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<!DOCTYPE PROOF SYSTEM "http://a3pat.ensiie.fr/pub/a3pat.dtd">
<PROOF><SIGNATURE><SYMBOLLIST><SYMBOL arity="1" unmarked="min"><NAME>Marked_min</NAME></SYMBOL><SYMBOL arity="2" unmarked=""><NAME>cons</NAME></SYMBOL><SYMBOL arity="4" unmarked=""><NAME>ifrepl</NAME></SYMBOL><SYMBOL arity="4" unmarked="ifrepl"><NAME>Marked_ifrepl</NAME></SYMBOL><SYMBOL arity="0" unmarked=""><NAME>false</NAME></SYMBOL><SYMBOL arity="2" unmarked=""><NAME>ifselsort</NAME></SYMBOL><SYMBOL arity="2" unmarked="le"><NAME>Marked_le</NAME></SYMBOL><SYMBOL arity="2" unmarked=""><NAME>le</NAME></SYMBOL><SYMBOL arity="2" unmarked=""><NAME>ifmin</NAME></SYMBOL><SYMBOL arity="3" unmarked="replace"><NAME>Marked_replace</NAME></SYMBOL><SYMBOL arity="2" unmarked=""><NAME>eq</NAME></SYMBOL><SYMBOL arity="2" unmarked="ifselsort"><NAME>Marked_ifselsort</NAME></SYMBOL><SYMBOL arity="1" unmarked=""><NAME>min</NAME></SYMBOL><SYMBOL arity="3" unmarked=""><NAME>replace</NAME></SYMBOL><SYMBOL arity="2" unmarked="eq"><NAME>Marked_eq</NAME></SYMBOL><SYMBOL arity="0" unmarked=""><NAME>0</NAME></SYMBOL><SYMBOL arity="1" unmarked=""><NAME>selsort</NAME></SYMBOL><SYMBOL arity="2" unmarked="ifmin"><NAME>Marked_ifmin</NAME></SYMBOL><SYMBOL arity="1" unmarked=""><NAME>s</NAME></SYMBOL><SYMBOL arity="0" unmarked=""><NAME>nil</NAME></SYMBOL><SYMBOL arity="1" unmarked="selsort"><NAME>Marked_selsort</NAME></SYMBOL><SYMBOL arity="0" unmarked=""><NAME>true</NAME></SYMBOL></SYMBOLLIST><VARLIST><VAR>L</VAR><VAR>M</VAR><VAR>N</VAR><VAR>K</VAR><VAR>Y</VAR><VAR>X</VAR></VARLIST></SIGNATURE><PROPERTY criterion="dp" prop="sntrs"><SYSTEM><REWSYS><RULE><LHS>eq(0,0)</LHS><RHS>true</RHS></RULE><RULE><LHS>eq(0,s(Y))</LHS><RHS>false</RHS></RULE><RULE><LHS>eq(s(X),0)</LHS><RHS>false</RHS></RULE><RULE><LHS>eq(s(X),s(Y))</LHS><RHS>eq(X,Y)</RHS></RULE><RULE><LHS>le(0,Y)</LHS><RHS>true</RHS></RULE><RULE><LHS>le(s(X),0)</LHS><RHS>false</RHS></RULE><RULE><LHS>le(s(X),s(Y))</LHS><RHS>le(X,Y)</RHS></RULE><RULE><LHS>min(cons(0,nil))</LHS><RHS>0</RHS></RULE><RULE><LHS>min(cons(s(N),nil))</LHS><RHS>s(N)</RHS></RULE><RULE><LHS>min(cons(N,cons(M,L)))</LHS><RHS>ifmin(le(N,M),cons(N,cons(M,L)))</RHS></RULE><RULE><LHS>ifmin(true,cons(N,cons(M,L)))</LHS><RHS>min(cons(N,L))</RHS></RULE><RULE><LHS>ifmin(false,cons(N,cons(M,L)))</LHS><RHS>min(cons(M,L))</RHS></RULE><RULE><LHS>replace(N,M,nil)</LHS><RHS>nil</RHS></RULE><RULE><LHS>replace(N,M,cons(K,L))</LHS><RHS>ifrepl(eq(N,K),N,M,cons(K,L))</RHS></RULE><RULE><LHS>ifrepl(true,N,M,cons(K,L))</LHS><RHS>cons(M,L)</RHS></RULE><RULE><LHS>ifrepl(false,N,M,cons(K,L))</LHS><RHS>cons(K,replace(N,M,L))</RHS></RULE><RULE><LHS>selsort(nil)</LHS><RHS>nil</RHS></RULE><RULE><LHS>selsort(cons(N,L))</LHS><RHS>ifselsort(eq(N,min(cons(N,L))),cons(N,L))</RHS></RULE><RULE><LHS>ifselsort(true,cons(N,L))</LHS><RHS>cons(N,selsort(L))</RHS></RULE><RULE><LHS>ifselsort(false,cons(N,L))</LHS><RHS>cons(min(cons(N,L)),selsort(replace(min(cons(N,L)),N,L)))</RHS></RULE></REWSYS></SYSTEM><CRITERION/><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>eq(0,0)</LHS><RHS>true</RHS></RULE><RULE><LHS>eq(0,s(Y))</LHS><RHS>false</RHS></RULE><RULE><LHS>eq(s(X),0)</LHS><RHS>false</RHS></RULE><RULE><LHS>eq(s(X),s(Y))</LHS><RHS>eq(X,Y)</RHS></RULE><RULE><LHS>le(0,Y)</LHS><RHS>true</RHS></RULE><RULE><LHS>le(s(X),0)</LHS><RHS>false</RHS></RULE><RULE><LHS>le(s(X),s(Y))</LHS><RHS>le(X,Y)</RHS></RULE><RULE><LHS>min(cons(0,nil))</LHS><RHS>0</RHS></RULE><RULE><LHS>min(cons(s(N),nil))</LHS><RHS>s(N)</RHS></RULE><RULE><LHS>min(cons(N,cons(M,L)))</LHS><RHS>ifmin(le(N,M),cons(N,cons(M,L)))</RHS></RULE><RULE><LHS>ifmin(true,cons(N,cons(M,L)))</LHS><RHS>min(cons(N,L))</RHS></RULE><RULE><LHS>ifmin(false,cons(N,cons(M,L)))</LHS><RHS>min(cons(M,L))</RHS></RULE><RULE><LHS>replace(N,M,nil)</LHS><RHS>nil</RHS></RULE><RULE><LHS>replace(N,M,cons(K,L))</LHS><RHS>ifrepl(eq(N,K),N,M,cons(K,L))</RHS></RULE><RULE><LHS>ifrepl(true,N,M,cons(K,L))</LHS><RHS>cons(M,L)</RHS></RULE><RULE><LHS>ifrepl(false,N,M,cons(K,L))</LHS><RHS>cons(K,replace(N,M,L))</RHS></RULE><RULE><LHS>selsort(nil)</LHS><RHS>nil</RHS></RULE><RULE><LHS>selsort(cons(N,L))</LHS><RHS>ifselsort(eq(N,min(cons(N,L))),cons(N,L))</RHS></RULE><RULE><LHS>ifselsort(true,cons(N,L))</LHS><RHS>cons(N,selsort(L))</RHS></RULE><RULE><LHS>ifselsort(false,cons(N,L))</LHS><RHS>cons(min(cons(N,L)),selsort(replace(min(cons(N,L)),N,L)))</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_eq(s(X),s(Y))</LHS><RHS>Marked_eq(X,Y)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_le(s(X),s(Y))</LHS><RHS>Marked_le(X,Y)</RHS></DPRULE><DPRULE num="2"><LHS>Marked_min(cons(N,cons(M,L)))</LHS><RHS>Marked_ifmin(le(N,M),cons(N,cons(M,L)))</RHS></DPRULE><DPRULE num="3"><LHS>Marked_min(cons(N,cons(M,L)))</LHS><RHS>Marked_le(N,M)</RHS></DPRULE><DPRULE num="4"><LHS>Marked_ifmin(true,cons(N,cons(M,L)))</LHS><RHS>Marked_min(cons(N,L))</RHS></DPRULE><DPRULE num="5"><LHS>Marked_ifmin(false,cons(N,cons(M,L)))</LHS><RHS>Marked_min(cons(M,L))</RHS></DPRULE><DPRULE num="6"><LHS>Marked_replace(N,M,cons(K,L))</LHS><RHS>Marked_ifrepl(eq(N,K),N,M,cons(K,L))</RHS></DPRULE><DPRULE num="7"><LHS>Marked_replace(N,M,cons(K,L))</LHS><RHS>Marked_eq(N,K)</RHS></DPRULE><DPRULE num="8"><LHS>Marked_ifrepl(false,N,M,cons(K,L))</LHS><RHS>Marked_replace(N,M,L)</RHS></DPRULE><DPRULE num="9"><LHS>Marked_selsort(cons(N,L))</LHS><RHS>Marked_ifselsort(eq(N,min(cons(N,L))),cons(N,L))</RHS></DPRULE><DPRULE num="10"><LHS>Marked_selsort(cons(N,L))</LHS><RHS>Marked_eq(N,min(cons(N,L)))</RHS></DPRULE><DPRULE num="11"><LHS>Marked_selsort(cons(N,L))</LHS><RHS>Marked_min(cons(N,L))</RHS></DPRULE><DPRULE num="12"><LHS>Marked_ifselsort(true,cons(N,L))</LHS><RHS>Marked_selsort(L)</RHS></DPRULE><DPRULE num="13"><LHS>Marked_ifselsort(false,cons(N,L))</LHS><RHS>Marked_min(cons(N,L))</RHS></DPRULE><DPRULE num="14"><LHS>Marked_ifselsort(false,cons(N,L))</LHS><RHS>Marked_selsort(replace(min(cons(N,L)),N,L))</RHS></DPRULE><DPRULE num="15"><LHS>Marked_ifselsort(false,cons(N,L))</LHS><RHS>Marked_replace(min(cons(N,L)),N,L)</RHS></DPRULE><DPRULE num="16"><LHS>Marked_ifselsort(false,cons(N,L))</LHS><RHS>Marked_min(cons(N,L))</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><DAG approx="simpl"><CCLIST><NONSCC num="0"><NODE ref="13"/></NONSCC><NONSCC num="1"><NODE ref="3"/></NONSCC><SCC num="2"><NODE ref="2"/><NODE ref="4"/><NODE ref="5"/></SCC><NONSCC num="3"><NODE ref="15"/></NONSCC><NONSCC num="4"><NODE ref="7"/></NONSCC><SCC num="5"><NODE ref="6"/><NODE ref="8"/></SCC><SCC num="6"><NODE ref="9"/><NODE ref="12"/><NODE ref="14"/></SCC><NONSCC num="7"><NODE ref="11"/></NONSCC><NONSCC num="8"><NODE ref="10"/></NONSCC><SCC num="9"><NODE ref="0"/></SCC><SCC num="10"><NODE ref="1"/></SCC></CCLIST><EDGE end="2" start="0"/><EDGE end="1" start="0"/><EDGE end="10" start="1"/><EDGE end="1" start="2"/><EDGE end="5" start="3"/><EDGE end="4" start="3"/><EDGE end="9" start="4"/><EDGE end="4" start="5"/><EDGE end="8" start="6"/><EDGE end="7" start="6"/><EDGE end="3" start="6"/><EDGE end="0" start="6"/><EDGE end="2" start="7"/><EDGE end="1" start="7"/><EDGE end="9" start="8"/></DAG></CRITERION><PROPERTY criterion="stronggraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>eq(0,0)</LHS><RHS>true</RHS></RULE><RULE><LHS>eq(0,s(Y))</LHS><RHS>false</RHS></RULE><RULE><LHS>eq(s(X),0)</LHS><RHS>false</RHS></RULE><RULE><LHS>eq(s(X),s(Y))</LHS><RHS>eq(X,Y)</RHS></RULE><RULE><LHS>le(0,Y)</LHS><RHS>true</RHS></RULE><RULE><LHS>le(s(X),0)</LHS><RHS>false</RHS></RULE><RULE><LHS>le(s(X),s(Y))</LHS><RHS>le(X,Y)</RHS></RULE><RULE><LHS>min(cons(0,nil))</LHS><RHS>0</RHS></RULE><RULE><LHS>min(cons(s(N),nil))</LHS><RHS>s(N)</RHS></RULE><RULE><LHS>min(cons(N,cons(M,L)))</LHS><RHS>ifmin(le(N,M),cons(N,cons(M,L)))</RHS></RULE><RULE><LHS>ifmin(true,cons(N,cons(M,L)))</LHS><RHS>min(cons(N,L))</RHS></RULE><RULE><LHS>ifmin(false,cons(N,cons(M,L)))</LHS><RHS>min(cons(M,L))</RHS></RULE><RULE><LHS>replace(N,M,nil)</LHS><RHS>nil</RHS></RULE><RULE><LHS>replace(N,M,cons(K,L))</LHS><RHS>ifrepl(eq(N,K),N,M,cons(K,L))</RHS></RULE><RULE><LHS>ifrepl(true,N,M,cons(K,L))</LHS><RHS>cons(M,L)</RHS></RULE><RULE><LHS>ifrepl(false,N,M,cons(K,L))</LHS><RHS>cons(K,replace(N,M,L))</RHS></RULE><RULE><LHS>selsort(nil)</LHS><RHS>nil</RHS></RULE><RULE><LHS>selsort(cons(N,L))</LHS><RHS>ifselsort(eq(N,min(cons(N,L))),cons(N,L))</RHS></RULE><RULE><LHS>ifselsort(true,cons(N,L))</LHS><RHS>cons(N,selsort(L))</RHS></RULE><RULE><LHS>ifselsort(false,cons(N,L))</LHS><RHS>cons(min(cons(N,L)),selsort(replace(min(cons(N,L)),N,L)))</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_selsort(cons(N,L))</LHS><RHS>Marked_ifselsort(eq(N,min(cons(N,L))),cons(N,L))</RHS></DPRULE><DPRULE num="1"><LHS>Marked_ifselsort(true,cons(N,L))</LHS><RHS>Marked_selsort(L)</RHS></DPRULE><DPRULE num="2"><LHS>Marked_ifselsort(false,cons(N,L))</LHS><RHS>Marked_selsort(replace(min(cons(N,L)),N,L))</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><ORDERING type="poly"><POLYSYMB><SYMBOL><NAME>true</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>Marked_selsort</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>nil</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>s</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>selsort</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</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>0</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>replace</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="2"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>min</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>Marked_ifselsort</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>eq</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>ifmin</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>le</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>ifselsort</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>3</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>false</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>ifrepl</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="3"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>cons</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB></ORDERING><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_ifselsort(true,cons(N,L))</LHS><RHS>Marked_selsort(L)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_ifselsort(false,cons(N,L))</LHS><RHS>Marked_selsort(replace(min(cons(N,L)),N,L))</RHS></DPRULE></DPLIST></STRICTPAIRS></CRITERION><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>eq(0,0)</LHS><RHS>true</RHS></RULE><RULE><LHS>eq(0,s(Y))</LHS><RHS>false</RHS></RULE><RULE><LHS>eq(s(X),0)</LHS><RHS>false</RHS></RULE><RULE><LHS>eq(s(X),s(Y))</LHS><RHS>eq(X,Y)</RHS></RULE><RULE><LHS>le(0,Y)</LHS><RHS>true</RHS></RULE><RULE><LHS>le(s(X),0)</LHS><RHS>false</RHS></RULE><RULE><LHS>le(s(X),s(Y))</LHS><RHS>le(X,Y)</RHS></RULE><RULE><LHS>min(cons(0,nil))</LHS><RHS>0</RHS></RULE><RULE><LHS>min(cons(s(N),nil))</LHS><RHS>s(N)</RHS></RULE><RULE><LHS>min(cons(N,cons(M,L)))</LHS><RHS>ifmin(le(N,M),cons(N,cons(M,L)))</RHS></RULE><RULE><LHS>ifmin(true,cons(N,cons(M,L)))</LHS><RHS>min(cons(N,L))</RHS></RULE><RULE><LHS>ifmin(false,cons(N,cons(M,L)))</LHS><RHS>min(cons(M,L))</RHS></RULE><RULE><LHS>replace(N,M,nil)</LHS><RHS>nil</RHS></RULE><RULE><LHS>replace(N,M,cons(K,L))</LHS><RHS>ifrepl(eq(N,K),N,M,cons(K,L))</RHS></RULE><RULE><LHS>ifrepl(true,N,M,cons(K,L))</LHS><RHS>cons(M,L)</RHS></RULE><RULE><LHS>ifrepl(false,N,M,cons(K,L))</LHS><RHS>cons(K,replace(N,M,L))</RHS></RULE><RULE><LHS>selsort(nil)</LHS><RHS>nil</RHS></RULE><RULE><LHS>selsort(cons(N,L))</LHS><RHS>ifselsort(eq(N,min(cons(N,L))),cons(N,L))</RHS></RULE><RULE><LHS>ifselsort(true,cons(N,L))</LHS><RHS>cons(N,selsort(L))</RHS></RULE><RULE><LHS>ifselsort(false,cons(N,L))</LHS><RHS>cons(min(cons(N,L)),selsort(replace(min(cons(N,L)),N,L)))</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_selsort(cons(N,L))</LHS><RHS>Marked_ifselsort(eq(N,min(cons(N,L))),cons(N,L))</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><DAG approx="simpl"><CCLIST><NONSCC num="0"><NODE ref="0"/></NONSCC></CCLIST></DAG></CRITERION></PROPERTY></PROPERTY><PROPERTY criterion="sterm" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>eq(0,0)</LHS><RHS>true</RHS></RULE><RULE><LHS>eq(0,s(Y))</LHS><RHS>false</RHS></RULE><RULE><LHS>eq(s(X),0)</LHS><RHS>false</RHS></RULE><RULE><LHS>eq(s(X),s(Y))</LHS><RHS>eq(X,Y)</RHS></RULE><RULE><LHS>le(0,Y)</LHS><RHS>true</RHS></RULE><RULE><LHS>le(s(X),0)</LHS><RHS>false</RHS></RULE><RULE><LHS>le(s(X),s(Y))</LHS><RHS>le(X,Y)</RHS></RULE><RULE><LHS>min(cons(0,nil))</LHS><RHS>0</RHS></RULE><RULE><LHS>min(cons(s(N),nil))</LHS><RHS>s(N)</RHS></RULE><RULE><LHS>min(cons(N,cons(M,L)))</LHS><RHS>ifmin(le(N,M),cons(N,cons(M,L)))</RHS></RULE><RULE><LHS>ifmin(true,cons(N,cons(M,L)))</LHS><RHS>min(cons(N,L))</RHS></RULE><RULE><LHS>ifmin(false,cons(N,cons(M,L)))</LHS><RHS>min(cons(M,L))</RHS></RULE><RULE><LHS>replace(N,M,nil)</LHS><RHS>nil</RHS></RULE><RULE><LHS>replace(N,M,cons(K,L))</LHS><RHS>ifrepl(eq(N,K),N,M,cons(K,L))</RHS></RULE><RULE><LHS>ifrepl(true,N,M,cons(K,L))</LHS><RHS>cons(M,L)</RHS></RULE><RULE><LHS>ifrepl(false,N,M,cons(K,L))</LHS><RHS>cons(K,replace(N,M,L))</RHS></RULE><RULE><LHS>selsort(nil)</LHS><RHS>nil</RHS></RULE><RULE><LHS>selsort(cons(N,L))</LHS><RHS>ifselsort(eq(N,min(cons(N,L))),cons(N,L))</RHS></RULE><RULE><LHS>ifselsort(true,cons(N,L))</LHS><RHS>cons(N,selsort(L))</RHS></RULE><RULE><LHS>ifselsort(false,cons(N,L))</LHS><RHS>cons(min(cons(N,L)),selsort(replace(min(cons(N,L)),N,L)))</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_replace(N,M,cons(K,L))</LHS><RHS>Marked_ifrepl(eq(N,K),N,M,cons(K,L))</RHS></DPRULE><DPRULE num="1"><LHS>Marked_ifrepl(false,N,M,cons(K,L))</LHS><RHS>Marked_replace(N,M,L)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><PROJECTION><PROJ><SYMBOL><NAME>Marked_ifrepl</NAME></SYMBOL><INT>4</INT></PROJ><PROJ><SYMBOL><NAME>Marked_replace</NAME></SYMBOL><INT>3</INT></PROJ></PROJECTION><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_ifrepl(false,N,M,cons(K,L))</LHS><RHS>Marked_replace(N,M,L)</RHS></DPRULE></DPLIST></STRICTPAIRS><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>eq(0,0)</LHS><RHS>true</RHS></RULE><RULE><LHS>eq(0,s(Y))</LHS><RHS>false</RHS></RULE><RULE><LHS>eq(s(X),0)</LHS><RHS>false</RHS></RULE><RULE><LHS>eq(s(X),s(Y))</LHS><RHS>eq(X,Y)</RHS></RULE><RULE><LHS>le(0,Y)</LHS><RHS>true</RHS></RULE><RULE><LHS>le(s(X),0)</LHS><RHS>false</RHS></RULE><RULE><LHS>le(s(X),s(Y))</LHS><RHS>le(X,Y)</RHS></RULE><RULE><LHS>min(cons(0,nil))</LHS><RHS>0</RHS></RULE><RULE><LHS>min(cons(s(N),nil))</LHS><RHS>s(N)</RHS></RULE><RULE><LHS>min(cons(N,cons(M,L)))</LHS><RHS>ifmin(le(N,M),cons(N,cons(M,L)))</RHS></RULE><RULE><LHS>ifmin(true,cons(N,cons(M,L)))</LHS><RHS>min(cons(N,L))</RHS></RULE><RULE><LHS>ifmin(false,cons(N,cons(M,L)))</LHS><RHS>min(cons(M,L))</RHS></RULE><RULE><LHS>replace(N,M,nil)</LHS><RHS>nil</RHS></RULE><RULE><LHS>replace(N,M,cons(K,L))</LHS><RHS>ifrepl(eq(N,K),N,M,cons(K,L))</RHS></RULE><RULE><LHS>ifrepl(true,N,M,cons(K,L))</LHS><RHS>cons(M,L)</RHS></RULE><RULE><LHS>ifrepl(false,N,M,cons(K,L))</LHS><RHS>cons(K,replace(N,M,L))</RHS></RULE><RULE><LHS>selsort(nil)</LHS><RHS>nil</RHS></RULE><RULE><LHS>selsort(cons(N,L))</LHS><RHS>ifselsort(eq(N,min(cons(N,L))),cons(N,L))</RHS></RULE><RULE><LHS>ifselsort(true,cons(N,L))</LHS><RHS>cons(N,selsort(L))</RHS></RULE><RULE><LHS>ifselsort(false,cons(N,L))</LHS><RHS>cons(min(cons(N,L)),selsort(replace(min(cons(N,L)),N,L)))</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_replace(N,M,cons(K,L))</LHS><RHS>Marked_ifrepl(eq(N,K),N,M,cons(K,L))</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><DAG approx="simpl"><CCLIST><NONSCC num="0"><NODE ref="0"/></NONSCC></CCLIST></DAG></CRITERION></PROPERTY></PROPERTY><PROPERTY criterion="sterm" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>eq(0,0)</LHS><RHS>true</RHS></RULE><RULE><LHS>eq(0,s(Y))</LHS><RHS>false</RHS></RULE><RULE><LHS>eq(s(X),0)</LHS><RHS>false</RHS></RULE><RULE><LHS>eq(s(X),s(Y))</LHS><RHS>eq(X,Y)</RHS></RULE><RULE><LHS>le(0,Y)</LHS><RHS>true</RHS></RULE><RULE><LHS>le(s(X),0)</LHS><RHS>false</RHS></RULE><RULE><LHS>le(s(X),s(Y))</LHS><RHS>le(X,Y)</RHS></RULE><RULE><LHS>min(cons(0,nil))</LHS><RHS>0</RHS></RULE><RULE><LHS>min(cons(s(N),nil))</LHS><RHS>s(N)</RHS></RULE><RULE><LHS>min(cons(N,cons(M,L)))</LHS><RHS>ifmin(le(N,M),cons(N,cons(M,L)))</RHS></RULE><RULE><LHS>ifmin(true,cons(N,cons(M,L)))</LHS><RHS>min(cons(N,L))</RHS></RULE><RULE><LHS>ifmin(false,cons(N,cons(M,L)))</LHS><RHS>min(cons(M,L))</RHS></RULE><RULE><LHS>replace(N,M,nil)</LHS><RHS>nil</RHS></RULE><RULE><LHS>replace(N,M,cons(K,L))</LHS><RHS>ifrepl(eq(N,K),N,M,cons(K,L))</RHS></RULE><RULE><LHS>ifrepl(true,N,M,cons(K,L))</LHS><RHS>cons(M,L)</RHS></RULE><RULE><LHS>ifrepl(false,N,M,cons(K,L))</LHS><RHS>cons(K,replace(N,M,L))</RHS></RULE><RULE><LHS>selsort(nil)</LHS><RHS>nil</RHS></RULE><RULE><LHS>selsort(cons(N,L))</LHS><RHS>ifselsort(eq(N,min(cons(N,L))),cons(N,L))</RHS></RULE><RULE><LHS>ifselsort(true,cons(N,L))</LHS><RHS>cons(N,selsort(L))</RHS></RULE><RULE><LHS>ifselsort(false,cons(N,L))</LHS><RHS>cons(min(cons(N,L)),selsort(replace(min(cons(N,L)),N,L)))</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_eq(s(X),s(Y))</LHS><RHS>Marked_eq(X,Y)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><PROJECTION><PROJ><SYMBOL><NAME>Marked_eq</NAME></SYMBOL><INT>1</INT></PROJ></PROJECTION><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_eq(s(X),s(Y))</LHS><RHS>Marked_eq(X,Y)</RHS></DPRULE></DPLIST></STRICTPAIRS><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>eq(0,0)</LHS><RHS>true</RHS></RULE><RULE><LHS>eq(0,s(Y))</LHS><RHS>false</RHS></RULE><RULE><LHS>eq(s(X),0)</LHS><RHS>false</RHS></RULE><RULE><LHS>eq(s(X),s(Y))</LHS><RHS>eq(X,Y)</RHS></RULE><RULE><LHS>le(0,Y)</LHS><RHS>true</RHS></RULE><RULE><LHS>le(s(X),0)</LHS><RHS>false</RHS></RULE><RULE><LHS>le(s(X),s(Y))</LHS><RHS>le(X,Y)</RHS></RULE><RULE><LHS>min(cons(0,nil))</LHS><RHS>0</RHS></RULE><RULE><LHS>min(cons(s(N),nil))</LHS><RHS>s(N)</RHS></RULE><RULE><LHS>min(cons(N,cons(M,L)))</LHS><RHS>ifmin(le(N,M),cons(N,cons(M,L)))</RHS></RULE><RULE><LHS>ifmin(true,cons(N,cons(M,L)))</LHS><RHS>min(cons(N,L))</RHS></RULE><RULE><LHS>ifmin(false,cons(N,cons(M,L)))</LHS><RHS>min(cons(M,L))</RHS></RULE><RULE><LHS>replace(N,M,nil)</LHS><RHS>nil</RHS></RULE><RULE><LHS>replace(N,M,cons(K,L))</LHS><RHS>ifrepl(eq(N,K),N,M,cons(K,L))</RHS></RULE><RULE><LHS>ifrepl(true,N,M,cons(K,L))</LHS><RHS>cons(M,L)</RHS></RULE><RULE><LHS>ifrepl(false,N,M,cons(K,L))</LHS><RHS>cons(K,replace(N,M,L))</RHS></RULE><RULE><LHS>selsort(nil)</LHS><RHS>nil</RHS></RULE><RULE><LHS>selsort(cons(N,L))</LHS><RHS>ifselsort(eq(N,min(cons(N,L))),cons(N,L))</RHS></RULE><RULE><LHS>ifselsort(true,cons(N,L))</LHS><RHS>cons(N,selsort(L))</RHS></RULE><RULE><LHS>ifselsort(false,cons(N,L))</LHS><RHS>cons(min(cons(N,L)),selsort(replace(min(cons(N,L)),N,L)))</RHS></RULE></REWSYS><DPLIST/></DPSYS></SYSTEM><CRITERION><DAG approx="simpl"><CCLIST/></DAG></CRITERION></PROPERTY></PROPERTY><PROPERTY criterion="stronggraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>eq(0,0)</LHS><RHS>true</RHS></RULE><RULE><LHS>eq(0,s(Y))</LHS><RHS>false</RHS></RULE><RULE><LHS>eq(s(X),0)</LHS><RHS>false</RHS></RULE><RULE><LHS>eq(s(X),s(Y))</LHS><RHS>eq(X,Y)</RHS></RULE><RULE><LHS>le(0,Y)</LHS><RHS>true</RHS></RULE><RULE><LHS>le(s(X),0)</LHS><RHS>false</RHS></RULE><RULE><LHS>le(s(X),s(Y))</LHS><RHS>le(X,Y)</RHS></RULE><RULE><LHS>min(cons(0,nil))</LHS><RHS>0</RHS></RULE><RULE><LHS>min(cons(s(N),nil))</LHS><RHS>s(N)</RHS></RULE><RULE><LHS>min(cons(N,cons(M,L)))</LHS><RHS>ifmin(le(N,M),cons(N,cons(M,L)))</RHS></RULE><RULE><LHS>ifmin(true,cons(N,cons(M,L)))</LHS><RHS>min(cons(N,L))</RHS></RULE><RULE><LHS>ifmin(false,cons(N,cons(M,L)))</LHS><RHS>min(cons(M,L))</RHS></RULE><RULE><LHS>replace(N,M,nil)</LHS><RHS>nil</RHS></RULE><RULE><LHS>replace(N,M,cons(K,L))</LHS><RHS>ifrepl(eq(N,K),N,M,cons(K,L))</RHS></RULE><RULE><LHS>ifrepl(true,N,M,cons(K,L))</LHS><RHS>cons(M,L)</RHS></RULE><RULE><LHS>ifrepl(false,N,M,cons(K,L))</LHS><RHS>cons(K,replace(N,M,L))</RHS></RULE><RULE><LHS>selsort(nil)</LHS><RHS>nil</RHS></RULE><RULE><LHS>selsort(cons(N,L))</LHS><RHS>ifselsort(eq(N,min(cons(N,L))),cons(N,L))</RHS></RULE><RULE><LHS>ifselsort(true,cons(N,L))</LHS><RHS>cons(N,selsort(L))</RHS></RULE><RULE><LHS>ifselsort(false,cons(N,L))</LHS><RHS>cons(min(cons(N,L)),selsort(replace(min(cons(N,L)),N,L)))</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_min(cons(N,cons(M,L)))</LHS><RHS>Marked_ifmin(le(N,M),cons(N,cons(M,L)))</RHS></DPRULE><DPRULE num="1"><LHS>Marked_ifmin(true,cons(N,cons(M,L)))</LHS><RHS>Marked_min(cons(N,L))</RHS></DPRULE><DPRULE num="2"><LHS>Marked_ifmin(false,cons(N,cons(M,L)))</LHS><RHS>Marked_min(cons(M,L))</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><ORDERING type="poly"><POLYSYMB><SYMBOL><NAME>true</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>nil</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>s</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>Marked_ifmin</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>selsort</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>0</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>replace</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="2"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>min</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>eq</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>ifmin</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>le</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>ifselsort</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>false</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>ifrepl</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="3"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>cons</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>Marked_min</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></ORDERING><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_min(cons(N,cons(M,L)))</LHS><RHS>Marked_ifmin(le(N,M),cons(N,cons(M,L)))</RHS></DPRULE></DPLIST></STRICTPAIRS></CRITERION><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>eq(0,0)</LHS><RHS>true</RHS></RULE><RULE><LHS>eq(0,s(Y))</LHS><RHS>false</RHS></RULE><RULE><LHS>eq(s(X),0)</LHS><RHS>false</RHS></RULE><RULE><LHS>eq(s(X),s(Y))</LHS><RHS>eq(X,Y)</RHS></RULE><RULE><LHS>le(0,Y)</LHS><RHS>true</RHS></RULE><RULE><LHS>le(s(X),0)</LHS><RHS>false</RHS></RULE><RULE><LHS>le(s(X),s(Y))</LHS><RHS>le(X,Y)</RHS></RULE><RULE><LHS>min(cons(0,nil))</LHS><RHS>0</RHS></RULE><RULE><LHS>min(cons(s(N),nil))</LHS><RHS>s(N)</RHS></RULE><RULE><LHS>min(cons(N,cons(M,L)))</LHS><RHS>ifmin(le(N,M),cons(N,cons(M,L)))</RHS></RULE><RULE><LHS>ifmin(true,cons(N,cons(M,L)))</LHS><RHS>min(cons(N,L))</RHS></RULE><RULE><LHS>ifmin(false,cons(N,cons(M,L)))</LHS><RHS>min(cons(M,L))</RHS></RULE><RULE><LHS>replace(N,M,nil)</LHS><RHS>nil</RHS></RULE><RULE><LHS>replace(N,M,cons(K,L))</LHS><RHS>ifrepl(eq(N,K),N,M,cons(K,L))</RHS></RULE><RULE><LHS>ifrepl(true,N,M,cons(K,L))</LHS><RHS>cons(M,L)</RHS></RULE><RULE><LHS>ifrepl(false,N,M,cons(K,L))</LHS><RHS>cons(K,replace(N,M,L))</RHS></RULE><RULE><LHS>selsort(nil)</LHS><RHS>nil</RHS></RULE><RULE><LHS>selsort(cons(N,L))</LHS><RHS>ifselsort(eq(N,min(cons(N,L))),cons(N,L))</RHS></RULE><RULE><LHS>ifselsort(true,cons(N,L))</LHS><RHS>cons(N,selsort(L))</RHS></RULE><RULE><LHS>ifselsort(false,cons(N,L))</LHS><RHS>cons(min(cons(N,L)),selsort(replace(min(cons(N,L)),N,L)))</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_ifmin(true,cons(N,cons(M,L)))</LHS><RHS>Marked_min(cons(N,L))</RHS></DPRULE><DPRULE num="1"><LHS>Marked_ifmin(false,cons(N,cons(M,L)))</LHS><RHS>Marked_min(cons(M,L))</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><DAG approx="simpl"><CCLIST><NONSCC num="0"><NODE ref="1"/></NONSCC><NONSCC num="1"><NODE ref="0"/></NONSCC></CCLIST></DAG></CRITERION></PROPERTY></PROPERTY><PROPERTY criterion="sterm" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>eq(0,0)</LHS><RHS>true</RHS></RULE><RULE><LHS>eq(0,s(Y))</LHS><RHS>false</RHS></RULE><RULE><LHS>eq(s(X),0)</LHS><RHS>false</RHS></RULE><RULE><LHS>eq(s(X),s(Y))</LHS><RHS>eq(X,Y)</RHS></RULE><RULE><LHS>le(0,Y)</LHS><RHS>true</RHS></RULE><RULE><LHS>le(s(X),0)</LHS><RHS>false</RHS></RULE><RULE><LHS>le(s(X),s(Y))</LHS><RHS>le(X,Y)</RHS></RULE><RULE><LHS>min(cons(0,nil))</LHS><RHS>0</RHS></RULE><RULE><LHS>min(cons(s(N),nil))</LHS><RHS>s(N)</RHS></RULE><RULE><LHS>min(cons(N,cons(M,L)))</LHS><RHS>ifmin(le(N,M),cons(N,cons(M,L)))</RHS></RULE><RULE><LHS>ifmin(true,cons(N,cons(M,L)))</LHS><RHS>min(cons(N,L))</RHS></RULE><RULE><LHS>ifmin(false,cons(N,cons(M,L)))</LHS><RHS>min(cons(M,L))</RHS></RULE><RULE><LHS>replace(N,M,nil)</LHS><RHS>nil</RHS></RULE><RULE><LHS>replace(N,M,cons(K,L))</LHS><RHS>ifrepl(eq(N,K),N,M,cons(K,L))</RHS></RULE><RULE><LHS>ifrepl(true,N,M,cons(K,L))</LHS><RHS>cons(M,L)</RHS></RULE><RULE><LHS>ifrepl(false,N,M,cons(K,L))</LHS><RHS>cons(K,replace(N,M,L))</RHS></RULE><RULE><LHS>selsort(nil)</LHS><RHS>nil</RHS></RULE><RULE><LHS>selsort(cons(N,L))</LHS><RHS>ifselsort(eq(N,min(cons(N,L))),cons(N,L))</RHS></RULE><RULE><LHS>ifselsort(true,cons(N,L))</LHS><RHS>cons(N,selsort(L))</RHS></RULE><RULE><LHS>ifselsort(false,cons(N,L))</LHS><RHS>cons(min(cons(N,L)),selsort(replace(min(cons(N,L)),N,L)))</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_le(s(X),s(Y))</LHS><RHS>Marked_le(X,Y)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><PROJECTION><PROJ><SYMBOL><NAME>Marked_le</NAME></SYMBOL><INT>1</INT></PROJ></PROJECTION><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_le(s(X),s(Y))</LHS><RHS>Marked_le(X,Y)</RHS></DPRULE></DPLIST></STRICTPAIRS><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>eq(0,0)</LHS><RHS>true</RHS></RULE><RULE><LHS>eq(0,s(Y))</LHS><RHS>false</RHS></RULE><RULE><LHS>eq(s(X),0)</LHS><RHS>false</RHS></RULE><RULE><LHS>eq(s(X),s(Y))</LHS><RHS>eq(X,Y)</RHS></RULE><RULE><LHS>le(0,Y)</LHS><RHS>true</RHS></RULE><RULE><LHS>le(s(X),0)</LHS><RHS>false</RHS></RULE><RULE><LHS>le(s(X),s(Y))</LHS><RHS>le(X,Y)</RHS></RULE><RULE><LHS>min(cons(0,nil))</LHS><RHS>0</RHS></RULE><RULE><LHS>min(cons(s(N),nil))</LHS><RHS>s(N)</RHS></RULE><RULE><LHS>min(cons(N,cons(M,L)))</LHS><RHS>ifmin(le(N,M),cons(N,cons(M,L)))</RHS></RULE><RULE><LHS>ifmin(true,cons(N,cons(M,L)))</LHS><RHS>min(cons(N,L))</RHS></RULE><RULE><LHS>ifmin(false,cons(N,cons(M,L)))</LHS><RHS>min(cons(M,L))</RHS></RULE><RULE><LHS>replace(N,M,nil)</LHS><RHS>nil</RHS></RULE><RULE><LHS>replace(N,M,cons(K,L))</LHS><RHS>ifrepl(eq(N,K),N,M,cons(K,L))</RHS></RULE><RULE><LHS>ifrepl(true,N,M,cons(K,L))</LHS><RHS>cons(M,L)</RHS></RULE><RULE><LHS>ifrepl(false,N,M,cons(K,L))</LHS><RHS>cons(K,replace(N,M,L))</RHS></RULE><RULE><LHS>selsort(nil)</LHS><RHS>nil</RHS></RULE><RULE><LHS>selsort(cons(N,L))</LHS><RHS>ifselsort(eq(N,min(cons(N,L))),cons(N,L))</RHS></RULE><RULE><LHS>ifselsort(true,cons(N,L))</LHS><RHS>cons(N,selsort(L))</RHS></RULE><RULE><LHS>ifselsort(false,cons(N,L))</LHS><RHS>cons(min(cons(N,L)),selsort(replace(min(cons(N,L)),N,L)))</RHS></RULE></REWSYS><DPLIST/></DPSYS></SYSTEM><CRITERION><DAG approx="simpl"><CCLIST/></DAG></CRITERION></PROPERTY></PROPERTY></PROPERTY></PROPERTY></PROOF>
