<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE PROOF SYSTEM "http://a3pat.ensiie.fr/pub/a3pat.dtd">
<PROOF><SIGNATURE><SYMBOLLIST><SYMBOL arity="2" unmarked=""><NAME>quot</NAME></SYMBOL><SYMBOL arity="2" unmarked="minus"><NAME>Marked_minus</NAME></SYMBOL><SYMBOL arity="0" unmarked=""><NAME>0</NAME></SYMBOL><SYMBOL arity="1" unmarked=""><NAME>s</NAME></SYMBOL><SYMBOL arity="2" unmarked="quot"><NAME>Marked_quot</NAME></SYMBOL><SYMBOL arity="2" unmarked=""><NAME>minus</NAME></SYMBOL></SYMBOLLIST><VARLIST><VAR>y</VAR><VAR>x</VAR></VARLIST></SIGNATURE><PROPERTY criterion="dp" prop="sntrs"><SYSTEM><REWSYS><RULE><LHS>minus(x,0)</LHS><RHS>x</RHS></RULE><RULE><LHS>minus(s(x),s(y))</LHS><RHS>minus(x,y)</RHS></RULE><RULE><LHS>quot(0,s(y))</LHS><RHS>0</RHS></RULE><RULE><LHS>quot(s(x),s(y))</LHS><RHS>s(quot(minus(x,y),s(y)))</RHS></RULE></REWSYS></SYSTEM><CRITERION/><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>minus(x,0)</LHS><RHS>x</RHS></RULE><RULE><LHS>minus(s(x),s(y))</LHS><RHS>minus(x,y)</RHS></RULE><RULE><LHS>quot(0,s(y))</LHS><RHS>0</RHS></RULE><RULE><LHS>quot(s(x),s(y))</LHS><RHS>s(quot(minus(x,y),s(y)))</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_minus(s(x),s(y))</LHS><RHS>Marked_minus(x,y)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_quot(s(x),s(y))</LHS><RHS>Marked_quot(minus(x,y),s(y))</RHS></DPRULE><DPRULE num="2"><LHS>Marked_quot(s(x),s(y))</LHS><RHS>Marked_minus(x,y)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><DAG approx="simpl"><CCLIST><NONSCC num="0"><NODE ref="2"/></NONSCC><SCC num="1"><NODE ref="0"/></SCC><SCC num="2"><NODE ref="1"/></SCC></CCLIST><EDGE end="1" start="0"/><EDGE end="0" start="2"/></DAG></CRITERION><PROPERTY criterion="ordering" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>minus(x,0)</LHS><RHS>x</RHS></RULE><RULE><LHS>minus(s(x),s(y))</LHS><RHS>minus(x,y)</RHS></RULE><RULE><LHS>quot(0,s(y))</LHS><RHS>0</RHS></RULE><RULE><LHS>quot(s(x),s(y))</LHS><RHS>s(quot(minus(x,y),s(y)))</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_quot(s(x),s(y))</LHS><RHS>Marked_quot(minus(x,y),s(y))</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><ORDERING type="poly"><POLYSYMB><SYMBOL><NAME>minus</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_quot</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>s</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>0</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>quot</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></ORDERING></CRITERION></PROPERTY><PROPERTY criterion="sterm" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>minus(x,0)</LHS><RHS>x</RHS></RULE><RULE><LHS>minus(s(x),s(y))</LHS><RHS>minus(x,y)</RHS></RULE><RULE><LHS>quot(0,s(y))</LHS><RHS>0</RHS></RULE><RULE><LHS>quot(s(x),s(y))</LHS><RHS>s(quot(minus(x,y),s(y)))</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_minus(s(x),s(y))</LHS><RHS>Marked_minus(x,y)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><PROJECTION><PROJ><SYMBOL><NAME>Marked_minus</NAME></SYMBOL><INT>1</INT></PROJ></PROJECTION><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_minus(s(x),s(y))</LHS><RHS>Marked_minus(x,y)</RHS></DPRULE></DPLIST></STRICTPAIRS><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>minus(x,0)</LHS><RHS>x</RHS></RULE><RULE><LHS>minus(s(x),s(y))</LHS><RHS>minus(x,y)</RHS></RULE><RULE><LHS>quot(0,s(y))</LHS><RHS>0</RHS></RULE><RULE><LHS>quot(s(x),s(y))</LHS><RHS>s(quot(minus(x,y),s(y)))</RHS></RULE></REWSYS><DPLIST/></DPSYS></SYSTEM><CRITERION><DAG approx="simpl"><CCLIST/></DAG></CRITERION></PROPERTY></PROPERTY></PROPERTY></PROPERTY></PROOF>
