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<!DOCTYPE PROOF SYSTEM "http://a3pat.ensiie.fr/pub/a3pat.dtd">
<PROOF><SIGNATURE><SYMBOLLIST><SYMBOL arity="2" unmarked="-"><NAME>Marked_-</NAME></SYMBOL><SYMBOL arity="1" unmarked=""><NAME>I</NAME></SYMBOL><SYMBOL arity="2" unmarked=""><NAME>-</NAME></SYMBOL><SYMBOL arity="2" unmarked="*"><NAME>Marked_*</NAME></SYMBOL><SYMBOL arity="1" unmarked=""><NAME>O</NAME></SYMBOL><SYMBOL arity="0" unmarked=""><NAME>1</NAME></SYMBOL><SYMBOL arity="2" unmarked="+"><NAME>Marked_+</NAME></SYMBOL><SYMBOL arity="2" unmarked=""><NAME>+</NAME></SYMBOL><SYMBOL arity="2" unmarked=""><NAME> *</NAME></SYMBOL><SYMBOL arity="1" unmarked="O"><NAME>Marked_O</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>O(0)</LHS><RHS>0</RHS></RULE><RULE><LHS>+(0,x)</LHS><RHS>x</RHS></RULE><RULE><LHS>+(x,0)</LHS><RHS>x</RHS></RULE><RULE><LHS>+(O(x),O(y))</LHS><RHS>O(+(x,y))</RHS></RULE><RULE><LHS>+(O(x),I(y))</LHS><RHS>I(+(x,y))</RHS></RULE><RULE><LHS>+(I(x),O(y))</LHS><RHS>I(+(x,y))</RHS></RULE><RULE><LHS>+(I(x),I(y))</LHS><RHS>O(+(+(x,y),I(0)))</RHS></RULE><RULE><LHS> *(0,x)</LHS><RHS>0</RHS></RULE><RULE><LHS> *(x,0)</LHS><RHS>0</RHS></RULE><RULE><LHS> *(O(x),y)</LHS><RHS>O( *(x,y))</RHS></RULE><RULE><LHS> *(I(x),y)</LHS><RHS>+(O( *(x,y)),y)</RHS></RULE><RULE><LHS>-(x,0)</LHS><RHS>x</RHS></RULE><RULE><LHS>-(0,x)</LHS><RHS>0</RHS></RULE><RULE><LHS>-(O(x),O(y))</LHS><RHS>O(-(x,y))</RHS></RULE><RULE><LHS>-(O(x),I(y))</LHS><RHS>I(-(-(x,y),I(1)))</RHS></RULE><RULE><LHS>-(I(x),O(y))</LHS><RHS>I(-(x,y))</RHS></RULE><RULE><LHS>-(I(x),I(y))</LHS><RHS>O(-(x,y))</RHS></RULE></REWSYS></SYSTEM><CRITERION/><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>O(0)</LHS><RHS>0</RHS></RULE><RULE><LHS>+(0,x)</LHS><RHS>x</RHS></RULE><RULE><LHS>+(x,0)</LHS><RHS>x</RHS></RULE><RULE><LHS>+(O(x),O(y))</LHS><RHS>O(+(x,y))</RHS></RULE><RULE><LHS>+(O(x),I(y))</LHS><RHS>I(+(x,y))</RHS></RULE><RULE><LHS>+(I(x),O(y))</LHS><RHS>I(+(x,y))</RHS></RULE><RULE><LHS>+(I(x),I(y))</LHS><RHS>O(+(+(x,y),I(0)))</RHS></RULE><RULE><LHS> *(0,x)</LHS><RHS>0</RHS></RULE><RULE><LHS> *(x,0)</LHS><RHS>0</RHS></RULE><RULE><LHS> *(O(x),y)</LHS><RHS>O( *(x,y))</RHS></RULE><RULE><LHS> *(I(x),y)</LHS><RHS>+(O( *(x,y)),y)</RHS></RULE><RULE><LHS>-(x,0)</LHS><RHS>x</RHS></RULE><RULE><LHS>-(0,x)</LHS><RHS>0</RHS></RULE><RULE><LHS>-(O(x),O(y))</LHS><RHS>O(-(x,y))</RHS></RULE><RULE><LHS>-(O(x),I(y))</LHS><RHS>I(-(-(x,y),I(1)))</RHS></RULE><RULE><LHS>-(I(x),O(y))</LHS><RHS>I(-(x,y))</RHS></RULE><RULE><LHS>-(I(x),I(y))</LHS><RHS>O(-(x,y))</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_+(O(x),O(y))</LHS><RHS>Marked_O(+(x,y))</RHS></DPRULE><DPRULE num="1"><LHS>Marked_+(O(x),O(y))</LHS><RHS>Marked_+(x,y)</RHS></DPRULE><DPRULE num="2"><LHS>Marked_+(O(x),I(y))</LHS><RHS>Marked_+(x,y)</RHS></DPRULE><DPRULE num="3"><LHS>Marked_+(I(x),O(y))</LHS><RHS>Marked_+(x,y)</RHS></DPRULE><DPRULE num="4"><LHS>Marked_+(I(x),I(y))</LHS><RHS>Marked_O(+(+(x,y),I(0)))</RHS></DPRULE><DPRULE num="5"><LHS>Marked_+(I(x),I(y))</LHS><RHS>Marked_+(+(x,y),I(0))</RHS></DPRULE><DPRULE num="6"><LHS>Marked_+(I(x),I(y))</LHS><RHS>Marked_+(x,y)</RHS></DPRULE><DPRULE num="7"><LHS>Marked_*(O(x),y)</LHS><RHS>Marked_O( *(x,y))</RHS></DPRULE><DPRULE num="8"><LHS>Marked_*(O(x),y)</LHS><RHS>Marked_*(x,y)</RHS></DPRULE><DPRULE num="9"><LHS>Marked_*(I(x),y)</LHS><RHS>Marked_+(O( *(x,y)),y)</RHS></DPRULE><DPRULE num="10"><LHS>Marked_*(I(x),y)</LHS><RHS>Marked_O( *(x,y))</RHS></DPRULE><DPRULE num="11"><LHS>Marked_*(I(x),y)</LHS><RHS>Marked_*(x,y)</RHS></DPRULE><DPRULE num="12"><LHS>Marked_-(O(x),O(y))</LHS><RHS>Marked_O(-(x,y))</RHS></DPRULE><DPRULE num="13"><LHS>Marked_-(O(x),O(y))</LHS><RHS>Marked_-(x,y)</RHS></DPRULE><DPRULE num="14"><LHS>Marked_-(O(x),I(y))</LHS><RHS>Marked_-(-(x,y),I(1))</RHS></DPRULE><DPRULE num="15"><LHS>Marked_-(O(x),I(y))</LHS><RHS>Marked_-(x,y)</RHS></DPRULE><DPRULE num="16"><LHS>Marked_-(I(x),O(y))</LHS><RHS>Marked_-(x,y)</RHS></DPRULE><DPRULE num="17"><LHS>Marked_-(I(x),I(y))</LHS><RHS>Marked_O(-(x,y))</RHS></DPRULE><DPRULE num="18"><LHS>Marked_-(I(x),I(y))</LHS><RHS>Marked_-(x,y)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><DAG approx="simpl"><CCLIST><SCC num="0"><NODE ref="13"/><NODE ref="14"/><NODE ref="15"/><NODE ref="16"/><NODE ref="18"/></SCC><NONSCC num="1"><NODE ref="17"/></NONSCC><NONSCC num="2"><NODE ref="12"/></NONSCC><SCC num="3"><NODE ref="8"/><NODE ref="11"/></SCC><NONSCC num="4"><NODE ref="10"/></NONSCC><NONSCC num="5"><NODE ref="9"/></NONSCC><NONSCC num="6"><NODE ref="7"/></NONSCC><SCC num="7"><NODE ref="1"/><NODE ref="2"/><NODE ref="3"/><NODE ref="5"/><NODE ref="6"/></SCC><NONSCC num="8"><NODE ref="4"/></NONSCC><NONSCC num="9"><NODE ref="0"/></NONSCC></CCLIST><EDGE end="2" start="0"/><EDGE end="1" start="0"/><EDGE end="6" start="3"/><EDGE end="5" start="3"/><EDGE end="4" start="3"/><EDGE end="9" start="5"/><EDGE end="8" start="5"/><EDGE end="7" start="5"/><EDGE end="9" start="7"/><EDGE end="8" start="7"/></DAG></CRITERION><PROPERTY criterion="sterm" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>O(0)</LHS><RHS>0</RHS></RULE><RULE><LHS>+(0,x)</LHS><RHS>x</RHS></RULE><RULE><LHS>+(x,0)</LHS><RHS>x</RHS></RULE><RULE><LHS>+(O(x),O(y))</LHS><RHS>O(+(x,y))</RHS></RULE><RULE><LHS>+(O(x),I(y))</LHS><RHS>I(+(x,y))</RHS></RULE><RULE><LHS>+(I(x),O(y))</LHS><RHS>I(+(x,y))</RHS></RULE><RULE><LHS>+(I(x),I(y))</LHS><RHS>O(+(+(x,y),I(0)))</RHS></RULE><RULE><LHS> *(0,x)</LHS><RHS>0</RHS></RULE><RULE><LHS> *(x,0)</LHS><RHS>0</RHS></RULE><RULE><LHS> *(O(x),y)</LHS><RHS>O( *(x,y))</RHS></RULE><RULE><LHS> *(I(x),y)</LHS><RHS>+(O( *(x,y)),y)</RHS></RULE><RULE><LHS>-(x,0)</LHS><RHS>x</RHS></RULE><RULE><LHS>-(0,x)</LHS><RHS>0</RHS></RULE><RULE><LHS>-(O(x),O(y))</LHS><RHS>O(-(x,y))</RHS></RULE><RULE><LHS>-(O(x),I(y))</LHS><RHS>I(-(-(x,y),I(1)))</RHS></RULE><RULE><LHS>-(I(x),O(y))</LHS><RHS>I(-(x,y))</RHS></RULE><RULE><LHS>-(I(x),I(y))</LHS><RHS>O(-(x,y))</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_*(O(x),y)</LHS><RHS>Marked_*(x,y)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_*(I(x),y)</LHS><RHS>Marked_*(x,y)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><PROJECTION><PROJ><SYMBOL><NAME>Marked_*</NAME></SYMBOL><INT>1</INT></PROJ></PROJECTION><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_*(I(x),y)</LHS><RHS>Marked_*(x,y)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_*(O(x),y)</LHS><RHS>Marked_*(x,y)</RHS></DPRULE></DPLIST></STRICTPAIRS><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>O(0)</LHS><RHS>0</RHS></RULE><RULE><LHS>+(0,x)</LHS><RHS>x</RHS></RULE><RULE><LHS>+(x,0)</LHS><RHS>x</RHS></RULE><RULE><LHS>+(O(x),O(y))</LHS><RHS>O(+(x,y))</RHS></RULE><RULE><LHS>+(O(x),I(y))</LHS><RHS>I(+(x,y))</RHS></RULE><RULE><LHS>+(I(x),O(y))</LHS><RHS>I(+(x,y))</RHS></RULE><RULE><LHS>+(I(x),I(y))</LHS><RHS>O(+(+(x,y),I(0)))</RHS></RULE><RULE><LHS> *(0,x)</LHS><RHS>0</RHS></RULE><RULE><LHS> *(x,0)</LHS><RHS>0</RHS></RULE><RULE><LHS> *(O(x),y)</LHS><RHS>O( *(x,y))</RHS></RULE><RULE><LHS> *(I(x),y)</LHS><RHS>+(O( *(x,y)),y)</RHS></RULE><RULE><LHS>-(x,0)</LHS><RHS>x</RHS></RULE><RULE><LHS>-(0,x)</LHS><RHS>0</RHS></RULE><RULE><LHS>-(O(x),O(y))</LHS><RHS>O(-(x,y))</RHS></RULE><RULE><LHS>-(O(x),I(y))</LHS><RHS>I(-(-(x,y),I(1)))</RHS></RULE><RULE><LHS>-(I(x),O(y))</LHS><RHS>I(-(x,y))</RHS></RULE><RULE><LHS>-(I(x),I(y))</LHS><RHS>O(-(x,y))</RHS></RULE></REWSYS><DPLIST/></DPSYS></SYSTEM><CRITERION><DAG approx="simpl"><CCLIST/></DAG></CRITERION></PROPERTY></PROPERTY><PROPERTY criterion="ordering" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>O(0)</LHS><RHS>0</RHS></RULE><RULE><LHS>+(0,x)</LHS><RHS>x</RHS></RULE><RULE><LHS>+(x,0)</LHS><RHS>x</RHS></RULE><RULE><LHS>+(O(x),O(y))</LHS><RHS>O(+(x,y))</RHS></RULE><RULE><LHS>+(O(x),I(y))</LHS><RHS>I(+(x,y))</RHS></RULE><RULE><LHS>+(I(x),O(y))</LHS><RHS>I(+(x,y))</RHS></RULE><RULE><LHS>+(I(x),I(y))</LHS><RHS>O(+(+(x,y),I(0)))</RHS></RULE><RULE><LHS> *(0,x)</LHS><RHS>0</RHS></RULE><RULE><LHS> *(x,0)</LHS><RHS>0</RHS></RULE><RULE><LHS> *(O(x),y)</LHS><RHS>O( *(x,y))</RHS></RULE><RULE><LHS> *(I(x),y)</LHS><RHS>+(O( *(x,y)),y)</RHS></RULE><RULE><LHS>-(x,0)</LHS><RHS>x</RHS></RULE><RULE><LHS>-(0,x)</LHS><RHS>0</RHS></RULE><RULE><LHS>-(O(x),O(y))</LHS><RHS>O(-(x,y))</RHS></RULE><RULE><LHS>-(O(x),I(y))</LHS><RHS>I(-(-(x,y),I(1)))</RHS></RULE><RULE><LHS>-(I(x),O(y))</LHS><RHS>I(-(x,y))</RHS></RULE><RULE><LHS>-(I(x),I(y))</LHS><RHS>O(-(x,y))</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_+(O(x),O(y))</LHS><RHS>Marked_+(x,y)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_+(O(x),I(y))</LHS><RHS>Marked_+(x,y)</RHS></DPRULE><DPRULE num="2"><LHS>Marked_+(I(x),O(y))</LHS><RHS>Marked_+(x,y)</RHS></DPRULE><DPRULE num="3"><LHS>Marked_+(I(x),I(y))</LHS><RHS>Marked_+(+(x,y),I(0))</RHS></DPRULE><DPRULE num="4"><LHS>Marked_+(I(x),I(y))</LHS><RHS>Marked_+(x,y)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><ORDERING type="poly"><POLYSYMB><SYMBOL><NAME>0</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><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="0"/><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>+</NAME></SYMBOL><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></POLYSYMB><POLYSYMB><SYMBOL><NAME>Marked_+</NAME></SYMBOL><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></POLYSYMB><POLYSYMB><SYMBOL><NAME>1</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>O</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>-</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>I</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></ORDERING></CRITERION></PROPERTY><PROPERTY criterion="stronggraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>O(0)</LHS><RHS>0</RHS></RULE><RULE><LHS>+(0,x)</LHS><RHS>x</RHS></RULE><RULE><LHS>+(x,0)</LHS><RHS>x</RHS></RULE><RULE><LHS>+(O(x),O(y))</LHS><RHS>O(+(x,y))</RHS></RULE><RULE><LHS>+(O(x),I(y))</LHS><RHS>I(+(x,y))</RHS></RULE><RULE><LHS>+(I(x),O(y))</LHS><RHS>I(+(x,y))</RHS></RULE><RULE><LHS>+(I(x),I(y))</LHS><RHS>O(+(+(x,y),I(0)))</RHS></RULE><RULE><LHS> *(0,x)</LHS><RHS>0</RHS></RULE><RULE><LHS> *(x,0)</LHS><RHS>0</RHS></RULE><RULE><LHS> *(O(x),y)</LHS><RHS>O( *(x,y))</RHS></RULE><RULE><LHS> *(I(x),y)</LHS><RHS>+(O( *(x,y)),y)</RHS></RULE><RULE><LHS>-(x,0)</LHS><RHS>x</RHS></RULE><RULE><LHS>-(0,x)</LHS><RHS>0</RHS></RULE><RULE><LHS>-(O(x),O(y))</LHS><RHS>O(-(x,y))</RHS></RULE><RULE><LHS>-(O(x),I(y))</LHS><RHS>I(-(-(x,y),I(1)))</RHS></RULE><RULE><LHS>-(I(x),O(y))</LHS><RHS>I(-(x,y))</RHS></RULE><RULE><LHS>-(I(x),I(y))</LHS><RHS>O(-(x,y))</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_-(O(x),O(y))</LHS><RHS>Marked_-(x,y)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_-(O(x),I(y))</LHS><RHS>Marked_-(-(x,y),I(1))</RHS></DPRULE><DPRULE num="2"><LHS>Marked_-(O(x),I(y))</LHS><RHS>Marked_-(x,y)</RHS></DPRULE><DPRULE num="3"><LHS>Marked_-(I(x),O(y))</LHS><RHS>Marked_-(x,y)</RHS></DPRULE><DPRULE num="4"><LHS>Marked_-(I(x),I(y))</LHS><RHS>Marked_-(x,y)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><ORDERING type="poly"><POLYSYMB><SYMBOL><NAME>0</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><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/><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>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></POLYSYMB><POLYSYMB><SYMBOL><NAME>1</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>O</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>-</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>I</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_-</NAME></SYMBOL><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></POLYSYMB></ORDERING><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_-(O(x),O(y))</LHS><RHS>Marked_-(x,y)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_-(O(x),I(y))</LHS><RHS>Marked_-(x,y)</RHS></DPRULE><DPRULE num="2"><LHS>Marked_-(I(x),O(y))</LHS><RHS>Marked_-(x,y)</RHS></DPRULE><DPRULE num="3"><LHS>Marked_-(I(x),I(y))</LHS><RHS>Marked_-(x,y)</RHS></DPRULE></DPLIST></STRICTPAIRS></CRITERION><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>O(0)</LHS><RHS>0</RHS></RULE><RULE><LHS>+(0,x)</LHS><RHS>x</RHS></RULE><RULE><LHS>+(x,0)</LHS><RHS>x</RHS></RULE><RULE><LHS>+(O(x),O(y))</LHS><RHS>O(+(x,y))</RHS></RULE><RULE><LHS>+(O(x),I(y))</LHS><RHS>I(+(x,y))</RHS></RULE><RULE><LHS>+(I(x),O(y))</LHS><RHS>I(+(x,y))</RHS></RULE><RULE><LHS>+(I(x),I(y))</LHS><RHS>O(+(+(x,y),I(0)))</RHS></RULE><RULE><LHS> *(0,x)</LHS><RHS>0</RHS></RULE><RULE><LHS> *(x,0)</LHS><RHS>0</RHS></RULE><RULE><LHS> *(O(x),y)</LHS><RHS>O( *(x,y))</RHS></RULE><RULE><LHS> *(I(x),y)</LHS><RHS>+(O( *(x,y)),y)</RHS></RULE><RULE><LHS>-(x,0)</LHS><RHS>x</RHS></RULE><RULE><LHS>-(0,x)</LHS><RHS>0</RHS></RULE><RULE><LHS>-(O(x),O(y))</LHS><RHS>O(-(x,y))</RHS></RULE><RULE><LHS>-(O(x),I(y))</LHS><RHS>I(-(-(x,y),I(1)))</RHS></RULE><RULE><LHS>-(I(x),O(y))</LHS><RHS>I(-(x,y))</RHS></RULE><RULE><LHS>-(I(x),I(y))</LHS><RHS>O(-(x,y))</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_-(O(x),I(y))</LHS><RHS>Marked_-(-(x,y),I(1))</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><DAG approx="simpl"><CCLIST><SCC num="0"><NODE ref="0"/></SCC></CCLIST></DAG></CRITERION><PROPERTY criterion="ordering" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>O(0)</LHS><RHS>0</RHS></RULE><RULE><LHS>+(0,x)</LHS><RHS>x</RHS></RULE><RULE><LHS>+(x,0)</LHS><RHS>x</RHS></RULE><RULE><LHS>+(O(x),O(y))</LHS><RHS>O(+(x,y))</RHS></RULE><RULE><LHS>+(O(x),I(y))</LHS><RHS>I(+(x,y))</RHS></RULE><RULE><LHS>+(I(x),O(y))</LHS><RHS>I(+(x,y))</RHS></RULE><RULE><LHS>+(I(x),I(y))</LHS><RHS>O(+(+(x,y),I(0)))</RHS></RULE><RULE><LHS> *(0,x)</LHS><RHS>0</RHS></RULE><RULE><LHS> *(x,0)</LHS><RHS>0</RHS></RULE><RULE><LHS> *(O(x),y)</LHS><RHS>O( *(x,y))</RHS></RULE><RULE><LHS> *(I(x),y)</LHS><RHS>+(O( *(x,y)),y)</RHS></RULE><RULE><LHS>-(x,0)</LHS><RHS>x</RHS></RULE><RULE><LHS>-(0,x)</LHS><RHS>0</RHS></RULE><RULE><LHS>-(O(x),O(y))</LHS><RHS>O(-(x,y))</RHS></RULE><RULE><LHS>-(O(x),I(y))</LHS><RHS>I(-(-(x,y),I(1)))</RHS></RULE><RULE><LHS>-(I(x),O(y))</LHS><RHS>I(-(x,y))</RHS></RULE><RULE><LHS>-(I(x),I(y))</LHS><RHS>O(-(x,y))</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_-(O(x),I(y))</LHS><RHS>Marked_-(-(x,y),I(1))</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><ORDERING type="poly"><POLYSYMB><SYMBOL><NAME>0</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME> *</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</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><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="0"/><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>1</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></POLYSYMB><POLYSYMB><SYMBOL><NAME>1</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>O</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>-</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>I</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_-</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></PROPERTY></PROPERTY></PROPERTY></PROOF>
