULE num="12"><LHS>Marked_mark(U31(X1,X2))</LHS><RHS>Marked_active(U31(mark(X1),X2))</RHS></DPRULE><DPRULE num="13"><LHS>Marked_mark(U31(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="14"><LHS>Marked_mark(and(X1,X2))</LHS><RHS>Marked_active(and(mark(X1),X2))</RHS></DPRULE><DPRULE num="15"><LHS>Marked_mark(and(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="16"><LHS>Marked_mark(isNatKind(X))</LHS><RHS>Marked_active(isNatKind(X))</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><ORDERING type="poly"><POLYSYMB><SYMBOL><NAME>mark</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U21</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U11</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U41</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>Marked_mark</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>isNat</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>s</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U13</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>0</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U12</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U31</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>tt</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>and</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>Marked_active</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>active</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>plus</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U22</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>isNatKind</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB></ORDERING><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_mark(U21(X1,X2))</LHS><RHS>Marked_active(U21(mark(X1),X2))</RHS></DPRULE></DPLIST></STRICTPAIRS></CRITERION><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(U11(tt,V1,V2))</LHS><RHS>mark(U12(isNat(V1),V2))</RHS></RULE><RULE><LHS>active(U12(tt,V2))</LHS><RHS>mark(U13(isNat(V2)))</RHS></RULE><RULE><LHS>active(U13(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U21(tt,V1))</LHS><RHS>mark(U22(isNat(V1)))</RHS></RULE><RULE><LHS>active(U22(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U31(tt,N))</LHS><RHS>mark(N)</RHS></RULE><RULE><LHS>active(U41(tt,M,N))</LHS><RHS>mark(s(plus(N,M)))</RHS></RULE><RULE><LHS>active(and(tt,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(isNat(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNat(plus(V1,V2)))</LHS><RHS>mark(U11(and(isNatKind(V1),isNatKind(V2)),V1,V2))</RHS></RULE><RULE><LHS>active(isNat(s(V1)))</LHS><RHS>mark(U21(isNatKind(V1),V1))</RHS></RULE><RULE><LHS>active(isNatKind(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNatKind(plus(V1,V2)))</LHS><RHS>mark(and(isNatKind(V1),isNatKind(V2)))</RHS></RULE><RULE><LHS>active(isNatKind(s(V1)))</LHS><RHS>mark(isNatKind(V1))</RHS></RULE><RULE><LHS>active(plus(N,0))</LHS><RHS>mark(U31(and(isNat(N),isNatKind(N)),N))</RHS></RULE><RULE><LHS>active(plus(N,s(M)))</LHS><RHS>mark(U41(and(and(isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),M,N))</RHS></RULE><RULE><LHS>mark(U11(X1,X2,X3))</LHS><RHS>active(U11(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(tt)</LHS><RHS>active(tt)</RHS></RULE><RULE><LHS>mark(U12(X1,X2))</LHS><RHS>active(U12(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(isNat(X))</LHS><RHS>active(isNat(X))</RHS></RULE><RULE><LHS>mark(U13(X))</LHS><RHS>active(U13(mark(X)))</RHS></RULE><RULE><LHS>mark(U21(X1,X2))</LHS><RHS>active(U21(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U22(X))</LHS><RHS>active(U22(mark(X)))</RHS></RULE><RULE><LHS>mark(U31(X1,X2))</LHS><RHS>active(U31(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U41(X1,X2,X3))</LHS><RHS>active(U41(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(mark(X)))</RHS></RULE><RULE><LHS>mark(plus(X1,X2))</LHS><RHS>active(plus(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(isNatKind(X))</LHS><RHS>active(isNatKind(X))</RHS></RULE><RULE><LHS>U11(mark(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,mark(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,mark(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(active(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,active(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,active(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U12(mark(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,mark(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(active(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,active(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>isNat(mark(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>isNat(active(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>U13(mark(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U13(active(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U21(mark(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,mark(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(active(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,active(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U22(mark(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U22(active(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U31(mark(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,mark(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(active(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,active(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U41(mark(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,mark(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,mark(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(active(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,active(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,active(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>s(mark(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>s(active(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>plus(mark(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,mark(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(active(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,active(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>and(mark(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,mark(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(active(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,active(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>isNatKind(mark(X))</LHS><RHS>isNatKind(X)</RHS></RULE><RULE><LHS>isNatKind(active(X))</LHS><RHS>isNatKind(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_active(U11(tt,V1,V2))</LHS><RHS>Marked_mark(U12(isNat(V1),V2))</RHS></DPRULE><DPRULE num="1"><LHS>Marked_active(U12(tt,V2))</LHS><RHS>Marked_mark(U13(isNat(V2)))</RHS></DPRULE><DPRULE num="2"><LHS>Marked_active(U31(tt,N))</LHS><RHS>Marked_mark(N)</RHS></DPRULE><DPRULE num="3"><LHS>Marked_active(and(tt,X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="4"><LHS>Marked_active(isNatKind(plus(V1,V2)))</LHS><RHS>Marked_mark(and(isNatKind(V1),isNatKind(V2)))</RHS></DPRULE><DPRULE num="5"><LHS>Marked_active(isNatKind(s(V1)))</LHS><RHS>Marked_mark(isNatKind(V1))</RHS></DPRULE><DPRULE num="6"><LHS>Marked_mark(U11(X1,X2,X3))</LHS><RHS>Marked_active(U11(mark(X1),X2,X3))</RHS></DPRULE><DPRULE num="7"><LHS>Marked_mark(U11(X1,X2,X3))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="8"><LHS>Marked_mark(U12(X1,X2))</LHS><RHS>Marked_active(U12(mark(X1),X2))</RHS></DPRULE><DPRULE num="9"><LHS>Marked_mark(U12(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="10"><LHS>Marked_mark(U13(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="11"><LHS>Marked_mark(U31(X1,X2))</LHS><RHS>Marked_active(U31(mark(X1),X2))</RHS></DPRULE><DPRULE num="12"><LHS>Marked_mark(U31(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="13"><LHS>Marked_mark(and(X1,X2))</LHS><RHS>Marked_active(and(mark(X1),X2))</RHS></DPRULE><DPRULE num="14"><LHS>Marked_mark(and(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="15"><LHS>Marked_mark(isNatKind(X))</LHS><RHS>Marked_active(isNatKind(X))</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><DAG approx="simpl"><CCLIST><SCC num="0"><NODE ref="0"/><NODE ref="1"/><NODE ref="2"/><NODE ref="3"/><NODE ref="4"/><NODE ref="5"/><NODE ref="6"/><NODE ref="7"/><NODE ref="8"/><NODE ref="9"/><NODE ref="10"/><NODE ref="11"/><NODE ref="12"/><NODE ref="13"/><NODE ref="14"/><NODE ref="15"/></SCC></CCLIST></DAG></CRITERION><PROPERTY criterion="stronggraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(U11(tt,V1,V2))</LHS><RHS>mark(U12(isNat(V1),V2))</RHS></RULE><RULE><LHS>active(U12(tt,V2))</LHS><RHS>mark(U13(isNat(V2)))</RHS></RULE><RULE><LHS>active(U13(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U21(tt,V1))</LHS><RHS>mark(U22(isNat(V1)))</RHS></RULE><RULE><LHS>active(U22(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U31(tt,N))</LHS><RHS>mark(N)</RHS></RULE><RULE><LHS>active(U41(tt,M,N))</LHS><RHS>mark(s(plus(N,M)))</RHS></RULE><RULE><LHS>active(and(tt,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(isNat(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNat(plus(V1,V2)))</LHS><RHS>mark(U11(and(isNatKind(V1),isNatKind(V2)),V1,V2))</RHS></RULE><RULE><LHS>active(isNat(s(V1)))</LHS><RHS>mark(U21(isNatKind(V1),V1))</RHS></RULE><RULE><LHS>active(isNatKind(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNatKind(plus(V1,V2)))</LHS><RHS>mark(and(isNatKind(V1),isNatKind(V2)))</RHS></RULE><RULE><LHS>active(isNatKind(s(V1)))</LHS><RHS>mark(isNatKind(V1))</RHS></RULE><RULE><LHS>active(plus(N,0))</LHS><RHS>mark(U31(and(isNat(N),isNatKind(N)),N))</RHS></RULE><RULE><LHS>active(plus(N,s(M)))</LHS><RHS>mark(U41(and(and(isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),M,N))</RHS></RULE><RULE><LHS>mark(U11(X1,X2,X3))</LHS><RHS>active(U11(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(tt)</LHS><RHS>active(tt)</RHS></RULE><RULE><LHS>mark(U12(X1,X2))</LHS><RHS>active(U12(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(isNat(X))</LHS><RHS>active(isNat(X))</RHS></RULE><RULE><LHS>mark(U13(X))</LHS><RHS>active(U13(mark(X)))</RHS></RULE><RULE><LHS>mark(U21(X1,X2))</LHS><RHS>active(U21(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U22(X))</LHS><RHS>active(U22(mark(X)))</RHS></RULE><RULE><LHS>mark(U31(X1,X2))</LHS><RHS>active(U31(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U41(X1,X2,X3))</LHS><RHS>active(U41(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(mark(X)))</RHS></RULE><RULE><LHS>mark(plus(X1,X2))</LHS><RHS>active(plus(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(isNatKind(X))</LHS><RHS>active(isNatKind(X))</RHS></RULE><RULE><LHS>U11(mark(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,mark(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,mark(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(active(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,active(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,active(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U12(mark(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,mark(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(active(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,active(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>isNat(mark(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>isNat(active(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>U13(mark(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U13(active(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U21(mark(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,mark(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(active(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,active(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U22(mark(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U22(active(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U31(mark(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,mark(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(active(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,active(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U41(mark(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,mark(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,mark(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(active(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,active(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,active(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>s(mark(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>s(active(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>plus(mark(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,mark(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(active(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,active(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>and(mark(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,mark(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(active(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,active(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>isNatKind(mark(X))</LHS><RHS>isNatKind(X)</RHS></RULE><RULE><LHS>isNatKind(active(X))</LHS><RHS>isNatKind(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_active(U11(tt,V1,V2))</LHS><RHS>Marked_mark(U12(isNat(V1),V2))</RHS></DPRULE><DPRULE num="1"><LHS>Marked_active(U12(tt,V2))</LHS><RHS>Marked_mark(U13(isNat(V2)))</RHS></DPRULE><DPRULE num="2"><LHS>Marked_active(U31(tt,N))</LHS><RHS>Marked_mark(N)</RHS></DPRULE><DPRULE num="3"><LHS>Marked_active(and(tt,X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="4"><LHS>Marked_active(isNatKind(plus(V1,V2)))</LHS><RHS>Marked_mark(and(isNatKind(V1),isNatKind(V2)))</RHS></DPRULE><DPRULE num="5"><LHS>Marked_active(isNatKind(s(V1)))</LHS><RHS>Marked_mark(isNatKind(V1))</RHS></DPRULE><DPRULE num="6"><LHS>Marked_mark(U11(X1,X2,X3))</LHS><RHS>Marked_active(U11(mark(X1),X2,X3))</RHS></DPRULE><DPRULE num="7"><LHS>Marked_mark(U11(X1,X2,X3))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="8"><LHS>Marked_mark(U12(X1,X2))</LHS><RHS>Marked_active(U12(mark(X1),X2))</RHS></DPRULE><DPRULE num="9"><LHS>Marked_mark(U12(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="10"><LHS>Marked_mark(U13(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="11"><LHS>Marked_mark(U31(X1,X2))</LHS><RHS>Marked_active(U31(mark(X1),X2))</RHS></DPRULE><DPRULE num="12"><LHS>Marked_mark(U31(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="13"><LHS>Marked_mark(and(X1,X2))</LHS><RHS>Marked_active(and(mark(X1),X2))</RHS></DPRULE><DPRULE num="14"><LHS>Marked_mark(and(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="15"><LHS>Marked_mark(isNatKind(X))</LHS><RHS>Marked_active(isNatKind(X))</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><ORDERING type="poly"><POLYSYMB><SYMBOL><NAME>mark</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U21</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U11</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U41</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="2"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>Marked_mark</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>isNat</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>s</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U13</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>0</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U12</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U31</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>tt</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>and</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>Marked_active</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>active</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>plus</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U22</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>isNatKind</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB></ORDERING><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_active(U31(tt,N))</LHS><RHS>Marked_mark(N)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_mark(U31(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE></DPLIST></STRICTPAIRS></CRITERION><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(U11(tt,V1,V2))</LHS><RHS>mark(U12(isNat(V1),V2))</RHS></RULE><RULE><LHS>active(U12(tt,V2))</LHS><RHS>mark(U13(isNat(V2)))</RHS></RULE><RULE><LHS>active(U13(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U21(tt,V1))</LHS><RHS>mark(U22(isNat(V1)))</RHS></RULE><RULE><LHS>active(U22(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U31(tt,N))</LHS><RHS>mark(N)</RHS></RULE><RULE><LHS>active(U41(tt,M,N))</LHS><RHS>mark(s(plus(N,M)))</RHS></RULE><RULE><LHS>active(and(tt,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(isNat(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNat(plus(V1,V2)))</LHS><RHS>mark(U11(and(isNatKind(V1),isNatKind(V2)),V1,V2))</RHS></RULE><RULE><LHS>active(isNat(s(V1)))</LHS><RHS>mark(U21(isNatKind(V1),V1))</RHS></RULE><RULE><LHS>active(isNatKind(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNatKind(plus(V1,V2)))</LHS><RHS>mark(and(isNatKind(V1),isNatKind(V2)))</RHS></RULE><RULE><LHS>active(isNatKind(s(V1)))</LHS><RHS>mark(isNatKind(V1))</RHS></RULE><RULE><LHS>active(plus(N,0))</LHS><RHS>mark(U31(and(isNat(N),isNatKind(N)),N))</RHS></RULE><RULE><LHS>active(plus(N,s(M)))</LHS><RHS>mark(U41(and(and(isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),M,N))</RHS></RULE><RULE><LHS>mark(U11(X1,X2,X3))</LHS><RHS>active(U11(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(tt)</LHS><RHS>active(tt)</RHS></RULE><RULE><LHS>mark(U12(X1,X2))</LHS><RHS>active(U12(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(isNat(X))</LHS><RHS>active(isNat(X))</RHS></RULE><RULE><LHS>mark(U13(X))</LHS><RHS>active(U13(mark(X)))</RHS></RULE><RULE><LHS>mark(U21(X1,X2))</LHS><RHS>active(U21(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U22(X))</LHS><RHS>active(U22(mark(X)))</RHS></RULE><RULE><LHS>mark(U31(X1,X2))</LHS><RHS>active(U31(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U41(X1,X2,X3))</LHS><RHS>active(U41(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(mark(X)))</RHS></RULE><RULE><LHS>mark(plus(X1,X2))</LHS><RHS>active(plus(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(isNatKind(X))</LHS><RHS>active(isNatKind(X))</RHS></RULE><RULE><LHS>U11(mark(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,mark(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,mark(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(active(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,active(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,active(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U12(mark(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,mark(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(active(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,active(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>isNat(mark(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>isNat(active(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>U13(mark(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U13(active(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U21(mark(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,mark(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(active(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,active(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U22(mark(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U22(active(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U31(mark(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,mark(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(active(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,active(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U41(mark(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,mark(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,mark(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(active(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,active(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,active(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>s(mark(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>s(active(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>plus(mark(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,mark(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(active(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,active(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>and(mark(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,mark(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(active(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,active(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>isNatKind(mark(X))</LHS><RHS>isNatKind(X)</RHS></RULE><RULE><LHS>isNatKind(active(X))</LHS><RHS>isNatKind(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_active(U11(tt,V1,V2))</LHS><RHS>Marked_mark(U12(isNat(V1),V2))</RHS></DPRULE><DPRULE num="1"><LHS>Marked_active(U12(tt,V2))</LHS><RHS>Marked_mark(U13(isNat(V2)))</RHS></DPRULE><DPRULE num="2"><LHS>Marked_active(and(tt,X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="3"><LHS>Marked_active(isNatKind(plus(V1,V2)))</LHS><RHS>Marked_mark(and(isNatKind(V1),isNatKind(V2)))</RHS></DPRULE><DPRULE num="4"><LHS>Marked_active(isNatKind(s(V1)))</LHS><RHS>Marked_mark(isNatKind(V1))</RHS></DPRULE><DPRULE num="5"><LHS>Marked_mark(U11(X1,X2,X3))</LHS><RHS>Marked_active(U11(mark(X1),X2,X3))</RHS></DPRULE><DPRULE num="6"><LHS>Marked_mark(U11(X1,X2,X3))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="7"><LHS>Marked_mark(U12(X1,X2))</LHS><RHS>Marked_active(U12(mark(X1),X2))</RHS></DPRULE><DPRULE num="8"><LHS>Marked_mark(U12(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="9"><LHS>Marked_mark(U13(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="10"><LHS>Marked_mark(U31(X1,X2))</LHS><RHS>Marked_active(U31(mark(X1),X2))</RHS></DPRULE><DPRULE num="11"><LHS>Marked_mark(and(X1,X2))</LHS><RHS>Marked_active(and(mark(X1),X2))</RHS></DPRULE><DPRULE num="12"><LHS>Marked_mark(and(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="13"><LHS>Marked_mark(isNatKind(X))</LHS><RHS>Marked_active(isNatKind(X))</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><DAG approx="simpl"><CCLIST><SCC num="0"><NODE ref="0"/><NODE ref="1"/><NODE ref="2"/><NODE ref="3"/><NODE ref="4"/><NODE ref="5"/><NODE ref="6"/><NODE ref="7"/><NODE ref="8"/><NODE ref="9"/><NODE ref="10"/><NODE ref="11"/><NODE ref="12"/><NODE ref="13"/></SCC></CCLIST></DAG></CRITERION><PROPERTY criterion="stronggraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(U11(tt,V1,V2))</LHS><RHS>mark(U12(isNat(V1),V2))</RHS></RULE><RULE><LHS>active(U12(tt,V2))</LHS><RHS>mark(U13(isNat(V2)))</RHS></RULE><RULE><LHS>active(U13(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U21(tt,V1))</LHS><RHS>mark(U22(isNat(V1)))</RHS></RULE><RULE><LHS>active(U22(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U31(tt,N))</LHS><RHS>mark(N)</RHS></RULE><RULE><LHS>active(U41(tt,M,N))</LHS><RHS>mark(s(plus(N,M)))</RHS></RULE><RULE><LHS>active(and(tt,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(isNat(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNat(plus(V1,V2)))</LHS><RHS>mark(U11(and(isNatKind(V1),isNatKind(V2)),V1,V2))</RHS></RULE><RULE><LHS>active(isNat(s(V1)))</LHS><RHS>mark(U21(isNatKind(V1),V1))</RHS></RULE><RULE><LHS>active(isNatKind(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNatKind(plus(V1,V2)))</LHS><RHS>mark(and(isNatKind(V1),isNatKind(V2)))</RHS></RULE><RULE><LHS>active(isNatKind(s(V1)))</LHS><RHS>mark(isNatKind(V1))</RHS></RULE><RULE><LHS>active(plus(N,0))</LHS><RHS>mark(U31(and(isNat(N),isNatKind(N)),N))</RHS></RULE><RULE><LHS>active(plus(N,s(M)))</LHS><RHS>mark(U41(and(and(isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),M,N))</RHS></RULE><RULE><LHS>mark(U11(X1,X2,X3))</LHS><RHS>active(U11(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(tt)</LHS><RHS>active(tt)</RHS></RULE><RULE><LHS>mark(U12(X1,X2))</LHS><RHS>active(U12(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(isNat(X))</LHS><RHS>active(isNat(X))</RHS></RULE><RULE><LHS>mark(U13(X))</LHS><RHS>active(U13(mark(X)))</RHS></RULE><RULE><LHS>mark(U21(X1,X2))</LHS><RHS>active(U21(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U22(X))</LHS><RHS>active(U22(mark(X)))</RHS></RULE><RULE><LHS>mark(U31(X1,X2))</LHS><RHS>active(U31(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U41(X1,X2,X3))</LHS><RHS>active(U41(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(mark(X)))</RHS></RULE><RULE><LHS>mark(plus(X1,X2))</LHS><RHS>active(plus(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(isNatKind(X))</LHS><RHS>active(isNatKind(X))</RHS></RULE><RULE><LHS>U11(mark(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,mark(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,mark(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(active(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,active(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,active(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U12(mark(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,mark(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(active(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,active(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>isNat(mark(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>isNat(active(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>U13(mark(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U13(active(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U21(mark(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,mark(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(active(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,active(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U22(mark(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U22(active(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U31(mark(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,mark(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(active(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,active(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U41(mark(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,mark(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,mark(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(active(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,active(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,active(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>s(mark(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>s(active(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>plus(mark(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,mark(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(active(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,active(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>and(mark(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,mark(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(active(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,active(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>isNatKind(mark(X))</LHS><RHS>isNatKind(X)</RHS></RULE><RULE><LHS>isNatKind(active(X))</LHS><RHS>isNatKind(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_active(U11(tt,V1,V2))</LHS><RHS>Marked_mark(U12(isNat(V1),V2))</RHS></DPRULE><DPRULE num="1"><LHS>Marked_active(U12(tt,V2))</LHS><RHS>Marked_mark(U13(isNat(V2)))</RHS></DPRULE><DPRULE num="2"><LHS>Marked_active(and(tt,X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="3"><LHS>Marked_active(isNatKind(plus(V1,V2)))</LHS><RHS>Marked_mark(and(isNatKind(V1),isNatKind(V2)))</RHS></DPRULE><DPRULE num="4"><LHS>Marked_active(isNatKind(s(V1)))</LHS><RHS>Marked_mark(isNatKind(V1))</RHS></DPRULE><DPRULE num="5"><LHS>Marked_mark(U11(X1,X2,X3))</LHS><RHS>Marked_active(U11(mark(X1),X2,X3))</RHS></DPRULE><DPRULE num="6"><LHS>Marked_mark(U11(X1,X2,X3))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="7"><LHS>Marked_mark(U12(X1,X2))</LHS><RHS>Marked_active(U12(mark(X1),X2))</RHS></DPRULE><DPRULE num="8"><LHS>Marked_mark(U12(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="9"><LHS>Marked_mark(U13(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="10"><LHS>Marked_mark(U31(X1,X2))</LHS><RHS>Marked_active(U31(mark(X1),X2))</RHS></DPRULE><DPRULE num="11"><LHS>Marked_mark(and(X1,X2))</LHS><RHS>Marked_active(and(mark(X1),X2))</RHS></DPRULE><DPRULE num="12"><LHS>Marked_mark(and(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="13"><LHS>Marked_mark(isNatKind(X))</LHS><RHS>Marked_active(isNatKind(X))</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><ORDERING type="poly"><POLYSYMB><SYMBOL><NAME>mark</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U21</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U11</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U41</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>Marked_mark</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>isNat</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>s</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U13</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>0</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U12</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U31</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>tt</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>and</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>Marked_active</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>active</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>plus</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U22</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>isNatKind</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB></ORDERING><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_mark(U31(X1,X2))</LHS><RHS>Marked_active(U31(mark(X1),X2))</RHS></DPRULE></DPLIST></STRICTPAIRS></CRITERION><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(U11(tt,V1,V2))</LHS><RHS>mark(U12(isNat(V1),V2))</RHS></RULE><RULE><LHS>active(U12(tt,V2))</LHS><RHS>mark(U13(isNat(V2)))</RHS></RULE><RULE><LHS>active(U13(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U21(tt,V1))</LHS><RHS>mark(U22(isNat(V1)))</RHS></RULE><RULE><LHS>active(U22(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U31(tt,N))</LHS><RHS>mark(N)</RHS></RULE><RULE><LHS>active(U41(tt,M,N))</LHS><RHS>mark(s(plus(N,M)))</RHS></RULE><RULE><LHS>active(and(tt,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(isNat(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNat(plus(V1,V2)))</LHS><RHS>mark(U11(and(isNatKind(V1),isNatKind(V2)),V1,V2))</RHS></RULE><RULE><LHS>active(isNat(s(V1)))</LHS><RHS>mark(U21(isNatKind(V1),V1))</RHS></RULE><RULE><LHS>active(isNatKind(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNatKind(plus(V1,V2)))</LHS><RHS>mark(and(isNatKind(V1),isNatKind(V2)))</RHS></RULE><RULE><LHS>active(isNatKind(s(V1)))</LHS><RHS>mark(isNatKind(V1))</RHS></RULE><RULE><LHS>active(plus(N,0))</LHS><RHS>mark(U31(and(isNat(N),isNatKind(N)),N))</RHS></RULE><RULE><LHS>active(plus(N,s(M)))</LHS><RHS>mark(U41(and(and(isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),M,N))</RHS></RULE><RULE><LHS>mark(U11(X1,X2,X3))</LHS><RHS>active(U11(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(tt)</LHS><RHS>active(tt)</RHS></RULE><RULE><LHS>mark(U12(X1,X2))</LHS><RHS>active(U12(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(isNat(X))</LHS><RHS>active(isNat(X))</RHS></RULE><RULE><LHS>mark(U13(X))</LHS><RHS>active(U13(mark(X)))</RHS></RULE><RULE><LHS>mark(U21(X1,X2))</LHS><RHS>active(U21(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U22(X))</LHS><RHS>active(U22(mark(X)))</RHS></RULE><RULE><LHS>mark(U31(X1,X2))</LHS><RHS>active(U31(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U41(X1,X2,X3))</LHS><RHS>active(U41(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(mark(X)))</RHS></RULE><RULE><LHS>mark(plus(X1,X2))</LHS><RHS>active(plus(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(isNatKind(X))</LHS><RHS>active(isNatKind(X))</RHS></RULE><RULE><LHS>U11(mark(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,mark(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,mark(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(active(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,active(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,active(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U12(mark(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,mark(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(active(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,active(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>isNat(mark(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>isNat(active(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>U13(mark(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U13(active(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U21(mark(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,mark(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(active(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,active(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U22(mark(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U22(active(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U31(mark(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,mark(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(active(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,active(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U41(mark(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,mark(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,mark(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(active(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,active(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,active(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>s(mark(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>s(active(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>plus(mark(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,mark(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(active(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,active(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>and(mark(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,mark(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(active(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,active(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>isNatKind(mark(X))</LHS><RHS>isNatKind(X)</RHS></RULE><RULE><LHS>isNatKind(active(X))</LHS><RHS>isNatKind(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_active(U11(tt,V1,V2))</LHS><RHS>Marked_mark(U12(isNat(V1),V2))</RHS></DPRULE><DPRULE num="1"><LHS>Marked_active(U12(tt,V2))</LHS><RHS>Marked_mark(U13(isNat(V2)))</RHS></DPRULE><DPRULE num="2"><LHS>Marked_active(and(tt,X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="3"><LHS>Marked_active(isNatKind(plus(V1,V2)))</LHS><RHS>Marked_mark(and(isNatKind(V1),isNatKind(V2)))</RHS></DPRULE><DPRULE num="4"><LHS>Marked_active(isNatKind(s(V1)))</LHS><RHS>Marked_mark(isNatKind(V1))</RHS></DPRULE><DPRULE num="5"><LHS>Marked_mark(U11(X1,X2,X3))</LHS><RHS>Marked_active(U11(mark(X1),X2,X3))</RHS></DPRULE><DPRULE num="6"><LHS>Marked_mark(U11(X1,X2,X3))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="7"><LHS>Marked_mark(U12(X1,X2))</LHS><RHS>Marked_active(U12(mark(X1),X2))</RHS></DPRULE><DPRULE num="8"><LHS>Marked_mark(U12(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="9"><LHS>Marked_mark(U13(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="10"><LHS>Marked_mark(and(X1,X2))</LHS><RHS>Marked_active(and(mark(X1),X2))</RHS></DPRULE><DPRULE num="11"><LHS>Marked_mark(and(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="12"><LHS>Marked_mark(isNatKind(X))</LHS><RHS>Marked_active(isNatKind(X))</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><DAG approx="simpl"><CCLIST><SCC num="0"><NODE ref="0"/><NODE ref="1"/><NODE ref="2"/><NODE ref="3"/><NODE ref="4"/><NODE ref="5"/><NODE ref="6"/><NODE ref="7"/><NODE ref="8"/><NODE ref="9"/><NODE ref="10"/><NODE ref="11"/><NODE ref="12"/></SCC></CCLIST></DAG></CRITERION><PROPERTY criterion="stronggraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(U11(tt,V1,V2))</LHS><RHS>mark(U12(isNat(V1),V2))</RHS></RULE><RULE><LHS>active(U12(tt,V2))</LHS><RHS>mark(U13(isNat(V2)))</RHS></RULE><RULE><LHS>active(U13(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U21(tt,V1))</LHS><RHS>mark(U22(isNat(V1)))</RHS></RULE><RULE><LHS>active(U22(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U31(tt,N))</LHS><RHS>mark(N)</RHS></RULE><RULE><LHS>active(U41(tt,M,N))</LHS><RHS>mark(s(plus(N,M)))</RHS></RULE><RULE><LHS>active(and(tt,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(isNat(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNat(plus(V1,V2)))</LHS><RHS>mark(U11(and(isNatKind(V1),isNatKind(V2)),V1,V2))</RHS></RULE><RULE><LHS>active(isNat(s(V1)))</LHS><RHS>mark(U21(isNatKind(V1),V1))</RHS></RULE><RULE><LHS>active(isNatKind(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNatKind(plus(V1,V2)))</LHS><RHS>mark(and(isNatKind(V1),isNatKind(V2)))</RHS></RULE><RULE><LHS>active(isNatKind(s(V1)))</LHS><RHS>mark(isNatKind(V1))</RHS></RULE><RULE><LHS>active(plus(N,0))</LHS><RHS>mark(U31(and(isNat(N),isNatKind(N)),N))</RHS></RULE><RULE><LHS>active(plus(N,s(M)))</LHS><RHS>mark(U41(and(and(isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),M,N))</RHS></RULE><RULE><LHS>mark(U11(X1,X2,X3))</LHS><RHS>active(U11(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(tt)</LHS><RHS>active(tt)</RHS></RULE><RULE><LHS>mark(U12(X1,X2))</LHS><RHS>active(U12(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(isNat(X))</LHS><RHS>active(isNat(X))</RHS></RULE><RULE><LHS>mark(U13(X))</LHS><RHS>active(U13(mark(X)))</RHS></RULE><RULE><LHS>mark(U21(X1,X2))</LHS><RHS>active(U21(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U22(X))</LHS><RHS>active(U22(mark(X)))</RHS></RULE><RULE><LHS>mark(U31(X1,X2))</LHS><RHS>active(U31(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U41(X1,X2,X3))</LHS><RHS>active(U41(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(mark(X)))</RHS></RULE><RULE><LHS>mark(plus(X1,X2))</LHS><RHS>active(plus(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(isNatKind(X))</LHS><RHS>active(isNatKind(X))</RHS></RULE><RULE><LHS>U11(mark(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,mark(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,mark(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(active(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,active(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,active(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U12(mark(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,mark(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(active(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,active(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>isNat(mark(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>isNat(active(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>U13(mark(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U13(active(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U21(mark(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,mark(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(active(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,active(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U22(mark(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U22(active(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U31(mark(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,mark(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(active(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,active(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U41(mark(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,mark(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,mark(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(active(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,active(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,active(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>s(mark(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>s(active(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>plus(mark(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,mark(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(active(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,active(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>and(mark(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,mark(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(active(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,active(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>isNatKind(mark(X))</LHS><RHS>isNatKind(X)</RHS></RULE><RULE><LHS>isNatKind(active(X))</LHS><RHS>isNatKind(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_active(U11(tt,V1,V2))</LHS><RHS>Marked_mark(U12(isNat(V1),V2))</RHS></DPRULE><DPRULE num="1"><LHS>Marked_active(U12(tt,V2))</LHS><RHS>Marked_mark(U13(isNat(V2)))</RHS></DPRULE><DPRULE num="2"><LHS>Marked_active(and(tt,X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="3"><LHS>Marked_active(isNatKind(plus(V1,V2)))</LHS><RHS>Marked_mark(and(isNatKind(V1),isNatKind(V2)))</RHS></DPRULE><DPRULE num="4"><LHS>Marked_active(isNatKind(s(V1)))</LHS><RHS>Marked_mark(isNatKind(V1))</RHS></DPRULE><DPRULE num="5"><LHS>Marked_mark(U11(X1,X2,X3))</LHS><RHS>Marked_active(U11(mark(X1),X2,X3))</RHS></DPRULE><DPRULE num="6"><LHS>Marked_mark(U11(X1,X2,X3))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="7"><LHS>Marked_mark(U12(X1,X2))</LHS><RHS>Marked_active(U12(mark(X1),X2))</RHS></DPRULE><DPRULE num="8"><LHS>Marked_mark(U12(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="9"><LHS>Marked_mark(U13(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="10"><LHS>Marked_mark(and(X1,X2))</LHS><RHS>Marked_active(and(mark(X1),X2))</RHS></DPRULE><DPRULE num="11"><LHS>Marked_mark(and(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="12"><LHS>Marked_mark(isNatKind(X))</LHS><RHS>Marked_active(isNatKind(X))</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><ORDERING type="poly"><POLYSYMB><SYMBOL><NAME>mark</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U21</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U11</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>3</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>3</INT></COEF><ARG degree="1" num="2"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U41</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>3</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>3</INT></COEF><ARG degree="1" num="2"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>Marked_mark</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>isNat</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>3</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>s</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U13</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>0</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U12</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>3</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U31</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>tt</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>and</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>Marked_active</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>active</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>plus</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>3</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>3</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U22</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>isNatKind</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB></ORDERING><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_active(isNatKind(s(V1)))</LHS><RHS>Marked_mark(isNatKind(V1))</RHS></DPRULE></DPLIST></STRICTPAIRS></CRITERION><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(U11(tt,V1,V2))</LHS><RHS>mark(U12(isNat(V1),V2))</RHS></RULE><RULE><LHS>active(U12(tt,V2))</LHS><RHS>mark(U13(isNat(V2)))</RHS></RULE><RULE><LHS>active(U13(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U21(tt,V1))</LHS><RHS>mark(U22(isNat(V1)))</RHS></RULE><RULE><LHS>active(U22(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U31(tt,N))</LHS><RHS>mark(N)</RHS></RULE><RULE><LHS>active(U41(tt,M,N))</LHS><RHS>mark(s(plus(N,M)))</RHS></RULE><RULE><LHS>active(and(tt,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(isNat(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNat(plus(V1,V2)))</LHS><RHS>mark(U11(and(isNatKind(V1),isNatKind(V2)),V1,V2))</RHS></RULE><RULE><LHS>active(isNat(s(V1)))</LHS><RHS>mark(U21(isNatKind(V1),V1))</RHS></RULE><RULE><LHS>active(isNatKind(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNatKind(plus(V1,V2)))</LHS><RHS>mark(and(isNatKind(V1),isNatKind(V2)))</RHS></RULE><RULE><LHS>active(isNatKind(s(V1)))</LHS><RHS>mark(isNatKind(V1))</RHS></RULE><RULE><LHS>active(plus(N,0))</LHS><RHS>mark(U31(and(isNat(N),isNatKind(N)),N))</RHS></RULE><RULE><LHS>active(plus(N,s(M)))</LHS><RHS>mark(U41(and(and(isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),M,N))</RHS></RULE><RULE><LHS>mark(U11(X1,X2,X3))</LHS><RHS>active(U11(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(tt)</LHS><RHS>active(tt)</RHS></RULE><RULE><LHS>mark(U12(X1,X2))</LHS><RHS>active(U12(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(isNat(X))</LHS><RHS>active(isNat(X))</RHS></RULE><RULE><LHS>mark(U13(X))</LHS><RHS>active(U13(mark(X)))</RHS></RULE><RULE><LHS>mark(U21(X1,X2))</LHS><RHS>active(U21(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U22(X))</LHS><RHS>active(U22(mark(X)))</RHS></RULE><RULE><LHS>mark(U31(X1,X2))</LHS><RHS>active(U31(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U41(X1,X2,X3))</LHS><RHS>active(U41(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(mark(X)))</RHS></RULE><RULE><LHS>mark(plus(X1,X2))</LHS><RHS>active(plus(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(isNatKind(X))</LHS><RHS>active(isNatKind(X))</RHS></RULE><RULE><LHS>U11(mark(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,mark(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,mark(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(active(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,active(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,active(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U12(mark(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,mark(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(active(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,active(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>isNat(mark(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>isNat(active(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>U13(mark(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U13(active(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U21(mark(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,mark(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(active(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,active(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U22(mark(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U22(active(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U31(mark(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,mark(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(active(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,active(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U41(mark(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,mark(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,mark(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(active(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,active(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,active(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>s(mark(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>s(active(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>plus(mark(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,mark(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(active(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,active(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>and(mark(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,mark(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(active(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,active(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>isNatKind(mark(X))</LHS><RHS>isNatKind(X)</RHS></RULE><RULE><LHS>isNatKind(active(X))</LHS><RHS>isNatKind(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_active(U11(tt,V1,V2))</LHS><RHS>Marked_mark(U12(isNat(V1),V2))</RHS></DPRULE><DPRULE num="1"><LHS>Marked_active(U12(tt,V2))</LHS><RHS>Marked_mark(U13(isNat(V2)))</RHS></DPRULE><DPRULE num="2"><LHS>Marked_active(and(tt,X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="3"><LHS>Marked_active(isNatKind(plus(V1,V2)))</LHS><RHS>Marked_mark(and(isNatKind(V1),isNatKind(V2)))</RHS></DPRULE><DPRULE num="4"><LHS>Marked_mark(U11(X1,X2,X3))</LHS><RHS>Marked_active(U11(mark(X1),X2,X3))</RHS></DPRULE><DPRULE num="5"><LHS>Marked_mark(U11(X1,X2,X3))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="6"><LHS>Marked_mark(U12(X1,X2))</LHS><RHS>Marked_active(U12(mark(X1),X2))</RHS></DPRULE><DPRULE num="7"><LHS>Marked_mark(U12(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="8"><LHS>Marked_mark(U13(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="9"><LHS>Marked_mark(and(X1,X2))</LHS><RHS>Marked_active(and(mark(X1),X2))</RHS></DPRULE><DPRULE num="10"><LHS>Marked_mark(and(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="11"><LHS>Marked_mark(isNatKind(X))</LHS><RHS>Marked_active(isNatKind(X))</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><DAG approx="simpl"><CCLIST><SCC num="0"><NODE ref="0"/><NODE ref="1"/><NODE ref="2"/><NODE ref="3"/><NODE ref="4"/><NODE ref="5"/><NODE ref="6"/><NODE ref="7"/><NODE ref="8"/><NODE ref="9"/><NODE ref="10"/><NODE ref="11"/></SCC></CCLIST></DAG></CRITERION><PROPERTY criterion="stronggraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(U11(tt,V1,V2))</LHS><RHS>mark(U12(isNat(V1),V2))</RHS></RULE><RULE><LHS>active(U12(tt,V2))</LHS><RHS>mark(U13(isNat(V2)))</RHS></RULE><RULE><LHS>active(U13(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U21(tt,V1))</LHS><RHS>mark(U22(isNat(V1)))</RHS></RULE><RULE><LHS>active(U22(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U31(tt,N))</LHS><RHS>mark(N)</RHS></RULE><RULE><LHS>active(U41(tt,M,N))</LHS><RHS>mark(s(plus(N,M)))</RHS></RULE><RULE><LHS>active(and(tt,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(isNat(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNat(plus(V1,V2)))</LHS><RHS>mark(U11(and(isNatKind(V1),isNatKind(V2)),V1,V2))</RHS></RULE><RULE><LHS>active(isNat(s(V1)))</LHS><RHS>mark(U21(isNatKind(V1),V1))</RHS></RULE><RULE><LHS>active(isNatKind(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNatKind(plus(V1,V2)))</LHS><RHS>mark(and(isNatKind(V1),isNatKind(V2)))</RHS></RULE><RULE><LHS>active(isNatKind(s(V1)))</LHS><RHS>mark(isNatKind(V1))</RHS></RULE><RULE><LHS>active(plus(N,0))</LHS><RHS>mark(U31(and(isNat(N),isNatKind(N)),N))</RHS></RULE><RULE><LHS>active(plus(N,s(M)))</LHS><RHS>mark(U41(and(and(isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),M,N))</RHS></RULE><RULE><LHS>mark(U11(X1,X2,X3))</LHS><RHS>active(U11(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(tt)</LHS><RHS>active(tt)</RHS></RULE><RULE><LHS>mark(U12(X1,X2))</LHS><RHS>active(U12(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(isNat(X))</LHS><RHS>active(isNat(X))</RHS></RULE><RULE><LHS>mark(U13(X))</LHS><RHS>active(U13(mark(X)))</RHS></RULE><RULE><LHS>mark(U21(X1,X2))</LHS><RHS>active(U21(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U22(X))</LHS><RHS>active(U22(mark(X)))</RHS></RULE><RULE><LHS>mark(U31(X1,X2))</LHS><RHS>active(U31(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U41(X1,X2,X3))</LHS><RHS>active(U41(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(mark(X)))</RHS></RULE><RULE><LHS>mark(plus(X1,X2))</LHS><RHS>active(plus(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(isNatKind(X))</LHS><RHS>active(isNatKind(X))</RHS></RULE><RULE><LHS>U11(mark(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,mark(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,mark(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(active(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,active(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,active(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U12(mark(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,mark(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(active(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,active(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>isNat(mark(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>isNat(active(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>U13(mark(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U13(active(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U21(mark(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,mark(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(active(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,active(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U22(mark(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U22(active(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U31(mark(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,mark(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(active(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,active(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U41(mark(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,mark(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,mark(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(active(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,active(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,active(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>s(mark(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>s(active(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>plus(mark(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,mark(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(active(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,active(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>and(mark(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,mark(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(active(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,active(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>isNatKind(mark(X))</LHS><RHS>isNatKind(X)</RHS></RULE><RULE><LHS>isNatKind(active(X))</LHS><RHS>isNatKind(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_active(U11(tt,V1,V2))</LHS><RHS>Marked_mark(U12(isNat(V1),V2))</RHS></DPRULE><DPRULE num="1"><LHS>Marked_active(U12(tt,V2))</LHS><RHS>Marked_mark(U13(isNat(V2)))</RHS></DPRULE><DPRULE num="2"><LHS>Marked_active(and(tt,X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="3"><LHS>Marked_active(isNatKind(plus(V1,V2)))</LHS><RHS>Marked_mark(and(isNatKind(V1),isNatKind(V2)))</RHS></DPRULE><DPRULE num="4"><LHS>Marked_mark(U11(X1,X2,X3))</LHS><RHS>Marked_active(U11(mark(X1),X2,X3))</RHS></DPRULE><DPRULE num="5"><LHS>Marked_mark(U11(X1,X2,X3))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="6"><LHS>Marked_mark(U12(X1,X2))</LHS><RHS>Marked_active(U12(mark(X1),X2))</RHS></DPRULE><DPRULE num="7"><LHS>Marked_mark(U12(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="8"><LHS>Marked_mark(U13(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="9"><LHS>Marked_mark(and(X1,X2))</LHS><RHS>Marked_active(and(mark(X1),X2))</RHS></DPRULE><DPRULE num="10"><LHS>Marked_mark(and(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="11"><LHS>Marked_mark(isNatKind(X))</LHS><RHS>Marked_active(isNatKind(X))</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><ORDERING type="poly"><POLYSYMB><SYMBOL><NAME>mark</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U21</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U11</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="2"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U41</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>3</INT></COEF><ARG degree="1" num="2"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>Marked_mark</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>isNat</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>s</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U13</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>0</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U12</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U31</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>tt</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>and</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>Marked_active</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>active</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>plus</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>3</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U22</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>isNatKind</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB></ORDERING><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_active(isNatKind(plus(V1,V2)))</LHS><RHS>Marked_mark(and(isNatKind(V1),isNatKind(V2)))</RHS></DPRULE></DPLIST></STRICTPAIRS></CRITERION><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(U11(tt,V1,V2))</LHS><RHS>mark(U12(isNat(V1),V2))</RHS></RULE><RULE><LHS>active(U12(tt,V2))</LHS><RHS>mark(U13(isNat(V2)))</RHS></RULE><RULE><LHS>active(U13(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U21(tt,V1))</LHS><RHS>mark(U22(isNat(V1)))</RHS></RULE><RULE><LHS>active(U22(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U31(tt,N))</LHS><RHS>mark(N)</RHS></RULE><RULE><LHS>active(U41(tt,M,N))</LHS><RHS>mark(s(plus(N,M)))</RHS></RULE><RULE><LHS>active(and(tt,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(isNat(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNat(plus(V1,V2)))</LHS><RHS>mark(U11(and(isNatKind(V1),isNatKind(V2)),V1,V2))</RHS></RULE><RULE><LHS>active(isNat(s(V1)))</LHS><RHS>mark(U21(isNatKind(V1),V1))</RHS></RULE><RULE><LHS>active(isNatKind(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNatKind(plus(V1,V2)))</LHS><RHS>mark(and(isNatKind(V1),isNatKind(V2)))</RHS></RULE><RULE><LHS>active(isNatKind(s(V1)))</LHS><RHS>mark(isNatKind(V1))</RHS></RULE><RULE><LHS>active(plus(N,0))</LHS><RHS>mark(U31(and(isNat(N),isNatKind(N)),N))</RHS></RULE><RULE><LHS>active(plus(N,s(M)))</LHS><RHS>mark(U41(and(and(isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),M,N))</RHS></RULE><RULE><LHS>mark(U11(X1,X2,X3))</LHS><RHS>active(U11(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(tt)</LHS><RHS>active(tt)</RHS></RULE><RULE><LHS>mark(U12(X1,X2))</LHS><RHS>active(U12(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(isNat(X))</LHS><RHS>active(isNat(X))</RHS></RULE><RULE><LHS>mark(U13(X))</LHS><RHS>active(U13(mark(X)))</RHS></RULE><RULE><LHS>mark(U21(X1,X2))</LHS><RHS>active(U21(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U22(X))</LHS><RHS>active(U22(mark(X)))</RHS></RULE><RULE><LHS>mark(U31(X1,X2))</LHS><RHS>active(U31(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U41(X1,X2,X3))</LHS><RHS>active(U41(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(mark(X)))</RHS></RULE><RULE><LHS>mark(plus(X1,X2))</LHS><RHS>active(plus(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(isNatKind(X))</LHS><RHS>active(isNatKind(X))</RHS></RULE><RULE><LHS>U11(mark(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,mark(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,mark(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(active(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,active(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,active(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U12(mark(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,mark(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(active(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,active(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>isNat(mark(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>isNat(active(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>U13(mark(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U13(active(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U21(mark(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,mark(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(active(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,active(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U22(mark(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U22(active(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U31(mark(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,mark(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(active(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,active(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U41(mark(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,mark(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,mark(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(active(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,active(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,active(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>s(mark(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>s(active(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>plus(mark(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,mark(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(active(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,active(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>and(mark(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,mark(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(active(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,active(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>isNatKind(mark(X))</LHS><RHS>isNatKind(X)</RHS></RULE><RULE><LHS>isNatKind(active(X))</LHS><RHS>isNatKind(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_active(U11(tt,V1,V2))</LHS><RHS>Marked_mark(U12(isNat(V1),V2))</RHS></DPRULE><DPRULE num="1"><LHS>Marked_active(U12(tt,V2))</LHS><RHS>Marked_mark(U13(isNat(V2)))</RHS></DPRULE><DPRULE num="2"><LHS>Marked_active(and(tt,X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="3"><LHS>Marked_mark(U11(X1,X2,X3))</LHS><RHS>Marked_active(U11(mark(X1),X2,X3))</RHS></DPRULE><DPRULE num="4"><LHS>Marked_mark(U11(X1,X2,X3))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="5"><LHS>Marked_mark(U12(X1,X2))</LHS><RHS>Marked_active(U12(mark(X1),X2))</RHS></DPRULE><DPRULE num="6"><LHS>Marked_mark(U12(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="7"><LHS>Marked_mark(U13(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="8"><LHS>Marked_mark(and(X1,X2))</LHS><RHS>Marked_active(and(mark(X1),X2))</RHS></DPRULE><DPRULE num="9"><LHS>Marked_mark(and(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="10"><LHS>Marked_mark(isNatKind(X))</LHS><RHS>Marked_active(isNatKind(X))</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><DAG approx="simpl"><CCLIST><SCC num="0"><NODE ref="0"/><NODE ref="1"/><NODE ref="2"/><NODE ref="3"/><NODE ref="4"/><NODE ref="5"/><NODE ref="6"/><NODE ref="7"/><NODE ref="8"/><NODE ref="9"/><NODE ref="10"/></SCC></CCLIST></DAG></CRITERION><PROPERTY criterion="stronggraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(U11(tt,V1,V2))</LHS><RHS>mark(U12(isNat(V1),V2))</RHS></RULE><RULE><LHS>active(U12(tt,V2))</LHS><RHS>mark(U13(isNat(V2)))</RHS></RULE><RULE><LHS>active(U13(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U21(tt,V1))</LHS><RHS>mark(U22(isNat(V1)))</RHS></RULE><RULE><LHS>active(U22(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U31(tt,N))</LHS><RHS>mark(N)</RHS></RULE><RULE><LHS>active(U41(tt,M,N))</LHS><RHS>mark(s(plus(N,M)))</RHS></RULE><RULE><LHS>active(and(tt,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(isNat(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNat(plus(V1,V2)))</LHS><RHS>mark(U11(and(isNatKind(V1),isNatKind(V2)),V1,V2))</RHS></RULE><RULE><LHS>active(isNat(s(V1)))</LHS><RHS>mark(U21(isNatKind(V1),V1))</RHS></RULE><RULE><LHS>active(isNatKind(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNatKind(plus(V1,V2)))</LHS><RHS>mark(and(isNatKind(V1),isNatKind(V2)))</RHS></RULE><RULE><LHS>active(isNatKind(s(V1)))</LHS><RHS>mark(isNatKind(V1))</RHS></RULE><RULE><LHS>active(plus(N,0))</LHS><RHS>mark(U31(and(isNat(N),isNatKind(N)),N))</RHS></RULE><RULE><LHS>active(plus(N,s(M)))</LHS><RHS>mark(U41(and(and(isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),M,N))</RHS></RULE><RULE><LHS>mark(U11(X1,X2,X3))</LHS><RHS>active(U11(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(tt)</LHS><RHS>active(tt)</RHS></RULE><RULE><LHS>mark(U12(X1,X2))</LHS><RHS>active(U12(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(isNat(X))</LHS><RHS>active(isNat(X))</RHS></RULE><RULE><LHS>mark(U13(X))</LHS><RHS>active(U13(mark(X)))</RHS></RULE><RULE><LHS>mark(U21(X1,X2))</LHS><RHS>active(U21(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U22(X))</LHS><RHS>active(U22(mark(X)))</RHS></RULE><RULE><LHS>mark(U31(X1,X2))</LHS><RHS>active(U31(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U41(X1,X2,X3))</LHS><RHS>active(U41(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(mark(X)))</RHS></RULE><RULE><LHS>mark(plus(X1,X2))</LHS><RHS>active(plus(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(isNatKind(X))</LHS><RHS>active(isNatKind(X))</RHS></RULE><RULE><LHS>U11(mark(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,mark(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,mark(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(active(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,active(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,active(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U12(mark(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,mark(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(active(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,active(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>isNat(mark(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>isNat(active(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>U13(mark(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U13(active(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U21(mark(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,mark(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(active(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,active(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U22(mark(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U22(active(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U31(mark(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,mark(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(active(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,active(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U41(mark(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,mark(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,mark(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(active(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,active(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,active(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>s(mark(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>s(active(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>plus(mark(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,mark(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(active(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,active(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>and(mark(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,mark(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(active(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,active(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>isNatKind(mark(X))</LHS><RHS>isNatKind(X)</RHS></RULE><RULE><LHS>isNatKind(active(X))</LHS><RHS>isNatKind(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_active(U11(tt,V1,V2))</LHS><RHS>Marked_mark(U12(isNat(V1),V2))</RHS></DPRULE><DPRULE num="1"><LHS>Marked_active(U12(tt,V2))</LHS><RHS>Marked_mark(U13(isNat(V2)))</RHS></DPRULE><DPRULE num="2"><LHS>Marked_active(and(tt,X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="3"><LHS>Marked_mark(U11(X1,X2,X3))</LHS><RHS>Marked_active(U11(mark(X1),X2,X3))</RHS></DPRULE><DPRULE num="4"><LHS>Marked_mark(U11(X1,X2,X3))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="5"><LHS>Marked_mark(U12(X1,X2))</LHS><RHS>Marked_active(U12(mark(X1),X2))</RHS></DPRULE><DPRULE num="6"><LHS>Marked_mark(U12(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="7"><LHS>Marked_mark(U13(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="8"><LHS>Marked_mark(and(X1,X2))</LHS><RHS>Marked_active(and(mark(X1),X2))</RHS></DPRULE><DPRULE num="9"><LHS>Marked_mark(and(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="10"><LHS>Marked_mark(isNatKind(X))</LHS><RHS>Marked_active(isNatKind(X))</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><ORDERING type="poly"><POLYSYMB><SYMBOL><NAME>mark</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U21</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U11</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U41</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>Marked_mark</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>isNat</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>s</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U13</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>0</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U12</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U31</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>tt</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>and</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>Marked_active</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>active</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>plus</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U22</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>isNatKind</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB></ORDERING><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_mark(isNatKind(X))</LHS><RHS>Marked_active(isNatKind(X))</RHS></DPRULE></DPLIST></STRICTPAIRS></CRITERION><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(U11(tt,V1,V2))</LHS><RHS>mark(U12(isNat(V1),V2))</RHS></RULE><RULE><LHS>active(U12(tt,V2))</LHS><RHS>mark(U13(isNat(V2)))</RHS></RULE><RULE><LHS>active(U13(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U21(tt,V1))</LHS><RHS>mark(U22(isNat(V1)))</RHS></RULE><RULE><LHS>active(U22(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U31(tt,N))</LHS><RHS>mark(N)</RHS></RULE><RULE><LHS>active(U41(tt,M,N))</LHS><RHS>mark(s(plus(N,M)))</RHS></RULE><RULE><LHS>active(and(tt,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(isNat(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNat(plus(V1,V2)))</LHS><RHS>mark(U11(and(isNatKind(V1),isNatKind(V2)),V1,V2))</RHS></RULE><RULE><LHS>active(isNat(s(V1)))</LHS><RHS>mark(U21(isNatKind(V1),V1))</RHS></RULE><RULE><LHS>active(isNatKind(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNatKind(plus(V1,V2)))</LHS><RHS>mark(and(isNatKind(V1),isNatKind(V2)))</RHS></RULE><RULE><LHS>active(isNatKind(s(V1)))</LHS><RHS>mark(isNatKind(V1))</RHS></RULE><RULE><LHS>active(plus(N,0))</LHS><RHS>mark(U31(and(isNat(N),isNatKind(N)),N))</RHS></RULE><RULE><LHS>active(plus(N,s(M)))</LHS><RHS>mark(U41(and(and(isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),M,N))</RHS></RULE><RULE><LHS>mark(U11(X1,X2,X3))</LHS><RHS>active(U11(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(tt)</LHS><RHS>active(tt)</RHS></RULE><RULE><LHS>mark(U12(X1,X2))</LHS><RHS>active(U12(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(isNat(X))</LHS><RHS>active(isNat(X))</RHS></RULE><RULE><LHS>mark(U13(X))</LHS><RHS>active(U13(mark(X)))</RHS></RULE><RULE><LHS>mark(U21(X1,X2))</LHS><RHS>active(U21(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U22(X))</LHS><RHS>active(U22(mark(X)))</RHS></RULE><RULE><LHS>mark(U31(X1,X2))</LHS><RHS>active(U31(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U41(X1,X2,X3))</LHS><RHS>active(U41(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(mark(X)))</RHS></RULE><RULE><LHS>mark(plus(X1,X2))</LHS><RHS>active(plus(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(isNatKind(X))</LHS><RHS>active(isNatKind(X))</RHS></RULE><RULE><LHS>U11(mark(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,mark(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,mark(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(active(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,active(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,active(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U12(mark(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,mark(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(active(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,active(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>isNat(mark(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>isNat(active(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>U13(mark(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U13(active(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U21(mark(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,mark(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(active(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,active(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U22(mark(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U22(active(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U31(mark(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,mark(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(active(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,active(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U41(mark(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,mark(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,mark(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(active(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,active(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,active(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>s(mark(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>s(active(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>plus(mark(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,mark(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(active(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,active(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>and(mark(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,mark(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(active(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,active(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>isNatKind(mark(X))</LHS><RHS>isNatKind(X)</RHS></RULE><RULE><LHS>isNatKind(active(X))</LHS><RHS>isNatKind(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_active(U11(tt,V1,V2))</LHS><RHS>Marked_mark(U12(isNat(V1),V2))</RHS></DPRULE><DPRULE num="1"><LHS>Marked_active(U12(tt,V2))</LHS><RHS>Marked_mark(U13(isNat(V2)))</RHS></DPRULE><DPRULE num="2"><LHS>Marked_active(and(tt,X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="3"><LHS>Marked_mark(U11(X1,X2,X3))</LHS><RHS>Marked_active(U11(mark(X1),X2,X3))</RHS></DPRULE><DPRULE num="4"><LHS>Marked_mark(U11(X1,X2,X3))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="5"><LHS>Marked_mark(U12(X1,X2))</LHS><RHS>Marked_active(U12(mark(X1),X2))</RHS></DPRULE><DPRULE num="6"><LHS>Marked_mark(U12(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="7"><LHS>Marked_mark(U13(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="8"><LHS>Marked_mark(and(X1,X2))</LHS><RHS>Marked_active(and(mark(X1),X2))</RHS></DPRULE><DPRULE num="9"><LHS>Marked_mark(and(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><DAG approx="simpl"><CCLIST><SCC num="0"><NODE ref="0"/><NODE ref="1"/><NODE ref="2"/><NODE ref="3"/><NODE ref="4"/><NODE ref="5"/><NODE ref="6"/><NODE ref="7"/><NODE ref="8"/><NODE ref="9"/></SCC></CCLIST></DAG></CRITERION><PROPERTY criterion="stronggraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(U11(tt,V1,V2))</LHS><RHS>mark(U12(isNat(V1),V2))</RHS></RULE><RULE><LHS>active(U12(tt,V2))</LHS><RHS>mark(U13(isNat(V2)))</RHS></RULE><RULE><LHS>active(U13(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U21(tt,V1))</LHS><RHS>mark(U22(isNat(V1)))</RHS></RULE><RULE><LHS>active(U22(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U31(tt,N))</LHS><RHS>mark(N)</RHS></RULE><RULE><LHS>active(U41(tt,M,N))</LHS><RHS>mark(s(plus(N,M)))</RHS></RULE><RULE><LHS>active(and(tt,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(isNat(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNat(plus(V1,V2)))</LHS><RHS>mark(U11(and(isNatKind(V1),isNatKind(V2)),V1,V2))</RHS></RULE><RULE><LHS>active(isNat(s(V1)))</LHS><RHS>mark(U21(isNatKind(V1),V1))</RHS></RULE><RULE><LHS>active(isNatKind(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNatKind(plus(V1,V2)))</LHS><RHS>mark(and(isNatKind(V1),isNatKind(V2)))</RHS></RULE><RULE><LHS>active(isNatKind(s(V1)))</LHS><RHS>mark(isNatKind(V1))</RHS></RULE><RULE><LHS>active(plus(N,0))</LHS><RHS>mark(U31(and(isNat(N),isNatKind(N)),N))</RHS></RULE><RULE><LHS>active(plus(N,s(M)))</LHS><RHS>mark(U41(and(and(isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),M,N))</RHS></RULE><RULE><LHS>mark(U11(X1,X2,X3))</LHS><RHS>active(U11(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(tt)</LHS><RHS>active(tt)</RHS></RULE><RULE><LHS>mark(U12(X1,X2))</LHS><RHS>active(U12(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(isNat(X))</LHS><RHS>active(isNat(X))</RHS></RULE><RULE><LHS>mark(U13(X))</LHS><RHS>active(U13(mark(X)))</RHS></RULE><RULE><LHS>mark(U21(X1,X2))</LHS><RHS>active(U21(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U22(X))</LHS><RHS>active(U22(mark(X)))</RHS></RULE><RULE><LHS>mark(U31(X1,X2))</LHS><RHS>active(U31(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U41(X1,X2,X3))</LHS><RHS>active(U41(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(mark(X)))</RHS></RULE><RULE><LHS>mark(plus(X1,X2))</LHS><RHS>active(plus(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(isNatKind(X))</LHS><RHS>active(isNatKind(X))</RHS></RULE><RULE><LHS>U11(mark(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,mark(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,mark(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(active(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,active(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,active(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U12(mark(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,mark(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(active(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,active(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>isNat(mark(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>isNat(active(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>U13(mark(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U13(active(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U21(mark(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,mark(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(active(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,active(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U22(mark(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U22(active(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U31(mark(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,mark(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(active(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,active(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U41(mark(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,mark(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,mark(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(active(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,active(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,active(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>s(mark(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>s(active(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>plus(mark(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,mark(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(active(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,active(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>and(mark(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,mark(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(active(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,active(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>isNatKind(mark(X))</LHS><RHS>isNatKind(X)</RHS></RULE><RULE><LHS>isNatKind(active(X))</LHS><RHS>isNatKind(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_active(U11(tt,V1,V2))</LHS><RHS>Marked_mark(U12(isNat(V1),V2))</RHS></DPRULE><DPRULE num="1"><LHS>Marked_active(U12(tt,V2))</LHS><RHS>Marked_mark(U13(isNat(V2)))</RHS></DPRULE><DPRULE num="2"><LHS>Marked_active(and(tt,X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="3"><LHS>Marked_mark(U11(X1,X2,X3))</LHS><RHS>Marked_active(U11(mark(X1),X2,X3))</RHS></DPRULE><DPRULE num="4"><LHS>Marked_mark(U11(X1,X2,X3))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="5"><LHS>Marked_mark(U12(X1,X2))</LHS><RHS>Marked_active(U12(mark(X1),X2))</RHS></DPRULE><DPRULE num="6"><LHS>Marked_mark(U12(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="7"><LHS>Marked_mark(U13(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="8"><LHS>Marked_mark(and(X1,X2))</LHS><RHS>Marked_active(and(mark(X1),X2))</RHS></DPRULE><DPRULE num="9"><LHS>Marked_mark(and(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><ORDERING type="poly"><POLYSYMB><SYMBOL><NAME>mark</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U21</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U11</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="2"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U41</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>3</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>3</INT></COEF><ARG degree="1" num="2"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>Marked_mark</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>isNat</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>s</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U13</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>0</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U12</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U31</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>tt</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>and</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>Marked_active</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>active</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>plus</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>3</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>3</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U22</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>isNatKind</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB></ORDERING><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_active(and(tt,X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_mark(and(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE></DPLIST></STRICTPAIRS></CRITERION><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(U11(tt,V1,V2))</LHS><RHS>mark(U12(isNat(V1),V2))</RHS></RULE><RULE><LHS>active(U12(tt,V2))</LHS><RHS>mark(U13(isNat(V2)))</RHS></RULE><RULE><LHS>active(U13(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U21(tt,V1))</LHS><RHS>mark(U22(isNat(V1)))</RHS></RULE><RULE><LHS>active(U22(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U31(tt,N))</LHS><RHS>mark(N)</RHS></RULE><RULE><LHS>active(U41(tt,M,N))</LHS><RHS>mark(s(plus(N,M)))</RHS></RULE><RULE><LHS>active(and(tt,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(isNat(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNat(plus(V1,V2)))</LHS><RHS>mark(U11(and(isNatKind(V1),isNatKind(V2)),V1,V2))</RHS></RULE><RULE><LHS>active(isNat(s(V1)))</LHS><RHS>mark(U21(isNatKind(V1),V1))</RHS></RULE><RULE><LHS>active(isNatKind(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNatKind(plus(V1,V2)))</LHS><RHS>mark(and(isNatKind(V1),isNatKind(V2)))</RHS></RULE><RULE><LHS>active(isNatKind(s(V1)))</LHS><RHS>mark(isNatKind(V1))</RHS></RULE><RULE><LHS>active(plus(N,0))</LHS><RHS>mark(U31(and(isNat(N),isNatKind(N)),N))</RHS></RULE><RULE><LHS>active(plus(N,s(M)))</LHS><RHS>mark(U41(and(and(isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),M,N))</RHS></RULE><RULE><LHS>mark(U11(X1,X2,X3))</LHS><RHS>active(U11(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(tt)</LHS><RHS>active(tt)</RHS></RULE><RULE><LHS>mark(U12(X1,X2))</LHS><RHS>active(U12(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(isNat(X))</LHS><RHS>active(isNat(X))</RHS></RULE><RULE><LHS>mark(U13(X))</LHS><RHS>active(U13(mark(X)))</RHS></RULE><RULE><LHS>mark(U21(X1,X2))</LHS><RHS>active(U21(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U22(X))</LHS><RHS>active(U22(mark(X)))</RHS></RULE><RULE><LHS>mark(U31(X1,X2))</LHS><RHS>active(U31(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U41(X1,X2,X3))</LHS><RHS>active(U41(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(mark(X)))</RHS></RULE><RULE><LHS>mark(plus(X1,X2))</LHS><RHS>active(plus(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(isNatKind(X))</LHS><RHS>active(isNatKind(X))</RHS></RULE><RULE><LHS>U11(mark(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,mark(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,mark(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(active(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,active(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,active(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U12(mark(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,mark(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(active(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,active(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>isNat(mark(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>isNat(active(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>U13(mark(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U13(active(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U21(mark(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,mark(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(active(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,active(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U22(mark(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U22(active(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U31(mark(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,mark(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(active(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,active(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U41(mark(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,mark(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,mark(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(active(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,active(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,active(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>s(mark(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>s(active(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>plus(mark(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,mark(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(active(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,active(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>and(mark(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,mark(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(active(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,active(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>isNatKind(mark(X))</LHS><RHS>isNatKind(X)</RHS></RULE><RULE><LHS>isNatKind(active(X))</LHS><RHS>isNatKind(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_active(U11(tt,V1,V2))</LHS><RHS>Marked_mark(U12(isNat(V1),V2))</RHS></DPRULE><DPRULE num="1"><LHS>Marked_active(U12(tt,V2))</LHS><RHS>Marked_mark(U13(isNat(V2)))</RHS></DPRULE><DPRULE num="2"><LHS>Marked_mark(U11(X1,X2,X3))</LHS><RHS>Marked_active(U11(mark(X1),X2,X3))</RHS></DPRULE><DPRULE num="3"><LHS>Marked_mark(U11(X1,X2,X3))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="4"><LHS>Marked_mark(U12(X1,X2))</LHS><RHS>Marked_active(U12(mark(X1),X2))</RHS></DPRULE><DPRULE num="5"><LHS>Marked_mark(U12(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="6"><LHS>Marked_mark(U13(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="7"><LHS>Marked_mark(and(X1,X2))</LHS><RHS>Marked_active(and(mark(X1),X2))</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><DAG approx="simpl"><CCLIST><SCC num="0"><NODE ref="0"/><NODE ref="1"/><NODE ref="2"/><NODE ref="3"/><NODE ref="4"/><NODE ref="5"/><NODE ref="6"/><NODE ref="7"/></SCC></CCLIST></DAG></CRITERION><PROPERTY criterion="stronggraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(U11(tt,V1,V2))</LHS><RHS>mark(U12(isNat(V1),V2))</RHS></RULE><RULE><LHS>active(U12(tt,V2))</LHS><RHS>mark(U13(isNat(V2)))</RHS></RULE><RULE><LHS>active(U13(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U21(tt,V1))</LHS><RHS>mark(U22(isNat(V1)))</RHS></RULE><RULE><LHS>active(U22(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U31(tt,N))</LHS><RHS>mark(N)</RHS></RULE><RULE><LHS>active(U41(tt,M,N))</LHS><RHS>mark(s(plus(N,M)))</RHS></RULE><RULE><LHS>active(and(tt,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(isNat(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNat(plus(V1,V2)))</LHS><RHS>mark(U11(and(isNatKind(V1),isNatKind(V2)),V1,V2))</RHS></RULE><RULE><LHS>active(isNat(s(V1)))</LHS><RHS>mark(U21(isNatKind(V1),V1))</RHS></RULE><RULE><LHS>active(isNatKind(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNatKind(plus(V1,V2)))</LHS><RHS>mark(and(isNatKind(V1),isNatKind(V2)))</RHS></RULE><RULE><LHS>active(isNatKind(s(V1)))</LHS><RHS>mark(isNatKind(V1))</RHS></RULE><RULE><LHS>active(plus(N,0))</LHS><RHS>mark(U31(and(isNat(N),isNatKind(N)),N))</RHS></RULE><RULE><LHS>active(plus(N,s(M)))</LHS><RHS>mark(U41(and(and(isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),M,N))</RHS></RULE><RULE><LHS>mark(U11(X1,X2,X3))</LHS><RHS>active(U11(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(tt)</LHS><RHS>active(tt)</RHS></RULE><RULE><LHS>mark(U12(X1,X2))</LHS><RHS>active(U12(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(isNat(X))</LHS><RHS>active(isNat(X))</RHS></RULE><RULE><LHS>mark(U13(X))</LHS><RHS>active(U13(mark(X)))</RHS></RULE><RULE><LHS>mark(U21(X1,X2))</LHS><RHS>active(U21(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U22(X))</LHS><RHS>active(U22(mark(X)))</RHS></RULE><RULE><LHS>mark(U31(X1,X2))</LHS><RHS>active(U31(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U41(X1,X2,X3))</LHS><RHS>active(U41(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(mark(X)))</RHS></RULE><RULE><LHS>mark(plus(X1,X2))</LHS><RHS>active(plus(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(isNatKind(X))</LHS><RHS>active(isNatKind(X))</RHS></RULE><RULE><LHS>U11(mark(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,mark(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,mark(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(active(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,active(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,active(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U12(mark(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,mark(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(active(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,active(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>isNat(mark(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>isNat(active(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>U13(mark(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U13(active(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U21(mark(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,mark(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(active(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,active(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U22(mark(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U22(active(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U31(mark(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,mark(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(active(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,active(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U41(mark(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,mark(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,mark(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(active(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,active(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,active(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>s(mark(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>s(active(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>plus(mark(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,mark(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(active(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,active(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>and(mark(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,mark(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(active(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,active(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>isNatKind(mark(X))</LHS><RHS>isNatKind(X)</RHS></RULE><RULE><LHS>isNatKind(active(X))</LHS><RHS>isNatKind(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_active(U11(tt,V1,V2))</LHS><RHS>Marked_mark(U12(isNat(V1),V2))</RHS></DPRULE><DPRULE num="1"><LHS>Marked_active(U12(tt,V2))</LHS><RHS>Marked_mark(U13(isNat(V2)))</RHS></DPRULE><DPRULE num="2"><LHS>Marked_mark(U11(X1,X2,X3))</LHS><RHS>Marked_active(U11(mark(X1),X2,X3))</RHS></DPRULE><DPRULE num="3"><LHS>Marked_mark(U11(X1,X2,X3))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="4"><LHS>Marked_mark(U12(X1,X2))</LHS><RHS>Marked_active(U12(mark(X1),X2))</RHS></DPRULE><DPRULE num="5"><LHS>Marked_mark(U12(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="6"><LHS>Marked_mark(U13(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="7"><LHS>Marked_mark(and(X1,X2))</LHS><RHS>Marked_active(and(mark(X1),X2))</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><ORDERING type="poly"><POLYSYMB><SYMBOL><NAME>mark</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U21</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U11</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U41</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>Marked_mark</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>isNat</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>s</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U13</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>0</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U12</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U31</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>tt</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>and</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>Marked_active</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>active</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>plus</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U22</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>isNatKind</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB></ORDERING><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_mark(and(X1,X2))</LHS><RHS>Marked_active(and(mark(X1),X2))</RHS></DPRULE></DPLIST></STRICTPAIRS></CRITERION><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(U11(tt,V1,V2))</LHS><RHS>mark(U12(isNat(V1),V2))</RHS></RULE><RULE><LHS>active(U12(tt,V2))</LHS><RHS>mark(U13(isNat(V2)))</RHS></RULE><RULE><LHS>active(U13(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U21(tt,V1))</LHS><RHS>mark(U22(isNat(V1)))</RHS></RULE><RULE><LHS>active(U22(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U31(tt,N))</LHS><RHS>mark(N)</RHS></RULE><RULE><LHS>active(U41(tt,M,N))</LHS><RHS>mark(s(plus(N,M)))</RHS></RULE><RULE><LHS>active(and(tt,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(isNat(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNat(plus(V1,V2)))</LHS><RHS>mark(U11(and(isNatKind(V1),isNatKind(V2)),V1,V2))</RHS></RULE><RULE><LHS>active(isNat(s(V1)))</LHS><RHS>mark(U21(isNatKind(V1),V1))</RHS></RULE><RULE><LHS>active(isNatKind(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNatKind(plus(V1,V2)))</LHS><RHS>mark(and(isNatKind(V1),isNatKind(V2)))</RHS></RULE><RULE><LHS>active(isNatKind(s(V1)))</LHS><RHS>mark(isNatKind(V1))</RHS></RULE><RULE><LHS>active(plus(N,0))</LHS><RHS>mark(U31(and(isNat(N),isNatKind(N)),N))</RHS></RULE><RULE><LHS>active(plus(N,s(M)))</LHS><RHS>mark(U41(and(and(isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),M,N))</RHS></RULE><RULE><LHS>mark(U11(X1,X2,X3))</LHS><RHS>active(U11(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(tt)</LHS><RHS>active(tt)</RHS></RULE><RULE><LHS>mark(U12(X1,X2))</LHS><RHS>active(U12(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(isNat(X))</LHS><RHS>active(isNat(X))</RHS></RULE><RULE><LHS>mark(U13(X))</LHS><RHS>active(U13(mark(X)))</RHS></RULE><RULE><LHS>mark(U21(X1,X2))</LHS><RHS>active(U21(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U22(X))</LHS><RHS>active(U22(mark(X)))</RHS></RULE><RULE><LHS>mark(U31(X1,X2))</LHS><RHS>active(U31(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U41(X1,X2,X3))</LHS><RHS>active(U41(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(mark(X)))</RHS></RULE><RULE><LHS>mark(plus(X1,X2))</LHS><RHS>active(plus(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(isNatKind(X))</LHS><RHS>active(isNatKind(X))</RHS></RULE><RULE><LHS>U11(mark(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,mark(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,mark(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(active(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,active(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,active(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U12(mark(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,mark(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(active(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,active(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>isNat(mark(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>isNat(active(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>U13(mark(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U13(active(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U21(mark(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,mark(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(active(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,active(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U22(mark(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U22(active(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U31(mark(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,mark(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(active(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,active(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U41(mark(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,mark(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,mark(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(active(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,active(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,active(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>s(mark(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>s(active(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>plus(mark(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,mark(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(active(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,active(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>and(mark(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,mark(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(active(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,active(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>isNatKind(mark(X))</LHS><RHS>isNatKind(X)</RHS></RULE><RULE><LHS>isNatKind(active(X))</LHS><RHS>isNatKind(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_active(U11(tt,V1,V2))</LHS><RHS>Marked_mark(U12(isNat(V1),V2))</RHS></DPRULE><DPRULE num="1"><LHS>Marked_active(U12(tt,V2))</LHS><RHS>Marked_mark(U13(isNat(V2)))</RHS></DPRULE><DPRULE num="2"><LHS>Marked_mark(U11(X1,X2,X3))</LHS><RHS>Marked_active(U11(mark(X1),X2,X3))</RHS></DPRULE><DPRULE num="3"><LHS>Marked_mark(U11(X1,X2,X3))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="4"><LHS>Marked_mark(U12(X1,X2))</LHS><RHS>Marked_active(U12(mark(X1),X2))</RHS></DPRULE><DPRULE num="5"><LHS>Marked_mark(U12(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="6"><LHS>Marked_mark(U13(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><DAG approx="simpl"><CCLIST><SCC num="0"><NODE ref="0"/><NODE ref="1"/><NODE ref="2"/><NODE ref="3"/><NODE ref="4"/><NODE ref="5"/><NODE ref="6"/></SCC></CCLIST></DAG></CRITERION><PROPERTY criterion="stronggraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(U11(tt,V1,V2))</LHS><RHS>mark(U12(isNat(V1),V2))</RHS></RULE><RULE><LHS>active(U12(tt,V2))</LHS><RHS>mark(U13(isNat(V2)))</RHS></RULE><RULE><LHS>active(U13(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U21(tt,V1))</LHS><RHS>mark(U22(isNat(V1)))</RHS></RULE><RULE><LHS>active(U22(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U31(tt,N))</LHS><RHS>mark(N)</RHS></RULE><RULE><LHS>active(U41(tt,M,N))</LHS><RHS>mark(s(plus(N,M)))</RHS></RULE><RULE><LHS>active(and(tt,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(isNat(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNat(plus(V1,V2)))</LHS><RHS>mark(U11(and(isNatKind(V1),isNatKind(V2)),V1,V2))</RHS></RULE><RULE><LHS>active(isNat(s(V1)))</LHS><RHS>mark(U21(isNatKind(V1),V1))</RHS></RULE><RULE><LHS>active(isNatKind(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNatKind(plus(V1,V2)))</LHS><RHS>mark(and(isNatKind(V1),isNatKind(V2)))</RHS></RULE><RULE><LHS>active(isNatKind(s(V1)))</LHS><RHS>mark(isNatKind(V1))</RHS></RULE><RULE><LHS>active(plus(N,0))</LHS><RHS>mark(U31(and(isNat(N),isNatKind(N)),N))</RHS></RULE><RULE><LHS>active(plus(N,s(M)))</LHS><RHS>mark(U41(and(and(isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),M,N))</RHS></RULE><RULE><LHS>mark(U11(X1,X2,X3))</LHS><RHS>active(U11(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(tt)</LHS><RHS>active(tt)</RHS></RULE><RULE><LHS>mark(U12(X1,X2))</LHS><RHS>active(U12(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(isNat(X))</LHS><RHS>active(isNat(X))</RHS></RULE><RULE><LHS>mark(U13(X))</LHS><RHS>active(U13(mark(X)))</RHS></RULE><RULE><LHS>mark(U21(X1,X2))</LHS><RHS>active(U21(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U22(X))</LHS><RHS>active(U22(mark(X)))</RHS></RULE><RULE><LHS>mark(U31(X1,X2))</LHS><RHS>active(U31(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U41(X1,X2,X3))</LHS><RHS>active(U41(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(mark(X)))</RHS></RULE><RULE><LHS>mark(plus(X1,X2))</LHS><RHS>active(plus(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(isNatKind(X))</LHS><RHS>active(isNatKind(X))</RHS></RULE><RULE><LHS>U11(mark(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,mark(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,mark(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(active(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,active(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,active(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U12(mark(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,mark(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(active(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,active(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>isNat(mark(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>isNat(active(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>U13(mark(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U13(active(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U21(mark(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,mark(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(active(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,active(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U22(mark(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U22(active(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U31(mark(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,mark(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(active(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,active(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U41(mark(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,mark(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,mark(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(active(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,active(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,active(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>s(mark(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>s(active(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>plus(mark(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,mark(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(active(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,active(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>and(mark(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,mark(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(active(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,active(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>isNatKind(mark(X))</LHS><RHS>isNatKind(X)</RHS></RULE><RULE><LHS>isNatKind(active(X))</LHS><RHS>isNatKind(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_active(U11(tt,V1,V2))</LHS><RHS>Marked_mark(U12(isNat(V1),V2))</RHS></DPRULE><DPRULE num="1"><LHS>Marked_active(U12(tt,V2))</LHS><RHS>Marked_mark(U13(isNat(V2)))</RHS></DPRULE><DPRULE num="2"><LHS>Marked_mark(U11(X1,X2,X3))</LHS><RHS>Marked_active(U11(mark(X1),X2,X3))</RHS></DPRULE><DPRULE num="3"><LHS>Marked_mark(U11(X1,X2,X3))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="4"><LHS>Marked_mark(U12(X1,X2))</LHS><RHS>Marked_active(U12(mark(X1),X2))</RHS></DPRULE><DPRULE num="5"><LHS>Marked_mark(U12(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="6"><LHS>Marked_mark(U13(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><ORDERING type="poly"><POLYSYMB><SYMBOL><NAME>mark</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U21</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U11</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="2"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U41</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>Marked_mark</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>isNat</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>s</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U13</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>0</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U12</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U31</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>tt</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>and</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>Marked_active</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>active</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>plus</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U22</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>3</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>isNatKind</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB></ORDERING><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_active(U12(tt,V2))</LHS><RHS>Marked_mark(U13(isNat(V2)))</RHS></DPRULE></DPLIST></STRICTPAIRS></CRITERION><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(U11(tt,V1,V2))</LHS><RHS>mark(U12(isNat(V1),V2))</RHS></RULE><RULE><LHS>active(U12(tt,V2))</LHS><RHS>mark(U13(isNat(V2)))</RHS></RULE><RULE><LHS>active(U13(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U21(tt,V1))</LHS><RHS>mark(U22(isNat(V1)))</RHS></RULE><RULE><LHS>active(U22(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U31(tt,N))</LHS><RHS>mark(N)</RHS></RULE><RULE><LHS>active(U41(tt,M,N))</LHS><RHS>mark(s(plus(N,M)))</RHS></RULE><RULE><LHS>active(and(tt,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(isNat(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNat(plus(V1,V2)))</LHS><RHS>mark(U11(and(isNatKind(V1),isNatKind(V2)),V1,V2))</RHS></RULE><RULE><LHS>active(isNat(s(V1)))</LHS><RHS>mark(U21(isNatKind(V1),V1))</RHS></RULE><RULE><LHS>active(isNatKind(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNatKind(plus(V1,V2)))</LHS><RHS>mark(and(isNatKind(V1),isNatKind(V2)))</RHS></RULE><RULE><LHS>active(isNatKind(s(V1)))</LHS><RHS>mark(isNatKind(V1))</RHS></RULE><RULE><LHS>active(plus(N,0))</LHS><RHS>mark(U31(and(isNat(N),isNatKind(N)),N))</RHS></RULE><RULE><LHS>active(plus(N,s(M)))</LHS><RHS>mark(U41(and(and(isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),M,N))</RHS></RULE><RULE><LHS>mark(U11(X1,X2,X3))</LHS><RHS>active(U11(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(tt)</LHS><RHS>active(tt)</RHS></RULE><RULE><LHS>mark(U12(X1,X2))</LHS><RHS>active(U12(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(isNat(X))</LHS><RHS>active(isNat(X))</RHS></RULE><RULE><LHS>mark(U13(X))</LHS><RHS>active(U13(mark(X)))</RHS></RULE><RULE><LHS>mark(U21(X1,X2))</LHS><RHS>active(U21(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U22(X))</LHS><RHS>active(U22(mark(X)))</RHS></RULE><RULE><LHS>mark(U31(X1,X2))</LHS><RHS>active(U31(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U41(X1,X2,X3))</LHS><RHS>active(U41(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(mark(X)))</RHS></RULE><RULE><LHS>mark(plus(X1,X2))</LHS><RHS>active(plus(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(isNatKind(X))</LHS><RHS>active(isNatKind(X))</RHS></RULE><RULE><LHS>U11(mark(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,mark(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,mark(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(active(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,active(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,active(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U12(mark(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,mark(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(active(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,active(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>isNat(mark(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>isNat(active(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>U13(mark(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U13(active(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U21(mark(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,mark(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(active(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,active(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U22(mark(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U22(active(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U31(mark(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,mark(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(active(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,active(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U41(mark(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,mark(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,mark(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(active(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,active(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,active(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>s(mark(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>s(active(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>plus(mark(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,mark(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(active(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,active(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>and(mark(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,mark(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(active(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,active(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>isNatKind(mark(X))</LHS><RHS>isNatKind(X)</RHS></RULE><RULE><LHS>isNatKind(active(X))</LHS><RHS>isNatKind(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_active(U11(tt,V1,V2))</LHS><RHS>Marked_mark(U12(isNat(V1),V2))</RHS></DPRULE><DPRULE num="1"><LHS>Marked_mark(U11(X1,X2,X3))</LHS><RHS>Marked_active(U11(mark(X1),X2,X3))</RHS></DPRULE><DPRULE num="2"><LHS>Marked_mark(U11(X1,X2,X3))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="3"><LHS>Marked_mark(U12(X1,X2))</LHS><RHS>Marked_active(U12(mark(X1),X2))</RHS></DPRULE><DPRULE num="4"><LHS>Marked_mark(U12(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="5"><LHS>Marked_mark(U13(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><DAG approx="simpl"><CCLIST><SCC num="0"><NODE ref="0"/><NODE ref="1"/><NODE ref="2"/><NODE ref="3"/><NODE ref="4"/><NODE ref="5"/></SCC></CCLIST></DAG></CRITERION><PROPERTY criterion="stronggraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(U11(tt,V1,V2))</LHS><RHS>mark(U12(isNat(V1),V2))</RHS></RULE><RULE><LHS>active(U12(tt,V2))</LHS><RHS>mark(U13(isNat(V2)))</RHS></RULE><RULE><LHS>active(U13(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U21(tt,V1))</LHS><RHS>mark(U22(isNat(V1)))</RHS></RULE><RULE><LHS>active(U22(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U31(tt,N))</LHS><RHS>mark(N)</RHS></RULE><RULE><LHS>active(U41(tt,M,N))</LHS><RHS>mark(s(plus(N,M)))</RHS></RULE><RULE><LHS>active(and(tt,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(isNat(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNat(plus(V1,V2)))</LHS><RHS>mark(U11(and(isNatKind(V1),isNatKind(V2)),V1,V2))</RHS></RULE><RULE><LHS>active(isNat(s(V1)))</LHS><RHS>mark(U21(isNatKind(V1),V1))</RHS></RULE><RULE><LHS>active(isNatKind(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNatKind(plus(V1,V2)))</LHS><RHS>mark(and(isNatKind(V1),isNatKind(V2)))</RHS></RULE><RULE><LHS>active(isNatKind(s(V1)))</LHS><RHS>mark(isNatKind(V1))</RHS></RULE><RULE><LHS>active(plus(N,0))</LHS><RHS>mark(U31(and(isNat(N),isNatKind(N)),N))</RHS></RULE><RULE><LHS>active(plus(N,s(M)))</LHS><RHS>mark(U41(and(and(isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),M,N))</RHS></RULE><RULE><LHS>mark(U11(X1,X2,X3))</LHS><RHS>active(U11(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(tt)</LHS><RHS>active(tt)</RHS></RULE><RULE><LHS>mark(U12(X1,X2))</LHS><RHS>active(U12(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(isNat(X))</LHS><RHS>active(isNat(X))</RHS></RULE><RULE><LHS>mark(U13(X))</LHS><RHS>active(U13(mark(X)))</RHS></RULE><RULE><LHS>mark(U21(X1,X2))</LHS><RHS>active(U21(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U22(X))</LHS><RHS>active(U22(mark(X)))</RHS></RULE><RULE><LHS>mark(U31(X1,X2))</LHS><RHS>active(U31(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U41(X1,X2,X3))</LHS><RHS>active(U41(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(mark(X)))</RHS></RULE><RULE><LHS>mark(plus(X1,X2))</LHS><RHS>active(plus(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(isNatKind(X))</LHS><RHS>active(isNatKind(X))</RHS></RULE><RULE><LHS>U11(mark(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,mark(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,mark(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(active(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,active(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,active(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U12(mark(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,mark(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(active(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,active(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>isNat(mark(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>isNat(active(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>U13(mark(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U13(active(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U21(mark(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,mark(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(active(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,active(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U22(mark(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U22(active(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U31(mark(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,mark(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(active(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,active(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U41(mark(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,mark(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,mark(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(active(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,active(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,active(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>s(mark(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>s(active(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>plus(mark(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,mark(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(active(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,active(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>and(mark(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,mark(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(active(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,active(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>isNatKind(mark(X))</LHS><RHS>isNatKind(X)</RHS></RULE><RULE><LHS>isNatKind(active(X))</LHS><RHS>isNatKind(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_active(U11(tt,V1,V2))</LHS><RHS>Marked_mark(U12(isNat(V1),V2))</RHS></DPRULE><DPRULE num="1"><LHS>Marked_mark(U11(X1,X2,X3))</LHS><RHS>Marked_active(U11(mark(X1),X2,X3))</RHS></DPRULE><DPRULE num="2"><LHS>Marked_mark(U11(X1,X2,X3))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="3"><LHS>Marked_mark(U12(X1,X2))</LHS><RHS>Marked_active(U12(mark(X1),X2))</RHS></DPRULE><DPRULE num="4"><LHS>Marked_mark(U12(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="5"><LHS>Marked_mark(U13(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><ORDERING type="poly"><POLYSYMB><SYMBOL><NAME>mark</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U21</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U11</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U41</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>Marked_mark</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>3</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>isNat</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>s</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U13</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>0</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U12</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U31</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>tt</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>and</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>Marked_active</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>active</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>plus</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U22</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>isNatKind</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB></ORDERING><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_mark(U12(X1,X2))</LHS><RHS>Marked_active(U12(mark(X1),X2))</RHS></DPRULE></DPLIST></STRICTPAIRS></CRITERION><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(U11(tt,V1,V2))</LHS><RHS>mark(U12(isNat(V1),V2))</RHS></RULE><RULE><LHS>active(U12(tt,V2))</LHS><RHS>mark(U13(isNat(V2)))</RHS></RULE><RULE><LHS>active(U13(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U21(tt,V1))</LHS><RHS>mark(U22(isNat(V1)))</RHS></RULE><RULE><LHS>active(U22(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U31(tt,N))</LHS><RHS>mark(N)</RHS></RULE><RULE><LHS>active(U41(tt,M,N))</LHS><RHS>mark(s(plus(N,M)))</RHS></RULE><RULE><LHS>active(and(tt,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(isNat(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNat(plus(V1,V2)))</LHS><RHS>mark(U11(and(isNatKind(V1),isNatKind(V2)),V1,V2))</RHS></RULE><RULE><LHS>active(isNat(s(V1)))</LHS><RHS>mark(U21(isNatKind(V1),V1))</RHS></RULE><RULE><LHS>active(isNatKind(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNatKind(plus(V1,V2)))</LHS><RHS>mark(and(isNatKind(V1),isNatKind(V2)))</RHS></RULE><RULE><LHS>active(isNatKind(s(V1)))</LHS><RHS>mark(isNatKind(V1))</RHS></RULE><RULE><LHS>active(plus(N,0))</LHS><RHS>mark(U31(and(isNat(N),isNatKind(N)),N))</RHS></RULE><RULE><LHS>active(plus(N,s(M)))</LHS><RHS>mark(U41(and(and(isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),M,N))</RHS></RULE><RULE><LHS>mark(U11(X1,X2,X3))</LHS><RHS>active(U11(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(tt)</LHS><RHS>active(tt)</RHS></RULE><RULE><LHS>mark(U12(X1,X2))</LHS><RHS>active(U12(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(isNat(X))</LHS><RHS>active(isNat(X))</RHS></RULE><RULE><LHS>mark(U13(X))</LHS><RHS>active(U13(mark(X)))</RHS></RULE><RULE><LHS>mark(U21(X1,X2))</LHS><RHS>active(U21(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U22(X))</LHS><RHS>active(U22(mark(X)))</RHS></RULE><RULE><LHS>mark(U31(X1,X2))</LHS><RHS>active(U31(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U41(X1,X2,X3))</LHS><RHS>active(U41(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(mark(X)))</RHS></RULE><RULE><LHS>mark(plus(X1,X2))</LHS><RHS>active(plus(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(isNatKind(X))</LHS><RHS>active(isNatKind(X))</RHS></RULE><RULE><LHS>U11(mark(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,mark(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,mark(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(active(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,active(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,active(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U12(mark(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,mark(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(active(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,active(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>isNat(mark(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>isNat(active(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>U13(mark(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U13(active(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U21(mark(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,mark(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(active(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,active(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U22(mark(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U22(active(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U31(mark(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,mark(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(active(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,active(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U41(mark(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,mark(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,mark(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(active(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,active(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,active(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>s(mark(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>s(active(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>plus(mark(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,mark(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(active(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,active(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>and(mark(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,mark(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(active(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,active(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>isNatKind(mark(X))</LHS><RHS>isNatKind(X)</RHS></RULE><RULE><LHS>isNatKind(active(X))</LHS><RHS>isNatKind(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_active(U11(tt,V1,V2))</LHS><RHS>Marked_mark(U12(isNat(V1),V2))</RHS></DPRULE><DPRULE num="1"><LHS>Marked_mark(U11(X1,X2,X3))</LHS><RHS>Marked_active(U11(mark(X1),X2,X3))</RHS></DPRULE><DPRULE num="2"><LHS>Marked_mark(U11(X1,X2,X3))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="3"><LHS>Marked_mark(U12(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="4"><LHS>Marked_mark(U13(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><DAG approx="simpl"><CCLIST><SCC num="0"><NODE ref="0"/><NODE ref="1"/><NODE ref="2"/><NODE ref="3"/><NODE ref="4"/></SCC></CCLIST></DAG></CRITERION><PROPERTY criterion="stronggraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(U11(tt,V1,V2))</LHS><RHS>mark(U12(isNat(V1),V2))</RHS></RULE><RULE><LHS>active(U12(tt,V2))</LHS><RHS>mark(U13(isNat(V2)))</RHS></RULE><RULE><LHS>active(U13(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U21(tt,V1))</LHS><RHS>mark(U22(isNat(V1)))</RHS></RULE><RULE><LHS>active(U22(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U31(tt,N))</LHS><RHS>mark(N)</RHS></RULE><RULE><LHS>active(U41(tt,M,N))</LHS><RHS>mark(s(plus(N,M)))</RHS></RULE><RULE><LHS>active(and(tt,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(isNat(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNat(plus(V1,V2)))</LHS><RHS>mark(U11(and(isNatKind(V1),isNatKind(V2)),V1,V2))</RHS></RULE><RULE><LHS>active(isNat(s(V1)))</LHS><RHS>mark(U21(isNatKind(V1),V1))</RHS></RULE><RULE><LHS>active(isNatKind(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNatKind(plus(V1,V2)))</LHS><RHS>mark(and(isNatKind(V1),isNatKind(V2)))</RHS></RULE><RULE><LHS>active(isNatKind(s(V1)))</LHS><RHS>mark(isNatKind(V1))</RHS></RULE><RULE><LHS>active(plus(N,0))</LHS><RHS>mark(U31(and(isNat(N),isNatKind(N)),N))</RHS></RULE><RULE><LHS>active(plus(N,s(M)))</LHS><RHS>mark(U41(and(and(isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),M,N))</RHS></RULE><RULE><LHS>mark(U11(X1,X2,X3))</LHS><RHS>active(U11(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(tt)</LHS><RHS>active(tt)</RHS></RULE><RULE><LHS>mark(U12(X1,X2))</LHS><RHS>active(U12(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(isNat(X))</LHS><RHS>active(isNat(X))</RHS></RULE><RULE><LHS>mark(U13(X))</LHS><RHS>active(U13(mark(X)))</RHS></RULE><RULE><LHS>mark(U21(X1,X2))</LHS><RHS>active(U21(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U22(X))</LHS><RHS>active(U22(mark(X)))</RHS></RULE><RULE><LHS>mark(U31(X1,X2))</LHS><RHS>active(U31(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U41(X1,X2,X3))</LHS><RHS>active(U41(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(mark(X)))</RHS></RULE><RULE><LHS>mark(plus(X1,X2))</LHS><RHS>active(plus(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(isNatKind(X))</LHS><RHS>active(isNatKind(X))</RHS></RULE><RULE><LHS>U11(mark(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,mark(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,mark(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(active(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,active(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,active(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U12(mark(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,mark(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(active(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,active(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>isNat(mark(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>isNat(active(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>U13(mark(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U13(active(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U21(mark(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,mark(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(active(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,active(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U22(mark(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U22(active(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U31(mark(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,mark(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(active(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,active(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U41(mark(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,mark(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,mark(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(active(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,active(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,active(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>s(mark(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>s(active(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>plus(mark(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,mark(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(active(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,active(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>and(mark(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,mark(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(active(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,active(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>isNatKind(mark(X))</LHS><RHS>isNatKind(X)</RHS></RULE><RULE><LHS>isNatKind(active(X))</LHS><RHS>isNatKind(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_active(U11(tt,V1,V2))</LHS><RHS>Marked_mark(U12(isNat(V1),V2))</RHS></DPRULE><DPRULE num="1"><LHS>Marked_mark(U11(X1,X2,X3))</LHS><RHS>Marked_active(U11(mark(X1),X2,X3))</RHS></DPRULE><DPRULE num="2"><LHS>Marked_mark(U11(X1,X2,X3))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="3"><LHS>Marked_mark(U12(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="4"><LHS>Marked_mark(U13(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><ORDERING type="poly"><POLYSYMB><SYMBOL><NAME>mark</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U21</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U11</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="2"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U41</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>3</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>3</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="2"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>Marked_mark</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>3</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>isNat</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>s</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U13</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>0</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U12</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U31</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>tt</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>and</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>Marked_active</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>active</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>plus</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>3</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U22</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>isNatKind</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB></ORDERING><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_active(U11(tt,V1,V2))</LHS><RHS>Marked_mark(U12(isNat(V1),V2))</RHS></DPRULE><DPRULE num="1"><LHS>Marked_mark(U11(X1,X2,X3))</LHS><RHS>Marked_active(U11(mark(X1),X2,X3))</RHS></DPRULE></DPLIST></STRICTPAIRS></CRITERION><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(U11(tt,V1,V2))</LHS><RHS>mark(U12(isNat(V1),V2))</RHS></RULE><RULE><LHS>active(U12(tt,V2))</LHS><RHS>mark(U13(isNat(V2)))</RHS></RULE><RULE><LHS>active(U13(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U21(tt,V1))</LHS><RHS>mark(U22(isNat(V1)))</RHS></RULE><RULE><LHS>active(U22(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U31(tt,N))</LHS><RHS>mark(N)</RHS></RULE><RULE><LHS>active(U41(tt,M,N))</LHS><RHS>mark(s(plus(N,M)))</RHS></RULE><RULE><LHS>active(and(tt,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(isNat(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNat(plus(V1,V2)))</LHS><RHS>mark(U11(and(isNatKind(V1),isNatKind(V2)),V1,V2))</RHS></RULE><RULE><LHS>active(isNat(s(V1)))</LHS><RHS>mark(U21(isNatKind(V1),V1))</RHS></RULE><RULE><LHS>active(isNatKind(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNatKind(plus(V1,V2)))</LHS><RHS>mark(and(isNatKind(V1),isNatKind(V2)))</RHS></RULE><RULE><LHS>active(isNatKind(s(V1)))</LHS><RHS>mark(isNatKind(V1))</RHS></RULE><RULE><LHS>active(plus(N,0))</LHS><RHS>mark(U31(and(isNat(N),isNatKind(N)),N))</RHS></RULE><RULE><LHS>active(plus(N,s(M)))</LHS><RHS>mark(U41(and(and(isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),M,N))</RHS></RULE><RULE><LHS>mark(U11(X1,X2,X3))</LHS><RHS>active(U11(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(tt)</LHS><RHS>active(tt)</RHS></RULE><RULE><LHS>mark(U12(X1,X2))</LHS><RHS>active(U12(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(isNat(X))</LHS><RHS>active(isNat(X))</RHS></RULE><RULE><LHS>mark(U13(X))</LHS><RHS>active(U13(mark(X)))</RHS></RULE><RULE><LHS>mark(U21(X1,X2))</LHS><RHS>active(U21(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U22(X))</LHS><RHS>active(U22(mark(X)))</RHS></RULE><RULE><LHS>mark(U31(X1,X2))</LHS><RHS>active(U31(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U41(X1,X2,X3))</LHS><RHS>active(U41(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(mark(X)))</RHS></RULE><RULE><LHS>mark(plus(X1,X2))</LHS><RHS>active(plus(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(isNatKind(X))</LHS><RHS>active(isNatKind(X))</RHS></RULE><RULE><LHS>U11(mark(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,mark(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,mark(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(active(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,active(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,active(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U12(mark(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,mark(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(active(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,active(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>isNat(mark(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>isNat(active(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>U13(mark(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U13(active(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U21(mark(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,mark(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(active(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,active(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U22(mark(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U22(active(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U31(mark(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,mark(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(active(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,active(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U41(mark(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,mark(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,mark(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(active(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,active(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,active(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>s(mark(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>s(active(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>plus(mark(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,mark(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(active(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,active(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>and(mark(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,mark(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(active(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,active(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>isNatKind(mark(X))</LHS><RHS>isNatKind(X)</RHS></RULE><RULE><LHS>isNatKind(active(X))</LHS><RHS>isNatKind(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_mark(U11(X1,X2,X3))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_mark(U12(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="2"><LHS>Marked_mark(U13(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><DAG approx="simpl"><CCLIST><SCC num="0"><NODE ref="0"/><NODE ref="1"/><NODE ref="2"/></SCC></CCLIST></DAG></CRITERION><PROPERTY criterion="sterm" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(U11(tt,V1,V2))</LHS><RHS>mark(U12(isNat(V1),V2))</RHS></RULE><RULE><LHS>active(U12(tt,V2))</LHS><RHS>mark(U13(isNat(V2)))</RHS></RULE><RULE><LHS>active(U13(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U21(tt,V1))</LHS><RHS>mark(U22(isNat(V1)))</RHS></RULE><RULE><LHS>active(U22(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U31(tt,N))</LHS><RHS>mark(N)</RHS></RULE><RULE><LHS>active(U41(tt,M,N))</LHS><RHS>mark(s(plus(N,M)))</RHS></RULE><RULE><LHS>active(and(tt,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(isNat(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNat(plus(V1,V2)))</LHS><RHS>mark(U11(and(isNatKind(V1),isNatKind(V2)),V1,V2))</RHS></RULE><RULE><LHS>active(isNat(s(V1)))</LHS><RHS>mark(U21(isNatKind(V1),V1))</RHS></RULE><RULE><LHS>active(isNatKind(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNatKind(plus(V1,V2)))</LHS><RHS>mark(and(isNatKind(V1),isNatKind(V2)))</RHS></RULE><RULE><LHS>active(isNatKind(s(V1)))</LHS><RHS>mark(isNatKind(V1))</RHS></RULE><RULE><LHS>active(plus(N,0))</LHS><RHS>mark(U31(and(isNat(N),isNatKind(N)),N))</RHS></RULE><RULE><LHS>active(plus(N,s(M)))</LHS><RHS>mark(U41(and(and(isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),M,N))</RHS></RULE><RULE><LHS>mark(U11(X1,X2,X3))</LHS><RHS>active(U11(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(tt)</LHS><RHS>active(tt)</RHS></RULE><RULE><LHS>mark(U12(X1,X2))</LHS><RHS>active(U12(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(isNat(X))</LHS><RHS>active(isNat(X))</RHS></RULE><RULE><LHS>mark(U13(X))</LHS><RHS>active(U13(mark(X)))</RHS></RULE><RULE><LHS>mark(U21(X1,X2))</LHS><RHS>active(U21(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U22(X))</LHS><RHS>active(U22(mark(X)))</RHS></RULE><RULE><LHS>mark(U31(X1,X2))</LHS><RHS>active(U31(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U41(X1,X2,X3))</LHS><RHS>active(U41(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(mark(X)))</RHS></RULE><RULE><LHS>mark(plus(X1,X2))</LHS><RHS>active(plus(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(isNatKind(X))</LHS><RHS>active(isNatKind(X))</RHS></RULE><RULE><LHS>U11(mark(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,mark(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,mark(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(active(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,active(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,active(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U12(mark(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,mark(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(active(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,active(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>isNat(mark(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>isNat(active(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>U13(mark(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U13(active(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U21(mark(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,mark(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(active(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,active(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U22(mark(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U22(active(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U31(mark(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,mark(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(active(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,active(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U41(mark(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,mark(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,mark(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(active(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,active(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,active(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>s(mark(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>s(active(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>plus(mark(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,mark(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(active(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,active(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>and(mark(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,mark(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(active(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,active(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>isNatKind(mark(X))</LHS><RHS>isNatKind(X)</RHS></RULE><RULE><LHS>isNatKind(active(X))</LHS><RHS>isNatKind(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_mark(U11(X1,X2,X3))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_mark(U12(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="2"><LHS>Marked_mark(U13(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><PROJECTION><PROJ><SYMBOL><NAME>Marked_mark</NAME></SYMBOL><INT>1</INT></PROJ></PROJECTION><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_mark(U13(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_mark(U12(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="2"><LHS>Marked_mark(U11(X1,X2,X3))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE></DPLIST></STRICTPAIRS><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(U11(tt,V1,V2))</LHS><RHS>mark(U12(isNat(V1),V2))</RHS></RULE><RULE><LHS>active(U12(tt,V2))</LHS><RHS>mark(U13(isNat(V2)))</RHS></RULE><RULE><LHS>active(U13(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U21(tt,V1))</LHS><RHS>mark(U22(isNat(V1)))</RHS></RULE><RULE><LHS>active(U22(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U31(tt,N))</LHS><RHS>mark(N)</RHS></RULE><RULE><LHS>active(U41(tt,M,N))</LHS><RHS>mark(s(plus(N,M)))</RHS></RULE><RULE><LHS>active(and(tt,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(isNat(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNat(plus(V1,V2)))</LHS><RHS>mark(U11(and(isNatKind(V1),isNatKind(V2)),V1,V2))</RHS></RULE><RULE><LHS>active(isNat(s(V1)))</LHS><RHS>mark(U21(isNatKind(V1),V1))</RHS></RULE><RULE><LHS>active(isNatKind(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNatKind(plus(V1,V2)))</LHS><RHS>mark(and(isNatKind(V1),isNatKind(V2)))</RHS></RULE><RULE><LHS>active(isNatKind(s(V1)))</LHS><RHS>mark(isNatKind(V1))</RHS></RULE><RULE><LHS>active(plus(N,0))</LHS><RHS>mark(U31(and(isNat(N),isNatKind(N)),N))</RHS></RULE><RULE><LHS>active(plus(N,s(M)))</LHS><RHS>mark(U41(and(and(isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),M,N))</RHS></RULE><RULE><LHS>mark(U11(X1,X2,X3))</LHS><RHS>active(U11(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(tt)</LHS><RHS>active(tt)</RHS></RULE><RULE><LHS>mark(U12(X1,X2))</LHS><RHS>active(U12(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(isNat(X))</LHS><RHS>active(isNat(X))</RHS></RULE><RULE><LHS>mark(U13(X))</LHS><RHS>active(U13(mark(X)))</RHS></RULE><RULE><LHS>mark(U21(X1,X2))</LHS><RHS>active(U21(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U22(X))</LHS><RHS>active(U22(mark(X)))</RHS></RULE><RULE><LHS>mark(U31(X1,X2))</LHS><RHS>active(U31(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U41(X1,X2,X3))</LHS><RHS>active(U41(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(mark(X)))</RHS></RULE><RULE><LHS>mark(plus(X1,X2))</LHS><RHS>active(plus(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(isNatKind(X))</LHS><RHS>active(isNatKind(X))</RHS></RULE><RULE><LHS>U11(mark(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,mark(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,mark(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(active(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,active(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,active(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U12(mark(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,mark(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(active(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,active(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>isNat(mark(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>isNat(active(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>U13(mark(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U13(active(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U21(mark(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,mark(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(active(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,active(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U22(mark(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U22(active(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U31(mark(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,mark(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(active(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,active(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U41(mark(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,mark(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,mark(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(active(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,active(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,active(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>s(mark(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>s(active(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>plus(mark(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,mark(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(active(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,active(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>and(mark(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,mark(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(active(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,active(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>isNatKind(mark(X))</LHS><RHS>isNatKind(X)</RHS></RULE><RULE><LHS>isNatKind(active(X))</LHS><RHS>isNatKind(X)</RHS></RULE></REWSYS><DPLIST/></DPSYS></SYSTEM><CRITERION><DAG approx="simpl"><CCLIST/></DAG></CRITERION></PROPERTY></PROPERTY></PROPERTY></PROPERTY></PROPERTY></PROPERTY></PROPERTY></PROPERTY></PROPERTY></PROPERTY></PROPERTY></PROPERTY></PROPERTY></PROPERTY></PROPERTY></PROPERTY></PROPERTY></PROPERTY></PROPERTY></PROPERTY></PROPERTY></PROPERTY></PROPERTY></PROPERTY></PROPERTY></PROPERTY></PROPERTY></PROPERTY></PROPERTY></PROPERTY></PROPERTY></PROPERTY></PROPERTY></PROPERTY></PROPERTY></PROPERTY></PROPERTY></PROPERTY></PROPERTY></PROPERTY></PROPERTY></PROPERTY></PROPERTY></PROPERTY></PROPERTY></PROPERTY></PROPERTY></PROPERTY><PROPERTY criterion="sterm" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(U11(tt,V1,V2))</LHS><RHS>mark(U12(isNat(V1),V2))</RHS></RULE><RULE><LHS>active(U12(tt,V2))</LHS><RHS>mark(U13(isNat(V2)))</RHS></RULE><RULE><LHS>active(U13(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U21(tt,V1))</LHS><RHS>mark(U22(isNat(V1)))</RHS></RULE><RULE><LHS>active(U22(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U31(tt,N))</LHS><RHS>mark(N)</RHS></RULE><RULE><LHS>active(U41(tt,M,N))</LHS><RHS>mark(s(plus(N,M)))</RHS></RULE><RULE><LHS>active(and(tt,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(isNat(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNat(plus(V1,V2)))</LHS><RHS>mark(U11(and(isNatKind(V1),isNatKind(V2)),V1,V2))</RHS></RULE><RULE><LHS>active(isNat(s(V1)))</LHS><RHS>mark(U21(isNatKind(V1),V1))</RHS></RULE><RULE><LHS>active(isNatKind(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNatKind(plus(V1,V2)))</LHS><RHS>mark(and(isNatKind(V1),isNatKind(V2)))</RHS></RULE><RULE><LHS>active(isNatKind(s(V1)))</LHS><RHS>mark(isNatKind(V1))</RHS></RULE><RULE><LHS>active(plus(N,0))</LHS><RHS>mark(U31(and(isNat(N),isNatKind(N)),N))</RHS></RULE><RULE><LHS>active(plus(N,s(M)))</LHS><RHS>mark(U41(and(and(isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),M,N))</RHS></RULE><RULE><LHS>mark(U11(X1,X2,X3))</LHS><RHS>active(U11(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(tt)</LHS><RHS>active(tt)</RHS></RULE><RULE><LHS>mark(U12(X1,X2))</LHS><RHS>active(U12(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(isNat(X))</LHS><RHS>active(isNat(X))</RHS></RULE><RULE><LHS>mark(U13(X))</LHS><RHS>active(U13(mark(X)))</RHS></RULE><RULE><LHS>mark(U21(X1,X2))</LHS><RHS>active(U21(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U22(X))</LHS><RHS>active(U22(mark(X)))</RHS></RULE><RULE><LHS>mark(U31(X1,X2))</LHS><RHS>active(U31(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U41(X1,X2,X3))</LHS><RHS>active(U41(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(mark(X)))</RHS></RULE><RULE><LHS>mark(plus(X1,X2))</LHS><RHS>active(plus(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(isNatKind(X))</LHS><RHS>active(isNatKind(X))</RHS></RULE><RULE><LHS>U11(mark(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,mark(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,mark(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(active(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,active(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,active(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U12(mark(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,mark(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(active(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,active(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>isNat(mark(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>isNat(active(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>U13(mark(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U13(active(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U21(mark(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,mark(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(active(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,active(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U22(mark(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U22(active(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U31(mark(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,mark(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(active(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,active(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U41(mark(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,mark(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,mark(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(active(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,active(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,active(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>s(mark(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>s(active(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>plus(mark(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,mark(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(active(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,active(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>and(mark(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,mark(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(active(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,active(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>isNatKind(mark(X))</LHS><RHS>isNatKind(X)</RHS></RULE><RULE><LHS>isNatKind(active(X))</LHS><RHS>isNatKind(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_U11(mark(X1),X2,X3)</LHS><RHS>Marked_U11(X1,X2,X3)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_U11(X1,mark(X2),X3)</LHS><RHS>Marked_U11(X1,X2,X3)</RHS></DPRULE><DPRULE num="2"><LHS>Marked_U11(X1,X2,mark(X3))</LHS><RHS>Marked_U11(X1,X2,X3)</RHS></DPRULE><DPRULE num="3"><LHS>Marked_U11(active(X1),X2,X3)</LHS><RHS>Marked_U11(X1,X2,X3)</RHS></DPRULE><DPRULE num="4"><LHS>Marked_U11(X1,active(X2),X3)</LHS><RHS>Marked_U11(X1,X2,X3)</RHS></DPRULE><DPRULE num="5"><LHS>Marked_U11(X1,X2,active(X3))</LHS><RHS>Marked_U11(X1,X2,X3)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><PROJECTION><PROJ><SYMBOL><NAME>Marked_U11</NAME></SYMBOL><INT>3</INT></PROJ></PROJECTION><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_U11(X1,X2,active(X3))</LHS><RHS>Marked_U11(X1,X2,X3)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_U11(X1,X2,mark(X3))</LHS><RHS>Marked_U11(X1,X2,X3)</RHS></DPRULE></DPLIST></STRICTPAIRS><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(U11(tt,V1,V2))</LHS><RHS>mark(U12(isNat(V1),V2))</RHS></RULE><RULE><LHS>active(U12(tt,V2))</LHS><RHS>mark(U13(isNat(V2)))</RHS></RULE><RULE><LHS>active(U13(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U21(tt,V1))</LHS><RHS>mark(U22(isNat(V1)))</RHS></RULE><RULE><LHS>active(U22(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U31(tt,N))</LHS><RHS>mark(N)</RHS></RULE><RULE><LHS>active(U41(tt,M,N))</LHS><RHS>mark(s(plus(N,M)))</RHS></RULE><RULE><LHS>active(and(tt,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(isNat(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNat(plus(V1,V2)))</LHS><RHS>mark(U11(and(isNatKind(V1),isNatKind(V2)),V1,V2))</RHS></RULE><RULE><LHS>active(isNat(s(V1)))</LHS><RHS>mark(U21(isNatKind(V1),V1))</RHS></RULE><RULE><LHS>active(isNatKind(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNatKind(plus(V1,V2)))</LHS><RHS>mark(and(isNatKind(V1),isNatKind(V2)))</RHS></RULE><RULE><LHS>active(isNatKind(s(V1)))</LHS><RHS>mark(isNatKind(V1))</RHS></RULE><RULE><LHS>active(plus(N,0))</LHS><RHS>mark(U31(and(isNat(N),isNatKind(N)),N))</RHS></RULE><RULE><LHS>active(plus(N,s(M)))</LHS><RHS>mark(U41(and(and(isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),M,N))</RHS></RULE><RULE><LHS>mark(U11(X1,X2,X3))</LHS><RHS>active(U11(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(tt)</LHS><RHS>active(tt)</RHS></RULE><RULE><LHS>mark(U12(X1,X2))</LHS><RHS>active(U12(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(isNat(X))</LHS><RHS>active(isNat(X))</RHS></RULE><RULE><LHS>mark(U13(X))</LHS><RHS>active(U13(mark(X)))</RHS></RULE><RULE><LHS>mark(U21(X1,X2))</LHS><RHS>active(U21(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U22(X))</LHS><RHS>active(U22(mark(X)))</RHS></RULE><RULE><LHS>mark(U31(X1,X2))</LHS><RHS>active(U31(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U41(X1,X2,X3))</LHS><RHS>active(U41(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(mark(X)))</RHS></RULE><RULE><LHS>mark(plus(X1,X2))</LHS><RHS>active(plus(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(isNatKind(X))</LHS><RHS>active(isNatKind(X))</RHS></RULE><RULE><LHS>U11(mark(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,mark(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,mark(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(active(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,active(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,active(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U12(mark(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,mark(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(active(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,active(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>isNat(mark(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>isNat(active(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>U13(mark(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U13(active(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U21(mark(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,mark(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(active(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,active(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U22(mark(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U22(active(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U31(mark(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,mark(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(active(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,active(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U41(mark(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,mark(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,mark(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(active(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,active(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,active(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>s(mark(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>s(active(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>plus(mark(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,mark(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(active(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,active(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>and(mark(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,mark(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(active(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,active(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>isNatKind(mark(X))</LHS><RHS>isNatKind(X)</RHS></RULE><RULE><LHS>isNatKind(active(X))</LHS><RHS>isNatKind(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_U11(X1,active(X2),X3)</LHS><RHS>Marked_U11(X1,X2,X3)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_U11(active(X1),X2,X3)</LHS><RHS>Marked_U11(X1,X2,X3)</RHS></DPRULE><DPRULE num="2"><LHS>Marked_U11(X1,mark(X2),X3)</LHS><RHS>Marked_U11(X1,X2,X3)</RHS></DPRULE><DPRULE num="3"><LHS>Marked_U11(mark(X1),X2,X3)</LHS><RHS>Marked_U11(X1,X2,X3)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><DAG approx="simpl"><CCLIST><SCC num="0"><NODE ref="0"/><NODE ref="1"/><NODE ref="2"/><NODE ref="3"/></SCC></CCLIST></DAG></CRITERION><PROPERTY criterion="sterm" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(U11(tt,V1,V2))</LHS><RHS>mark(U12(isNat(V1),V2))</RHS></RULE><RULE><LHS>active(U12(tt,V2))</LHS><RHS>mark(U13(isNat(V2)))</RHS></RULE><RULE><LHS>active(U13(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U21(tt,V1))</LHS><RHS>mark(U22(isNat(V1)))</RHS></RULE><RULE><LHS>active(U22(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U31(tt,N))</LHS><RHS>mark(N)</RHS></RULE><RULE><LHS>active(U41(tt,M,N))</LHS><RHS>mark(s(plus(N,M)))</RHS></RULE><RULE><LHS>active(and(tt,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(isNat(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNat(plus(V1,V2)))</LHS><RHS>mark(U11(and(isNatKind(V1),isNatKind(V2)),V1,V2))</RHS></RULE><RULE><LHS>active(isNat(s(V1)))</LHS><RHS>mark(U21(isNatKind(V1),V1))</RHS></RULE><RULE><LHS>active(isNatKind(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNatKind(plus(V1,V2)))</LHS><RHS>mark(and(isNatKind(V1),isNatKind(V2)))</RHS></RULE><RULE><LHS>active(isNatKind(s(V1)))</LHS><RHS>mark(isNatKind(V1))</RHS></RULE><RULE><LHS>active(plus(N,0))</LHS><RHS>mark(U31(and(isNat(N),isNatKind(N)),N))</RHS></RULE><RULE><LHS>active(plus(N,s(M)))</LHS><RHS>mark(U41(and(and(isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),M,N))</RHS></RULE><RULE><LHS>mark(U11(X1,X2,X3))</LHS><RHS>active(U11(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(tt)</LHS><RHS>active(tt)</RHS></RULE><RULE><LHS>mark(U12(X1,X2))</LHS><RHS>active(U12(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(isNat(X))</LHS><RHS>active(isNat(X))</RHS></RULE><RULE><LHS>mark(U13(X))</LHS><RHS>active(U13(mark(X)))</RHS></RULE><RULE><LHS>mark(U21(X1,X2))</LHS><RHS>active(U21(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U22(X))</LHS><RHS>active(U22(mark(X)))</RHS></RULE><RULE><LHS>mark(U31(X1,X2))</LHS><RHS>active(U31(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U41(X1,X2,X3))</LHS><RHS>active(U41(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(mark(X)))</RHS></RULE><RULE><LHS>mark(plus(X1,X2))</LHS><RHS>active(plus(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(isNatKind(X))</LHS><RHS>active(isNatKind(X))</RHS></RULE><RULE><LHS>U11(mark(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,mark(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,mark(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(active(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,active(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,active(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U12(mark(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,mark(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(active(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,active(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>isNat(mark(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>isNat(active(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>U13(mark(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U13(active(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U21(mark(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,mark(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(active(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,active(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U22(mark(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U22(active(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U31(mark(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,mark(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(active(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,active(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U41(mark(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,mark(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,mark(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(active(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,active(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,active(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>s(mark(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>s(active(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>plus(mark(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,mark(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(active(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,active(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>and(mark(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,mark(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(active(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,active(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>isNatKind(mark(X))</LHS><RHS>isNatKind(X)</RHS></RULE><RULE><LHS>isNatKind(active(X))</LHS><RHS>isNatKind(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_U11(X1,active(X2),X3)</LHS><RHS>Marked_U11(X1,X2,X3)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_U11(active(X1),X2,X3)</LHS><RHS>Marked_U11(X1,X2,X3)</RHS></DPRULE><DPRULE num="2"><LHS>Marked_U11(X1,mark(X2),X3)</LHS><RHS>Marked_U11(X1,X2,X3)</RHS></DPRULE><DPRULE num="3"><LHS>Marked_U11(mark(X1),X2,X3)</LHS><RHS>Marked_U11(X1,X2,X3)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><PROJECTION><PROJ><SYMBOL><NAME>Marked_U11</NAME></SYMBOL><INT>2</INT></PROJ></PROJECTION><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_U11(X1,mark(X2),X3)</LHS><RHS>Marked_U11(X1,X2,X3)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_U11(X1,active(X2),X3)</LHS><RHS>Marked_U11(X1,X2,X3)</RHS></DPRULE></DPLIST></STRICTPAIRS><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(U11(tt,V1,V2))</LHS><RHS>mark(U12(isNat(V1),V2))</RHS></RULE><RULE><LHS>active(U12(tt,V2))</LHS><RHS>mark(U13(isNat(V2)))</RHS></RULE><RULE><LHS>active(U13(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U21(tt,V1))</LHS><RHS>mark(U22(isNat(V1)))</RHS></RULE><RULE><LHS>active(U22(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U31(tt,N))</LHS><RHS>mark(N)</RHS></RULE><RULE><LHS>active(U41(tt,M,N))</LHS><RHS>mark(s(plus(N,M)))</RHS></RULE><RULE><LHS>active(and(tt,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(isNat(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNat(plus(V1,V2)))</LHS><RHS>mark(U11(and(isNatKind(V1),isNatKind(V2)),V1,V2))</RHS></RULE><RULE><LHS>active(isNat(s(V1)))</LHS><RHS>mark(U21(isNatKind(V1),V1))</RHS></RULE><RULE><LHS>active(isNatKind(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNatKind(plus(V1,V2)))</LHS><RHS>mark(and(isNatKind(V1),isNatKind(V2)))</RHS></RULE><RULE><LHS>active(isNatKind(s(V1)))</LHS><RHS>mark(isNatKind(V1))</RHS></RULE><RULE><LHS>active(plus(N,0))</LHS><RHS>mark(U31(and(isNat(N),isNatKind(N)),N))</RHS></RULE><RULE><LHS>active(plus(N,s(M)))</LHS><RHS>mark(U41(and(and(isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),M,N))</RHS></RULE><RULE><LHS>mark(U11(X1,X2,X3))</LHS><RHS>active(U11(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(tt)</LHS><RHS>active(tt)</RHS></RULE><RULE><LHS>mark(U12(X1,X2))</LHS><RHS>active(U12(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(isNat(X))</LHS><RHS>active(isNat(X))</RHS></RULE><RULE><LHS>mark(U13(X))</LHS><RHS>active(U13(mark(X)))</RHS></RULE><RULE><LHS>mark(U21(X1,X2))</LHS><RHS>active(U21(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U22(X))</LHS><RHS>active(U22(mark(X)))</RHS></RULE><RULE><LHS>mark(U31(X1,X2))</LHS><RHS>active(U31(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U41(X1,X2,X3))</LHS><RHS>active(U41(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(mark(X)))</RHS></RULE><RULE><LHS>mark(plus(X1,X2))</LHS><RHS>active(plus(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(isNatKind(X))</LHS><RHS>active(isNatKind(X))</RHS></RULE><RULE><LHS>U11(mark(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,mark(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,mark(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(active(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,active(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,active(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U12(mark(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,mark(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(active(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,active(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>isNat(mark(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>isNat(active(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>U13(mark(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U13(active(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U21(mark(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,mark(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(active(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,active(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U22(mark(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U22(active(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U31(mark(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,mark(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(active(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,active(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U41(mark(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,mark(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,mark(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(active(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,active(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,active(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>s(mark(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>s(active(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>plus(mark(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,mark(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(active(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,active(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>and(mark(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,mark(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(active(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,active(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>isNatKind(mark(X))</LHS><RHS>isNatKind(X)</RHS></RULE><RULE><LHS>isNatKind(active(X))</LHS><RHS>isNatKind(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_U11(mark(X1),X2,X3)</LHS><RHS>Marked_U11(X1,X2,X3)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_U11(active(X1),X2,X3)</LHS><RHS>Marked_U11(X1,X2,X3)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><DAG approx="simpl"><CCLIST><SCC num="0"><NODE ref="0"/><NODE ref="1"/></SCC></CCLIST></DAG></CRITERION><PROPERTY criterion="sterm" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(U11(tt,V1,V2))</LHS><RHS>mark(U12(isNat(V1),V2))</RHS></RULE><RULE><LHS>active(U12(tt,V2))</LHS><RHS>mark(U13(isNat(V2)))</RHS></RULE><RULE><LHS>active(U13(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U21(tt,V1))</LHS><RHS>mark(U22(isNat(V1)))</RHS></RULE><RULE><LHS>active(U22(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U31(tt,N))</LHS><RHS>mark(N)</RHS></RULE><RULE><LHS>active(U41(tt,M,N))</LHS><RHS>mark(s(plus(N,M)))</RHS></RULE><RULE><LHS>active(and(tt,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(isNat(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNat(plus(V1,V2)))</LHS><RHS>mark(U11(and(isNatKind(V1),isNatKind(V2)),V1,V2))</RHS></RULE><RULE><LHS>active(isNat(s(V1)))</LHS><RHS>mark(U21(isNatKind(V1),V1))</RHS></RULE><RULE><LHS>active(isNatKind(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNatKind(plus(V1,V2)))</LHS><RHS>mark(and(isNatKind(V1),isNatKind(V2)))</RHS></RULE><RULE><LHS>active(isNatKind(s(V1)))</LHS><RHS>mark(isNatKind(V1))</RHS></RULE><RULE><LHS>active(plus(N,0))</LHS><RHS>mark(U31(and(isNat(N),isNatKind(N)),N))</RHS></RULE><RULE><LHS>active(plus(N,s(M)))</LHS><RHS>mark(U41(and(and(isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),M,N))</RHS></RULE><RULE><LHS>mark(U11(X1,X2,X3))</LHS><RHS>active(U11(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(tt)</LHS><RHS>active(tt)</RHS></RULE><RULE><LHS>mark(U12(X1,X2))</LHS><RHS>active(U12(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(isNat(X))</LHS><RHS>active(isNat(X))</RHS></RULE><RULE><LHS>mark(U13(X))</LHS><RHS>active(U13(mark(X)))</RHS></RULE><RULE><LHS>mark(U21(X1,X2))</LHS><RHS>active(U21(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U22(X))</LHS><RHS>active(U22(mark(X)))</RHS></RULE><RULE><LHS>mark(U31(X1,X2))</LHS><RHS>active(U31(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U41(X1,X2,X3))</LHS><RHS>active(U41(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(mark(X)))</RHS></RULE><RULE><LHS>mark(plus(X1,X2))</LHS><RHS>active(plus(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(isNatKind(X))</LHS><RHS>active(isNatKind(X))</RHS></RULE><RULE><LHS>U11(mark(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,mark(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,mark(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(active(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,active(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,active(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U12(mark(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,mark(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(active(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,active(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>isNat(mark(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>isNat(active(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>U13(mark(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U13(active(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U21(mark(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,mark(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(active(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,active(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U22(mark(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U22(active(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U31(mark(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,mark(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(active(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,active(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U41(mark(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,mark(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,mark(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(active(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,active(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,active(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>s(mark(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>s(active(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>plus(mark(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,mark(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(active(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,active(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>and(mark(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,mark(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(active(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,active(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>isNatKind(mark(X))</LHS><RHS>isNatKind(X)</RHS></RULE><RULE><LHS>isNatKind(active(X))</LHS><RHS>isNatKind(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_U11(mark(X1),X2,X3)</LHS><RHS>Marked_U11(X1,X2,X3)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_U11(active(X1),X2,X3)</LHS><RHS>Marked_U11(X1,X2,X3)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><PROJECTION><PROJ><SYMBOL><NAME>Marked_U11</NAME></SYMBOL><INT>1</INT></PROJ></PROJECTION><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_U11(active(X1),X2,X3)</LHS><RHS>Marked_U11(X1,X2,X3)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_U11(mark(X1),X2,X3)</LHS><RHS>Marked_U11(X1,X2,X3)</RHS></DPRULE></DPLIST></STRICTPAIRS><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(U11(tt,V1,V2))</LHS><RHS>mark(U12(isNat(V1),V2))</RHS></RULE><RULE><LHS>active(U12(tt,V2))</LHS><RHS>mark(U13(isNat(V2)))</RHS></RULE><RULE><LHS>active(U13(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U21(tt,V1))</LHS><RHS>mark(U22(isNat(V1)))</RHS></RULE><RULE><LHS>active(U22(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U31(tt,N))</LHS><RHS>mark(N)</RHS></RULE><RULE><LHS>active(U41(tt,M,N))</LHS><RHS>mark(s(plus(N,M)))</RHS></RULE><RULE><LHS>active(and(tt,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(isNat(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNat(plus(V1,V2)))</LHS><RHS>mark(U11(and(isNatKind(V1),isNatKind(V2)),V1,V2))</RHS></RULE><RULE><LHS>active(isNat(s(V1)))</LHS><RHS>mark(U21(isNatKind(V1),V1))</RHS></RULE><RULE><LHS>active(isNatKind(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNatKind(plus(V1,V2)))</LHS><RHS>mark(and(isNatKind(V1),isNatKind(V2)))</RHS></RULE><RULE><LHS>active(isNatKind(s(V1)))</LHS><RHS>mark(isNatKind(V1))</RHS></RULE><RULE><LHS>active(plus(N,0))</LHS><RHS>mark(U31(and(isNat(N),isNatKind(N)),N))</RHS></RULE><RULE><LHS>active(plus(N,s(M)))</LHS><RHS>mark(U41(and(and(isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),M,N))</RHS></RULE><RULE><LHS>mark(U11(X1,X2,X3))</LHS><RHS>active(U11(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(tt)</LHS><RHS>active(tt)</RHS></RULE><RULE><LHS>mark(U12(X1,X2))</LHS><RHS>active(U12(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(isNat(X))</LHS><RHS>active(isNat(X))</RHS></RULE><RULE><LHS>mark(U13(X))</LHS><RHS>active(U13(mark(X)))</RHS></RULE><RULE><LHS>mark(U21(X1,X2))</LHS><RHS>active(U21(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U22(X))</LHS><RHS>active(U22(mark(X)))</RHS></RULE><RULE><LHS>mark(U31(X1,X2))</LHS><RHS>active(U31(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U41(X1,X2,X3))</LHS><RHS>active(U41(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(mark(X)))</RHS></RULE><RULE><LHS>mark(plus(X1,X2))</LHS><RHS>active(plus(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(isNatKind(X))</LHS><RHS>active(isNatKind(X))</RHS></RULE><RULE><LHS>U11(mark(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,mark(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,mark(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(active(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,active(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,active(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U12(mark(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,mark(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(active(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,active(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>isNat(mark(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>isNat(active(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>U13(mark(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U13(active(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U21(mark(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,mark(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(active(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,active(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U22(mark(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U22(active(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U31(mark(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,mark(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(active(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,active(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U41(mark(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,mark(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,mark(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(active(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,active(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,active(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>s(mark(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>s(active(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>plus(mark(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,mark(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(active(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,active(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>and(mark(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,mark(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(active(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,active(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>isNatKind(mark(X))</LHS><RHS>isNatKind(X)</RHS></RULE><RULE><LHS>isNatKind(active(X))</LHS><RHS>isNatKind(X)</RHS></RULE></REWSYS><DPLIST/></DPSYS></SYSTEM><CRITERION><DAG approx="simpl"><CCLIST/></DAG></CRITERION></PROPERTY></PROPERTY></PROPERTY></PROPERTY></PROPERTY></PROPERTY><PROPERTY criterion="sterm" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(U11(tt,V1,V2))</LHS><RHS>mark(U12(isNat(V1),V2))</RHS></RULE><RULE><LHS>active(U12(tt,V2))</LHS><RHS>mark(U13(isNat(V2)))</RHS></RULE><RULE><LHS>active(U13(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U21(tt,V1))</LHS><RHS>mark(U22(isNat(V1)))</RHS></RULE><RULE><LHS>active(U22(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U31(tt,N))</LHS><RHS>mark(N)</RHS></RULE><RULE><LHS>active(U41(tt,M,N))</LHS><RHS>mark(s(plus(N,M)))</RHS></RULE><RULE><LHS>active(and(tt,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(isNat(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNat(plus(V1,V2)))</LHS><RHS>mark(U11(and(isNatKind(V1),isNatKind(V2)),V1,V2))</RHS></RULE><RULE><LHS>active(isNat(s(V1)))</LHS><RHS>mark(U21(isNatKind(V1),V1))</RHS></RULE><RULE><LHS>active(isNatKind(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNatKind(plus(V1,V2)))</LHS><RHS>mark(and(isNatKind(V1),isNatKind(V2)))</RHS></RULE><RULE><LHS>active(isNatKind(s(V1)))</LHS><RHS>mark(isNatKind(V1))</RHS></RULE><RULE><LHS>active(plus(N,0))</LHS><RHS>mark(U31(and(isNat(N),isNatKind(N)),N))</RHS></RULE><RULE><LHS>active(plus(N,s(M)))</LHS><RHS>mark(U41(and(and(isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),M,N))</RHS></RULE><RULE><LHS>mark(U11(X1,X2,X3))</LHS><RHS>active(U11(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(tt)</LHS><RHS>active(tt)</RHS></RULE><RULE><LHS>mark(U12(X1,X2))</LHS><RHS>active(U12(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(isNat(X))</LHS><RHS>active(isNat(X))</RHS></RULE><RULE><LHS>mark(U13(X))</LHS><RHS>active(U13(mark(X)))</RHS></RULE><RULE><LHS>mark(U21(X1,X2))</LHS><RHS>active(U21(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U22(X))</LHS><RHS>active(U22(mark(X)))</RHS></RULE><RULE><LHS>mark(U31(X1,X2))</LHS><RHS>active(U31(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U41(X1,X2,X3))</LHS><RHS>active(U41(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(mark(X)))</RHS></RULE><RULE><LHS>mark(plus(X1,X2))</LHS><RHS>active(plus(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(isNatKind(X))</LHS><RHS>active(isNatKind(X))</RHS></RULE><RULE><LHS>U11(mark(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,mark(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,mark(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(active(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,active(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,active(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U12(mark(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,mark(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(active(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,active(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>isNat(mark(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>isNat(active(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>U13(mark(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U13(active(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U21(mark(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,mark(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(active(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,active(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U22(mark(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U22(active(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U31(mark(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,mark(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(active(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,active(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U41(mark(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,mark(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,mark(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(active(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,active(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,active(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>s(mark(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>s(active(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>plus(mark(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,mark(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(active(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,active(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>and(mark(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,mark(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(active(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,active(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>isNatKind(mark(X))</LHS><RHS>isNatKind(X)</RHS></RULE><RULE><LHS>isNatKind(active(X))</LHS><RHS>isNatKind(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_U12(mark(X1),X2)</LHS><RHS>Marked_U12(X1,X2)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_U12(X1,mark(X2))</LHS><RHS>Marked_U12(X1,X2)</RHS></DPRULE><DPRULE num="2"><LHS>Marked_U12(active(X1),X2)</LHS><RHS>Marked_U12(X1,X2)</RHS></DPRULE><DPRULE num="3"><LHS>Marked_U12(X1,active(X2))</LHS><RHS>Marked_U12(X1,X2)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><PROJECTION><PROJ><SYMBOL><NAME>Marked_U12</NAME></SYMBOL><INT>2</INT></PROJ></PROJECTION><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_U12(X1,active(X2))</LHS><RHS>Marked_U12(X1,X2)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_U12(X1,mark(X2))</LHS><RHS>Marked_U12(X1,X2)</RHS></DPRULE></DPLIST></STRICTPAIRS><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(U11(tt,V1,V2))</LHS><RHS>mark(U12(isNat(V1),V2))</RHS></RULE><RULE><LHS>active(U12(tt,V2))</LHS><RHS>mark(U13(isNat(V2)))</RHS></RULE><RULE><LHS>active(U13(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U21(tt,V1))</LHS><RHS>mark(U22(isNat(V1)))</RHS></RULE><RULE><LHS>active(U22(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U31(tt,N))</LHS><RHS>mark(N)</RHS></RULE><RULE><LHS>active(U41(tt,M,N))</LHS><RHS>mark(s(plus(N,M)))</RHS></RULE><RULE><LHS>active(and(tt,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(isNat(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNat(plus(V1,V2)))</LHS><RHS>mark(U11(and(isNatKind(V1),isNatKind(V2)),V1,V2))</RHS></RULE><RULE><LHS>active(isNat(s(V1)))</LHS><RHS>mark(U21(isNatKind(V1),V1))</RHS></RULE><RULE><LHS>active(isNatKind(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNatKind(plus(V1,V2)))</LHS><RHS>mark(and(isNatKind(V1),isNatKind(V2)))</RHS></RULE><RULE><LHS>active(isNatKind(s(V1)))</LHS><RHS>mark(isNatKind(V1))</RHS></RULE><RULE><LHS>active(plus(N,0))</LHS><RHS>mark(U31(and(isNat(N),isNatKind(N)),N))</RHS></RULE><RULE><LHS>active(plus(N,s(M)))</LHS><RHS>mark(U41(and(and(isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),M,N))</RHS></RULE><RULE><LHS>mark(U11(X1,X2,X3))</LHS><RHS>active(U11(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(tt)</LHS><RHS>active(tt)</RHS></RULE><RULE><LHS>mark(U12(X1,X2))</LHS><RHS>active(U12(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(isNat(X))</LHS><RHS>active(isNat(X))</RHS></RULE><RULE><LHS>mark(U13(X))</LHS><RHS>active(U13(mark(X)))</RHS></RULE><RULE><LHS>mark(U21(X1,X2))</LHS><RHS>active(U21(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U22(X))</LHS><RHS>active(U22(mark(X)))</RHS></RULE><RULE><LHS>mark(U31(X1,X2))</LHS><RHS>active(U31(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U41(X1,X2,X3))</LHS><RHS>active(U41(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(mark(X)))</RHS></RULE><RULE><LHS>mark(plus(X1,X2))</LHS><RHS>active(plus(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(isNatKind(X))</LHS><RHS>active(isNatKind(X))</RHS></RULE><RULE><LHS>U11(mark(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,mark(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,mark(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(active(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,active(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,active(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U12(mark(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,mark(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(active(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,active(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>isNat(mark(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>isNat(active(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>U13(mark(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U13(active(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U21(mark(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,mark(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(active(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,active(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U22(mark(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U22(active(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U31(mark(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,mark(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(active(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,active(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U41(mark(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,mark(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,mark(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(active(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,active(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,active(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>s(mark(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>s(active(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>plus(mark(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,mark(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(active(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,active(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>and(mark(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,mark(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(active(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,active(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>isNatKind(mark(X))</LHS><RHS>isNatKind(X)</RHS></RULE><RULE><LHS>isNatKind(active(X))</LHS><RHS>isNatKind(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_U12(active(X1),X2)</LHS><RHS>Marked_U12(X1,X2)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_U12(mark(X1),X2)</LHS><RHS>Marked_U12(X1,X2)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><DAG approx="simpl"><CCLIST><SCC num="0"><NODE ref="0"/><NODE ref="1"/></SCC></CCLIST></DAG></CRITERION><PROPERTY criterion="sterm" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(U11(tt,V1,V2))</LHS><RHS>mark(U12(isNat(V1),V2))</RHS></RULE><RULE><LHS>active(U12(tt,V2))</LHS><RHS>mark(U13(isNat(V2)))</RHS></RULE><RULE><LHS>active(U13(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U21(tt,V1))</LHS><RHS>mark(U22(isNat(V1)))</RHS></RULE><RULE><LHS>active(U22(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U31(tt,N))</LHS><RHS>mark(N)</RHS></RULE><RULE><LHS>active(U41(tt,M,N))</LHS><RHS>mark(s(plus(N,M)))</RHS></RULE><RULE><LHS>active(and(tt,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(isNat(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNat(plus(V1,V2)))</LHS><RHS>mark(U11(and(isNatKind(V1),isNatKind(V2)),V1,V2))</RHS></RULE><RULE><LHS>active(isNat(s(V1)))</LHS><RHS>mark(U21(isNatKind(V1),V1))</RHS></RULE><RULE><LHS>active(isNatKind(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNatKind(plus(V1,V2)))</LHS><RHS>mark(and(isNatKind(V1),isNatKind(V2)))</RHS></RULE><RULE><LHS>active(isNatKind(s(V1)))</LHS><RHS>mark(isNatKind(V1))</RHS></RULE><RULE><LHS>active(plus(N,0))</LHS><RHS>mark(U31(and(isNat(N),isNatKind(N)),N))</RHS></RULE><RULE><LHS>active(plus(N,s(M)))</LHS><RHS>mark(U41(and(and(isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),M,N))</RHS></RULE><RULE><LHS>mark(U11(X1,X2,X3))</LHS><RHS>active(U11(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(tt)</LHS><RHS>active(tt)</RHS></RULE><RULE><LHS>mark(U12(X1,X2))</LHS><RHS>active(U12(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(isNat(X))</LHS><RHS>active(isNat(X))</RHS></RULE><RULE><LHS>mark(U13(X))</LHS><RHS>active(U13(mark(X)))</RHS></RULE><RULE><LHS>mark(U21(X1,X2))</LHS><RHS>active(U21(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U22(X))</LHS><RHS>active(U22(mark(X)))</RHS></RULE><RULE><LHS>mark(U31(X1,X2))</LHS><RHS>active(U31(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U41(X1,X2,X3))</LHS><RHS>active(U41(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(mark(X)))</RHS></RULE><RULE><LHS>mark(plus(X1,X2))</LHS><RHS>active(plus(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(isNatKind(X))</LHS><RHS>active(isNatKind(X))</RHS></RULE><RULE><LHS>U11(mark(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,mark(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,mark(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(active(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,active(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,active(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U12(mark(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,mark(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(active(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,active(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>isNat(mark(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>isNat(active(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>U13(mark(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U13(active(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U21(mark(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,mark(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(active(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,active(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U22(mark(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U22(active(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U31(mark(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,mark(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(active(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,active(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U41(mark(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,mark(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,mark(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(active(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,active(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,active(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>s(mark(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>s(active(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>plus(mark(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,mark(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(active(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,active(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>and(mark(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,mark(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(active(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,active(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>isNatKind(mark(X))</LHS><RHS>isNatKind(X)</RHS></RULE><RULE><LHS>isNatKind(active(X))</LHS><RHS>isNatKind(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_U12(active(X1),X2)</LHS><RHS>Marked_U12(X1,X2)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_U12(mark(X1),X2)</LHS><RHS>Marked_U12(X1,X2)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><PROJECTION><PROJ><SYMBOL><NAME>Marked_U12</NAME></SYMBOL><INT>1</INT></PROJ></PROJECTION><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_U12(mark(X1),X2)</LHS><RHS>Marked_U12(X1,X2)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_U12(active(X1),X2)</LHS><RHS>Marked_U12(X1,X2)</RHS></DPRULE></DPLIST></STRICTPAIRS><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(U11(tt,V1,V2))</LHS><RHS>mark(U12(isNat(V1),V2))</RHS></RULE><RULE><LHS>active(U12(tt,V2))</LHS><RHS>mark(U13(isNat(V2)))</RHS></RULE><RULE><LHS>active(U13(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U21(tt,V1))</LHS><RHS>mark(U22(isNat(V1)))</RHS></RULE><RULE><LHS>active(U22(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U31(tt,N))</LHS><RHS>mark(N)</RHS></RULE><RULE><LHS>active(U41(tt,M,N))</LHS><RHS>mark(s(plus(N,M)))</RHS></RULE><RULE><LHS>active(and(tt,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(isNat(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNat(plus(V1,V2)))</LHS><RHS>mark(U11(and(isNatKind(V1),isNatKind(V2)),V1,V2))</RHS></RULE><RULE><LHS>active(isNat(s(V1)))</LHS><RHS>mark(U21(isNatKind(V1),V1))</RHS></RULE><RULE><LHS>active(isNatKind(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNatKind(plus(V1,V2)))</LHS><RHS>mark(and(isNatKind(V1),isNatKind(V2)))</RHS></RULE><RULE><LHS>active(isNatKind(s(V1)))</LHS><RHS>mark(isNatKind(V1))</RHS></RULE><RULE><LHS>active(plus(N,0))</LHS><RHS>mark(U31(and(isNat(N),isNatKind(N)),N))</RHS></RULE><RULE><LHS>active(plus(N,s(M)))</LHS><RHS>mark(U41(and(and(isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),M,N))</RHS></RULE><RULE><LHS>mark(U11(X1,X2,X3))</LHS><RHS>active(U11(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(tt)</LHS><RHS>active(tt)</RHS></RULE><RULE><LHS>mark(U12(X1,X2))</LHS><RHS>active(U12(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(isNat(X))</LHS><RHS>active(isNat(X))</RHS></RULE><RULE><LHS>mark(U13(X))</LHS><RHS>active(U13(mark(X)))</RHS></RULE><RULE><LHS>mark(U21(X1,X2))</LHS><RHS>active(U21(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U22(X))</LHS><RHS>active(U22(mark(X)))</RHS></RULE><RULE><LHS>mark(U31(X1,X2))</LHS><RHS>active(U31(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U41(X1,X2,X3))</LHS><RHS>active(U41(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(mark(X)))</RHS></RULE><RULE><LHS>mark(plus(X1,X2))</LHS><RHS>active(plus(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(isNatKind(X))</LHS><RHS>active(isNatKind(X))</RHS></RULE><RULE><LHS>U11(mark(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,mark(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,mark(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(active(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,active(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,active(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U12(mark(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,mark(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(active(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,active(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>isNat(mark(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>isNat(active(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>U13(mark(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U13(active(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U21(mark(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,mark(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(active(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,active(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U22(mark(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U22(active(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U31(mark(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,mark(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(active(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,active(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U41(mark(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,mark(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,mark(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(active(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,active(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,active(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>s(mark(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>s(active(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>plus(mark(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,mark(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(active(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,active(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>and(mark(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,mark(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(active(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,active(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>isNatKind(mark(X))</LHS><RHS>isNatKind(X)</RHS></RULE><RULE><LHS>isNatKind(active(X))</LHS><RHS>isNatKind(X)</RHS></RULE></REWSYS><DPLIST/></DPSYS></SYSTEM><CRITERION><DAG approx="simpl"><CCLIST/></DAG></CRITERION></PROPERTY></PROPERTY></PROPERTY></PROPERTY><PROPERTY criterion="sterm" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(U11(tt,V1,V2))</LHS><RHS>mark(U12(isNat(V1),V2))</RHS></RULE><RULE><LHS>active(U12(tt,V2))</LHS><RHS>mark(U13(isNat(V2)))</RHS></RULE><RULE><LHS>active(U13(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U21(tt,V1))</LHS><RHS>mark(U22(isNat(V1)))</RHS></RULE><RULE><LHS>active(U22(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U31(tt,N))</LHS><RHS>mark(N)</RHS></RULE><RULE><LHS>active(U41(tt,M,N))</LHS><RHS>mark(s(plus(N,M)))</RHS></RULE><RULE><LHS>active(and(tt,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(isNat(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNat(plus(V1,V2)))</LHS><RHS>mark(U11(and(isNatKind(V1),isNatKind(V2)),V1,V2))</RHS></RULE><RULE><LHS>active(isNat(s(V1)))</LHS><RHS>mark(U21(isNatKind(V1),V1))</RHS></RULE><RULE><LHS>active(isNatKind(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNatKind(plus(V1,V2)))</LHS><RHS>mark(and(isNatKind(V1),isNatKind(V2)))</RHS></RULE><RULE><LHS>active(isNatKind(s(V1)))</LHS><RHS>mark(isNatKind(V1))</RHS></RULE><RULE><LHS>active(plus(N,0))</LHS><RHS>mark(U31(and(isNat(N),isNatKind(N)),N))</RHS></RULE><RULE><LHS>active(plus(N,s(M)))</LHS><RHS>mark(U41(and(and(isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),M,N))</RHS></RULE><RULE><LHS>mark(U11(X1,X2,X3))</LHS><RHS>active(U11(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(tt)</LHS><RHS>active(tt)</RHS></RULE><RULE><LHS>mark(U12(X1,X2))</LHS><RHS>active(U12(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(isNat(X))</LHS><RHS>active(isNat(X))</RHS></RULE><RULE><LHS>mark(U13(X))</LHS><RHS>active(U13(mark(X)))</RHS></RULE><RULE><LHS>mark(U21(X1,X2))</LHS><RHS>active(U21(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U22(X))</LHS><RHS>active(U22(mark(X)))</RHS></RULE><RULE><LHS>mark(U31(X1,X2))</LHS><RHS>active(U31(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U41(X1,X2,X3))</LHS><RHS>active(U41(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(mark(X)))</RHS></RULE><RULE><LHS>mark(plus(X1,X2))</LHS><RHS>active(plus(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(isNatKind(X))</LHS><RHS>active(isNatKind(X))</RHS></RULE><RULE><LHS>U11(mark(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,mark(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,mark(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(active(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,active(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,active(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U12(mark(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,mark(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(active(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,active(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>isNat(mark(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>isNat(active(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>U13(mark(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U13(active(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U21(mark(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,mark(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(active(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,active(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U22(mark(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U22(active(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U31(mark(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,mark(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(active(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,active(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U41(mark(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,mark(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,mark(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(active(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,active(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,active(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>s(mark(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>s(active(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>plus(mark(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,mark(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(active(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,active(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>and(mark(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,mark(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(active(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,active(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>isNatKind(mark(X))</LHS><RHS>isNatKind(X)</RHS></RULE><RULE><LHS>isNatKind(active(X))</LHS><RHS>isNatKind(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_isNat(mark(X))</LHS><RHS>Marked_isNat(X)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_isNat(active(X))</LHS><RHS>Marked_isNat(X)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><PROJECTION><PROJ><SYMBOL><NAME>Marked_isNat</NAME></SYMBOL><INT>1</INT></PROJ></PROJECTION><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_isNat(active(X))</LHS><RHS>Marked_isNat(X)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_isNat(mark(X))</LHS><RHS>Marked_isNat(X)</RHS></DPRULE></DPLIST></STRICTPAIRS><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(U11(tt,V1,V2))</LHS><RHS>mark(U12(isNat(V1),V2))</RHS></RULE><RULE><LHS>active(U12(tt,V2))</LHS><RHS>mark(U13(isNat(V2)))</RHS></RULE><RULE><LHS>active(U13(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U21(tt,V1))</LHS><RHS>mark(U22(isNat(V1)))</RHS></RULE><RULE><LHS>active(U22(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U31(tt,N))</LHS><RHS>mark(N)</RHS></RULE><RULE><LHS>active(U41(tt,M,N))</LHS><RHS>mark(s(plus(N,M)))</RHS></RULE><RULE><LHS>active(and(tt,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(isNat(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNat(plus(V1,V2)))</LHS><RHS>mark(U11(and(isNatKind(V1),isNatKind(V2)),V1,V2))</RHS></RULE><RULE><LHS>active(isNat(s(V1)))</LHS><RHS>mark(U21(isNatKind(V1),V1))</RHS></RULE><RULE><LHS>active(isNatKind(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNatKind(plus(V1,V2)))</LHS><RHS>mark(and(isNatKind(V1),isNatKind(V2)))</RHS></RULE><RULE><LHS>active(isNatKind(s(V1)))</LHS><RHS>mark(isNatKind(V1))</RHS></RULE><RULE><LHS>active(plus(N,0))</LHS><RHS>mark(U31(and(isNat(N),isNatKind(N)),N))</RHS></RULE><RULE><LHS>active(plus(N,s(M)))</LHS><RHS>mark(U41(and(and(isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),M,N))</RHS></RULE><RULE><LHS>mark(U11(X1,X2,X3))</LHS><RHS>active(U11(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(tt)</LHS><RHS>active(tt)</RHS></RULE><RULE><LHS>mark(U12(X1,X2))</LHS><RHS>active(U12(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(isNat(X))</LHS><RHS>active(isNat(X))</RHS></RULE><RULE><LHS>mark(U13(X))</LHS><RHS>active(U13(mark(X)))</RHS></RULE><RULE><LHS>mark(U21(X1,X2))</LHS><RHS>active(U21(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U22(X))</LHS><RHS>active(U22(mark(X)))</RHS></RULE><RULE><LHS>mark(U31(X1,X2))</LHS><RHS>active(U31(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U41(X1,X2,X3))</LHS><RHS>active(U41(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(mark(X)))</RHS></RULE><RULE><LHS>mark(plus(X1,X2))</LHS><RHS>active(plus(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(isNatKind(X))</LHS><RHS>active(isNatKind(X))</RHS></RULE><RULE><LHS>U11(mark(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,mark(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,mark(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(active(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,active(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,active(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U12(mark(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,mark(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(active(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,active(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>isNat(mark(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>isNat(active(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>U13(mark(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U13(active(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U21(mark(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,mark(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(active(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,active(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U22(mark(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U22(active(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U31(mark(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,mark(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(active(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,active(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U41(mark(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,mark(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,mark(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(active(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,active(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,active(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>s(mark(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>s(active(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>plus(mark(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,mark(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(active(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,active(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>and(mark(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,mark(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(active(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,active(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>isNatKind(mark(X))</LHS><RHS>isNatKind(X)</RHS></RULE><RULE><LHS>isNatKind(active(X))</LHS><RHS>isNatKind(X)</RHS></RULE></REWSYS><DPLIST/></DPSYS></SYSTEM><CRITERION><DAG approx="simpl"><CCLIST/></DAG></CRITERION></PROPERTY></PROPERTY><PROPERTY criterion="sterm" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(U11(tt,V1,V2))</LHS><RHS>mark(U12(isNat(V1),V2))</RHS></RULE><RULE><LHS>active(U12(tt,V2))</LHS><RHS>mark(U13(isNat(V2)))</RHS></RULE><RULE><LHS>active(U13(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U21(tt,V1))</LHS><RHS>mark(U22(isNat(V1)))</RHS></RULE><RULE><LHS>active(U22(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U31(tt,N))</LHS><RHS>mark(N)</RHS></RULE><RULE><LHS>active(U41(tt,M,N))</LHS><RHS>mark(s(plus(N,M)))</RHS></RULE><RULE><LHS>active(and(tt,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(isNat(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNat(plus(V1,V2)))</LHS><RHS>mark(U11(and(isNatKind(V1),isNatKind(V2)),V1,V2))</RHS></RULE><RULE><LHS>active(isNat(s(V1)))</LHS><RHS>mark(U21(isNatKind(V1),V1))</RHS></RULE><RULE><LHS>active(isNatKind(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNatKind(plus(V1,V2)))</LHS><RHS>mark(and(isNatKind(V1),isNatKind(V2)))</RHS></RULE><RULE><LHS>active(isNatKind(s(V1)))</LHS><RHS>mark(isNatKind(V1))</RHS></RULE><RULE><LHS>active(plus(N,0))</LHS><RHS>mark(U31(and(isNat(N),isNatKind(N)),N))</RHS></RULE><RULE><LHS>active(plus(N,s(M)))</LHS><RHS>mark(U41(and(and(isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),M,N))</RHS></RULE><RULE><LHS>mark(U11(X1,X2,X3))</LHS><RHS>active(U11(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(tt)</LHS><RHS>active(tt)</RHS></RULE><RULE><LHS>mark(U12(X1,X2))</LHS><RHS>active(U12(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(isNat(X))</LHS><RHS>active(isNat(X))</RHS></RULE><RULE><LHS>mark(U13(X))</LHS><RHS>active(U13(mark(X)))</RHS></RULE><RULE><LHS>mark(U21(X1,X2))</LHS><RHS>active(U21(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U22(X))</LHS><RHS>active(U22(mark(X)))</RHS></RULE><RULE><LHS>mark(U31(X1,X2))</LHS><RHS>active(U31(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U41(X1,X2,X3))</LHS><RHS>active(U41(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(mark(X)))</RHS></RULE><RULE><LHS>mark(plus(X1,X2))</LHS><RHS>active(plus(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(isNatKind(X))</LHS><RHS>active(isNatKind(X))</RHS></RULE><RULE><LHS>U11(mark(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,mark(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,mark(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(active(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,active(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,active(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U12(mark(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,mark(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(active(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,active(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>isNat(mark(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>isNat(active(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>U13(mark(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U13(active(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U21(mark(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,mark(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(active(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,active(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U22(mark(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U22(active(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U31(mark(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,mark(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(active(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,active(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U41(mark(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,mark(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,mark(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(active(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,active(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,active(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>s(mark(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>s(active(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>plus(mark(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,mark(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(active(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,active(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>and(mark(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,mark(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(active(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,active(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>isNatKind(mark(X))</LHS><RHS>isNatKind(X)</RHS></RULE><RULE><LHS>isNatKind(active(X))</LHS><RHS>isNatKind(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_U13(mark(X))</LHS><RHS>Marked_U13(X)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_U13(active(X))</LHS><RHS>Marked_U13(X)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><PROJECTION><PROJ><SYMBOL><NAME>Marked_U13</NAME></SYMBOL><INT>1</INT></PROJ></PROJECTION><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_U13(active(X))</LHS><RHS>Marked_U13(X)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_U13(mark(X))</LHS><RHS>Marked_U13(X)</RHS></DPRULE></DPLIST></STRICTPAIRS><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(U11(tt,V1,V2))</LHS><RHS>mark(U12(isNat(V1),V2))</RHS></RULE><RULE><LHS>active(U12(tt,V2))</LHS><RHS>mark(U13(isNat(V2)))</RHS></RULE><RULE><LHS>active(U13(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U21(tt,V1))</LHS><RHS>mark(U22(isNat(V1)))</RHS></RULE><RULE><LHS>active(U22(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U31(tt,N))</LHS><RHS>mark(N)</RHS></RULE><RULE><LHS>active(U41(tt,M,N))</LHS><RHS>mark(s(plus(N,M)))</RHS></RULE><RULE><LHS>active(and(tt,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(isNat(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNat(plus(V1,V2)))</LHS><RHS>mark(U11(and(isNatKind(V1),isNatKind(V2)),V1,V2))</RHS></RULE><RULE><LHS>active(isNat(s(V1)))</LHS><RHS>mark(U21(isNatKind(V1),V1))</RHS></RULE><RULE><LHS>active(isNatKind(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNatKind(plus(V1,V2)))</LHS><RHS>mark(and(isNatKind(V1),isNatKind(V2)))</RHS></RULE><RULE><LHS>active(isNatKind(s(V1)))</LHS><RHS>mark(isNatKind(V1))</RHS></RULE><RULE><LHS>active(plus(N,0))</LHS><RHS>mark(U31(and(isNat(N),isNatKind(N)),N))</RHS></RULE><RULE><LHS>active(plus(N,s(M)))</LHS><RHS>mark(U41(and(and(isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),M,N))</RHS></RULE><RULE><LHS>mark(U11(X1,X2,X3))</LHS><RHS>active(U11(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(tt)</LHS><RHS>active(tt)</RHS></RULE><RULE><LHS>mark(U12(X1,X2))</LHS><RHS>active(U12(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(isNat(X))</LHS><RHS>active(isNat(X))</RHS></RULE><RULE><LHS>mark(U13(X))</LHS><RHS>active(U13(mark(X)))</RHS></RULE><RULE><LHS>mark(U21(X1,X2))</LHS><RHS>active(U21(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U22(X))</LHS><RHS>active(U22(mark(X)))</RHS></RULE><RULE><LHS>mark(U31(X1,X2))</LHS><RHS>active(U31(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U41(X1,X2,X3))</LHS><RHS>active(U41(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(mark(X)))</RHS></RULE><RULE><LHS>mark(plus(X1,X2))</LHS><RHS>active(plus(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(isNatKind(X))</LHS><RHS>active(isNatKind(X))</RHS></RULE><RULE><LHS>U11(mark(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,mark(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,mark(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(active(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,active(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,active(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U12(mark(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,mark(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(active(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,active(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>isNat(mark(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>isNat(active(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>U13(mark(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U13(active(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U21(mark(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,mark(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(active(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,active(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U22(mark(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U22(active(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U31(mark(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,mark(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(active(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,active(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U41(mark(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,mark(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,mark(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(active(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,active(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,active(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>s(mark(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>s(active(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>plus(mark(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,mark(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(active(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,active(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>and(mark(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,mark(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(active(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,active(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>isNatKind(mark(X))</LHS><RHS>isNatKind(X)</RHS></RULE><RULE><LHS>isNatKind(active(X))</LHS><RHS>isNatKind(X)</RHS></RULE></REWSYS><DPLIST/></DPSYS></SYSTEM><CRITERION><DAG approx="simpl"><CCLIST/></DAG></CRITERION></PROPERTY></PROPERTY><PROPERTY criterion="sterm" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(U11(tt,V1,V2))</LHS><RHS>mark(U12(isNat(V1),V2))</RHS></RULE><RULE><LHS>active(U12(tt,V2))</LHS><RHS>mark(U13(isNat(V2)))</RHS></RULE><RULE><LHS>active(U13(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U21(tt,V1))</LHS><RHS>mark(U22(isNat(V1)))</RHS></RULE><RULE><LHS>active(U22(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U31(tt,N))</LHS><RHS>mark(N)</RHS></RULE><RULE><LHS>active(U41(tt,M,N))</LHS><RHS>mark(s(plus(N,M)))</RHS></RULE><RULE><LHS>active(and(tt,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(isNat(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNat(plus(V1,V2)))</LHS><RHS>mark(U11(and(isNatKind(V1),isNatKind(V2)),V1,V2))</RHS></RULE><RULE><LHS>active(isNat(s(V1)))</LHS><RHS>mark(U21(isNatKind(V1),V1))</RHS></RULE><RULE><LHS>active(isNatKind(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNatKind(plus(V1,V2)))</LHS><RHS>mark(and(isNatKind(V1),isNatKind(V2)))</RHS></RULE><RULE><LHS>active(isNatKind(s(V1)))</LHS><RHS>mark(isNatKind(V1))</RHS></RULE><RULE><LHS>active(plus(N,0))</LHS><RHS>mark(U31(and(isNat(N),isNatKind(N)),N))</RHS></RULE><RULE><LHS>active(plus(N,s(M)))</LHS><RHS>mark(U41(and(and(isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),M,N))</RHS></RULE><RULE><LHS>mark(U11(X1,X2,X3))</LHS><RHS>active(U11(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(tt)</LHS><RHS>active(tt)</RHS></RULE><RULE><LHS>mark(U12(X1,X2))</LHS><RHS>active(U12(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(isNat(X))</LHS><RHS>active(isNat(X))</RHS></RULE><RULE><LHS>mark(U13(X))</LHS><RHS>active(U13(mark(X)))</RHS></RULE><RULE><LHS>mark(U21(X1,X2))</LHS><RHS>active(U21(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U22(X))</LHS><RHS>active(U22(mark(X)))</RHS></RULE><RULE><LHS>mark(U31(X1,X2))</LHS><RHS>active(U31(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U41(X1,X2,X3))</LHS><RHS>active(U41(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(mark(X)))</RHS></RULE><RULE><LHS>mark(plus(X1,X2))</LHS><RHS>active(plus(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(isNatKind(X))</LHS><RHS>active(isNatKind(X))</RHS></RULE><RULE><LHS>U11(mark(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,mark(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,mark(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(active(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,active(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,active(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U12(mark(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,mark(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(active(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,active(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>isNat(mark(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>isNat(active(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>U13(mark(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U13(active(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U21(mark(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,mark(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(active(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,active(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U22(mark(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U22(active(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U31(mark(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,mark(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(active(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,active(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U41(mark(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,mark(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,mark(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(active(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,active(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,active(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>s(mark(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>s(active(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>plus(mark(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,mark(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(active(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,active(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>and(mark(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,mark(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(active(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,active(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>isNatKind(mark(X))</LHS><RHS>isNatKind(X)</RHS></RULE><RULE><LHS>isNatKind(active(X))</LHS><RHS>isNatKind(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_U21(mark(X1),X2)</LHS><RHS>Marked_U21(X1,X2)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_U21(X1,mark(X2))</LHS><RHS>Marked_U21(X1,X2)</RHS></DPRULE><DPRULE num="2"><LHS>Marked_U21(active(X1),X2)</LHS><RHS>Marked_U21(X1,X2)</RHS></DPRULE><DPRULE num="3"><LHS>Marked_U21(X1,active(X2))</LHS><RHS>Marked_U21(X1,X2)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><PROJECTION><PROJ><SYMBOL><NAME>Marked_U21</NAME></SYMBOL><INT>2</INT></PROJ></PROJECTION><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_U21(X1,active(X2))</LHS><RHS>Marked_U21(X1,X2)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_U21(X1,mark(X2))</LHS><RHS>Marked_U21(X1,X2)</RHS></DPRULE></DPLIST></STRICTPAIRS><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(U11(tt,V1,V2))</LHS><RHS>mark(U12(isNat(V1),V2))</RHS></RULE><RULE><LHS>active(U12(tt,V2))</LHS><RHS>mark(U13(isNat(V2)))</RHS></RULE><RULE><LHS>active(U13(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U21(tt,V1))</LHS><RHS>mark(U22(isNat(V1)))</RHS></RULE><RULE><LHS>active(U22(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U31(tt,N))</LHS><RHS>mark(N)</RHS></RULE><RULE><LHS>active(U41(tt,M,N))</LHS><RHS>mark(s(plus(N,M)))</RHS></RULE><RULE><LHS>active(and(tt,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(isNat(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNat(plus(V1,V2)))</LHS><RHS>mark(U11(and(isNatKind(V1),isNatKind(V2)),V1,V2))</RHS></RULE><RULE><LHS>active(isNat(s(V1)))</LHS><RHS>mark(U21(isNatKind(V1),V1))</RHS></RULE><RULE><LHS>active(isNatKind(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNatKind(plus(V1,V2)))</LHS><RHS>mark(and(isNatKind(V1),isNatKind(V2)))</RHS></RULE><RULE><LHS>active(isNatKind(s(V1)))</LHS><RHS>mark(isNatKind(V1))</RHS></RULE><RULE><LHS>active(plus(N,0))</LHS><RHS>mark(U31(and(isNat(N),isNatKind(N)),N))</RHS></RULE><RULE><LHS>active(plus(N,s(M)))</LHS><RHS>mark(U41(and(and(isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),M,N))</RHS></RULE><RULE><LHS>mark(U11(X1,X2,X3))</LHS><RHS>active(U11(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(tt)</LHS><RHS>active(tt)</RHS></RULE><RULE><LHS>mark(U12(X1,X2))</LHS><RHS>active(U12(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(isNat(X))</LHS><RHS>active(isNat(X))</RHS></RULE><RULE><LHS>mark(U13(X))</LHS><RHS>active(U13(mark(X)))</RHS></RULE><RULE><LHS>mark(U21(X1,X2))</LHS><RHS>active(U21(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U22(X))</LHS><RHS>active(U22(mark(X)))</RHS></RULE><RULE><LHS>mark(U31(X1,X2))</LHS><RHS>active(U31(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U41(X1,X2,X3))</LHS><RHS>active(U41(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(mark(X)))</RHS></RULE><RULE><LHS>mark(plus(X1,X2))</LHS><RHS>active(plus(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(isNatKind(X))</LHS><RHS>active(isNatKind(X))</RHS></RULE><RULE><LHS>U11(mark(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,mark(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,mark(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(active(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,active(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,active(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U12(mark(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,mark(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(active(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,active(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>isNat(mark(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>isNat(active(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>U13(mark(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U13(active(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U21(mark(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,mark(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(active(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,active(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U22(mark(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U22(active(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U31(mark(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,mark(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(active(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,active(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U41(mark(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,mark(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,mark(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(active(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,active(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,active(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>s(mark(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>s(active(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>plus(mark(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,mark(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(active(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,active(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>and(mark(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,mark(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(active(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,active(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>isNatKind(mark(X))</LHS><RHS>isNatKind(X)</RHS></RULE><RULE><LHS>isNatKind(active(X))</LHS><RHS>isNatKind(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_U21(active(X1),X2)</LHS><RHS>Marked_U21(X1,X2)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_U21(mark(X1),X2)</LHS><RHS>Marked_U21(X1,X2)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><DAG approx="simpl"><CCLIST><SCC num="0"><NODE ref="0"/><NODE ref="1"/></SCC></CCLIST></DAG></CRITERION><PROPERTY criterion="sterm" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(U11(tt,V1,V2))</LHS><RHS>mark(U12(isNat(V1),V2))</RHS></RULE><RULE><LHS>active(U12(tt,V2))</LHS><RHS>mark(U13(isNat(V2)))</RHS></RULE><RULE><LHS>active(U13(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U21(tt,V1))</LHS><RHS>mark(U22(isNat(V1)))</RHS></RULE><RULE><LHS>active(U22(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U31(tt,N))</LHS><RHS>mark(N)</RHS></RULE><RULE><LHS>active(U41(tt,M,N))</LHS><RHS>mark(s(plus(N,M)))</RHS></RULE><RULE><LHS>active(and(tt,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(isNat(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNat(plus(V1,V2)))</LHS><RHS>mark(U11(and(isNatKind(V1),isNatKind(V2)),V1,V2))</RHS></RULE><RULE><LHS>active(isNat(s(V1)))</LHS><RHS>mark(U21(isNatKind(V1),V1))</RHS></RULE><RULE><LHS>active(isNatKind(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNatKind(plus(V1,V2)))</LHS><RHS>mark(and(isNatKind(V1),isNatKind(V2)))</RHS></RULE><RULE><LHS>active(isNatKind(s(V1)))</LHS><RHS>mark(isNatKind(V1))</RHS></RULE><RULE><LHS>active(plus(N,0))</LHS><RHS>mark(U31(and(isNat(N),isNatKind(N)),N))</RHS></RULE><RULE><LHS>active(plus(N,s(M)))</LHS><RHS>mark(U41(and(and(isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),M,N))</RHS></RULE><RULE><LHS>mark(U11(X1,X2,X3))</LHS><RHS>active(U11(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(tt)</LHS><RHS>active(tt)</RHS></RULE><RULE><LHS>mark(U12(X1,X2))</LHS><RHS>active(U12(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(isNat(X))</LHS><RHS>active(isNat(X))</RHS></RULE><RULE><LHS>mark(U13(X))</LHS><RHS>active(U13(mark(X)))</RHS></RULE><RULE><LHS>mark(U21(X1,X2))</LHS><RHS>active(U21(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U22(X))</LHS><RHS>active(U22(mark(X)))</RHS></RULE><RULE><LHS>mark(U31(X1,X2))</LHS><RHS>active(U31(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U41(X1,X2,X3))</LHS><RHS>active(U41(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(mark(X)))</RHS></RULE><RULE><LHS>mark(plus(X1,X2))</LHS><RHS>active(plus(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(isNatKind(X))</LHS><RHS>active(isNatKind(X))</RHS></RULE><RULE><LHS>U11(mark(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,mark(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,mark(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(active(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,active(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,active(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U12(mark(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,mark(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(active(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,active(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>isNat(mark(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>isNat(active(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>U13(mark(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U13(active(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U21(mark(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,mark(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(active(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,active(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U22(mark(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U22(active(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U31(mark(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,mark(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(active(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,active(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U41(mark(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,mark(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,mark(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(active(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,active(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,active(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>s(mark(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>s(active(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>plus(mark(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,mark(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(active(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,active(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>and(mark(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,mark(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(active(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,active(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>isNatKind(mark(X))</LHS><RHS>isNatKind(X)</RHS></RULE><RULE><LHS>isNatKind(active(X))</LHS><RHS>isNatKind(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_U21(active(X1),X2)</LHS><RHS>Marked_U21(X1,X2)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_U21(mark(X1),X2)</LHS><RHS>Marked_U21(X1,X2)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><PROJECTION><PROJ><SYMBOL><NAME>Marked_U21</NAME></SYMBOL><INT>1</INT></PROJ></PROJECTION><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_U21(mark(X1),X2)</LHS><RHS>Marked_U21(X1,X2)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_U21(active(X1),X2)</LHS><RHS>Marked_U21(X1,X2)</RHS></DPRULE></DPLIST></STRICTPAIRS><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(U11(tt,V1,V2))</LHS><RHS>mark(U12(isNat(V1),V2))</RHS></RULE><RULE><LHS>active(U12(tt,V2))</LHS><RHS>mark(U13(isNat(V2)))</RHS></RULE><RULE><LHS>active(U13(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U21(tt,V1))</LHS><RHS>mark(U22(isNat(V1)))</RHS></RULE><RULE><LHS>active(U22(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U31(tt,N))</LHS><RHS>mark(N)</RHS></RULE><RULE><LHS>active(U41(tt,M,N))</LHS><RHS>mark(s(plus(N,M)))</RHS></RULE><RULE><LHS>active(and(tt,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(isNat(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNat(plus(V1,V2)))</LHS><RHS>mark(U11(and(isNatKind(V1),isNatKind(V2)),V1,V2))</RHS></RULE><RULE><LHS>active(isNat(s(V1)))</LHS><RHS>mark(U21(isNatKind(V1),V1))</RHS></RULE><RULE><LHS>active(isNatKind(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNatKind(plus(V1,V2)))</LHS><RHS>mark(and(isNatKind(V1),isNatKind(V2)))</RHS></RULE><RULE><LHS>active(isNatKind(s(V1)))</LHS><RHS>mark(isNatKind(V1))</RHS></RULE><RULE><LHS>active(plus(N,0))</LHS><RHS>mark(U31(and(isNat(N),isNatKind(N)),N))</RHS></RULE><RULE><LHS>active(plus(N,s(M)))</LHS><RHS>mark(U41(and(and(isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),M,N))</RHS></RULE><RULE><LHS>mark(U11(X1,X2,X3))</LHS><RHS>active(U11(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(tt)</LHS><RHS>active(tt)</RHS></RULE><RULE><LHS>mark(U12(X1,X2))</LHS><RHS>active(U12(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(isNat(X))</LHS><RHS>active(isNat(X))</RHS></RULE><RULE><LHS>mark(U13(X))</LHS><RHS>active(U13(mark(X)))</RHS></RULE><RULE><LHS>mark(U21(X1,X2))</LHS><RHS>active(U21(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U22(X))</LHS><RHS>active(U22(mark(X)))</RHS></RULE><RULE><LHS>mark(U31(X1,X2))</LHS><RHS>active(U31(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U41(X1,X2,X3))</LHS><RHS>active(U41(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(mark(X)))</RHS></RULE><RULE><LHS>mark(plus(X1,X2))</LHS><RHS>active(plus(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(isNatKind(X))</LHS><RHS>active(isNatKind(X))</RHS></RULE><RULE><LHS>U11(mark(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,mark(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,mark(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(active(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,active(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,active(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U12(mark(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,mark(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(active(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,active(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>isNat(mark(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>isNat(active(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>U13(mark(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U13(active(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U21(mark(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,mark(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(active(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,active(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U22(mark(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U22(active(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U31(mark(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,mark(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(active(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,active(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U41(mark(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,mark(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,mark(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(active(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,active(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,active(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>s(mark(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>s(active(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>plus(mark(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,mark(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(active(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,active(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>and(mark(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,mark(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(active(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,active(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>isNatKind(mark(X))</LHS><RHS>isNatKind(X)</RHS></RULE><RULE><LHS>isNatKind(active(X))</LHS><RHS>isNatKind(X)</RHS></RULE></REWSYS><DPLIST/></DPSYS></SYSTEM><CRITERION><DAG approx="simpl"><CCLIST/></DAG></CRITERION></PROPERTY></PROPERTY></PROPERTY></PROPERTY><PROPERTY criterion="sterm" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(U11(tt,V1,V2))</LHS><RHS>mark(U12(isNat(V1),V2))</RHS></RULE><RULE><LHS>active(U12(tt,V2))</LHS><RHS>mark(U13(isNat(V2)))</RHS></RULE><RULE><LHS>active(U13(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U21(tt,V1))</LHS><RHS>mark(U22(isNat(V1)))</RHS></RULE><RULE><LHS>active(U22(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U31(tt,N))</LHS><RHS>mark(N)</RHS></RULE><RULE><LHS>active(U41(tt,M,N))</LHS><RHS>mark(s(plus(N,M)))</RHS></RULE><RULE><LHS>active(and(tt,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(isNat(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNat(plus(V1,V2)))</LHS><RHS>mark(U11(and(isNatKind(V1),isNatKind(V2)),V1,V2))</RHS></RULE><RULE><LHS>active(isNat(s(V1)))</LHS><RHS>mark(U21(isNatKind(V1),V1))</RHS></RULE><RULE><LHS>active(isNatKind(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNatKind(plus(V1,V2)))</LHS><RHS>mark(and(isNatKind(V1),isNatKind(V2)))</RHS></RULE><RULE><LHS>active(isNatKind(s(V1)))</LHS><RHS>mark(isNatKind(V1))</RHS></RULE><RULE><LHS>active(plus(N,0))</LHS><RHS>mark(U31(and(isNat(N),isNatKind(N)),N))</RHS></RULE><RULE><LHS>active(plus(N,s(M)))</LHS><RHS>mark(U41(and(and(isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),M,N))</RHS></RULE><RULE><LHS>mark(U11(X1,X2,X3))</LHS><RHS>active(U11(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(tt)</LHS><RHS>active(tt)</RHS></RULE><RULE><LHS>mark(U12(X1,X2))</LHS><RHS>active(U12(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(isNat(X))</LHS><RHS>active(isNat(X))</RHS></RULE><RULE><LHS>mark(U13(X))</LHS><RHS>active(U13(mark(X)))</RHS></RULE><RULE><LHS>mark(U21(X1,X2))</LHS><RHS>active(U21(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U22(X))</LHS><RHS>active(U22(mark(X)))</RHS></RULE><RULE><LHS>mark(U31(X1,X2))</LHS><RHS>active(U31(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U41(X1,X2,X3))</LHS><RHS>active(U41(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(mark(X)))</RHS></RULE><RULE><LHS>mark(plus(X1,X2))</LHS><RHS>active(plus(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(isNatKind(X))</LHS><RHS>active(isNatKind(X))</RHS></RULE><RULE><LHS>U11(mark(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,mark(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,mark(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(active(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,active(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,active(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U12(mark(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,mark(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(active(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,active(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>isNat(mark(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>isNat(active(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>U13(mark(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U13(active(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U21(mark(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,mark(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(active(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,active(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U22(mark(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U22(active(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U31(mark(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,mark(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(active(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,active(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U41(mark(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,mark(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,mark(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(active(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,active(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,active(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>s(mark(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>s(active(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>plus(mark(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,mark(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(active(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,active(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>and(mark(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,mark(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(active(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,active(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>isNatKind(mark(X))</LHS><RHS>isNatKind(X)</RHS></RULE><RULE><LHS>isNatKind(active(X))</LHS><RHS>isNatKind(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_U22(mark(X))</LHS><RHS>Marked_U22(X)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_U22(active(X))</LHS><RHS>Marked_U22(X)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><PROJECTION><PROJ><SYMBOL><NAME>Marked_U22</NAME></SYMBOL><INT>1</INT></PROJ></PROJECTION><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_U22(active(X))</LHS><RHS>Marked_U22(X)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_U22(mark(X))</LHS><RHS>Marked_U22(X)</RHS></DPRULE></DPLIST></STRICTPAIRS><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(U11(tt,V1,V2))</LHS><RHS>mark(U12(isNat(V1),V2))</RHS></RULE><RULE><LHS>active(U12(tt,V2))</LHS><RHS>mark(U13(isNat(V2)))</RHS></RULE><RULE><LHS>active(U13(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U21(tt,V1))</LHS><RHS>mark(U22(isNat(V1)))</RHS></RULE><RULE><LHS>active(U22(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U31(tt,N))</LHS><RHS>mark(N)</RHS></RULE><RULE><LHS>active(U41(tt,M,N))</LHS><RHS>mark(s(plus(N,M)))</RHS></RULE><RULE><LHS>active(and(tt,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(isNat(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNat(plus(V1,V2)))</LHS><RHS>mark(U11(and(isNatKind(V1),isNatKind(V2)),V1,V2))</RHS></RULE><RULE><LHS>active(isNat(s(V1)))</LHS><RHS>mark(U21(isNatKind(V1),V1))</RHS></RULE><RULE><LHS>active(isNatKind(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNatKind(plus(V1,V2)))</LHS><RHS>mark(and(isNatKind(V1),isNatKind(V2)))</RHS></RULE><RULE><LHS>active(isNatKind(s(V1)))</LHS><RHS>mark(isNatKind(V1))</RHS></RULE><RULE><LHS>active(plus(N,0))</LHS><RHS>mark(U31(and(isNat(N),isNatKind(N)),N))</RHS></RULE><RULE><LHS>active(plus(N,s(M)))</LHS><RHS>mark(U41(and(and(isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),M,N))</RHS></RULE><RULE><LHS>mark(U11(X1,X2,X3))</LHS><RHS>active(U11(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(tt)</LHS><RHS>active(tt)</RHS></RULE><RULE><LHS>mark(U12(X1,X2))</LHS><RHS>active(U12(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(isNat(X))</LHS><RHS>active(isNat(X))</RHS></RULE><RULE><LHS>mark(U13(X))</LHS><RHS>active(U13(mark(X)))</RHS></RULE><RULE><LHS>mark(U21(X1,X2))</LHS><RHS>active(U21(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U22(X))</LHS><RHS>active(U22(mark(X)))</RHS></RULE><RULE><LHS>mark(U31(X1,X2))</LHS><RHS>active(U31(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U41(X1,X2,X3))</LHS><RHS>active(U41(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(mark(X)))</RHS></RULE><RULE><LHS>mark(plus(X1,X2))</LHS><RHS>active(plus(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(isNatKind(X))</LHS><RHS>active(isNatKind(X))</RHS></RULE><RULE><LHS>U11(mark(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,mark(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,mark(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(active(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,active(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,active(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U12(mark(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,mark(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(active(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,active(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>isNat(mark(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>isNat(active(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>U13(mark(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U13(active(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U21(mark(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,mark(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(active(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,active(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U22(mark(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U22(active(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U31(mark(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,mark(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(active(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,active(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U41(mark(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,mark(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,mark(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(active(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,active(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,active(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>s(mark(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>s(active(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>plus(mark(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,mark(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(active(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,active(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>and(mark(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,mark(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(active(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,active(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>isNatKind(mark(X))</LHS><RHS>isNatKind(X)</RHS></RULE><RULE><LHS>isNatKind(active(X))</LHS><RHS>isNatKind(X)</RHS></RULE></REWSYS><DPLIST/></DPSYS></SYSTEM><CRITERION><DAG approx="simpl"><CCLIST/></DAG></CRITERION></PROPERTY></PROPERTY><PROPERTY criterion="sterm" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(U11(tt,V1,V2))</LHS><RHS>mark(U12(isNat(V1),V2))</RHS></RULE><RULE><LHS>active(U12(tt,V2))</LHS><RHS>mark(U13(isNat(V2)))</RHS></RULE><RULE><LHS>active(U13(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U21(tt,V1))</LHS><RHS>mark(U22(isNat(V1)))</RHS></RULE><RULE><LHS>active(U22(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U31(tt,N))</LHS><RHS>mark(N)</RHS></RULE><RULE><LHS>active(U41(tt,M,N))</LHS><RHS>mark(s(plus(N,M)))</RHS></RULE><RULE><LHS>active(and(tt,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(isNat(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNat(plus(V1,V2)))</LHS><RHS>mark(U11(and(isNatKind(V1),isNatKind(V2)),V1,V2))</RHS></RULE><RULE><LHS>active(isNat(s(V1)))</LHS><RHS>mark(U21(isNatKind(V1),V1))</RHS></RULE><RULE><LHS>active(isNatKind(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNatKind(plus(V1,V2)))</LHS><RHS>mark(and(isNatKind(V1),isNatKind(V2)))</RHS></RULE><RULE><LHS>active(isNatKind(s(V1)))</LHS><RHS>mark(isNatKind(V1))</RHS></RULE><RULE><LHS>active(plus(N,0))</LHS><RHS>mark(U31(and(isNat(N),isNatKind(N)),N))</RHS></RULE><RULE><LHS>active(plus(N,s(M)))</LHS><RHS>mark(U41(and(and(isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),M,N))</RHS></RULE><RULE><LHS>mark(U11(X1,X2,X3))</LHS><RHS>active(U11(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(tt)</LHS><RHS>active(tt)</RHS></RULE><RULE><LHS>mark(U12(X1,X2))</LHS><RHS>active(U12(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(isNat(X))</LHS><RHS>active(isNat(X))</RHS></RULE><RULE><LHS>mark(U13(X))</LHS><RHS>active(U13(mark(X)))</RHS></RULE><RULE><LHS>mark(U21(X1,X2))</LHS><RHS>active(U21(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U22(X))</LHS><RHS>active(U22(mark(X)))</RHS></RULE><RULE><LHS>mark(U31(X1,X2))</LHS><RHS>active(U31(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U41(X1,X2,X3))</LHS><RHS>active(U41(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(mark(X)))</RHS></RULE><RULE><LHS>mark(plus(X1,X2))</LHS><RHS>active(plus(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(isNatKind(X))</LHS><RHS>active(isNatKind(X))</RHS></RULE><RULE><LHS>U11(mark(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,mark(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,mark(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(active(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,active(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,active(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U12(mark(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,mark(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(active(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,active(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>isNat(mark(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>isNat(active(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>U13(mark(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U13(active(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U21(mark(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,mark(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(active(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,active(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U22(mark(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U22(active(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U31(mark(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,mark(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(active(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,active(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U41(mark(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,mark(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,mark(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(active(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,active(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,active(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>s(mark(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>s(active(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>plus(mark(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,mark(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(active(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,active(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>and(mark(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,mark(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(active(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,active(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>isNatKind(mark(X))</LHS><RHS>isNatKind(X)</RHS></RULE><RULE><LHS>isNatKind(active(X))</LHS><RHS>isNatKind(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_U31(mark(X1),X2)</LHS><RHS>Marked_U31(X1,X2)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_U31(X1,mark(X2))</LHS><RHS>Marked_U31(X1,X2)</RHS></DPRULE><DPRULE num="2"><LHS>Marked_U31(active(X1),X2)</LHS><RHS>Marked_U31(X1,X2)</RHS></DPRULE><DPRULE num="3"><LHS>Marked_U31(X1,active(X2))</LHS><RHS>Marked_U31(X1,X2)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><PROJECTION><PROJ><SYMBOL><NAME>Marked_U31</NAME></SYMBOL><INT>2</INT></PROJ></PROJECTION><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_U31(X1,active(X2))</LHS><RHS>Marked_U31(X1,X2)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_U31(X1,mark(X2))</LHS><RHS>Marked_U31(X1,X2)</RHS></DPRULE></DPLIST></STRICTPAIRS><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(U11(tt,V1,V2))</LHS><RHS>mark(U12(isNat(V1),V2))</RHS></RULE><RULE><LHS>active(U12(tt,V2))</LHS><RHS>mark(U13(isNat(V2)))</RHS></RULE><RULE><LHS>active(U13(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U21(tt,V1))</LHS><RHS>mark(U22(isNat(V1)))</RHS></RULE><RULE><LHS>active(U22(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U31(tt,N))</LHS><RHS>mark(N)</RHS></RULE><RULE><LHS>active(U41(tt,M,N))</LHS><RHS>mark(s(plus(N,M)))</RHS></RULE><RULE><LHS>active(and(tt,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(isNat(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNat(plus(V1,V2)))</LHS><RHS>mark(U11(and(isNatKind(V1),isNatKind(V2)),V1,V2))</RHS></RULE><RULE><LHS>active(isNat(s(V1)))</LHS><RHS>mark(U21(isNatKind(V1),V1))</RHS></RULE><RULE><LHS>active(isNatKind(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNatKind(plus(V1,V2)))</LHS><RHS>mark(and(isNatKind(V1),isNatKind(V2)))</RHS></RULE><RULE><LHS>active(isNatKind(s(V1)))</LHS><RHS>mark(isNatKind(V1))</RHS></RULE><RULE><LHS>active(plus(N,0))</LHS><RHS>mark(U31(and(isNat(N),isNatKind(N)),N))</RHS></RULE><RULE><LHS>active(plus(N,s(M)))</LHS><RHS>mark(U41(and(and(isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),M,N))</RHS></RULE><RULE><LHS>mark(U11(X1,X2,X3))</LHS><RHS>active(U11(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(tt)</LHS><RHS>active(tt)</RHS></RULE><RULE><LHS>mark(U12(X1,X2))</LHS><RHS>active(U12(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(isNat(X))</LHS><RHS>active(isNat(X))</RHS></RULE><RULE><LHS>mark(U13(X))</LHS><RHS>active(U13(mark(X)))</RHS></RULE><RULE><LHS>mark(U21(X1,X2))</LHS><RHS>active(U21(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U22(X))</LHS><RHS>active(U22(mark(X)))</RHS></RULE><RULE><LHS>mark(U31(X1,X2))</LHS><RHS>active(U31(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U41(X1,X2,X3))</LHS><RHS>active(U41(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(mark(X)))</RHS></RULE><RULE><LHS>mark(plus(X1,X2))</LHS><RHS>active(plus(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(isNatKind(X))</LHS><RHS>active(isNatKind(X))</RHS></RULE><RULE><LHS>U11(mark(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,mark(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,mark(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(active(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,active(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,active(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U12(mark(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,mark(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(active(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,active(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>isNat(mark(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>isNat(active(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>U13(mark(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U13(active(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U21(mark(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,mark(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(active(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,active(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U22(mark(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U22(active(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U31(mark(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,mark(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(active(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,active(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U41(mark(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,mark(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,mark(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(active(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,active(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,active(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>s(mark(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>s(active(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>plus(mark(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,mark(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(active(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,active(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>and(mark(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,mark(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(active(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,active(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>isNatKind(mark(X))</LHS><RHS>isNatKind(X)</RHS></RULE><RULE><LHS>isNatKind(active(X))</LHS><RHS>isNatKind(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_U31(active(X1),X2)</LHS><RHS>Marked_U31(X1,X2)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_U31(mark(X1),X2)</LHS><RHS>Marked_U31(X1,X2)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><DAG approx="simpl"><CCLIST><SCC num="0"><NODE ref="0"/><NODE ref="1"/></SCC></CCLIST></DAG></CRITERION><PROPERTY criterion="sterm" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(U11(tt,V1,V2))</LHS><RHS>mark(U12(isNat(V1),V2))</RHS></RULE><RULE><LHS>active(U12(tt,V2))</LHS><RHS>mark(U13(isNat(V2)))</RHS></RULE><RULE><LHS>active(U13(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U21(tt,V1))</LHS><RHS>mark(U22(isNat(V1)))</RHS></RULE><RULE><LHS>active(U22(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U31(tt,N))</LHS><RHS>mark(N)</RHS></RULE><RULE><LHS>active(U41(tt,M,N))</LHS><RHS>mark(s(plus(N,M)))</RHS></RULE><RULE><LHS>active(and(tt,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(isNat(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNat(plus(V1,V2)))</LHS><RHS>mark(U11(and(isNatKind(V1),isNatKind(V2)),V1,V2))</RHS></RULE><RULE><LHS>active(isNat(s(V1)))</LHS><RHS>mark(U21(isNatKind(V1),V1))</RHS></RULE><RULE><LHS>active(isNatKind(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNatKind(plus(V1,V2)))</LHS><RHS>mark(and(isNatKind(V1),isNatKind(V2)))</RHS></RULE><RULE><LHS>active(isNatKind(s(V1)))</LHS><RHS>mark(isNatKind(V1))</RHS></RULE><RULE><LHS>active(plus(N,0))</LHS><RHS>mark(U31(and(isNat(N),isNatKind(N)),N))</RHS></RULE><RULE><LHS>active(plus(N,s(M)))</LHS><RHS>mark(U41(and(and(isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),M,N))</RHS></RULE><RULE><LHS>mark(U11(X1,X2,X3))</LHS><RHS>active(U11(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(tt)</LHS><RHS>active(tt)</RHS></RULE><RULE><LHS>mark(U12(X1,X2))</LHS><RHS>active(U12(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(isNat(X))</LHS><RHS>active(isNat(X))</RHS></RULE><RULE><LHS>mark(U13(X))</LHS><RHS>active(U13(mark(X)))</RHS></RULE><RULE><LHS>mark(U21(X1,X2))</LHS><RHS>active(U21(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U22(X))</LHS><RHS>active(U22(mark(X)))</RHS></RULE><RULE><LHS>mark(U31(X1,X2))</LHS><RHS>active(U31(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U41(X1,X2,X3))</LHS><RHS>active(U41(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(mark(X)))</RHS></RULE><RULE><LHS>mark(plus(X1,X2))</LHS><RHS>active(plus(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(isNatKind(X))</LHS><RHS>active(isNatKind(X))</RHS></RULE><RULE><LHS>U11(mark(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,mark(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,mark(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(active(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,active(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,active(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U12(mark(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,mark(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(active(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,active(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>isNat(mark(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>isNat(active(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>U13(mark(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U13(active(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U21(mark(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,mark(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(active(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,active(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U22(mark(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U22(active(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U31(mark(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,mark(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(active(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,active(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U41(mark(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,mark(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,mark(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(active(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,active(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,active(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>s(mark(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>s(active(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>plus(mark(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,mark(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(active(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,active(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>and(mark(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,mark(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(active(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,active(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>isNatKind(mark(X))</LHS><RHS>isNatKind(X)</RHS></RULE><RULE><LHS>isNatKind(active(X))</LHS><RHS>isNatKind(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_U31(active(X1),X2)</LHS><RHS>Marked_U31(X1,X2)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_U31(mark(X1),X2)</LHS><RHS>Marked_U31(X1,X2)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><PROJECTION><PROJ><SYMBOL><NAME>Marked_U31</NAME></SYMBOL><INT>1</INT></PROJ></PROJECTION><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_U31(mark(X1),X2)</LHS><RHS>Marked_U31(X1,X2)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_U31(active(X1),X2)</LHS><RHS>Marked_U31(X1,X2)</RHS></DPRULE></DPLIST></STRICTPAIRS><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(U11(tt,V1,V2))</LHS><RHS>mark(U12(isNat(V1),V2))</RHS></RULE><RULE><LHS>active(U12(tt,V2))</LHS><RHS>mark(U13(isNat(V2)))</RHS></RULE><RULE><LHS>active(U13(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U21(tt,V1))</LHS><RHS>mark(U22(isNat(V1)))</RHS></RULE><RULE><LHS>active(U22(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U31(tt,N))</LHS><RHS>mark(N)</RHS></RULE><RULE><LHS>active(U41(tt,M,N))</LHS><RHS>mark(s(plus(N,M)))</RHS></RULE><RULE><LHS>active(and(tt,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(isNat(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNat(plus(V1,V2)))</LHS><RHS>mark(U11(and(isNatKind(V1),isNatKind(V2)),V1,V2))</RHS></RULE><RULE><LHS>active(isNat(s(V1)))</LHS><RHS>mark(U21(isNatKind(V1),V1))</RHS></RULE><RULE><LHS>active(isNatKind(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNatKind(plus(V1,V2)))</LHS><RHS>mark(and(isNatKind(V1),isNatKind(V2)))</RHS></RULE><RULE><LHS>active(isNatKind(s(V1)))</LHS><RHS>mark(isNatKind(V1))</RHS></RULE><RULE><LHS>active(plus(N,0))</LHS><RHS>mark(U31(and(isNat(N),isNatKind(N)),N))</RHS></RULE><RULE><LHS>active(plus(N,s(M)))</LHS><RHS>mark(U41(and(and(isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),M,N))</RHS></RULE><RULE><LHS>mark(U11(X1,X2,X3))</LHS><RHS>active(U11(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(tt)</LHS><RHS>active(tt)</RHS></RULE><RULE><LHS>mark(U12(X1,X2))</LHS><RHS>active(U12(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(isNat(X))</LHS><RHS>active(isNat(X))</RHS></RULE><RULE><LHS>mark(U13(X))</LHS><RHS>active(U13(mark(X)))</RHS></RULE><RULE><LHS>mark(U21(X1,X2))</LHS><RHS>active(U21(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U22(X))</LHS><RHS>active(U22(mark(X)))</RHS></RULE><RULE><LHS>mark(U31(X1,X2))</LHS><RHS>active(U31(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U41(X1,X2,X3))</LHS><RHS>active(U41(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(mark(X)))</RHS></RULE><RULE><LHS>mark(plus(X1,X2))</LHS><RHS>active(plus(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(isNatKind(X))</LHS><RHS>active(isNatKind(X))</RHS></RULE><RULE><LHS>U11(mark(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,mark(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,mark(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(active(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,active(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,active(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U12(mark(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,mark(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(active(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,active(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>isNat(mark(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>isNat(active(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>U13(mark(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U13(active(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U21(mark(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,mark(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(active(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,active(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U22(mark(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U22(active(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U31(mark(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,mark(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(active(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,active(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U41(mark(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,mark(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,mark(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(active(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,active(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,active(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>s(mark(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>s(active(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>plus(mark(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,mark(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(active(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,active(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>and(mark(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,mark(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(active(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,active(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>isNatKind(mark(X))</LHS><RHS>isNatKind(X)</RHS></RULE><RULE><LHS>isNatKind(active(X))</LHS><RHS>isNatKind(X)</RHS></RULE></REWSYS><DPLIST/></DPSYS></SYSTEM><CRITERION><DAG approx="simpl"><CCLIST/></DAG></CRITERION></PROPERTY></PROPERTY></PROPERTY></PROPERTY><PROPERTY criterion="sterm" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(U11(tt,V1,V2))</LHS><RHS>mark(U12(isNat(V1),V2))</RHS></RULE><RULE><LHS>active(U12(tt,V2))</LHS><RHS>mark(U13(isNat(V2)))</RHS></RULE><RULE><LHS>active(U13(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U21(tt,V1))</LHS><RHS>mark(U22(isNat(V1)))</RHS></RULE><RULE><LHS>active(U22(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U31(tt,N))</LHS><RHS>mark(N)</RHS></RULE><RULE><LHS>active(U41(tt,M,N))</LHS><RHS>mark(s(plus(N,M)))</RHS></RULE><RULE><LHS>active(and(tt,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(isNat(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNat(plus(V1,V2)))</LHS><RHS>mark(U11(and(isNatKind(V1),isNatKind(V2)),V1,V2))</RHS></RULE><RULE><LHS>active(isNat(s(V1)))</LHS><RHS>mark(U21(isNatKind(V1),V1))</RHS></RULE><RULE><LHS>active(isNatKind(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNatKind(plus(V1,V2)))</LHS><RHS>mark(and(isNatKind(V1),isNatKind(V2)))</RHS></RULE><RULE><LHS>active(isNatKind(s(V1)))</LHS><RHS>mark(isNatKind(V1))</RHS></RULE><RULE><LHS>active(plus(N,0))</LHS><RHS>mark(U31(and(isNat(N),isNatKind(N)),N))</RHS></RULE><RULE><LHS>active(plus(N,s(M)))</LHS><RHS>mark(U41(and(and(isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),M,N))</RHS></RULE><RULE><LHS>mark(U11(X1,X2,X3))</LHS><RHS>active(U11(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(tt)</LHS><RHS>active(tt)</RHS></RULE><RULE><LHS>mark(U12(X1,X2))</LHS><RHS>active(U12(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(isNat(X))</LHS><RHS>active(isNat(X))</RHS></RULE><RULE><LHS>mark(U13(X))</LHS><RHS>active(U13(mark(X)))</RHS></RULE><RULE><LHS>mark(U21(X1,X2))</LHS><RHS>active(U21(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U22(X))</LHS><RHS>active(U22(mark(X)))</RHS></RULE><RULE><LHS>mark(U31(X1,X2))</LHS><RHS>active(U31(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U41(X1,X2,X3))</LHS><RHS>active(U41(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(mark(X)))</RHS></RULE><RULE><LHS>mark(plus(X1,X2))</LHS><RHS>active(plus(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(isNatKind(X))</LHS><RHS>active(isNatKind(X))</RHS></RULE><RULE><LHS>U11(mark(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,mark(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,mark(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(active(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,active(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,active(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U12(mark(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,mark(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(active(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,active(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>isNat(mark(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>isNat(active(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>U13(mark(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U13(active(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U21(mark(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,mark(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(active(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,active(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U22(mark(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U22(active(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U31(mark(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,mark(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(active(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,active(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U41(mark(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,mark(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,mark(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(active(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,active(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,active(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>s(mark(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>s(active(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>plus(mark(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,mark(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(active(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,active(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>and(mark(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,mark(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(active(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,active(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>isNatKind(mark(X))</LHS><RHS>isNatKind(X)</RHS></RULE><RULE><LHS>isNatKind(active(X))</LHS><RHS>isNatKind(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_U41(mark(X1),X2,X3)</LHS><RHS>Marked_U41(X1,X2,X3)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_U41(X1,mark(X2),X3)</LHS><RHS>Marked_U41(X1,X2,X3)</RHS></DPRULE><DPRULE num="2"><LHS>Marked_U41(X1,X2,mark(X3))</LHS><RHS>Marked_U41(X1,X2,X3)</RHS></DPRULE><DPRULE num="3"><LHS>Marked_U41(active(X1),X2,X3)</LHS><RHS>Marked_U41(X1,X2,X3)</RHS></DPRULE><DPRULE num="4"><LHS>Marked_U41(X1,active(X2),X3)</LHS><RHS>Marked_U41(X1,X2,X3)</RHS></DPRULE><DPRULE num="5"><LHS>Marked_U41(X1,X2,active(X3))</LHS><RHS>Marked_U41(X1,X2,X3)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><PROJECTION><PROJ><SYMBOL><NAME>Marked_U41</NAME></SYMBOL><INT>3</INT></PROJ></PROJECTION><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_U41(X1,X2,active(X3))</LHS><RHS>Marked_U41(X1,X2,X3)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_U41(X1,X2,mark(X3))</LHS><RHS>Marked_U41(X1,X2,X3)</RHS></DPRULE></DPLIST></STRICTPAIRS><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(U11(tt,V1,V2))</LHS><RHS>mark(U12(isNat(V1),V2))</RHS></RULE><RULE><LHS>active(U12(tt,V2))</LHS><RHS>mark(U13(isNat(V2)))</RHS></RULE><RULE><LHS>active(U13(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U21(tt,V1))</LHS><RHS>mark(U22(isNat(V1)))</RHS></RULE><RULE><LHS>active(U22(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U31(tt,N))</LHS><RHS>mark(N)</RHS></RULE><RULE><LHS>active(U41(tt,M,N))</LHS><RHS>mark(s(plus(N,M)))</RHS></RULE><RULE><LHS>active(and(tt,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(isNat(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNat(plus(V1,V2)))</LHS><RHS>mark(U11(and(isNatKind(V1),isNatKind(V2)),V1,V2))</RHS></RULE><RULE><LHS>active(isNat(s(V1)))</LHS><RHS>mark(U21(isNatKind(V1),V1))</RHS></RULE><RULE><LHS>active(isNatKind(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNatKind(plus(V1,V2)))</LHS><RHS>mark(and(isNatKind(V1),isNatKind(V2)))</RHS></RULE><RULE><LHS>active(isNatKind(s(V1)))</LHS><RHS>mark(isNatKind(V1))</RHS></RULE><RULE><LHS>active(plus(N,0))</LHS><RHS>mark(U31(and(isNat(N),isNatKind(N)),N))</RHS></RULE><RULE><LHS>active(plus(N,s(M)))</LHS><RHS>mark(U41(and(and(isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),M,N))</RHS></RULE><RULE><LHS>mark(U11(X1,X2,X3))</LHS><RHS>active(U11(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(tt)</LHS><RHS>active(tt)</RHS></RULE><RULE><LHS>mark(U12(X1,X2))</LHS><RHS>active(U12(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(isNat(X))</LHS><RHS>active(isNat(X))</RHS></RULE><RULE><LHS>mark(U13(X))</LHS><RHS>active(U13(mark(X)))</RHS></RULE><RULE><LHS>mark(U21(X1,X2))</LHS><RHS>active(U21(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U22(X))</LHS><RHS>active(U22(mark(X)))</RHS></RULE><RULE><LHS>mark(U31(X1,X2))</LHS><RHS>active(U31(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U41(X1,X2,X3))</LHS><RHS>active(U41(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(mark(X)))</RHS></RULE><RULE><LHS>mark(plus(X1,X2))</LHS><RHS>active(plus(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(isNatKind(X))</LHS><RHS>active(isNatKind(X))</RHS></RULE><RULE><LHS>U11(mark(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,mark(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,mark(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(active(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,active(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,active(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U12(mark(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,mark(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(active(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,active(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>isNat(mark(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>isNat(active(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>U13(mark(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U13(active(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U21(mark(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,mark(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(active(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,active(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U22(mark(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U22(active(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U31(mark(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,mark(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(active(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,active(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U41(mark(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,mark(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,mark(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(active(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,active(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,active(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>s(mark(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>s(active(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>plus(mark(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,mark(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(active(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,active(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>and(mark(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,mark(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(active(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,active(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>isNatKind(mark(X))</LHS><RHS>isNatKind(X)</RHS></RULE><RULE><LHS>isNatKind(active(X))</LHS><RHS>isNatKind(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_U41(X1,active(X2),X3)</LHS><RHS>Marked_U41(X1,X2,X3)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_U41(active(X1),X2,X3)</LHS><RHS>Marked_U41(X1,X2,X3)</RHS></DPRULE><DPRULE num="2"><LHS>Marked_U41(X1,mark(X2),X3)</LHS><RHS>Marked_U41(X1,X2,X3)</RHS></DPRULE><DPRULE num="3"><LHS>Marked_U41(mark(X1),X2,X3)</LHS><RHS>Marked_U41(X1,X2,X3)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><DAG approx="simpl"><CCLIST><SCC num="0"><NODE ref="0"/><NODE ref="1"/><NODE ref="2"/><NODE ref="3"/></SCC></CCLIST></DAG></CRITERION><PROPERTY criterion="sterm" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(U11(tt,V1,V2))</LHS><RHS>mark(U12(isNat(V1),V2))</RHS></RULE><RULE><LHS>active(U12(tt,V2))</LHS><RHS>mark(U13(isNat(V2)))</RHS></RULE><RULE><LHS>active(U13(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U21(tt,V1))</LHS><RHS>mark(U22(isNat(V1)))</RHS></RULE><RULE><LHS>active(U22(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U31(tt,N))</LHS><RHS>mark(N)</RHS></RULE><RULE><LHS>active(U41(tt,M,N))</LHS><RHS>mark(s(plus(N,M)))</RHS></RULE><RULE><LHS>active(and(tt,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(isNat(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNat(plus(V1,V2)))</LHS><RHS>mark(U11(and(isNatKind(V1),isNatKind(V2)),V1,V2))</RHS></RULE><RULE><LHS>active(isNat(s(V1)))</LHS><RHS>mark(U21(isNatKind(V1),V1))</RHS></RULE><RULE><LHS>active(isNatKind(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNatKind(plus(V1,V2)))</LHS><RHS>mark(and(isNatKind(V1),isNatKind(V2)))</RHS></RULE><RULE><LHS>active(isNatKind(s(V1)))</LHS><RHS>mark(isNatKind(V1))</RHS></RULE><RULE><LHS>active(plus(N,0))</LHS><RHS>mark(U31(and(isNat(N),isNatKind(N)),N))</RHS></RULE><RULE><LHS>active(plus(N,s(M)))</LHS><RHS>mark(U41(and(and(isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),M,N))</RHS></RULE><RULE><LHS>mark(U11(X1,X2,X3))</LHS><RHS>active(U11(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(tt)</LHS><RHS>active(tt)</RHS></RULE><RULE><LHS>mark(U12(X1,X2))</LHS><RHS>active(U12(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(isNat(X))</LHS><RHS>active(isNat(X))</RHS></RULE><RULE><LHS>mark(U13(X))</LHS><RHS>active(U13(mark(X)))</RHS></RULE><RULE><LHS>mark(U21(X1,X2))</LHS><RHS>active(U21(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U22(X))</LHS><RHS>active(U22(mark(X)))</RHS></RULE><RULE><LHS>mark(U31(X1,X2))</LHS><RHS>active(U31(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U41(X1,X2,X3))</LHS><RHS>active(U41(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(mark(X)))</RHS></RULE><RULE><LHS>mark(plus(X1,X2))</LHS><RHS>active(plus(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(isNatKind(X))</LHS><RHS>active(isNatKind(X))</RHS></RULE><RULE><LHS>U11(mark(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,mark(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,mark(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(active(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,active(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,active(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U12(mark(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,mark(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(active(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,active(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>isNat(mark(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>isNat(active(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>U13(mark(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U13(active(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U21(mark(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,mark(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(active(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,active(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U22(mark(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U22(active(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U31(mark(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,mark(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(active(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,active(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U41(mark(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,mark(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,mark(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(active(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,active(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,active(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>s(mark(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>s(active(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>plus(mark(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,mark(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(active(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,active(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>and(mark(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,mark(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(active(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,active(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>isNatKind(mark(X))</LHS><RHS>isNatKind(X)</RHS></RULE><RULE><LHS>isNatKind(active(X))</LHS><RHS>isNatKind(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_U41(X1,active(X2),X3)</LHS><RHS>Marked_U41(X1,X2,X3)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_U41(active(X1),X2,X3)</LHS><RHS>Marked_U41(X1,X2,X3)</RHS></DPRULE><DPRULE num="2"><LHS>Marked_U41(X1,mark(X2),X3)</LHS><RHS>Marked_U41(X1,X2,X3)</RHS></DPRULE><DPRULE num="3"><LHS>Marked_U41(mark(X1),X2,X3)</LHS><RHS>Marked_U41(X1,X2,X3)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><PROJECTION><PROJ><SYMBOL><NAME>Marked_U41</NAME></SYMBOL><INT>2</INT></PROJ></PROJECTION><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_U41(X1,mark(X2),X3)</LHS><RHS>Marked_U41(X1,X2,X3)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_U41(X1,active(X2),X3)</LHS><RHS>Marked_U41(X1,X2,X3)</RHS></DPRULE></DPLIST></STRICTPAIRS><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(U11(tt,V1,V2))</LHS><RHS>mark(U12(isNat(V1),V2))</RHS></RULE><RULE><LHS>active(U12(tt,V2))</LHS><RHS>mark(U13(isNat(V2)))</RHS></RULE><RULE><LHS>active(U13(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U21(tt,V1))</LHS><RHS>mark(U22(isNat(V1)))</RHS></RULE><RULE><LHS>active(U22(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U31(tt,N))</LHS><RHS>mark(N)</RHS></RULE><RULE><LHS>active(U41(tt,M,N))</LHS><RHS>mark(s(plus(N,M)))</RHS></RULE><RULE><LHS>active(and(tt,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(isNat(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNat(plus(V1,V2)))</LHS><RHS>mark(U11(and(isNatKind(V1),isNatKind(V2)),V1,V2))</RHS></RULE><RULE><LHS>active(isNat(s(V1)))</LHS><RHS>mark(U21(isNatKind(V1),V1))</RHS></RULE><RULE><LHS>active(isNatKind(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNatKind(plus(V1,V2)))</LHS><RHS>mark(and(isNatKind(V1),isNatKind(V2)))</RHS></RULE><RULE><LHS>active(isNatKind(s(V1)))</LHS><RHS>mark(isNatKind(V1))</RHS></RULE><RULE><LHS>active(plus(N,0))</LHS><RHS>mark(U31(and(isNat(N),isNatKind(N)),N))</RHS></RULE><RULE><LHS>active(plus(N,s(M)))</LHS><RHS>mark(U41(and(and(isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),M,N))</RHS></RULE><RULE><LHS>mark(U11(X1,X2,X3))</LHS><RHS>active(U11(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(tt)</LHS><RHS>active(tt)</RHS></RULE><RULE><LHS>mark(U12(X1,X2))</LHS><RHS>active(U12(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(isNat(X))</LHS><RHS>active(isNat(X))</RHS></RULE><RULE><LHS>mark(U13(X))</LHS><RHS>active(U13(mark(X)))</RHS></RULE><RULE><LHS>mark(U21(X1,X2))</LHS><RHS>active(U21(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U22(X))</LHS><RHS>active(U22(mark(X)))</RHS></RULE><RULE><LHS>mark(U31(X1,X2))</LHS><RHS>active(U31(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U41(X1,X2,X3))</LHS><RHS>active(U41(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(mark(X)))</RHS></RULE><RULE><LHS>mark(plus(X1,X2))</LHS><RHS>active(plus(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(isNatKind(X))</LHS><RHS>active(isNatKind(X))</RHS></RULE><RULE><LHS>U11(mark(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,mark(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,mark(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(active(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,active(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,active(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U12(mark(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,mark(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(active(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,active(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>isNat(mark(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>isNat(active(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>U13(mark(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U13(active(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U21(mark(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,mark(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(active(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,active(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U22(mark(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U22(active(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U31(mark(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,mark(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(active(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,active(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U41(mark(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,mark(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,mark(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(active(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,active(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,active(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>s(mark(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>s(active(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>plus(mark(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,mark(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(active(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,active(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>and(mark(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,mark(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(active(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,active(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>isNatKind(mark(X))</LHS><RHS>isNatKind(X)</RHS></RULE><RULE><LHS>isNatKind(active(X))</LHS><RHS>isNatKind(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_U41(mark(X1),X2,X3)</LHS><RHS>Marked_U41(X1,X2,X3)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_U41(active(X1),X2,X3)</LHS><RHS>Marked_U41(X1,X2,X3)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><DAG approx="simpl"><CCLIST><SCC num="0"><NODE ref="0"/><NODE ref="1"/></SCC></CCLIST></DAG></CRITERION><PROPERTY criterion="sterm" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(U11(tt,V1,V2))</LHS><RHS>mark(U12(isNat(V1),V2))</RHS></RULE><RULE><LHS>active(U12(tt,V2))</LHS><RHS>mark(U13(isNat(V2)))</RHS></RULE><RULE><LHS>active(U13(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U21(tt,V1))</LHS><RHS>mark(U22(isNat(V1)))</RHS></RULE><RULE><LHS>active(U22(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U31(tt,N))</LHS><RHS>mark(N)</RHS></RULE><RULE><LHS>active(U41(tt,M,N))</LHS><RHS>mark(s(plus(N,M)))</RHS></RULE><RULE><LHS>active(and(tt,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(isNat(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNat(plus(V1,V2)))</LHS><RHS>mark(U11(and(isNatKind(V1),isNatKind(V2)),V1,V2))</RHS></RULE><RULE><LHS>active(isNat(s(V1)))</LHS><RHS>mark(U21(isNatKind(V1),V1))</RHS></RULE><RULE><LHS>active(isNatKind(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNatKind(plus(V1,V2)))</LHS><RHS>mark(and(isNatKind(V1),isNatKind(V2)))</RHS></RULE><RULE><LHS>active(isNatKind(s(V1)))</LHS><RHS>mark(isNatKind(V1))</RHS></RULE><RULE><LHS>active(plus(N,0))</LHS><RHS>mark(U31(and(isNat(N),isNatKind(N)),N))</RHS></RULE><RULE><LHS>active(plus(N,s(M)))</LHS><RHS>mark(U41(and(and(isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),M,N))</RHS></RULE><RULE><LHS>mark(U11(X1,X2,X3))</LHS><RHS>active(U11(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(tt)</LHS><RHS>active(tt)</RHS></RULE><RULE><LHS>mark(U12(X1,X2))</LHS><RHS>active(U12(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(isNat(X))</LHS><RHS>active(isNat(X))</RHS></RULE><RULE><LHS>mark(U13(X))</LHS><RHS>active(U13(mark(X)))</RHS></RULE><RULE><LHS>mark(U21(X1,X2))</LHS><RHS>active(U21(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U22(X))</LHS><RHS>active(U22(mark(X)))</RHS></RULE><RULE><LHS>mark(U31(X1,X2))</LHS><RHS>active(U31(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U41(X1,X2,X3))</LHS><RHS>active(U41(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(mark(X)))</RHS></RULE><RULE><LHS>mark(plus(X1,X2))</LHS><RHS>active(plus(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(isNatKind(X))</LHS><RHS>active(isNatKind(X))</RHS></RULE><RULE><LHS>U11(mark(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,mark(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,mark(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(active(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,active(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,active(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U12(mark(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,mark(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(active(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,active(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>isNat(mark(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>isNat(active(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>U13(mark(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U13(active(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U21(mark(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,mark(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(active(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,active(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U22(mark(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U22(active(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U31(mark(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,mark(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(active(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,active(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U41(mark(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,mark(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,mark(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(active(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,active(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,active(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>s(mark(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>s(active(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>plus(mark(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,mark(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(active(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,active(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>and(mark(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,mark(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(active(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,active(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>isNatKind(mark(X))</LHS><RHS>isNatKind(X)</RHS></RULE><RULE><LHS>isNatKind(active(X))</LHS><RHS>isNatKind(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_U41(mark(X1),X2,X3)</LHS><RHS>Marked_U41(X1,X2,X3)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_U41(active(X1),X2,X3)</LHS><RHS>Marked_U41(X1,X2,X3)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><PROJECTION><PROJ><SYMBOL><NAME>Marked_U41</NAME></SYMBOL><INT>1</INT></PROJ></PROJECTION><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_U41(active(X1),X2,X3)</LHS><RHS>Marked_U41(X1,X2,X3)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_U41(mark(X1),X2,X3)</LHS><RHS>Marked_U41(X1,X2,X3)</RHS></DPRULE></DPLIST></STRICTPAIRS><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(U11(tt,V1,V2))</LHS><RHS>mark(U12(isNat(V1),V2))</RHS></RULE><RULE><LHS>active(U12(tt,V2))</LHS><RHS>mark(U13(isNat(V2)))</RHS></RULE><RULE><LHS>active(U13(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U21(tt,V1))</LHS><RHS>mark(U22(isNat(V1)))</RHS></RULE><RULE><LHS>active(U22(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U31(tt,N))</LHS><RHS>mark(N)</RHS></RULE><RULE><LHS>active(U41(tt,M,N))</LHS><RHS>mark(s(plus(N,M)))</RHS></RULE><RULE><LHS>active(and(tt,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(isNat(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNat(plus(V1,V2)))</LHS><RHS>mark(U11(and(isNatKind(V1),isNatKind(V2)),V1,V2))</RHS></RULE><RULE><LHS>active(isNat(s(V1)))</LHS><RHS>mark(U21(isNatKind(V1),V1))</RHS></RULE><RULE><LHS>active(isNatKind(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNatKind(plus(V1,V2)))</LHS><RHS>mark(and(isNatKind(V1),isNatKind(V2)))</RHS></RULE><RULE><LHS>active(isNatKind(s(V1)))</LHS><RHS>mark(isNatKind(V1))</RHS></RULE><RULE><LHS>active(plus(N,0))</LHS><RHS>mark(U31(and(isNat(N),isNatKind(N)),N))</RHS></RULE><RULE><LHS>active(plus(N,s(M)))</LHS><RHS>mark(U41(and(and(isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),M,N))</RHS></RULE><RULE><LHS>mark(U11(X1,X2,X3))</LHS><RHS>active(U11(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(tt)</LHS><RHS>active(tt)</RHS></RULE><RULE><LHS>mark(U12(X1,X2))</LHS><RHS>active(U12(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(isNat(X))</LHS><RHS>active(isNat(X))</RHS></RULE><RULE><LHS>mark(U13(X))</LHS><RHS>active(U13(mark(X)))</RHS></RULE><RULE><LHS>mark(U21(X1,X2))</LHS><RHS>active(U21(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U22(X))</LHS><RHS>active(U22(mark(X)))</RHS></RULE><RULE><LHS>mark(U31(X1,X2))</LHS><RHS>active(U31(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U41(X1,X2,X3))</LHS><RHS>active(U41(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(mark(X)))</RHS></RULE><RULE><LHS>mark(plus(X1,X2))</LHS><RHS>active(plus(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(isNatKind(X))</LHS><RHS>active(isNatKind(X))</RHS></RULE><RULE><LHS>U11(mark(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,mark(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,mark(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(active(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,active(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,active(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U12(mark(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,mark(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(active(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,active(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>isNat(mark(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>isNat(active(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>U13(mark(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U13(active(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U21(mark(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,mark(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(active(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,active(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U22(mark(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U22(active(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U31(mark(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,mark(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(active(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,active(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U41(mark(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,mark(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,mark(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(active(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,active(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,active(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>s(mark(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>s(active(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>plus(mark(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,mark(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(active(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,active(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>and(mark(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,mark(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(active(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,active(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>isNatKind(mark(X))</LHS><RHS>isNatKind(X)</RHS></RULE><RULE><LHS>isNatKind(active(X))</LHS><RHS>isNatKind(X)</RHS></RULE></REWSYS><DPLIST/></DPSYS></SYSTEM><CRITERION><DAG approx="simpl"><CCLIST/></DAG></CRITERION></PROPERTY></PROPERTY></PROPERTY></PROPERTY></PROPERTY></PROPERTY><PROPERTY criterion="sterm" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(U11(tt,V1,V2))</LHS><RHS>mark(U12(isNat(V1),V2))</RHS></RULE><RULE><LHS>active(U12(tt,V2))</LHS><RHS>mark(U13(isNat(V2)))</RHS></RULE><RULE><LHS>active(U13(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U21(tt,V1))</LHS><RHS>mark(U22(isNat(V1)))</RHS></RULE><RULE><LHS>active(U22(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U31(tt,N))</LHS><RHS>mark(N)</RHS></RULE><RULE><LHS>active(U41(tt,M,N))</LHS><RHS>mark(s(plus(N,M)))</RHS></RULE><RULE><LHS>active(and(tt,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(isNat(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNat(plus(V1,V2)))</LHS><RHS>mark(U11(and(isNatKind(V1),isNatKind(V2)),V1,V2))</RHS></RULE><RULE><LHS>active(isNat(s(V1)))</LHS><RHS>mark(U21(isNatKind(V1),V1))</RHS></RULE><RULE><LHS>active(isNatKind(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNatKind(plus(V1,V2)))</LHS><RHS>mark(and(isNatKind(V1),isNatKind(V2)))</RHS></RULE><RULE><LHS>active(isNatKind(s(V1)))</LHS><RHS>mark(isNatKind(V1))</RHS></RULE><RULE><LHS>active(plus(N,0))</LHS><RHS>mark(U31(and(isNat(N),isNatKind(N)),N))</RHS></RULE><RULE><LHS>active(plus(N,s(M)))</LHS><RHS>mark(U41(and(and(isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),M,N))</RHS></RULE><RULE><LHS>mark(U11(X1,X2,X3))</LHS><RHS>active(U11(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(tt)</LHS><RHS>active(tt)</RHS></RULE><RULE><LHS>mark(U12(X1,X2))</LHS><RHS>active(U12(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(isNat(X))</LHS><RHS>active(isNat(X))</RHS></RULE><RULE><LHS>mark(U13(X))</LHS><RHS>active(U13(mark(X)))</RHS></RULE><RULE><LHS>mark(U21(X1,X2))</LHS><RHS>active(U21(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U22(X))</LHS><RHS>active(U22(mark(X)))</RHS></RULE><RULE><LHS>mark(U31(X1,X2))</LHS><RHS>active(U31(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U41(X1,X2,X3))</LHS><RHS>active(U41(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(mark(X)))</RHS></RULE><RULE><LHS>mark(plus(X1,X2))</LHS><RHS>active(plus(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(isNatKind(X))</LHS><RHS>active(isNatKind(X))</RHS></RULE><RULE><LHS>U11(mark(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,mark(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,mark(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(active(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,active(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,active(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U12(mark(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,mark(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(active(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,active(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>isNat(mark(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>isNat(active(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>U13(mark(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U13(active(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U21(mark(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,mark(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(active(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,active(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U22(mark(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U22(active(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U31(mark(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,mark(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(active(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,active(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U41(mark(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,mark(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,mark(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(active(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,active(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,active(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>s(mark(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>s(active(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>plus(mark(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,mark(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(active(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,active(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>and(mark(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,mark(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(active(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,active(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>isNatKind(mark(X))</LHS><RHS>isNatKind(X)</RHS></RULE><RULE><LHS>isNatKind(active(X))</LHS><RHS>isNatKind(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_s(mark(X))</LHS><RHS>Marked_s(X)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_s(active(X))</LHS><RHS>Marked_s(X)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><PROJECTION><PROJ><SYMBOL><NAME>Marked_s</NAME></SYMBOL><INT>1</INT></PROJ></PROJECTION><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_s(active(X))</LHS><RHS>Marked_s(X)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_s(mark(X))</LHS><RHS>Marked_s(X)</RHS></DPRULE></DPLIST></STRICTPAIRS><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(U11(tt,V1,V2))</LHS><RHS>mark(U12(isNat(V1),V2))</RHS></RULE><RULE><LHS>active(U12(tt,V2))</LHS><RHS>mark(U13(isNat(V2)))</RHS></RULE><RULE><LHS>active(U13(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U21(tt,V1))</LHS><RHS>mark(U22(isNat(V1)))</RHS></RULE><RULE><LHS>active(U22(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U31(tt,N))</LHS><RHS>mark(N)</RHS></RULE><RULE><LHS>active(U41(tt,M,N))</LHS><RHS>mark(s(plus(N,M)))</RHS></RULE><RULE><LHS>active(and(tt,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(isNat(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNat(plus(V1,V2)))</LHS><RHS>mark(U11(and(isNatKind(V1),isNatKind(V2)),V1,V2))</RHS></RULE><RULE><LHS>active(isNat(s(V1)))</LHS><RHS>mark(U21(isNatKind(V1),V1))</RHS></RULE><RULE><LHS>active(isNatKind(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNatKind(plus(V1,V2)))</LHS><RHS>mark(and(isNatKind(V1),isNatKind(V2)))</RHS></RULE><RULE><LHS>active(isNatKind(s(V1)))</LHS><RHS>mark(isNatKind(V1))</RHS></RULE><RULE><LHS>active(plus(N,0))</LHS><RHS>mark(U31(and(isNat(N),isNatKind(N)),N))</RHS></RULE><RULE><LHS>active(plus(N,s(M)))</LHS><RHS>mark(U41(and(and(isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),M,N))</RHS></RULE><RULE><LHS>mark(U11(X1,X2,X3))</LHS><RHS>active(U11(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(tt)</LHS><RHS>active(tt)</RHS></RULE><RULE><LHS>mark(U12(X1,X2))</LHS><RHS>active(U12(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(isNat(X))</LHS><RHS>active(isNat(X))</RHS></RULE><RULE><LHS>mark(U13(X))</LHS><RHS>active(U13(mark(X)))</RHS></RULE><RULE><LHS>mark(U21(X1,X2))</LHS><RHS>active(U21(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U22(X))</LHS><RHS>active(U22(mark(X)))</RHS></RULE><RULE><LHS>mark(U31(X1,X2))</LHS><RHS>active(U31(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U41(X1,X2,X3))</LHS><RHS>active(U41(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(mark(X)))</RHS></RULE><RULE><LHS>mark(plus(X1,X2))</LHS><RHS>active(plus(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(isNatKind(X))</LHS><RHS>active(isNatKind(X))</RHS></RULE><RULE><LHS>U11(mark(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,mark(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,mark(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(active(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,active(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,active(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U12(mark(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,mark(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(active(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,active(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>isNat(mark(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>isNat(active(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>U13(mark(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U13(active(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U21(mark(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,mark(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(active(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,active(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U22(mark(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U22(active(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U31(mark(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,mark(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(active(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,active(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U41(mark(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,mark(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,mark(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(active(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,active(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,active(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>s(mark(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>s(active(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>plus(mark(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,mark(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(active(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,active(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>and(mark(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,mark(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(active(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,active(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>isNatKind(mark(X))</LHS><RHS>isNatKind(X)</RHS></RULE><RULE><LHS>isNatKind(active(X))</LHS><RHS>isNatKind(X)</RHS></RULE></REWSYS><DPLIST/></DPSYS></SYSTEM><CRITERION><DAG approx="simpl"><CCLIST/></DAG></CRITERION></PROPERTY></PROPERTY><PROPERTY criterion="sterm" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(U11(tt,V1,V2))</LHS><RHS>mark(U12(isNat(V1),V2))</RHS></RULE><RULE><LHS>active(U12(tt,V2))</LHS><RHS>mark(U13(isNat(V2)))</RHS></RULE><RULE><LHS>active(U13(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U21(tt,V1))</LHS><RHS>mark(U22(isNat(V1)))</RHS></RULE><RULE><LHS>active(U22(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U31(tt,N))</LHS><RHS>mark(N)</RHS></RULE><RULE><LHS>active(U41(tt,M,N))</LHS><RHS>mark(s(plus(N,M)))</RHS></RULE><RULE><LHS>active(and(tt,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(isNat(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNat(plus(V1,V2)))</LHS><RHS>mark(U11(and(isNatKind(V1),isNatKind(V2)),V1,V2))</RHS></RULE><RULE><LHS>active(isNat(s(V1)))</LHS><RHS>mark(U21(isNatKind(V1),V1))</RHS></RULE><RULE><LHS>active(isNatKind(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNatKind(plus(V1,V2)))</LHS><RHS>mark(and(isNatKind(V1),isNatKind(V2)))</RHS></RULE><RULE><LHS>active(isNatKind(s(V1)))</LHS><RHS>mark(isNatKind(V1))</RHS></RULE><RULE><LHS>active(plus(N,0))</LHS><RHS>mark(U31(and(isNat(N),isNatKind(N)),N))</RHS></RULE><RULE><LHS>active(plus(N,s(M)))</LHS><RHS>mark(U41(and(and(isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),M,N))</RHS></RULE><RULE><LHS>mark(U11(X1,X2,X3))</LHS><RHS>active(U11(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(tt)</LHS><RHS>active(tt)</RHS></RULE><RULE><LHS>mark(U12(X1,X2))</LHS><RHS>active(U12(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(isNat(X))</LHS><RHS>active(isNat(X))</RHS></RULE><RULE><LHS>mark(U13(X))</LHS><RHS>active(U13(mark(X)))</RHS></RULE><RULE><LHS>mark(U21(X1,X2))</LHS><RHS>active(U21(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U22(X))</LHS><RHS>active(U22(mark(X)))</RHS></RULE><RULE><LHS>mark(U31(X1,X2))</LHS><RHS>active(U31(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U41(X1,X2,X3))</LHS><RHS>active(U41(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(mark(X)))</RHS></RULE><RULE><LHS>mark(plus(X1,X2))</LHS><RHS>active(plus(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(isNatKind(X))</LHS><RHS>active(isNatKind(X))</RHS></RULE><RULE><LHS>U11(mark(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,mark(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,mark(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(active(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,active(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,active(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U12(mark(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,mark(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(active(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,active(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>isNat(mark(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>isNat(active(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>U13(mark(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U13(active(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U21(mark(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,mark(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(active(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,active(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U22(mark(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U22(active(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U31(mark(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,mark(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(active(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,active(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U41(mark(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,mark(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,mark(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(active(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,active(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,active(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>s(mark(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>s(active(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>plus(mark(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,mark(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(active(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,active(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>and(mark(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,mark(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(active(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,active(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>isNatKind(mark(X))</LHS><RHS>isNatKind(X)</RHS></RULE><RULE><LHS>isNatKind(active(X))</LHS><RHS>isNatKind(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_plus(mark(X1),X2)</LHS><RHS>Marked_plus(X1,X2)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_plus(X1,mark(X2))</LHS><RHS>Marked_plus(X1,X2)</RHS></DPRULE><DPRULE num="2"><LHS>Marked_plus(active(X1),X2)</LHS><RHS>Marked_plus(X1,X2)</RHS></DPRULE><DPRULE num="3"><LHS>Marked_plus(X1,active(X2))</LHS><RHS>Marked_plus(X1,X2)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><PROJECTION><PROJ><SYMBOL><NAME>Marked_plus</NAME></SYMBOL><INT>2</INT></PROJ></PROJECTION><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_plus(X1,active(X2))</LHS><RHS>Marked_plus(X1,X2)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_plus(X1,mark(X2))</LHS><RHS>Marked_plus(X1,X2)</RHS></DPRULE></DPLIST></STRICTPAIRS><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(U11(tt,V1,V2))</LHS><RHS>mark(U12(isNat(V1),V2))</RHS></RULE><RULE><LHS>active(U12(tt,V2))</LHS><RHS>mark(U13(isNat(V2)))</RHS></RULE><RULE><LHS>active(U13(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U21(tt,V1))</LHS><RHS>mark(U22(isNat(V1)))</RHS></RULE><RULE><LHS>active(U22(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U31(tt,N))</LHS><RHS>mark(N)</RHS></RULE><RULE><LHS>active(U41(tt,M,N))</LHS><RHS>mark(s(plus(N,M)))</RHS></RULE><RULE><LHS>active(and(tt,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(isNat(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNat(plus(V1,V2)))</LHS><RHS>mark(U11(and(isNatKind(V1),isNatKind(V2)),V1,V2))</RHS></RULE><RULE><LHS>active(isNat(s(V1)))</LHS><RHS>mark(U21(isNatKind(V1),V1))</RHS></RULE><RULE><LHS>active(isNatKind(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNatKind(plus(V1,V2)))</LHS><RHS>mark(and(isNatKind(V1),isNatKind(V2)))</RHS></RULE><RULE><LHS>active(isNatKind(s(V1)))</LHS><RHS>mark(isNatKind(V1))</RHS></RULE><RULE><LHS>active(plus(N,0))</LHS><RHS>mark(U31(and(isNat(N),isNatKind(N)),N))</RHS></RULE><RULE><LHS>active(plus(N,s(M)))</LHS><RHS>mark(U41(and(and(isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),M,N))</RHS></RULE><RULE><LHS>mark(U11(X1,X2,X3))</LHS><RHS>active(U11(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(tt)</LHS><RHS>active(tt)</RHS></RULE><RULE><LHS>mark(U12(X1,X2))</LHS><RHS>active(U12(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(isNat(X))</LHS><RHS>active(isNat(X))</RHS></RULE><RULE><LHS>mark(U13(X))</LHS><RHS>active(U13(mark(X)))</RHS></RULE><RULE><LHS>mark(U21(X1,X2))</LHS><RHS>active(U21(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U22(X))</LHS><RHS>active(U22(mark(X)))</RHS></RULE><RULE><LHS>mark(U31(X1,X2))</LHS><RHS>active(U31(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U41(X1,X2,X3))</LHS><RHS>active(U41(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(mark(X)))</RHS></RULE><RULE><LHS>mark(plus(X1,X2))</LHS><RHS>active(plus(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(isNatKind(X))</LHS><RHS>active(isNatKind(X))</RHS></RULE><RULE><LHS>U11(mark(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,mark(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,mark(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(active(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,active(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,active(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U12(mark(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,mark(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(active(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,active(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>isNat(mark(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>isNat(active(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>U13(mark(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U13(active(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U21(mark(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,mark(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(active(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,active(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U22(mark(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U22(active(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U31(mark(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,mark(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(active(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,active(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U41(mark(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,mark(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,mark(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(active(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,active(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,active(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>s(mark(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>s(active(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>plus(mark(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,mark(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(active(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,active(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>and(mark(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,mark(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(active(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,active(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>isNatKind(mark(X))</LHS><RHS>isNatKind(X)</RHS></RULE><RULE><LHS>isNatKind(active(X))</LHS><RHS>isNatKind(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_plus(active(X1),X2)</LHS><RHS>Marked_plus(X1,X2)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_plus(mark(X1),X2)</LHS><RHS>Marked_plus(X1,X2)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><DAG approx="simpl"><CCLIST><SCC num="0"><NODE ref="0"/><NODE ref="1"/></SCC></CCLIST></DAG></CRITERION><PROPERTY criterion="sterm" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(U11(tt,V1,V2))</LHS><RHS>mark(U12(isNat(V1),V2))</RHS></RULE><RULE><LHS>active(U12(tt,V2))</LHS><RHS>mark(U13(isNat(V2)))</RHS></RULE><RULE><LHS>active(U13(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U21(tt,V1))</LHS><RHS>mark(U22(isNat(V1)))</RHS></RULE><RULE><LHS>active(U22(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U31(tt,N))</LHS><RHS>mark(N)</RHS></RULE><RULE><LHS>active(U41(tt,M,N))</LHS><RHS>mark(s(plus(N,M)))</RHS></RULE><RULE><LHS>active(and(tt,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(isNat(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNat(plus(V1,V2)))</LHS><RHS>mark(U11(and(isNatKind(V1),isNatKind(V2)),V1,V2))</RHS></RULE><RULE><LHS>active(isNat(s(V1)))</LHS><RHS>mark(U21(isNatKind(V1),V1))</RHS></RULE><RULE><LHS>active(isNatKind(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNatKind(plus(V1,V2)))</LHS><RHS>mark(and(isNatKind(V1),isNatKind(V2)))</RHS></RULE><RULE><LHS>active(isNatKind(s(V1)))</LHS><RHS>mark(isNatKind(V1))</RHS></RULE><RULE><LHS>active(plus(N,0))</LHS><RHS>mark(U31(and(isNat(N),isNatKind(N)),N))</RHS></RULE><RULE><LHS>active(plus(N,s(M)))</LHS><RHS>mark(U41(and(and(isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),M,N))</RHS></RULE><RULE><LHS>mark(U11(X1,X2,X3))</LHS><RHS>active(U11(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(tt)</LHS><RHS>active(tt)</RHS></RULE><RULE><LHS>mark(U12(X1,X2))</LHS><RHS>active(U12(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(isNat(X))</LHS><RHS>active(isNat(X))</RHS></RULE><RULE><LHS>mark(U13(X))</LHS><RHS>active(U13(mark(X)))</RHS></RULE><RULE><LHS>mark(U21(X1,X2))</LHS><RHS>active(U21(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U22(X))</LHS><RHS>active(U22(mark(X)))</RHS></RULE><RULE><LHS>mark(U31(X1,X2))</LHS><RHS>active(U31(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U41(X1,X2,X3))</LHS><RHS>active(U41(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(mark(X)))</RHS></RULE><RULE><LHS>mark(plus(X1,X2))</LHS><RHS>active(plus(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(isNatKind(X))</LHS><RHS>active(isNatKind(X))</RHS></RULE><RULE><LHS>U11(mark(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,mark(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,mark(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(active(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,active(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,active(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U12(mark(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,mark(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(active(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,active(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>isNat(mark(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>isNat(active(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>U13(mark(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U13(active(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U21(mark(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,mark(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(active(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,active(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U22(mark(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U22(active(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U31(mark(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,mark(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(active(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,active(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U41(mark(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,mark(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,mark(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(active(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,active(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,active(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>s(mark(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>s(active(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>plus(mark(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,mark(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(active(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,active(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>and(mark(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,mark(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(active(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,active(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>isNatKind(mark(X))</LHS><RHS>isNatKind(X)</RHS></RULE><RULE><LHS>isNatKind(active(X))</LHS><RHS>isNatKind(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_plus(active(X1),X2)</LHS><RHS>Marked_plus(X1,X2)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_plus(mark(X1),X2)</LHS><RHS>Marked_plus(X1,X2)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><PROJECTION><PROJ><SYMBOL><NAME>Marked_plus</NAME></SYMBOL><INT>1</INT></PROJ></PROJECTION><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_plus(mark(X1),X2)</LHS><RHS>Marked_plus(X1,X2)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_plus(active(X1),X2)</LHS><RHS>Marked_plus(X1,X2)</RHS></DPRULE></DPLIST></STRICTPAIRS><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(U11(tt,V1,V2))</LHS><RHS>mark(U12(isNat(V1),V2))</RHS></RULE><RULE><LHS>active(U12(tt,V2))</LHS><RHS>mark(U13(isNat(V2)))</RHS></RULE><RULE><LHS>active(U13(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U21(tt,V1))</LHS><RHS>mark(U22(isNat(V1)))</RHS></RULE><RULE><LHS>active(U22(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U31(tt,N))</LHS><RHS>mark(N)</RHS></RULE><RULE><LHS>active(U41(tt,M,N))</LHS><RHS>mark(s(plus(N,M)))</RHS></RULE><RULE><LHS>active(and(tt,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(isNat(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNat(plus(V1,V2)))</LHS><RHS>mark(U11(and(isNatKind(V1),isNatKind(V2)),V1,V2))</RHS></RULE><RULE><LHS>active(isNat(s(V1)))</LHS><RHS>mark(U21(isNatKind(V1),V1))</RHS></RULE><RULE><LHS>active(isNatKind(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNatKind(plus(V1,V2)))</LHS><RHS>mark(and(isNatKind(V1),isNatKind(V2)))</RHS></RULE><RULE><LHS>active(isNatKind(s(V1)))</LHS><RHS>mark(isNatKind(V1))</RHS></RULE><RULE><LHS>active(plus(N,0))</LHS><RHS>mark(U31(and(isNat(N),isNatKind(N)),N))</RHS></RULE><RULE><LHS>active(plus(N,s(M)))</LHS><RHS>mark(U41(and(and(isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),M,N))</RHS></RULE><RULE><LHS>mark(U11(X1,X2,X3))</LHS><RHS>active(U11(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(tt)</LHS><RHS>active(tt)</RHS></RULE><RULE><LHS>mark(U12(X1,X2))</LHS><RHS>active(U12(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(isNat(X))</LHS><RHS>active(isNat(X))</RHS></RULE><RULE><LHS>mark(U13(X))</LHS><RHS>active(U13(mark(X)))</RHS></RULE><RULE><LHS>mark(U21(X1,X2))</LHS><RHS>active(U21(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U22(X))</LHS><RHS>active(U22(mark(X)))</RHS></RULE><RULE><LHS>mark(U31(X1,X2))</LHS><RHS>active(U31(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U41(X1,X2,X3))</LHS><RHS>active(U41(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(mark(X)))</RHS></RULE><RULE><LHS>mark(plus(X1,X2))</LHS><RHS>active(plus(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(isNatKind(X))</LHS><RHS>active(isNatKind(X))</RHS></RULE><RULE><LHS>U11(mark(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,mark(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,mark(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(active(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,active(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,active(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U12(mark(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,mark(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(active(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,active(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>isNat(mark(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>isNat(active(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>U13(mark(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U13(active(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U21(mark(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,mark(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(active(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,active(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U22(mark(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U22(active(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U31(mark(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,mark(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(active(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,active(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U41(mark(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,mark(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,mark(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(active(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,active(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,active(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>s(mark(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>s(active(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>plus(mark(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,mark(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(active(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,active(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>and(mark(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,mark(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(active(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,active(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>isNatKind(mark(X))</LHS><RHS>isNatKind(X)</RHS></RULE><RULE><LHS>isNatKind(active(X))</LHS><RHS>isNatKind(X)</RHS></RULE></REWSYS><DPLIST/></DPSYS></SYSTEM><CRITERION><DAG approx="simpl"><CCLIST/></DAG></CRITERION></PROPERTY></PROPERTY></PROPERTY></PROPERTY><PROPERTY criterion="sterm" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(U11(tt,V1,V2))</LHS><RHS>mark(U12(isNat(V1),V2))</RHS></RULE><RULE><LHS>active(U12(tt,V2))</LHS><RHS>mark(U13(isNat(V2)))</RHS></RULE><RULE><LHS>active(U13(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U21(tt,V1))</LHS><RHS>mark(U22(isNat(V1)))</RHS></RULE><RULE><LHS>active(U22(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U31(tt,N))</LHS><RHS>mark(N)</RHS></RULE><RULE><LHS>active(U41(tt,M,N))</LHS><RHS>mark(s(plus(N,M)))</RHS></RULE><RULE><LHS>active(and(tt,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(isNat(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNat(plus(V1,V2)))</LHS><RHS>mark(U11(and(isNatKind(V1),isNatKind(V2)),V1,V2))</RHS></RULE><RULE><LHS>active(isNat(s(V1)))</LHS><RHS>mark(U21(isNatKind(V1),V1))</RHS></RULE><RULE><LHS>active(isNatKind(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNatKind(plus(V1,V2)))</LHS><RHS>mark(and(isNatKind(V1),isNatKind(V2)))</RHS></RULE><RULE><LHS>active(isNatKind(s(V1)))</LHS><RHS>mark(isNatKind(V1))</RHS></RULE><RULE><LHS>active(plus(N,0))</LHS><RHS>mark(U31(and(isNat(N),isNatKind(N)),N))</RHS></RULE><RULE><LHS>active(plus(N,s(M)))</LHS><RHS>mark(U41(and(and(isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),M,N))</RHS></RULE><RULE><LHS>mark(U11(X1,X2,X3))</LHS><RHS>active(U11(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(tt)</LHS><RHS>active(tt)</RHS></RULE><RULE><LHS>mark(U12(X1,X2))</LHS><RHS>active(U12(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(isNat(X))</LHS><RHS>active(isNat(X))</RHS></RULE><RULE><LHS>mark(U13(X))</LHS><RHS>active(U13(mark(X)))</RHS></RULE><RULE><LHS>mark(U21(X1,X2))</LHS><RHS>active(U21(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U22(X))</LHS><RHS>active(U22(mark(X)))</RHS></RULE><RULE><LHS>mark(U31(X1,X2))</LHS><RHS>active(U31(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U41(X1,X2,X3))</LHS><RHS>active(U41(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(mark(X)))</RHS></RULE><RULE><LHS>mark(plus(X1,X2))</LHS><RHS>active(plus(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(isNatKind(X))</LHS><RHS>active(isNatKind(X))</RHS></RULE><RULE><LHS>U11(mark(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,mark(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,mark(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(active(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,active(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,active(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U12(mark(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,mark(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(active(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,active(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>isNat(mark(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>isNat(active(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>U13(mark(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U13(active(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U21(mark(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,mark(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(active(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,active(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U22(mark(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U22(active(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U31(mark(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,mark(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(active(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,active(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U41(mark(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,mark(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,mark(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(active(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,active(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,active(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>s(mark(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>s(active(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>plus(mark(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,mark(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(active(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,active(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>and(mark(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,mark(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(active(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,active(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>isNatKind(mark(X))</LHS><RHS>isNatKind(X)</RHS></RULE><RULE><LHS>isNatKind(active(X))</LHS><RHS>isNatKind(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_and(mark(X1),X2)</LHS><RHS>Marked_and(X1,X2)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_and(X1,mark(X2))</LHS><RHS>Marked_and(X1,X2)</RHS></DPRULE><DPRULE num="2"><LHS>Marked_and(active(X1),X2)</LHS><RHS>Marked_and(X1,X2)</RHS></DPRULE><DPRULE num="3"><LHS>Marked_and(X1,active(X2))</LHS><RHS>Marked_and(X1,X2)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><PROJECTION><PROJ><SYMBOL><NAME>Marked_and</NAME></SYMBOL><INT>2</INT></PROJ></PROJECTION><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_and(X1,active(X2))</LHS><RHS>Marked_and(X1,X2)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_and(X1,mark(X2))</LHS><RHS>Marked_and(X1,X2)</RHS></DPRULE></DPLIST></STRICTPAIRS><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(U11(tt,V1,V2))</LHS><RHS>mark(U12(isNat(V1),V2))</RHS></RULE><RULE><LHS>active(U12(tt,V2))</LHS><RHS>mark(U13(isNat(V2)))</RHS></RULE><RULE><LHS>active(U13(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U21(tt,V1))</LHS><RHS>mark(U22(isNat(V1)))</RHS></RULE><RULE><LHS>active(U22(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U31(tt,N))</LHS><RHS>mark(N)</RHS></RULE><RULE><LHS>active(U41(tt,M,N))</LHS><RHS>mark(s(plus(N,M)))</RHS></RULE><RULE><LHS>active(and(tt,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(isNat(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNat(plus(V1,V2)))</LHS><RHS>mark(U11(and(isNatKind(V1),isNatKind(V2)),V1,V2))</RHS></RULE><RULE><LHS>active(isNat(s(V1)))</LHS><RHS>mark(U21(isNatKind(V1),V1))</RHS></RULE><RULE><LHS>active(isNatKind(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNatKind(plus(V1,V2)))</LHS><RHS>mark(and(isNatKind(V1),isNatKind(V2)))</RHS></RULE><RULE><LHS>active(isNatKind(s(V1)))</LHS><RHS>mark(isNatKind(V1))</RHS></RULE><RULE><LHS>active(plus(N,0))</LHS><RHS>mark(U31(and(isNat(N),isNatKind(N)),N))</RHS></RULE><RULE><LHS>active(plus(N,s(M)))</LHS><RHS>mark(U41(and(and(isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),M,N))</RHS></RULE><RULE><LHS>mark(U11(X1,X2,X3))</LHS><RHS>active(U11(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(tt)</LHS><RHS>active(tt)</RHS></RULE><RULE><LHS>mark(U12(X1,X2))</LHS><RHS>active(U12(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(isNat(X))</LHS><RHS>active(isNat(X))</RHS></RULE><RULE><LHS>mark(U13(X))</LHS><RHS>active(U13(mark(X)))</RHS></RULE><RULE><LHS>mark(U21(X1,X2))</LHS><RHS>active(U21(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U22(X))</LHS><RHS>active(U22(mark(X)))</RHS></RULE><RULE><LHS>mark(U31(X1,X2))</LHS><RHS>active(U31(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U41(X1,X2,X3))</LHS><RHS>active(U41(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(mark(X)))</RHS></RULE><RULE><LHS>mark(plus(X1,X2))</LHS><RHS>active(plus(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(isNatKind(X))</LHS><RHS>active(isNatKind(X))</RHS></RULE><RULE><LHS>U11(mark(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,mark(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,mark(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(active(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,active(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,active(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U12(mark(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,mark(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(active(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,active(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>isNat(mark(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>isNat(active(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>U13(mark(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U13(active(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U21(mark(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,mark(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(active(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,active(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U22(mark(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U22(active(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U31(mark(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,mark(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(active(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,active(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U41(mark(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,mark(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,mark(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(active(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,active(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,active(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>s(mark(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>s(active(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>plus(mark(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,mark(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(active(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,active(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>and(mark(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,mark(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(active(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,active(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>isNatKind(mark(X))</LHS><RHS>isNatKind(X)</RHS></RULE><RULE><LHS>isNatKind(active(X))</LHS><RHS>isNatKind(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_and(active(X1),X2)</LHS><RHS>Marked_and(X1,X2)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_and(mark(X1),X2)</LHS><RHS>Marked_and(X1,X2)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><DAG approx="simpl"><CCLIST><SCC num="0"><NODE ref="0"/><NODE ref="1"/></SCC></CCLIST></DAG></CRITERION><PROPERTY criterion="sterm" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(U11(tt,V1,V2))</LHS><RHS>mark(U12(isNat(V1),V2))</RHS></RULE><RULE><LHS>active(U12(tt,V2))</LHS><RHS>mark(U13(isNat(V2)))</RHS></RULE><RULE><LHS>active(U13(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U21(tt,V1))</LHS><RHS>mark(U22(isNat(V1)))</RHS></RULE><RULE><LHS>active(U22(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U31(tt,N))</LHS><RHS>mark(N)</RHS></RULE><RULE><LHS>active(U41(tt,M,N))</LHS><RHS>mark(s(plus(N,M)))</RHS></RULE><RULE><LHS>active(and(tt,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(isNat(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNat(plus(V1,V2)))</LHS><RHS>mark(U11(and(isNatKind(V1),isNatKind(V2)),V1,V2))</RHS></RULE><RULE><LHS>active(isNat(s(V1)))</LHS><RHS>mark(U21(isNatKind(V1),V1))</RHS></RULE><RULE><LHS>active(isNatKind(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNatKind(plus(V1,V2)))</LHS><RHS>mark(and(isNatKind(V1),isNatKind(V2)))</RHS></RULE><RULE><LHS>active(isNatKind(s(V1)))</LHS><RHS>mark(isNatKind(V1))</RHS></RULE><RULE><LHS>active(plus(N,0))</LHS><RHS>mark(U31(and(isNat(N),isNatKind(N)),N))</RHS></RULE><RULE><LHS>active(plus(N,s(M)))</LHS><RHS>mark(U41(and(and(isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),M,N))</RHS></RULE><RULE><LHS>mark(U11(X1,X2,X3))</LHS><RHS>active(U11(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(tt)</LHS><RHS>active(tt)</RHS></RULE><RULE><LHS>mark(U12(X1,X2))</LHS><RHS>active(U12(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(isNat(X))</LHS><RHS>active(isNat(X))</RHS></RULE><RULE><LHS>mark(U13(X))</LHS><RHS>active(U13(mark(X)))</RHS></RULE><RULE><LHS>mark(U21(X1,X2))</LHS><RHS>active(U21(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U22(X))</LHS><RHS>active(U22(mark(X)))</RHS></RULE><RULE><LHS>mark(U31(X1,X2))</LHS><RHS>active(U31(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U41(X1,X2,X3))</LHS><RHS>active(U41(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(mark(X)))</RHS></RULE><RULE><LHS>mark(plus(X1,X2))</LHS><RHS>active(plus(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(isNatKind(X))</LHS><RHS>active(isNatKind(X))</RHS></RULE><RULE><LHS>U11(mark(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,mark(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,mark(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(active(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,active(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,active(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U12(mark(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,mark(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(active(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,active(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>isNat(mark(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>isNat(active(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>U13(mark(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U13(active(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U21(mark(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,mark(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(active(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,active(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U22(mark(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U22(active(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U31(mark(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,mark(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(active(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,active(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U41(mark(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,mark(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,mark(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(active(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,active(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,active(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>s(mark(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>s(active(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>plus(mark(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,mark(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(active(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,active(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>and(mark(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,mark(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(active(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,active(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>isNatKind(mark(X))</LHS><RHS>isNatKind(X)</RHS></RULE><RULE><LHS>isNatKind(active(X))</LHS><RHS>isNatKind(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_and(active(X1),X2)</LHS><RHS>Marked_and(X1,X2)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_and(mark(X1),X2)</LHS><RHS>Marked_and(X1,X2)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><PROJECTION><PROJ><SYMBOL><NAME>Marked_and</NAME></SYMBOL><INT>1</INT></PROJ></PROJECTION><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_and(mark(X1),X2)</LHS><RHS>Marked_and(X1,X2)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_and(active(X1),X2)</LHS><RHS>Marked_and(X1,X2)</RHS></DPRULE></DPLIST></STRICTPAIRS><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(U11(tt,V1,V2))</LHS><RHS>mark(U12(isNat(V1),V2))</RHS></RULE><RULE><LHS>active(U12(tt,V2))</LHS><RHS>mark(U13(isNat(V2)))</RHS></RULE><RULE><LHS>active(U13(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U21(tt,V1))</LHS><RHS>mark(U22(isNat(V1)))</RHS></RULE><RULE><LHS>active(U22(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U31(tt,N))</LHS><RHS>mark(N)</RHS></RULE><RULE><LHS>active(U41(tt,M,N))</LHS><RHS>mark(s(plus(N,M)))</RHS></RULE><RULE><LHS>active(and(tt,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(isNat(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNat(plus(V1,V2)))</LHS><RHS>mark(U11(and(isNatKind(V1),isNatKind(V2)),V1,V2))</RHS></RULE><RULE><LHS>active(isNat(s(V1)))</LHS><RHS>mark(U21(isNatKind(V1),V1))</RHS></RULE><RULE><LHS>active(isNatKind(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNatKind(plus(V1,V2)))</LHS><RHS>mark(and(isNatKind(V1),isNatKind(V2)))</RHS></RULE><RULE><LHS>active(isNatKind(s(V1)))</LHS><RHS>mark(isNatKind(V1))</RHS></RULE><RULE><LHS>active(plus(N,0))</LHS><RHS>mark(U31(and(isNat(N),isNatKind(N)),N))</RHS></RULE><RULE><LHS>active(plus(N,s(M)))</LHS><RHS>mark(U41(and(and(isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),M,N))</RHS></RULE><RULE><LHS>mark(U11(X1,X2,X3))</LHS><RHS>active(U11(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(tt)</LHS><RHS>active(tt)</RHS></RULE><RULE><LHS>mark(U12(X1,X2))</LHS><RHS>active(U12(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(isNat(X))</LHS><RHS>active(isNat(X))</RHS></RULE><RULE><LHS>mark(U13(X))</LHS><RHS>active(U13(mark(X)))</RHS></RULE><RULE><LHS>mark(U21(X1,X2))</LHS><RHS>active(U21(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U22(X))</LHS><RHS>active(U22(mark(X)))</RHS></RULE><RULE><LHS>mark(U31(X1,X2))</LHS><RHS>active(U31(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U41(X1,X2,X3))</LHS><RHS>active(U41(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(mark(X)))</RHS></RULE><RULE><LHS>mark(plus(X1,X2))</LHS><RHS>active(plus(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(isNatKind(X))</LHS><RHS>active(isNatKind(X))</RHS></RULE><RULE><LHS>U11(mark(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,mark(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,mark(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(active(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,active(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,active(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U12(mark(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,mark(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(active(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,active(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>isNat(mark(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>isNat(active(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>U13(mark(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U13(active(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U21(mark(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,mark(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(active(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,active(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U22(mark(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U22(active(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U31(mark(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,mark(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(active(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,active(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U41(mark(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,mark(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,mark(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(active(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,active(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,active(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>s(mark(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>s(active(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>plus(mark(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,mark(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(active(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,active(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>and(mark(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,mark(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(active(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,active(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>isNatKind(mark(X))</LHS><RHS>isNatKind(X)</RHS></RULE><RULE><LHS>isNatKind(active(X))</LHS><RHS>isNatKind(X)</RHS></RULE></REWSYS><DPLIST/></DPSYS></SYSTEM><CRITERION><DAG approx="simpl"><CCLIST/></DAG></CRITERION></PROPERTY></PROPERTY></PROPERTY></PROPERTY><PROPERTY criterion="sterm" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(U11(tt,V1,V2))</LHS><RHS>mark(U12(isNat(V1),V2))</RHS></RULE><RULE><LHS>active(U12(tt,V2))</LHS><RHS>mark(U13(isNat(V2)))</RHS></RULE><RULE><LHS>active(U13(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U21(tt,V1))</LHS><RHS>mark(U22(isNat(V1)))</RHS></RULE><RULE><LHS>active(U22(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U31(tt,N))</LHS><RHS>mark(N)</RHS></RULE><RULE><LHS>active(U41(tt,M,N))</LHS><RHS>mark(s(plus(N,M)))</RHS></RULE><RULE><LHS>active(and(tt,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(isNat(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNat(plus(V1,V2)))</LHS><RHS>mark(U11(and(isNatKind(V1),isNatKind(V2)),V1,V2))</RHS></RULE><RULE><LHS>active(isNat(s(V1)))</LHS><RHS>mark(U21(isNatKind(V1),V1))</RHS></RULE><RULE><LHS>active(isNatKind(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNatKind(plus(V1,V2)))</LHS><RHS>mark(and(isNatKind(V1),isNatKind(V2)))</RHS></RULE><RULE><LHS>active(isNatKind(s(V1)))</LHS><RHS>mark(isNatKind(V1))</RHS></RULE><RULE><LHS>active(plus(N,0))</LHS><RHS>mark(U31(and(isNat(N),isNatKind(N)),N))</RHS></RULE><RULE><LHS>active(plus(N,s(M)))</LHS><RHS>mark(U41(and(and(isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),M,N))</RHS></RULE><RULE><LHS>mark(U11(X1,X2,X3))</LHS><RHS>active(U11(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(tt)</LHS><RHS>active(tt)</RHS></RULE><RULE><LHS>mark(U12(X1,X2))</LHS><RHS>active(U12(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(isNat(X))</LHS><RHS>active(isNat(X))</RHS></RULE><RULE><LHS>mark(U13(X))</LHS><RHS>active(U13(mark(X)))</RHS></RULE><RULE><LHS>mark(U21(X1,X2))</LHS><RHS>active(U21(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U22(X))</LHS><RHS>active(U22(mark(X)))</RHS></RULE><RULE><LHS>mark(U31(X1,X2))</LHS><RHS>active(U31(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U41(X1,X2,X3))</LHS><RHS>active(U41(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(mark(X)))</RHS></RULE><RULE><LHS>mark(plus(X1,X2))</LHS><RHS>active(plus(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(isNatKind(X))</LHS><RHS>active(isNatKind(X))</RHS></RULE><RULE><LHS>U11(mark(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,mark(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,mark(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(active(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,active(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,active(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U12(mark(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,mark(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(active(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,active(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>isNat(mark(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>isNat(active(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>U13(mark(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U13(active(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U21(mark(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,mark(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(active(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,active(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U22(mark(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U22(active(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U31(mark(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,mark(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(active(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,active(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U41(mark(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,mark(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,mark(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(active(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,active(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,active(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>s(mark(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>s(active(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>plus(mark(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,mark(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(active(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,active(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>and(mark(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,mark(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(active(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,active(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>isNatKind(mark(X))</LHS><RHS>isNatKind(X)</RHS></RULE><RULE><LHS>isNatKind(active(X))</LHS><RHS>isNatKind(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_isNatKind(mark(X))</LHS><RHS>Marked_isNatKind(X)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_isNatKind(active(X))</LHS><RHS>Marked_isNatKind(X)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><PROJECTION><PROJ><SYMBOL><NAME>Marked_isNatKind</NAME></SYMBOL><INT>1</INT></PROJ></PROJECTION><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_isNatKind(active(X))</LHS><RHS>Marked_isNatKind(X)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_isNatKind(mark(X))</LHS><RHS>Marked_isNatKind(X)</RHS></DPRULE></DPLIST></STRICTPAIRS><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(U11(tt,V1,V2))</LHS><RHS>mark(U12(isNat(V1),V2))</RHS></RULE><RULE><LHS>active(U12(tt,V2))</LHS><RHS>mark(U13(isNat(V2)))</RHS></RULE><RULE><LHS>active(U13(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U21(tt,V1))</LHS><RHS>mark(U22(isNat(V1)))</RHS></RULE><RULE><LHS>active(U22(tt))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(U31(tt,N))</LHS><RHS>mark(N)</RHS></RULE><RULE><LHS>active(U41(tt,M,N))</LHS><RHS>mark(s(plus(N,M)))</RHS></RULE><RULE><LHS>active(and(tt,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(isNat(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNat(plus(V1,V2)))</LHS><RHS>mark(U11(and(isNatKind(V1),isNatKind(V2)),V1,V2))</RHS></RULE><RULE><LHS>active(isNat(s(V1)))</LHS><RHS>mark(U21(isNatKind(V1),V1))</RHS></RULE><RULE><LHS>active(isNatKind(0))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>active(isNatKind(plus(V1,V2)))</LHS><RHS>mark(and(isNatKind(V1),isNatKind(V2)))</RHS></RULE><RULE><LHS>active(isNatKind(s(V1)))</LHS><RHS>mark(isNatKind(V1))</RHS></RULE><RULE><LHS>active(plus(N,0))</LHS><RHS>mark(U31(and(isNat(N),isNatKind(N)),N))</RHS></RULE><RULE><LHS>active(plus(N,s(M)))</LHS><RHS>mark(U41(and(and(isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),M,N))</RHS></RULE><RULE><LHS>mark(U11(X1,X2,X3))</LHS><RHS>active(U11(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(tt)</LHS><RHS>active(tt)</RHS></RULE><RULE><LHS>mark(U12(X1,X2))</LHS><RHS>active(U12(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(isNat(X))</LHS><RHS>active(isNat(X))</RHS></RULE><RULE><LHS>mark(U13(X))</LHS><RHS>active(U13(mark(X)))</RHS></RULE><RULE><LHS>mark(U21(X1,X2))</LHS><RHS>active(U21(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U22(X))</LHS><RHS>active(U22(mark(X)))</RHS></RULE><RULE><LHS>mark(U31(X1,X2))</LHS><RHS>active(U31(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(U41(X1,X2,X3))</LHS><RHS>active(U41(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(mark(X)))</RHS></RULE><RULE><LHS>mark(plus(X1,X2))</LHS><RHS>active(plus(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(isNatKind(X))</LHS><RHS>active(isNatKind(X))</RHS></RULE><RULE><LHS>U11(mark(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,mark(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,mark(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(active(X1),X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,active(X2),X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U11(X1,X2,active(X3))</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>U12(mark(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,mark(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(active(X1),X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>U12(X1,active(X2))</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>isNat(mark(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>isNat(active(X))</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>U13(mark(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U13(active(X))</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>U21(mark(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,mark(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(active(X1),X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U21(X1,active(X2))</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>U22(mark(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U22(active(X))</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>U31(mark(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,mark(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(active(X1),X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U31(X1,active(X2))</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>U41(mark(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,mark(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,mark(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(active(X1),X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,active(X2),X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>U41(X1,X2,active(X3))</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>s(mark(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>s(active(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>plus(mark(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,mark(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(active(X1),X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>plus(X1,active(X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>and(mark(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,mark(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(active(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,active(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>isNatKind(mark(X))</LHS><RHS>isNatKind(X)</RHS></RULE><RULE><LHS>isNatKind(active(X))</LHS><RHS>isNatKind(X)</RHS></RULE></REWSYS><DPLIST/></DPSYS></SYSTEM><CRITERION><DAG approx="simpl"><CCLIST/></DAG></CRITERION></PROPERTY></PROPERTY></PROPERTY></PROPERTY></PROOF>
