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