<?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>++</NAME></SYMBOL><SYMBOL arity="1" unmarked=""><NAME>rev</NAME></SYMBOL><SYMBOL arity="0" unmarked=""><NAME>b</NAME></SYMBOL><SYMBOL arity="1" unmarked="rev"><NAME>Marked_rev</NAME></SYMBOL><SYMBOL arity="0" unmarked=""><NAME>a</NAME></SYMBOL></SYMBOLLIST><VARLIST><VAR>z</VAR><VAR>y</VAR><VAR>x</VAR></VARLIST></SIGNATURE><PROPERTY criterion="dp" prop="sntrs"><SYSTEM><REWSYS><RULE><LHS>rev(a)</LHS><RHS>a</RHS></RULE><RULE><LHS>rev(b)</LHS><RHS>b</RHS></RULE><RULE><LHS>rev(++(x,y))</LHS><RHS>++(rev(y),rev(x))</RHS></RULE><RULE><LHS>rev(++(x,x))</LHS><RHS>rev(x)</RHS></RULE></REWSYS></SYSTEM><CRITERION/><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>rev(a)</LHS><RHS>a</RHS></RULE><RULE><LHS>rev(b)</LHS><RHS>b</RHS></RULE><RULE><LHS>rev(++(x,y))</LHS><RHS>++(rev(y),rev(x))</RHS></RULE><RULE><LHS>rev(++(x,x))</LHS><RHS>rev(x)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_rev(++(x,y))</LHS><RHS>Marked_rev(y)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_rev(++(x,y))</LHS><RHS>Marked_rev(x)</RHS></DPRULE><DPRULE num="2"><LHS>Marked_rev(++(x,x))</LHS><RHS>Marked_rev(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="ordering" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>rev(a)</LHS><RHS>a</RHS></RULE><RULE><LHS>rev(b)</LHS><RHS>b</RHS></RULE><RULE><LHS>rev(++(x,y))</LHS><RHS>++(rev(y),rev(x))</RHS></RULE><RULE><LHS>rev(++(x,x))</LHS><RHS>rev(x)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_rev(++(x,y))</LHS><RHS>Marked_rev(y)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_rev(++(x,y))</LHS><RHS>Marked_rev(x)</RHS></DPRULE><DPRULE num="2"><LHS>Marked_rev(++(x,x))</LHS><RHS>Marked_rev(x)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><ORDERING type="poly"><POLYSYMB><SYMBOL><NAME>a</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>Marked_rev</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>b</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>rev</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>++</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>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></ORDERING></CRITERION></PROPERTY></PROPERTY></PROPERTY></PROOF>
