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<!DOCTYPE PROOF SYSTEM "http://a3pat.ensiie.fr/pub/a3pat.dtd">
<PROOF><SIGNATURE><SYMBOLLIST><SYMBOL arity="1" unmarked=""><NAME>f</NAME></SYMBOL><SYMBOL arity="1" unmarked="minus"><NAME>Marked_minus</NAME></SYMBOL><SYMBOL arity="2" unmarked=""><NAME> *</NAME></SYMBOL><SYMBOL arity="2" unmarked=""><NAME>+</NAME></SYMBOL><SYMBOL arity="1" unmarked="f"><NAME>Marked_f</NAME></SYMBOL><SYMBOL arity="1" 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(minus(x))</LHS><RHS>x</RHS></RULE><RULE><LHS>minus(+(x,y))</LHS><RHS> *(minus(minus(minus(x))),minus(minus(minus(y))))</RHS></RULE><RULE><LHS>minus( *(x,y))</LHS><RHS>+(minus(minus(minus(x))),minus(minus(minus(y))))</RHS></RULE><RULE><LHS>f(minus(x))</LHS><RHS>minus(minus(minus(f(x))))</RHS></RULE></REWSYS></SYSTEM><CRITERION/><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>minus(minus(x))</LHS><RHS>x</RHS></RULE><RULE><LHS>minus(+(x,y))</LHS><RHS> *(minus(minus(minus(x))),minus(minus(minus(y))))</RHS></RULE><RULE><LHS>minus( *(x,y))</LHS><RHS>+(minus(minus(minus(x))),minus(minus(minus(y))))</RHS></RULE><RULE><LHS>f(minus(x))</LHS><RHS>minus(minus(minus(f(x))))</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_minus(+(x,y))</LHS><RHS>Marked_minus(minus(minus(x)))</RHS></DPRULE><DPRULE num="1"><LHS>Marked_minus(+(x,y))</LHS><RHS>Marked_minus(minus(x))</RHS></DPRULE><DPRULE num="2"><LHS>Marked_minus(+(x,y))</LHS><RHS>Marked_minus(x)</RHS></DPRULE><DPRULE num="3"><LHS>Marked_minus(+(x,y))</LHS><RHS>Marked_minus(minus(minus(y)))</RHS></DPRULE><DPRULE num="4"><LHS>Marked_minus(+(x,y))</LHS><RHS>Marked_minus(minus(y))</RHS></DPRULE><DPRULE num="5"><LHS>Marked_minus(+(x,y))</LHS><RHS>Marked_minus(y)</RHS></DPRULE><DPRULE num="6"><LHS>Marked_minus( *(x,y))</LHS><RHS>Marked_minus(minus(minus(x)))</RHS></DPRULE><DPRULE num="7"><LHS>Marked_minus( *(x,y))</LHS><RHS>Marked_minus(minus(x))</RHS></DPRULE><DPRULE num="8"><LHS>Marked_minus( *(x,y))</LHS><RHS>Marked_minus(x)</RHS></DPRULE><DPRULE num="9"><LHS>Marked_minus( *(x,y))</LHS><RHS>Marked_minus(minus(minus(y)))</RHS></DPRULE><DPRULE num="10"><LHS>Marked_minus( *(x,y))</LHS><RHS>Marked_minus(minus(y))</RHS></DPRULE><DPRULE num="11"><LHS>Marked_minus( *(x,y))</LHS><RHS>Marked_minus(y)</RHS></DPRULE><DPRULE num="12"><LHS>Marked_f(minus(x))</LHS><RHS>Marked_minus(minus(minus(f(x))))</RHS></DPRULE><DPRULE num="13"><LHS>Marked_f(minus(x))</LHS><RHS>Marked_minus(minus(f(x)))</RHS></DPRULE><DPRULE num="14"><LHS>Marked_f(minus(x))</LHS><RHS>Marked_minus(f(x))</RHS></DPRULE><DPRULE num="15"><LHS>Marked_f(minus(x))</LHS><RHS>Marked_f(x)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><DAG approx="simpl"><CCLIST><SCC num="0"><NODE ref="15"/></SCC><NONSCC num="1"><NODE ref="14"/></NONSCC><NONSCC num="2"><NODE ref="13"/></NONSCC><NONSCC num="3"><NODE ref="12"/></NONSCC><SCC num="4"><NODE ref="0"/><NODE ref="1"/><NODE ref="2"/><NODE ref="3"/><NODE ref="4"/><NODE ref="5"/><NODE ref="6"/><NODE ref="7"/><NODE ref="8"/><NODE ref="9"/><NODE ref="10"/><NODE ref="11"/></SCC></CCLIST><EDGE end="3" start="0"/><EDGE end="2" start="0"/><EDGE end="1" start="0"/><EDGE end="4" start="1"/><EDGE end="4" start="2"/><EDGE end="4" start="3"/></DAG></CRITERION><PROPERTY criterion="ordering" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>minus(minus(x))</LHS><RHS>x</RHS></RULE><RULE><LHS>minus(+(x,y))</LHS><RHS> *(minus(minus(minus(x))),minus(minus(minus(y))))</RHS></RULE><RULE><LHS>minus( *(x,y))</LHS><RHS>+(minus(minus(minus(x))),minus(minus(minus(y))))</RHS></RULE><RULE><LHS>f(minus(x))</LHS><RHS>minus(minus(minus(f(x))))</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_f(minus(x))</LHS><RHS>Marked_f(x)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><ORDERING type="poly"><POLYSYMB><SYMBOL><NAME>minus</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><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>Marked_f</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>+</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME> *</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>f</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></ORDERING></CRITERION></PROPERTY><PROPERTY criterion="ordering" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>minus(minus(x))</LHS><RHS>x</RHS></RULE><RULE><LHS>minus(+(x,y))</LHS><RHS> *(minus(minus(minus(x))),minus(minus(minus(y))))</RHS></RULE><RULE><LHS>minus( *(x,y))</LHS><RHS>+(minus(minus(minus(x))),minus(minus(minus(y))))</RHS></RULE><RULE><LHS>f(minus(x))</LHS><RHS>minus(minus(minus(f(x))))</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_minus(+(x,y))</LHS><RHS>Marked_minus(minus(minus(x)))</RHS></DPRULE><DPRULE num="1"><LHS>Marked_minus(+(x,y))</LHS><RHS>Marked_minus(minus(x))</RHS></DPRULE><DPRULE num="2"><LHS>Marked_minus(+(x,y))</LHS><RHS>Marked_minus(x)</RHS></DPRULE><DPRULE num="3"><LHS>Marked_minus(+(x,y))</LHS><RHS>Marked_minus(minus(minus(y)))</RHS></DPRULE><DPRULE num="4"><LHS>Marked_minus(+(x,y))</LHS><RHS>Marked_minus(minus(y))</RHS></DPRULE><DPRULE num="5"><LHS>Marked_minus(+(x,y))</LHS><RHS>Marked_minus(y)</RHS></DPRULE><DPRULE num="6"><LHS>Marked_minus( *(x,y))</LHS><RHS>Marked_minus(minus(minus(x)))</RHS></DPRULE><DPRULE num="7"><LHS>Marked_minus( *(x,y))</LHS><RHS>Marked_minus(minus(x))</RHS></DPRULE><DPRULE num="8"><LHS>Marked_minus( *(x,y))</LHS><RHS>Marked_minus(x)</RHS></DPRULE><DPRULE num="9"><LHS>Marked_minus( *(x,y))</LHS><RHS>Marked_minus(minus(minus(y)))</RHS></DPRULE><DPRULE num="10"><LHS>Marked_minus( *(x,y))</LHS><RHS>Marked_minus(minus(y))</RHS></DPRULE><DPRULE num="11"><LHS>Marked_minus( *(x,y))</LHS><RHS>Marked_minus(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>+</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><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></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>2</INT></COEF><ARG degree="1" num="0"/></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></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>Marked_minus</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>f</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB></ORDERING></CRITERION></PROPERTY></PROPERTY></PROPERTY></PROOF>
