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<!DOCTYPE PROOF SYSTEM "http://a3pat.ensiie.fr/pub/a3pat.dtd">
<PROOF><SIGNATURE><SYMBOLLIST><SYMBOL arity="2" unmarked=""><NAME>cons</NAME></SYMBOL><SYMBOL arity="1" unmarked="sum"><NAME>Marked_sum</NAME></SYMBOL><SYMBOL arity="1" unmarked=""><NAME>1</NAME></SYMBOL><SYMBOL arity="1" unmarked="0"><NAME>Marked_0</NAME></SYMBOL><SYMBOL arity="1" unmarked=""><NAME>sum</NAME></SYMBOL><SYMBOL arity="1" unmarked="prod"><NAME>Marked_prod</NAME></SYMBOL><SYMBOL arity="1" unmarked=""><NAME>0</NAME></SYMBOL><SYMBOL arity="0" unmarked=""><NAME>nil</NAME></SYMBOL><SYMBOL arity="2" unmarked="*"><NAME>Marked_*</NAME></SYMBOL><SYMBOL arity="2" unmarked=""><NAME>+</NAME></SYMBOL><SYMBOL arity="2" unmarked="+"><NAME>Marked_+</NAME></SYMBOL><SYMBOL arity="2" unmarked=""><NAME> *</NAME></SYMBOL><SYMBOL arity="1" unmarked=""><NAME>prod</NAME></SYMBOL><SYMBOL arity="0" unmarked=""><NAME>#</NAME></SYMBOL></SYMBOLLIST><VARLIST><VAR>x</VAR><VAR>y</VAR><VAR>z</VAR><VAR>l</VAR></VARLIST></SIGNATURE><PROPERTY criterion="dp" prop="sntrs"><SYSTEM><REWSYS><RULE><LHS>0(#)</LHS><RHS>#</RHS></RULE><RULE><LHS>+(x,#)</LHS><RHS>x</RHS></RULE><RULE><LHS>+(#,x)</LHS><RHS>x</RHS></RULE><RULE><LHS>+(0(x),0(y))</LHS><RHS>0(+(x,y))</RHS></RULE><RULE><LHS>+(0(x),1(y))</LHS><RHS>1(+(x,y))</RHS></RULE><RULE><LHS>+(1(x),0(y))</LHS><RHS>1(+(x,y))</RHS></RULE><RULE><LHS>+(1(x),1(y))</LHS><RHS>0(+(+(x,y),1(#)))</RHS></RULE><RULE><LHS>+(+(x,y),z)</LHS><RHS>+(x,+(y,z))</RHS></RULE><RULE><LHS> *(#,x)</LHS><RHS>#</RHS></RULE><RULE><LHS> *(0(x),y)</LHS><RHS>0( *(x,y))</RHS></RULE><RULE><LHS> *(1(x),y)</LHS><RHS>+(0( *(x,y)),y)</RHS></RULE><RULE><LHS> *( *(x,y),z)</LHS><RHS> *(x, *(y,z))</RHS></RULE><RULE><LHS>sum(nil)</LHS><RHS>0(#)</RHS></RULE><RULE><LHS>sum(cons(x,l))</LHS><RHS>+(x,sum(l))</RHS></RULE><RULE><LHS>prod(nil)</LHS><RHS>1(#)</RHS></RULE><RULE><LHS>prod(cons(x,l))</LHS><RHS> *(x,prod(l))</RHS></RULE></REWSYS></SYSTEM><CRITERION/><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>0(#)</LHS><RHS>#</RHS></RULE><RULE><LHS>+(x,#)</LHS><RHS>x</RHS></RULE><RULE><LHS>+(#,x)</LHS><RHS>x</RHS></RULE><RULE><LHS>+(0(x),0(y))</LHS><RHS>0(+(x,y))</RHS></RULE><RULE><LHS>+(0(x),1(y))</LHS><RHS>1(+(x,y))</RHS></RULE><RULE><LHS>+(1(x),0(y))</LHS><RHS>1(+(x,y))</RHS></RULE><RULE><LHS>+(1(x),1(y))</LHS><RHS>0(+(+(x,y),1(#)))</RHS></RULE><RULE><LHS>+(+(x,y),z)</LHS><RHS>+(x,+(y,z))</RHS></RULE><RULE><LHS> *(#,x)</LHS><RHS>#</RHS></RULE><RULE><LHS> *(0(x),y)</LHS><RHS>0( *(x,y))</RHS></RULE><RULE><LHS> *(1(x),y)</LHS><RHS>+(0( *(x,y)),y)</RHS></RULE><RULE><LHS> *( *(x,y),z)</LHS><RHS> *(x, *(y,z))</RHS></RULE><RULE><LHS>sum(nil)</LHS><RHS>0(#)</RHS></RULE><RULE><LHS>sum(cons(x,l))</LHS><RHS>+(x,sum(l))</RHS></RULE><RULE><LHS>prod(nil)</LHS><RHS>1(#)</RHS></RULE><RULE><LHS>prod(cons(x,l))</LHS><RHS> *(x,prod(l))</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_+(0(x),0(y))</LHS><RHS>Marked_0(+(x,y))</RHS></DPRULE><DPRULE num="1"><LHS>Marked_+(0(x),0(y))</LHS><RHS>Marked_+(x,y)</RHS></DPRULE><DPRULE num="2"><LHS>Marked_+(0(x),1(y))</LHS><RHS>Marked_+(x,y)</RHS></DPRULE><DPRULE num="3"><LHS>Marked_+(1(x),0(y))</LHS><RHS>Marked_+(x,y)</RHS></DPRULE><DPRULE num="4"><LHS>Marked_+(1(x),1(y))</LHS><RHS>Marked_0(+(+(x,y),1(#)))</RHS></DPRULE><DPRULE num="5"><LHS>Marked_+(1(x),1(y))</LHS><RHS>Marked_+(+(x,y),1(#))</RHS></DPRULE><DPRULE num="6"><LHS>Marked_+(1(x),1(y))</LHS><RHS>Marked_+(x,y)</RHS></DPRULE><DPRULE num="7"><LHS>Marked_+(+(x,y),z)</LHS><RHS>Marked_+(x,+(y,z))</RHS></DPRULE><DPRULE num="8"><LHS>Marked_+(+(x,y),z)</LHS><RHS>Marked_+(y,z)</RHS></DPRULE><DPRULE num="9"><LHS>Marked_*(0(x),y)</LHS><RHS>Marked_0( *(x,y))</RHS></DPRULE><DPRULE num="10"><LHS>Marked_*(0(x),y)</LHS><RHS>Marked_*(x,y)</RHS></DPRULE><DPRULE num="11"><LHS>Marked_*(1(x),y)</LHS><RHS>Marked_+(0( *(x,y)),y)</RHS></DPRULE><DPRULE num="12"><LHS>Marked_*(1(x),y)</LHS><RHS>Marked_0( *(x,y))</RHS></DPRULE><DPRULE num="13"><LHS>Marked_*(1(x),y)</LHS><RHS>Marked_*(x,y)</RHS></DPRULE><DPRULE num="14"><LHS>Marked_*( *(x,y),z)</LHS><RHS>Marked_*(x, *(y,z))</RHS></DPRULE><DPRULE num="15"><LHS>Marked_*( *(x,y),z)</LHS><RHS>Marked_*(y,z)</RHS></DPRULE><DPRULE num="16"><LHS>Marked_sum(nil)</LHS><RHS>Marked_0(#)</RHS></DPRULE><DPRULE num="17"><LHS>Marked_sum(cons(x,l))</LHS><RHS>Marked_+(x,sum(l))</RHS></DPRULE><DPRULE num="18"><LHS>Marked_sum(cons(x,l))</LHS><RHS>Marked_sum(l)</RHS></DPRULE><DPRULE num="19"><LHS>Marked_prod(cons(x,l))</LHS><RHS>Marked_*(x,prod(l))</RHS></DPRULE><DPRULE num="20"><LHS>Marked_prod(cons(x,l))</LHS><RHS>Marked_prod(l)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><DAG approx="simpl"><CCLIST><SCC num="0"><NODE ref="20"/></SCC><NONSCC num="1"><NODE ref="19"/></NONSCC><SCC num="2"><NODE ref="10"/><NODE ref="13"/><NODE ref="14"/><NODE ref="15"/></SCC><NONSCC num="3"><NODE ref="12"/></NONSCC><NONSCC num="4"><NODE ref="11"/></NONSCC><NONSCC num="5"><NODE ref="9"/></NONSCC><SCC num="6"><NODE ref="18"/></SCC><NONSCC num="7"><NODE ref="17"/></NONSCC><NONSCC num="8"><NODE ref="16"/></NONSCC><SCC num="9"><NODE ref="1"/><NODE ref="2"/><NODE ref="3"/><NODE ref="5"/><NODE ref="6"/><NODE ref="7"/><NODE ref="8"/></SCC><NONSCC num="10"><NODE ref="4"/></NONSCC><NONSCC num="11"><NODE ref="0"/></NONSCC></CCLIST><EDGE end="1" start="0"/><EDGE end="5" start="1"/><EDGE end="4" start="1"/><EDGE end="3" start="1"/><EDGE end="2" start="1"/><EDGE end="5" start="2"/><EDGE end="4" start="2"/><EDGE end="3" start="2"/><EDGE end="11" start="4"/><EDGE end="10" start="4"/><EDGE end="9" start="4"/><EDGE end="8" start="6"/><EDGE end="7" start="6"/><EDGE end="11" start="7"/><EDGE end="10" start="7"/><EDGE end="9" start="7"/><EDGE end="11" start="9"/><EDGE end="10" start="9"/></DAG></CRITERION><PROPERTY criterion="ordering" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>0(#)</LHS><RHS>#</RHS></RULE><RULE><LHS>+(x,#)</LHS><RHS>x</RHS></RULE><RULE><LHS>+(#,x)</LHS><RHS>x</RHS></RULE><RULE><LHS>+(0(x),0(y))</LHS><RHS>0(+(x,y))</RHS></RULE><RULE><LHS>+(0(x),1(y))</LHS><RHS>1(+(x,y))</RHS></RULE><RULE><LHS>+(1(x),0(y))</LHS><RHS>1(+(x,y))</RHS></RULE><RULE><LHS>+(1(x),1(y))</LHS><RHS>0(+(+(x,y),1(#)))</RHS></RULE><RULE><LHS>+(+(x,y),z)</LHS><RHS>+(x,+(y,z))</RHS></RULE><RULE><LHS> *(#,x)</LHS><RHS>#</RHS></RULE><RULE><LHS> *(0(x),y)</LHS><RHS>0( *(x,y))</RHS></RULE><RULE><LHS> *(1(x),y)</LHS><RHS>+(0( *(x,y)),y)</RHS></RULE><RULE><LHS> *( *(x,y),z)</LHS><RHS> *(x, *(y,z))</RHS></RULE><RULE><LHS>sum(nil)</LHS><RHS>0(#)</RHS></RULE><RULE><LHS>sum(cons(x,l))</LHS><RHS>+(x,sum(l))</RHS></RULE><RULE><LHS>prod(nil)</LHS><RHS>1(#)</RHS></RULE><RULE><LHS>prod(cons(x,l))</LHS><RHS> *(x,prod(l))</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_sum(cons(x,l))</LHS><RHS>Marked_sum(l)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><ORDERING type="poly"><POLYSYMB><SYMBOL><NAME>#</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>prod</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> *</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>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>+</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><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>nil</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>0</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>sum</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><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>1</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>Marked_sum</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>cons</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>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 criterion="ordering" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>0(#)</LHS><RHS>#</RHS></RULE><RULE><LHS>+(x,#)</LHS><RHS>x</RHS></RULE><RULE><LHS>+(#,x)</LHS><RHS>x</RHS></RULE><RULE><LHS>+(0(x),0(y))</LHS><RHS>0(+(x,y))</RHS></RULE><RULE><LHS>+(0(x),1(y))</LHS><RHS>1(+(x,y))</RHS></RULE><RULE><LHS>+(1(x),0(y))</LHS><RHS>1(+(x,y))</RHS></RULE><RULE><LHS>+(1(x),1(y))</LHS><RHS>0(+(+(x,y),1(#)))</RHS></RULE><RULE><LHS>+(+(x,y),z)</LHS><RHS>+(x,+(y,z))</RHS></RULE><RULE><LHS> *(#,x)</LHS><RHS>#</RHS></RULE><RULE><LHS> *(0(x),y)</LHS><RHS>0( *(x,y))</RHS></RULE><RULE><LHS> *(1(x),y)</LHS><RHS>+(0( *(x,y)),y)</RHS></RULE><RULE><LHS> *( *(x,y),z)</LHS><RHS> *(x, *(y,z))</RHS></RULE><RULE><LHS>sum(nil)</LHS><RHS>0(#)</RHS></RULE><RULE><LHS>sum(cons(x,l))</LHS><RHS>+(x,sum(l))</RHS></RULE><RULE><LHS>prod(nil)</LHS><RHS>1(#)</RHS></RULE><RULE><LHS>prod(cons(x,l))</LHS><RHS> *(x,prod(l))</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_prod(cons(x,l))</LHS><RHS>Marked_prod(l)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><ORDERING type="poly"><POLYSYMB><SYMBOL><NAME>#</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>prod</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>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>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>+</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><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>nil</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>0</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>Marked_prod</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>sum</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>1</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>cons</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></ORDERING></CRITERION></PROPERTY><PROPERTY criterion="stronggraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>0(#)</LHS><RHS>#</RHS></RULE><RULE><LHS>+(x,#)</LHS><RHS>x</RHS></RULE><RULE><LHS>+(#,x)</LHS><RHS>x</RHS></RULE><RULE><LHS>+(0(x),0(y))</LHS><RHS>0(+(x,y))</RHS></RULE><RULE><LHS>+(0(x),1(y))</LHS><RHS>1(+(x,y))</RHS></RULE><RULE><LHS>+(1(x),0(y))</LHS><RHS>1(+(x,y))</RHS></RULE><RULE><LHS>+(1(x),1(y))</LHS><RHS>0(+(+(x,y),1(#)))</RHS></RULE><RULE><LHS>+(+(x,y),z)</LHS><RHS>+(x,+(y,z))</RHS></RULE><RULE><LHS> *(#,x)</LHS><RHS>#</RHS></RULE><RULE><LHS> *(0(x),y)</LHS><RHS>0( *(x,y))</RHS></RULE><RULE><LHS> *(1(x),y)</LHS><RHS>+(0( *(x,y)),y)</RHS></RULE><RULE><LHS> *( *(x,y),z)</LHS><RHS> *(x, *(y,z))</RHS></RULE><RULE><LHS>sum(nil)</LHS><RHS>0(#)</RHS></RULE><RULE><LHS>sum(cons(x,l))</LHS><RHS>+(x,sum(l))</RHS></RULE><RULE><LHS>prod(nil)</LHS><RHS>1(#)</RHS></RULE><RULE><LHS>prod(cons(x,l))</LHS><RHS> *(x,prod(l))</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_*(0(x),y)</LHS><RHS>Marked_*(x,y)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_*(1(x),y)</LHS><RHS>Marked_*(x,y)</RHS></DPRULE><DPRULE num="2"><LHS>Marked_*( *(x,y),z)</LHS><RHS>Marked_*(x, *(y,z))</RHS></DPRULE><DPRULE num="3"><LHS>Marked_*( *(x,y),z)</LHS><RHS>Marked_*(y,z)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><ORDERING type="poly"><POLYSYMB><SYMBOL><NAME>#</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>prod</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>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><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>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><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</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>nil</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>0</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>sum</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>1</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>cons</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>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></SUMPOLY></POLYNOMIAL></POLYSYMB></ORDERING><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_*(1(x),y)</LHS><RHS>Marked_*(x,y)</RHS></DPRULE></DPLIST></STRICTPAIRS></CRITERION><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>0(#)</LHS><RHS>#</RHS></RULE><RULE><LHS>+(x,#)</LHS><RHS>x</RHS></RULE><RULE><LHS>+(#,x)</LHS><RHS>x</RHS></RULE><RULE><LHS>+(0(x),0(y))</LHS><RHS>0(+(x,y))</RHS></RULE><RULE><LHS>+(0(x),1(y))</LHS><RHS>1(+(x,y))</RHS></RULE><RULE><LHS>+(1(x),0(y))</LHS><RHS>1(+(x,y))</RHS></RULE><RULE><LHS>+(1(x),1(y))</LHS><RHS>0(+(+(x,y),1(#)))</RHS></RULE><RULE><LHS>+(+(x,y),z)</LHS><RHS>+(x,+(y,z))</RHS></RULE><RULE><LHS> *(#,x)</LHS><RHS>#</RHS></RULE><RULE><LHS> *(0(x),y)</LHS><RHS>0( *(x,y))</RHS></RULE><RULE><LHS> *(1(x),y)</LHS><RHS>+(0( *(x,y)),y)</RHS></RULE><RULE><LHS> *( *(x,y),z)</LHS><RHS> *(x, *(y,z))</RHS></RULE><RULE><LHS>sum(nil)</LHS><RHS>0(#)</RHS></RULE><RULE><LHS>sum(cons(x,l))</LHS><RHS>+(x,sum(l))</RHS></RULE><RULE><LHS>prod(nil)</LHS><RHS>1(#)</RHS></RULE><RULE><LHS>prod(cons(x,l))</LHS><RHS> *(x,prod(l))</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_*(0(x),y)</LHS><RHS>Marked_*(x,y)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_*( *(x,y),z)</LHS><RHS>Marked_*(x, *(y,z))</RHS></DPRULE><DPRULE num="2"><LHS>Marked_*( *(x,y),z)</LHS><RHS>Marked_*(y,z)</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="stronggraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>0(#)</LHS><RHS>#</RHS></RULE><RULE><LHS>+(x,#)</LHS><RHS>x</RHS></RULE><RULE><LHS>+(#,x)</LHS><RHS>x</RHS></RULE><RULE><LHS>+(0(x),0(y))</LHS><RHS>0(+(x,y))</RHS></RULE><RULE><LHS>+(0(x),1(y))</LHS><RHS>1(+(x,y))</RHS></RULE><RULE><LHS>+(1(x),0(y))</LHS><RHS>1(+(x,y))</RHS></RULE><RULE><LHS>+(1(x),1(y))</LHS><RHS>0(+(+(x,y),1(#)))</RHS></RULE><RULE><LHS>+(+(x,y),z)</LHS><RHS>+(x,+(y,z))</RHS></RULE><RULE><LHS> *(#,x)</LHS><RHS>#</RHS></RULE><RULE><LHS> *(0(x),y)</LHS><RHS>0( *(x,y))</RHS></RULE><RULE><LHS> *(1(x),y)</LHS><RHS>+(0( *(x,y)),y)</RHS></RULE><RULE><LHS> *( *(x,y),z)</LHS><RHS> *(x, *(y,z))</RHS></RULE><RULE><LHS>sum(nil)</LHS><RHS>0(#)</RHS></RULE><RULE><LHS>sum(cons(x,l))</LHS><RHS>+(x,sum(l))</RHS></RULE><RULE><LHS>prod(nil)</LHS><RHS>1(#)</RHS></RULE><RULE><LHS>prod(cons(x,l))</LHS><RHS> *(x,prod(l))</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_*(0(x),y)</LHS><RHS>Marked_*(x,y)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_*( *(x,y),z)</LHS><RHS>Marked_*(x, *(y,z))</RHS></DPRULE><DPRULE num="2"><LHS>Marked_*( *(x,y),z)</LHS><RHS>Marked_*(y,z)</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><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>prod</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>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></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>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>nil</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>0</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>sum</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>1</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>cons</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><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></SUMPOLY></POLYNOMIAL></POLYSYMB></ORDERING><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_*( *(x,y),z)</LHS><RHS>Marked_*(x, *(y,z))</RHS></DPRULE><DPRULE num="1"><LHS>Marked_*( *(x,y),z)</LHS><RHS>Marked_*(y,z)</RHS></DPRULE></DPLIST></STRICTPAIRS></CRITERION><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>0(#)</LHS><RHS>#</RHS></RULE><RULE><LHS>+(x,#)</LHS><RHS>x</RHS></RULE><RULE><LHS>+(#,x)</LHS><RHS>x</RHS></RULE><RULE><LHS>+(0(x),0(y))</LHS><RHS>0(+(x,y))</RHS></RULE><RULE><LHS>+(0(x),1(y))</LHS><RHS>1(+(x,y))</RHS></RULE><RULE><LHS>+(1(x),0(y))</LHS><RHS>1(+(x,y))</RHS></RULE><RULE><LHS>+(1(x),1(y))</LHS><RHS>0(+(+(x,y),1(#)))</RHS></RULE><RULE><LHS>+(+(x,y),z)</LHS><RHS>+(x,+(y,z))</RHS></RULE><RULE><LHS> *(#,x)</LHS><RHS>#</RHS></RULE><RULE><LHS> *(0(x),y)</LHS><RHS>0( *(x,y))</RHS></RULE><RULE><LHS> *(1(x),y)</LHS><RHS>+(0( *(x,y)),y)</RHS></RULE><RULE><LHS> *( *(x,y),z)</LHS><RHS> *(x, *(y,z))</RHS></RULE><RULE><LHS>sum(nil)</LHS><RHS>0(#)</RHS></RULE><RULE><LHS>sum(cons(x,l))</LHS><RHS>+(x,sum(l))</RHS></RULE><RULE><LHS>prod(nil)</LHS><RHS>1(#)</RHS></RULE><RULE><LHS>prod(cons(x,l))</LHS><RHS> *(x,prod(l))</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_*(0(x),y)</LHS><RHS>Marked_*(x,y)</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>0(#)</LHS><RHS>#</RHS></RULE><RULE><LHS>+(x,#)</LHS><RHS>x</RHS></RULE><RULE><LHS>+(#,x)</LHS><RHS>x</RHS></RULE><RULE><LHS>+(0(x),0(y))</LHS><RHS>0(+(x,y))</RHS></RULE><RULE><LHS>+(0(x),1(y))</LHS><RHS>1(+(x,y))</RHS></RULE><RULE><LHS>+(1(x),0(y))</LHS><RHS>1(+(x,y))</RHS></RULE><RULE><LHS>+(1(x),1(y))</LHS><RHS>0(+(+(x,y),1(#)))</RHS></RULE><RULE><LHS>+(+(x,y),z)</LHS><RHS>+(x,+(y,z))</RHS></RULE><RULE><LHS> *(#,x)</LHS><RHS>#</RHS></RULE><RULE><LHS> *(0(x),y)</LHS><RHS>0( *(x,y))</RHS></RULE><RULE><LHS> *(1(x),y)</LHS><RHS>+(0( *(x,y)),y)</RHS></RULE><RULE><LHS> *( *(x,y),z)</LHS><RHS> *(x, *(y,z))</RHS></RULE><RULE><LHS>sum(nil)</LHS><RHS>0(#)</RHS></RULE><RULE><LHS>sum(cons(x,l))</LHS><RHS>+(x,sum(l))</RHS></RULE><RULE><LHS>prod(nil)</LHS><RHS>1(#)</RHS></RULE><RULE><LHS>prod(cons(x,l))</LHS><RHS> *(x,prod(l))</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_*(0(x),y)</LHS><RHS>Marked_*(x,y)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><ORDERING type="poly"><POLYSYMB><SYMBOL><NAME>#</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>prod</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>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><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>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="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>nil</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>0</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>sum</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>1</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>cons</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><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></SUMPOLY></POLYNOMIAL></POLYSYMB></ORDERING></CRITERION></PROPERTY></PROPERTY></PROPERTY></PROPERTY></PROPERTY><PROPERTY criterion="stronggraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>0(#)</LHS><RHS>#</RHS></RULE><RULE><LHS>+(x,#)</LHS><RHS>x</RHS></RULE><RULE><LHS>+(#,x)</LHS><RHS>x</RHS></RULE><RULE><LHS>+(0(x),0(y))</LHS><RHS>0(+(x,y))</RHS></RULE><RULE><LHS>+(0(x),1(y))</LHS><RHS>1(+(x,y))</RHS></RULE><RULE><LHS>+(1(x),0(y))</LHS><RHS>1(+(x,y))</RHS></RULE><RULE><LHS>+(1(x),1(y))</LHS><RHS>0(+(+(x,y),1(#)))</RHS></RULE><RULE><LHS>+(+(x,y),z)</LHS><RHS>+(x,+(y,z))</RHS></RULE><RULE><LHS> *(#,x)</LHS><RHS>#</RHS></RULE><RULE><LHS> *(0(x),y)</LHS><RHS>0( *(x,y))</RHS></RULE><RULE><LHS> *(1(x),y)</LHS><RHS>+(0( *(x,y)),y)</RHS></RULE><RULE><LHS> *( *(x,y),z)</LHS><RHS> *(x, *(y,z))</RHS></RULE><RULE><LHS>sum(nil)</LHS><RHS>0(#)</RHS></RULE><RULE><LHS>sum(cons(x,l))</LHS><RHS>+(x,sum(l))</RHS></RULE><RULE><LHS>prod(nil)</LHS><RHS>1(#)</RHS></RULE><RULE><LHS>prod(cons(x,l))</LHS><RHS> *(x,prod(l))</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_+(0(x),0(y))</LHS><RHS>Marked_+(x,y)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_+(0(x),1(y))</LHS><RHS>Marked_+(x,y)</RHS></DPRULE><DPRULE num="2"><LHS>Marked_+(1(x),0(y))</LHS><RHS>Marked_+(x,y)</RHS></DPRULE><DPRULE num="3"><LHS>Marked_+(1(x),1(y))</LHS><RHS>Marked_+(+(x,y),1(#))</RHS></DPRULE><DPRULE num="4"><LHS>Marked_+(1(x),1(y))</LHS><RHS>Marked_+(x,y)</RHS></DPRULE><DPRULE num="5"><LHS>Marked_+(+(x,y),z)</LHS><RHS>Marked_+(x,+(y,z))</RHS></DPRULE><DPRULE num="6"><LHS>Marked_+(+(x,y),z)</LHS><RHS>Marked_+(y,z)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><ORDERING type="poly"><POLYSYMB><SYMBOL><NAME>#</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>prod</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> *</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><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>Marked_+</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>+</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>nil</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>0</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>sum</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><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>1</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>cons</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><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="0"/><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB></ORDERING><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_+(0(x),1(y))</LHS><RHS>Marked_+(x,y)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_+(1(x),0(y))</LHS><RHS>Marked_+(x,y)</RHS></DPRULE><DPRULE num="2"><LHS>Marked_+(1(x),1(y))</LHS><RHS>Marked_+(x,y)</RHS></DPRULE></DPLIST></STRICTPAIRS></CRITERION><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>0(#)</LHS><RHS>#</RHS></RULE><RULE><LHS>+(x,#)</LHS><RHS>x</RHS></RULE><RULE><LHS>+(#,x)</LHS><RHS>x</RHS></RULE><RULE><LHS>+(0(x),0(y))</LHS><RHS>0(+(x,y))</RHS></RULE><RULE><LHS>+(0(x),1(y))</LHS><RHS>1(+(x,y))</RHS></RULE><RULE><LHS>+(1(x),0(y))</LHS><RHS>1(+(x,y))</RHS></RULE><RULE><LHS>+(1(x),1(y))</LHS><RHS>0(+(+(x,y),1(#)))</RHS></RULE><RULE><LHS>+(+(x,y),z)</LHS><RHS>+(x,+(y,z))</RHS></RULE><RULE><LHS> *(#,x)</LHS><RHS>#</RHS></RULE><RULE><LHS> *(0(x),y)</LHS><RHS>0( *(x,y))</RHS></RULE><RULE><LHS> *(1(x),y)</LHS><RHS>+(0( *(x,y)),y)</RHS></RULE><RULE><LHS> *( *(x,y),z)</LHS><RHS> *(x, *(y,z))</RHS></RULE><RULE><LHS>sum(nil)</LHS><RHS>0(#)</RHS></RULE><RULE><LHS>sum(cons(x,l))</LHS><RHS>+(x,sum(l))</RHS></RULE><RULE><LHS>prod(nil)</LHS><RHS>1(#)</RHS></RULE><RULE><LHS>prod(cons(x,l))</LHS><RHS> *(x,prod(l))</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_+(0(x),0(y))</LHS><RHS>Marked_+(x,y)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_+(1(x),1(y))</LHS><RHS>Marked_+(+(x,y),1(#))</RHS></DPRULE><DPRULE num="2"><LHS>Marked_+(+(x,y),z)</LHS><RHS>Marked_+(x,+(y,z))</RHS></DPRULE><DPRULE num="3"><LHS>Marked_+(+(x,y),z)</LHS><RHS>Marked_+(y,z)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><DAG approx="simpl"><CCLIST><SCC num="0"><NODE ref="0"/><NODE ref="1"/><NODE ref="2"/><NODE ref="3"/></SCC></CCLIST></DAG></CRITERION><PROPERTY criterion="stronggraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>0(#)</LHS><RHS>#</RHS></RULE><RULE><LHS>+(x,#)</LHS><RHS>x</RHS></RULE><RULE><LHS>+(#,x)</LHS><RHS>x</RHS></RULE><RULE><LHS>+(0(x),0(y))</LHS><RHS>0(+(x,y))</RHS></RULE><RULE><LHS>+(0(x),1(y))</LHS><RHS>1(+(x,y))</RHS></RULE><RULE><LHS>+(1(x),0(y))</LHS><RHS>1(+(x,y))</RHS></RULE><RULE><LHS>+(1(x),1(y))</LHS><RHS>0(+(+(x,y),1(#)))</RHS></RULE><RULE><LHS>+(+(x,y),z)</LHS><RHS>+(x,+(y,z))</RHS></RULE><RULE><LHS> *(#,x)</LHS><RHS>#</RHS></RULE><RULE><LHS> *(0(x),y)</LHS><RHS>0( *(x,y))</RHS></RULE><RULE><LHS> *(1(x),y)</LHS><RHS>+(0( *(x,y)),y)</RHS></RULE><RULE><LHS> *( *(x,y),z)</LHS><RHS> *(x, *(y,z))</RHS></RULE><RULE><LHS>sum(nil)</LHS><RHS>0(#)</RHS></RULE><RULE><LHS>sum(cons(x,l))</LHS><RHS>+(x,sum(l))</RHS></RULE><RULE><LHS>prod(nil)</LHS><RHS>1(#)</RHS></RULE><RULE><LHS>prod(cons(x,l))</LHS><RHS> *(x,prod(l))</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_+(0(x),0(y))</LHS><RHS>Marked_+(x,y)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_+(1(x),1(y))</LHS><RHS>Marked_+(+(x,y),1(#))</RHS></DPRULE><DPRULE num="2"><LHS>Marked_+(+(x,y),z)</LHS><RHS>Marked_+(x,+(y,z))</RHS></DPRULE><DPRULE num="3"><LHS>Marked_+(+(x,y),z)</LHS><RHS>Marked_+(y,z)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><ORDERING type="poly"><POLYSYMB><SYMBOL><NAME>#</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>prod</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>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></POLYSYMB><POLYSYMB><SYMBOL><NAME>Marked_+</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>+</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>nil</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>0</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>sum</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>1</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>cons</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>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></ORDERING><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_+(1(x),1(y))</LHS><RHS>Marked_+(+(x,y),1(#))</RHS></DPRULE></DPLIST></STRICTPAIRS></CRITERION><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>0(#)</LHS><RHS>#</RHS></RULE><RULE><LHS>+(x,#)</LHS><RHS>x</RHS></RULE><RULE><LHS>+(#,x)</LHS><RHS>x</RHS></RULE><RULE><LHS>+(0(x),0(y))</LHS><RHS>0(+(x,y))</RHS></RULE><RULE><LHS>+(0(x),1(y))</LHS><RHS>1(+(x,y))</RHS></RULE><RULE><LHS>+(1(x),0(y))</LHS><RHS>1(+(x,y))</RHS></RULE><RULE><LHS>+(1(x),1(y))</LHS><RHS>0(+(+(x,y),1(#)))</RHS></RULE><RULE><LHS>+(+(x,y),z)</LHS><RHS>+(x,+(y,z))</RHS></RULE><RULE><LHS> *(#,x)</LHS><RHS>#</RHS></RULE><RULE><LHS> *(0(x),y)</LHS><RHS>0( *(x,y))</RHS></RULE><RULE><LHS> *(1(x),y)</LHS><RHS>+(0( *(x,y)),y)</RHS></RULE><RULE><LHS> *( *(x,y),z)</LHS><RHS> *(x, *(y,z))</RHS></RULE><RULE><LHS>sum(nil)</LHS><RHS>0(#)</RHS></RULE><RULE><LHS>sum(cons(x,l))</LHS><RHS>+(x,sum(l))</RHS></RULE><RULE><LHS>prod(nil)</LHS><RHS>1(#)</RHS></RULE><RULE><LHS>prod(cons(x,l))</LHS><RHS> *(x,prod(l))</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_+(0(x),0(y))</LHS><RHS>Marked_+(x,y)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_+(+(x,y),z)</LHS><RHS>Marked_+(x,+(y,z))</RHS></DPRULE><DPRULE num="2"><LHS>Marked_+(+(x,y),z)</LHS><RHS>Marked_+(y,z)</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="stronggraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>0(#)</LHS><RHS>#</RHS></RULE><RULE><LHS>+(x,#)</LHS><RHS>x</RHS></RULE><RULE><LHS>+(#,x)</LHS><RHS>x</RHS></RULE><RULE><LHS>+(0(x),0(y))</LHS><RHS>0(+(x,y))</RHS></RULE><RULE><LHS>+(0(x),1(y))</LHS><RHS>1(+(x,y))</RHS></RULE><RULE><LHS>+(1(x),0(y))</LHS><RHS>1(+(x,y))</RHS></RULE><RULE><LHS>+(1(x),1(y))</LHS><RHS>0(+(+(x,y),1(#)))</RHS></RULE><RULE><LHS>+(+(x,y),z)</LHS><RHS>+(x,+(y,z))</RHS></RULE><RULE><LHS> *(#,x)</LHS><RHS>#</RHS></RULE><RULE><LHS> *(0(x),y)</LHS><RHS>0( *(x,y))</RHS></RULE><RULE><LHS> *(1(x),y)</LHS><RHS>+(0( *(x,y)),y)</RHS></RULE><RULE><LHS> *( *(x,y),z)</LHS><RHS> *(x, *(y,z))</RHS></RULE><RULE><LHS>sum(nil)</LHS><RHS>0(#)</RHS></RULE><RULE><LHS>sum(cons(x,l))</LHS><RHS>+(x,sum(l))</RHS></RULE><RULE><LHS>prod(nil)</LHS><RHS>1(#)</RHS></RULE><RULE><LHS>prod(cons(x,l))</LHS><RHS> *(x,prod(l))</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_+(0(x),0(y))</LHS><RHS>Marked_+(x,y)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_+(+(x,y),z)</LHS><RHS>Marked_+(x,+(y,z))</RHS></DPRULE><DPRULE num="2"><LHS>Marked_+(+(x,y),z)</LHS><RHS>Marked_+(y,z)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><ORDERING type="poly"><POLYSYMB><SYMBOL><NAME>#</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>prod</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>1</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="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>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>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>+</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><POLYSYMB><SYMBOL><NAME>nil</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>0</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>sum</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>1</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>cons</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><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</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></SUMPOLY></POLYNOMIAL></POLYSYMB></ORDERING><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_+(+(x,y),z)</LHS><RHS>Marked_+(x,+(y,z))</RHS></DPRULE><DPRULE num="1"><LHS>Marked_+(+(x,y),z)</LHS><RHS>Marked_+(y,z)</RHS></DPRULE></DPLIST></STRICTPAIRS></CRITERION><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>0(#)</LHS><RHS>#</RHS></RULE><RULE><LHS>+(x,#)</LHS><RHS>x</RHS></RULE><RULE><LHS>+(#,x)</LHS><RHS>x</RHS></RULE><RULE><LHS>+(0(x),0(y))</LHS><RHS>0(+(x,y))</RHS></RULE><RULE><LHS>+(0(x),1(y))</LHS><RHS>1(+(x,y))</RHS></RULE><RULE><LHS>+(1(x),0(y))</LHS><RHS>1(+(x,y))</RHS></RULE><RULE><LHS>+(1(x),1(y))</LHS><RHS>0(+(+(x,y),1(#)))</RHS></RULE><RULE><LHS>+(+(x,y),z)</LHS><RHS>+(x,+(y,z))</RHS></RULE><RULE><LHS> *(#,x)</LHS><RHS>#</RHS></RULE><RULE><LHS> *(0(x),y)</LHS><RHS>0( *(x,y))</RHS></RULE><RULE><LHS> *(1(x),y)</LHS><RHS>+(0( *(x,y)),y)</RHS></RULE><RULE><LHS> *( *(x,y),z)</LHS><RHS> *(x, *(y,z))</RHS></RULE><RULE><LHS>sum(nil)</LHS><RHS>0(#)</RHS></RULE><RULE><LHS>sum(cons(x,l))</LHS><RHS>+(x,sum(l))</RHS></RULE><RULE><LHS>prod(nil)</LHS><RHS>1(#)</RHS></RULE><RULE><LHS>prod(cons(x,l))</LHS><RHS> *(x,prod(l))</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_+(0(x),0(y))</LHS><RHS>Marked_+(x,y)</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>0(#)</LHS><RHS>#</RHS></RULE><RULE><LHS>+(x,#)</LHS><RHS>x</RHS></RULE><RULE><LHS>+(#,x)</LHS><RHS>x</RHS></RULE><RULE><LHS>+(0(x),0(y))</LHS><RHS>0(+(x,y))</RHS></RULE><RULE><LHS>+(0(x),1(y))</LHS><RHS>1(+(x,y))</RHS></RULE><RULE><LHS>+(1(x),0(y))</LHS><RHS>1(+(x,y))</RHS></RULE><RULE><LHS>+(1(x),1(y))</LHS><RHS>0(+(+(x,y),1(#)))</RHS></RULE><RULE><LHS>+(+(x,y),z)</LHS><RHS>+(x,+(y,z))</RHS></RULE><RULE><LHS> *(#,x)</LHS><RHS>#</RHS></RULE><RULE><LHS> *(0(x),y)</LHS><RHS>0( *(x,y))</RHS></RULE><RULE><LHS> *(1(x),y)</LHS><RHS>+(0( *(x,y)),y)</RHS></RULE><RULE><LHS> *( *(x,y),z)</LHS><RHS> *(x, *(y,z))</RHS></RULE><RULE><LHS>sum(nil)</LHS><RHS>0(#)</RHS></RULE><RULE><LHS>sum(cons(x,l))</LHS><RHS>+(x,sum(l))</RHS></RULE><RULE><LHS>prod(nil)</LHS><RHS>1(#)</RHS></RULE><RULE><LHS>prod(cons(x,l))</LHS><RHS> *(x,prod(l))</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_+(0(x),0(y))</LHS><RHS>Marked_+(x,y)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><ORDERING type="poly"><POLYSYMB><SYMBOL><NAME>#</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>prod</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>1</INT></COEF><ARG degree="1" num="0"/></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></POLYSYMB><POLYSYMB><SYMBOL><NAME>Marked_+</NAME></SYMBOL><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></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>nil</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>0</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>sum</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>1</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>cons</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>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></ORDERING></CRITERION></PROPERTY></PROPERTY></PROPERTY></PROPERTY></PROPERTY></PROPERTY></PROPERTY></PROPERTY></PROPERTY></PROOF>
