<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE PROOF SYSTEM "http://a3pat.ensiie.fr/pub/a3pat.dtd">
<PROOF><SIGNATURE><SYMBOLLIST><SYMBOL arity="0" unmarked=""><NAME>p5</NAME></SYMBOL><SYMBOL arity="2" unmarked="+"><NAME>Marked_+</NAME></SYMBOL><SYMBOL arity="2" unmarked=""><NAME>+</NAME></SYMBOL><SYMBOL arity="0" unmarked=""><NAME>p1</NAME></SYMBOL><SYMBOL arity="0" unmarked=""><NAME>p10</NAME></SYMBOL><SYMBOL arity="0" unmarked=""><NAME>p2</NAME></SYMBOL></SYMBOLLIST><VARLIST><VAR>z</VAR><VAR>y</VAR><VAR>x</VAR></VARLIST></SIGNATURE><PROPERTY criterion="dp" prop="sntrs"><SYSTEM><REWSYS><RULE><LHS>+(p1,p1)</LHS><RHS>p2</RHS></RULE><RULE><LHS>+(p1,+(p2,p2))</LHS><RHS>p5</RHS></RULE><RULE><LHS>+(p5,p5)</LHS><RHS>p10</RHS></RULE><RULE><LHS>+(+(x,y),z)</LHS><RHS>+(x,+(y,z))</RHS></RULE><RULE><LHS>+(p1,+(p1,x))</LHS><RHS>+(p2,x)</RHS></RULE><RULE><LHS>+(p1,+(p2,+(p2,x)))</LHS><RHS>+(p5,x)</RHS></RULE><RULE><LHS>+(p2,p1)</LHS><RHS>+(p1,p2)</RHS></RULE><RULE><LHS>+(p2,+(p1,x))</LHS><RHS>+(p1,+(p2,x))</RHS></RULE><RULE><LHS>+(p2,+(p2,p2))</LHS><RHS>+(p1,p5)</RHS></RULE><RULE><LHS>+(p2,+(p2,+(p2,x)))</LHS><RHS>+(p1,+(p5,x))</RHS></RULE><RULE><LHS>+(p5,p1)</LHS><RHS>+(p1,p5)</RHS></RULE><RULE><LHS>+(p5,+(p1,x))</LHS><RHS>+(p1,+(p5,x))</RHS></RULE><RULE><LHS>+(p5,p2)</LHS><RHS>+(p2,p5)</RHS></RULE><RULE><LHS>+(p5,+(p2,x))</LHS><RHS>+(p2,+(p5,x))</RHS></RULE><RULE><LHS>+(p5,+(p5,x))</LHS><RHS>+(p10,x)</RHS></RULE><RULE><LHS>+(p10,p1)</LHS><RHS>+(p1,p10)</RHS></RULE><RULE><LHS>+(p10,+(p1,x))</LHS><RHS>+(p1,+(p10,x))</RHS></RULE><RULE><LHS>+(p10,p2)</LHS><RHS>+(p2,p10)</RHS></RULE><RULE><LHS>+(p10,+(p2,x))</LHS><RHS>+(p2,+(p10,x))</RHS></RULE><RULE><LHS>+(p10,p5)</LHS><RHS>+(p5,p10)</RHS></RULE><RULE><LHS>+(p10,+(p5,x))</LHS><RHS>+(p5,+(p10,x))</RHS></RULE></REWSYS></SYSTEM><CRITERION/><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>+(p1,p1)</LHS><RHS>p2</RHS></RULE><RULE><LHS>+(p1,+(p2,p2))</LHS><RHS>p5</RHS></RULE><RULE><LHS>+(p5,p5)</LHS><RHS>p10</RHS></RULE><RULE><LHS>+(+(x,y),z)</LHS><RHS>+(x,+(y,z))</RHS></RULE><RULE><LHS>+(p1,+(p1,x))</LHS><RHS>+(p2,x)</RHS></RULE><RULE><LHS>+(p1,+(p2,+(p2,x)))</LHS><RHS>+(p5,x)</RHS></RULE><RULE><LHS>+(p2,p1)</LHS><RHS>+(p1,p2)</RHS></RULE><RULE><LHS>+(p2,+(p1,x))</LHS><RHS>+(p1,+(p2,x))</RHS></RULE><RULE><LHS>+(p2,+(p2,p2))</LHS><RHS>+(p1,p5)</RHS></RULE><RULE><LHS>+(p2,+(p2,+(p2,x)))</LHS><RHS>+(p1,+(p5,x))</RHS></RULE><RULE><LHS>+(p5,p1)</LHS><RHS>+(p1,p5)</RHS></RULE><RULE><LHS>+(p5,+(p1,x))</LHS><RHS>+(p1,+(p5,x))</RHS></RULE><RULE><LHS>+(p5,p2)</LHS><RHS>+(p2,p5)</RHS></RULE><RULE><LHS>+(p5,+(p2,x))</LHS><RHS>+(p2,+(p5,x))</RHS></RULE><RULE><LHS>+(p5,+(p5,x))</LHS><RHS>+(p10,x)</RHS></RULE><RULE><LHS>+(p10,p1)</LHS><RHS>+(p1,p10)</RHS></RULE><RULE><LHS>+(p10,+(p1,x))</LHS><RHS>+(p1,+(p10,x))</RHS></RULE><RULE><LHS>+(p10,p2)</LHS><RHS>+(p2,p10)</RHS></RULE><RULE><LHS>+(p10,+(p2,x))</LHS><RHS>+(p2,+(p10,x))</RHS></RULE><RULE><LHS>+(p10,p5)</LHS><RHS>+(p5,p10)</RHS></RULE><RULE><LHS>+(p10,+(p5,x))</LHS><RHS>+(p5,+(p10,x))</RHS></RULE></REWSYS><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><DPRULE num="2"><LHS>Marked_+(p1,+(p1,x))</LHS><RHS>Marked_+(p2,x)</RHS></DPRULE><DPRULE num="3"><LHS>Marked_+(p1,+(p2,+(p2,x)))</LHS><RHS>Marked_+(p5,x)</RHS></DPRULE><DPRULE num="4"><LHS>Marked_+(p2,p1)</LHS><RHS>Marked_+(p1,p2)</RHS></DPRULE><DPRULE num="5"><LHS>Marked_+(p2,+(p1,x))</LHS><RHS>Marked_+(p1,+(p2,x))</RHS></DPRULE><DPRULE num="6"><LHS>Marked_+(p2,+(p1,x))</LHS><RHS>Marked_+(p2,x)</RHS></DPRULE><DPRULE num="7"><LHS>Marked_+(p2,+(p2,p2))</LHS><RHS>Marked_+(p1,p5)</RHS></DPRULE><DPRULE num="8"><LHS>Marked_+(p2,+(p2,+(p2,x)))</LHS><RHS>Marked_+(p1,+(p5,x))</RHS></DPRULE><DPRULE num="9"><LHS>Marked_+(p2,+(p2,+(p2,x)))</LHS><RHS>Marked_+(p5,x)</RHS></DPRULE><DPRULE num="10"><LHS>Marked_+(p5,p1)</LHS><RHS>Marked_+(p1,p5)</RHS></DPRULE><DPRULE num="11"><LHS>Marked_+(p5,+(p1,x))</LHS><RHS>Marked_+(p1,+(p5,x))</RHS></DPRULE><DPRULE num="12"><LHS>Marked_+(p5,+(p1,x))</LHS><RHS>Marked_+(p5,x)</RHS></DPRULE><DPRULE num="13"><LHS>Marked_+(p5,p2)</LHS><RHS>Marked_+(p2,p5)</RHS></DPRULE><DPRULE num="14"><LHS>Marked_+(p5,+(p2,x))</LHS><RHS>Marked_+(p2,+(p5,x))</RHS></DPRULE><DPRULE num="15"><LHS>Marked_+(p5,+(p2,x))</LHS><RHS>Marked_+(p5,x)</RHS></DPRULE><DPRULE num="16"><LHS>Marked_+(p5,+(p5,x))</LHS><RHS>Marked_+(p10,x)</RHS></DPRULE><DPRULE num="17"><LHS>Marked_+(p10,p1)</LHS><RHS>Marked_+(p1,p10)</RHS></DPRULE><DPRULE num="18"><LHS>Marked_+(p10,+(p1,x))</LHS><RHS>Marked_+(p1,+(p10,x))</RHS></DPRULE><DPRULE num="19"><LHS>Marked_+(p10,+(p1,x))</LHS><RHS>Marked_+(p10,x)</RHS></DPRULE><DPRULE num="20"><LHS>Marked_+(p10,p2)</LHS><RHS>Marked_+(p2,p10)</RHS></DPRULE><DPRULE num="21"><LHS>Marked_+(p10,+(p2,x))</LHS><RHS>Marked_+(p2,+(p10,x))</RHS></DPRULE><DPRULE num="22"><LHS>Marked_+(p10,+(p2,x))</LHS><RHS>Marked_+(p10,x)</RHS></DPRULE><DPRULE num="23"><LHS>Marked_+(p10,p5)</LHS><RHS>Marked_+(p5,p10)</RHS></DPRULE><DPRULE num="24"><LHS>Marked_+(p10,+(p5,x))</LHS><RHS>Marked_+(p5,+(p10,x))</RHS></DPRULE><DPRULE num="25"><LHS>Marked_+(p10,+(p5,x))</LHS><RHS>Marked_+(p10,x)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><DAG approx="simpl"><CCLIST><SCC num="0"><NODE ref="2"/><NODE ref="3"/><NODE ref="5"/><NODE ref="6"/><NODE ref="8"/><NODE ref="9"/><NODE ref="11"/><NODE ref="12"/><NODE ref="14"/><NODE ref="15"/><NODE ref="16"/><NODE ref="18"/><NODE ref="19"/><NODE ref="21"/><NODE ref="22"/><NODE ref="24"/><NODE ref="25"/></SCC><NONSCC num="1"><NODE ref="23"/></NONSCC><NONSCC num="2"><NODE ref="20"/></NONSCC><NONSCC num="3"><NODE ref="17"/></NONSCC><NONSCC num="4"><NODE ref="13"/></NONSCC><NONSCC num="5"><NODE ref="10"/></NONSCC><NONSCC num="6"><NODE ref="7"/></NONSCC><NONSCC num="7"><NODE ref="4"/></NONSCC><SCC num="8"><NODE ref="0"/><NODE ref="1"/></SCC></CCLIST><EDGE end="7" start="0"/><EDGE end="6" start="0"/><EDGE end="5" start="0"/><EDGE end="4" start="0"/><EDGE end="3" start="0"/><EDGE end="2" start="0"/><EDGE end="1" start="0"/><EDGE end="7" start="8"/><EDGE end="6" start="8"/><EDGE end="5" start="8"/><EDGE end="4" start="8"/><EDGE end="3" start="8"/><EDGE end="2" start="8"/><EDGE end="1" start="8"/><EDGE end="0" start="8"/></DAG></CRITERION><PROPERTY criterion="sterm" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>+(p1,p1)</LHS><RHS>p2</RHS></RULE><RULE><LHS>+(p1,+(p2,p2))</LHS><RHS>p5</RHS></RULE><RULE><LHS>+(p5,p5)</LHS><RHS>p10</RHS></RULE><RULE><LHS>+(+(x,y),z)</LHS><RHS>+(x,+(y,z))</RHS></RULE><RULE><LHS>+(p1,+(p1,x))</LHS><RHS>+(p2,x)</RHS></RULE><RULE><LHS>+(p1,+(p2,+(p2,x)))</LHS><RHS>+(p5,x)</RHS></RULE><RULE><LHS>+(p2,p1)</LHS><RHS>+(p1,p2)</RHS></RULE><RULE><LHS>+(p2,+(p1,x))</LHS><RHS>+(p1,+(p2,x))</RHS></RULE><RULE><LHS>+(p2,+(p2,p2))</LHS><RHS>+(p1,p5)</RHS></RULE><RULE><LHS>+(p2,+(p2,+(p2,x)))</LHS><RHS>+(p1,+(p5,x))</RHS></RULE><RULE><LHS>+(p5,p1)</LHS><RHS>+(p1,p5)</RHS></RULE><RULE><LHS>+(p5,+(p1,x))</LHS><RHS>+(p1,+(p5,x))</RHS></RULE><RULE><LHS>+(p5,p2)</LHS><RHS>+(p2,p5)</RHS></RULE><RULE><LHS>+(p5,+(p2,x))</LHS><RHS>+(p2,+(p5,x))</RHS></RULE><RULE><LHS>+(p5,+(p5,x))</LHS><RHS>+(p10,x)</RHS></RULE><RULE><LHS>+(p10,p1)</LHS><RHS>+(p1,p10)</RHS></RULE><RULE><LHS>+(p10,+(p1,x))</LHS><RHS>+(p1,+(p10,x))</RHS></RULE><RULE><LHS>+(p10,p2)</LHS><RHS>+(p2,p10)</RHS></RULE><RULE><LHS>+(p10,+(p2,x))</LHS><RHS>+(p2,+(p10,x))</RHS></RULE><RULE><LHS>+(p10,p5)</LHS><RHS>+(p5,p10)</RHS></RULE><RULE><LHS>+(p10,+(p5,x))</LHS><RHS>+(p5,+(p10,x))</RHS></RULE></REWSYS><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></DPSYS></SYSTEM><PROJECTION><PROJ><SYMBOL><NAME>Marked_+</NAME></SYMBOL><INT>1</INT></PROJ></PROJECTION><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_+(+(x,y),z)</LHS><RHS>Marked_+(y,z)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_+(+(x,y),z)</LHS><RHS>Marked_+(x,+(y,z))</RHS></DPRULE></DPLIST></STRICTPAIRS><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>+(p1,p1)</LHS><RHS>p2</RHS></RULE><RULE><LHS>+(p1,+(p2,p2))</LHS><RHS>p5</RHS></RULE><RULE><LHS>+(p5,p5)</LHS><RHS>p10</RHS></RULE><RULE><LHS>+(+(x,y),z)</LHS><RHS>+(x,+(y,z))</RHS></RULE><RULE><LHS>+(p1,+(p1,x))</LHS><RHS>+(p2,x)</RHS></RULE><RULE><LHS>+(p1,+(p2,+(p2,x)))</LHS><RHS>+(p5,x)</RHS></RULE><RULE><LHS>+(p2,p1)</LHS><RHS>+(p1,p2)</RHS></RULE><RULE><LHS>+(p2,+(p1,x))</LHS><RHS>+(p1,+(p2,x))</RHS></RULE><RULE><LHS>+(p2,+(p2,p2))</LHS><RHS>+(p1,p5)</RHS></RULE><RULE><LHS>+(p2,+(p2,+(p2,x)))</LHS><RHS>+(p1,+(p5,x))</RHS></RULE><RULE><LHS>+(p5,p1)</LHS><RHS>+(p1,p5)</RHS></RULE><RULE><LHS>+(p5,+(p1,x))</LHS><RHS>+(p1,+(p5,x))</RHS></RULE><RULE><LHS>+(p5,p2)</LHS><RHS>+(p2,p5)</RHS></RULE><RULE><LHS>+(p5,+(p2,x))</LHS><RHS>+(p2,+(p5,x))</RHS></RULE><RULE><LHS>+(p5,+(p5,x))</LHS><RHS>+(p10,x)</RHS></RULE><RULE><LHS>+(p10,p1)</LHS><RHS>+(p1,p10)</RHS></RULE><RULE><LHS>+(p10,+(p1,x))</LHS><RHS>+(p1,+(p10,x))</RHS></RULE><RULE><LHS>+(p10,p2)</LHS><RHS>+(p2,p10)</RHS></RULE><RULE><LHS>+(p10,+(p2,x))</LHS><RHS>+(p2,+(p10,x))</RHS></RULE><RULE><LHS>+(p10,p5)</LHS><RHS>+(p5,p10)</RHS></RULE><RULE><LHS>+(p10,+(p5,x))</LHS><RHS>+(p5,+(p10,x))</RHS></RULE></REWSYS><DPLIST/></DPSYS></SYSTEM><CRITERION><DAG approx="simpl"><CCLIST/></DAG></CRITERION></PROPERTY></PROPERTY><PROPERTY criterion="stronggraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>+(p1,p1)</LHS><RHS>p2</RHS></RULE><RULE><LHS>+(p1,+(p2,p2))</LHS><RHS>p5</RHS></RULE><RULE><LHS>+(p5,p5)</LHS><RHS>p10</RHS></RULE><RULE><LHS>+(+(x,y),z)</LHS><RHS>+(x,+(y,z))</RHS></RULE><RULE><LHS>+(p1,+(p1,x))</LHS><RHS>+(p2,x)</RHS></RULE><RULE><LHS>+(p1,+(p2,+(p2,x)))</LHS><RHS>+(p5,x)</RHS></RULE><RULE><LHS>+(p2,p1)</LHS><RHS>+(p1,p2)</RHS></RULE><RULE><LHS>+(p2,+(p1,x))</LHS><RHS>+(p1,+(p2,x))</RHS></RULE><RULE><LHS>+(p2,+(p2,p2))</LHS><RHS>+(p1,p5)</RHS></RULE><RULE><LHS>+(p2,+(p2,+(p2,x)))</LHS><RHS>+(p1,+(p5,x))</RHS></RULE><RULE><LHS>+(p5,p1)</LHS><RHS>+(p1,p5)</RHS></RULE><RULE><LHS>+(p5,+(p1,x))</LHS><RHS>+(p1,+(p5,x))</RHS></RULE><RULE><LHS>+(p5,p2)</LHS><RHS>+(p2,p5)</RHS></RULE><RULE><LHS>+(p5,+(p2,x))</LHS><RHS>+(p2,+(p5,x))</RHS></RULE><RULE><LHS>+(p5,+(p5,x))</LHS><RHS>+(p10,x)</RHS></RULE><RULE><LHS>+(p10,p1)</LHS><RHS>+(p1,p10)</RHS></RULE><RULE><LHS>+(p10,+(p1,x))</LHS><RHS>+(p1,+(p10,x))</RHS></RULE><RULE><LHS>+(p10,p2)</LHS><RHS>+(p2,p10)</RHS></RULE><RULE><LHS>+(p10,+(p2,x))</LHS><RHS>+(p2,+(p10,x))</RHS></RULE><RULE><LHS>+(p10,p5)</LHS><RHS>+(p5,p10)</RHS></RULE><RULE><LHS>+(p10,+(p5,x))</LHS><RHS>+(p5,+(p10,x))</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_+(p1,+(p1,x))</LHS><RHS>Marked_+(p2,x)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_+(p1,+(p2,+(p2,x)))</LHS><RHS>Marked_+(p5,x)</RHS></DPRULE><DPRULE num="2"><LHS>Marked_+(p2,+(p1,x))</LHS><RHS>Marked_+(p1,+(p2,x))</RHS></DPRULE><DPRULE num="3"><LHS>Marked_+(p2,+(p1,x))</LHS><RHS>Marked_+(p2,x)</RHS></DPRULE><DPRULE num="4"><LHS>Marked_+(p2,+(p2,+(p2,x)))</LHS><RHS>Marked_+(p1,+(p5,x))</RHS></DPRULE><DPRULE num="5"><LHS>Marked_+(p2,+(p2,+(p2,x)))</LHS><RHS>Marked_+(p5,x)</RHS></DPRULE><DPRULE num="6"><LHS>Marked_+(p5,+(p1,x))</LHS><RHS>Marked_+(p1,+(p5,x))</RHS></DPRULE><DPRULE num="7"><LHS>Marked_+(p5,+(p1,x))</LHS><RHS>Marked_+(p5,x)</RHS></DPRULE><DPRULE num="8"><LHS>Marked_+(p5,+(p2,x))</LHS><RHS>Marked_+(p2,+(p5,x))</RHS></DPRULE><DPRULE num="9"><LHS>Marked_+(p5,+(p2,x))</LHS><RHS>Marked_+(p5,x)</RHS></DPRULE><DPRULE num="10"><LHS>Marked_+(p5,+(p5,x))</LHS><RHS>Marked_+(p10,x)</RHS></DPRULE><DPRULE num="11"><LHS>Marked_+(p10,+(p1,x))</LHS><RHS>Marked_+(p1,+(p10,x))</RHS></DPRULE><DPRULE num="12"><LHS>Marked_+(p10,+(p1,x))</LHS><RHS>Marked_+(p10,x)</RHS></DPRULE><DPRULE num="13"><LHS>Marked_+(p10,+(p2,x))</LHS><RHS>Marked_+(p2,+(p10,x))</RHS></DPRULE><DPRULE num="14"><LHS>Marked_+(p10,+(p2,x))</LHS><RHS>Marked_+(p10,x)</RHS></DPRULE><DPRULE num="15"><LHS>Marked_+(p10,+(p5,x))</LHS><RHS>Marked_+(p5,+(p10,x))</RHS></DPRULE><DPRULE num="16"><LHS>Marked_+(p10,+(p5,x))</LHS><RHS>Marked_+(p10,x)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><ORDERING type="poly"><POLYSYMB><SYMBOL><NAME>p2</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>p10</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>p1</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>+</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF></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>Marked_+</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>p5</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB></ORDERING><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_+(p1,+(p1,x))</LHS><RHS>Marked_+(p2,x)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_+(p1,+(p2,+(p2,x)))</LHS><RHS>Marked_+(p5,x)</RHS></DPRULE><DPRULE num="2"><LHS>Marked_+(p2,+(p1,x))</LHS><RHS>Marked_+(p2,x)</RHS></DPRULE><DPRULE num="3"><LHS>Marked_+(p2,+(p2,+(p2,x)))</LHS><RHS>Marked_+(p1,+(p5,x))</RHS></DPRULE><DPRULE num="4"><LHS>Marked_+(p2,+(p2,+(p2,x)))</LHS><RHS>Marked_+(p5,x)</RHS></DPRULE><DPRULE num="5"><LHS>Marked_+(p5,+(p1,x))</LHS><RHS>Marked_+(p5,x)</RHS></DPRULE><DPRULE num="6"><LHS>Marked_+(p5,+(p2,x))</LHS><RHS>Marked_+(p5,x)</RHS></DPRULE><DPRULE num="7"><LHS>Marked_+(p5,+(p5,x))</LHS><RHS>Marked_+(p10,x)</RHS></DPRULE><DPRULE num="8"><LHS>Marked_+(p10,+(p1,x))</LHS><RHS>Marked_+(p10,x)</RHS></DPRULE><DPRULE num="9"><LHS>Marked_+(p10,+(p2,x))</LHS><RHS>Marked_+(p10,x)</RHS></DPRULE><DPRULE num="10"><LHS>Marked_+(p10,+(p5,x))</LHS><RHS>Marked_+(p10,x)</RHS></DPRULE></DPLIST></STRICTPAIRS></CRITERION><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>+(p1,p1)</LHS><RHS>p2</RHS></RULE><RULE><LHS>+(p1,+(p2,p2))</LHS><RHS>p5</RHS></RULE><RULE><LHS>+(p5,p5)</LHS><RHS>p10</RHS></RULE><RULE><LHS>+(+(x,y),z)</LHS><RHS>+(x,+(y,z))</RHS></RULE><RULE><LHS>+(p1,+(p1,x))</LHS><RHS>+(p2,x)</RHS></RULE><RULE><LHS>+(p1,+(p2,+(p2,x)))</LHS><RHS>+(p5,x)</RHS></RULE><RULE><LHS>+(p2,p1)</LHS><RHS>+(p1,p2)</RHS></RULE><RULE><LHS>+(p2,+(p1,x))</LHS><RHS>+(p1,+(p2,x))</RHS></RULE><RULE><LHS>+(p2,+(p2,p2))</LHS><RHS>+(p1,p5)</RHS></RULE><RULE><LHS>+(p2,+(p2,+(p2,x)))</LHS><RHS>+(p1,+(p5,x))</RHS></RULE><RULE><LHS>+(p5,p1)</LHS><RHS>+(p1,p5)</RHS></RULE><RULE><LHS>+(p5,+(p1,x))</LHS><RHS>+(p1,+(p5,x))</RHS></RULE><RULE><LHS>+(p5,p2)</LHS><RHS>+(p2,p5)</RHS></RULE><RULE><LHS>+(p5,+(p2,x))</LHS><RHS>+(p2,+(p5,x))</RHS></RULE><RULE><LHS>+(p5,+(p5,x))</LHS><RHS>+(p10,x)</RHS></RULE><RULE><LHS>+(p10,p1)</LHS><RHS>+(p1,p10)</RHS></RULE><RULE><LHS>+(p10,+(p1,x))</LHS><RHS>+(p1,+(p10,x))</RHS></RULE><RULE><LHS>+(p10,p2)</LHS><RHS>+(p2,p10)</RHS></RULE><RULE><LHS>+(p10,+(p2,x))</LHS><RHS>+(p2,+(p10,x))</RHS></RULE><RULE><LHS>+(p10,p5)</LHS><RHS>+(p5,p10)</RHS></RULE><RULE><LHS>+(p10,+(p5,x))</LHS><RHS>+(p5,+(p10,x))</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_+(p2,+(p1,x))</LHS><RHS>Marked_+(p1,+(p2,x))</RHS></DPRULE><DPRULE num="1"><LHS>Marked_+(p5,+(p1,x))</LHS><RHS>Marked_+(p1,+(p5,x))</RHS></DPRULE><DPRULE num="2"><LHS>Marked_+(p5,+(p2,x))</LHS><RHS>Marked_+(p2,+(p5,x))</RHS></DPRULE><DPRULE num="3"><LHS>Marked_+(p10,+(p1,x))</LHS><RHS>Marked_+(p1,+(p10,x))</RHS></DPRULE><DPRULE num="4"><LHS>Marked_+(p10,+(p2,x))</LHS><RHS>Marked_+(p2,+(p10,x))</RHS></DPRULE><DPRULE num="5"><LHS>Marked_+(p10,+(p5,x))</LHS><RHS>Marked_+(p5,+(p10,x))</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><DAG approx="simpl"><CCLIST><NONSCC num="0"><NODE ref="5"/></NONSCC><NONSCC num="1"><NODE ref="2"/></NONSCC><NONSCC num="2"><NODE ref="1"/></NONSCC><NONSCC num="3"><NODE ref="4"/></NONSCC><NONSCC num="4"><NODE ref="0"/></NONSCC><NONSCC num="5"><NODE ref="3"/></NONSCC></CCLIST><EDGE end="2" start="0"/><EDGE end="1" start="0"/><EDGE end="4" start="1"/><EDGE end="4" start="3"/></DAG></CRITERION></PROPERTY></PROPERTY></PROPERTY></PROPERTY></PROOF>
