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<!DOCTYPE PROOF SYSTEM "http://a3pat.ensiie.fr/pub/a3pat.dtd">
<PROOF><SIGNATURE><SYMBOLLIST><SYMBOL arity="0" unmarked="0"><NAME>Marked_0</NAME></SYMBOL><SYMBOL arity="1" unmarked="U16"><NAME>Marked_U16</NAME></SYMBOL><SYMBOL arity="1" unmarked=""><NAME>U41</NAME></SYMBOL><SYMBOL arity="2" unmarked=""><NAME>plus</NAME></SYMBOL><SYMBOL arity="3" unmarked="U11"><NAME>Marked_U11</NAME></SYMBOL><SYMBOL arity="2" unmarked=""><NAME>U15</NAME></SYMBOL><SYMBOL arity="0" unmarked=""><NAME>0</NAME></SYMBOL><SYMBOL arity="2" unmarked="U52"><NAME>Marked_U52</NAME></SYMBOL><SYMBOL arity="2" unmarked=""><NAME>U21</NAME></SYMBOL><SYMBOL arity="3" unmarked="U12"><NAME>Marked_U12</NAME></SYMBOL><SYMBOL arity="3" unmarked=""><NAME>U61</NAME></SYMBOL><SYMBOL arity="1" unmarked="isNatKind"><NAME>Marked_isNatKind</NAME></SYMBOL><SYMBOL arity="3" unmarked=""><NAME>U11</NAME></SYMBOL><SYMBOL arity="1" unmarked="s"><NAME>Marked_s</NAME></SYMBOL><SYMBOL arity="1" unmarked="U23"><NAME>Marked_U23</NAME></SYMBOL><SYMBOL arity="1" unmarked=""><NAME>U32</NAME></SYMBOL><SYMBOL arity="3" unmarked=""><NAME>U64</NAME></SYMBOL><SYMBOL arity="2" unmarked="U31"><NAME>Marked_U31</NAME></SYMBOL><SYMBOL arity="3" unmarked=""><NAME>U13</NAME></SYMBOL><SYMBOL arity="2" unmarked=""><NAME>n__plus</NAME></SYMBOL><SYMBOL arity="3" unmarked="U63"><NAME>Marked_U63</NAME></SYMBOL><SYMBOL arity="1" unmarked=""><NAME>U16</NAME></SYMBOL><SYMBOL arity="3" unmarked="U14"><NAME>Marked_U14</NAME></SYMBOL><SYMBOL arity="2" unmarked=""><NAME>U51</NAME></SYMBOL><SYMBOL arity="1" unmarked="isNat"><NAME>Marked_isNat</NAME></SYMBOL><SYMBOL arity="1" unmarked=""><NAME>isNatKind</NAME></SYMBOL><SYMBOL arity="2" unmarked="plus"><NAME>Marked_plus</NAME></SYMBOL><SYMBOL arity="2" unmarked="U22"><NAME>Marked_U22</NAME></SYMBOL><SYMBOL arity="2" unmarked=""><NAME>U31</NAME></SYMBOL><SYMBOL arity="1" unmarked=""><NAME>s</NAME></SYMBOL><SYMBOL arity="2" unmarked="U21"><NAME>Marked_U21</NAME></SYMBOL><SYMBOL arity="3" unmarked=""><NAME>U14</NAME></SYMBOL><SYMBOL arity="1" unmarked=""><NAME>n__s</NAME></SYMBOL><SYMBOL arity="3" unmarked="U62"><NAME>Marked_U62</NAME></SYMBOL><SYMBOL arity="2" unmarked=""><NAME>U22</NAME></SYMBOL><SYMBOL arity="3" unmarked="U13"><NAME>Marked_U13</NAME></SYMBOL><SYMBOL arity="3" unmarked=""><NAME>U62</NAME></SYMBOL><SYMBOL arity="2" unmarked="U51"><NAME>Marked_U51</NAME></SYMBOL><SYMBOL arity="1" unmarked=""><NAME>activate</NAME></SYMBOL><SYMBOL arity="1" unmarked="activate"><NAME>Marked_activate</NAME></SYMBOL><SYMBOL arity="1" unmarked="U32"><NAME>Marked_U32</NAME></SYMBOL><SYMBOL arity="1" unmarked=""><NAME>U23</NAME></SYMBOL><SYMBOL arity="3" unmarked=""><NAME>U63</NAME></SYMBOL><SYMBOL arity="1" unmarked="U41"><NAME>Marked_U41</NAME></SYMBOL><SYMBOL arity="0" unmarked=""><NAME>tt</NAME></SYMBOL><SYMBOL arity="0" unmarked=""><NAME>n__0</NAME></SYMBOL><SYMBOL arity="3" unmarked="U64"><NAME>Marked_U64</NAME></SYMBOL><SYMBOL arity="1" unmarked=""><NAME>isNat</NAME></SYMBOL><SYMBOL arity="2" unmarked="U15"><NAME>Marked_U15</NAME></SYMBOL><SYMBOL arity="2" unmarked=""><NAME>U52</NAME></SYMBOL><SYMBOL arity="3" unmarked="U61"><NAME>Marked_U61</NAME></SYMBOL><SYMBOL arity="3" unmarked=""><NAME>U12</NAME></SYMBOL></SYMBOLLIST><VARLIST><VAR>X</VAR><VAR>X2</VAR><VAR>X1</VAR><VAR>M</VAR><VAR>N</VAR><VAR>V2</VAR><VAR>V1</VAR></VARLIST></SIGNATURE><PROPERTY criterion="dp" prop="sntrs"><SYSTEM><REWSYS><RULE><LHS>U11(tt,V1,V2)</LHS><RHS>U12(isNatKind(activate(V1)),activate(V1),activate(V2))</RHS></RULE><RULE><LHS>U12(tt,V1,V2)</LHS><RHS>U13(isNatKind(activate(V2)),activate(V1),activate(V2))</RHS></RULE><RULE><LHS>U13(tt,V1,V2)</LHS><RHS>U14(isNatKind(activate(V2)),activate(V1),activate(V2))</RHS></RULE><RULE><LHS>U14(tt,V1,V2)</LHS><RHS>U15(isNat(activate(V1)),activate(V2))</RHS></RULE><RULE><LHS>U15(tt,V2)</LHS><RHS>U16(isNat(activate(V2)))</RHS></RULE><RULE><LHS>U16(tt)</LHS><RHS>tt</RHS></RULE><RULE><LHS>U21(tt,V1)</LHS><RHS>U22(isNatKind(activate(V1)),activate(V1))</RHS></RULE><RULE><LHS>U22(tt,V1)</LHS><RHS>U23(isNat(activate(V1)))</RHS></RULE><RULE><LHS>U23(tt)</LHS><RHS>tt</RHS></RULE><RULE><LHS>U31(tt,V2)</LHS><RHS>U32(isNatKind(activate(V2)))</RHS></RULE><RULE><LHS>U32(tt)</LHS><RHS>tt</RHS></RULE><RULE><LHS>U41(tt)</LHS><RHS>tt</RHS></RULE><RULE><LHS>U51(tt,N)</LHS><RHS>U52(isNatKind(activate(N)),activate(N))</RHS></RULE><RULE><LHS>U52(tt,N)</LHS><RHS>activate(N)</RHS></RULE><RULE><LHS>U61(tt,M,N)</LHS><RHS>U62(isNatKind(activate(M)),activate(M),activate(N))</RHS></RULE><RULE><LHS>U62(tt,M,N)</LHS><RHS>U63(isNat(activate(N)),activate(M),activate(N))</RHS></RULE><RULE><LHS>U63(tt,M,N)</LHS><RHS>U64(isNatKind(activate(N)),activate(M),activate(N))</RHS></RULE><RULE><LHS>U64(tt,M,N)</LHS><RHS>s(plus(activate(N),activate(M)))</RHS></RULE><RULE><LHS>isNat(n__0)</LHS><RHS>tt</RHS></RULE><RULE><LHS>isNat(n__plus(V1,V2))</LHS><RHS>U11(isNatKind(activate(V1)),activate(V1),activate(V2))</RHS></RULE><RULE><LHS>isNat(n__s(V1))</LHS><RHS>U21(isNatKind(activate(V1)),activate(V1))</RHS></RULE><RULE><LHS>isNatKind(n__0)</LHS><RHS>tt</RHS></RULE><RULE><LHS>isNatKind(n__plus(V1,V2))</LHS><RHS>U31(isNatKind(activate(V1)),activate(V2))</RHS></RULE><RULE><LHS>isNatKind(n__s(V1))</LHS><RHS>U41(isNatKind(activate(V1)))</RHS></RULE><RULE><LHS>plus(N,0)</LHS><RHS>U51(isNat(N),N)</RHS></RULE><RULE><LHS>plus(N,s(M))</LHS><RHS>U61(isNat(M),M,N)</RHS></RULE><RULE><LHS>0</LHS><RHS>n__0</RHS></RULE><RULE><LHS>plus(X1,X2)</LHS><RHS>n__plus(X1,X2)</RHS></RULE><RULE><LHS>s(X)</LHS><RHS>n__s(X)</RHS></RULE><RULE><LHS>activate(n__0)</LHS><RHS>0</RHS></RULE><RULE><LHS>activate(n__plus(X1,X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>activate(n__s(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>activate(X)</LHS><RHS>X</RHS></RULE></REWSYS></SYSTEM><CRITERION/><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>U11(tt,V1,V2)</LHS><RHS>U12(isNatKind(activate(V1)),activate(V1),activate(V2))</RHS></RULE><RULE><LHS>U12(tt,V1,V2)</LHS><RHS>U13(isNatKind(activate(V2)),activate(V1),activate(V2))</RHS></RULE><RULE><LHS>U13(tt,V1,V2)</LHS><RHS>U14(isNatKind(activate(V2)),activate(V1),activate(V2))</RHS></RULE><RULE><LHS>U14(tt,V1,V2)</LHS><RHS>U15(isNat(activate(V1)),activate(V2))</RHS></RULE><RULE><LHS>U15(tt,V2)</LHS><RHS>U16(isNat(activate(V2)))</RHS></RULE><RULE><LHS>U16(tt)</LHS><RHS>tt</RHS></RULE><RULE><LHS>U21(tt,V1)</LHS><RHS>U22(isNatKind(activate(V1)),activate(V1))</RHS></RULE><RULE><LHS>U22(tt,V1)</LHS><RHS>U23(isNat(activate(V1)))</RHS></RULE><RULE><LHS>U23(tt)</LHS><RHS>tt</RHS></RULE><RULE><LHS>U31(tt,V2)</LHS><RHS>U32(isNatKind(activate(V2)))</RHS></RULE><RULE><LHS>U32(tt)</LHS><RHS>tt</RHS></RULE><RULE><LHS>U41(tt)</LHS><RHS>tt</RHS></RULE><RULE><LHS>U51(tt,N)</LHS><RHS>U52(isNatKind(activate(N)),activate(N))</RHS></RULE><RULE><LHS>U52(tt,N)</LHS><RHS>activate(N)</RHS></RULE><RULE><LHS>U61(tt,M,N)</LHS><RHS>U62(isNatKind(activate(M)),activate(M),activate(N))</RHS></RULE><RULE><LHS>U62(tt,M,N)</LHS><RHS>U63(isNat(activate(N)),activate(M),activate(N))</RHS></RULE><RULE><LHS>U63(tt,M,N)</LHS><RHS>U64(isNatKind(activate(N)),activate(M),activate(N))</RHS></RULE><RULE><LHS>U64(tt,M,N)</LHS><RHS>s(plus(activate(N),activate(M)))</RHS></RULE><RULE><LHS>isNat(n__0)</LHS><RHS>tt</RHS></RULE><RULE><LHS>isNat(n__plus(V1,V2))</LHS><RHS>U11(isNatKind(activate(V1)),activate(V1),activate(V2))</RHS></RULE><RULE><LHS>isNat(n__s(V1))</LHS><RHS>U21(isNatKind(activate(V1)),activate(V1))</RHS></RULE><RULE><LHS>isNatKind(n__0)</LHS><RHS>tt</RHS></RULE><RULE><LHS>isNatKind(n__plus(V1,V2))</LHS><RHS>U31(isNatKind(activate(V1)),activate(V2))</RHS></RULE><RULE><LHS>isNatKind(n__s(V1))</LHS><RHS>U41(isNatKind(activate(V1)))</RHS></RULE><RULE><LHS>plus(N,0)</LHS><RHS>U51(isNat(N),N)</RHS></RULE><RULE><LHS>plus(N,s(M))</LHS><RHS>U61(isNat(M),M,N)</RHS></RULE><RULE><LHS>0</LHS><RHS>n__0</RHS></RULE><RULE><LHS>plus(X1,X2)</LHS><RHS>n__plus(X1,X2)</RHS></RULE><RULE><LHS>s(X)</LHS><RHS>n__s(X)</RHS></RULE><RULE><LHS>activate(n__0)</LHS><RHS>0</RHS></RULE><RULE><LHS>activate(n__plus(X1,X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>activate(n__s(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>activate(X)</LHS><RHS>X</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_U11(tt,V1,V2)</LHS><RHS>Marked_U12(isNatKind(activate(V1)),activate(V1),activate(V2))</RHS></DPRULE><DPRULE num="1"><LHS>Marked_U11(tt,V1,V2)</LHS><RHS>Marked_isNatKind(activate(V1))</RHS></DPRULE><DPRULE num="2"><LHS>Marked_U11(tt,V1,V2)</LHS><RHS>Marked_activate(V1)</RHS></DPRULE><DPRULE num="3"><LHS>Marked_U11(tt,V1,V2)</LHS><RHS>Marked_activate(V1)</RHS></DPRULE><DPRULE num="4"><LHS>Marked_U11(tt,V1,V2)</LHS><RHS>Marked_activate(V2)</RHS></DPRULE><DPRULE num="5"><LHS>Marked_U12(tt,V1,V2)</LHS><RHS>Marked_U13(isNatKind(activate(V2)),activate(V1),activate(V2))</RHS></DPRULE><DPRULE num="6"><LHS>Marked_U12(tt,V1,V2)</LHS><RHS>Marked_isNatKind(activate(V2))</RHS></DPRULE><DPRULE num="7"><LHS>Marked_U12(tt,V1,V2)</LHS><RHS>Marked_activate(V2)</RHS></DPRULE><DPRULE num="8"><LHS>Marked_U12(tt,V1,V2)</LHS><RHS>Marked_activate(V1)</RHS></DPRULE><DPRULE num="9"><LHS>Marked_U12(tt,V1,V2)</LHS><RHS>Marked_activate(V2)</RHS></DPRULE><DPRULE num="10"><LHS>Marked_U13(tt,V1,V2)</LHS><RHS>Marked_U14(isNatKind(activate(V2)),activate(V1),activate(V2))</RHS></DPRULE><DPRULE num="11"><LHS>Marked_U13(tt,V1,V2)</LHS><RHS>Marked_isNatKind(activate(V2))</RHS></DPRULE><DPRULE num="12"><LHS>Marked_U13(tt,V1,V2)</LHS><RHS>Marked_activate(V2)</RHS></DPRULE><DPRULE num="13"><LHS>Marked_U13(tt,V1,V2)</LHS><RHS>Marked_activate(V1)</RHS></DPRULE><DPRULE num="14"><LHS>Marked_U13(tt,V1,V2)</LHS><RHS>Marked_activate(V2)</RHS></DPRULE><DPRULE num="15"><LHS>Marked_U14(tt,V1,V2)</LHS><RHS>Marked_U15(isNat(activate(V1)),activate(V2))</RHS></DPRULE><DPRULE num="16"><LHS>Marked_U14(tt,V1,V2)</LHS><RHS>Marked_isNat(activate(V1))</RHS></DPRULE><DPRULE num="17"><LHS>Marked_U14(tt,V1,V2)</LHS><RHS>Marked_activate(V1)</RHS></DPRULE><DPRULE num="18"><LHS>Marked_U14(tt,V1,V2)</LHS><RHS>Marked_activate(V2)</RHS></DPRULE><DPRULE num="19"><LHS>Marked_U15(tt,V2)</LHS><RHS>Marked_U16(isNat(activate(V2)))</RHS></DPRULE><DPRULE num="20"><LHS>Marked_U15(tt,V2)</LHS><RHS>Marked_isNat(activate(V2))</RHS></DPRULE><DPRULE num="21"><LHS>Marked_U15(tt,V2)</LHS><RHS>Marked_activate(V2)</RHS></DPRULE><DPRULE num="22"><LHS>Marked_U21(tt,V1)</LHS><RHS>Marked_U22(isNatKind(activate(V1)),activate(V1))</RHS></DPRULE><DPRULE num="23"><LHS>Marked_U21(tt,V1)</LHS><RHS>Marked_isNatKind(activate(V1))</RHS></DPRULE><DPRULE num="24"><LHS>Marked_U21(tt,V1)</LHS><RHS>Marked_activate(V1)</RHS></DPRULE><DPRULE num="25"><LHS>Marked_U21(tt,V1)</LHS><RHS>Marked_activate(V1)</RHS></DPRULE><DPRULE num="26"><LHS>Marked_U22(tt,V1)</LHS><RHS>Marked_U23(isNat(activate(V1)))</RHS></DPRULE><DPRULE num="27"><LHS>Marked_U22(tt,V1)</LHS><RHS>Marked_isNat(activate(V1))</RHS></DPRULE><DPRULE num="28"><LHS>Marked_U22(tt,V1)</LHS><RHS>Marked_activate(V1)</RHS></DPRULE><DPRULE num="29"><LHS>Marked_U31(tt,V2)</LHS><RHS>Marked_U32(isNatKind(activate(V2)))</RHS></DPRULE><DPRULE num="30"><LHS>Marked_U31(tt,V2)</LHS><RHS>Marked_isNatKind(activate(V2))</RHS></DPRULE><DPRULE num="31"><LHS>Marked_U31(tt,V2)</LHS><RHS>Marked_activate(V2)</RHS></DPRULE><DPRULE num="32"><LHS>Marked_U51(tt,N)</LHS><RHS>Marked_U52(isNatKind(activate(N)),activate(N))</RHS></DPRULE><DPRULE num="33"><LHS>Marked_U51(tt,N)</LHS><RHS>Marked_isNatKind(activate(N))</RHS></DPRULE><DPRULE num="34"><LHS>Marked_U51(tt,N)</LHS><RHS>Marked_activate(N)</RHS></DPRULE><DPRULE num="35"><LHS>Marked_U51(tt,N)</LHS><RHS>Marked_activate(N)</RHS></DPRULE><DPRULE num="36"><LHS>Marked_U52(tt,N)</LHS><RHS>Marked_activate(N)</RHS></DPRULE><DPRULE num="37"><LHS>Marked_U61(tt,M,N)</LHS><RHS>Marked_U62(isNatKind(activate(M)),activate(M),activate(N))</RHS></DPRULE><DPRULE num="38"><LHS>Marked_U61(tt,M,N)</LHS><RHS>Marked_isNatKind(activate(M))</RHS></DPRULE><DPRULE num="39"><LHS>Marked_U61(tt,M,N)</LHS><RHS>Marked_activate(M)</RHS></DPRULE><DPRULE num="40"><LHS>Marked_U61(tt,M,N)</LHS><RHS>Marked_activate(M)</RHS></DPRULE><DPRULE num="41"><LHS>Marked_U61(tt,M,N)</LHS><RHS>Marked_activate(N)</RHS></DPRULE><DPRULE num="42"><LHS>Marked_U62(tt,M,N)</LHS><RHS>Marked_U63(isNat(activate(N)),activate(M),activate(N))</RHS></DPRULE><DPRULE num="43"><LHS>Marked_U62(tt,M,N)</LHS><RHS>Marked_isNat(activate(N))</RHS></DPRULE><DPRULE num="44"><LHS>Marked_U62(tt,M,N)</LHS><RHS>Marked_activate(N)</RHS></DPRULE><DPRULE num="45"><LHS>Marked_U62(tt,M,N)</LHS><RHS>Marked_activate(M)</RHS></DPRULE><DPRULE num="46"><LHS>Marked_U62(tt,M,N)</LHS><RHS>Marked_activate(N)</RHS></DPRULE><DPRULE num="47"><LHS>Marked_U63(tt,M,N)</LHS><RHS>Marked_U64(isNatKind(activate(N)),activate(M),activate(N))</RHS></DPRULE><DPRULE num="48"><LHS>Marked_U63(tt,M,N)</LHS><RHS>Marked_isNatKind(activate(N))</RHS></DPRULE><DPRULE num="49"><LHS>Marked_U63(tt,M,N)</LHS><RHS>Marked_activate(N)</RHS></DPRULE><DPRULE num="50"><LHS>Marked_U63(tt,M,N)</LHS><RHS>Marked_activate(M)</RHS></DPRULE><DPRULE num="51"><LHS>Marked_U63(tt,M,N)</LHS><RHS>Marked_activate(N)</RHS></DPRULE><DPRULE num="52"><LHS>Marked_U64(tt,M,N)</LHS><RHS>Marked_s(plus(activate(N),activate(M)))</RHS></DPRULE><DPRULE num="53"><LHS>Marked_U64(tt,M,N)</LHS><RHS>Marked_plus(activate(N),activate(M))</RHS></DPRULE><DPRULE num="54"><LHS>Marked_U64(tt,M,N)</LHS><RHS>Marked_activate(N)</RHS></DPRULE><DPRULE num="55"><LHS>Marked_U64(tt,M,N)</LHS><RHS>Marked_activate(M)</RHS></DPRULE><DPRULE num="56"><LHS>Marked_isNat(n__plus(V1,V2))</LHS><RHS>Marked_U11(isNatKind(activate(V1)),activate(V1),activate(V2))</RHS></DPRULE><DPRULE num="57"><LHS>Marked_isNat(n__plus(V1,V2))</LHS><RHS>Marked_isNatKind(activate(V1))</RHS></DPRULE><DPRULE num="58"><LHS>Marked_isNat(n__plus(V1,V2))</LHS><RHS>Marked_activate(V1)</RHS></DPRULE><DPRULE num="59"><LHS>Marked_isNat(n__plus(V1,V2))</LHS><RHS>Marked_activate(V1)</RHS></DPRULE><DPRULE num="60"><LHS>Marked_isNat(n__plus(V1,V2))</LHS><RHS>Marked_activate(V2)</RHS></DPRULE><DPRULE num="61"><LHS>Marked_isNat(n__s(V1))</LHS><RHS>Marked_U21(isNatKind(activate(V1)),activate(V1))</RHS></DPRULE><DPRULE num="62"><LHS>Marked_isNat(n__s(V1))</LHS><RHS>Marked_isNatKind(activate(V1))</RHS></DPRULE><DPRULE num="63"><LHS>Marked_isNat(n__s(V1))</LHS><RHS>Marked_activate(V1)</RHS></DPRULE><DPRULE num="64"><LHS>Marked_isNat(n__s(V1))</LHS><RHS>Marked_activate(V1)</RHS></DPRULE><DPRULE num="65"><LHS>Marked_isNatKind(n__plus(V1,V2))</LHS><RHS>Marked_U31(isNatKind(activate(V1)),activate(V2))</RHS></DPRULE><DPRULE num="66"><LHS>Marked_isNatKind(n__plus(V1,V2))</LHS><RHS>Marked_isNatKind(activate(V1))</RHS></DPRULE><DPRULE num="67"><LHS>Marked_isNatKind(n__plus(V1,V2))</LHS><RHS>Marked_activate(V1)</RHS></DPRULE><DPRULE num="68"><LHS>Marked_isNatKind(n__plus(V1,V2))</LHS><RHS>Marked_activate(V2)</RHS></DPRULE><DPRULE num="69"><LHS>Marked_isNatKind(n__s(V1))</LHS><RHS>Marked_U41(isNatKind(activate(V1)))</RHS></DPRULE><DPRULE num="70"><LHS>Marked_isNatKind(n__s(V1))</LHS><RHS>Marked_isNatKind(activate(V1))</RHS></DPRULE><DPRULE num="71"><LHS>Marked_isNatKind(n__s(V1))</LHS><RHS>Marked_activate(V1)</RHS></DPRULE><DPRULE num="72"><LHS>Marked_plus(N,0)</LHS><RHS>Marked_U51(isNat(N),N)</RHS></DPRULE><DPRULE num="73"><LHS>Marked_plus(N,0)</LHS><RHS>Marked_isNat(N)</RHS></DPRULE><DPRULE num="74"><LHS>Marked_plus(N,s(M))</LHS><RHS>Marked_U61(isNat(M),M,N)</RHS></DPRULE><DPRULE num="75"><LHS>Marked_plus(N,s(M))</LHS><RHS>Marked_isNat(M)</RHS></DPRULE><DPRULE num="76"><LHS>Marked_activate(n__0)</LHS><RHS>Marked_0</RHS></DPRULE><DPRULE num="77"><LHS>Marked_activate(n__plus(X1,X2))</LHS><RHS>Marked_plus(X1,X2)</RHS></DPRULE><DPRULE num="78"><LHS>Marked_activate(n__s(X))</LHS><RHS>Marked_s(X)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><DAG approx="simpl"><CCLIST><NONSCC num="0"><NODE ref="78"/></NONSCC><SCC num="1"><NODE ref="0"/><NODE ref="1"/><NODE ref="2"/><NODE ref="2"/><NODE ref="4"/><NODE ref="5"/><NODE ref="6"/><NODE ref="7"/><NODE ref="8"/><NODE ref="7"/><NODE ref="10"/><NODE ref="11"/><NODE ref="12"/><NODE ref="13"/><NODE ref="12"/><NODE ref="15"/><NODE ref="16"/><NODE ref="17"/><NODE ref="18"/><NODE ref="20"/><NODE ref="21"/><NODE ref="22"/><NODE ref="23"/><NODE ref="24"/><NODE ref="24"/><NODE ref="27"/><NODE ref="28"/><NODE ref="30"/><NODE ref="31"/><NODE ref="32"/><NODE ref="33"/><NODE ref="34"/><NODE ref="34"/><NODE ref="36"/><NODE ref="37"/><NODE ref="38"/><NODE ref="39"/><NODE ref="39"/><NODE ref="41"/><NODE ref="42"/><NODE ref="43"/><NODE ref="44"/><NODE ref="45"/><NODE ref="44"/><NODE ref="47"/><NODE ref="48"/><NODE ref="49"/><NODE ref="50"/><NODE ref="49"/><NODE ref="53"/><NODE ref="54"/><NODE ref="55"/><NODE ref="56"/><NODE ref="57"/><NODE ref="58"/><NODE ref="58"/><NODE ref="60"/><NODE ref="61"/><NODE ref="62"/><NODE ref="63"/><NODE ref="63"/><NODE ref="65"/><NODE ref="66"/><NODE ref="67"/><NODE ref="68"/><NODE ref="70"/><NODE ref="71"/><NODE ref="72"/><NODE ref="73"/><NODE ref="74"/><NODE ref="75"/><NODE ref="77"/></SCC><NONSCC num="2"><NODE ref="76"/></NONSCC><NONSCC num="3"><NODE ref="69"/></NONSCC><NONSCC num="4"><NODE ref="29"/></NONSCC><NONSCC num="5"><NODE ref="52"/></NONSCC><NONSCC num="6"><NODE ref="26"/></NONSCC><NONSCC num="7"><NODE ref="19"/></NONSCC></CCLIST><EDGE end="7" start="1"/><EDGE end="6" start="1"/><EDGE end="5" start="1"/><EDGE end="4" start="1"/><EDGE end="3" start="1"/><EDGE end="2" start="1"/><EDGE end="0" start="1"/></DAG></CRITERION><PROPERTY criterion="stronggraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>U11(tt,V1,V2)</LHS><RHS>U12(isNatKind(activate(V1)),activate(V1),activate(V2))</RHS></RULE><RULE><LHS>U12(tt,V1,V2)</LHS><RHS>U13(isNatKind(activate(V2)),activate(V1),activate(V2))</RHS></RULE><RULE><LHS>U13(tt,V1,V2)</LHS><RHS>U14(isNatKind(activate(V2)),activate(V1),activate(V2))</RHS></RULE><RULE><LHS>U14(tt,V1,V2)</LHS><RHS>U15(isNat(activate(V1)),activate(V2))</RHS></RULE><RULE><LHS>U15(tt,V2)</LHS><RHS>U16(isNat(activate(V2)))</RHS></RULE><RULE><LHS>U16(tt)</LHS><RHS>tt</RHS></RULE><RULE><LHS>U21(tt,V1)</LHS><RHS>U22(isNatKind(activate(V1)),activate(V1))</RHS></RULE><RULE><LHS>U22(tt,V1)</LHS><RHS>U23(isNat(activate(V1)))</RHS></RULE><RULE><LHS>U23(tt)</LHS><RHS>tt</RHS></RULE><RULE><LHS>U31(tt,V2)</LHS><RHS>U32(isNatKind(activate(V2)))</RHS></RULE><RULE><LHS>U32(tt)</LHS><RHS>tt</RHS></RULE><RULE><LHS>U41(tt)</LHS><RHS>tt</RHS></RULE><RULE><LHS>U51(tt,N)</LHS><RHS>U52(isNatKind(activate(N)),activate(N))</RHS></RULE><RULE><LHS>U52(tt,N)</LHS><RHS>activate(N)</RHS></RULE><RULE><LHS>U61(tt,M,N)</LHS><RHS>U62(isNatKind(activate(M)),activate(M),activate(N))</RHS></RULE><RULE><LHS>U62(tt,M,N)</LHS><RHS>U63(isNat(activate(N)),activate(M),activate(N))</RHS></RULE><RULE><LHS>U63(tt,M,N)</LHS><RHS>U64(isNatKind(activate(N)),activate(M),activate(N))</RHS></RULE><RULE><LHS>U64(tt,M,N)</LHS><RHS>s(plus(activate(N),activate(M)))</RHS></RULE><RULE><LHS>isNat(n__0)</LHS><RHS>tt</RHS></RULE><RULE><LHS>isNat(n__plus(V1,V2))</LHS><RHS>U11(isNatKind(activate(V1)),activate(V1),activate(V2))</RHS></RULE><RULE><LHS>isNat(n__s(V1))</LHS><RHS>U21(isNatKind(activate(V1)),activate(V1))</RHS></RULE><RULE><LHS>isNatKind(n__0)</LHS><RHS>tt</RHS></RULE><RULE><LHS>isNatKind(n__plus(V1,V2))</LHS><RHS>U31(isNatKind(activate(V1)),activate(V2))</RHS></RULE><RULE><LHS>isNatKind(n__s(V1))</LHS><RHS>U41(isNatKind(activate(V1)))</RHS></RULE><RULE><LHS>plus(N,0)</LHS><RHS>U51(isNat(N),N)</RHS></RULE><RULE><LHS>plus(N,s(M))</LHS><RHS>U61(isNat(M),M,N)</RHS></RULE><RULE><LHS>0</LHS><RHS>n__0</RHS></RULE><RULE><LHS>plus(X1,X2)</LHS><RHS>n__plus(X1,X2)</RHS></RULE><RULE><LHS>s(X)</LHS><RHS>n__s(X)</RHS></RULE><RULE><LHS>activate(n__0)</LHS><RHS>0</RHS></RULE><RULE><LHS>activate(n__plus(X1,X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>activate(n__s(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>activate(X)</LHS><RHS>X</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_U11(tt,V1,V2)</LHS><RHS>Marked_U12(isNatKind(activate(V1)),activate(V1),activate(V2))</RHS></DPRULE><DPRULE num="1"><LHS>Marked_U11(tt,V1,V2)</LHS><RHS>Marked_isNatKind(activate(V1))</RHS></DPRULE><DPRULE num="2"><LHS>Marked_U11(tt,V1,V2)</LHS><RHS>Marked_activate(V1)</RHS></DPRULE><DPRULE num="3"><LHS>Marked_U11(tt,V1,V2)</LHS><RHS>Marked_activate(V1)</RHS></DPRULE><DPRULE num="4"><LHS>Marked_U11(tt,V1,V2)</LHS><RHS>Marked_activate(V2)</RHS></DPRULE><DPRULE num="5"><LHS>Marked_U12(tt,V1,V2)</LHS><RHS>Marked_U13(isNatKind(activate(V2)),activate(V1),activate(V2))</RHS></DPRULE><DPRULE num="6"><LHS>Marked_U12(tt,V1,V2)</LHS><RHS>Marked_isNatKind(activate(V2))</RHS></DPRULE><DPRULE num="7"><LHS>Marked_U12(tt,V1,V2)</LHS><RHS>Marked_activate(V2)</RHS></DPRULE><DPRULE num="8"><LHS>Marked_U12(tt,V1,V2)</LHS><RHS>Marked_activate(V1)</RHS></DPRULE><DPRULE num="9"><LHS>Marked_U12(tt,V1,V2)</LHS><RHS>Marked_activate(V2)</RHS></DPRULE><DPRULE num="10"><LHS>Marked_U13(tt,V1,V2)</LHS><RHS>Marked_U14(isNatKind(activate(V2)),activate(V1),activate(V2))</RHS></DPRULE><DPRULE num="11"><LHS>Marked_U13(tt,V1,V2)</LHS><RHS>Marked_isNatKind(activate(V2))</RHS></DPRULE><DPRULE num="12"><LHS>Marked_U13(tt,V1,V2)</LHS><RHS>Marked_activate(V2)</RHS></DPRULE><DPRULE num="13"><LHS>Marked_U13(tt,V1,V2)</LHS><RHS>Marked_activate(V1)</RHS></DPRULE><DPRULE num="14"><LHS>Marked_U13(tt,V1,V2)</LHS><RHS>Marked_activate(V2)</RHS></DPRULE><DPRULE num="15"><LHS>Marked_U14(tt,V1,V2)</LHS><RHS>Marked_U15(isNat(activate(V1)),activate(V2))</RHS></DPRULE><DPRULE num="16"><LHS>Marked_U14(tt,V1,V2)</LHS><RHS>Marked_isNat(activate(V1))</RHS></DPRULE><DPRULE num="17"><LHS>Marked_U14(tt,V1,V2)</LHS><RHS>Marked_activate(V1)</RHS></DPRULE><DPRULE num="18"><LHS>Marked_U14(tt,V1,V2)</LHS><RHS>Marked_activate(V2)</RHS></DPRULE><DPRULE num="19"><LHS>Marked_U15(tt,V2)</LHS><RHS>Marked_isNat(activate(V2))</RHS></DPRULE><DPRULE num="20"><LHS>Marked_U15(tt,V2)</LHS><RHS>Marked_activate(V2)</RHS></DPRULE><DPRULE num="21"><LHS>Marked_U21(tt,V1)</LHS><RHS>Marked_U22(isNatKind(activate(V1)),activate(V1))</RHS></DPRULE><DPRULE num="22"><LHS>Marked_U21(tt,V1)</LHS><RHS>Marked_isNatKind(activate(V1))</RHS></DPRULE><DPRULE num="23"><LHS>Marked_U21(tt,V1)</LHS><RHS>Marked_activate(V1)</RHS></DPRULE><DPRULE num="24"><LHS>Marked_U21(tt,V1)</LHS><RHS>Marked_activate(V1)</RHS></DPRULE><DPRULE num="25"><LHS>Marked_U22(tt,V1)</LHS><RHS>Marked_isNat(activate(V1))</RHS></DPRULE><DPRULE num="26"><LHS>Marked_U22(tt,V1)</LHS><RHS>Marked_activate(V1)</RHS></DPRULE><DPRULE num="27"><LHS>Marked_U31(tt,V2)</LHS><RHS>Marked_isNatKind(activate(V2))</RHS></DPRULE><DPRULE num="28"><LHS>Marked_U31(tt,V2)</LHS><RHS>Marked_activate(V2)</RHS></DPRULE><DPRULE num="29"><LHS>Marked_U51(tt,N)</LHS><RHS>Marked_U52(isNatKind(activate(N)),activate(N))</RHS></DPRULE><DPRULE num="30"><LHS>Marked_U51(tt,N)</LHS><RHS>Marked_isNatKind(activate(N))</RHS></DPRULE><DPRULE num="31"><LHS>Marked_U51(tt,N)</LHS><RHS>Marked_activate(N)</RHS></DPRULE><DPRULE num="32"><LHS>Marked_U51(tt,N)</LHS><RHS>Marked_activate(N)</RHS></DPRULE><DPRULE num="33"><LHS>Marked_U52(tt,N)</LHS><RHS>Marked_activate(N)</RHS></DPRULE><DPRULE num="34"><LHS>Marked_U61(tt,M,N)</LHS><RHS>Marked_U62(isNatKind(activate(M)),activate(M),activate(N))</RHS></DPRULE><DPRULE num="35"><LHS>Marked_U61(tt,M,N)</LHS><RHS>Marked_isNatKind(activate(M))</RHS></DPRULE><DPRULE num="36"><LHS>Marked_U61(tt,M,N)</LHS><RHS>Marked_activate(M)</RHS></DPRULE><DPRULE num="37"><LHS>Marked_U61(tt,M,N)</LHS><RHS>Marked_activate(M)</RHS></DPRULE><DPRULE num="38"><LHS>Marked_U61(tt,M,N)</LHS><RHS>Marked_activate(N)</RHS></DPRULE><DPRULE num="39"><LHS>Marked_U62(tt,M,N)</LHS><RHS>Marked_U63(isNat(activate(N)),activate(M),activate(N))</RHS></DPRULE><DPRULE num="40"><LHS>Marked_U62(tt,M,N)</LHS><RHS>Marked_isNat(activate(N))</RHS></DPRULE><DPRULE num="41"><LHS>Marked_U62(tt,M,N)</LHS><RHS>Marked_activate(N)</RHS></DPRULE><DPRULE num="42"><LHS>Marked_U62(tt,M,N)</LHS><RHS>Marked_activate(M)</RHS></DPRULE><DPRULE num="43"><LHS>Marked_U62(tt,M,N)</LHS><RHS>Marked_activate(N)</RHS></DPRULE><DPRULE num="44"><LHS>Marked_U63(tt,M,N)</LHS><RHS>Marked_U64(isNatKind(activate(N)),activate(M),activate(N))</RHS></DPRULE><DPRULE num="45"><LHS>Marked_U63(tt,M,N)</LHS><RHS>Marked_isNatKind(activate(N))</RHS></DPRULE><DPRULE num="46"><LHS>Marked_U63(tt,M,N)</LHS><RHS>Marked_activate(N)</RHS></DPRULE><DPRULE num="47"><LHS>Marked_U63(tt,M,N)</LHS><RHS>Marked_activate(M)</RHS></DPRULE><DPRULE num="48"><LHS>Marked_U63(tt,M,N)</LHS><RHS>Marked_activate(N)</RHS></DPRULE><DPRULE num="49"><LHS>Marked_U64(tt,M,N)</LHS><RHS>Marked_plus(activate(N),activate(M))</RHS></DPRULE><DPRULE num="50"><LHS>Marked_U64(tt,M,N)</LHS><RHS>Marked_activate(N)</RHS></DPRULE><DPRULE num="51"><LHS>Marked_U64(tt,M,N)</LHS><RHS>Marked_activate(M)</RHS></DPRULE><DPRULE num="52"><LHS>Marked_isNat(n__plus(V1,V2))</LHS><RHS>Marked_U11(isNatKind(activate(V1)),activate(V1),activate(V2))</RHS></DPRULE><DPRULE num="53"><LHS>Marked_isNat(n__plus(V1,V2))</LHS><RHS>Marked_isNatKind(activate(V1))</RHS></DPRULE><DPRULE num="54"><LHS>Marked_isNat(n__plus(V1,V2))</LHS><RHS>Marked_activate(V1)</RHS></DPRULE><DPRULE num="55"><LHS>Marked_isNat(n__plus(V1,V2))</LHS><RHS>Marked_activate(V1)</RHS></DPRULE><DPRULE num="56"><LHS>Marked_isNat(n__plus(V1,V2))</LHS><RHS>Marked_activate(V2)</RHS></DPRULE><DPRULE num="57"><LHS>Marked_isNat(n__s(V1))</LHS><RHS>Marked_U21(isNatKind(activate(V1)),activate(V1))</RHS></DPRULE><DPRULE num="58"><LHS>Marked_isNat(n__s(V1))</LHS><RHS>Marked_isNatKind(activate(V1))</RHS></DPRULE><DPRULE num="59"><LHS>Marked_isNat(n__s(V1))</LHS><RHS>Marked_activate(V1)</RHS></DPRULE><DPRULE num="60"><LHS>Marked_isNat(n__s(V1))</LHS><RHS>Marked_activate(V1)</RHS></DPRULE><DPRULE num="61"><LHS>Marked_isNatKind(n__plus(V1,V2))</LHS><RHS>Marked_U31(isNatKind(activate(V1)),activate(V2))</RHS></DPRULE><DPRULE num="62"><LHS>Marked_isNatKind(n__plus(V1,V2))</LHS><RHS>Marked_isNatKind(activate(V1))</RHS></DPRULE><DPRULE num="63"><LHS>Marked_isNatKind(n__plus(V1,V2))</LHS><RHS>Marked_activate(V1)</RHS></DPRULE><DPRULE num="64"><LHS>Marked_isNatKind(n__plus(V1,V2))</LHS><RHS>Marked_activate(V2)</RHS></DPRULE><DPRULE num="65"><LHS>Marked_isNatKind(n__s(V1))</LHS><RHS>Marked_isNatKind(activate(V1))</RHS></DPRULE><DPRULE num="66"><LHS>Marked_isNatKind(n__s(V1))</LHS><RHS>Marked_activate(V1)</RHS></DPRULE><DPRULE num="67"><LHS>Marked_plus(N,0)</LHS><RHS>Marked_U51(isNat(N),N)</RHS></DPRULE><DPRULE num="68"><LHS>Marked_plus(N,0)</LHS><RHS>Marked_isNat(N)</RHS></DPRULE><DPRULE num="69"><LHS>Marked_plus(N,s(M))</LHS><RHS>Marked_U61(isNat(M),M,N)</RHS></DPRULE><DPRULE num="70"><LHS>Marked_plus(N,s(M))</LHS><RHS>Marked_isNat(M)</RHS></DPRULE><DPRULE num="71"><LHS>Marked_activate(n__plus(X1,X2))</LHS><RHS>Marked_plus(X1,X2)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><ORDERING type="poly"><POLYSYMB><SYMBOL><NAME>U12</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>Marked_U61</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>U52</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>Marked_U15</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>isNat</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>Marked_U64</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>n__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><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U63</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>U23</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>Marked_activate</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>activate</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_U51</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="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U62</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_U13</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="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>U22</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>Marked_U62</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>n__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>U14</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>Marked_U21</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="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>U31</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>Marked_U22</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>Marked_plus</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>isNatKind</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>Marked_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>U51</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>Marked_U14</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>U16</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>Marked_U63</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>n__plus</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><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U13</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>Marked_U31</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U64</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>U32</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U11</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>Marked_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>U61</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_U12</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>U21</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>Marked_U52</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>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>U15</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>Marked_U11</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>plus</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><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U41</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB></ORDERING><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_U11(tt,V1,V2)</LHS><RHS>Marked_isNatKind(activate(V1))</RHS></DPRULE><DPRULE num="1"><LHS>Marked_U11(tt,V1,V2)</LHS><RHS>Marked_activate(V1)</RHS></DPRULE><DPRULE num="2"><LHS>Marked_U11(tt,V1,V2)</LHS><RHS>Marked_activate(V1)</RHS></DPRULE><DPRULE num="3"><LHS>Marked_U11(tt,V1,V2)</LHS><RHS>Marked_activate(V2)</RHS></DPRULE><DPRULE num="4"><LHS>Marked_U12(tt,V1,V2)</LHS><RHS>Marked_U13(isNatKind(activate(V2)),activate(V1),activate(V2))</RHS></DPRULE><DPRULE num="5"><LHS>Marked_U12(tt,V1,V2)</LHS><RHS>Marked_isNatKind(activate(V2))</RHS></DPRULE><DPRULE num="6"><LHS>Marked_U12(tt,V1,V2)</LHS><RHS>Marked_activate(V2)</RHS></DPRULE><DPRULE num="7"><LHS>Marked_U12(tt,V1,V2)</LHS><RHS>Marked_activate(V1)</RHS></DPRULE><DPRULE num="8"><LHS>Marked_U12(tt,V1,V2)</LHS><RHS>Marked_activate(V2)</RHS></DPRULE><DPRULE num="9"><LHS>Marked_U13(tt,V1,V2)</LHS><RHS>Marked_U14(isNatKind(activate(V2)),activate(V1),activate(V2))</RHS></DPRULE><DPRULE num="10"><LHS>Marked_U13(tt,V1,V2)</LHS><RHS>Marked_activate(V2)</RHS></DPRULE><DPRULE num="11"><LHS>Marked_U13(tt,V1,V2)</LHS><RHS>Marked_activate(V1)</RHS></DPRULE><DPRULE num="12"><LHS>Marked_U13(tt,V1,V2)</LHS><RHS>Marked_activate(V2)</RHS></DPRULE><DPRULE num="13"><LHS>Marked_U21(tt,V1)</LHS><RHS>Marked_U22(isNatKind(activate(V1)),activate(V1))</RHS></DPRULE><DPRULE num="14"><LHS>Marked_U21(tt,V1)</LHS><RHS>Marked_isNatKind(activate(V1))</RHS></DPRULE><DPRULE num="15"><LHS>Marked_U21(tt,V1)</LHS><RHS>Marked_activate(V1)</RHS></DPRULE><DPRULE num="16"><LHS>Marked_U21(tt,V1)</LHS><RHS>Marked_activate(V1)</RHS></DPRULE><DPRULE num="17"><LHS>Marked_U31(tt,V2)</LHS><RHS>Marked_activate(V2)</RHS></DPRULE><DPRULE num="18"><LHS>Marked_U51(tt,N)</LHS><RHS>Marked_U52(isNatKind(activate(N)),activate(N))</RHS></DPRULE><DPRULE num="19"><LHS>Marked_U51(tt,N)</LHS><RHS>Marked_activate(N)</RHS></DPRULE><DPRULE num="20"><LHS>Marked_U51(tt,N)</LHS><RHS>Marked_activate(N)</RHS></DPRULE><DPRULE num="21"><LHS>Marked_U61(tt,M,N)</LHS><RHS>Marked_isNatKind(activate(M))</RHS></DPRULE><DPRULE num="22"><LHS>Marked_U61(tt,M,N)</LHS><RHS>Marked_activate(M)</RHS></DPRULE><DPRULE num="23"><LHS>Marked_U61(tt,M,N)</LHS><RHS>Marked_activate(M)</RHS></DPRULE><DPRULE num="24"><LHS>Marked_U61(tt,M,N)</LHS><RHS>Marked_activate(N)</RHS></DPRULE><DPRULE num="25"><LHS>Marked_U62(tt,M,N)</LHS><RHS>Marked_isNat(activate(N))</RHS></DPRULE><DPRULE num="26"><LHS>Marked_U62(tt,M,N)</LHS><RHS>Marked_activate(N)</RHS></DPRULE><DPRULE num="27"><LHS>Marked_U62(tt,M,N)</LHS><RHS>Marked_activate(M)</RHS></DPRULE><DPRULE num="28"><LHS>Marked_U62(tt,M,N)</LHS><RHS>Marked_activate(N)</RHS></DPRULE><DPRULE num="29"><LHS>Marked_U63(tt,M,N)</LHS><RHS>Marked_isNatKind(activate(N))</RHS></DPRULE><DPRULE num="30"><LHS>Marked_U63(tt,M,N)</LHS><RHS>Marked_activate(N)</RHS></DPRULE><DPRULE num="31"><LHS>Marked_U63(tt,M,N)</LHS><RHS>Marked_activate(M)</RHS></DPRULE><DPRULE num="32"><LHS>Marked_U63(tt,M,N)</LHS><RHS>Marked_activate(N)</RHS></DPRULE><DPRULE num="33"><LHS>Marked_U64(tt,M,N)</LHS><RHS>Marked_activate(N)</RHS></DPRULE><DPRULE num="34"><LHS>Marked_U64(tt,M,N)</LHS><RHS>Marked_activate(M)</RHS></DPRULE><DPRULE num="35"><LHS>Marked_isNat(n__plus(V1,V2))</LHS><RHS>Marked_isNatKind(activate(V1))</RHS></DPRULE><DPRULE num="36"><LHS>Marked_isNat(n__plus(V1,V2))</LHS><RHS>Marked_activate(V1)</RHS></DPRULE><DPRULE num="37"><LHS>Marked_isNat(n__plus(V1,V2))</LHS><RHS>Marked_activate(V1)</RHS></DPRULE><DPRULE num="38"><LHS>Marked_isNat(n__plus(V1,V2))</LHS><RHS>Marked_activate(V2)</RHS></DPRULE><DPRULE num="39"><LHS>Marked_isNat(n__s(V1))</LHS><RHS>Marked_isNatKind(activate(V1))</RHS></DPRULE><DPRULE num="40"><LHS>Marked_isNat(n__s(V1))</LHS><RHS>Marked_activate(V1)</RHS></DPRULE><DPRULE num="41"><LHS>Marked_isNat(n__s(V1))</LHS><RHS>Marked_activate(V1)</RHS></DPRULE><DPRULE num="42"><LHS>Marked_isNatKind(n__plus(V1,V2))</LHS><RHS>Marked_U31(isNatKind(activate(V1)),activate(V2))</RHS></DPRULE><DPRULE num="43"><LHS>Marked_isNatKind(n__plus(V1,V2))</LHS><RHS>Marked_isNatKind(activate(V1))</RHS></DPRULE><DPRULE num="44"><LHS>Marked_isNatKind(n__plus(V1,V2))</LHS><RHS>Marked_activate(V1)</RHS></DPRULE><DPRULE num="45"><LHS>Marked_isNatKind(n__plus(V1,V2))</LHS><RHS>Marked_activate(V2)</RHS></DPRULE><DPRULE num="46"><LHS>Marked_isNatKind(n__s(V1))</LHS><RHS>Marked_isNatKind(activate(V1))</RHS></DPRULE><DPRULE num="47"><LHS>Marked_isNatKind(n__s(V1))</LHS><RHS>Marked_activate(V1)</RHS></DPRULE><DPRULE num="48"><LHS>Marked_plus(N,0)</LHS><RHS>Marked_U51(isNat(N),N)</RHS></DPRULE><DPRULE num="49"><LHS>Marked_plus(N,0)</LHS><RHS>Marked_isNat(N)</RHS></DPRULE><DPRULE num="50"><LHS>Marked_plus(N,s(M))</LHS><RHS>Marked_U61(isNat(M),M,N)</RHS></DPRULE><DPRULE num="51"><LHS>Marked_plus(N,s(M))</LHS><RHS>Marked_isNat(M)</RHS></DPRULE></DPLIST></STRICTPAIRS></CRITERION><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>U11(tt,V1,V2)</LHS><RHS>U12(isNatKind(activate(V1)),activate(V1),activate(V2))</RHS></RULE><RULE><LHS>U12(tt,V1,V2)</LHS><RHS>U13(isNatKind(activate(V2)),activate(V1),activate(V2))</RHS></RULE><RULE><LHS>U13(tt,V1,V2)</LHS><RHS>U14(isNatKind(activate(V2)),activate(V1),activate(V2))</RHS></RULE><RULE><LHS>U14(tt,V1,V2)</LHS><RHS>U15(isNat(activate(V1)),activate(V2))</RHS></RULE><RULE><LHS>U15(tt,V2)</LHS><RHS>U16(isNat(activate(V2)))</RHS></RULE><RULE><LHS>U16(tt)</LHS><RHS>tt</RHS></RULE><RULE><LHS>U21(tt,V1)</LHS><RHS>U22(isNatKind(activate(V1)),activate(V1))</RHS></RULE><RULE><LHS>U22(tt,V1)</LHS><RHS>U23(isNat(activate(V1)))</RHS></RULE><RULE><LHS>U23(tt)</LHS><RHS>tt</RHS></RULE><RULE><LHS>U31(tt,V2)</LHS><RHS>U32(isNatKind(activate(V2)))</RHS></RULE><RULE><LHS>U32(tt)</LHS><RHS>tt</RHS></RULE><RULE><LHS>U41(tt)</LHS><RHS>tt</RHS></RULE><RULE><LHS>U51(tt,N)</LHS><RHS>U52(isNatKind(activate(N)),activate(N))</RHS></RULE><RULE><LHS>U52(tt,N)</LHS><RHS>activate(N)</RHS></RULE><RULE><LHS>U61(tt,M,N)</LHS><RHS>U62(isNatKind(activate(M)),activate(M),activate(N))</RHS></RULE><RULE><LHS>U62(tt,M,N)</LHS><RHS>U63(isNat(activate(N)),activate(M),activate(N))</RHS></RULE><RULE><LHS>U63(tt,M,N)</LHS><RHS>U64(isNatKind(activate(N)),activate(M),activate(N))</RHS></RULE><RULE><LHS>U64(tt,M,N)</LHS><RHS>s(plus(activate(N),activate(M)))</RHS></RULE><RULE><LHS>isNat(n__0)</LHS><RHS>tt</RHS></RULE><RULE><LHS>isNat(n__plus(V1,V2))</LHS><RHS>U11(isNatKind(activate(V1)),activate(V1),activate(V2))</RHS></RULE><RULE><LHS>isNat(n__s(V1))</LHS><RHS>U21(isNatKind(activate(V1)),activate(V1))</RHS></RULE><RULE><LHS>isNatKind(n__0)</LHS><RHS>tt</RHS></RULE><RULE><LHS>isNatKind(n__plus(V1,V2))</LHS><RHS>U31(isNatKind(activate(V1)),activate(V2))</RHS></RULE><RULE><LHS>isNatKind(n__s(V1))</LHS><RHS>U41(isNatKind(activate(V1)))</RHS></RULE><RULE><LHS>plus(N,0)</LHS><RHS>U51(isNat(N),N)</RHS></RULE><RULE><LHS>plus(N,s(M))</LHS><RHS>U61(isNat(M),M,N)</RHS></RULE><RULE><LHS>0</LHS><RHS>n__0</RHS></RULE><RULE><LHS>plus(X1,X2)</LHS><RHS>n__plus(X1,X2)</RHS></RULE><RULE><LHS>s(X)</LHS><RHS>n__s(X)</RHS></RULE><RULE><LHS>activate(n__0)</LHS><RHS>0</RHS></RULE><RULE><LHS>activate(n__plus(X1,X2))</LHS><RHS>plus(X1,X2)</RHS></RULE><RULE><LHS>activate(n__s(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>activate(X)</LHS><RHS>X</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_U11(tt,V1,V2)</LHS><RHS>Marked_U12(isNatKind(activate(V1)),activate(V1),activate(V2))</RHS></DPRULE><DPRULE num="1"><LHS>Marked_U13(tt,V1,V2)</LHS><RHS>Marked_isNatKind(activate(V2))</RHS></DPRULE><DPRULE num="2"><LHS>Marked_U14(tt,V1,V2)</LHS><RHS>Marked_U15(isNat(activate(V1)),activate(V2))</RHS></DPRULE><DPRULE num="3"><LHS>Marked_U14(tt,V1,V2)</LHS><RHS>Marked_isNat(activate(V1))</RHS></DPRULE><DPRULE num="4"><LHS>Marked_U14(tt,V1,V2)</LHS><RHS>Marked_activate(V1)</RHS></DPRULE><DPRULE num="5"><LHS>Marked_U14(tt,V1,V2)</LHS><RHS>Marked_activate(V2)</RHS></DPRULE><DPRULE num="6"><LHS>Marked_U15(tt,V2)</LHS><RHS>Marked_isNat(activate(V2))</RHS></DPRULE><DPRULE num="7"><LHS>Marked_U15(tt,V2)</LHS><RHS>Marked_activate(V2)</RHS></DPRULE><DPRULE num="8"><LHS>Marked_U22(tt,V1)</LHS><RHS>Marked_isNat(activate(V1))</RHS></DPRULE><DPRULE num="9"><LHS>Marked_U22(tt,V1)</LHS><RHS>Marked_activate(V1)</RHS></DPRULE><DPRULE num="10"><LHS>Marked_U31(tt,V2)</LHS><RHS>Marked_isNatKind(activate(V2))</RHS></DPRULE><DPRULE num="11"><LHS>Marked_U51(tt,N)</LHS><RHS>Marked_isNatKind(activate(N))</RHS></DPRULE><DPRULE num="12"><LHS>Marked_U52(tt,N)</LHS><RHS>Marked_activate(N)</RHS></DPRULE><DPRULE num="13"><LHS>Marked_U61(tt,M,N)</LHS><RHS>Marked_U62(isNatKind(activate(M)),activate(M),activate(N))</RHS></DPRULE><DPRULE num="14"><LHS>Marked_U62(tt,M,N)</LHS><RHS>Marked_U63(isNat(activate(N)),activate(M),activate(N))</RHS></DPRULE><DPRULE num="15"><LHS>Marked_U63(tt,M,N)</LHS><RHS>Marked_U64(isNatKind(activate(N)),activate(M),activate(N))</RHS></DPRULE><DPRULE num="16"><LHS>Marked_U64(tt,M,N)</LHS><RHS>Marked_plus(activate(N),activate(M))</RHS></DPRULE><DPRULE num="17"><LHS>Marked_isNat(n__plus(V1,V2))</LHS><RHS>Marked_U11(isNatKind(activate(V1)),activate(V1),activate(V2))</RHS></DPRULE><DPRULE num="18"><LHS>Marked_isNat(n__s(V1))</LHS><RHS>Marked_U21(isNatKind(activate(V1)),activate(V1))</RHS></DPRULE><DPRULE num="19"><LHS>Marked_activate(n__plus(X1,X2))</LHS><RHS>Marked_plus(X1,X2)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><DAG approx="simpl"><CCLIST><NONSCC num="0"><NODE ref="19"/></NONSCC><NONSCC num="1"><NODE ref="18"/></NONSCC><NONSCC num="2"><NODE ref="17"/></NONSCC><NONSCC num="3"><NODE ref="0"/></NONSCC><NONSCC num="4"><NODE ref="16"/></NONSCC><NONSCC num="5"><NODE ref="15"/></NONSCC><NONSCC num="6"><NODE ref="14"/></NONSCC><NONSCC num="7"><NODE ref="13"/></NONSCC><NONSCC num="8"><NODE ref="12"/></NONSCC><NONSCC num="9"><NODE ref="11"/></NONSCC><NONSCC num="10"><NODE ref="10"/></NONSCC><NONSCC num="11"><NODE ref="9"/></NONSCC><NONSCC num="12"><NODE ref="8"/></NONSCC><NONSCC num="13"><NODE ref="7"/></NONSCC><NONSCC num="14"><NODE ref="6"/></NONSCC><NONSCC num="15"><NODE ref="5"/></NONSCC><NONSCC num="16"><NODE ref="4"/></NONSCC><NONSCC num="17"><NODE ref="3"/></NONSCC><NONSCC num="18"><NODE ref="2"/></NONSCC><NONSCC num="19"><NODE ref="1"/></NONSCC></CCLIST><EDGE end="3" start="2"/><EDGE end="4" start="5"/><EDGE end="5" start="6"/><EDGE end="6" start="7"/><EDGE end="0" start="8"/><EDGE end="0" start="11"/><EDGE end="2" start="12"/><EDGE end="1" start="12"/><EDGE end="0" start="13"/><EDGE end="2" start="14"/><EDGE end="1" start="14"/><EDGE end="0" start="15"/><EDGE end="0" start="16"/><EDGE end="2" start="17"/><EDGE end="1" start="17"/><EDGE end="14" start="18"/><EDGE end="13" start="18"/></DAG></CRITERION></PROPERTY></PROPERTY></PROPERTY></PROPERTY></PROOF>
