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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="2" unmarked=""><NAME>max</NAME></SYMBOL><SYMBOL arity="3" unmarked=""><NAME>gcd</NAME></SYMBOL><SYMBOL arity="2" unmarked="min"><NAME>Marked_min</NAME></SYMBOL><SYMBOL arity="2" unmarked=""><NAME>min</NAME></SYMBOL><SYMBOL arity="3" unmarked="gcd"><NAME>Marked_gcd</NAME></SYMBOL><SYMBOL arity="1" unmarked=""><NAME>s</NAME></SYMBOL><SYMBOL arity="2" unmarked=""><NAME>-</NAME></SYMBOL><SYMBOL arity="2" unmarked="max"><NAME>Marked_max</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>min(x,0)</LHS><RHS>0</RHS></RULE><RULE><LHS>min(0,y)</LHS><RHS>0</RHS></RULE><RULE><LHS>min(s(x),s(y))</LHS><RHS>s(min(x,y))</RHS></RULE><RULE><LHS>max(x,0)</LHS><RHS>x</RHS></RULE><RULE><LHS>max(0,y)</LHS><RHS>y</RHS></RULE><RULE><LHS>max(s(x),s(y))</LHS><RHS>s(max(x,y))</RHS></RULE><RULE><LHS>-(x,0)</LHS><RHS>x</RHS></RULE><RULE><LHS>-(s(x),s(y))</LHS><RHS>-(x,y)</RHS></RULE><RULE><LHS>gcd(s(x),s(y),z)</LHS><RHS>gcd(-(max(x,y),min(x,y)),s(min(x,y)),z)</RHS></RULE><RULE><LHS>gcd(x,s(y),s(z))</LHS><RHS>gcd(x,-(max(y,z),min(y,z)),s(min(y,z)))</RHS></RULE><RULE><LHS>gcd(s(x),y,s(z))</LHS><RHS>gcd(-(max(x,z),min(x,z)),y,s(min(x,z)))</RHS></RULE><RULE><LHS>gcd(x,0,0)</LHS><RHS>x</RHS></RULE><RULE><LHS>gcd(0,y,0)</LHS><RHS>y</RHS></RULE><RULE><LHS>gcd(0,0,z)</LHS><RHS>z</RHS></RULE></REWSYS></SYSTEM><CRITERION/><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>min(x,0)</LHS><RHS>0</RHS></RULE><RULE><LHS>min(0,y)</LHS><RHS>0</RHS></RULE><RULE><LHS>min(s(x),s(y))</LHS><RHS>s(min(x,y))</RHS></RULE><RULE><LHS>max(x,0)</LHS><RHS>x</RHS></RULE><RULE><LHS>max(0,y)</LHS><RHS>y</RHS></RULE><RULE><LHS>max(s(x),s(y))</LHS><RHS>s(max(x,y))</RHS></RULE><RULE><LHS>-(x,0)</LHS><RHS>x</RHS></RULE><RULE><LHS>-(s(x),s(y))</LHS><RHS>-(x,y)</RHS></RULE><RULE><LHS>gcd(s(x),s(y),z)</LHS><RHS>gcd(-(max(x,y),min(x,y)),s(min(x,y)),z)</RHS></RULE><RULE><LHS>gcd(x,s(y),s(z))</LHS><RHS>gcd(x,-(max(y,z),min(y,z)),s(min(y,z)))</RHS></RULE><RULE><LHS>gcd(s(x),y,s(z))</LHS><RHS>gcd(-(max(x,z),min(x,z)),y,s(min(x,z)))</RHS></RULE><RULE><LHS>gcd(x,0,0)</LHS><RHS>x</RHS></RULE><RULE><LHS>gcd(0,y,0)</LHS><RHS>y</RHS></RULE><RULE><LHS>gcd(0,0,z)</LHS><RHS>z</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_min(s(x),s(y))</LHS><RHS>Marked_min(x,y)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_max(s(x),s(y))</LHS><RHS>Marked_max(x,y)</RHS></DPRULE><DPRULE num="2"><LHS>Marked_-(s(x),s(y))</LHS><RHS>Marked_-(x,y)</RHS></DPRULE><DPRULE num="3"><LHS>Marked_gcd(s(x),s(y),z)</LHS><RHS>Marked_gcd(-(max(x,y),min(x,y)),s(min(x,y)),z)</RHS></DPRULE><DPRULE num="4"><LHS>Marked_gcd(s(x),s(y),z)</LHS><RHS>Marked_-(max(x,y),min(x,y))</RHS></DPRULE><DPRULE num="5"><LHS>Marked_gcd(s(x),s(y),z)</LHS><RHS>Marked_max(x,y)</RHS></DPRULE><DPRULE num="6"><LHS>Marked_gcd(s(x),s(y),z)</LHS><RHS>Marked_min(x,y)</RHS></DPRULE><DPRULE num="7"><LHS>Marked_gcd(s(x),s(y),z)</LHS><RHS>Marked_min(x,y)</RHS></DPRULE><DPRULE num="8"><LHS>Marked_gcd(x,s(y),s(z))</LHS><RHS>Marked_gcd(x,-(max(y,z),min(y,z)),s(min(y,z)))</RHS></DPRULE><DPRULE num="9"><LHS>Marked_gcd(x,s(y),s(z))</LHS><RHS>Marked_-(max(y,z),min(y,z))</RHS></DPRULE><DPRULE num="10"><LHS>Marked_gcd(x,s(y),s(z))</LHS><RHS>Marked_max(y,z)</RHS></DPRULE><DPRULE num="11"><LHS>Marked_gcd(x,s(y),s(z))</LHS><RHS>Marked_min(y,z)</RHS></DPRULE><DPRULE num="12"><LHS>Marked_gcd(x,s(y),s(z))</LHS><RHS>Marked_min(y,z)</RHS></DPRULE><DPRULE num="13"><LHS>Marked_gcd(s(x),y,s(z))</LHS><RHS>Marked_gcd(-(max(x,z),min(x,z)),y,s(min(x,z)))</RHS></DPRULE><DPRULE num="14"><LHS>Marked_gcd(s(x),y,s(z))</LHS><RHS>Marked_-(max(x,z),min(x,z))</RHS></DPRULE><DPRULE num="15"><LHS>Marked_gcd(s(x),y,s(z))</LHS><RHS>Marked_max(x,z)</RHS></DPRULE><DPRULE num="16"><LHS>Marked_gcd(s(x),y,s(z))</LHS><RHS>Marked_min(x,z)</RHS></DPRULE><DPRULE num="17"><LHS>Marked_gcd(s(x),y,s(z))</LHS><RHS>Marked_min(x,z)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><DAG approx="simpl"><CCLIST><NONSCC num="0"><NODE ref="16"/></NONSCC><SCC num="1"><NODE ref="0"/></SCC><NONSCC num="2"><NODE ref="15"/></NONSCC><SCC num="3"><NODE ref="1"/></SCC><NONSCC num="4"><NODE ref="14"/></NONSCC><SCC num="5"><NODE ref="2"/></SCC><SCC num="6"><NODE ref="3"/><NODE ref="8"/><NODE ref="13"/></SCC><NONSCC num="7"><NODE ref="11"/></NONSCC><NONSCC num="8"><NODE ref="10"/></NONSCC><NONSCC num="9"><NODE ref="9"/></NONSCC><NONSCC num="10"><NODE ref="6"/></NONSCC><NONSCC num="11"><NODE ref="5"/></NONSCC><NONSCC num="12"><NODE ref="4"/></NONSCC></CCLIST><EDGE end="1" start="0"/><EDGE end="3" start="2"/><EDGE end="5" start="4"/><EDGE end="12" start="6"/><EDGE end="11" start="6"/><EDGE end="10" start="6"/><EDGE end="9" start="6"/><EDGE end="8" start="6"/><EDGE end="7" start="6"/><EDGE end="4" start="6"/><EDGE end="2" start="6"/><EDGE end="0" start="6"/><EDGE end="1" start="7"/><EDGE end="3" start="8"/><EDGE end="5" start="9"/><EDGE end="1" start="10"/><EDGE end="3" start="11"/><EDGE end="5" start="12"/></DAG></CRITERION><PROPERTY criterion="ordering" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>min(x,0)</LHS><RHS>0</RHS></RULE><RULE><LHS>min(0,y)</LHS><RHS>0</RHS></RULE><RULE><LHS>min(s(x),s(y))</LHS><RHS>s(min(x,y))</RHS></RULE><RULE><LHS>max(x,0)</LHS><RHS>x</RHS></RULE><RULE><LHS>max(0,y)</LHS><RHS>y</RHS></RULE><RULE><LHS>max(s(x),s(y))</LHS><RHS>s(max(x,y))</RHS></RULE><RULE><LHS>-(x,0)</LHS><RHS>x</RHS></RULE><RULE><LHS>-(s(x),s(y))</LHS><RHS>-(x,y)</RHS></RULE><RULE><LHS>gcd(s(x),s(y),z)</LHS><RHS>gcd(-(max(x,y),min(x,y)),s(min(x,y)),z)</RHS></RULE><RULE><LHS>gcd(x,s(y),s(z))</LHS><RHS>gcd(x,-(max(y,z),min(y,z)),s(min(y,z)))</RHS></RULE><RULE><LHS>gcd(s(x),y,s(z))</LHS><RHS>gcd(-(max(x,z),min(x,z)),y,s(min(x,z)))</RHS></RULE><RULE><LHS>gcd(x,0,0)</LHS><RHS>x</RHS></RULE><RULE><LHS>gcd(0,y,0)</LHS><RHS>y</RHS></RULE><RULE><LHS>gcd(0,0,z)</LHS><RHS>z</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_gcd(s(x),s(y),z)</LHS><RHS>Marked_gcd(-(max(x,y),min(x,y)),s(min(x,y)),z)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_gcd(x,s(y),s(z))</LHS><RHS>Marked_gcd(x,-(max(y,z),min(y,z)),s(min(y,z)))</RHS></DPRULE><DPRULE num="2"><LHS>Marked_gcd(s(x),y,s(z))</LHS><RHS>Marked_gcd(-(max(x,z),min(x,z)),y,s(min(x,z)))</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><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>3</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_gcd</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>3</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>1</INT></COEF><ARG degree="1" num="2"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>min</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>gcd</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>3</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>3</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>1</INT></COEF><ARG degree="1" num="2"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>max</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></ORDERING></CRITERION></PROPERTY><PROPERTY criterion="ordering" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>min(x,0)</LHS><RHS>0</RHS></RULE><RULE><LHS>min(0,y)</LHS><RHS>0</RHS></RULE><RULE><LHS>min(s(x),s(y))</LHS><RHS>s(min(x,y))</RHS></RULE><RULE><LHS>max(x,0)</LHS><RHS>x</RHS></RULE><RULE><LHS>max(0,y)</LHS><RHS>y</RHS></RULE><RULE><LHS>max(s(x),s(y))</LHS><RHS>s(max(x,y))</RHS></RULE><RULE><LHS>-(x,0)</LHS><RHS>x</RHS></RULE><RULE><LHS>-(s(x),s(y))</LHS><RHS>-(x,y)</RHS></RULE><RULE><LHS>gcd(s(x),s(y),z)</LHS><RHS>gcd(-(max(x,y),min(x,y)),s(min(x,y)),z)</RHS></RULE><RULE><LHS>gcd(x,s(y),s(z))</LHS><RHS>gcd(x,-(max(y,z),min(y,z)),s(min(y,z)))</RHS></RULE><RULE><LHS>gcd(s(x),y,s(z))</LHS><RHS>gcd(-(max(x,z),min(x,z)),y,s(min(x,z)))</RHS></RULE><RULE><LHS>gcd(x,0,0)</LHS><RHS>x</RHS></RULE><RULE><LHS>gcd(0,y,0)</LHS><RHS>y</RHS></RULE><RULE><LHS>gcd(0,0,z)</LHS><RHS>z</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_-(s(x),s(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>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>s</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF></MONOME></POLYNOMIAL><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></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>min</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>gcd</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>3</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>3</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>1</INT></COEF><ARG degree="1" num="2"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>max</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>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="ordering" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>min(x,0)</LHS><RHS>0</RHS></RULE><RULE><LHS>min(0,y)</LHS><RHS>0</RHS></RULE><RULE><LHS>min(s(x),s(y))</LHS><RHS>s(min(x,y))</RHS></RULE><RULE><LHS>max(x,0)</LHS><RHS>x</RHS></RULE><RULE><LHS>max(0,y)</LHS><RHS>y</RHS></RULE><RULE><LHS>max(s(x),s(y))</LHS><RHS>s(max(x,y))</RHS></RULE><RULE><LHS>-(x,0)</LHS><RHS>x</RHS></RULE><RULE><LHS>-(s(x),s(y))</LHS><RHS>-(x,y)</RHS></RULE><RULE><LHS>gcd(s(x),s(y),z)</LHS><RHS>gcd(-(max(x,y),min(x,y)),s(min(x,y)),z)</RHS></RULE><RULE><LHS>gcd(x,s(y),s(z))</LHS><RHS>gcd(x,-(max(y,z),min(y,z)),s(min(y,z)))</RHS></RULE><RULE><LHS>gcd(s(x),y,s(z))</LHS><RHS>gcd(-(max(x,z),min(x,z)),y,s(min(x,z)))</RHS></RULE><RULE><LHS>gcd(x,0,0)</LHS><RHS>x</RHS></RULE><RULE><LHS>gcd(0,y,0)</LHS><RHS>y</RHS></RULE><RULE><LHS>gcd(0,0,z)</LHS><RHS>z</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_max(s(x),s(y))</LHS><RHS>Marked_max(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>Marked_max</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>-</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>s</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF></MONOME></POLYNOMIAL><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></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>min</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>gcd</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>3</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>3</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>1</INT></COEF><ARG degree="1" num="2"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>max</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></ORDERING></CRITERION></PROPERTY><PROPERTY criterion="ordering" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>min(x,0)</LHS><RHS>0</RHS></RULE><RULE><LHS>min(0,y)</LHS><RHS>0</RHS></RULE><RULE><LHS>min(s(x),s(y))</LHS><RHS>s(min(x,y))</RHS></RULE><RULE><LHS>max(x,0)</LHS><RHS>x</RHS></RULE><RULE><LHS>max(0,y)</LHS><RHS>y</RHS></RULE><RULE><LHS>max(s(x),s(y))</LHS><RHS>s(max(x,y))</RHS></RULE><RULE><LHS>-(x,0)</LHS><RHS>x</RHS></RULE><RULE><LHS>-(s(x),s(y))</LHS><RHS>-(x,y)</RHS></RULE><RULE><LHS>gcd(s(x),s(y),z)</LHS><RHS>gcd(-(max(x,y),min(x,y)),s(min(x,y)),z)</RHS></RULE><RULE><LHS>gcd(x,s(y),s(z))</LHS><RHS>gcd(x,-(max(y,z),min(y,z)),s(min(y,z)))</RHS></RULE><RULE><LHS>gcd(s(x),y,s(z))</LHS><RHS>gcd(-(max(x,z),min(x,z)),y,s(min(x,z)))</RHS></RULE><RULE><LHS>gcd(x,0,0)</LHS><RHS>x</RHS></RULE><RULE><LHS>gcd(0,y,0)</LHS><RHS>y</RHS></RULE><RULE><LHS>gcd(0,0,z)</LHS><RHS>z</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_min(s(x),s(y))</LHS><RHS>Marked_min(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>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>s</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF></MONOME></POLYNOMIAL><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></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>min</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_min</NAME></SYMBOL><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></POLYSYMB><POLYSYMB><SYMBOL><NAME>gcd</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>3</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>1</INT></COEF><ARG degree="1" num="2"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>max</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></ORDERING></CRITERION></PROPERTY></PROPERTY></PROPERTY></PROOF>
