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<!DOCTYPE PROOF SYSTEM "http://a3pat.ensiie.fr/pub/a3pat.dtd">
<PROOF><SIGNATURE><SYMBOLLIST><SYMBOL arity="1" unmarked="a__U22"><NAME>Marked_a__U22</NAME></SYMBOL><SYMBOL arity="1" unmarked=""><NAME>isNatKind</NAME></SYMBOL><SYMBOL arity="1" unmarked=""><NAME>U22</NAME></SYMBOL><SYMBOL arity="1" unmarked=""><NAME>mark</NAME></SYMBOL><SYMBOL arity="2" unmarked="a__and"><NAME>Marked_a__and</NAME></SYMBOL><SYMBOL arity="3" unmarked=""><NAME>a__U41</NAME></SYMBOL><SYMBOL arity="3" unmarked=""><NAME>U11</NAME></SYMBOL><SYMBOL arity="2" unmarked="a__U12"><NAME>Marked_a__U12</NAME></SYMBOL><SYMBOL arity="0" unmarked=""><NAME>tt</NAME></SYMBOL><SYMBOL arity="3" unmarked="a__U41"><NAME>Marked_a__U41</NAME></SYMBOL><SYMBOL arity="0" unmarked=""><NAME>0</NAME></SYMBOL><SYMBOL arity="1" unmarked=""><NAME>U13</NAME></SYMBOL><SYMBOL arity="1" unmarked="mark"><NAME>Marked_mark</NAME></SYMBOL><SYMBOL arity="1" unmarked=""><NAME>a__U22</NAME></SYMBOL><SYMBOL arity="3" unmarked=""><NAME>U41</NAME></SYMBOL><SYMBOL arity="1" unmarked=""><NAME>s</NAME></SYMBOL><SYMBOL arity="2" unmarked=""><NAME>and</NAME></SYMBOL><SYMBOL arity="1" unmarked="a__U13"><NAME>Marked_a__U13</NAME></SYMBOL><SYMBOL arity="1" unmarked=""><NAME>a__isNat</NAME></SYMBOL><SYMBOL arity="2" unmarked="a__U31"><NAME>Marked_a__U31</NAME></SYMBOL><SYMBOL arity="1" unmarked=""><NAME>a__isNatKind</NAME></SYMBOL><SYMBOL arity="2" unmarked=""><NAME>U21</NAME></SYMBOL><SYMBOL arity="2" unmarked=""><NAME>a__U21</NAME></SYMBOL><SYMBOL arity="1" unmarked="a__isNatKind"><NAME>Marked_a__isNatKind</NAME></SYMBOL><SYMBOL arity="2" unmarked=""><NAME>a__plus</NAME></SYMBOL><SYMBOL arity="1" unmarked=""><NAME>isNat</NAME></SYMBOL><SYMBOL arity="1" unmarked="a__isNat"><NAME>Marked_a__isNat</NAME></SYMBOL><SYMBOL arity="3" unmarked=""><NAME>a__U11</NAME></SYMBOL><SYMBOL arity="2" unmarked="a__plus"><NAME>Marked_a__plus</NAME></SYMBOL><SYMBOL arity="2" unmarked=""><NAME>a__and</NAME></SYMBOL><SYMBOL arity="2" unmarked=""><NAME>U12</NAME></SYMBOL><SYMBOL arity="3" unmarked="a__U11"><NAME>Marked_a__U11</NAME></SYMBOL><SYMBOL arity="1" unmarked=""><NAME>a__U13</NAME></SYMBOL><SYMBOL arity="2" unmarked=""><NAME>U31</NAME></SYMBOL><SYMBOL arity="2" unmarked=""><NAME>a__U31</NAME></SYMBOL><SYMBOL arity="2" unmarked=""><NAME>plus</NAME></SYMBOL><SYMBOL arity="2" unmarked="a__U21"><NAME>Marked_a__U21</NAME></SYMBOL><SYMBOL arity="2" unmarked=""><NAME>a__U12</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>a__U11(tt,V1,V2)</LHS><RHS>a__U12(a__isNat(V1),V2)</RHS></RULE><RULE><LHS>a__U12(tt,V2)</LHS><RHS>a__U13(a__isNat(V2))</RHS></RULE><RULE><LHS>a__U13(tt)</LHS><RHS>tt</RHS></RULE><RULE><LHS>a__U21(tt,V1)</LHS><RHS>a__U22(a__isNat(V1))</RHS></RULE><RULE><LHS>a__U22(tt)</LHS><RHS>tt</RHS></RULE><RULE><LHS>a__U31(tt,N)</LHS><RHS>mark(N)</RHS></RULE><RULE><LHS>a__U41(tt,M,N)</LHS><RHS>s(a__plus(mark(N),mark(M)))</RHS></RULE><RULE><LHS>a__and(tt,X)</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>a__isNat(0)</LHS><RHS>tt</RHS></RULE><RULE><LHS>a__isNat(plus(V1,V2))</LHS><RHS>a__U11(a__and(a__isNatKind(V1),isNatKind(V2)),V1,V2)</RHS></RULE><RULE><LHS>a__isNat(s(V1))</LHS><RHS>a__U21(a__isNatKind(V1),V1)</RHS></RULE><RULE><LHS>a__isNatKind(0)</LHS><RHS>tt</RHS></RULE><RULE><LHS>a__isNatKind(plus(V1,V2))</LHS><RHS>a__and(a__isNatKind(V1),isNatKind(V2))</RHS></RULE><RULE><LHS>a__isNatKind(s(V1))</LHS><RHS>a__isNatKind(V1)</RHS></RULE><RULE><LHS>a__plus(N,0)</LHS><RHS>a__U31(a__and(a__isNat(N),isNatKind(N)),N)</RHS></RULE><RULE><LHS>a__plus(N,s(M))</LHS><RHS>a__U41(a__and(a__and(a__isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),
 M,N)</RHS></RULE><RULE><LHS>mark(U11(X1,X2,X3))</LHS><RHS>a__U11(mark(X1),X2,X3)</RHS></RULE><RULE><LHS>mark(U12(X1,X2))</LHS><RHS>a__U12(mark(X1),X2)</RHS></RULE><RULE><LHS>mark(isNat(X))</LHS><RHS>a__isNat(X)</RHS></RULE><RULE><LHS>mark(U13(X))</LHS><RHS>a__U13(mark(X))</RHS></RULE><RULE><LHS>mark(U21(X1,X2))</LHS><RHS>a__U21(mark(X1),X2)</RHS></RULE><RULE><LHS>mark(U22(X))</LHS><RHS>a__U22(mark(X))</RHS></RULE><RULE><LHS>mark(U31(X1,X2))</LHS><RHS>a__U31(mark(X1),X2)</RHS></RULE><RULE><LHS>mark(U41(X1,X2,X3))</LHS><RHS>a__U41(mark(X1),X2,X3)</RHS></RULE><RULE><LHS>mark(plus(X1,X2))</LHS><RHS>a__plus(mark(X1),mark(X2))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>a__and(mark(X1),X2)</RHS></RULE><RULE><LHS>mark(isNatKind(X))</LHS><RHS>a__isNatKind(X)</RHS></RULE><RULE><LHS>mark(tt)</LHS><RHS>tt</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>s(mark(X))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>0</RHS></RULE><RULE><LHS>a__U11(X1,X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>a__U12(X1,X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>a__isNat(X)</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>a__U13(X)</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>a__U21(X1,X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>a__U22(X)</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>a__U31(X1,X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>a__U41(X1,X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>a__plus(X1,X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>a__and(X1,X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>a__isNatKind(X)</LHS><RHS>isNatKind(X)</RHS></RULE></REWSYS></SYSTEM><CRITERION/><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>a__U11(tt,V1,V2)</LHS><RHS>a__U12(a__isNat(V1),V2)</RHS></RULE><RULE><LHS>a__U12(tt,V2)</LHS><RHS>a__U13(a__isNat(V2))</RHS></RULE><RULE><LHS>a__U13(tt)</LHS><RHS>tt</RHS></RULE><RULE><LHS>a__U21(tt,V1)</LHS><RHS>a__U22(a__isNat(V1))</RHS></RULE><RULE><LHS>a__U22(tt)</LHS><RHS>tt</RHS></RULE><RULE><LHS>a__U31(tt,N)</LHS><RHS>mark(N)</RHS></RULE><RULE><LHS>a__U41(tt,M,N)</LHS><RHS>s(a__plus(mark(N),mark(M)))</RHS></RULE><RULE><LHS>a__and(tt,X)</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>a__isNat(0)</LHS><RHS>tt</RHS></RULE><RULE><LHS>a__isNat(plus(V1,V2))</LHS><RHS>a__U11(a__and(a__isNatKind(V1),isNatKind(V2)),V1,V2)</RHS></RULE><RULE><LHS>a__isNat(s(V1))</LHS><RHS>a__U21(a__isNatKind(V1),V1)</RHS></RULE><RULE><LHS>a__isNatKind(0)</LHS><RHS>tt</RHS></RULE><RULE><LHS>a__isNatKind(plus(V1,V2))</LHS><RHS>a__and(a__isNatKind(V1),isNatKind(V2))</RHS></RULE><RULE><LHS>a__isNatKind(s(V1))</LHS><RHS>a__isNatKind(V1)</RHS></RULE><RULE><LHS>a__plus(N,0)</LHS><RHS>a__U31(a__and(a__isNat(N),isNatKind(N)),N)</RHS></RULE><RULE><LHS>a__plus(N,s(M))</LHS><RHS>a__U41(a__and(a__and(a__isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),
 M,N)</RHS></RULE><RULE><LHS>mark(U11(X1,X2,X3))</LHS><RHS>a__U11(mark(X1),X2,X3)</RHS></RULE><RULE><LHS>mark(U12(X1,X2))</LHS><RHS>a__U12(mark(X1),X2)</RHS></RULE><RULE><LHS>mark(isNat(X))</LHS><RHS>a__isNat(X)</RHS></RULE><RULE><LHS>mark(U13(X))</LHS><RHS>a__U13(mark(X))</RHS></RULE><RULE><LHS>mark(U21(X1,X2))</LHS><RHS>a__U21(mark(X1),X2)</RHS></RULE><RULE><LHS>mark(U22(X))</LHS><RHS>a__U22(mark(X))</RHS></RULE><RULE><LHS>mark(U31(X1,X2))</LHS><RHS>a__U31(mark(X1),X2)</RHS></RULE><RULE><LHS>mark(U41(X1,X2,X3))</LHS><RHS>a__U41(mark(X1),X2,X3)</RHS></RULE><RULE><LHS>mark(plus(X1,X2))</LHS><RHS>a__plus(mark(X1),mark(X2))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>a__and(mark(X1),X2)</RHS></RULE><RULE><LHS>mark(isNatKind(X))</LHS><RHS>a__isNatKind(X)</RHS></RULE><RULE><LHS>mark(tt)</LHS><RHS>tt</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>s(mark(X))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>0</RHS></RULE><RULE><LHS>a__U11(X1,X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>a__U12(X1,X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>a__isNat(X)</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>a__U13(X)</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>a__U21(X1,X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>a__U22(X)</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>a__U31(X1,X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>a__U41(X1,X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>a__plus(X1,X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>a__and(X1,X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>a__isNatKind(X)</LHS><RHS>isNatKind(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_a__U11(tt,V1,V2)</LHS><RHS>Marked_a__U12(a__isNat(V1),V2)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_a__U11(tt,V1,V2)</LHS><RHS>Marked_a__isNat(V1)</RHS></DPRULE><DPRULE num="2"><LHS>Marked_a__U12(tt,V2)</LHS><RHS>Marked_a__U13(a__isNat(V2))</RHS></DPRULE><DPRULE num="3"><LHS>Marked_a__U12(tt,V2)</LHS><RHS>Marked_a__isNat(V2)</RHS></DPRULE><DPRULE num="4"><LHS>Marked_a__U21(tt,V1)</LHS><RHS>Marked_a__U22(a__isNat(V1))</RHS></DPRULE><DPRULE num="5"><LHS>Marked_a__U21(tt,V1)</LHS><RHS>Marked_a__isNat(V1)</RHS></DPRULE><DPRULE num="6"><LHS>Marked_a__U31(tt,N)</LHS><RHS>Marked_mark(N)</RHS></DPRULE><DPRULE num="7"><LHS>Marked_a__U41(tt,M,N)</LHS><RHS>Marked_a__plus(mark(N),mark(M))</RHS></DPRULE><DPRULE num="8"><LHS>Marked_a__U41(tt,M,N)</LHS><RHS>Marked_mark(N)</RHS></DPRULE><DPRULE num="9"><LHS>Marked_a__U41(tt,M,N)</LHS><RHS>Marked_mark(M)</RHS></DPRULE><DPRULE num="10"><LHS>Marked_a__and(tt,X)</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="11"><LHS>Marked_a__isNat(plus(V1,V2))</LHS><RHS>Marked_a__U11(a__and(a__isNatKind(V1),isNatKind(V2)),V1,V2)</RHS></DPRULE><DPRULE num="12"><LHS>Marked_a__isNat(plus(V1,V2))</LHS><RHS>Marked_a__and(a__isNatKind(V1),isNatKind(V2))</RHS></DPRULE><DPRULE num="13"><LHS>Marked_a__isNat(plus(V1,V2))</LHS><RHS>Marked_a__isNatKind(V1)</RHS></DPRULE><DPRULE num="14"><LHS>Marked_a__isNat(s(V1))</LHS><RHS>Marked_a__U21(a__isNatKind(V1),V1)</RHS></DPRULE><DPRULE num="15"><LHS>Marked_a__isNat(s(V1))</LHS><RHS>Marked_a__isNatKind(V1)</RHS></DPRULE><DPRULE num="16"><LHS>Marked_a__isNatKind(plus(V1,V2))</LHS><RHS>Marked_a__and(a__isNatKind(V1),isNatKind(V2))</RHS></DPRULE><DPRULE num="17"><LHS>Marked_a__isNatKind(plus(V1,V2))</LHS><RHS>Marked_a__isNatKind(V1)</RHS></DPRULE><DPRULE num="18"><LHS>Marked_a__isNatKind(s(V1))</LHS><RHS>Marked_a__isNatKind(V1)</RHS></DPRULE><DPRULE num="19"><LHS>Marked_a__plus(N,0)</LHS><RHS>Marked_a__U31(a__and(a__isNat(N),isNatKind(N)),N)</RHS></DPRULE><DPRULE num="20"><LHS>Marked_a__plus(N,0)</LHS><RHS>Marked_a__and(a__isNat(N),isNatKind(N))</RHS></DPRULE><DPRULE num="21"><LHS>Marked_a__plus(N,0)</LHS><RHS>Marked_a__isNat(N)</RHS></DPRULE><DPRULE num="22"><LHS>Marked_a__plus(N,s(M))</LHS><RHS>Marked_a__U41(a__and(a__and(a__isNat(M),isNatKind(M)),
               and(isNat(N),isNatKind(N))),M,N)</RHS></DPRULE><DPRULE num="23"><LHS>Marked_a__plus(N,s(M))</LHS><RHS>Marked_a__and(a__and(a__isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N)))</RHS></DPRULE><DPRULE num="24"><LHS>Marked_a__plus(N,s(M))</LHS><RHS>Marked_a__and(a__isNat(M),isNatKind(M))</RHS></DPRULE><DPRULE num="25"><LHS>Marked_a__plus(N,s(M))</LHS><RHS>Marked_a__isNat(M)</RHS></DPRULE><DPRULE num="26"><LHS>Marked_mark(U11(X1,X2,X3))</LHS><RHS>Marked_a__U11(mark(X1),X2,X3)</RHS></DPRULE><DPRULE num="27"><LHS>Marked_mark(U11(X1,X2,X3))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="28"><LHS>Marked_mark(U12(X1,X2))</LHS><RHS>Marked_a__U12(mark(X1),X2)</RHS></DPRULE><DPRULE num="29"><LHS>Marked_mark(U12(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="30"><LHS>Marked_mark(isNat(X))</LHS><RHS>Marked_a__isNat(X)</RHS></DPRULE><DPRULE num="31"><LHS>Marked_mark(U13(X))</LHS><RHS>Marked_a__U13(mark(X))</RHS></DPRULE><DPRULE num="32"><LHS>Marked_mark(U13(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="33"><LHS>Marked_mark(U21(X1,X2))</LHS><RHS>Marked_a__U21(mark(X1),X2)</RHS></DPRULE><DPRULE num="34"><LHS>Marked_mark(U21(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="35"><LHS>Marked_mark(U22(X))</LHS><RHS>Marked_a__U22(mark(X))</RHS></DPRULE><DPRULE num="36"><LHS>Marked_mark(U22(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="37"><LHS>Marked_mark(U31(X1,X2))</LHS><RHS>Marked_a__U31(mark(X1),X2)</RHS></DPRULE><DPRULE num="38"><LHS>Marked_mark(U31(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="39"><LHS>Marked_mark(U41(X1,X2,X3))</LHS><RHS>Marked_a__U41(mark(X1),X2,X3)</RHS></DPRULE><DPRULE num="40"><LHS>Marked_mark(U41(X1,X2,X3))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="41"><LHS>Marked_mark(plus(X1,X2))</LHS><RHS>Marked_a__plus(mark(X1),mark(X2))</RHS></DPRULE><DPRULE num="42"><LHS>Marked_mark(plus(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="43"><LHS>Marked_mark(plus(X1,X2))</LHS><RHS>Marked_mark(X2)</RHS></DPRULE><DPRULE num="44"><LHS>Marked_mark(and(X1,X2))</LHS><RHS>Marked_a__and(mark(X1),X2)</RHS></DPRULE><DPRULE num="45"><LHS>Marked_mark(and(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="46"><LHS>Marked_mark(isNatKind(X))</LHS><RHS>Marked_a__isNatKind(X)</RHS></DPRULE><DPRULE num="47"><LHS>Marked_mark(s(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="3"/><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="32"/><NODE ref="33"/><NODE ref="34"/><NODE ref="36"/><NODE ref="37"/><NODE ref="38"/><NODE ref="39"/><NODE ref="40"/><NODE ref="41"/><NODE ref="42"/><NODE ref="43"/><NODE ref="44"/><NODE ref="45"/><NODE ref="46"/><NODE ref="47"/></SCC><NONSCC num="1"><NODE ref="35"/></NONSCC><NONSCC num="2"><NODE ref="31"/></NONSCC><NONSCC num="3"><NODE ref="4"/></NONSCC><NONSCC num="4"><NODE ref="2"/></NONSCC></CCLIST><EDGE end="4" start="0"/><EDGE end="3" start="0"/><EDGE end="2" start="0"/><EDGE end="1" start="0"/></DAG></CRITERION><PROPERTY criterion="stronggraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>a__U11(tt,V1,V2)</LHS><RHS>a__U12(a__isNat(V1),V2)</RHS></RULE><RULE><LHS>a__U12(tt,V2)</LHS><RHS>a__U13(a__isNat(V2))</RHS></RULE><RULE><LHS>a__U13(tt)</LHS><RHS>tt</RHS></RULE><RULE><LHS>a__U21(tt,V1)</LHS><RHS>a__U22(a__isNat(V1))</RHS></RULE><RULE><LHS>a__U22(tt)</LHS><RHS>tt</RHS></RULE><RULE><LHS>a__U31(tt,N)</LHS><RHS>mark(N)</RHS></RULE><RULE><LHS>a__U41(tt,M,N)</LHS><RHS>s(a__plus(mark(N),mark(M)))</RHS></RULE><RULE><LHS>a__and(tt,X)</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>a__isNat(0)</LHS><RHS>tt</RHS></RULE><RULE><LHS>a__isNat(plus(V1,V2))</LHS><RHS>a__U11(a__and(a__isNatKind(V1),isNatKind(V2)),V1,V2)</RHS></RULE><RULE><LHS>a__isNat(s(V1))</LHS><RHS>a__U21(a__isNatKind(V1),V1)</RHS></RULE><RULE><LHS>a__isNatKind(0)</LHS><RHS>tt</RHS></RULE><RULE><LHS>a__isNatKind(plus(V1,V2))</LHS><RHS>a__and(a__isNatKind(V1),isNatKind(V2))</RHS></RULE><RULE><LHS>a__isNatKind(s(V1))</LHS><RHS>a__isNatKind(V1)</RHS></RULE><RULE><LHS>a__plus(N,0)</LHS><RHS>a__U31(a__and(a__isNat(N),isNatKind(N)),N)</RHS></RULE><RULE><LHS>a__plus(N,s(M))</LHS><RHS>a__U41(a__and(a__and(a__isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),
 M,N)</RHS></RULE><RULE><LHS>mark(U11(X1,X2,X3))</LHS><RHS>a__U11(mark(X1),X2,X3)</RHS></RULE><RULE><LHS>mark(U12(X1,X2))</LHS><RHS>a__U12(mark(X1),X2)</RHS></RULE><RULE><LHS>mark(isNat(X))</LHS><RHS>a__isNat(X)</RHS></RULE><RULE><LHS>mark(U13(X))</LHS><RHS>a__U13(mark(X))</RHS></RULE><RULE><LHS>mark(U21(X1,X2))</LHS><RHS>a__U21(mark(X1),X2)</RHS></RULE><RULE><LHS>mark(U22(X))</LHS><RHS>a__U22(mark(X))</RHS></RULE><RULE><LHS>mark(U31(X1,X2))</LHS><RHS>a__U31(mark(X1),X2)</RHS></RULE><RULE><LHS>mark(U41(X1,X2,X3))</LHS><RHS>a__U41(mark(X1),X2,X3)</RHS></RULE><RULE><LHS>mark(plus(X1,X2))</LHS><RHS>a__plus(mark(X1),mark(X2))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>a__and(mark(X1),X2)</RHS></RULE><RULE><LHS>mark(isNatKind(X))</LHS><RHS>a__isNatKind(X)</RHS></RULE><RULE><LHS>mark(tt)</LHS><RHS>tt</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>s(mark(X))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>0</RHS></RULE><RULE><LHS>a__U11(X1,X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>a__U12(X1,X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>a__isNat(X)</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>a__U13(X)</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>a__U21(X1,X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>a__U22(X)</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>a__U31(X1,X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>a__U41(X1,X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>a__plus(X1,X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>a__and(X1,X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>a__isNatKind(X)</LHS><RHS>isNatKind(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_a__U11(tt,V1,V2)</LHS><RHS>Marked_a__U12(a__isNat(V1),V2)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_a__U11(tt,V1,V2)</LHS><RHS>Marked_a__isNat(V1)</RHS></DPRULE><DPRULE num="2"><LHS>Marked_a__U12(tt,V2)</LHS><RHS>Marked_a__isNat(V2)</RHS></DPRULE><DPRULE num="3"><LHS>Marked_a__U21(tt,V1)</LHS><RHS>Marked_a__isNat(V1)</RHS></DPRULE><DPRULE num="4"><LHS>Marked_a__U31(tt,N)</LHS><RHS>Marked_mark(N)</RHS></DPRULE><DPRULE num="5"><LHS>Marked_a__U41(tt,M,N)</LHS><RHS>Marked_a__plus(mark(N),mark(M))</RHS></DPRULE><DPRULE num="6"><LHS>Marked_a__U41(tt,M,N)</LHS><RHS>Marked_mark(N)</RHS></DPRULE><DPRULE num="7"><LHS>Marked_a__U41(tt,M,N)</LHS><RHS>Marked_mark(M)</RHS></DPRULE><DPRULE num="8"><LHS>Marked_a__and(tt,X)</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="9"><LHS>Marked_a__isNat(plus(V1,V2))</LHS><RHS>Marked_a__U11(a__and(a__isNatKind(V1),isNatKind(V2)),V1,V2)</RHS></DPRULE><DPRULE num="10"><LHS>Marked_a__isNat(plus(V1,V2))</LHS><RHS>Marked_a__and(a__isNatKind(V1),isNatKind(V2))</RHS></DPRULE><DPRULE num="11"><LHS>Marked_a__isNat(plus(V1,V2))</LHS><RHS>Marked_a__isNatKind(V1)</RHS></DPRULE><DPRULE num="12"><LHS>Marked_a__isNat(s(V1))</LHS><RHS>Marked_a__U21(a__isNatKind(V1),V1)</RHS></DPRULE><DPRULE num="13"><LHS>Marked_a__isNat(s(V1))</LHS><RHS>Marked_a__isNatKind(V1)</RHS></DPRULE><DPRULE num="14"><LHS>Marked_a__isNatKind(plus(V1,V2))</LHS><RHS>Marked_a__and(a__isNatKind(V1),isNatKind(V2))</RHS></DPRULE><DPRULE num="15"><LHS>Marked_a__isNatKind(plus(V1,V2))</LHS><RHS>Marked_a__isNatKind(V1)</RHS></DPRULE><DPRULE num="16"><LHS>Marked_a__isNatKind(s(V1))</LHS><RHS>Marked_a__isNatKind(V1)</RHS></DPRULE><DPRULE num="17"><LHS>Marked_a__plus(N,0)</LHS><RHS>Marked_a__U31(a__and(a__isNat(N),isNatKind(N)),N)</RHS></DPRULE><DPRULE num="18"><LHS>Marked_a__plus(N,0)</LHS><RHS>Marked_a__and(a__isNat(N),isNatKind(N))</RHS></DPRULE><DPRULE num="19"><LHS>Marked_a__plus(N,0)</LHS><RHS>Marked_a__isNat(N)</RHS></DPRULE><DPRULE num="20"><LHS>Marked_a__plus(N,s(M))</LHS><RHS>Marked_a__U41(a__and(a__and(a__isNat(M),isNatKind(M)),
               and(isNat(N),isNatKind(N))),M,N)</RHS></DPRULE><DPRULE num="21"><LHS>Marked_a__plus(N,s(M))</LHS><RHS>Marked_a__and(a__and(a__isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N)))</RHS></DPRULE><DPRULE num="22"><LHS>Marked_a__plus(N,s(M))</LHS><RHS>Marked_a__and(a__isNat(M),isNatKind(M))</RHS></DPRULE><DPRULE num="23"><LHS>Marked_a__plus(N,s(M))</LHS><RHS>Marked_a__isNat(M)</RHS></DPRULE><DPRULE num="24"><LHS>Marked_mark(U11(X1,X2,X3))</LHS><RHS>Marked_a__U11(mark(X1),X2,X3)</RHS></DPRULE><DPRULE num="25"><LHS>Marked_mark(U11(X1,X2,X3))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="26"><LHS>Marked_mark(U12(X1,X2))</LHS><RHS>Marked_a__U12(mark(X1),X2)</RHS></DPRULE><DPRULE num="27"><LHS>Marked_mark(U12(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="28"><LHS>Marked_mark(isNat(X))</LHS><RHS>Marked_a__isNat(X)</RHS></DPRULE><DPRULE num="29"><LHS>Marked_mark(U13(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="30"><LHS>Marked_mark(U21(X1,X2))</LHS><RHS>Marked_a__U21(mark(X1),X2)</RHS></DPRULE><DPRULE num="31"><LHS>Marked_mark(U21(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="32"><LHS>Marked_mark(U22(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="33"><LHS>Marked_mark(U31(X1,X2))</LHS><RHS>Marked_a__U31(mark(X1),X2)</RHS></DPRULE><DPRULE num="34"><LHS>Marked_mark(U31(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="35"><LHS>Marked_mark(U41(X1,X2,X3))</LHS><RHS>Marked_a__U41(mark(X1),X2,X3)</RHS></DPRULE><DPRULE num="36"><LHS>Marked_mark(U41(X1,X2,X3))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="37"><LHS>Marked_mark(plus(X1,X2))</LHS><RHS>Marked_a__plus(mark(X1),mark(X2))</RHS></DPRULE><DPRULE num="38"><LHS>Marked_mark(plus(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="39"><LHS>Marked_mark(plus(X1,X2))</LHS><RHS>Marked_mark(X2)</RHS></DPRULE><DPRULE num="40"><LHS>Marked_mark(and(X1,X2))</LHS><RHS>Marked_a__and(mark(X1),X2)</RHS></DPRULE><DPRULE num="41"><LHS>Marked_mark(and(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="42"><LHS>Marked_mark(isNatKind(X))</LHS><RHS>Marked_a__isNatKind(X)</RHS></DPRULE><DPRULE num="43"><LHS>Marked_mark(s(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><ORDERING type="poly"><POLYSYMB><SYMBOL><NAME>a__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>Marked_a__U21</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><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>a__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>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>a__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>Marked_a__U11</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>a__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_a__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>a__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>Marked_a__isNat</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>isNat</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>a__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>Marked_a__isNatKind</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>a__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>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>a__isNatKind</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>Marked_a__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>a__isNat</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>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>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>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>a__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>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>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>Marked_a__U41</NAME></SYMBOL><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></POLYSYMB><POLYSYMB><SYMBOL><NAME>tt</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>Marked_a__U12</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><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>a__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>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>Marked_a__and</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>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>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_a__plus(N,0)</LHS><RHS>Marked_a__U31(a__and(a__isNat(N),isNatKind(N)),N)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_a__plus(N,0)</LHS><RHS>Marked_a__and(a__isNat(N),isNatKind(N))</RHS></DPRULE><DPRULE num="2"><LHS>Marked_a__plus(N,0)</LHS><RHS>Marked_a__isNat(N)</RHS></DPRULE></DPLIST></STRICTPAIRS></CRITERION><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>a__U11(tt,V1,V2)</LHS><RHS>a__U12(a__isNat(V1),V2)</RHS></RULE><RULE><LHS>a__U12(tt,V2)</LHS><RHS>a__U13(a__isNat(V2))</RHS></RULE><RULE><LHS>a__U13(tt)</LHS><RHS>tt</RHS></RULE><RULE><LHS>a__U21(tt,V1)</LHS><RHS>a__U22(a__isNat(V1))</RHS></RULE><RULE><LHS>a__U22(tt)</LHS><RHS>tt</RHS></RULE><RULE><LHS>a__U31(tt,N)</LHS><RHS>mark(N)</RHS></RULE><RULE><LHS>a__U41(tt,M,N)</LHS><RHS>s(a__plus(mark(N),mark(M)))</RHS></RULE><RULE><LHS>a__and(tt,X)</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>a__isNat(0)</LHS><RHS>tt</RHS></RULE><RULE><LHS>a__isNat(plus(V1,V2))</LHS><RHS>a__U11(a__and(a__isNatKind(V1),isNatKind(V2)),V1,V2)</RHS></RULE><RULE><LHS>a__isNat(s(V1))</LHS><RHS>a__U21(a__isNatKind(V1),V1)</RHS></RULE><RULE><LHS>a__isNatKind(0)</LHS><RHS>tt</RHS></RULE><RULE><LHS>a__isNatKind(plus(V1,V2))</LHS><RHS>a__and(a__isNatKind(V1),isNatKind(V2))</RHS></RULE><RULE><LHS>a__isNatKind(s(V1))</LHS><RHS>a__isNatKind(V1)</RHS></RULE><RULE><LHS>a__plus(N,0)</LHS><RHS>a__U31(a__and(a__isNat(N),isNatKind(N)),N)</RHS></RULE><RULE><LHS>a__plus(N,s(M))</LHS><RHS>a__U41(a__and(a__and(a__isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),
 M,N)</RHS></RULE><RULE><LHS>mark(U11(X1,X2,X3))</LHS><RHS>a__U11(mark(X1),X2,X3)</RHS></RULE><RULE><LHS>mark(U12(X1,X2))</LHS><RHS>a__U12(mark(X1),X2)</RHS></RULE><RULE><LHS>mark(isNat(X))</LHS><RHS>a__isNat(X)</RHS></RULE><RULE><LHS>mark(U13(X))</LHS><RHS>a__U13(mark(X))</RHS></RULE><RULE><LHS>mark(U21(X1,X2))</LHS><RHS>a__U21(mark(X1),X2)</RHS></RULE><RULE><LHS>mark(U22(X))</LHS><RHS>a__U22(mark(X))</RHS></RULE><RULE><LHS>mark(U31(X1,X2))</LHS><RHS>a__U31(mark(X1),X2)</RHS></RULE><RULE><LHS>mark(U41(X1,X2,X3))</LHS><RHS>a__U41(mark(X1),X2,X3)</RHS></RULE><RULE><LHS>mark(plus(X1,X2))</LHS><RHS>a__plus(mark(X1),mark(X2))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>a__and(mark(X1),X2)</RHS></RULE><RULE><LHS>mark(isNatKind(X))</LHS><RHS>a__isNatKind(X)</RHS></RULE><RULE><LHS>mark(tt)</LHS><RHS>tt</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>s(mark(X))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>0</RHS></RULE><RULE><LHS>a__U11(X1,X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>a__U12(X1,X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>a__isNat(X)</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>a__U13(X)</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>a__U21(X1,X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>a__U22(X)</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>a__U31(X1,X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>a__U41(X1,X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>a__plus(X1,X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>a__and(X1,X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>a__isNatKind(X)</LHS><RHS>isNatKind(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_a__U11(tt,V1,V2)</LHS><RHS>Marked_a__U12(a__isNat(V1),V2)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_a__U11(tt,V1,V2)</LHS><RHS>Marked_a__isNat(V1)</RHS></DPRULE><DPRULE num="2"><LHS>Marked_a__U12(tt,V2)</LHS><RHS>Marked_a__isNat(V2)</RHS></DPRULE><DPRULE num="3"><LHS>Marked_a__U21(tt,V1)</LHS><RHS>Marked_a__isNat(V1)</RHS></DPRULE><DPRULE num="4"><LHS>Marked_a__U31(tt,N)</LHS><RHS>Marked_mark(N)</RHS></DPRULE><DPRULE num="5"><LHS>Marked_a__U41(tt,M,N)</LHS><RHS>Marked_a__plus(mark(N),mark(M))</RHS></DPRULE><DPRULE num="6"><LHS>Marked_a__U41(tt,M,N)</LHS><RHS>Marked_mark(N)</RHS></DPRULE><DPRULE num="7"><LHS>Marked_a__U41(tt,M,N)</LHS><RHS>Marked_mark(M)</RHS></DPRULE><DPRULE num="8"><LHS>Marked_a__and(tt,X)</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="9"><LHS>Marked_a__isNat(plus(V1,V2))</LHS><RHS>Marked_a__U11(a__and(a__isNatKind(V1),isNatKind(V2)),V1,V2)</RHS></DPRULE><DPRULE num="10"><LHS>Marked_a__isNat(plus(V1,V2))</LHS><RHS>Marked_a__and(a__isNatKind(V1),isNatKind(V2))</RHS></DPRULE><DPRULE num="11"><LHS>Marked_a__isNat(plus(V1,V2))</LHS><RHS>Marked_a__isNatKind(V1)</RHS></DPRULE><DPRULE num="12"><LHS>Marked_a__isNat(s(V1))</LHS><RHS>Marked_a__U21(a__isNatKind(V1),V1)</RHS></DPRULE><DPRULE num="13"><LHS>Marked_a__isNat(s(V1))</LHS><RHS>Marked_a__isNatKind(V1)</RHS></DPRULE><DPRULE num="14"><LHS>Marked_a__isNatKind(plus(V1,V2))</LHS><RHS>Marked_a__and(a__isNatKind(V1),isNatKind(V2))</RHS></DPRULE><DPRULE num="15"><LHS>Marked_a__isNatKind(plus(V1,V2))</LHS><RHS>Marked_a__isNatKind(V1)</RHS></DPRULE><DPRULE num="16"><LHS>Marked_a__isNatKind(s(V1))</LHS><RHS>Marked_a__isNatKind(V1)</RHS></DPRULE><DPRULE num="17"><LHS>Marked_a__plus(N,s(M))</LHS><RHS>Marked_a__U41(a__and(a__and(a__isNat(M),isNatKind(M)),
               and(isNat(N),isNatKind(N))),M,N)</RHS></DPRULE><DPRULE num="18"><LHS>Marked_a__plus(N,s(M))</LHS><RHS>Marked_a__and(a__and(a__isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N)))</RHS></DPRULE><DPRULE num="19"><LHS>Marked_a__plus(N,s(M))</LHS><RHS>Marked_a__and(a__isNat(M),isNatKind(M))</RHS></DPRULE><DPRULE num="20"><LHS>Marked_a__plus(N,s(M))</LHS><RHS>Marked_a__isNat(M)</RHS></DPRULE><DPRULE num="21"><LHS>Marked_mark(U11(X1,X2,X3))</LHS><RHS>Marked_a__U11(mark(X1),X2,X3)</RHS></DPRULE><DPRULE num="22"><LHS>Marked_mark(U11(X1,X2,X3))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="23"><LHS>Marked_mark(U12(X1,X2))</LHS><RHS>Marked_a__U12(mark(X1),X2)</RHS></DPRULE><DPRULE num="24"><LHS>Marked_mark(U12(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="25"><LHS>Marked_mark(isNat(X))</LHS><RHS>Marked_a__isNat(X)</RHS></DPRULE><DPRULE num="26"><LHS>Marked_mark(U13(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="27"><LHS>Marked_mark(U21(X1,X2))</LHS><RHS>Marked_a__U21(mark(X1),X2)</RHS></DPRULE><DPRULE num="28"><LHS>Marked_mark(U21(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="29"><LHS>Marked_mark(U22(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="30"><LHS>Marked_mark(U31(X1,X2))</LHS><RHS>Marked_a__U31(mark(X1),X2)</RHS></DPRULE><DPRULE num="31"><LHS>Marked_mark(U31(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="32"><LHS>Marked_mark(U41(X1,X2,X3))</LHS><RHS>Marked_a__U41(mark(X1),X2,X3)</RHS></DPRULE><DPRULE num="33"><LHS>Marked_mark(U41(X1,X2,X3))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="34"><LHS>Marked_mark(plus(X1,X2))</LHS><RHS>Marked_a__plus(mark(X1),mark(X2))</RHS></DPRULE><DPRULE num="35"><LHS>Marked_mark(plus(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="36"><LHS>Marked_mark(plus(X1,X2))</LHS><RHS>Marked_mark(X2)</RHS></DPRULE><DPRULE num="37"><LHS>Marked_mark(and(X1,X2))</LHS><RHS>Marked_a__and(mark(X1),X2)</RHS></DPRULE><DPRULE num="38"><LHS>Marked_mark(and(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="39"><LHS>Marked_mark(isNatKind(X))</LHS><RHS>Marked_a__isNatKind(X)</RHS></DPRULE><DPRULE num="40"><LHS>Marked_mark(s(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"/><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"/><NODE ref="34"/><NODE ref="35"/><NODE ref="36"/><NODE ref="37"/><NODE ref="38"/><NODE ref="39"/><NODE ref="40"/></SCC></CCLIST></DAG></CRITERION><PROPERTY criterion="stronggraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>a__U11(tt,V1,V2)</LHS><RHS>a__U12(a__isNat(V1),V2)</RHS></RULE><RULE><LHS>a__U12(tt,V2)</LHS><RHS>a__U13(a__isNat(V2))</RHS></RULE><RULE><LHS>a__U13(tt)</LHS><RHS>tt</RHS></RULE><RULE><LHS>a__U21(tt,V1)</LHS><RHS>a__U22(a__isNat(V1))</RHS></RULE><RULE><LHS>a__U22(tt)</LHS><RHS>tt</RHS></RULE><RULE><LHS>a__U31(tt,N)</LHS><RHS>mark(N)</RHS></RULE><RULE><LHS>a__U41(tt,M,N)</LHS><RHS>s(a__plus(mark(N),mark(M)))</RHS></RULE><RULE><LHS>a__and(tt,X)</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>a__isNat(0)</LHS><RHS>tt</RHS></RULE><RULE><LHS>a__isNat(plus(V1,V2))</LHS><RHS>a__U11(a__and(a__isNatKind(V1),isNatKind(V2)),V1,V2)</RHS></RULE><RULE><LHS>a__isNat(s(V1))</LHS><RHS>a__U21(a__isNatKind(V1),V1)</RHS></RULE><RULE><LHS>a__isNatKind(0)</LHS><RHS>tt</RHS></RULE><RULE><LHS>a__isNatKind(plus(V1,V2))</LHS><RHS>a__and(a__isNatKind(V1),isNatKind(V2))</RHS></RULE><RULE><LHS>a__isNatKind(s(V1))</LHS><RHS>a__isNatKind(V1)</RHS></RULE><RULE><LHS>a__plus(N,0)</LHS><RHS>a__U31(a__and(a__isNat(N),isNatKind(N)),N)</RHS></RULE><RULE><LHS>a__plus(N,s(M))</LHS><RHS>a__U41(a__and(a__and(a__isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),
 M,N)</RHS></RULE><RULE><LHS>mark(U11(X1,X2,X3))</LHS><RHS>a__U11(mark(X1),X2,X3)</RHS></RULE><RULE><LHS>mark(U12(X1,X2))</LHS><RHS>a__U12(mark(X1),X2)</RHS></RULE><RULE><LHS>mark(isNat(X))</LHS><RHS>a__isNat(X)</RHS></RULE><RULE><LHS>mark(U13(X))</LHS><RHS>a__U13(mark(X))</RHS></RULE><RULE><LHS>mark(U21(X1,X2))</LHS><RHS>a__U21(mark(X1),X2)</RHS></RULE><RULE><LHS>mark(U22(X))</LHS><RHS>a__U22(mark(X))</RHS></RULE><RULE><LHS>mark(U31(X1,X2))</LHS><RHS>a__U31(mark(X1),X2)</RHS></RULE><RULE><LHS>mark(U41(X1,X2,X3))</LHS><RHS>a__U41(mark(X1),X2,X3)</RHS></RULE><RULE><LHS>mark(plus(X1,X2))</LHS><RHS>a__plus(mark(X1),mark(X2))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>a__and(mark(X1),X2)</RHS></RULE><RULE><LHS>mark(isNatKind(X))</LHS><RHS>a__isNatKind(X)</RHS></RULE><RULE><LHS>mark(tt)</LHS><RHS>tt</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>s(mark(X))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>0</RHS></RULE><RULE><LHS>a__U11(X1,X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>a__U12(X1,X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>a__isNat(X)</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>a__U13(X)</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>a__U21(X1,X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>a__U22(X)</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>a__U31(X1,X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>a__U41(X1,X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>a__plus(X1,X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>a__and(X1,X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>a__isNatKind(X)</LHS><RHS>isNatKind(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_a__U11(tt,V1,V2)</LHS><RHS>Marked_a__U12(a__isNat(V1),V2)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_a__U11(tt,V1,V2)</LHS><RHS>Marked_a__isNat(V1)</RHS></DPRULE><DPRULE num="2"><LHS>Marked_a__U12(tt,V2)</LHS><RHS>Marked_a__isNat(V2)</RHS></DPRULE><DPRULE num="3"><LHS>Marked_a__U21(tt,V1)</LHS><RHS>Marked_a__isNat(V1)</RHS></DPRULE><DPRULE num="4"><LHS>Marked_a__U31(tt,N)</LHS><RHS>Marked_mark(N)</RHS></DPRULE><DPRULE num="5"><LHS>Marked_a__U41(tt,M,N)</LHS><RHS>Marked_a__plus(mark(N),mark(M))</RHS></DPRULE><DPRULE num="6"><LHS>Marked_a__U41(tt,M,N)</LHS><RHS>Marked_mark(N)</RHS></DPRULE><DPRULE num="7"><LHS>Marked_a__U41(tt,M,N)</LHS><RHS>Marked_mark(M)</RHS></DPRULE><DPRULE num="8"><LHS>Marked_a__and(tt,X)</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="9"><LHS>Marked_a__isNat(plus(V1,V2))</LHS><RHS>Marked_a__U11(a__and(a__isNatKind(V1),isNatKind(V2)),V1,V2)</RHS></DPRULE><DPRULE num="10"><LHS>Marked_a__isNat(plus(V1,V2))</LHS><RHS>Marked_a__and(a__isNatKind(V1),isNatKind(V2))</RHS></DPRULE><DPRULE num="11"><LHS>Marked_a__isNat(plus(V1,V2))</LHS><RHS>Marked_a__isNatKind(V1)</RHS></DPRULE><DPRULE num="12"><LHS>Marked_a__isNat(s(V1))</LHS><RHS>Marked_a__U21(a__isNatKind(V1),V1)</RHS></DPRULE><DPRULE num="13"><LHS>Marked_a__isNat(s(V1))</LHS><RHS>Marked_a__isNatKind(V1)</RHS></DPRULE><DPRULE num="14"><LHS>Marked_a__isNatKind(plus(V1,V2))</LHS><RHS>Marked_a__and(a__isNatKind(V1),isNatKind(V2))</RHS></DPRULE><DPRULE num="15"><LHS>Marked_a__isNatKind(plus(V1,V2))</LHS><RHS>Marked_a__isNatKind(V1)</RHS></DPRULE><DPRULE num="16"><LHS>Marked_a__isNatKind(s(V1))</LHS><RHS>Marked_a__isNatKind(V1)</RHS></DPRULE><DPRULE num="17"><LHS>Marked_a__plus(N,s(M))</LHS><RHS>Marked_a__U41(a__and(a__and(a__isNat(M),isNatKind(M)),
               and(isNat(N),isNatKind(N))),M,N)</RHS></DPRULE><DPRULE num="18"><LHS>Marked_a__plus(N,s(M))</LHS><RHS>Marked_a__and(a__and(a__isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N)))</RHS></DPRULE><DPRULE num="19"><LHS>Marked_a__plus(N,s(M))</LHS><RHS>Marked_a__and(a__isNat(M),isNatKind(M))</RHS></DPRULE><DPRULE num="20"><LHS>Marked_a__plus(N,s(M))</LHS><RHS>Marked_a__isNat(M)</RHS></DPRULE><DPRULE num="21"><LHS>Marked_mark(U11(X1,X2,X3))</LHS><RHS>Marked_a__U11(mark(X1),X2,X3)</RHS></DPRULE><DPRULE num="22"><LHS>Marked_mark(U11(X1,X2,X3))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="23"><LHS>Marked_mark(U12(X1,X2))</LHS><RHS>Marked_a__U12(mark(X1),X2)</RHS></DPRULE><DPRULE num="24"><LHS>Marked_mark(U12(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="25"><LHS>Marked_mark(isNat(X))</LHS><RHS>Marked_a__isNat(X)</RHS></DPRULE><DPRULE num="26"><LHS>Marked_mark(U13(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="27"><LHS>Marked_mark(U21(X1,X2))</LHS><RHS>Marked_a__U21(mark(X1),X2)</RHS></DPRULE><DPRULE num="28"><LHS>Marked_mark(U21(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="29"><LHS>Marked_mark(U22(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="30"><LHS>Marked_mark(U31(X1,X2))</LHS><RHS>Marked_a__U31(mark(X1),X2)</RHS></DPRULE><DPRULE num="31"><LHS>Marked_mark(U31(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="32"><LHS>Marked_mark(U41(X1,X2,X3))</LHS><RHS>Marked_a__U41(mark(X1),X2,X3)</RHS></DPRULE><DPRULE num="33"><LHS>Marked_mark(U41(X1,X2,X3))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="34"><LHS>Marked_mark(plus(X1,X2))</LHS><RHS>Marked_a__plus(mark(X1),mark(X2))</RHS></DPRULE><DPRULE num="35"><LHS>Marked_mark(plus(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="36"><LHS>Marked_mark(plus(X1,X2))</LHS><RHS>Marked_mark(X2)</RHS></DPRULE><DPRULE num="37"><LHS>Marked_mark(and(X1,X2))</LHS><RHS>Marked_a__and(mark(X1),X2)</RHS></DPRULE><DPRULE num="38"><LHS>Marked_mark(and(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="39"><LHS>Marked_mark(isNatKind(X))</LHS><RHS>Marked_a__isNatKind(X)</RHS></DPRULE><DPRULE num="40"><LHS>Marked_mark(s(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><ORDERING type="poly"><POLYSYMB><SYMBOL><NAME>a__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>Marked_a__U21</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></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>a__U31</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>U31</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>a__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>Marked_a__U11</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>a__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_a__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>a__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>Marked_a__isNat</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>isNat</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>a__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>Marked_a__isNatKind</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>a__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>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>a__isNatKind</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>Marked_a__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>a__isNat</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>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>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>a__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>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>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>2</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>Marked_a__U41</NAME></SYMBOL><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></POLYSYMB><POLYSYMB><SYMBOL><NAME>tt</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>Marked_a__U12</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><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>a__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_a__and</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>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>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(U31(X1,X2))</LHS><RHS>Marked_a__U31(mark(X1),X2)</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>a__U11(tt,V1,V2)</LHS><RHS>a__U12(a__isNat(V1),V2)</RHS></RULE><RULE><LHS>a__U12(tt,V2)</LHS><RHS>a__U13(a__isNat(V2))</RHS></RULE><RULE><LHS>a__U13(tt)</LHS><RHS>tt</RHS></RULE><RULE><LHS>a__U21(tt,V1)</LHS><RHS>a__U22(a__isNat(V1))</RHS></RULE><RULE><LHS>a__U22(tt)</LHS><RHS>tt</RHS></RULE><RULE><LHS>a__U31(tt,N)</LHS><RHS>mark(N)</RHS></RULE><RULE><LHS>a__U41(tt,M,N)</LHS><RHS>s(a__plus(mark(N),mark(M)))</RHS></RULE><RULE><LHS>a__and(tt,X)</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>a__isNat(0)</LHS><RHS>tt</RHS></RULE><RULE><LHS>a__isNat(plus(V1,V2))</LHS><RHS>a__U11(a__and(a__isNatKind(V1),isNatKind(V2)),V1,V2)</RHS></RULE><RULE><LHS>a__isNat(s(V1))</LHS><RHS>a__U21(a__isNatKind(V1),V1)</RHS></RULE><RULE><LHS>a__isNatKind(0)</LHS><RHS>tt</RHS></RULE><RULE><LHS>a__isNatKind(plus(V1,V2))</LHS><RHS>a__and(a__isNatKind(V1),isNatKind(V2))</RHS></RULE><RULE><LHS>a__isNatKind(s(V1))</LHS><RHS>a__isNatKind(V1)</RHS></RULE><RULE><LHS>a__plus(N,0)</LHS><RHS>a__U31(a__and(a__isNat(N),isNatKind(N)),N)</RHS></RULE><RULE><LHS>a__plus(N,s(M))</LHS><RHS>a__U41(a__and(a__and(a__isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),
 M,N)</RHS></RULE><RULE><LHS>mark(U11(X1,X2,X3))</LHS><RHS>a__U11(mark(X1),X2,X3)</RHS></RULE><RULE><LHS>mark(U12(X1,X2))</LHS><RHS>a__U12(mark(X1),X2)</RHS></RULE><RULE><LHS>mark(isNat(X))</LHS><RHS>a__isNat(X)</RHS></RULE><RULE><LHS>mark(U13(X))</LHS><RHS>a__U13(mark(X))</RHS></RULE><RULE><LHS>mark(U21(X1,X2))</LHS><RHS>a__U21(mark(X1),X2)</RHS></RULE><RULE><LHS>mark(U22(X))</LHS><RHS>a__U22(mark(X))</RHS></RULE><RULE><LHS>mark(U31(X1,X2))</LHS><RHS>a__U31(mark(X1),X2)</RHS></RULE><RULE><LHS>mark(U41(X1,X2,X3))</LHS><RHS>a__U41(mark(X1),X2,X3)</RHS></RULE><RULE><LHS>mark(plus(X1,X2))</LHS><RHS>a__plus(mark(X1),mark(X2))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>a__and(mark(X1),X2)</RHS></RULE><RULE><LHS>mark(isNatKind(X))</LHS><RHS>a__isNatKind(X)</RHS></RULE><RULE><LHS>mark(tt)</LHS><RHS>tt</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>s(mark(X))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>0</RHS></RULE><RULE><LHS>a__U11(X1,X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>a__U12(X1,X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>a__isNat(X)</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>a__U13(X)</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>a__U21(X1,X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>a__U22(X)</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>a__U31(X1,X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>a__U41(X1,X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>a__plus(X1,X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>a__and(X1,X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>a__isNatKind(X)</LHS><RHS>isNatKind(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_a__U11(tt,V1,V2)</LHS><RHS>Marked_a__U12(a__isNat(V1),V2)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_a__U11(tt,V1,V2)</LHS><RHS>Marked_a__isNat(V1)</RHS></DPRULE><DPRULE num="2"><LHS>Marked_a__U12(tt,V2)</LHS><RHS>Marked_a__isNat(V2)</RHS></DPRULE><DPRULE num="3"><LHS>Marked_a__U21(tt,V1)</LHS><RHS>Marked_a__isNat(V1)</RHS></DPRULE><DPRULE num="4"><LHS>Marked_a__U31(tt,N)</LHS><RHS>Marked_mark(N)</RHS></DPRULE><DPRULE num="5"><LHS>Marked_a__U41(tt,M,N)</LHS><RHS>Marked_a__plus(mark(N),mark(M))</RHS></DPRULE><DPRULE num="6"><LHS>Marked_a__U41(tt,M,N)</LHS><RHS>Marked_mark(N)</RHS></DPRULE><DPRULE num="7"><LHS>Marked_a__U41(tt,M,N)</LHS><RHS>Marked_mark(M)</RHS></DPRULE><DPRULE num="8"><LHS>Marked_a__and(tt,X)</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="9"><LHS>Marked_a__isNat(plus(V1,V2))</LHS><RHS>Marked_a__U11(a__and(a__isNatKind(V1),isNatKind(V2)),V1,V2)</RHS></DPRULE><DPRULE num="10"><LHS>Marked_a__isNat(plus(V1,V2))</LHS><RHS>Marked_a__and(a__isNatKind(V1),isNatKind(V2))</RHS></DPRULE><DPRULE num="11"><LHS>Marked_a__isNat(plus(V1,V2))</LHS><RHS>Marked_a__isNatKind(V1)</RHS></DPRULE><DPRULE num="12"><LHS>Marked_a__isNat(s(V1))</LHS><RHS>Marked_a__U21(a__isNatKind(V1),V1)</RHS></DPRULE><DPRULE num="13"><LHS>Marked_a__isNat(s(V1))</LHS><RHS>Marked_a__isNatKind(V1)</RHS></DPRULE><DPRULE num="14"><LHS>Marked_a__isNatKind(plus(V1,V2))</LHS><RHS>Marked_a__and(a__isNatKind(V1),isNatKind(V2))</RHS></DPRULE><DPRULE num="15"><LHS>Marked_a__isNatKind(plus(V1,V2))</LHS><RHS>Marked_a__isNatKind(V1)</RHS></DPRULE><DPRULE num="16"><LHS>Marked_a__isNatKind(s(V1))</LHS><RHS>Marked_a__isNatKind(V1)</RHS></DPRULE><DPRULE num="17"><LHS>Marked_a__plus(N,s(M))</LHS><RHS>Marked_a__U41(a__and(a__and(a__isNat(M),isNatKind(M)),
               and(isNat(N),isNatKind(N))),M,N)</RHS></DPRULE><DPRULE num="18"><LHS>Marked_a__plus(N,s(M))</LHS><RHS>Marked_a__and(a__and(a__isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N)))</RHS></DPRULE><DPRULE num="19"><LHS>Marked_a__plus(N,s(M))</LHS><RHS>Marked_a__and(a__isNat(M),isNatKind(M))</RHS></DPRULE><DPRULE num="20"><LHS>Marked_a__plus(N,s(M))</LHS><RHS>Marked_a__isNat(M)</RHS></DPRULE><DPRULE num="21"><LHS>Marked_mark(U11(X1,X2,X3))</LHS><RHS>Marked_a__U11(mark(X1),X2,X3)</RHS></DPRULE><DPRULE num="22"><LHS>Marked_mark(U11(X1,X2,X3))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="23"><LHS>Marked_mark(U12(X1,X2))</LHS><RHS>Marked_a__U12(mark(X1),X2)</RHS></DPRULE><DPRULE num="24"><LHS>Marked_mark(U12(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="25"><LHS>Marked_mark(isNat(X))</LHS><RHS>Marked_a__isNat(X)</RHS></DPRULE><DPRULE num="26"><LHS>Marked_mark(U13(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="27"><LHS>Marked_mark(U21(X1,X2))</LHS><RHS>Marked_a__U21(mark(X1),X2)</RHS></DPRULE><DPRULE num="28"><LHS>Marked_mark(U21(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="29"><LHS>Marked_mark(U22(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="30"><LHS>Marked_mark(U41(X1,X2,X3))</LHS><RHS>Marked_a__U41(mark(X1),X2,X3)</RHS></DPRULE><DPRULE num="31"><LHS>Marked_mark(U41(X1,X2,X3))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="32"><LHS>Marked_mark(plus(X1,X2))</LHS><RHS>Marked_a__plus(mark(X1),mark(X2))</RHS></DPRULE><DPRULE num="33"><LHS>Marked_mark(plus(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="34"><LHS>Marked_mark(plus(X1,X2))</LHS><RHS>Marked_mark(X2)</RHS></DPRULE><DPRULE num="35"><LHS>Marked_mark(and(X1,X2))</LHS><RHS>Marked_a__and(mark(X1),X2)</RHS></DPRULE><DPRULE num="36"><LHS>Marked_mark(and(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="37"><LHS>Marked_mark(isNatKind(X))</LHS><RHS>Marked_a__isNatKind(X)</RHS></DPRULE><DPRULE num="38"><LHS>Marked_mark(s(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="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"/><NODE ref="34"/><NODE ref="35"/><NODE ref="36"/><NODE ref="37"/><NODE ref="38"/></SCC><NONSCC num="1"><NODE ref="4"/></NONSCC></CCLIST><EDGE end="0" start="1"/></DAG></CRITERION><PROPERTY criterion="stronggraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>a__U11(tt,V1,V2)</LHS><RHS>a__U12(a__isNat(V1),V2)</RHS></RULE><RULE><LHS>a__U12(tt,V2)</LHS><RHS>a__U13(a__isNat(V2))</RHS></RULE><RULE><LHS>a__U13(tt)</LHS><RHS>tt</RHS></RULE><RULE><LHS>a__U21(tt,V1)</LHS><RHS>a__U22(a__isNat(V1))</RHS></RULE><RULE><LHS>a__U22(tt)</LHS><RHS>tt</RHS></RULE><RULE><LHS>a__U31(tt,N)</LHS><RHS>mark(N)</RHS></RULE><RULE><LHS>a__U41(tt,M,N)</LHS><RHS>s(a__plus(mark(N),mark(M)))</RHS></RULE><RULE><LHS>a__and(tt,X)</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>a__isNat(0)</LHS><RHS>tt</RHS></RULE><RULE><LHS>a__isNat(plus(V1,V2))</LHS><RHS>a__U11(a__and(a__isNatKind(V1),isNatKind(V2)),V1,V2)</RHS></RULE><RULE><LHS>a__isNat(s(V1))</LHS><RHS>a__U21(a__isNatKind(V1),V1)</RHS></RULE><RULE><LHS>a__isNatKind(0)</LHS><RHS>tt</RHS></RULE><RULE><LHS>a__isNatKind(plus(V1,V2))</LHS><RHS>a__and(a__isNatKind(V1),isNatKind(V2))</RHS></RULE><RULE><LHS>a__isNatKind(s(V1))</LHS><RHS>a__isNatKind(V1)</RHS></RULE><RULE><LHS>a__plus(N,0)</LHS><RHS>a__U31(a__and(a__isNat(N),isNatKind(N)),N)</RHS></RULE><RULE><LHS>a__plus(N,s(M))</LHS><RHS>a__U41(a__and(a__and(a__isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),
 M,N)</RHS></RULE><RULE><LHS>mark(U11(X1,X2,X3))</LHS><RHS>a__U11(mark(X1),X2,X3)</RHS></RULE><RULE><LHS>mark(U12(X1,X2))</LHS><RHS>a__U12(mark(X1),X2)</RHS></RULE><RULE><LHS>mark(isNat(X))</LHS><RHS>a__isNat(X)</RHS></RULE><RULE><LHS>mark(U13(X))</LHS><RHS>a__U13(mark(X))</RHS></RULE><RULE><LHS>mark(U21(X1,X2))</LHS><RHS>a__U21(mark(X1),X2)</RHS></RULE><RULE><LHS>mark(U22(X))</LHS><RHS>a__U22(mark(X))</RHS></RULE><RULE><LHS>mark(U31(X1,X2))</LHS><RHS>a__U31(mark(X1),X2)</RHS></RULE><RULE><LHS>mark(U41(X1,X2,X3))</LHS><RHS>a__U41(mark(X1),X2,X3)</RHS></RULE><RULE><LHS>mark(plus(X1,X2))</LHS><RHS>a__plus(mark(X1),mark(X2))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>a__and(mark(X1),X2)</RHS></RULE><RULE><LHS>mark(isNatKind(X))</LHS><RHS>a__isNatKind(X)</RHS></RULE><RULE><LHS>mark(tt)</LHS><RHS>tt</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>s(mark(X))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>0</RHS></RULE><RULE><LHS>a__U11(X1,X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>a__U12(X1,X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>a__isNat(X)</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>a__U13(X)</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>a__U21(X1,X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>a__U22(X)</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>a__U31(X1,X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>a__U41(X1,X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>a__plus(X1,X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>a__and(X1,X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>a__isNatKind(X)</LHS><RHS>isNatKind(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_a__U11(tt,V1,V2)</LHS><RHS>Marked_a__U12(a__isNat(V1),V2)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_a__U11(tt,V1,V2)</LHS><RHS>Marked_a__isNat(V1)</RHS></DPRULE><DPRULE num="2"><LHS>Marked_a__U12(tt,V2)</LHS><RHS>Marked_a__isNat(V2)</RHS></DPRULE><DPRULE num="3"><LHS>Marked_a__U21(tt,V1)</LHS><RHS>Marked_a__isNat(V1)</RHS></DPRULE><DPRULE num="4"><LHS>Marked_a__U41(tt,M,N)</LHS><RHS>Marked_a__plus(mark(N),mark(M))</RHS></DPRULE><DPRULE num="5"><LHS>Marked_a__U41(tt,M,N)</LHS><RHS>Marked_mark(N)</RHS></DPRULE><DPRULE num="6"><LHS>Marked_a__U41(tt,M,N)</LHS><RHS>Marked_mark(M)</RHS></DPRULE><DPRULE num="7"><LHS>Marked_a__and(tt,X)</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="8"><LHS>Marked_a__isNat(plus(V1,V2))</LHS><RHS>Marked_a__U11(a__and(a__isNatKind(V1),isNatKind(V2)),V1,V2)</RHS></DPRULE><DPRULE num="9"><LHS>Marked_a__isNat(plus(V1,V2))</LHS><RHS>Marked_a__and(a__isNatKind(V1),isNatKind(V2))</RHS></DPRULE><DPRULE num="10"><LHS>Marked_a__isNat(plus(V1,V2))</LHS><RHS>Marked_a__isNatKind(V1)</RHS></DPRULE><DPRULE num="11"><LHS>Marked_a__isNat(s(V1))</LHS><RHS>Marked_a__U21(a__isNatKind(V1),V1)</RHS></DPRULE><DPRULE num="12"><LHS>Marked_a__isNat(s(V1))</LHS><RHS>Marked_a__isNatKind(V1)</RHS></DPRULE><DPRULE num="13"><LHS>Marked_a__isNatKind(plus(V1,V2))</LHS><RHS>Marked_a__and(a__isNatKind(V1),isNatKind(V2))</RHS></DPRULE><DPRULE num="14"><LHS>Marked_a__isNatKind(plus(V1,V2))</LHS><RHS>Marked_a__isNatKind(V1)</RHS></DPRULE><DPRULE num="15"><LHS>Marked_a__isNatKind(s(V1))</LHS><RHS>Marked_a__isNatKind(V1)</RHS></DPRULE><DPRULE num="16"><LHS>Marked_a__plus(N,s(M))</LHS><RHS>Marked_a__U41(a__and(a__and(a__isNat(M),isNatKind(M)),
               and(isNat(N),isNatKind(N))),M,N)</RHS></DPRULE><DPRULE num="17"><LHS>Marked_a__plus(N,s(M))</LHS><RHS>Marked_a__and(a__and(a__isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N)))</RHS></DPRULE><DPRULE num="18"><LHS>Marked_a__plus(N,s(M))</LHS><RHS>Marked_a__and(a__isNat(M),isNatKind(M))</RHS></DPRULE><DPRULE num="19"><LHS>Marked_a__plus(N,s(M))</LHS><RHS>Marked_a__isNat(M)</RHS></DPRULE><DPRULE num="20"><LHS>Marked_mark(U11(X1,X2,X3))</LHS><RHS>Marked_a__U11(mark(X1),X2,X3)</RHS></DPRULE><DPRULE num="21"><LHS>Marked_mark(U11(X1,X2,X3))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="22"><LHS>Marked_mark(U12(X1,X2))</LHS><RHS>Marked_a__U12(mark(X1),X2)</RHS></DPRULE><DPRULE num="23"><LHS>Marked_mark(U12(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="24"><LHS>Marked_mark(isNat(X))</LHS><RHS>Marked_a__isNat(X)</RHS></DPRULE><DPRULE num="25"><LHS>Marked_mark(U13(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="26"><LHS>Marked_mark(U21(X1,X2))</LHS><RHS>Marked_a__U21(mark(X1),X2)</RHS></DPRULE><DPRULE num="27"><LHS>Marked_mark(U21(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="28"><LHS>Marked_mark(U22(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="29"><LHS>Marked_mark(U41(X1,X2,X3))</LHS><RHS>Marked_a__U41(mark(X1),X2,X3)</RHS></DPRULE><DPRULE num="30"><LHS>Marked_mark(U41(X1,X2,X3))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="31"><LHS>Marked_mark(plus(X1,X2))</LHS><RHS>Marked_a__plus(mark(X1),mark(X2))</RHS></DPRULE><DPRULE num="32"><LHS>Marked_mark(plus(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="33"><LHS>Marked_mark(plus(X1,X2))</LHS><RHS>Marked_mark(X2)</RHS></DPRULE><DPRULE num="34"><LHS>Marked_mark(and(X1,X2))</LHS><RHS>Marked_a__and(mark(X1),X2)</RHS></DPRULE><DPRULE num="35"><LHS>Marked_mark(and(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="36"><LHS>Marked_mark(isNatKind(X))</LHS><RHS>Marked_a__isNatKind(X)</RHS></DPRULE><DPRULE num="37"><LHS>Marked_mark(s(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><ORDERING type="poly"><POLYSYMB><SYMBOL><NAME>a__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>Marked_a__U21</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><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>a__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>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>a__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>Marked_a__U11</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>a__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_a__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>a__U11</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>Marked_a__isNat</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>isNat</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>a__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>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_a__isNatKind</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>a__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>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>a__isNatKind</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>a__isNat</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>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>U41</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><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</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></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>a__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>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>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>Marked_a__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>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>tt</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>Marked_a__U12</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U11</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>a__U41</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><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</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></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>Marked_a__and</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>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>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_a__U41(tt,M,N)</LHS><RHS>Marked_a__plus(mark(N),mark(M))</RHS></DPRULE><DPRULE num="1"><LHS>Marked_a__U41(tt,M,N)</LHS><RHS>Marked_mark(N)</RHS></DPRULE><DPRULE num="2"><LHS>Marked_a__U41(tt,M,N)</LHS><RHS>Marked_mark(M)</RHS></DPRULE><DPRULE num="3"><LHS>Marked_a__plus(N,s(M))</LHS><RHS>Marked_a__and(a__and(a__isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N)))</RHS></DPRULE><DPRULE num="4"><LHS>Marked_a__plus(N,s(M))</LHS><RHS>Marked_a__and(a__isNat(M),isNatKind(M))</RHS></DPRULE><DPRULE num="5"><LHS>Marked_a__plus(N,s(M))</LHS><RHS>Marked_a__isNat(M)</RHS></DPRULE><DPRULE num="6"><LHS>Marked_mark(U41(X1,X2,X3))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="7"><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>a__U11(tt,V1,V2)</LHS><RHS>a__U12(a__isNat(V1),V2)</RHS></RULE><RULE><LHS>a__U12(tt,V2)</LHS><RHS>a__U13(a__isNat(V2))</RHS></RULE><RULE><LHS>a__U13(tt)</LHS><RHS>tt</RHS></RULE><RULE><LHS>a__U21(tt,V1)</LHS><RHS>a__U22(a__isNat(V1))</RHS></RULE><RULE><LHS>a__U22(tt)</LHS><RHS>tt</RHS></RULE><RULE><LHS>a__U31(tt,N)</LHS><RHS>mark(N)</RHS></RULE><RULE><LHS>a__U41(tt,M,N)</LHS><RHS>s(a__plus(mark(N),mark(M)))</RHS></RULE><RULE><LHS>a__and(tt,X)</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>a__isNat(0)</LHS><RHS>tt</RHS></RULE><RULE><LHS>a__isNat(plus(V1,V2))</LHS><RHS>a__U11(a__and(a__isNatKind(V1),isNatKind(V2)),V1,V2)</RHS></RULE><RULE><LHS>a__isNat(s(V1))</LHS><RHS>a__U21(a__isNatKind(V1),V1)</RHS></RULE><RULE><LHS>a__isNatKind(0)</LHS><RHS>tt</RHS></RULE><RULE><LHS>a__isNatKind(plus(V1,V2))</LHS><RHS>a__and(a__isNatKind(V1),isNatKind(V2))</RHS></RULE><RULE><LHS>a__isNatKind(s(V1))</LHS><RHS>a__isNatKind(V1)</RHS></RULE><RULE><LHS>a__plus(N,0)</LHS><RHS>a__U31(a__and(a__isNat(N),isNatKind(N)),N)</RHS></RULE><RULE><LHS>a__plus(N,s(M))</LHS><RHS>a__U41(a__and(a__and(a__isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),
 M,N)</RHS></RULE><RULE><LHS>mark(U11(X1,X2,X3))</LHS><RHS>a__U11(mark(X1),X2,X3)</RHS></RULE><RULE><LHS>mark(U12(X1,X2))</LHS><RHS>a__U12(mark(X1),X2)</RHS></RULE><RULE><LHS>mark(isNat(X))</LHS><RHS>a__isNat(X)</RHS></RULE><RULE><LHS>mark(U13(X))</LHS><RHS>a__U13(mark(X))</RHS></RULE><RULE><LHS>mark(U21(X1,X2))</LHS><RHS>a__U21(mark(X1),X2)</RHS></RULE><RULE><LHS>mark(U22(X))</LHS><RHS>a__U22(mark(X))</RHS></RULE><RULE><LHS>mark(U31(X1,X2))</LHS><RHS>a__U31(mark(X1),X2)</RHS></RULE><RULE><LHS>mark(U41(X1,X2,X3))</LHS><RHS>a__U41(mark(X1),X2,X3)</RHS></RULE><RULE><LHS>mark(plus(X1,X2))</LHS><RHS>a__plus(mark(X1),mark(X2))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>a__and(mark(X1),X2)</RHS></RULE><RULE><LHS>mark(isNatKind(X))</LHS><RHS>a__isNatKind(X)</RHS></RULE><RULE><LHS>mark(tt)</LHS><RHS>tt</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>s(mark(X))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>0</RHS></RULE><RULE><LHS>a__U11(X1,X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>a__U12(X1,X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>a__isNat(X)</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>a__U13(X)</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>a__U21(X1,X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>a__U22(X)</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>a__U31(X1,X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>a__U41(X1,X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>a__plus(X1,X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>a__and(X1,X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>a__isNatKind(X)</LHS><RHS>isNatKind(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_a__U11(tt,V1,V2)</LHS><RHS>Marked_a__U12(a__isNat(V1),V2)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_a__U11(tt,V1,V2)</LHS><RHS>Marked_a__isNat(V1)</RHS></DPRULE><DPRULE num="2"><LHS>Marked_a__U12(tt,V2)</LHS><RHS>Marked_a__isNat(V2)</RHS></DPRULE><DPRULE num="3"><LHS>Marked_a__U21(tt,V1)</LHS><RHS>Marked_a__isNat(V1)</RHS></DPRULE><DPRULE num="4"><LHS>Marked_a__and(tt,X)</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="5"><LHS>Marked_a__isNat(plus(V1,V2))</LHS><RHS>Marked_a__U11(a__and(a__isNatKind(V1),isNatKind(V2)),V1,V2)</RHS></DPRULE><DPRULE num="6"><LHS>Marked_a__isNat(plus(V1,V2))</LHS><RHS>Marked_a__and(a__isNatKind(V1),isNatKind(V2))</RHS></DPRULE><DPRULE num="7"><LHS>Marked_a__isNat(plus(V1,V2))</LHS><RHS>Marked_a__isNatKind(V1)</RHS></DPRULE><DPRULE num="8"><LHS>Marked_a__isNat(s(V1))</LHS><RHS>Marked_a__U21(a__isNatKind(V1),V1)</RHS></DPRULE><DPRULE num="9"><LHS>Marked_a__isNat(s(V1))</LHS><RHS>Marked_a__isNatKind(V1)</RHS></DPRULE><DPRULE num="10"><LHS>Marked_a__isNatKind(plus(V1,V2))</LHS><RHS>Marked_a__and(a__isNatKind(V1),isNatKind(V2))</RHS></DPRULE><DPRULE num="11"><LHS>Marked_a__isNatKind(plus(V1,V2))</LHS><RHS>Marked_a__isNatKind(V1)</RHS></DPRULE><DPRULE num="12"><LHS>Marked_a__isNatKind(s(V1))</LHS><RHS>Marked_a__isNatKind(V1)</RHS></DPRULE><DPRULE num="13"><LHS>Marked_a__plus(N,s(M))</LHS><RHS>Marked_a__U41(a__and(a__and(a__isNat(M),isNatKind(M)),
               and(isNat(N),isNatKind(N))),M,N)</RHS></DPRULE><DPRULE num="14"><LHS>Marked_mark(U11(X1,X2,X3))</LHS><RHS>Marked_a__U11(mark(X1),X2,X3)</RHS></DPRULE><DPRULE num="15"><LHS>Marked_mark(U11(X1,X2,X3))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="16"><LHS>Marked_mark(U12(X1,X2))</LHS><RHS>Marked_a__U12(mark(X1),X2)</RHS></DPRULE><DPRULE num="17"><LHS>Marked_mark(U12(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="18"><LHS>Marked_mark(isNat(X))</LHS><RHS>Marked_a__isNat(X)</RHS></DPRULE><DPRULE num="19"><LHS>Marked_mark(U13(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="20"><LHS>Marked_mark(U21(X1,X2))</LHS><RHS>Marked_a__U21(mark(X1),X2)</RHS></DPRULE><DPRULE num="21"><LHS>Marked_mark(U21(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="22"><LHS>Marked_mark(U22(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="23"><LHS>Marked_mark(U41(X1,X2,X3))</LHS><RHS>Marked_a__U41(mark(X1),X2,X3)</RHS></DPRULE><DPRULE num="24"><LHS>Marked_mark(plus(X1,X2))</LHS><RHS>Marked_a__plus(mark(X1),mark(X2))</RHS></DPRULE><DPRULE num="25"><LHS>Marked_mark(plus(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="26"><LHS>Marked_mark(plus(X1,X2))</LHS><RHS>Marked_mark(X2)</RHS></DPRULE><DPRULE num="27"><LHS>Marked_mark(and(X1,X2))</LHS><RHS>Marked_a__and(mark(X1),X2)</RHS></DPRULE><DPRULE num="28"><LHS>Marked_mark(and(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="29"><LHS>Marked_mark(isNatKind(X))</LHS><RHS>Marked_a__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="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="25"/><NODE ref="26"/><NODE ref="27"/><NODE ref="28"/><NODE ref="29"/></SCC><NONSCC num="1"><NODE ref="24"/></NONSCC><NONSCC num="2"><NODE ref="23"/></NONSCC><NONSCC num="3"><NODE ref="13"/></NONSCC></CCLIST><EDGE end="2" start="0"/><EDGE end="1" start="0"/><EDGE end="3" start="1"/></DAG></CRITERION><PROPERTY criterion="stronggraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>a__U11(tt,V1,V2)</LHS><RHS>a__U12(a__isNat(V1),V2)</RHS></RULE><RULE><LHS>a__U12(tt,V2)</LHS><RHS>a__U13(a__isNat(V2))</RHS></RULE><RULE><LHS>a__U13(tt)</LHS><RHS>tt</RHS></RULE><RULE><LHS>a__U21(tt,V1)</LHS><RHS>a__U22(a__isNat(V1))</RHS></RULE><RULE><LHS>a__U22(tt)</LHS><RHS>tt</RHS></RULE><RULE><LHS>a__U31(tt,N)</LHS><RHS>mark(N)</RHS></RULE><RULE><LHS>a__U41(tt,M,N)</LHS><RHS>s(a__plus(mark(N),mark(M)))</RHS></RULE><RULE><LHS>a__and(tt,X)</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>a__isNat(0)</LHS><RHS>tt</RHS></RULE><RULE><LHS>a__isNat(plus(V1,V2))</LHS><RHS>a__U11(a__and(a__isNatKind(V1),isNatKind(V2)),V1,V2)</RHS></RULE><RULE><LHS>a__isNat(s(V1))</LHS><RHS>a__U21(a__isNatKind(V1),V1)</RHS></RULE><RULE><LHS>a__isNatKind(0)</LHS><RHS>tt</RHS></RULE><RULE><LHS>a__isNatKind(plus(V1,V2))</LHS><RHS>a__and(a__isNatKind(V1),isNatKind(V2))</RHS></RULE><RULE><LHS>a__isNatKind(s(V1))</LHS><RHS>a__isNatKind(V1)</RHS></RULE><RULE><LHS>a__plus(N,0)</LHS><RHS>a__U31(a__and(a__isNat(N),isNatKind(N)),N)</RHS></RULE><RULE><LHS>a__plus(N,s(M))</LHS><RHS>a__U41(a__and(a__and(a__isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),
 M,N)</RHS></RULE><RULE><LHS>mark(U11(X1,X2,X3))</LHS><RHS>a__U11(mark(X1),X2,X3)</RHS></RULE><RULE><LHS>mark(U12(X1,X2))</LHS><RHS>a__U12(mark(X1),X2)</RHS></RULE><RULE><LHS>mark(isNat(X))</LHS><RHS>a__isNat(X)</RHS></RULE><RULE><LHS>mark(U13(X))</LHS><RHS>a__U13(mark(X))</RHS></RULE><RULE><LHS>mark(U21(X1,X2))</LHS><RHS>a__U21(mark(X1),X2)</RHS></RULE><RULE><LHS>mark(U22(X))</LHS><RHS>a__U22(mark(X))</RHS></RULE><RULE><LHS>mark(U31(X1,X2))</LHS><RHS>a__U31(mark(X1),X2)</RHS></RULE><RULE><LHS>mark(U41(X1,X2,X3))</LHS><RHS>a__U41(mark(X1),X2,X3)</RHS></RULE><RULE><LHS>mark(plus(X1,X2))</LHS><RHS>a__plus(mark(X1),mark(X2))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>a__and(mark(X1),X2)</RHS></RULE><RULE><LHS>mark(isNatKind(X))</LHS><RHS>a__isNatKind(X)</RHS></RULE><RULE><LHS>mark(tt)</LHS><RHS>tt</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>s(mark(X))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>0</RHS></RULE><RULE><LHS>a__U11(X1,X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>a__U12(X1,X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>a__isNat(X)</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>a__U13(X)</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>a__U21(X1,X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>a__U22(X)</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>a__U31(X1,X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>a__U41(X1,X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>a__plus(X1,X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>a__and(X1,X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>a__isNatKind(X)</LHS><RHS>isNatKind(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_a__U11(tt,V1,V2)</LHS><RHS>Marked_a__U12(a__isNat(V1),V2)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_a__U11(tt,V1,V2)</LHS><RHS>Marked_a__isNat(V1)</RHS></DPRULE><DPRULE num="2"><LHS>Marked_a__U12(tt,V2)</LHS><RHS>Marked_a__isNat(V2)</RHS></DPRULE><DPRULE num="3"><LHS>Marked_a__U21(tt,V1)</LHS><RHS>Marked_a__isNat(V1)</RHS></DPRULE><DPRULE num="4"><LHS>Marked_a__and(tt,X)</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="5"><LHS>Marked_a__isNat(plus(V1,V2))</LHS><RHS>Marked_a__U11(a__and(a__isNatKind(V1),isNatKind(V2)),V1,V2)</RHS></DPRULE><DPRULE num="6"><LHS>Marked_a__isNat(plus(V1,V2))</LHS><RHS>Marked_a__and(a__isNatKind(V1),isNatKind(V2))</RHS></DPRULE><DPRULE num="7"><LHS>Marked_a__isNat(plus(V1,V2))</LHS><RHS>Marked_a__isNatKind(V1)</RHS></DPRULE><DPRULE num="8"><LHS>Marked_a__isNat(s(V1))</LHS><RHS>Marked_a__U21(a__isNatKind(V1),V1)</RHS></DPRULE><DPRULE num="9"><LHS>Marked_a__isNat(s(V1))</LHS><RHS>Marked_a__isNatKind(V1)</RHS></DPRULE><DPRULE num="10"><LHS>Marked_a__isNatKind(plus(V1,V2))</LHS><RHS>Marked_a__and(a__isNatKind(V1),isNatKind(V2))</RHS></DPRULE><DPRULE num="11"><LHS>Marked_a__isNatKind(plus(V1,V2))</LHS><RHS>Marked_a__isNatKind(V1)</RHS></DPRULE><DPRULE num="12"><LHS>Marked_a__isNatKind(s(V1))</LHS><RHS>Marked_a__isNatKind(V1)</RHS></DPRULE><DPRULE num="13"><LHS>Marked_mark(U11(X1,X2,X3))</LHS><RHS>Marked_a__U11(mark(X1),X2,X3)</RHS></DPRULE><DPRULE num="14"><LHS>Marked_mark(U11(X1,X2,X3))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="15"><LHS>Marked_mark(U12(X1,X2))</LHS><RHS>Marked_a__U12(mark(X1),X2)</RHS></DPRULE><DPRULE num="16"><LHS>Marked_mark(U12(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="17"><LHS>Marked_mark(isNat(X))</LHS><RHS>Marked_a__isNat(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_a__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_mark(X)</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_a__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_a__isNatKind(X)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><ORDERING type="poly"><POLYSYMB><SYMBOL><NAME>a__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>Marked_a__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>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>a__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>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>a__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>Marked_a__U11</NAME></SYMBOL><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></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>a__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>a__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>Marked_a__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>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>a__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>Marked_a__isNatKind</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>a__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>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>a__isNatKind</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>a__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>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>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>U41</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="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>a__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>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>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>tt</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>Marked_a__U12</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>a__U41</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="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_a__and</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>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>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_a__isNat(s(V1))</LHS><RHS>Marked_a__U21(a__isNatKind(V1),V1)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_a__isNat(s(V1))</LHS><RHS>Marked_a__isNatKind(V1)</RHS></DPRULE></DPLIST></STRICTPAIRS></CRITERION><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>a__U11(tt,V1,V2)</LHS><RHS>a__U12(a__isNat(V1),V2)</RHS></RULE><RULE><LHS>a__U12(tt,V2)</LHS><RHS>a__U13(a__isNat(V2))</RHS></RULE><RULE><LHS>a__U13(tt)</LHS><RHS>tt</RHS></RULE><RULE><LHS>a__U21(tt,V1)</LHS><RHS>a__U22(a__isNat(V1))</RHS></RULE><RULE><LHS>a__U22(tt)</LHS><RHS>tt</RHS></RULE><RULE><LHS>a__U31(tt,N)</LHS><RHS>mark(N)</RHS></RULE><RULE><LHS>a__U41(tt,M,N)</LHS><RHS>s(a__plus(mark(N),mark(M)))</RHS></RULE><RULE><LHS>a__and(tt,X)</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>a__isNat(0)</LHS><RHS>tt</RHS></RULE><RULE><LHS>a__isNat(plus(V1,V2))</LHS><RHS>a__U11(a__and(a__isNatKind(V1),isNatKind(V2)),V1,V2)</RHS></RULE><RULE><LHS>a__isNat(s(V1))</LHS><RHS>a__U21(a__isNatKind(V1),V1)</RHS></RULE><RULE><LHS>a__isNatKind(0)</LHS><RHS>tt</RHS></RULE><RULE><LHS>a__isNatKind(plus(V1,V2))</LHS><RHS>a__and(a__isNatKind(V1),isNatKind(V2))</RHS></RULE><RULE><LHS>a__isNatKind(s(V1))</LHS><RHS>a__isNatKind(V1)</RHS></RULE><RULE><LHS>a__plus(N,0)</LHS><RHS>a__U31(a__and(a__isNat(N),isNatKind(N)),N)</RHS></RULE><RULE><LHS>a__plus(N,s(M))</LHS><RHS>a__U41(a__and(a__and(a__isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),
 M,N)</RHS></RULE><RULE><LHS>mark(U11(X1,X2,X3))</LHS><RHS>a__U11(mark(X1),X2,X3)</RHS></RULE><RULE><LHS>mark(U12(X1,X2))</LHS><RHS>a__U12(mark(X1),X2)</RHS></RULE><RULE><LHS>mark(isNat(X))</LHS><RHS>a__isNat(X)</RHS></RULE><RULE><LHS>mark(U13(X))</LHS><RHS>a__U13(mark(X))</RHS></RULE><RULE><LHS>mark(U21(X1,X2))</LHS><RHS>a__U21(mark(X1),X2)</RHS></RULE><RULE><LHS>mark(U22(X))</LHS><RHS>a__U22(mark(X))</RHS></RULE><RULE><LHS>mark(U31(X1,X2))</LHS><RHS>a__U31(mark(X1),X2)</RHS></RULE><RULE><LHS>mark(U41(X1,X2,X3))</LHS><RHS>a__U41(mark(X1),X2,X3)</RHS></RULE><RULE><LHS>mark(plus(X1,X2))</LHS><RHS>a__plus(mark(X1),mark(X2))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>a__and(mark(X1),X2)</RHS></RULE><RULE><LHS>mark(isNatKind(X))</LHS><RHS>a__isNatKind(X)</RHS></RULE><RULE><LHS>mark(tt)</LHS><RHS>tt</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>s(mark(X))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>0</RHS></RULE><RULE><LHS>a__U11(X1,X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>a__U12(X1,X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>a__isNat(X)</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>a__U13(X)</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>a__U21(X1,X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>a__U22(X)</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>a__U31(X1,X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>a__U41(X1,X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>a__plus(X1,X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>a__and(X1,X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>a__isNatKind(X)</LHS><RHS>isNatKind(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_a__U11(tt,V1,V2)</LHS><RHS>Marked_a__U12(a__isNat(V1),V2)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_a__U11(tt,V1,V2)</LHS><RHS>Marked_a__isNat(V1)</RHS></DPRULE><DPRULE num="2"><LHS>Marked_a__U12(tt,V2)</LHS><RHS>Marked_a__isNat(V2)</RHS></DPRULE><DPRULE num="3"><LHS>Marked_a__U21(tt,V1)</LHS><RHS>Marked_a__isNat(V1)</RHS></DPRULE><DPRULE num="4"><LHS>Marked_a__and(tt,X)</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="5"><LHS>Marked_a__isNat(plus(V1,V2))</LHS><RHS>Marked_a__U11(a__and(a__isNatKind(V1),isNatKind(V2)),V1,V2)</RHS></DPRULE><DPRULE num="6"><LHS>Marked_a__isNat(plus(V1,V2))</LHS><RHS>Marked_a__and(a__isNatKind(V1),isNatKind(V2))</RHS></DPRULE><DPRULE num="7"><LHS>Marked_a__isNat(plus(V1,V2))</LHS><RHS>Marked_a__isNatKind(V1)</RHS></DPRULE><DPRULE num="8"><LHS>Marked_a__isNatKind(plus(V1,V2))</LHS><RHS>Marked_a__and(a__isNatKind(V1),isNatKind(V2))</RHS></DPRULE><DPRULE num="9"><LHS>Marked_a__isNatKind(plus(V1,V2))</LHS><RHS>Marked_a__isNatKind(V1)</RHS></DPRULE><DPRULE num="10"><LHS>Marked_a__isNatKind(s(V1))</LHS><RHS>Marked_a__isNatKind(V1)</RHS></DPRULE><DPRULE num="11"><LHS>Marked_mark(U11(X1,X2,X3))</LHS><RHS>Marked_a__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_a__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_a__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_a__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(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_a__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_a__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>a__U11(tt,V1,V2)</LHS><RHS>a__U12(a__isNat(V1),V2)</RHS></RULE><RULE><LHS>a__U12(tt,V2)</LHS><RHS>a__U13(a__isNat(V2))</RHS></RULE><RULE><LHS>a__U13(tt)</LHS><RHS>tt</RHS></RULE><RULE><LHS>a__U21(tt,V1)</LHS><RHS>a__U22(a__isNat(V1))</RHS></RULE><RULE><LHS>a__U22(tt)</LHS><RHS>tt</RHS></RULE><RULE><LHS>a__U31(tt,N)</LHS><RHS>mark(N)</RHS></RULE><RULE><LHS>a__U41(tt,M,N)</LHS><RHS>s(a__plus(mark(N),mark(M)))</RHS></RULE><RULE><LHS>a__and(tt,X)</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>a__isNat(0)</LHS><RHS>tt</RHS></RULE><RULE><LHS>a__isNat(plus(V1,V2))</LHS><RHS>a__U11(a__and(a__isNatKind(V1),isNatKind(V2)),V1,V2)</RHS></RULE><RULE><LHS>a__isNat(s(V1))</LHS><RHS>a__U21(a__isNatKind(V1),V1)</RHS></RULE><RULE><LHS>a__isNatKind(0)</LHS><RHS>tt</RHS></RULE><RULE><LHS>a__isNatKind(plus(V1,V2))</LHS><RHS>a__and(a__isNatKind(V1),isNatKind(V2))</RHS></RULE><RULE><LHS>a__isNatKind(s(V1))</LHS><RHS>a__isNatKind(V1)</RHS></RULE><RULE><LHS>a__plus(N,0)</LHS><RHS>a__U31(a__and(a__isNat(N),isNatKind(N)),N)</RHS></RULE><RULE><LHS>a__plus(N,s(M))</LHS><RHS>a__U41(a__and(a__and(a__isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),
 M,N)</RHS></RULE><RULE><LHS>mark(U11(X1,X2,X3))</LHS><RHS>a__U11(mark(X1),X2,X3)</RHS></RULE><RULE><LHS>mark(U12(X1,X2))</LHS><RHS>a__U12(mark(X1),X2)</RHS></RULE><RULE><LHS>mark(isNat(X))</LHS><RHS>a__isNat(X)</RHS></RULE><RULE><LHS>mark(U13(X))</LHS><RHS>a__U13(mark(X))</RHS></RULE><RULE><LHS>mark(U21(X1,X2))</LHS><RHS>a__U21(mark(X1),X2)</RHS></RULE><RULE><LHS>mark(U22(X))</LHS><RHS>a__U22(mark(X))</RHS></RULE><RULE><LHS>mark(U31(X1,X2))</LHS><RHS>a__U31(mark(X1),X2)</RHS></RULE><RULE><LHS>mark(U41(X1,X2,X3))</LHS><RHS>a__U41(mark(X1),X2,X3)</RHS></RULE><RULE><LHS>mark(plus(X1,X2))</LHS><RHS>a__plus(mark(X1),mark(X2))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>a__and(mark(X1),X2)</RHS></RULE><RULE><LHS>mark(isNatKind(X))</LHS><RHS>a__isNatKind(X)</RHS></RULE><RULE><LHS>mark(tt)</LHS><RHS>tt</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>s(mark(X))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>0</RHS></RULE><RULE><LHS>a__U11(X1,X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>a__U12(X1,X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>a__isNat(X)</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>a__U13(X)</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>a__U21(X1,X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>a__U22(X)</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>a__U31(X1,X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>a__U41(X1,X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>a__plus(X1,X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>a__and(X1,X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>a__isNatKind(X)</LHS><RHS>isNatKind(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_a__U11(tt,V1,V2)</LHS><RHS>Marked_a__U12(a__isNat(V1),V2)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_a__U11(tt,V1,V2)</LHS><RHS>Marked_a__isNat(V1)</RHS></DPRULE><DPRULE num="2"><LHS>Marked_a__U12(tt,V2)</LHS><RHS>Marked_a__isNat(V2)</RHS></DPRULE><DPRULE num="3"><LHS>Marked_a__U21(tt,V1)</LHS><RHS>Marked_a__isNat(V1)</RHS></DPRULE><DPRULE num="4"><LHS>Marked_a__and(tt,X)</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="5"><LHS>Marked_a__isNat(plus(V1,V2))</LHS><RHS>Marked_a__U11(a__and(a__isNatKind(V1),isNatKind(V2)),V1,V2)</RHS></DPRULE><DPRULE num="6"><LHS>Marked_a__isNat(plus(V1,V2))</LHS><RHS>Marked_a__and(a__isNatKind(V1),isNatKind(V2))</RHS></DPRULE><DPRULE num="7"><LHS>Marked_a__isNat(plus(V1,V2))</LHS><RHS>Marked_a__isNatKind(V1)</RHS></DPRULE><DPRULE num="8"><LHS>Marked_a__isNatKind(plus(V1,V2))</LHS><RHS>Marked_a__and(a__isNatKind(V1),isNatKind(V2))</RHS></DPRULE><DPRULE num="9"><LHS>Marked_a__isNatKind(plus(V1,V2))</LHS><RHS>Marked_a__isNatKind(V1)</RHS></DPRULE><DPRULE num="10"><LHS>Marked_a__isNatKind(s(V1))</LHS><RHS>Marked_a__isNatKind(V1)</RHS></DPRULE><DPRULE num="11"><LHS>Marked_mark(U11(X1,X2,X3))</LHS><RHS>Marked_a__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_a__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_a__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_a__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(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_a__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_a__isNatKind(X)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><ORDERING type="poly"><POLYSYMB><SYMBOL><NAME>a__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>Marked_a__U21</NAME></SYMBOL><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></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>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>a__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>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>a__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>Marked_a__U11</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>a__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>a__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>Marked_a__isNat</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></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>a__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>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_a__isNatKind</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>a__U21</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><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></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>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></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>a__isNatKind</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>a__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>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>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>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>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>a__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>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>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>tt</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>Marked_a__U12</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><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>a__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>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>Marked_a__and</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>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>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_mark(U21(X1,X2))</LHS><RHS>Marked_a__U21(mark(X1),X2)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_mark(U21(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE></DPLIST></STRICTPAIRS></CRITERION><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>a__U11(tt,V1,V2)</LHS><RHS>a__U12(a__isNat(V1),V2)</RHS></RULE><RULE><LHS>a__U12(tt,V2)</LHS><RHS>a__U13(a__isNat(V2))</RHS></RULE><RULE><LHS>a__U13(tt)</LHS><RHS>tt</RHS></RULE><RULE><LHS>a__U21(tt,V1)</LHS><RHS>a__U22(a__isNat(V1))</RHS></RULE><RULE><LHS>a__U22(tt)</LHS><RHS>tt</RHS></RULE><RULE><LHS>a__U31(tt,N)</LHS><RHS>mark(N)</RHS></RULE><RULE><LHS>a__U41(tt,M,N)</LHS><RHS>s(a__plus(mark(N),mark(M)))</RHS></RULE><RULE><LHS>a__and(tt,X)</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>a__isNat(0)</LHS><RHS>tt</RHS></RULE><RULE><LHS>a__isNat(plus(V1,V2))</LHS><RHS>a__U11(a__and(a__isNatKind(V1),isNatKind(V2)),V1,V2)</RHS></RULE><RULE><LHS>a__isNat(s(V1))</LHS><RHS>a__U21(a__isNatKind(V1),V1)</RHS></RULE><RULE><LHS>a__isNatKind(0)</LHS><RHS>tt</RHS></RULE><RULE><LHS>a__isNatKind(plus(V1,V2))</LHS><RHS>a__and(a__isNatKind(V1),isNatKind(V2))</RHS></RULE><RULE><LHS>a__isNatKind(s(V1))</LHS><RHS>a__isNatKind(V1)</RHS></RULE><RULE><LHS>a__plus(N,0)</LHS><RHS>a__U31(a__and(a__isNat(N),isNatKind(N)),N)</RHS></RULE><RULE><LHS>a__plus(N,s(M))</LHS><RHS>a__U41(a__and(a__and(a__isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),
 M,N)</RHS></RULE><RULE><LHS>mark(U11(X1,X2,X3))</LHS><RHS>a__U11(mark(X1),X2,X3)</RHS></RULE><RULE><LHS>mark(U12(X1,X2))</LHS><RHS>a__U12(mark(X1),X2)</RHS></RULE><RULE><LHS>mark(isNat(X))</LHS><RHS>a__isNat(X)</RHS></RULE><RULE><LHS>mark(U13(X))</LHS><RHS>a__U13(mark(X))</RHS></RULE><RULE><LHS>mark(U21(X1,X2))</LHS><RHS>a__U21(mark(X1),X2)</RHS></RULE><RULE><LHS>mark(U22(X))</LHS><RHS>a__U22(mark(X))</RHS></RULE><RULE><LHS>mark(U31(X1,X2))</LHS><RHS>a__U31(mark(X1),X2)</RHS></RULE><RULE><LHS>mark(U41(X1,X2,X3))</LHS><RHS>a__U41(mark(X1),X2,X3)</RHS></RULE><RULE><LHS>mark(plus(X1,X2))</LHS><RHS>a__plus(mark(X1),mark(X2))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>a__and(mark(X1),X2)</RHS></RULE><RULE><LHS>mark(isNatKind(X))</LHS><RHS>a__isNatKind(X)</RHS></RULE><RULE><LHS>mark(tt)</LHS><RHS>tt</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>s(mark(X))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>0</RHS></RULE><RULE><LHS>a__U11(X1,X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>a__U12(X1,X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>a__isNat(X)</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>a__U13(X)</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>a__U21(X1,X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>a__U22(X)</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>a__U31(X1,X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>a__U41(X1,X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>a__plus(X1,X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>a__and(X1,X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>a__isNatKind(X)</LHS><RHS>isNatKind(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_a__U11(tt,V1,V2)</LHS><RHS>Marked_a__U12(a__isNat(V1),V2)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_a__U11(tt,V1,V2)</LHS><RHS>Marked_a__isNat(V1)</RHS></DPRULE><DPRULE num="2"><LHS>Marked_a__U12(tt,V2)</LHS><RHS>Marked_a__isNat(V2)</RHS></DPRULE><DPRULE num="3"><LHS>Marked_a__U21(tt,V1)</LHS><RHS>Marked_a__isNat(V1)</RHS></DPRULE><DPRULE num="4"><LHS>Marked_a__and(tt,X)</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="5"><LHS>Marked_a__isNat(plus(V1,V2))</LHS><RHS>Marked_a__U11(a__and(a__isNatKind(V1),isNatKind(V2)),V1,V2)</RHS></DPRULE><DPRULE num="6"><LHS>Marked_a__isNat(plus(V1,V2))</LHS><RHS>Marked_a__and(a__isNatKind(V1),isNatKind(V2))</RHS></DPRULE><DPRULE num="7"><LHS>Marked_a__isNat(plus(V1,V2))</LHS><RHS>Marked_a__isNatKind(V1)</RHS></DPRULE><DPRULE num="8"><LHS>Marked_a__isNatKind(plus(V1,V2))</LHS><RHS>Marked_a__and(a__isNatKind(V1),isNatKind(V2))</RHS></DPRULE><DPRULE num="9"><LHS>Marked_a__isNatKind(plus(V1,V2))</LHS><RHS>Marked_a__isNatKind(V1)</RHS></DPRULE><DPRULE num="10"><LHS>Marked_a__isNatKind(s(V1))</LHS><RHS>Marked_a__isNatKind(V1)</RHS></DPRULE><DPRULE num="11"><LHS>Marked_mark(U11(X1,X2,X3))</LHS><RHS>Marked_a__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_a__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_a__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(U22(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="18"><LHS>Marked_mark(plus(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="19"><LHS>Marked_mark(plus(X1,X2))</LHS><RHS>Marked_mark(X2)</RHS></DPRULE><DPRULE num="20"><LHS>Marked_mark(and(X1,X2))</LHS><RHS>Marked_a__and(mark(X1),X2)</RHS></DPRULE><DPRULE num="21"><LHS>Marked_mark(and(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="22"><LHS>Marked_mark(isNatKind(X))</LHS><RHS>Marked_a__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="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"/></SCC><NONSCC num="1"><NODE ref="3"/></NONSCC></CCLIST><EDGE end="0" start="1"/></DAG></CRITERION><PROPERTY criterion="stronggraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>a__U11(tt,V1,V2)</LHS><RHS>a__U12(a__isNat(V1),V2)</RHS></RULE><RULE><LHS>a__U12(tt,V2)</LHS><RHS>a__U13(a__isNat(V2))</RHS></RULE><RULE><LHS>a__U13(tt)</LHS><RHS>tt</RHS></RULE><RULE><LHS>a__U21(tt,V1)</LHS><RHS>a__U22(a__isNat(V1))</RHS></RULE><RULE><LHS>a__U22(tt)</LHS><RHS>tt</RHS></RULE><RULE><LHS>a__U31(tt,N)</LHS><RHS>mark(N)</RHS></RULE><RULE><LHS>a__U41(tt,M,N)</LHS><RHS>s(a__plus(mark(N),mark(M)))</RHS></RULE><RULE><LHS>a__and(tt,X)</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>a__isNat(0)</LHS><RHS>tt</RHS></RULE><RULE><LHS>a__isNat(plus(V1,V2))</LHS><RHS>a__U11(a__and(a__isNatKind(V1),isNatKind(V2)),V1,V2)</RHS></RULE><RULE><LHS>a__isNat(s(V1))</LHS><RHS>a__U21(a__isNatKind(V1),V1)</RHS></RULE><RULE><LHS>a__isNatKind(0)</LHS><RHS>tt</RHS></RULE><RULE><LHS>a__isNatKind(plus(V1,V2))</LHS><RHS>a__and(a__isNatKind(V1),isNatKind(V2))</RHS></RULE><RULE><LHS>a__isNatKind(s(V1))</LHS><RHS>a__isNatKind(V1)</RHS></RULE><RULE><LHS>a__plus(N,0)</LHS><RHS>a__U31(a__and(a__isNat(N),isNatKind(N)),N)</RHS></RULE><RULE><LHS>a__plus(N,s(M))</LHS><RHS>a__U41(a__and(a__and(a__isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),
 M,N)</RHS></RULE><RULE><LHS>mark(U11(X1,X2,X3))</LHS><RHS>a__U11(mark(X1),X2,X3)</RHS></RULE><RULE><LHS>mark(U12(X1,X2))</LHS><RHS>a__U12(mark(X1),X2)</RHS></RULE><RULE><LHS>mark(isNat(X))</LHS><RHS>a__isNat(X)</RHS></RULE><RULE><LHS>mark(U13(X))</LHS><RHS>a__U13(mark(X))</RHS></RULE><RULE><LHS>mark(U21(X1,X2))</LHS><RHS>a__U21(mark(X1),X2)</RHS></RULE><RULE><LHS>mark(U22(X))</LHS><RHS>a__U22(mark(X))</RHS></RULE><RULE><LHS>mark(U31(X1,X2))</LHS><RHS>a__U31(mark(X1),X2)</RHS></RULE><RULE><LHS>mark(U41(X1,X2,X3))</LHS><RHS>a__U41(mark(X1),X2,X3)</RHS></RULE><RULE><LHS>mark(plus(X1,X2))</LHS><RHS>a__plus(mark(X1),mark(X2))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>a__and(mark(X1),X2)</RHS></RULE><RULE><LHS>mark(isNatKind(X))</LHS><RHS>a__isNatKind(X)</RHS></RULE><RULE><LHS>mark(tt)</LHS><RHS>tt</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>s(mark(X))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>0</RHS></RULE><RULE><LHS>a__U11(X1,X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>a__U12(X1,X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>a__isNat(X)</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>a__U13(X)</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>a__U21(X1,X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>a__U22(X)</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>a__U31(X1,X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>a__U41(X1,X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>a__plus(X1,X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>a__and(X1,X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>a__isNatKind(X)</LHS><RHS>isNatKind(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_a__U11(tt,V1,V2)</LHS><RHS>Marked_a__U12(a__isNat(V1),V2)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_a__U11(tt,V1,V2)</LHS><RHS>Marked_a__isNat(V1)</RHS></DPRULE><DPRULE num="2"><LHS>Marked_a__U12(tt,V2)</LHS><RHS>Marked_a__isNat(V2)</RHS></DPRULE><DPRULE num="3"><LHS>Marked_a__and(tt,X)</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="4"><LHS>Marked_a__isNat(plus(V1,V2))</LHS><RHS>Marked_a__U11(a__and(a__isNatKind(V1),isNatKind(V2)),V1,V2)</RHS></DPRULE><DPRULE num="5"><LHS>Marked_a__isNat(plus(V1,V2))</LHS><RHS>Marked_a__and(a__isNatKind(V1),isNatKind(V2))</RHS></DPRULE><DPRULE num="6"><LHS>Marked_a__isNat(plus(V1,V2))</LHS><RHS>Marked_a__isNatKind(V1)</RHS></DPRULE><DPRULE num="7"><LHS>Marked_a__isNatKind(plus(V1,V2))</LHS><RHS>Marked_a__and(a__isNatKind(V1),isNatKind(V2))</RHS></DPRULE><DPRULE num="8"><LHS>Marked_a__isNatKind(plus(V1,V2))</LHS><RHS>Marked_a__isNatKind(V1)</RHS></DPRULE><DPRULE num="9"><LHS>Marked_a__isNatKind(s(V1))</LHS><RHS>Marked_a__isNatKind(V1)</RHS></DPRULE><DPRULE num="10"><LHS>Marked_mark(U11(X1,X2,X3))</LHS><RHS>Marked_a__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_a__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_a__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(U22(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="17"><LHS>Marked_mark(plus(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="18"><LHS>Marked_mark(plus(X1,X2))</LHS><RHS>Marked_mark(X2)</RHS></DPRULE><DPRULE num="19"><LHS>Marked_mark(and(X1,X2))</LHS><RHS>Marked_a__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_a__isNatKind(X)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><ORDERING type="poly"><POLYSYMB><SYMBOL><NAME>a__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>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>a__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>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>a__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>Marked_a__U11</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>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>a__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>a__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>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_a__isNat</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><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>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>a__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>Marked_a__isNatKind</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>a__U21</NAME></SYMBOL><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></POLYSYMB><POLYSYMB><SYMBOL><NAME>U21</NAME></SYMBOL><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></POLYSYMB><POLYSYMB><SYMBOL><NAME>a__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><POLYSYMB><SYMBOL><NAME>a__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>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>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>U41</NAME></SYMBOL><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></POLYSYMB><POLYSYMB><SYMBOL><NAME>a__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>Marked_mark</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><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>1</INT></COEF></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>1</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>Marked_a__U12</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><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>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>a__U41</NAME></SYMBOL><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></POLYSYMB><POLYSYMB><SYMBOL><NAME>Marked_a__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>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>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><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_a__isNat(plus(V1,V2))</LHS><RHS>Marked_a__and(a__isNatKind(V1),isNatKind(V2))</RHS></DPRULE><DPRULE num="1"><LHS>Marked_a__isNat(plus(V1,V2))</LHS><RHS>Marked_a__isNatKind(V1)</RHS></DPRULE><DPRULE num="2"><LHS>Marked_a__isNatKind(plus(V1,V2))</LHS><RHS>Marked_a__and(a__isNatKind(V1),isNatKind(V2))</RHS></DPRULE><DPRULE num="3"><LHS>Marked_mark(and(X1,X2))</LHS><RHS>Marked_a__and(mark(X1),X2)</RHS></DPRULE><DPRULE num="4"><LHS>Marked_mark(isNatKind(X))</LHS><RHS>Marked_a__isNatKind(X)</RHS></DPRULE></DPLIST></STRICTPAIRS></CRITERION><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>a__U11(tt,V1,V2)</LHS><RHS>a__U12(a__isNat(V1),V2)</RHS></RULE><RULE><LHS>a__U12(tt,V2)</LHS><RHS>a__U13(a__isNat(V2))</RHS></RULE><RULE><LHS>a__U13(tt)</LHS><RHS>tt</RHS></RULE><RULE><LHS>a__U21(tt,V1)</LHS><RHS>a__U22(a__isNat(V1))</RHS></RULE><RULE><LHS>a__U22(tt)</LHS><RHS>tt</RHS></RULE><RULE><LHS>a__U31(tt,N)</LHS><RHS>mark(N)</RHS></RULE><RULE><LHS>a__U41(tt,M,N)</LHS><RHS>s(a__plus(mark(N),mark(M)))</RHS></RULE><RULE><LHS>a__and(tt,X)</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>a__isNat(0)</LHS><RHS>tt</RHS></RULE><RULE><LHS>a__isNat(plus(V1,V2))</LHS><RHS>a__U11(a__and(a__isNatKind(V1),isNatKind(V2)),V1,V2)</RHS></RULE><RULE><LHS>a__isNat(s(V1))</LHS><RHS>a__U21(a__isNatKind(V1),V1)</RHS></RULE><RULE><LHS>a__isNatKind(0)</LHS><RHS>tt</RHS></RULE><RULE><LHS>a__isNatKind(plus(V1,V2))</LHS><RHS>a__and(a__isNatKind(V1),isNatKind(V2))</RHS></RULE><RULE><LHS>a__isNatKind(s(V1))</LHS><RHS>a__isNatKind(V1)</RHS></RULE><RULE><LHS>a__plus(N,0)</LHS><RHS>a__U31(a__and(a__isNat(N),isNatKind(N)),N)</RHS></RULE><RULE><LHS>a__plus(N,s(M))</LHS><RHS>a__U41(a__and(a__and(a__isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),
 M,N)</RHS></RULE><RULE><LHS>mark(U11(X1,X2,X3))</LHS><RHS>a__U11(mark(X1),X2,X3)</RHS></RULE><RULE><LHS>mark(U12(X1,X2))</LHS><RHS>a__U12(mark(X1),X2)</RHS></RULE><RULE><LHS>mark(isNat(X))</LHS><RHS>a__isNat(X)</RHS></RULE><RULE><LHS>mark(U13(X))</LHS><RHS>a__U13(mark(X))</RHS></RULE><RULE><LHS>mark(U21(X1,X2))</LHS><RHS>a__U21(mark(X1),X2)</RHS></RULE><RULE><LHS>mark(U22(X))</LHS><RHS>a__U22(mark(X))</RHS></RULE><RULE><LHS>mark(U31(X1,X2))</LHS><RHS>a__U31(mark(X1),X2)</RHS></RULE><RULE><LHS>mark(U41(X1,X2,X3))</LHS><RHS>a__U41(mark(X1),X2,X3)</RHS></RULE><RULE><LHS>mark(plus(X1,X2))</LHS><RHS>a__plus(mark(X1),mark(X2))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>a__and(mark(X1),X2)</RHS></RULE><RULE><LHS>mark(isNatKind(X))</LHS><RHS>a__isNatKind(X)</RHS></RULE><RULE><LHS>mark(tt)</LHS><RHS>tt</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>s(mark(X))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>0</RHS></RULE><RULE><LHS>a__U11(X1,X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>a__U12(X1,X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>a__isNat(X)</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>a__U13(X)</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>a__U21(X1,X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>a__U22(X)</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>a__U31(X1,X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>a__U41(X1,X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>a__plus(X1,X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>a__and(X1,X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>a__isNatKind(X)</LHS><RHS>isNatKind(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_a__U11(tt,V1,V2)</LHS><RHS>Marked_a__U12(a__isNat(V1),V2)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_a__U11(tt,V1,V2)</LHS><RHS>Marked_a__isNat(V1)</RHS></DPRULE><DPRULE num="2"><LHS>Marked_a__U12(tt,V2)</LHS><RHS>Marked_a__isNat(V2)</RHS></DPRULE><DPRULE num="3"><LHS>Marked_a__and(tt,X)</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="4"><LHS>Marked_a__isNat(plus(V1,V2))</LHS><RHS>Marked_a__U11(a__and(a__isNatKind(V1),isNatKind(V2)),V1,V2)</RHS></DPRULE><DPRULE num="5"><LHS>Marked_a__isNatKind(plus(V1,V2))</LHS><RHS>Marked_a__isNatKind(V1)</RHS></DPRULE><DPRULE num="6"><LHS>Marked_a__isNatKind(s(V1))</LHS><RHS>Marked_a__isNatKind(V1)</RHS></DPRULE><DPRULE num="7"><LHS>Marked_mark(U11(X1,X2,X3))</LHS><RHS>Marked_a__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_a__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_a__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(U22(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="14"><LHS>Marked_mark(plus(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="15"><LHS>Marked_mark(plus(X1,X2))</LHS><RHS>Marked_mark(X2)</RHS></DPRULE><DPRULE num="16"><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="8"/><NODE ref="10"/><NODE ref="12"/><NODE ref="13"/><NODE ref="14"/><NODE ref="15"/><NODE ref="16"/></SCC><NONSCC num="1"><NODE ref="11"/></NONSCC><NONSCC num="2"><NODE ref="9"/></NONSCC><NONSCC num="3"><NODE ref="7"/></NONSCC><SCC num="4"><NODE ref="0"/><NODE ref="1"/><NODE ref="2"/><NODE ref="4"/></SCC><SCC num="5"><NODE ref="5"/><NODE ref="6"/></SCC><NONSCC num="6"><NODE ref="3"/></NONSCC></CCLIST><EDGE end="3" start="0"/><EDGE end="2" start="0"/><EDGE end="1" start="0"/><EDGE end="4" start="1"/><EDGE end="4" start="2"/><EDGE end="4" start="3"/><EDGE end="3" start="6"/><EDGE end="2" start="6"/><EDGE end="1" start="6"/><EDGE end="0" start="6"/></DAG></CRITERION><PROPERTY criterion="sterm" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>a__U11(tt,V1,V2)</LHS><RHS>a__U12(a__isNat(V1),V2)</RHS></RULE><RULE><LHS>a__U12(tt,V2)</LHS><RHS>a__U13(a__isNat(V2))</RHS></RULE><RULE><LHS>a__U13(tt)</LHS><RHS>tt</RHS></RULE><RULE><LHS>a__U21(tt,V1)</LHS><RHS>a__U22(a__isNat(V1))</RHS></RULE><RULE><LHS>a__U22(tt)</LHS><RHS>tt</RHS></RULE><RULE><LHS>a__U31(tt,N)</LHS><RHS>mark(N)</RHS></RULE><RULE><LHS>a__U41(tt,M,N)</LHS><RHS>s(a__plus(mark(N),mark(M)))</RHS></RULE><RULE><LHS>a__and(tt,X)</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>a__isNat(0)</LHS><RHS>tt</RHS></RULE><RULE><LHS>a__isNat(plus(V1,V2))</LHS><RHS>a__U11(a__and(a__isNatKind(V1),isNatKind(V2)),V1,V2)</RHS></RULE><RULE><LHS>a__isNat(s(V1))</LHS><RHS>a__U21(a__isNatKind(V1),V1)</RHS></RULE><RULE><LHS>a__isNatKind(0)</LHS><RHS>tt</RHS></RULE><RULE><LHS>a__isNatKind(plus(V1,V2))</LHS><RHS>a__and(a__isNatKind(V1),isNatKind(V2))</RHS></RULE><RULE><LHS>a__isNatKind(s(V1))</LHS><RHS>a__isNatKind(V1)</RHS></RULE><RULE><LHS>a__plus(N,0)</LHS><RHS>a__U31(a__and(a__isNat(N),isNatKind(N)),N)</RHS></RULE><RULE><LHS>a__plus(N,s(M))</LHS><RHS>a__U41(a__and(a__and(a__isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),
 M,N)</RHS></RULE><RULE><LHS>mark(U11(X1,X2,X3))</LHS><RHS>a__U11(mark(X1),X2,X3)</RHS></RULE><RULE><LHS>mark(U12(X1,X2))</LHS><RHS>a__U12(mark(X1),X2)</RHS></RULE><RULE><LHS>mark(isNat(X))</LHS><RHS>a__isNat(X)</RHS></RULE><RULE><LHS>mark(U13(X))</LHS><RHS>a__U13(mark(X))</RHS></RULE><RULE><LHS>mark(U21(X1,X2))</LHS><RHS>a__U21(mark(X1),X2)</RHS></RULE><RULE><LHS>mark(U22(X))</LHS><RHS>a__U22(mark(X))</RHS></RULE><RULE><LHS>mark(U31(X1,X2))</LHS><RHS>a__U31(mark(X1),X2)</RHS></RULE><RULE><LHS>mark(U41(X1,X2,X3))</LHS><RHS>a__U41(mark(X1),X2,X3)</RHS></RULE><RULE><LHS>mark(plus(X1,X2))</LHS><RHS>a__plus(mark(X1),mark(X2))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>a__and(mark(X1),X2)</RHS></RULE><RULE><LHS>mark(isNatKind(X))</LHS><RHS>a__isNatKind(X)</RHS></RULE><RULE><LHS>mark(tt)</LHS><RHS>tt</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>s(mark(X))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>0</RHS></RULE><RULE><LHS>a__U11(X1,X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>a__U12(X1,X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>a__isNat(X)</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>a__U13(X)</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>a__U21(X1,X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>a__U22(X)</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>a__U31(X1,X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>a__U41(X1,X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>a__plus(X1,X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>a__and(X1,X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>a__isNatKind(X)</LHS><RHS>isNatKind(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_a__isNatKind(plus(V1,V2))</LHS><RHS>Marked_a__isNatKind(V1)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_a__isNatKind(s(V1))</LHS><RHS>Marked_a__isNatKind(V1)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><PROJECTION><PROJ><SYMBOL><NAME>Marked_a__isNatKind</NAME></SYMBOL><INT>1</INT></PROJ></PROJECTION><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_a__isNatKind(s(V1))</LHS><RHS>Marked_a__isNatKind(V1)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_a__isNatKind(plus(V1,V2))</LHS><RHS>Marked_a__isNatKind(V1)</RHS></DPRULE></DPLIST></STRICTPAIRS><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>a__U11(tt,V1,V2)</LHS><RHS>a__U12(a__isNat(V1),V2)</RHS></RULE><RULE><LHS>a__U12(tt,V2)</LHS><RHS>a__U13(a__isNat(V2))</RHS></RULE><RULE><LHS>a__U13(tt)</LHS><RHS>tt</RHS></RULE><RULE><LHS>a__U21(tt,V1)</LHS><RHS>a__U22(a__isNat(V1))</RHS></RULE><RULE><LHS>a__U22(tt)</LHS><RHS>tt</RHS></RULE><RULE><LHS>a__U31(tt,N)</LHS><RHS>mark(N)</RHS></RULE><RULE><LHS>a__U41(tt,M,N)</LHS><RHS>s(a__plus(mark(N),mark(M)))</RHS></RULE><RULE><LHS>a__and(tt,X)</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>a__isNat(0)</LHS><RHS>tt</RHS></RULE><RULE><LHS>a__isNat(plus(V1,V2))</LHS><RHS>a__U11(a__and(a__isNatKind(V1),isNatKind(V2)),V1,V2)</RHS></RULE><RULE><LHS>a__isNat(s(V1))</LHS><RHS>a__U21(a__isNatKind(V1),V1)</RHS></RULE><RULE><LHS>a__isNatKind(0)</LHS><RHS>tt</RHS></RULE><RULE><LHS>a__isNatKind(plus(V1,V2))</LHS><RHS>a__and(a__isNatKind(V1),isNatKind(V2))</RHS></RULE><RULE><LHS>a__isNatKind(s(V1))</LHS><RHS>a__isNatKind(V1)</RHS></RULE><RULE><LHS>a__plus(N,0)</LHS><RHS>a__U31(a__and(a__isNat(N),isNatKind(N)),N)</RHS></RULE><RULE><LHS>a__plus(N,s(M))</LHS><RHS>a__U41(a__and(a__and(a__isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),
 M,N)</RHS></RULE><RULE><LHS>mark(U11(X1,X2,X3))</LHS><RHS>a__U11(mark(X1),X2,X3)</RHS></RULE><RULE><LHS>mark(U12(X1,X2))</LHS><RHS>a__U12(mark(X1),X2)</RHS></RULE><RULE><LHS>mark(isNat(X))</LHS><RHS>a__isNat(X)</RHS></RULE><RULE><LHS>mark(U13(X))</LHS><RHS>a__U13(mark(X))</RHS></RULE><RULE><LHS>mark(U21(X1,X2))</LHS><RHS>a__U21(mark(X1),X2)</RHS></RULE><RULE><LHS>mark(U22(X))</LHS><RHS>a__U22(mark(X))</RHS></RULE><RULE><LHS>mark(U31(X1,X2))</LHS><RHS>a__U31(mark(X1),X2)</RHS></RULE><RULE><LHS>mark(U41(X1,X2,X3))</LHS><RHS>a__U41(mark(X1),X2,X3)</RHS></RULE><RULE><LHS>mark(plus(X1,X2))</LHS><RHS>a__plus(mark(X1),mark(X2))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>a__and(mark(X1),X2)</RHS></RULE><RULE><LHS>mark(isNatKind(X))</LHS><RHS>a__isNatKind(X)</RHS></RULE><RULE><LHS>mark(tt)</LHS><RHS>tt</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>s(mark(X))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>0</RHS></RULE><RULE><LHS>a__U11(X1,X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>a__U12(X1,X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>a__isNat(X)</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>a__U13(X)</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>a__U21(X1,X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>a__U22(X)</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>a__U31(X1,X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>a__U41(X1,X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>a__plus(X1,X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>a__and(X1,X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>a__isNatKind(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>a__U11(tt,V1,V2)</LHS><RHS>a__U12(a__isNat(V1),V2)</RHS></RULE><RULE><LHS>a__U12(tt,V2)</LHS><RHS>a__U13(a__isNat(V2))</RHS></RULE><RULE><LHS>a__U13(tt)</LHS><RHS>tt</RHS></RULE><RULE><LHS>a__U21(tt,V1)</LHS><RHS>a__U22(a__isNat(V1))</RHS></RULE><RULE><LHS>a__U22(tt)</LHS><RHS>tt</RHS></RULE><RULE><LHS>a__U31(tt,N)</LHS><RHS>mark(N)</RHS></RULE><RULE><LHS>a__U41(tt,M,N)</LHS><RHS>s(a__plus(mark(N),mark(M)))</RHS></RULE><RULE><LHS>a__and(tt,X)</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>a__isNat(0)</LHS><RHS>tt</RHS></RULE><RULE><LHS>a__isNat(plus(V1,V2))</LHS><RHS>a__U11(a__and(a__isNatKind(V1),isNatKind(V2)),V1,V2)</RHS></RULE><RULE><LHS>a__isNat(s(V1))</LHS><RHS>a__U21(a__isNatKind(V1),V1)</RHS></RULE><RULE><LHS>a__isNatKind(0)</LHS><RHS>tt</RHS></RULE><RULE><LHS>a__isNatKind(plus(V1,V2))</LHS><RHS>a__and(a__isNatKind(V1),isNatKind(V2))</RHS></RULE><RULE><LHS>a__isNatKind(s(V1))</LHS><RHS>a__isNatKind(V1)</RHS></RULE><RULE><LHS>a__plus(N,0)</LHS><RHS>a__U31(a__and(a__isNat(N),isNatKind(N)),N)</RHS></RULE><RULE><LHS>a__plus(N,s(M))</LHS><RHS>a__U41(a__and(a__and(a__isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),
 M,N)</RHS></RULE><RULE><LHS>mark(U11(X1,X2,X3))</LHS><RHS>a__U11(mark(X1),X2,X3)</RHS></RULE><RULE><LHS>mark(U12(X1,X2))</LHS><RHS>a__U12(mark(X1),X2)</RHS></RULE><RULE><LHS>mark(isNat(X))</LHS><RHS>a__isNat(X)</RHS></RULE><RULE><LHS>mark(U13(X))</LHS><RHS>a__U13(mark(X))</RHS></RULE><RULE><LHS>mark(U21(X1,X2))</LHS><RHS>a__U21(mark(X1),X2)</RHS></RULE><RULE><LHS>mark(U22(X))</LHS><RHS>a__U22(mark(X))</RHS></RULE><RULE><LHS>mark(U31(X1,X2))</LHS><RHS>a__U31(mark(X1),X2)</RHS></RULE><RULE><LHS>mark(U41(X1,X2,X3))</LHS><RHS>a__U41(mark(X1),X2,X3)</RHS></RULE><RULE><LHS>mark(plus(X1,X2))</LHS><RHS>a__plus(mark(X1),mark(X2))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>a__and(mark(X1),X2)</RHS></RULE><RULE><LHS>mark(isNatKind(X))</LHS><RHS>a__isNatKind(X)</RHS></RULE><RULE><LHS>mark(tt)</LHS><RHS>tt</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>s(mark(X))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>0</RHS></RULE><RULE><LHS>a__U11(X1,X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>a__U12(X1,X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>a__isNat(X)</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>a__U13(X)</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>a__U21(X1,X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>a__U22(X)</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>a__U31(X1,X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>a__U41(X1,X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>a__plus(X1,X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>a__and(X1,X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>a__isNatKind(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><DPRULE num="3"><LHS>Marked_mark(U22(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="4"><LHS>Marked_mark(plus(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="5"><LHS>Marked_mark(plus(X1,X2))</LHS><RHS>Marked_mark(X2)</RHS></DPRULE><DPRULE num="6"><LHS>Marked_mark(and(X1,X2))</LHS><RHS>Marked_mark(X1)</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(and(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><DPRULE num="2"><LHS>Marked_mark(plus(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="3"><LHS>Marked_mark(U22(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="4"><LHS>Marked_mark(U13(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="5"><LHS>Marked_mark(U12(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="6"><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>a__U11(tt,V1,V2)</LHS><RHS>a__U12(a__isNat(V1),V2)</RHS></RULE><RULE><LHS>a__U12(tt,V2)</LHS><RHS>a__U13(a__isNat(V2))</RHS></RULE><RULE><LHS>a__U13(tt)</LHS><RHS>tt</RHS></RULE><RULE><LHS>a__U21(tt,V1)</LHS><RHS>a__U22(a__isNat(V1))</RHS></RULE><RULE><LHS>a__U22(tt)</LHS><RHS>tt</RHS></RULE><RULE><LHS>a__U31(tt,N)</LHS><RHS>mark(N)</RHS></RULE><RULE><LHS>a__U41(tt,M,N)</LHS><RHS>s(a__plus(mark(N),mark(M)))</RHS></RULE><RULE><LHS>a__and(tt,X)</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>a__isNat(0)</LHS><RHS>tt</RHS></RULE><RULE><LHS>a__isNat(plus(V1,V2))</LHS><RHS>a__U11(a__and(a__isNatKind(V1),isNatKind(V2)),V1,V2)</RHS></RULE><RULE><LHS>a__isNat(s(V1))</LHS><RHS>a__U21(a__isNatKind(V1),V1)</RHS></RULE><RULE><LHS>a__isNatKind(0)</LHS><RHS>tt</RHS></RULE><RULE><LHS>a__isNatKind(plus(V1,V2))</LHS><RHS>a__and(a__isNatKind(V1),isNatKind(V2))</RHS></RULE><RULE><LHS>a__isNatKind(s(V1))</LHS><RHS>a__isNatKind(V1)</RHS></RULE><RULE><LHS>a__plus(N,0)</LHS><RHS>a__U31(a__and(a__isNat(N),isNatKind(N)),N)</RHS></RULE><RULE><LHS>a__plus(N,s(M))</LHS><RHS>a__U41(a__and(a__and(a__isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),
 M,N)</RHS></RULE><RULE><LHS>mark(U11(X1,X2,X3))</LHS><RHS>a__U11(mark(X1),X2,X3)</RHS></RULE><RULE><LHS>mark(U12(X1,X2))</LHS><RHS>a__U12(mark(X1),X2)</RHS></RULE><RULE><LHS>mark(isNat(X))</LHS><RHS>a__isNat(X)</RHS></RULE><RULE><LHS>mark(U13(X))</LHS><RHS>a__U13(mark(X))</RHS></RULE><RULE><LHS>mark(U21(X1,X2))</LHS><RHS>a__U21(mark(X1),X2)</RHS></RULE><RULE><LHS>mark(U22(X))</LHS><RHS>a__U22(mark(X))</RHS></RULE><RULE><LHS>mark(U31(X1,X2))</LHS><RHS>a__U31(mark(X1),X2)</RHS></RULE><RULE><LHS>mark(U41(X1,X2,X3))</LHS><RHS>a__U41(mark(X1),X2,X3)</RHS></RULE><RULE><LHS>mark(plus(X1,X2))</LHS><RHS>a__plus(mark(X1),mark(X2))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>a__and(mark(X1),X2)</RHS></RULE><RULE><LHS>mark(isNatKind(X))</LHS><RHS>a__isNatKind(X)</RHS></RULE><RULE><LHS>mark(tt)</LHS><RHS>tt</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>s(mark(X))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>0</RHS></RULE><RULE><LHS>a__U11(X1,X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>a__U12(X1,X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>a__isNat(X)</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>a__U13(X)</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>a__U21(X1,X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>a__U22(X)</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>a__U31(X1,X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>a__U41(X1,X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>a__plus(X1,X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>a__and(X1,X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>a__isNatKind(X)</LHS><RHS>isNatKind(X)</RHS></RULE></REWSYS><DPLIST/></DPSYS></SYSTEM><CRITERION><DAG approx="simpl"><CCLIST/></DAG></CRITERION></PROPERTY></PROPERTY><PROPERTY criterion="stronggraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>a__U11(tt,V1,V2)</LHS><RHS>a__U12(a__isNat(V1),V2)</RHS></RULE><RULE><LHS>a__U12(tt,V2)</LHS><RHS>a__U13(a__isNat(V2))</RHS></RULE><RULE><LHS>a__U13(tt)</LHS><RHS>tt</RHS></RULE><RULE><LHS>a__U21(tt,V1)</LHS><RHS>a__U22(a__isNat(V1))</RHS></RULE><RULE><LHS>a__U22(tt)</LHS><RHS>tt</RHS></RULE><RULE><LHS>a__U31(tt,N)</LHS><RHS>mark(N)</RHS></RULE><RULE><LHS>a__U41(tt,M,N)</LHS><RHS>s(a__plus(mark(N),mark(M)))</RHS></RULE><RULE><LHS>a__and(tt,X)</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>a__isNat(0)</LHS><RHS>tt</RHS></RULE><RULE><LHS>a__isNat(plus(V1,V2))</LHS><RHS>a__U11(a__and(a__isNatKind(V1),isNatKind(V2)),V1,V2)</RHS></RULE><RULE><LHS>a__isNat(s(V1))</LHS><RHS>a__U21(a__isNatKind(V1),V1)</RHS></RULE><RULE><LHS>a__isNatKind(0)</LHS><RHS>tt</RHS></RULE><RULE><LHS>a__isNatKind(plus(V1,V2))</LHS><RHS>a__and(a__isNatKind(V1),isNatKind(V2))</RHS></RULE><RULE><LHS>a__isNatKind(s(V1))</LHS><RHS>a__isNatKind(V1)</RHS></RULE><RULE><LHS>a__plus(N,0)</LHS><RHS>a__U31(a__and(a__isNat(N),isNatKind(N)),N)</RHS></RULE><RULE><LHS>a__plus(N,s(M))</LHS><RHS>a__U41(a__and(a__and(a__isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),
 M,N)</RHS></RULE><RULE><LHS>mark(U11(X1,X2,X3))</LHS><RHS>a__U11(mark(X1),X2,X3)</RHS></RULE><RULE><LHS>mark(U12(X1,X2))</LHS><RHS>a__U12(mark(X1),X2)</RHS></RULE><RULE><LHS>mark(isNat(X))</LHS><RHS>a__isNat(X)</RHS></RULE><RULE><LHS>mark(U13(X))</LHS><RHS>a__U13(mark(X))</RHS></RULE><RULE><LHS>mark(U21(X1,X2))</LHS><RHS>a__U21(mark(X1),X2)</RHS></RULE><RULE><LHS>mark(U22(X))</LHS><RHS>a__U22(mark(X))</RHS></RULE><RULE><LHS>mark(U31(X1,X2))</LHS><RHS>a__U31(mark(X1),X2)</RHS></RULE><RULE><LHS>mark(U41(X1,X2,X3))</LHS><RHS>a__U41(mark(X1),X2,X3)</RHS></RULE><RULE><LHS>mark(plus(X1,X2))</LHS><RHS>a__plus(mark(X1),mark(X2))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>a__and(mark(X1),X2)</RHS></RULE><RULE><LHS>mark(isNatKind(X))</LHS><RHS>a__isNatKind(X)</RHS></RULE><RULE><LHS>mark(tt)</LHS><RHS>tt</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>s(mark(X))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>0</RHS></RULE><RULE><LHS>a__U11(X1,X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>a__U12(X1,X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>a__isNat(X)</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>a__U13(X)</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>a__U21(X1,X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>a__U22(X)</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>a__U31(X1,X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>a__U41(X1,X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>a__plus(X1,X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>a__and(X1,X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>a__isNatKind(X)</LHS><RHS>isNatKind(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_a__U11(tt,V1,V2)</LHS><RHS>Marked_a__U12(a__isNat(V1),V2)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_a__U11(tt,V1,V2)</LHS><RHS>Marked_a__isNat(V1)</RHS></DPRULE><DPRULE num="2"><LHS>Marked_a__U12(tt,V2)</LHS><RHS>Marked_a__isNat(V2)</RHS></DPRULE><DPRULE num="3"><LHS>Marked_a__isNat(plus(V1,V2))</LHS><RHS>Marked_a__U11(a__and(a__isNatKind(V1),isNatKind(V2)),V1,V2)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><ORDERING type="poly"><POLYSYMB><SYMBOL><NAME>a__U12</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>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>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>a__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>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>a__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>Marked_a__U11</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>3</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>U12</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>a__and</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="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>a__U11</NAME></SYMBOL><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></POLYSYMB><POLYSYMB><SYMBOL><NAME>Marked_a__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>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>a__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>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>a__U21</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>U21</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>a__isNatKind</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>a__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>and</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="1"/></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><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>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>a__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>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>3</INT></COEF></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>3</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>Marked_a__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>U11</NAME></SYMBOL><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></POLYSYMB><POLYSYMB><SYMBOL><NAME>a__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>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>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>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><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></ORDERING><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_a__U11(tt,V1,V2)</LHS><RHS>Marked_a__U12(a__isNat(V1),V2)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_a__U11(tt,V1,V2)</LHS><RHS>Marked_a__isNat(V1)</RHS></DPRULE><DPRULE num="2"><LHS>Marked_a__U12(tt,V2)</LHS><RHS>Marked_a__isNat(V2)</RHS></DPRULE></DPLIST></STRICTPAIRS></CRITERION><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>a__U11(tt,V1,V2)</LHS><RHS>a__U12(a__isNat(V1),V2)</RHS></RULE><RULE><LHS>a__U12(tt,V2)</LHS><RHS>a__U13(a__isNat(V2))</RHS></RULE><RULE><LHS>a__U13(tt)</LHS><RHS>tt</RHS></RULE><RULE><LHS>a__U21(tt,V1)</LHS><RHS>a__U22(a__isNat(V1))</RHS></RULE><RULE><LHS>a__U22(tt)</LHS><RHS>tt</RHS></RULE><RULE><LHS>a__U31(tt,N)</LHS><RHS>mark(N)</RHS></RULE><RULE><LHS>a__U41(tt,M,N)</LHS><RHS>s(a__plus(mark(N),mark(M)))</RHS></RULE><RULE><LHS>a__and(tt,X)</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>a__isNat(0)</LHS><RHS>tt</RHS></RULE><RULE><LHS>a__isNat(plus(V1,V2))</LHS><RHS>a__U11(a__and(a__isNatKind(V1),isNatKind(V2)),V1,V2)</RHS></RULE><RULE><LHS>a__isNat(s(V1))</LHS><RHS>a__U21(a__isNatKind(V1),V1)</RHS></RULE><RULE><LHS>a__isNatKind(0)</LHS><RHS>tt</RHS></RULE><RULE><LHS>a__isNatKind(plus(V1,V2))</LHS><RHS>a__and(a__isNatKind(V1),isNatKind(V2))</RHS></RULE><RULE><LHS>a__isNatKind(s(V1))</LHS><RHS>a__isNatKind(V1)</RHS></RULE><RULE><LHS>a__plus(N,0)</LHS><RHS>a__U31(a__and(a__isNat(N),isNatKind(N)),N)</RHS></RULE><RULE><LHS>a__plus(N,s(M))</LHS><RHS>a__U41(a__and(a__and(a__isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),
 M,N)</RHS></RULE><RULE><LHS>mark(U11(X1,X2,X3))</LHS><RHS>a__U11(mark(X1),X2,X3)</RHS></RULE><RULE><LHS>mark(U12(X1,X2))</LHS><RHS>a__U12(mark(X1),X2)</RHS></RULE><RULE><LHS>mark(isNat(X))</LHS><RHS>a__isNat(X)</RHS></RULE><RULE><LHS>mark(U13(X))</LHS><RHS>a__U13(mark(X))</RHS></RULE><RULE><LHS>mark(U21(X1,X2))</LHS><RHS>a__U21(mark(X1),X2)</RHS></RULE><RULE><LHS>mark(U22(X))</LHS><RHS>a__U22(mark(X))</RHS></RULE><RULE><LHS>mark(U31(X1,X2))</LHS><RHS>a__U31(mark(X1),X2)</RHS></RULE><RULE><LHS>mark(U41(X1,X2,X3))</LHS><RHS>a__U41(mark(X1),X2,X3)</RHS></RULE><RULE><LHS>mark(plus(X1,X2))</LHS><RHS>a__plus(mark(X1),mark(X2))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>a__and(mark(X1),X2)</RHS></RULE><RULE><LHS>mark(isNatKind(X))</LHS><RHS>a__isNatKind(X)</RHS></RULE><RULE><LHS>mark(tt)</LHS><RHS>tt</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>s(mark(X))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>0</RHS></RULE><RULE><LHS>a__U11(X1,X2,X3)</LHS><RHS>U11(X1,X2,X3)</RHS></RULE><RULE><LHS>a__U12(X1,X2)</LHS><RHS>U12(X1,X2)</RHS></RULE><RULE><LHS>a__isNat(X)</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>a__U13(X)</LHS><RHS>U13(X)</RHS></RULE><RULE><LHS>a__U21(X1,X2)</LHS><RHS>U21(X1,X2)</RHS></RULE><RULE><LHS>a__U22(X)</LHS><RHS>U22(X)</RHS></RULE><RULE><LHS>a__U31(X1,X2)</LHS><RHS>U31(X1,X2)</RHS></RULE><RULE><LHS>a__U41(X1,X2,X3)</LHS><RHS>U41(X1,X2,X3)</RHS></RULE><RULE><LHS>a__plus(X1,X2)</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>a__and(X1,X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>a__isNatKind(X)</LHS><RHS>isNatKind(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_a__isNat(plus(V1,V2))</LHS><RHS>Marked_a__U11(a__and(a__isNatKind(V1),isNatKind(V2)),V1,V2)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><DAG approx="simpl"><CCLIST><NONSCC num="0"><NODE ref="0"/></NONSCC></CCLIST></DAG></CRITERION></PROPERTY></PROPERTY></PROPERTY></PROPERTY></PROPERTY></PROPERTY></PROPERTY></PROPERTY></PROPERTY></PROPERTY></PROPERTY></PROPERTY></PROPERTY></PROPERTY></PROPERTY></PROPERTY></PROOF>
