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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="0" unmarked=""><NAME>false</NAME></SYMBOL><SYMBOL arity="2" unmarked=""><NAME>pow</NAME></SYMBOL><SYMBOL arity="2" unmarked=""><NAME> *</NAME></SYMBOL><SYMBOL arity="3" unmarked="if"><NAME>Marked_if</NAME></SYMBOL><SYMBOL arity="3" unmarked=""><NAME>if</NAME></SYMBOL><SYMBOL arity="1" unmarked=""><NAME>half</NAME></SYMBOL><SYMBOL arity="2" unmarked="pow"><NAME>Marked_pow</NAME></SYMBOL><SYMBOL arity="0" unmarked=""><NAME>0</NAME></SYMBOL><SYMBOL arity="1" unmarked="odd"><NAME>Marked_odd</NAME></SYMBOL><SYMBOL arity="0" unmarked=""><NAME>true</NAME></SYMBOL><SYMBOL arity="3" unmarked=""><NAME>f</NAME></SYMBOL><SYMBOL arity="2" unmarked="-"><NAME>Marked_-</NAME></SYMBOL><SYMBOL arity="1" unmarked=""><NAME>s</NAME></SYMBOL><SYMBOL arity="3" unmarked="f"><NAME>Marked_f</NAME></SYMBOL><SYMBOL arity="2" unmarked=""><NAME>+</NAME></SYMBOL><SYMBOL arity="1" unmarked=""><NAME>odd</NAME></SYMBOL><SYMBOL arity="1" unmarked="half"><NAME>Marked_half</NAME></SYMBOL><SYMBOL arity="2" unmarked=""><NAME>-</NAME></SYMBOL></SYMBOLLIST><VARLIST><VAR>u</VAR><VAR>z</VAR><VAR>y</VAR><VAR>x</VAR></VARLIST></SIGNATURE><PROPERTY criterion="dp" prop="sntrs"><SYSTEM><REWSYS><RULE><LHS>-(x,0)</LHS><RHS>x</RHS></RULE><RULE><LHS>-(s(x),s(y))</LHS><RHS>-(x,y)</RHS></RULE><RULE><LHS> *(x,0)</LHS><RHS>0</RHS></RULE><RULE><LHS> *(x,s(y))</LHS><RHS>+( *(x,y),x)</RHS></RULE><RULE><LHS>if(true,x,y)</LHS><RHS>x</RHS></RULE><RULE><LHS>if(false,x,y)</LHS><RHS>y</RHS></RULE><RULE><LHS>odd(0)</LHS><RHS>false</RHS></RULE><RULE><LHS>odd(s(0))</LHS><RHS>true</RHS></RULE><RULE><LHS>odd(s(s(x)))</LHS><RHS>odd(x)</RHS></RULE><RULE><LHS>half(0)</LHS><RHS>0</RHS></RULE><RULE><LHS>half(s(0))</LHS><RHS>0</RHS></RULE><RULE><LHS>half(s(s(x)))</LHS><RHS>s(half(x))</RHS></RULE><RULE><LHS>if(true,x,y)</LHS><RHS>true</RHS></RULE><RULE><LHS>if(false,x,y)</LHS><RHS>false</RHS></RULE><RULE><LHS>pow(x,y)</LHS><RHS>f(x,y,s(0))</RHS></RULE><RULE><LHS>f(x,0,z)</LHS><RHS>z</RHS></RULE><RULE><LHS>f(x,s(y),z)</LHS><RHS>if(odd(s(y)),f(x,y, *(x,z)),f( *(x,x),half(s(y)),z))</RHS></RULE></REWSYS></SYSTEM><CRITERION/><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>-(x,0)</LHS><RHS>x</RHS></RULE><RULE><LHS>-(s(x),s(y))</LHS><RHS>-(x,y)</RHS></RULE><RULE><LHS> *(x,0)</LHS><RHS>0</RHS></RULE><RULE><LHS> *(x,s(y))</LHS><RHS>+( *(x,y),x)</RHS></RULE><RULE><LHS>if(true,x,y)</LHS><RHS>x</RHS></RULE><RULE><LHS>if(false,x,y)</LHS><RHS>y</RHS></RULE><RULE><LHS>odd(0)</LHS><RHS>false</RHS></RULE><RULE><LHS>odd(s(0))</LHS><RHS>true</RHS></RULE><RULE><LHS>odd(s(s(x)))</LHS><RHS>odd(x)</RHS></RULE><RULE><LHS>half(0)</LHS><RHS>0</RHS></RULE><RULE><LHS>half(s(0))</LHS><RHS>0</RHS></RULE><RULE><LHS>half(s(s(x)))</LHS><RHS>s(half(x))</RHS></RULE><RULE><LHS>if(true,x,y)</LHS><RHS>true</RHS></RULE><RULE><LHS>if(false,x,y)</LHS><RHS>false</RHS></RULE><RULE><LHS>pow(x,y)</LHS><RHS>f(x,y,s(0))</RHS></RULE><RULE><LHS>f(x,0,z)</LHS><RHS>z</RHS></RULE><RULE><LHS>f(x,s(y),z)</LHS><RHS>if(odd(s(y)),f(x,y, *(x,z)),f( *(x,x),half(s(y)),z))</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_-(s(x),s(y))</LHS><RHS>Marked_-(x,y)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_*(x,s(y))</LHS><RHS>Marked_*(x,y)</RHS></DPRULE><DPRULE num="2"><LHS>Marked_odd(s(s(x)))</LHS><RHS>Marked_odd(x)</RHS></DPRULE><DPRULE num="3"><LHS>Marked_half(s(s(x)))</LHS><RHS>Marked_half(x)</RHS></DPRULE><DPRULE num="4"><LHS>Marked_pow(x,y)</LHS><RHS>Marked_f(x,y,s(0))</RHS></DPRULE><DPRULE num="5"><LHS>Marked_f(x,s(y),z)</LHS><RHS>Marked_if(odd(s(y)),f(x,y, *(x,z)),f( *(x,x),half(s(y)),z))</RHS></DPRULE><DPRULE num="6"><LHS>Marked_f(x,s(y),z)</LHS><RHS>Marked_odd(s(y))</RHS></DPRULE><DPRULE num="7"><LHS>Marked_f(x,s(y),z)</LHS><RHS>Marked_f(x,y, *(x,z))</RHS></DPRULE><DPRULE num="8"><LHS>Marked_f(x,s(y),z)</LHS><RHS>Marked_*(x,z)</RHS></DPRULE><DPRULE num="9"><LHS>Marked_f(x,s(y),z)</LHS><RHS>Marked_f( *(x,x),half(s(y)),z)</RHS></DPRULE><DPRULE num="10"><LHS>Marked_f(x,s(y),z)</LHS><RHS>Marked_*(x,x)</RHS></DPRULE><DPRULE num="11"><LHS>Marked_f(x,s(y),z)</LHS><RHS>Marked_half(s(y))</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><DAG approx="simpl"><CCLIST><NONSCC num="0"><NODE ref="11"/></NONSCC><SCC num="1"><NODE ref="3"/></SCC><NONSCC num="2"><NODE ref="10"/></NONSCC><SCC num="3"><NODE ref="1"/></SCC><SCC num="4"><NODE ref="7"/><NODE ref="9"/></SCC><NONSCC num="5"><NODE ref="8"/></NONSCC><NONSCC num="6"><NODE ref="6"/></NONSCC><NONSCC num="7"><NODE ref="5"/></NONSCC><SCC num="8"><NODE ref="2"/></SCC><NONSCC num="9"><NODE ref="4"/></NONSCC><SCC num="10"><NODE ref="0"/></SCC></CCLIST><EDGE end="1" start="0"/><EDGE end="3" start="2"/><EDGE end="7" start="4"/><EDGE end="6" start="4"/><EDGE end="5" start="4"/><EDGE end="2" start="4"/><EDGE end="0" start="4"/><EDGE end="3" start="5"/><EDGE end="8" start="6"/><EDGE end="7" start="9"/><EDGE end="6" start="9"/><EDGE end="5" start="9"/><EDGE end="4" start="9"/><EDGE end="2" start="9"/><EDGE end="0" start="9"/></DAG></CRITERION><PROPERTY criterion="ordering" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>-(x,0)</LHS><RHS>x</RHS></RULE><RULE><LHS>-(s(x),s(y))</LHS><RHS>-(x,y)</RHS></RULE><RULE><LHS> *(x,0)</LHS><RHS>0</RHS></RULE><RULE><LHS> *(x,s(y))</LHS><RHS>+( *(x,y),x)</RHS></RULE><RULE><LHS>if(true,x,y)</LHS><RHS>x</RHS></RULE><RULE><LHS>if(false,x,y)</LHS><RHS>y</RHS></RULE><RULE><LHS>odd(0)</LHS><RHS>false</RHS></RULE><RULE><LHS>odd(s(0))</LHS><RHS>true</RHS></RULE><RULE><LHS>odd(s(s(x)))</LHS><RHS>odd(x)</RHS></RULE><RULE><LHS>half(0)</LHS><RHS>0</RHS></RULE><RULE><LHS>half(s(0))</LHS><RHS>0</RHS></RULE><RULE><LHS>half(s(s(x)))</LHS><RHS>s(half(x))</RHS></RULE><RULE><LHS>if(true,x,y)</LHS><RHS>true</RHS></RULE><RULE><LHS>if(false,x,y)</LHS><RHS>false</RHS></RULE><RULE><LHS>pow(x,y)</LHS><RHS>f(x,y,s(0))</RHS></RULE><RULE><LHS>f(x,0,z)</LHS><RHS>z</RHS></RULE><RULE><LHS>f(x,s(y),z)</LHS><RHS>if(odd(s(y)),f(x,y, *(x,z)),f( *(x,x),half(s(y)),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>-</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>3</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>odd</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>+</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></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>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><POLYSYMB><SYMBOL><NAME>f</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="2"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>true</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>0</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>half</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>if</NAME></SYMBOL><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></POLYSYMB><POLYSYMB><SYMBOL><NAME> *</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>pow</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>3</INT></COEF></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>false</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB></ORDERING></CRITERION></PROPERTY><PROPERTY criterion="stronggraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>-(x,0)</LHS><RHS>x</RHS></RULE><RULE><LHS>-(s(x),s(y))</LHS><RHS>-(x,y)</RHS></RULE><RULE><LHS> *(x,0)</LHS><RHS>0</RHS></RULE><RULE><LHS> *(x,s(y))</LHS><RHS>+( *(x,y),x)</RHS></RULE><RULE><LHS>if(true,x,y)</LHS><RHS>x</RHS></RULE><RULE><LHS>if(false,x,y)</LHS><RHS>y</RHS></RULE><RULE><LHS>odd(0)</LHS><RHS>false</RHS></RULE><RULE><LHS>odd(s(0))</LHS><RHS>true</RHS></RULE><RULE><LHS>odd(s(s(x)))</LHS><RHS>odd(x)</RHS></RULE><RULE><LHS>half(0)</LHS><RHS>0</RHS></RULE><RULE><LHS>half(s(0))</LHS><RHS>0</RHS></RULE><RULE><LHS>half(s(s(x)))</LHS><RHS>s(half(x))</RHS></RULE><RULE><LHS>if(true,x,y)</LHS><RHS>true</RHS></RULE><RULE><LHS>if(false,x,y)</LHS><RHS>false</RHS></RULE><RULE><LHS>pow(x,y)</LHS><RHS>f(x,y,s(0))</RHS></RULE><RULE><LHS>f(x,0,z)</LHS><RHS>z</RHS></RULE><RULE><LHS>f(x,s(y),z)</LHS><RHS>if(odd(s(y)),f(x,y, *(x,z)),f( *(x,x),half(s(y)),z))</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_f(x,s(y),z)</LHS><RHS>Marked_f(x,y, *(x,z))</RHS></DPRULE><DPRULE num="1"><LHS>Marked_f(x,s(y),z)</LHS><RHS>Marked_f( *(x,x),half(s(y)),z)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><ORDERING type="poly"><POLYSYMB><SYMBOL><NAME>-</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>3</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>odd</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>+</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>Marked_f</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>3</INT></COEF><ARG degree="1" num="1"/></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>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>f</NAME></SYMBOL><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></POLYSYMB><POLYSYMB><SYMBOL><NAME>true</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>0</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>half</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>if</NAME></SYMBOL><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="2"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME> *</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>pow</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>3</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>false</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB></ORDERING><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_f(x,s(y),z)</LHS><RHS>Marked_f(x,y, *(x,z))</RHS></DPRULE></DPLIST></STRICTPAIRS></CRITERION><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>-(x,0)</LHS><RHS>x</RHS></RULE><RULE><LHS>-(s(x),s(y))</LHS><RHS>-(x,y)</RHS></RULE><RULE><LHS> *(x,0)</LHS><RHS>0</RHS></RULE><RULE><LHS> *(x,s(y))</LHS><RHS>+( *(x,y),x)</RHS></RULE><RULE><LHS>if(true,x,y)</LHS><RHS>x</RHS></RULE><RULE><LHS>if(false,x,y)</LHS><RHS>y</RHS></RULE><RULE><LHS>odd(0)</LHS><RHS>false</RHS></RULE><RULE><LHS>odd(s(0))</LHS><RHS>true</RHS></RULE><RULE><LHS>odd(s(s(x)))</LHS><RHS>odd(x)</RHS></RULE><RULE><LHS>half(0)</LHS><RHS>0</RHS></RULE><RULE><LHS>half(s(0))</LHS><RHS>0</RHS></RULE><RULE><LHS>half(s(s(x)))</LHS><RHS>s(half(x))</RHS></RULE><RULE><LHS>if(true,x,y)</LHS><RHS>true</RHS></RULE><RULE><LHS>if(false,x,y)</LHS><RHS>false</RHS></RULE><RULE><LHS>pow(x,y)</LHS><RHS>f(x,y,s(0))</RHS></RULE><RULE><LHS>f(x,0,z)</LHS><RHS>z</RHS></RULE><RULE><LHS>f(x,s(y),z)</LHS><RHS>if(odd(s(y)),f(x,y, *(x,z)),f( *(x,x),half(s(y)),z))</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_f(x,s(y),z)</LHS><RHS>Marked_f( *(x,x),half(s(y)),z)</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>-(x,0)</LHS><RHS>x</RHS></RULE><RULE><LHS>-(s(x),s(y))</LHS><RHS>-(x,y)</RHS></RULE><RULE><LHS> *(x,0)</LHS><RHS>0</RHS></RULE><RULE><LHS> *(x,s(y))</LHS><RHS>+( *(x,y),x)</RHS></RULE><RULE><LHS>if(true,x,y)</LHS><RHS>x</RHS></RULE><RULE><LHS>if(false,x,y)</LHS><RHS>y</RHS></RULE><RULE><LHS>odd(0)</LHS><RHS>false</RHS></RULE><RULE><LHS>odd(s(0))</LHS><RHS>true</RHS></RULE><RULE><LHS>odd(s(s(x)))</LHS><RHS>odd(x)</RHS></RULE><RULE><LHS>half(0)</LHS><RHS>0</RHS></RULE><RULE><LHS>half(s(0))</LHS><RHS>0</RHS></RULE><RULE><LHS>half(s(s(x)))</LHS><RHS>s(half(x))</RHS></RULE><RULE><LHS>if(true,x,y)</LHS><RHS>true</RHS></RULE><RULE><LHS>if(false,x,y)</LHS><RHS>false</RHS></RULE><RULE><LHS>pow(x,y)</LHS><RHS>f(x,y,s(0))</RHS></RULE><RULE><LHS>f(x,0,z)</LHS><RHS>z</RHS></RULE><RULE><LHS>f(x,s(y),z)</LHS><RHS>if(odd(s(y)),f(x,y, *(x,z)),f( *(x,x),half(s(y)),z))</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_f(x,s(y),z)</LHS><RHS>Marked_f( *(x,x),half(s(y)),z)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><ORDERING numstrictcol="1" size="3" type="matrix"><POLYSYMB><SYMBOL><NAME>-</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><MATRIX><COLUMN><INT>1</INT><INT>1</INT><INT>1</INT></COLUMN><COLUMN><INT>1</INT><INT>1</INT><INT>1</INT></COLUMN><COLUMN><INT>1</INT><INT>1</INT><INT>1</INT></COLUMN></MATRIX></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><MATRIX><COLUMN><INT>1</INT><INT>1</INT><INT>1</INT></COLUMN><COLUMN><INT>1</INT><INT>1</INT><INT>1</INT></COLUMN><COLUMN><INT>1</INT><INT>1</INT><INT>1</INT></COLUMN></MATRIX></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><MATRIX><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN></MATRIX></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><MATRIX><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN></MATRIX></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>odd</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><MATRIX><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN></MATRIX></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><MATRIX><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN></MATRIX></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><MATRIX><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN></MATRIX></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>+</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><MATRIX><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN></MATRIX></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><MATRIX><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN></MATRIX></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><MATRIX><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN></MATRIX></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><MATRIX><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN></MATRIX></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>Marked_f</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><MATRIX><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN></MATRIX></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><MATRIX><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN></MATRIX></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><MATRIX><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>1</INT><INT>0</INT><INT>0</INT></COLUMN></MATRIX></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><MATRIX><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN></MATRIX></COEF><ARG degree="1" num="2"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><MATRIX><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN></MATRIX></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>s</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><MATRIX><COLUMN><INT>0</INT><INT>0</INT><INT>1</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN></MATRIX></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><MATRIX><COLUMN><INT>0</INT><INT>0</INT><INT>1</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>1</INT></COLUMN><COLUMN><INT>0</INT><INT>1</INT><INT>1</INT></COLUMN></MATRIX></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><MATRIX><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN></MATRIX></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>f</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><MATRIX><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN></MATRIX></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><MATRIX><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN></MATRIX></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><MATRIX><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN></MATRIX></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><MATRIX><COLUMN><INT>1</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>1</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>1</INT></COLUMN></MATRIX></COEF><ARG degree="1" num="2"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><MATRIX><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN></MATRIX></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>true</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><MATRIX><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN></MATRIX></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><MATRIX><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN></MATRIX></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>0</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><MATRIX><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN></MATRIX></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><MATRIX><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN></MATRIX></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>half</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><MATRIX><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN></MATRIX></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><MATRIX><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>1</INT></COLUMN><COLUMN><INT>0</INT><INT>1</INT><INT>0</INT></COLUMN></MATRIX></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><MATRIX><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN></MATRIX></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>if</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><MATRIX><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN></MATRIX></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><MATRIX><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN></MATRIX></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><MATRIX><COLUMN><INT>1</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>1</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>1</INT></COLUMN></MATRIX></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><MATRIX><COLUMN><INT>1</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>1</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>1</INT></COLUMN></MATRIX></COEF><ARG degree="1" num="2"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><MATRIX><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN></MATRIX></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME> *</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><MATRIX><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN></MATRIX></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><MATRIX><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN></MATRIX></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><MATRIX><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN></MATRIX></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><MATRIX><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN></MATRIX></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>pow</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><MATRIX><COLUMN><INT>0</INT><INT>1</INT><INT>1</INT></COLUMN><COLUMN><INT>0</INT><INT>1</INT><INT>1</INT></COLUMN><COLUMN><INT>1</INT><INT>1</INT><INT>1</INT></COLUMN></MATRIX></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><MATRIX><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN></MATRIX></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><MATRIX><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN></MATRIX></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><MATRIX><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN></MATRIX></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>false</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><MATRIX><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN></MATRIX></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><MATRIX><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN></MATRIX></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB></ORDERING></CRITERION></PROPERTY></PROPERTY></PROPERTY><PROPERTY criterion="ordering" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>-(x,0)</LHS><RHS>x</RHS></RULE><RULE><LHS>-(s(x),s(y))</LHS><RHS>-(x,y)</RHS></RULE><RULE><LHS> *(x,0)</LHS><RHS>0</RHS></RULE><RULE><LHS> *(x,s(y))</LHS><RHS>+( *(x,y),x)</RHS></RULE><RULE><LHS>if(true,x,y)</LHS><RHS>x</RHS></RULE><RULE><LHS>if(false,x,y)</LHS><RHS>y</RHS></RULE><RULE><LHS>odd(0)</LHS><RHS>false</RHS></RULE><RULE><LHS>odd(s(0))</LHS><RHS>true</RHS></RULE><RULE><LHS>odd(s(s(x)))</LHS><RHS>odd(x)</RHS></RULE><RULE><LHS>half(0)</LHS><RHS>0</RHS></RULE><RULE><LHS>half(s(0))</LHS><RHS>0</RHS></RULE><RULE><LHS>half(s(s(x)))</LHS><RHS>s(half(x))</RHS></RULE><RULE><LHS>if(true,x,y)</LHS><RHS>true</RHS></RULE><RULE><LHS>if(false,x,y)</LHS><RHS>false</RHS></RULE><RULE><LHS>pow(x,y)</LHS><RHS>f(x,y,s(0))</RHS></RULE><RULE><LHS>f(x,0,z)</LHS><RHS>z</RHS></RULE><RULE><LHS>f(x,s(y),z)</LHS><RHS>if(odd(s(y)),f(x,y, *(x,z)),f( *(x,x),half(s(y)),z))</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_odd(s(s(x)))</LHS><RHS>Marked_odd(x)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><ORDERING type="poly"><POLYSYMB><SYMBOL><NAME>-</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>3</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>odd</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>+</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></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>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>f</NAME></SYMBOL><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></POLYSYMB><POLYSYMB><SYMBOL><NAME>true</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>Marked_odd</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>0</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>half</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>if</NAME></SYMBOL><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></POLYSYMB><POLYSYMB><SYMBOL><NAME> *</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>pow</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>3</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>false</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB></ORDERING></CRITERION></PROPERTY><PROPERTY criterion="ordering" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>-(x,0)</LHS><RHS>x</RHS></RULE><RULE><LHS>-(s(x),s(y))</LHS><RHS>-(x,y)</RHS></RULE><RULE><LHS> *(x,0)</LHS><RHS>0</RHS></RULE><RULE><LHS> *(x,s(y))</LHS><RHS>+( *(x,y),x)</RHS></RULE><RULE><LHS>if(true,x,y)</LHS><RHS>x</RHS></RULE><RULE><LHS>if(false,x,y)</LHS><RHS>y</RHS></RULE><RULE><LHS>odd(0)</LHS><RHS>false</RHS></RULE><RULE><LHS>odd(s(0))</LHS><RHS>true</RHS></RULE><RULE><LHS>odd(s(s(x)))</LHS><RHS>odd(x)</RHS></RULE><RULE><LHS>half(0)</LHS><RHS>0</RHS></RULE><RULE><LHS>half(s(0))</LHS><RHS>0</RHS></RULE><RULE><LHS>half(s(s(x)))</LHS><RHS>s(half(x))</RHS></RULE><RULE><LHS>if(true,x,y)</LHS><RHS>true</RHS></RULE><RULE><LHS>if(false,x,y)</LHS><RHS>false</RHS></RULE><RULE><LHS>pow(x,y)</LHS><RHS>f(x,y,s(0))</RHS></RULE><RULE><LHS>f(x,0,z)</LHS><RHS>z</RHS></RULE><RULE><LHS>f(x,s(y),z)</LHS><RHS>if(odd(s(y)),f(x,y, *(x,z)),f( *(x,x),half(s(y)),z))</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_*(x,s(y))</LHS><RHS>Marked_*(x,y)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><ORDERING type="poly"><POLYSYMB><SYMBOL><NAME>-</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>3</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>odd</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>+</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></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>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>f</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="2"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>true</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>0</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>half</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>if</NAME></SYMBOL><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></POLYSYMB><POLYSYMB><SYMBOL><NAME> *</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>pow</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>3</INT></COEF></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>false</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>Marked_*</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>3</INT></COEF><ARG degree="1" num="1"/></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>-(x,0)</LHS><RHS>x</RHS></RULE><RULE><LHS>-(s(x),s(y))</LHS><RHS>-(x,y)</RHS></RULE><RULE><LHS> *(x,0)</LHS><RHS>0</RHS></RULE><RULE><LHS> *(x,s(y))</LHS><RHS>+( *(x,y),x)</RHS></RULE><RULE><LHS>if(true,x,y)</LHS><RHS>x</RHS></RULE><RULE><LHS>if(false,x,y)</LHS><RHS>y</RHS></RULE><RULE><LHS>odd(0)</LHS><RHS>false</RHS></RULE><RULE><LHS>odd(s(0))</LHS><RHS>true</RHS></RULE><RULE><LHS>odd(s(s(x)))</LHS><RHS>odd(x)</RHS></RULE><RULE><LHS>half(0)</LHS><RHS>0</RHS></RULE><RULE><LHS>half(s(0))</LHS><RHS>0</RHS></RULE><RULE><LHS>half(s(s(x)))</LHS><RHS>s(half(x))</RHS></RULE><RULE><LHS>if(true,x,y)</LHS><RHS>true</RHS></RULE><RULE><LHS>if(false,x,y)</LHS><RHS>false</RHS></RULE><RULE><LHS>pow(x,y)</LHS><RHS>f(x,y,s(0))</RHS></RULE><RULE><LHS>f(x,0,z)</LHS><RHS>z</RHS></RULE><RULE><LHS>f(x,s(y),z)</LHS><RHS>if(odd(s(y)),f(x,y, *(x,z)),f( *(x,x),half(s(y)),z))</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_half(s(s(x)))</LHS><RHS>Marked_half(x)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><ORDERING type="poly"><POLYSYMB><SYMBOL><NAME>-</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>3</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_half</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>odd</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>+</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></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>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>f</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="2"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>true</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>0</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>half</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>if</NAME></SYMBOL><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></POLYSYMB><POLYSYMB><SYMBOL><NAME> *</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>pow</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>3</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><POLYSYMB><SYMBOL><NAME>false</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB></ORDERING></CRITERION></PROPERTY></PROPERTY></PROPERTY></PROOF>
