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<!DOCTYPE PROOF SYSTEM "http://a3pat.ensiie.fr/pub/a3pat.dtd">
<PROOF><SIGNATURE><SYMBOLLIST><SYMBOL arity="1" unmarked=""><NAME>isNat</NAME></SYMBOL><SYMBOL arity="2" unmarked="a__U31"><NAME>Marked_a__U31</NAME></SYMBOL><SYMBOL arity="3" unmarked=""><NAME>a__U42</NAME></SYMBOL><SYMBOL arity="2" unmarked="a__U11"><NAME>Marked_a__U11</NAME></SYMBOL><SYMBOL arity="0" unmarked=""><NAME>0</NAME></SYMBOL><SYMBOL arity="3" unmarked=""><NAME>U42</NAME></SYMBOL><SYMBOL arity="0" unmarked=""><NAME>tt</NAME></SYMBOL><SYMBOL arity="2" unmarked=""><NAME>U11</NAME></SYMBOL><SYMBOL arity="3" unmarked="a__U42"><NAME>Marked_a__U42</NAME></SYMBOL><SYMBOL arity="1" unmarked=""><NAME>mark</NAME></SYMBOL><SYMBOL arity="1" unmarked="a__isNat"><NAME>Marked_a__isNat</NAME></SYMBOL><SYMBOL arity="1" unmarked=""><NAME>s</NAME></SYMBOL><SYMBOL arity="2" unmarked=""><NAME>U31</NAME></SYMBOL><SYMBOL arity="1" unmarked=""><NAME>a__isNat</NAME></SYMBOL><SYMBOL arity="1" unmarked=""><NAME>U12</NAME></SYMBOL><SYMBOL arity="3" unmarked="a__U41"><NAME>Marked_a__U41</NAME></SYMBOL><SYMBOL arity="2" unmarked=""><NAME>a__U31</NAME></SYMBOL><SYMBOL arity="1" unmarked="a__U12"><NAME>Marked_a__U12</NAME></SYMBOL><SYMBOL arity="2" unmarked=""><NAME>a__plus</NAME></SYMBOL><SYMBOL arity="3" unmarked=""><NAME>U41</NAME></SYMBOL><SYMBOL arity="2" unmarked=""><NAME>a__U11</NAME></SYMBOL><SYMBOL arity="1" unmarked="mark"><NAME>Marked_mark</NAME></SYMBOL><SYMBOL arity="2" unmarked=""><NAME>plus</NAME></SYMBOL><SYMBOL arity="2" unmarked="a__plus"><NAME>Marked_a__plus</NAME></SYMBOL><SYMBOL arity="1" unmarked=""><NAME>a__U21</NAME></SYMBOL><SYMBOL arity="1" unmarked="a__U21"><NAME>Marked_a__U21</NAME></SYMBOL><SYMBOL arity="3" unmarked=""><NAME>a__U41</NAME></SYMBOL><SYMBOL arity="1" unmarked=""><NAME>U21</NAME></SYMBOL><SYMBOL arity="1" unmarked=""><NAME>a__U12</NAME></SYMBOL></SYMBOLLIST><VARLIST><VAR>X</VAR><VAR>X3</VAR><VAR>X2</VAR><VAR>X1</VAR><VAR>V1</VAR><VAR>M</VAR><VAR>N</VAR><VAR>V2</VAR></VARLIST></SIGNATURE><PROPERTY criterion="dp" prop="sntrs"><SYSTEM><REWSYS><RULE><LHS>a__U11(tt,V2)</LHS><RHS>a__U12(a__isNat(V2))</RHS></RULE><RULE><LHS>a__U12(tt)</LHS><RHS>tt</RHS></RULE><RULE><LHS>a__U21(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>a__U42(a__isNat(N),M,N)</RHS></RULE><RULE><LHS>a__U42(tt,M,N)</LHS><RHS>s(a__plus(mark(N),mark(M)))</RHS></RULE><RULE><LHS>a__isNat(0)</LHS><RHS>tt</RHS></RULE><RULE><LHS>a__isNat(plus(V1,V2))</LHS><RHS>a__U11(a__isNat(V1),V2)</RHS></RULE><RULE><LHS>a__isNat(s(V1))</LHS><RHS>a__U21(a__isNat(V1))</RHS></RULE><RULE><LHS>a__plus(N,0)</LHS><RHS>a__U31(a__isNat(N),N)</RHS></RULE><RULE><LHS>a__plus(N,s(M))</LHS><RHS>a__U41(a__isNat(M),M,N)</RHS></RULE><RULE><LHS>mark(U11(X1,X2))</LHS><RHS>a__U11(mark(X1),X2)</RHS></RULE><RULE><LHS>mark(U12(X))</LHS><RHS>a__U12(mark(X))</RHS></RULE><RULE><LHS>mark(isNat(X))</LHS><RHS>a__isNat(X)</RHS></RULE><RULE><LHS>mark(U21(X))</LHS><RHS>a__U21(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(U42(X1,X2,X3))</LHS><RHS>a__U42(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(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)</LHS><RHS>U11(X1,X2)</RHS></RULE><RULE><LHS>a__U12(X)</LHS><RHS>U12(X)</RHS></RULE><RULE><LHS>a__isNat(X)</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>a__U21(X)</LHS><RHS>U21(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__U42(X1,X2,X3)</LHS><RHS>U42(X1,X2,X3)</RHS></RULE><RULE><LHS>a__plus(X1,X2)</LHS><RHS>plus(X1,X2)</RHS></RULE></REWSYS></SYSTEM><CRITERION/><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>a__U11(tt,V2)</LHS><RHS>a__U12(a__isNat(V2))</RHS></RULE><RULE><LHS>a__U12(tt)</LHS><RHS>tt</RHS></RULE><RULE><LHS>a__U21(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>a__U42(a__isNat(N),M,N)</RHS></RULE><RULE><LHS>a__U42(tt,M,N)</LHS><RHS>s(a__plus(mark(N),mark(M)))</RHS></RULE><RULE><LHS>a__isNat(0)</LHS><RHS>tt</RHS></RULE><RULE><LHS>a__isNat(plus(V1,V2))</LHS><RHS>a__U11(a__isNat(V1),V2)</RHS></RULE><RULE><LHS>a__isNat(s(V1))</LHS><RHS>a__U21(a__isNat(V1))</RHS></RULE><RULE><LHS>a__plus(N,0)</LHS><RHS>a__U31(a__isNat(N),N)</RHS></RULE><RULE><LHS>a__plus(N,s(M))</LHS><RHS>a__U41(a__isNat(M),M,N)</RHS></RULE><RULE><LHS>mark(U11(X1,X2))</LHS><RHS>a__U11(mark(X1),X2)</RHS></RULE><RULE><LHS>mark(U12(X))</LHS><RHS>a__U12(mark(X))</RHS></RULE><RULE><LHS>mark(isNat(X))</LHS><RHS>a__isNat(X)</RHS></RULE><RULE><LHS>mark(U21(X))</LHS><RHS>a__U21(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(U42(X1,X2,X3))</LHS><RHS>a__U42(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(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)</LHS><RHS>U11(X1,X2)</RHS></RULE><RULE><LHS>a__U12(X)</LHS><RHS>U12(X)</RHS></RULE><RULE><LHS>a__isNat(X)</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>a__U21(X)</LHS><RHS>U21(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__U42(X1,X2,X3)</LHS><RHS>U42(X1,X2,X3)</RHS></RULE><RULE><LHS>a__plus(X1,X2)</LHS><RHS>plus(X1,X2)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_a__U11(tt,V2)</LHS><RHS>Marked_a__U12(a__isNat(V2))</RHS></DPRULE><DPRULE num="1"><LHS>Marked_a__U11(tt,V2)</LHS><RHS>Marked_a__isNat(V2)</RHS></DPRULE><DPRULE num="2"><LHS>Marked_a__U31(tt,N)</LHS><RHS>Marked_mark(N)</RHS></DPRULE><DPRULE num="3"><LHS>Marked_a__U41(tt,M,N)</LHS><RHS>Marked_a__U42(a__isNat(N),M,N)</RHS></DPRULE><DPRULE num="4"><LHS>Marked_a__U41(tt,M,N)</LHS><RHS>Marked_a__isNat(N)</RHS></DPRULE><DPRULE num="5"><LHS>Marked_a__U42(tt,M,N)</LHS><RHS>Marked_a__plus(mark(N),mark(M))</RHS></DPRULE><DPRULE num="6"><LHS>Marked_a__U42(tt,M,N)</LHS><RHS>Marked_mark(N)</RHS></DPRULE><DPRULE num="7"><LHS>Marked_a__U42(tt,M,N)</LHS><RHS>Marked_mark(M)</RHS></DPRULE><DPRULE num="8"><LHS>Marked_a__isNat(plus(V1,V2))</LHS><RHS>Marked_a__U11(a__isNat(V1),V2)</RHS></DPRULE><DPRULE num="9"><LHS>Marked_a__isNat(plus(V1,V2))</LHS><RHS>Marked_a__isNat(V1)</RHS></DPRULE><DPRULE num="10"><LHS>Marked_a__isNat(s(V1))</LHS><RHS>Marked_a__U21(a__isNat(V1))</RHS></DPRULE><DPRULE num="11"><LHS>Marked_a__isNat(s(V1))</LHS><RHS>Marked_a__isNat(V1)</RHS></DPRULE><DPRULE num="12"><LHS>Marked_a__plus(N,0)</LHS><RHS>Marked_a__U31(a__isNat(N),N)</RHS></DPRULE><DPRULE num="13"><LHS>Marked_a__plus(N,0)</LHS><RHS>Marked_a__isNat(N)</RHS></DPRULE><DPRULE num="14"><LHS>Marked_a__plus(N,s(M))</LHS><RHS>Marked_a__U41(a__isNat(M),M,N)</RHS></DPRULE><DPRULE num="15"><LHS>Marked_a__plus(N,s(M))</LHS><RHS>Marked_a__isNat(M)</RHS></DPRULE><DPRULE num="16"><LHS>Marked_mark(U11(X1,X2))</LHS><RHS>Marked_a__U11(mark(X1),X2)</RHS></DPRULE><DPRULE num="17"><LHS>Marked_mark(U11(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="18"><LHS>Marked_mark(U12(X))</LHS><RHS>Marked_a__U12(mark(X))</RHS></DPRULE><DPRULE num="19"><LHS>Marked_mark(U12(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="20"><LHS>Marked_mark(isNat(X))</LHS><RHS>Marked_a__isNat(X)</RHS></DPRULE><DPRULE num="21"><LHS>Marked_mark(U21(X))</LHS><RHS>Marked_a__U21(mark(X))</RHS></DPRULE><DPRULE num="22"><LHS>Marked_mark(U21(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="23"><LHS>Marked_mark(U31(X1,X2))</LHS><RHS>Marked_a__U31(mark(X1),X2)</RHS></DPRULE><DPRULE num="24"><LHS>Marked_mark(U31(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="25"><LHS>Marked_mark(U41(X1,X2,X3))</LHS><RHS>Marked_a__U41(mark(X1),X2,X3)</RHS></DPRULE><DPRULE num="26"><LHS>Marked_mark(U41(X1,X2,X3))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="27"><LHS>Marked_mark(U42(X1,X2,X3))</LHS><RHS>Marked_a__U42(mark(X1),X2,X3)</RHS></DPRULE><DPRULE num="28"><LHS>Marked_mark(U42(X1,X2,X3))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="29"><LHS>Marked_mark(plus(X1,X2))</LHS><RHS>Marked_a__plus(mark(X1),mark(X2))</RHS></DPRULE><DPRULE num="30"><LHS>Marked_mark(plus(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="31"><LHS>Marked_mark(plus(X1,X2))</LHS><RHS>Marked_mark(X2)</RHS></DPRULE><DPRULE num="32"><LHS>Marked_mark(s(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><DAG approx="simpl"><CCLIST><SCC num="0"><NODE ref="2"/><NODE ref="3"/><NODE ref="5"/><NODE ref="6"/><NODE ref="7"/><NODE ref="12"/><NODE ref="14"/><NODE ref="17"/><NODE ref="19"/><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"/></SCC><NONSCC num="1"><NODE ref="21"/></NONSCC><NONSCC num="2"><NODE ref="20"/></NONSCC><NONSCC num="3"><NODE ref="18"/></NONSCC><NONSCC num="4"><NODE ref="16"/></NONSCC><NONSCC num="5"><NODE ref="15"/></NONSCC><NONSCC num="6"><NODE ref="13"/></NONSCC><NONSCC num="7"><NODE ref="4"/></NONSCC><SCC num="8"><NODE ref="1"/><NODE ref="8"/><NODE ref="9"/><NODE ref="11"/></SCC><NONSCC num="9"><NODE ref="10"/></NONSCC><NONSCC num="10"><NODE ref="0"/></NONSCC></CCLIST><EDGE end="7" start="0"/><EDGE end="6" start="0"/><EDGE end="5" start="0"/><EDGE end="4" start="0"/><EDGE end="3" start="0"/><EDGE end="2" start="0"/><EDGE end="1" start="0"/><EDGE end="9" start="2"/><EDGE end="8" start="2"/><EDGE end="10" start="4"/><EDGE end="8" start="4"/><EDGE end="9" start="5"/><EDGE end="8" start="5"/><EDGE end="9" start="6"/><EDGE end="8" start="6"/><EDGE end="9" start="7"/><EDGE end="8" start="7"/><EDGE end="10" start="8"/><EDGE end="9" start="8"/></DAG></CRITERION><PROPERTY criterion="stronggraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>a__U11(tt,V2)</LHS><RHS>a__U12(a__isNat(V2))</RHS></RULE><RULE><LHS>a__U12(tt)</LHS><RHS>tt</RHS></RULE><RULE><LHS>a__U21(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>a__U42(a__isNat(N),M,N)</RHS></RULE><RULE><LHS>a__U42(tt,M,N)</LHS><RHS>s(a__plus(mark(N),mark(M)))</RHS></RULE><RULE><LHS>a__isNat(0)</LHS><RHS>tt</RHS></RULE><RULE><LHS>a__isNat(plus(V1,V2))</LHS><RHS>a__U11(a__isNat(V1),V2)</RHS></RULE><RULE><LHS>a__isNat(s(V1))</LHS><RHS>a__U21(a__isNat(V1))</RHS></RULE><RULE><LHS>a__plus(N,0)</LHS><RHS>a__U31(a__isNat(N),N)</RHS></RULE><RULE><LHS>a__plus(N,s(M))</LHS><RHS>a__U41(a__isNat(M),M,N)</RHS></RULE><RULE><LHS>mark(U11(X1,X2))</LHS><RHS>a__U11(mark(X1),X2)</RHS></RULE><RULE><LHS>mark(U12(X))</LHS><RHS>a__U12(mark(X))</RHS></RULE><RULE><LHS>mark(isNat(X))</LHS><RHS>a__isNat(X)</RHS></RULE><RULE><LHS>mark(U21(X))</LHS><RHS>a__U21(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(U42(X1,X2,X3))</LHS><RHS>a__U42(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(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)</LHS><RHS>U11(X1,X2)</RHS></RULE><RULE><LHS>a__U12(X)</LHS><RHS>U12(X)</RHS></RULE><RULE><LHS>a__isNat(X)</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>a__U21(X)</LHS><RHS>U21(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__U42(X1,X2,X3)</LHS><RHS>U42(X1,X2,X3)</RHS></RULE><RULE><LHS>a__plus(X1,X2)</LHS><RHS>plus(X1,X2)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_a__U31(tt,N)</LHS><RHS>Marked_mark(N)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_a__U41(tt,M,N)</LHS><RHS>Marked_a__U42(a__isNat(N),M,N)</RHS></DPRULE><DPRULE num="2"><LHS>Marked_a__U42(tt,M,N)</LHS><RHS>Marked_a__plus(mark(N),mark(M))</RHS></DPRULE><DPRULE num="3"><LHS>Marked_a__U42(tt,M,N)</LHS><RHS>Marked_mark(N)</RHS></DPRULE><DPRULE num="4"><LHS>Marked_a__U42(tt,M,N)</LHS><RHS>Marked_mark(M)</RHS></DPRULE><DPRULE num="5"><LHS>Marked_a__plus(N,0)</LHS><RHS>Marked_a__U31(a__isNat(N),N)</RHS></DPRULE><DPRULE num="6"><LHS>Marked_a__plus(N,s(M))</LHS><RHS>Marked_a__U41(a__isNat(M),M,N)</RHS></DPRULE><DPRULE num="7"><LHS>Marked_mark(U11(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="8"><LHS>Marked_mark(U12(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="9"><LHS>Marked_mark(U21(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="10"><LHS>Marked_mark(U31(X1,X2))</LHS><RHS>Marked_a__U31(mark(X1),X2)</RHS></DPRULE><DPRULE num="11"><LHS>Marked_mark(U31(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="12"><LHS>Marked_mark(U41(X1,X2,X3))</LHS><RHS>Marked_a__U41(mark(X1),X2,X3)</RHS></DPRULE><DPRULE num="13"><LHS>Marked_mark(U41(X1,X2,X3))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="14"><LHS>Marked_mark(U42(X1,X2,X3))</LHS><RHS>Marked_a__U42(mark(X1),X2,X3)</RHS></DPRULE><DPRULE num="15"><LHS>Marked_mark(U42(X1,X2,X3))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="16"><LHS>Marked_mark(plus(X1,X2))</LHS><RHS>Marked_a__plus(mark(X1),mark(X2))</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(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>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__U41</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>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__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>Marked_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>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>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_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>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>U41</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>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__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></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>Marked_a__U41</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>3</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>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>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__isNat</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U31</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>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>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>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>Marked_a__U42</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>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>tt</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U42</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>3</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><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></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>a__U42</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>3</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><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></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>Marked_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>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>isNat</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__U42(a__isNat(N),M,N)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_a__plus(N,0)</LHS><RHS>Marked_a__U31(a__isNat(N),N)</RHS></DPRULE><DPRULE num="2"><LHS>Marked_a__plus(N,s(M))</LHS><RHS>Marked_a__U41(a__isNat(M),M,N)</RHS></DPRULE><DPRULE num="3"><LHS>Marked_mark(U31(X1,X2))</LHS><RHS>Marked_a__U31(mark(X1),X2)</RHS></DPRULE><DPRULE num="4"><LHS>Marked_mark(U31(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="5"><LHS>Marked_mark(U41(X1,X2,X3))</LHS><RHS>Marked_a__U41(mark(X1),X2,X3)</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(U42(X1,X2,X3))</LHS><RHS>Marked_a__U42(mark(X1),X2,X3)</RHS></DPRULE><DPRULE num="8"><LHS>Marked_mark(U42(X1,X2,X3))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="9"><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,V2)</LHS><RHS>a__U12(a__isNat(V2))</RHS></RULE><RULE><LHS>a__U12(tt)</LHS><RHS>tt</RHS></RULE><RULE><LHS>a__U21(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>a__U42(a__isNat(N),M,N)</RHS></RULE><RULE><LHS>a__U42(tt,M,N)</LHS><RHS>s(a__plus(mark(N),mark(M)))</RHS></RULE><RULE><LHS>a__isNat(0)</LHS><RHS>tt</RHS></RULE><RULE><LHS>a__isNat(plus(V1,V2))</LHS><RHS>a__U11(a__isNat(V1),V2)</RHS></RULE><RULE><LHS>a__isNat(s(V1))</LHS><RHS>a__U21(a__isNat(V1))</RHS></RULE><RULE><LHS>a__plus(N,0)</LHS><RHS>a__U31(a__isNat(N),N)</RHS></RULE><RULE><LHS>a__plus(N,s(M))</LHS><RHS>a__U41(a__isNat(M),M,N)</RHS></RULE><RULE><LHS>mark(U11(X1,X2))</LHS><RHS>a__U11(mark(X1),X2)</RHS></RULE><RULE><LHS>mark(U12(X))</LHS><RHS>a__U12(mark(X))</RHS></RULE><RULE><LHS>mark(isNat(X))</LHS><RHS>a__isNat(X)</RHS></RULE><RULE><LHS>mark(U21(X))</LHS><RHS>a__U21(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(U42(X1,X2,X3))</LHS><RHS>a__U42(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(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)</LHS><RHS>U11(X1,X2)</RHS></RULE><RULE><LHS>a__U12(X)</LHS><RHS>U12(X)</RHS></RULE><RULE><LHS>a__isNat(X)</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>a__U21(X)</LHS><RHS>U21(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__U42(X1,X2,X3)</LHS><RHS>U42(X1,X2,X3)</RHS></RULE><RULE><LHS>a__plus(X1,X2)</LHS><RHS>plus(X1,X2)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_a__U31(tt,N)</LHS><RHS>Marked_mark(N)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_a__U42(tt,M,N)</LHS><RHS>Marked_a__plus(mark(N),mark(M))</RHS></DPRULE><DPRULE num="2"><LHS>Marked_a__U42(tt,M,N)</LHS><RHS>Marked_mark(N)</RHS></DPRULE><DPRULE num="3"><LHS>Marked_a__U42(tt,M,N)</LHS><RHS>Marked_mark(M)</RHS></DPRULE><DPRULE num="4"><LHS>Marked_mark(U11(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="5"><LHS>Marked_mark(U12(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="6"><LHS>Marked_mark(U21(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="7"><LHS>Marked_mark(plus(X1,X2))</LHS><RHS>Marked_a__plus(mark(X1),mark(X2))</RHS></DPRULE><DPRULE num="8"><LHS>Marked_mark(plus(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="9"><LHS>Marked_mark(plus(X1,X2))</LHS><RHS>Marked_mark(X2)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><DAG approx="simpl"><CCLIST><SCC num="0"><NODE ref="4"/><NODE ref="5"/><NODE ref="6"/><NODE ref="8"/><NODE ref="9"/></SCC><NONSCC num="1"><NODE ref="7"/></NONSCC><NONSCC num="2"><NODE ref="3"/></NONSCC><NONSCC num="3"><NODE ref="2"/></NONSCC><NONSCC num="4"><NODE ref="1"/></NONSCC><NONSCC num="5"><NODE ref="0"/></NONSCC></CCLIST><EDGE end="1" start="0"/><EDGE end="1" start="2"/><EDGE end="0" start="2"/><EDGE end="1" start="3"/><EDGE end="0" start="3"/><EDGE end="1" start="5"/><EDGE end="0" start="5"/></DAG></CRITERION><PROPERTY criterion="stronggraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>a__U11(tt,V2)</LHS><RHS>a__U12(a__isNat(V2))</RHS></RULE><RULE><LHS>a__U12(tt)</LHS><RHS>tt</RHS></RULE><RULE><LHS>a__U21(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>a__U42(a__isNat(N),M,N)</RHS></RULE><RULE><LHS>a__U42(tt,M,N)</LHS><RHS>s(a__plus(mark(N),mark(M)))</RHS></RULE><RULE><LHS>a__isNat(0)</LHS><RHS>tt</RHS></RULE><RULE><LHS>a__isNat(plus(V1,V2))</LHS><RHS>a__U11(a__isNat(V1),V2)</RHS></RULE><RULE><LHS>a__isNat(s(V1))</LHS><RHS>a__U21(a__isNat(V1))</RHS></RULE><RULE><LHS>a__plus(N,0)</LHS><RHS>a__U31(a__isNat(N),N)</RHS></RULE><RULE><LHS>a__plus(N,s(M))</LHS><RHS>a__U41(a__isNat(M),M,N)</RHS></RULE><RULE><LHS>mark(U11(X1,X2))</LHS><RHS>a__U11(mark(X1),X2)</RHS></RULE><RULE><LHS>mark(U12(X))</LHS><RHS>a__U12(mark(X))</RHS></RULE><RULE><LHS>mark(isNat(X))</LHS><RHS>a__isNat(X)</RHS></RULE><RULE><LHS>mark(U21(X))</LHS><RHS>a__U21(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(U42(X1,X2,X3))</LHS><RHS>a__U42(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(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)</LHS><RHS>U11(X1,X2)</RHS></RULE><RULE><LHS>a__U12(X)</LHS><RHS>U12(X)</RHS></RULE><RULE><LHS>a__isNat(X)</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>a__U21(X)</LHS><RHS>U21(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__U42(X1,X2,X3)</LHS><RHS>U42(X1,X2,X3)</RHS></RULE><RULE><LHS>a__plus(X1,X2)</LHS><RHS>plus(X1,X2)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_mark(U11(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_mark(U12(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="2"><LHS>Marked_mark(U21(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="3"><LHS>Marked_mark(plus(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="4"><LHS>Marked_mark(plus(X1,X2))</LHS><RHS>Marked_mark(X2)</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>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__U41</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>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>plus</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>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>Marked_mark</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__U11</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U41</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF></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>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__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>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__isNat</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></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>s</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>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>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>tt</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U42</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>0</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>a__U42</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>isNat</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB></ORDERING><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_mark(plus(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_mark(plus(X1,X2))</LHS><RHS>Marked_mark(X2)</RHS></DPRULE></DPLIST></STRICTPAIRS></CRITERION><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>a__U11(tt,V2)</LHS><RHS>a__U12(a__isNat(V2))</RHS></RULE><RULE><LHS>a__U12(tt)</LHS><RHS>tt</RHS></RULE><RULE><LHS>a__U21(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>a__U42(a__isNat(N),M,N)</RHS></RULE><RULE><LHS>a__U42(tt,M,N)</LHS><RHS>s(a__plus(mark(N),mark(M)))</RHS></RULE><RULE><LHS>a__isNat(0)</LHS><RHS>tt</RHS></RULE><RULE><LHS>a__isNat(plus(V1,V2))</LHS><RHS>a__U11(a__isNat(V1),V2)</RHS></RULE><RULE><LHS>a__isNat(s(V1))</LHS><RHS>a__U21(a__isNat(V1))</RHS></RULE><RULE><LHS>a__plus(N,0)</LHS><RHS>a__U31(a__isNat(N),N)</RHS></RULE><RULE><LHS>a__plus(N,s(M))</LHS><RHS>a__U41(a__isNat(M),M,N)</RHS></RULE><RULE><LHS>mark(U11(X1,X2))</LHS><RHS>a__U11(mark(X1),X2)</RHS></RULE><RULE><LHS>mark(U12(X))</LHS><RHS>a__U12(mark(X))</RHS></RULE><RULE><LHS>mark(isNat(X))</LHS><RHS>a__isNat(X)</RHS></RULE><RULE><LHS>mark(U21(X))</LHS><RHS>a__U21(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(U42(X1,X2,X3))</LHS><RHS>a__U42(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(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)</LHS><RHS>U11(X1,X2)</RHS></RULE><RULE><LHS>a__U12(X)</LHS><RHS>U12(X)</RHS></RULE><RULE><LHS>a__isNat(X)</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>a__U21(X)</LHS><RHS>U21(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__U42(X1,X2,X3)</LHS><RHS>U42(X1,X2,X3)</RHS></RULE><RULE><LHS>a__plus(X1,X2)</LHS><RHS>plus(X1,X2)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_mark(U11(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_mark(U12(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="2"><LHS>Marked_mark(U21(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><DAG approx="simpl"><CCLIST><SCC num="0"><NODE ref="0"/><NODE ref="1"/><NODE ref="2"/></SCC></CCLIST></DAG></CRITERION><PROPERTY criterion="stronggraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>a__U11(tt,V2)</LHS><RHS>a__U12(a__isNat(V2))</RHS></RULE><RULE><LHS>a__U12(tt)</LHS><RHS>tt</RHS></RULE><RULE><LHS>a__U21(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>a__U42(a__isNat(N),M,N)</RHS></RULE><RULE><LHS>a__U42(tt,M,N)</LHS><RHS>s(a__plus(mark(N),mark(M)))</RHS></RULE><RULE><LHS>a__isNat(0)</LHS><RHS>tt</RHS></RULE><RULE><LHS>a__isNat(plus(V1,V2))</LHS><RHS>a__U11(a__isNat(V1),V2)</RHS></RULE><RULE><LHS>a__isNat(s(V1))</LHS><RHS>a__U21(a__isNat(V1))</RHS></RULE><RULE><LHS>a__plus(N,0)</LHS><RHS>a__U31(a__isNat(N),N)</RHS></RULE><RULE><LHS>a__plus(N,s(M))</LHS><RHS>a__U41(a__isNat(M),M,N)</RHS></RULE><RULE><LHS>mark(U11(X1,X2))</LHS><RHS>a__U11(mark(X1),X2)</RHS></RULE><RULE><LHS>mark(U12(X))</LHS><RHS>a__U12(mark(X))</RHS></RULE><RULE><LHS>mark(isNat(X))</LHS><RHS>a__isNat(X)</RHS></RULE><RULE><LHS>mark(U21(X))</LHS><RHS>a__U21(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(U42(X1,X2,X3))</LHS><RHS>a__U42(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(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)</LHS><RHS>U11(X1,X2)</RHS></RULE><RULE><LHS>a__U12(X)</LHS><RHS>U12(X)</RHS></RULE><RULE><LHS>a__isNat(X)</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>a__U21(X)</LHS><RHS>U21(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__U42(X1,X2,X3)</LHS><RHS>U42(X1,X2,X3)</RHS></RULE><RULE><LHS>a__plus(X1,X2)</LHS><RHS>plus(X1,X2)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_mark(U11(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_mark(U12(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="2"><LHS>Marked_mark(U21(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></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>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__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>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__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>plus</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>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>Marked_mark</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__U11</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>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>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>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__plus</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>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__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>U12</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>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>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>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>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>U11</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>2</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>tt</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U42</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>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>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>a__U42</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>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>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></ORDERING><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_mark(U11(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_mark(U12(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE></DPLIST></STRICTPAIRS></CRITERION><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>a__U11(tt,V2)</LHS><RHS>a__U12(a__isNat(V2))</RHS></RULE><RULE><LHS>a__U12(tt)</LHS><RHS>tt</RHS></RULE><RULE><LHS>a__U21(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>a__U42(a__isNat(N),M,N)</RHS></RULE><RULE><LHS>a__U42(tt,M,N)</LHS><RHS>s(a__plus(mark(N),mark(M)))</RHS></RULE><RULE><LHS>a__isNat(0)</LHS><RHS>tt</RHS></RULE><RULE><LHS>a__isNat(plus(V1,V2))</LHS><RHS>a__U11(a__isNat(V1),V2)</RHS></RULE><RULE><LHS>a__isNat(s(V1))</LHS><RHS>a__U21(a__isNat(V1))</RHS></RULE><RULE><LHS>a__plus(N,0)</LHS><RHS>a__U31(a__isNat(N),N)</RHS></RULE><RULE><LHS>a__plus(N,s(M))</LHS><RHS>a__U41(a__isNat(M),M,N)</RHS></RULE><RULE><LHS>mark(U11(X1,X2))</LHS><RHS>a__U11(mark(X1),X2)</RHS></RULE><RULE><LHS>mark(U12(X))</LHS><RHS>a__U12(mark(X))</RHS></RULE><RULE><LHS>mark(isNat(X))</LHS><RHS>a__isNat(X)</RHS></RULE><RULE><LHS>mark(U21(X))</LHS><RHS>a__U21(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(U42(X1,X2,X3))</LHS><RHS>a__U42(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(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)</LHS><RHS>U11(X1,X2)</RHS></RULE><RULE><LHS>a__U12(X)</LHS><RHS>U12(X)</RHS></RULE><RULE><LHS>a__isNat(X)</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>a__U21(X)</LHS><RHS>U21(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__U42(X1,X2,X3)</LHS><RHS>U42(X1,X2,X3)</RHS></RULE><RULE><LHS>a__plus(X1,X2)</LHS><RHS>plus(X1,X2)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_mark(U21(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><DAG approx="simpl"><CCLIST><SCC num="0"><NODE ref="0"/></SCC></CCLIST></DAG></CRITERION><PROPERTY criterion="ordering" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>a__U11(tt,V2)</LHS><RHS>a__U12(a__isNat(V2))</RHS></RULE><RULE><LHS>a__U12(tt)</LHS><RHS>tt</RHS></RULE><RULE><LHS>a__U21(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>a__U42(a__isNat(N),M,N)</RHS></RULE><RULE><LHS>a__U42(tt,M,N)</LHS><RHS>s(a__plus(mark(N),mark(M)))</RHS></RULE><RULE><LHS>a__isNat(0)</LHS><RHS>tt</RHS></RULE><RULE><LHS>a__isNat(plus(V1,V2))</LHS><RHS>a__U11(a__isNat(V1),V2)</RHS></RULE><RULE><LHS>a__isNat(s(V1))</LHS><RHS>a__U21(a__isNat(V1))</RHS></RULE><RULE><LHS>a__plus(N,0)</LHS><RHS>a__U31(a__isNat(N),N)</RHS></RULE><RULE><LHS>a__plus(N,s(M))</LHS><RHS>a__U41(a__isNat(M),M,N)</RHS></RULE><RULE><LHS>mark(U11(X1,X2))</LHS><RHS>a__U11(mark(X1),X2)</RHS></RULE><RULE><LHS>mark(U12(X))</LHS><RHS>a__U12(mark(X))</RHS></RULE><RULE><LHS>mark(isNat(X))</LHS><RHS>a__isNat(X)</RHS></RULE><RULE><LHS>mark(U21(X))</LHS><RHS>a__U21(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(U42(X1,X2,X3))</LHS><RHS>a__U42(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(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)</LHS><RHS>U11(X1,X2)</RHS></RULE><RULE><LHS>a__U12(X)</LHS><RHS>U12(X)</RHS></RULE><RULE><LHS>a__isNat(X)</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>a__U21(X)</LHS><RHS>U21(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__U42(X1,X2,X3)</LHS><RHS>U42(X1,X2,X3)</RHS></RULE><RULE><LHS>a__plus(X1,X2)</LHS><RHS>plus(X1,X2)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_mark(U21(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><ORDERING type="poly"><POLYSYMB><SYMBOL><NAME>a__U12</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U21</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><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>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>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__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><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>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_mark</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__U11</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></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>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__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>U12</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>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>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>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>U11</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>U42</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>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>0</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>a__U42</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>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>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></ORDERING></CRITERION></PROPERTY></PROPERTY></PROPERTY></PROPERTY></PROPERTY></PROPERTY></PROPERTY><PROPERTY criterion="stronggraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>a__U11(tt,V2)</LHS><RHS>a__U12(a__isNat(V2))</RHS></RULE><RULE><LHS>a__U12(tt)</LHS><RHS>tt</RHS></RULE><RULE><LHS>a__U21(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>a__U42(a__isNat(N),M,N)</RHS></RULE><RULE><LHS>a__U42(tt,M,N)</LHS><RHS>s(a__plus(mark(N),mark(M)))</RHS></RULE><RULE><LHS>a__isNat(0)</LHS><RHS>tt</RHS></RULE><RULE><LHS>a__isNat(plus(V1,V2))</LHS><RHS>a__U11(a__isNat(V1),V2)</RHS></RULE><RULE><LHS>a__isNat(s(V1))</LHS><RHS>a__U21(a__isNat(V1))</RHS></RULE><RULE><LHS>a__plus(N,0)</LHS><RHS>a__U31(a__isNat(N),N)</RHS></RULE><RULE><LHS>a__plus(N,s(M))</LHS><RHS>a__U41(a__isNat(M),M,N)</RHS></RULE><RULE><LHS>mark(U11(X1,X2))</LHS><RHS>a__U11(mark(X1),X2)</RHS></RULE><RULE><LHS>mark(U12(X))</LHS><RHS>a__U12(mark(X))</RHS></RULE><RULE><LHS>mark(isNat(X))</LHS><RHS>a__isNat(X)</RHS></RULE><RULE><LHS>mark(U21(X))</LHS><RHS>a__U21(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(U42(X1,X2,X3))</LHS><RHS>a__U42(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(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)</LHS><RHS>U11(X1,X2)</RHS></RULE><RULE><LHS>a__U12(X)</LHS><RHS>U12(X)</RHS></RULE><RULE><LHS>a__isNat(X)</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>a__U21(X)</LHS><RHS>U21(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__U42(X1,X2,X3)</LHS><RHS>U42(X1,X2,X3)</RHS></RULE><RULE><LHS>a__plus(X1,X2)</LHS><RHS>plus(X1,X2)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_a__U11(tt,V2)</LHS><RHS>Marked_a__isNat(V2)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_a__isNat(plus(V1,V2))</LHS><RHS>Marked_a__U11(a__isNat(V1),V2)</RHS></DPRULE><DPRULE num="2"><LHS>Marked_a__isNat(plus(V1,V2))</LHS><RHS>Marked_a__isNat(V1)</RHS></DPRULE><DPRULE num="3"><LHS>Marked_a__isNat(s(V1))</LHS><RHS>Marked_a__isNat(V1)</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></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__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>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__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>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>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>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>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__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>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>U12</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>a__isNat</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>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>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>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>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>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>tt</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U42</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>0</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>Marked_a__U11</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>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__U42</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>isNat</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB></ORDERING><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_a__U11(tt,V2)</LHS><RHS>Marked_a__isNat(V2)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_a__isNat(plus(V1,V2))</LHS><RHS>Marked_a__U11(a__isNat(V1),V2)</RHS></DPRULE><DPRULE num="2"><LHS>Marked_a__isNat(plus(V1,V2))</LHS><RHS>Marked_a__isNat(V1)</RHS></DPRULE></DPLIST></STRICTPAIRS></CRITERION><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>a__U11(tt,V2)</LHS><RHS>a__U12(a__isNat(V2))</RHS></RULE><RULE><LHS>a__U12(tt)</LHS><RHS>tt</RHS></RULE><RULE><LHS>a__U21(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>a__U42(a__isNat(N),M,N)</RHS></RULE><RULE><LHS>a__U42(tt,M,N)</LHS><RHS>s(a__plus(mark(N),mark(M)))</RHS></RULE><RULE><LHS>a__isNat(0)</LHS><RHS>tt</RHS></RULE><RULE><LHS>a__isNat(plus(V1,V2))</LHS><RHS>a__U11(a__isNat(V1),V2)</RHS></RULE><RULE><LHS>a__isNat(s(V1))</LHS><RHS>a__U21(a__isNat(V1))</RHS></RULE><RULE><LHS>a__plus(N,0)</LHS><RHS>a__U31(a__isNat(N),N)</RHS></RULE><RULE><LHS>a__plus(N,s(M))</LHS><RHS>a__U41(a__isNat(M),M,N)</RHS></RULE><RULE><LHS>mark(U11(X1,X2))</LHS><RHS>a__U11(mark(X1),X2)</RHS></RULE><RULE><LHS>mark(U12(X))</LHS><RHS>a__U12(mark(X))</RHS></RULE><RULE><LHS>mark(isNat(X))</LHS><RHS>a__isNat(X)</RHS></RULE><RULE><LHS>mark(U21(X))</LHS><RHS>a__U21(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(U42(X1,X2,X3))</LHS><RHS>a__U42(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(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)</LHS><RHS>U11(X1,X2)</RHS></RULE><RULE><LHS>a__U12(X)</LHS><RHS>U12(X)</RHS></RULE><RULE><LHS>a__isNat(X)</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>a__U21(X)</LHS><RHS>U21(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__U42(X1,X2,X3)</LHS><RHS>U42(X1,X2,X3)</RHS></RULE><RULE><LHS>a__plus(X1,X2)</LHS><RHS>plus(X1,X2)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_a__isNat(s(V1))</LHS><RHS>Marked_a__isNat(V1)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><DAG approx="simpl"><CCLIST><SCC num="0"><NODE ref="0"/></SCC></CCLIST></DAG></CRITERION><PROPERTY criterion="ordering" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>a__U11(tt,V2)</LHS><RHS>a__U12(a__isNat(V2))</RHS></RULE><RULE><LHS>a__U12(tt)</LHS><RHS>tt</RHS></RULE><RULE><LHS>a__U21(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>a__U42(a__isNat(N),M,N)</RHS></RULE><RULE><LHS>a__U42(tt,M,N)</LHS><RHS>s(a__plus(mark(N),mark(M)))</RHS></RULE><RULE><LHS>a__isNat(0)</LHS><RHS>tt</RHS></RULE><RULE><LHS>a__isNat(plus(V1,V2))</LHS><RHS>a__U11(a__isNat(V1),V2)</RHS></RULE><RULE><LHS>a__isNat(s(V1))</LHS><RHS>a__U21(a__isNat(V1))</RHS></RULE><RULE><LHS>a__plus(N,0)</LHS><RHS>a__U31(a__isNat(N),N)</RHS></RULE><RULE><LHS>a__plus(N,s(M))</LHS><RHS>a__U41(a__isNat(M),M,N)</RHS></RULE><RULE><LHS>mark(U11(X1,X2))</LHS><RHS>a__U11(mark(X1),X2)</RHS></RULE><RULE><LHS>mark(U12(X))</LHS><RHS>a__U12(mark(X))</RHS></RULE><RULE><LHS>mark(isNat(X))</LHS><RHS>a__isNat(X)</RHS></RULE><RULE><LHS>mark(U21(X))</LHS><RHS>a__U21(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(U42(X1,X2,X3))</LHS><RHS>a__U42(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(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)</LHS><RHS>U11(X1,X2)</RHS></RULE><RULE><LHS>a__U12(X)</LHS><RHS>U12(X)</RHS></RULE><RULE><LHS>a__isNat(X)</LHS><RHS>isNat(X)</RHS></RULE><RULE><LHS>a__U21(X)</LHS><RHS>U21(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__U42(X1,X2,X3)</LHS><RHS>U42(X1,X2,X3)</RHS></RULE><RULE><LHS>a__plus(X1,X2)</LHS><RHS>plus(X1,X2)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_a__isNat(s(V1))</LHS><RHS>Marked_a__isNat(V1)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><ORDERING type="poly"><POLYSYMB><SYMBOL><NAME>a__U12</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U21</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>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>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__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__U11</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U41</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>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__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="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>U12</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>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>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>Marked_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>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>U11</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>U42</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>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>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>a__U42</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>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>isNat</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB></ORDERING></CRITERION></PROPERTY></PROPERTY></PROPERTY></PROPERTY></PROPERTY></PROOF>
