<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE PROOF SYSTEM "http://a3pat.ensiie.fr/pub/a3pat.dtd">
<PROOF><SIGNATURE><SYMBOLLIST><SYMBOL arity="2" unmarked="int"><NAME>Marked_int</NAME></SYMBOL><SYMBOL arity="1" unmarked=""><NAME>s</NAME></SYMBOL><SYMBOL arity="2" unmarked=""><NAME>cons</NAME></SYMBOL><SYMBOL arity="1" unmarked=""><NAME>intlist</NAME></SYMBOL><SYMBOL arity="1" unmarked="intlist"><NAME>Marked_intlist</NAME></SYMBOL><SYMBOL arity="2" unmarked=""><NAME>int</NAME></SYMBOL><SYMBOL arity="0" unmarked=""><NAME>0</NAME></SYMBOL><SYMBOL arity="0" unmarked=""><NAME>nil</NAME></SYMBOL></SYMBOLLIST><VARLIST><VAR>y</VAR><VAR>x</VAR></VARLIST></SIGNATURE><PROPERTY criterion="dp" prop="sntrs"><SYSTEM><REWSYS><RULE><LHS>intlist(nil)</LHS><RHS>nil</RHS></RULE><RULE><LHS>int(s(x),0)</LHS><RHS>nil</RHS></RULE><RULE><LHS>int(x,x)</LHS><RHS>cons(x,nil)</RHS></RULE><RULE><LHS>intlist(cons(x,y))</LHS><RHS>cons(s(x),intlist(y))</RHS></RULE><RULE><LHS>int(s(x),s(y))</LHS><RHS>intlist(int(x,y))</RHS></RULE><RULE><LHS>int(0,s(y))</LHS><RHS>cons(0,int(s(0),s(y)))</RHS></RULE><RULE><LHS>intlist(cons(x,nil))</LHS><RHS>cons(s(x),nil)</RHS></RULE></REWSYS></SYSTEM><CRITERION/><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>intlist(nil)</LHS><RHS>nil</RHS></RULE><RULE><LHS>int(s(x),0)</LHS><RHS>nil</RHS></RULE><RULE><LHS>int(x,x)</LHS><RHS>cons(x,nil)</RHS></RULE><RULE><LHS>intlist(cons(x,y))</LHS><RHS>cons(s(x),intlist(y))</RHS></RULE><RULE><LHS>int(s(x),s(y))</LHS><RHS>intlist(int(x,y))</RHS></RULE><RULE><LHS>int(0,s(y))</LHS><RHS>cons(0,int(s(0),s(y)))</RHS></RULE><RULE><LHS>intlist(cons(x,nil))</LHS><RHS>cons(s(x),nil)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_intlist(cons(x,y))</LHS><RHS>Marked_intlist(y)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_int(s(x),s(y))</LHS><RHS>Marked_intlist(int(x,y))</RHS></DPRULE><DPRULE num="2"><LHS>Marked_int(s(x),s(y))</LHS><RHS>Marked_int(x,y)</RHS></DPRULE><DPRULE num="3"><LHS>Marked_int(0,s(y))</LHS><RHS>Marked_int(s(0),s(y))</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><DAG approx="simpl"><CCLIST><SCC num="0"><NODE ref="2"/><NODE ref="3"/></SCC><NONSCC num="1"><NODE ref="1"/></NONSCC><SCC num="2"><NODE ref="0"/></SCC></CCLIST><EDGE end="1" start="0"/><EDGE end="2" start="1"/></DAG></CRITERION><PROPERTY criterion="sterm" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>intlist(nil)</LHS><RHS>nil</RHS></RULE><RULE><LHS>int(s(x),0)</LHS><RHS>nil</RHS></RULE><RULE><LHS>int(x,x)</LHS><RHS>cons(x,nil)</RHS></RULE><RULE><LHS>intlist(cons(x,y))</LHS><RHS>cons(s(x),intlist(y))</RHS></RULE><RULE><LHS>int(s(x),s(y))</LHS><RHS>intlist(int(x,y))</RHS></RULE><RULE><LHS>int(0,s(y))</LHS><RHS>cons(0,int(s(0),s(y)))</RHS></RULE><RULE><LHS>intlist(cons(x,nil))</LHS><RHS>cons(s(x),nil)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_int(s(x),s(y))</LHS><RHS>Marked_int(x,y)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_int(0,s(y))</LHS><RHS>Marked_int(s(0),s(y))</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><PROJECTION><PROJ><SYMBOL><NAME>Marked_int</NAME></SYMBOL><INT>2</INT></PROJ></PROJECTION><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_int(s(x),s(y))</LHS><RHS>Marked_int(x,y)</RHS></DPRULE></DPLIST></STRICTPAIRS><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>intlist(nil)</LHS><RHS>nil</RHS></RULE><RULE><LHS>int(s(x),0)</LHS><RHS>nil</RHS></RULE><RULE><LHS>int(x,x)</LHS><RHS>cons(x,nil)</RHS></RULE><RULE><LHS>intlist(cons(x,y))</LHS><RHS>cons(s(x),intlist(y))</RHS></RULE><RULE><LHS>int(s(x),s(y))</LHS><RHS>intlist(int(x,y))</RHS></RULE><RULE><LHS>int(0,s(y))</LHS><RHS>cons(0,int(s(0),s(y)))</RHS></RULE><RULE><LHS>intlist(cons(x,nil))</LHS><RHS>cons(s(x),nil)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_int(0,s(y))</LHS><RHS>Marked_int(s(0),s(y))</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>intlist(nil)</LHS><RHS>nil</RHS></RULE><RULE><LHS>int(s(x),0)</LHS><RHS>nil</RHS></RULE><RULE><LHS>int(x,x)</LHS><RHS>cons(x,nil)</RHS></RULE><RULE><LHS>intlist(cons(x,y))</LHS><RHS>cons(s(x),intlist(y))</RHS></RULE><RULE><LHS>int(s(x),s(y))</LHS><RHS>intlist(int(x,y))</RHS></RULE><RULE><LHS>int(0,s(y))</LHS><RHS>cons(0,int(s(0),s(y)))</RHS></RULE><RULE><LHS>intlist(cons(x,nil))</LHS><RHS>cons(s(x),nil)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_intlist(cons(x,y))</LHS><RHS>Marked_intlist(y)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><PROJECTION><PROJ><SYMBOL><NAME>Marked_intlist</NAME></SYMBOL><INT>1</INT></PROJ></PROJECTION><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_intlist(cons(x,y))</LHS><RHS>Marked_intlist(y)</RHS></DPRULE></DPLIST></STRICTPAIRS><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>intlist(nil)</LHS><RHS>nil</RHS></RULE><RULE><LHS>int(s(x),0)</LHS><RHS>nil</RHS></RULE><RULE><LHS>int(x,x)</LHS><RHS>cons(x,nil)</RHS></RULE><RULE><LHS>intlist(cons(x,y))</LHS><RHS>cons(s(x),intlist(y))</RHS></RULE><RULE><LHS>int(s(x),s(y))</LHS><RHS>intlist(int(x,y))</RHS></RULE><RULE><LHS>int(0,s(y))</LHS><RHS>cons(0,int(s(0),s(y)))</RHS></RULE><RULE><LHS>intlist(cons(x,nil))</LHS><RHS>cons(s(x),nil)</RHS></RULE></REWSYS><DPLIST/></DPSYS></SYSTEM><CRITERION><DAG approx="simpl"><CCLIST/></DAG></CRITERION></PROPERTY></PROPERTY></PROPERTY></PROPERTY></PROOF>
