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<!DOCTYPE PROOF SYSTEM "http://a3pat.ensiie.fr/pub/a3pat.dtd">
<PROOF><SIGNATURE><SYMBOLLIST><SYMBOL arity="1" unmarked="s"><NAME>Marked_s</NAME></SYMBOL><SYMBOL arity="2" unmarked=""><NAME>+</NAME></SYMBOL><SYMBOL arity="2" unmarked=""><NAME> *</NAME></SYMBOL><SYMBOL arity="4" unmarked="a"><NAME>Marked_a</NAME></SYMBOL><SYMBOL arity="4" unmarked=""><NAME>a</NAME></SYMBOL><SYMBOL arity="2" unmarked="*"><NAME>Marked_*</NAME></SYMBOL><SYMBOL arity="0" unmarked=""><NAME>h</NAME></SYMBOL><SYMBOL arity="0" unmarked=""><NAME>1</NAME></SYMBOL><SYMBOL arity="2" unmarked="+"><NAME>Marked_+</NAME></SYMBOL><SYMBOL arity="1" unmarked=""><NAME>s</NAME></SYMBOL></SYMBOLLIST><VARLIST><VAR>l</VAR><VAR>x</VAR><VAR>y</VAR><VAR>z</VAR></VARLIST></SIGNATURE><PROPERTY criterion="dp" prop="sntrs"><SYSTEM><REWSYS><RULE><LHS>a(h,h,h,x)</LHS><RHS>s(x)</RHS></RULE><RULE><LHS>a(l,x,s(y),h)</LHS><RHS>a(l,x,y,s(h))</RHS></RULE><RULE><LHS>a(l,x,s(y),s(z))</LHS><RHS>a(l,x,y,a(l,x,s(y),z))</RHS></RULE><RULE><LHS>a(l,s(x),h,z)</LHS><RHS>a(l,x,z,z)</RHS></RULE><RULE><LHS>a(s(l),h,h,z)</LHS><RHS>a(l,z,h,z)</RHS></RULE><RULE><LHS>+(x,h)</LHS><RHS>x</RHS></RULE><RULE><LHS>+(h,x)</LHS><RHS>x</RHS></RULE><RULE><LHS>+(s(x),s(y))</LHS><RHS>s(s(+(x,y)))</RHS></RULE><RULE><LHS>+(+(x,y),z)</LHS><RHS>+(x,+(y,z))</RHS></RULE><RULE><LHS>s(h)</LHS><RHS>1</RHS></RULE><RULE><LHS> *(h,x)</LHS><RHS>h</RHS></RULE><RULE><LHS> *(x,h)</LHS><RHS>h</RHS></RULE><RULE><LHS> *(s(x),s(y))</LHS><RHS>s(+(+( *(x,y),x),y))</RHS></RULE></REWSYS></SYSTEM><CRITERION/><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>a(h,h,h,x)</LHS><RHS>s(x)</RHS></RULE><RULE><LHS>a(l,x,s(y),h)</LHS><RHS>a(l,x,y,s(h))</RHS></RULE><RULE><LHS>a(l,x,s(y),s(z))</LHS><RHS>a(l,x,y,a(l,x,s(y),z))</RHS></RULE><RULE><LHS>a(l,s(x),h,z)</LHS><RHS>a(l,x,z,z)</RHS></RULE><RULE><LHS>a(s(l),h,h,z)</LHS><RHS>a(l,z,h,z)</RHS></RULE><RULE><LHS>+(x,h)</LHS><RHS>x</RHS></RULE><RULE><LHS>+(h,x)</LHS><RHS>x</RHS></RULE><RULE><LHS>+(s(x),s(y))</LHS><RHS>s(s(+(x,y)))</RHS></RULE><RULE><LHS>+(+(x,y),z)</LHS><RHS>+(x,+(y,z))</RHS></RULE><RULE><LHS>s(h)</LHS><RHS>1</RHS></RULE><RULE><LHS> *(h,x)</LHS><RHS>h</RHS></RULE><RULE><LHS> *(x,h)</LHS><RHS>h</RHS></RULE><RULE><LHS> *(s(x),s(y))</LHS><RHS>s(+(+( *(x,y),x),y))</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_a(h,h,h,x)</LHS><RHS>Marked_s(x)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_a(l,x,s(y),h)</LHS><RHS>Marked_a(l,x,y,s(h))</RHS></DPRULE><DPRULE num="2"><LHS>Marked_a(l,x,s(y),h)</LHS><RHS>Marked_s(h)</RHS></DPRULE><DPRULE num="3"><LHS>Marked_a(l,x,s(y),s(z))</LHS><RHS>Marked_a(l,x,y,a(l,x,s(y),z))</RHS></DPRULE><DPRULE num="4"><LHS>Marked_a(l,x,s(y),s(z))</LHS><RHS>Marked_a(l,x,s(y),z)</RHS></DPRULE><DPRULE num="5"><LHS>Marked_a(l,s(x),h,z)</LHS><RHS>Marked_a(l,x,z,z)</RHS></DPRULE><DPRULE num="6"><LHS>Marked_a(s(l),h,h,z)</LHS><RHS>Marked_a(l,z,h,z)</RHS></DPRULE><DPRULE num="7"><LHS>Marked_+(s(x),s(y))</LHS><RHS>Marked_s(s(+(x,y)))</RHS></DPRULE><DPRULE num="8"><LHS>Marked_+(s(x),s(y))</LHS><RHS>Marked_s(+(x,y))</RHS></DPRULE><DPRULE num="9"><LHS>Marked_+(s(x),s(y))</LHS><RHS>Marked_+(x,y)</RHS></DPRULE><DPRULE num="10"><LHS>Marked_+(+(x,y),z)</LHS><RHS>Marked_+(x,+(y,z))</RHS></DPRULE><DPRULE num="11"><LHS>Marked_+(+(x,y),z)</LHS><RHS>Marked_+(y,z)</RHS></DPRULE><DPRULE num="12"><LHS>Marked_*(s(x),s(y))</LHS><RHS>Marked_s(+(+( *(x,y),x),y))</RHS></DPRULE><DPRULE num="13"><LHS>Marked_*(s(x),s(y))</LHS><RHS>Marked_+(+( *(x,y),x),y)</RHS></DPRULE><DPRULE num="14"><LHS>Marked_*(s(x),s(y))</LHS><RHS>Marked_+( *(x,y),x)</RHS></DPRULE><DPRULE num="15"><LHS>Marked_*(s(x),s(y))</LHS><RHS>Marked_*(x,y)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><DAG approx="simpl"><CCLIST><SCC num="0"><NODE ref="15"/></SCC><NONSCC num="1"><NODE ref="14"/></NONSCC><NONSCC num="2"><NODE ref="13"/></NONSCC><NONSCC num="3"><NODE ref="12"/></NONSCC><SCC num="4"><NODE ref="9"/><NODE ref="10"/><NODE ref="11"/></SCC><NONSCC num="5"><NODE ref="8"/></NONSCC><NONSCC num="6"><NODE ref="7"/></NONSCC><SCC num="7"><NODE ref="1"/><NODE ref="3"/><NODE ref="4"/><NODE ref="5"/><NODE ref="6"/></SCC><NONSCC num="8"><NODE ref="0"/></NONSCC><NONSCC num="9"><NODE ref="2"/></NONSCC></CCLIST><EDGE end="3" start="0"/><EDGE end="2" start="0"/><EDGE end="1" start="0"/><EDGE end="6" start="1"/><EDGE end="5" start="1"/><EDGE end="4" start="1"/><EDGE end="6" start="2"/><EDGE end="5" start="2"/><EDGE end="4" start="2"/><EDGE end="6" start="4"/><EDGE end="5" start="4"/><EDGE end="9" start="7"/><EDGE end="8" start="7"/></DAG></CRITERION><PROPERTY criterion="sterm" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>a(h,h,h,x)</LHS><RHS>s(x)</RHS></RULE><RULE><LHS>a(l,x,s(y),h)</LHS><RHS>a(l,x,y,s(h))</RHS></RULE><RULE><LHS>a(l,x,s(y),s(z))</LHS><RHS>a(l,x,y,a(l,x,s(y),z))</RHS></RULE><RULE><LHS>a(l,s(x),h,z)</LHS><RHS>a(l,x,z,z)</RHS></RULE><RULE><LHS>a(s(l),h,h,z)</LHS><RHS>a(l,z,h,z)</RHS></RULE><RULE><LHS>+(x,h)</LHS><RHS>x</RHS></RULE><RULE><LHS>+(h,x)</LHS><RHS>x</RHS></RULE><RULE><LHS>+(s(x),s(y))</LHS><RHS>s(s(+(x,y)))</RHS></RULE><RULE><LHS>+(+(x,y),z)</LHS><RHS>+(x,+(y,z))</RHS></RULE><RULE><LHS>s(h)</LHS><RHS>1</RHS></RULE><RULE><LHS> *(h,x)</LHS><RHS>h</RHS></RULE><RULE><LHS> *(x,h)</LHS><RHS>h</RHS></RULE><RULE><LHS> *(s(x),s(y))</LHS><RHS>s(+(+( *(x,y),x),y))</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_a(l,x,s(y),h)</LHS><RHS>Marked_a(l,x,y,s(h))</RHS></DPRULE><DPRULE num="1"><LHS>Marked_a(l,x,s(y),s(z))</LHS><RHS>Marked_a(l,x,y,a(l,x,s(y),z))</RHS></DPRULE><DPRULE num="2"><LHS>Marked_a(l,x,s(y),s(z))</LHS><RHS>Marked_a(l,x,s(y),z)</RHS></DPRULE><DPRULE num="3"><LHS>Marked_a(l,s(x),h,z)</LHS><RHS>Marked_a(l,x,z,z)</RHS></DPRULE><DPRULE num="4"><LHS>Marked_a(s(l),h,h,z)</LHS><RHS>Marked_a(l,z,h,z)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><PROJECTION><PROJ><SYMBOL><NAME>Marked_a</NAME></SYMBOL><INT>1</INT></PROJ></PROJECTION><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_a(s(l),h,h,z)</LHS><RHS>Marked_a(l,z,h,z)</RHS></DPRULE></DPLIST></STRICTPAIRS><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>a(h,h,h,x)</LHS><RHS>s(x)</RHS></RULE><RULE><LHS>a(l,x,s(y),h)</LHS><RHS>a(l,x,y,s(h))</RHS></RULE><RULE><LHS>a(l,x,s(y),s(z))</LHS><RHS>a(l,x,y,a(l,x,s(y),z))</RHS></RULE><RULE><LHS>a(l,s(x),h,z)</LHS><RHS>a(l,x,z,z)</RHS></RULE><RULE><LHS>a(s(l),h,h,z)</LHS><RHS>a(l,z,h,z)</RHS></RULE><RULE><LHS>+(x,h)</LHS><RHS>x</RHS></RULE><RULE><LHS>+(h,x)</LHS><RHS>x</RHS></RULE><RULE><LHS>+(s(x),s(y))</LHS><RHS>s(s(+(x,y)))</RHS></RULE><RULE><LHS>+(+(x,y),z)</LHS><RHS>+(x,+(y,z))</RHS></RULE><RULE><LHS>s(h)</LHS><RHS>1</RHS></RULE><RULE><LHS> *(h,x)</LHS><RHS>h</RHS></RULE><RULE><LHS> *(x,h)</LHS><RHS>h</RHS></RULE><RULE><LHS> *(s(x),s(y))</LHS><RHS>s(+(+( *(x,y),x),y))</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_a(l,s(x),h,z)</LHS><RHS>Marked_a(l,x,z,z)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_a(l,x,s(y),s(z))</LHS><RHS>Marked_a(l,x,s(y),z)</RHS></DPRULE><DPRULE num="2"><LHS>Marked_a(l,x,s(y),s(z))</LHS><RHS>Marked_a(l,x,y,a(l,x,s(y),z))</RHS></DPRULE><DPRULE num="3"><LHS>Marked_a(l,x,s(y),h)</LHS><RHS>Marked_a(l,x,y,s(h))</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="sterm" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>a(h,h,h,x)</LHS><RHS>s(x)</RHS></RULE><RULE><LHS>a(l,x,s(y),h)</LHS><RHS>a(l,x,y,s(h))</RHS></RULE><RULE><LHS>a(l,x,s(y),s(z))</LHS><RHS>a(l,x,y,a(l,x,s(y),z))</RHS></RULE><RULE><LHS>a(l,s(x),h,z)</LHS><RHS>a(l,x,z,z)</RHS></RULE><RULE><LHS>a(s(l),h,h,z)</LHS><RHS>a(l,z,h,z)</RHS></RULE><RULE><LHS>+(x,h)</LHS><RHS>x</RHS></RULE><RULE><LHS>+(h,x)</LHS><RHS>x</RHS></RULE><RULE><LHS>+(s(x),s(y))</LHS><RHS>s(s(+(x,y)))</RHS></RULE><RULE><LHS>+(+(x,y),z)</LHS><RHS>+(x,+(y,z))</RHS></RULE><RULE><LHS>s(h)</LHS><RHS>1</RHS></RULE><RULE><LHS> *(h,x)</LHS><RHS>h</RHS></RULE><RULE><LHS> *(x,h)</LHS><RHS>h</RHS></RULE><RULE><LHS> *(s(x),s(y))</LHS><RHS>s(+(+( *(x,y),x),y))</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_a(l,s(x),h,z)</LHS><RHS>Marked_a(l,x,z,z)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_a(l,x,s(y),s(z))</LHS><RHS>Marked_a(l,x,s(y),z)</RHS></DPRULE><DPRULE num="2"><LHS>Marked_a(l,x,s(y),s(z))</LHS><RHS>Marked_a(l,x,y,a(l,x,s(y),z))</RHS></DPRULE><DPRULE num="3"><LHS>Marked_a(l,x,s(y),h)</LHS><RHS>Marked_a(l,x,y,s(h))</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><PROJECTION><PROJ><SYMBOL><NAME>Marked_a</NAME></SYMBOL><INT>2</INT></PROJ></PROJECTION><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_a(l,s(x),h,z)</LHS><RHS>Marked_a(l,x,z,z)</RHS></DPRULE></DPLIST></STRICTPAIRS><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>a(h,h,h,x)</LHS><RHS>s(x)</RHS></RULE><RULE><LHS>a(l,x,s(y),h)</LHS><RHS>a(l,x,y,s(h))</RHS></RULE><RULE><LHS>a(l,x,s(y),s(z))</LHS><RHS>a(l,x,y,a(l,x,s(y),z))</RHS></RULE><RULE><LHS>a(l,s(x),h,z)</LHS><RHS>a(l,x,z,z)</RHS></RULE><RULE><LHS>a(s(l),h,h,z)</LHS><RHS>a(l,z,h,z)</RHS></RULE><RULE><LHS>+(x,h)</LHS><RHS>x</RHS></RULE><RULE><LHS>+(h,x)</LHS><RHS>x</RHS></RULE><RULE><LHS>+(s(x),s(y))</LHS><RHS>s(s(+(x,y)))</RHS></RULE><RULE><LHS>+(+(x,y),z)</LHS><RHS>+(x,+(y,z))</RHS></RULE><RULE><LHS>s(h)</LHS><RHS>1</RHS></RULE><RULE><LHS> *(h,x)</LHS><RHS>h</RHS></RULE><RULE><LHS> *(x,h)</LHS><RHS>h</RHS></RULE><RULE><LHS> *(s(x),s(y))</LHS><RHS>s(+(+( *(x,y),x),y))</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_a(l,x,s(y),h)</LHS><RHS>Marked_a(l,x,y,s(h))</RHS></DPRULE><DPRULE num="1"><LHS>Marked_a(l,x,s(y),s(z))</LHS><RHS>Marked_a(l,x,y,a(l,x,s(y),z))</RHS></DPRULE><DPRULE num="2"><LHS>Marked_a(l,x,s(y),s(z))</LHS><RHS>Marked_a(l,x,s(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="sterm" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>a(h,h,h,x)</LHS><RHS>s(x)</RHS></RULE><RULE><LHS>a(l,x,s(y),h)</LHS><RHS>a(l,x,y,s(h))</RHS></RULE><RULE><LHS>a(l,x,s(y),s(z))</LHS><RHS>a(l,x,y,a(l,x,s(y),z))</RHS></RULE><RULE><LHS>a(l,s(x),h,z)</LHS><RHS>a(l,x,z,z)</RHS></RULE><RULE><LHS>a(s(l),h,h,z)</LHS><RHS>a(l,z,h,z)</RHS></RULE><RULE><LHS>+(x,h)</LHS><RHS>x</RHS></RULE><RULE><LHS>+(h,x)</LHS><RHS>x</RHS></RULE><RULE><LHS>+(s(x),s(y))</LHS><RHS>s(s(+(x,y)))</RHS></RULE><RULE><LHS>+(+(x,y),z)</LHS><RHS>+(x,+(y,z))</RHS></RULE><RULE><LHS>s(h)</LHS><RHS>1</RHS></RULE><RULE><LHS> *(h,x)</LHS><RHS>h</RHS></RULE><RULE><LHS> *(x,h)</LHS><RHS>h</RHS></RULE><RULE><LHS> *(s(x),s(y))</LHS><RHS>s(+(+( *(x,y),x),y))</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_a(l,x,s(y),h)</LHS><RHS>Marked_a(l,x,y,s(h))</RHS></DPRULE><DPRULE num="1"><LHS>Marked_a(l,x,s(y),s(z))</LHS><RHS>Marked_a(l,x,y,a(l,x,s(y),z))</RHS></DPRULE><DPRULE num="2"><LHS>Marked_a(l,x,s(y),s(z))</LHS><RHS>Marked_a(l,x,s(y),z)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><PROJECTION><PROJ><SYMBOL><NAME>Marked_a</NAME></SYMBOL><INT>3</INT></PROJ></PROJECTION><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_a(l,x,s(y),s(z))</LHS><RHS>Marked_a(l,x,y,a(l,x,s(y),z))</RHS></DPRULE><DPRULE num="1"><LHS>Marked_a(l,x,s(y),h)</LHS><RHS>Marked_a(l,x,y,s(h))</RHS></DPRULE></DPLIST></STRICTPAIRS><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>a(h,h,h,x)</LHS><RHS>s(x)</RHS></RULE><RULE><LHS>a(l,x,s(y),h)</LHS><RHS>a(l,x,y,s(h))</RHS></RULE><RULE><LHS>a(l,x,s(y),s(z))</LHS><RHS>a(l,x,y,a(l,x,s(y),z))</RHS></RULE><RULE><LHS>a(l,s(x),h,z)</LHS><RHS>a(l,x,z,z)</RHS></RULE><RULE><LHS>a(s(l),h,h,z)</LHS><RHS>a(l,z,h,z)</RHS></RULE><RULE><LHS>+(x,h)</LHS><RHS>x</RHS></RULE><RULE><LHS>+(h,x)</LHS><RHS>x</RHS></RULE><RULE><LHS>+(s(x),s(y))</LHS><RHS>s(s(+(x,y)))</RHS></RULE><RULE><LHS>+(+(x,y),z)</LHS><RHS>+(x,+(y,z))</RHS></RULE><RULE><LHS>s(h)</LHS><RHS>1</RHS></RULE><RULE><LHS> *(h,x)</LHS><RHS>h</RHS></RULE><RULE><LHS> *(x,h)</LHS><RHS>h</RHS></RULE><RULE><LHS> *(s(x),s(y))</LHS><RHS>s(+(+( *(x,y),x),y))</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_a(l,x,s(y),s(z))</LHS><RHS>Marked_a(l,x,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="sterm" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>a(h,h,h,x)</LHS><RHS>s(x)</RHS></RULE><RULE><LHS>a(l,x,s(y),h)</LHS><RHS>a(l,x,y,s(h))</RHS></RULE><RULE><LHS>a(l,x,s(y),s(z))</LHS><RHS>a(l,x,y,a(l,x,s(y),z))</RHS></RULE><RULE><LHS>a(l,s(x),h,z)</LHS><RHS>a(l,x,z,z)</RHS></RULE><RULE><LHS>a(s(l),h,h,z)</LHS><RHS>a(l,z,h,z)</RHS></RULE><RULE><LHS>+(x,h)</LHS><RHS>x</RHS></RULE><RULE><LHS>+(h,x)</LHS><RHS>x</RHS></RULE><RULE><LHS>+(s(x),s(y))</LHS><RHS>s(s(+(x,y)))</RHS></RULE><RULE><LHS>+(+(x,y),z)</LHS><RHS>+(x,+(y,z))</RHS></RULE><RULE><LHS>s(h)</LHS><RHS>1</RHS></RULE><RULE><LHS> *(h,x)</LHS><RHS>h</RHS></RULE><RULE><LHS> *(x,h)</LHS><RHS>h</RHS></RULE><RULE><LHS> *(s(x),s(y))</LHS><RHS>s(+(+( *(x,y),x),y))</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_a(l,x,s(y),s(z))</LHS><RHS>Marked_a(l,x,s(y),z)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><PROJECTION><PROJ><SYMBOL><NAME>Marked_a</NAME></SYMBOL><INT>4</INT></PROJ></PROJECTION><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_a(l,x,s(y),s(z))</LHS><RHS>Marked_a(l,x,s(y),z)</RHS></DPRULE></DPLIST></STRICTPAIRS><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>a(h,h,h,x)</LHS><RHS>s(x)</RHS></RULE><RULE><LHS>a(l,x,s(y),h)</LHS><RHS>a(l,x,y,s(h))</RHS></RULE><RULE><LHS>a(l,x,s(y),s(z))</LHS><RHS>a(l,x,y,a(l,x,s(y),z))</RHS></RULE><RULE><LHS>a(l,s(x),h,z)</LHS><RHS>a(l,x,z,z)</RHS></RULE><RULE><LHS>a(s(l),h,h,z)</LHS><RHS>a(l,z,h,z)</RHS></RULE><RULE><LHS>+(x,h)</LHS><RHS>x</RHS></RULE><RULE><LHS>+(h,x)</LHS><RHS>x</RHS></RULE><RULE><LHS>+(s(x),s(y))</LHS><RHS>s(s(+(x,y)))</RHS></RULE><RULE><LHS>+(+(x,y),z)</LHS><RHS>+(x,+(y,z))</RHS></RULE><RULE><LHS>s(h)</LHS><RHS>1</RHS></RULE><RULE><LHS> *(h,x)</LHS><RHS>h</RHS></RULE><RULE><LHS> *(x,h)</LHS><RHS>h</RHS></RULE><RULE><LHS> *(s(x),s(y))</LHS><RHS>s(+(+( *(x,y),x),y))</RHS></RULE></REWSYS><DPLIST/></DPSYS></SYSTEM><CRITERION><DAG approx="simpl"><CCLIST/></DAG></CRITERION></PROPERTY></PROPERTY></PROPERTY></PROPERTY></PROPERTY></PROPERTY></PROPERTY></PROPERTY><PROPERTY criterion="sterm" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>a(h,h,h,x)</LHS><RHS>s(x)</RHS></RULE><RULE><LHS>a(l,x,s(y),h)</LHS><RHS>a(l,x,y,s(h))</RHS></RULE><RULE><LHS>a(l,x,s(y),s(z))</LHS><RHS>a(l,x,y,a(l,x,s(y),z))</RHS></RULE><RULE><LHS>a(l,s(x),h,z)</LHS><RHS>a(l,x,z,z)</RHS></RULE><RULE><LHS>a(s(l),h,h,z)</LHS><RHS>a(l,z,h,z)</RHS></RULE><RULE><LHS>+(x,h)</LHS><RHS>x</RHS></RULE><RULE><LHS>+(h,x)</LHS><RHS>x</RHS></RULE><RULE><LHS>+(s(x),s(y))</LHS><RHS>s(s(+(x,y)))</RHS></RULE><RULE><LHS>+(+(x,y),z)</LHS><RHS>+(x,+(y,z))</RHS></RULE><RULE><LHS>s(h)</LHS><RHS>1</RHS></RULE><RULE><LHS> *(h,x)</LHS><RHS>h</RHS></RULE><RULE><LHS> *(x,h)</LHS><RHS>h</RHS></RULE><RULE><LHS> *(s(x),s(y))</LHS><RHS>s(+(+( *(x,y),x),y))</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_*(s(x),s(y))</LHS><RHS>Marked_*(x,y)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><PROJECTION><PROJ><SYMBOL><NAME>Marked_*</NAME></SYMBOL><INT>1</INT></PROJ></PROJECTION><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_*(s(x),s(y))</LHS><RHS>Marked_*(x,y)</RHS></DPRULE></DPLIST></STRICTPAIRS><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>a(h,h,h,x)</LHS><RHS>s(x)</RHS></RULE><RULE><LHS>a(l,x,s(y),h)</LHS><RHS>a(l,x,y,s(h))</RHS></RULE><RULE><LHS>a(l,x,s(y),s(z))</LHS><RHS>a(l,x,y,a(l,x,s(y),z))</RHS></RULE><RULE><LHS>a(l,s(x),h,z)</LHS><RHS>a(l,x,z,z)</RHS></RULE><RULE><LHS>a(s(l),h,h,z)</LHS><RHS>a(l,z,h,z)</RHS></RULE><RULE><LHS>+(x,h)</LHS><RHS>x</RHS></RULE><RULE><LHS>+(h,x)</LHS><RHS>x</RHS></RULE><RULE><LHS>+(s(x),s(y))</LHS><RHS>s(s(+(x,y)))</RHS></RULE><RULE><LHS>+(+(x,y),z)</LHS><RHS>+(x,+(y,z))</RHS></RULE><RULE><LHS>s(h)</LHS><RHS>1</RHS></RULE><RULE><LHS> *(h,x)</LHS><RHS>h</RHS></RULE><RULE><LHS> *(x,h)</LHS><RHS>h</RHS></RULE><RULE><LHS> *(s(x),s(y))</LHS><RHS>s(+(+( *(x,y),x),y))</RHS></RULE></REWSYS><DPLIST/></DPSYS></SYSTEM><CRITERION><DAG approx="simpl"><CCLIST/></DAG></CRITERION></PROPERTY></PROPERTY><PROPERTY criterion="sterm" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>a(h,h,h,x)</LHS><RHS>s(x)</RHS></RULE><RULE><LHS>a(l,x,s(y),h)</LHS><RHS>a(l,x,y,s(h))</RHS></RULE><RULE><LHS>a(l,x,s(y),s(z))</LHS><RHS>a(l,x,y,a(l,x,s(y),z))</RHS></RULE><RULE><LHS>a(l,s(x),h,z)</LHS><RHS>a(l,x,z,z)</RHS></RULE><RULE><LHS>a(s(l),h,h,z)</LHS><RHS>a(l,z,h,z)</RHS></RULE><RULE><LHS>+(x,h)</LHS><RHS>x</RHS></RULE><RULE><LHS>+(h,x)</LHS><RHS>x</RHS></RULE><RULE><LHS>+(s(x),s(y))</LHS><RHS>s(s(+(x,y)))</RHS></RULE><RULE><LHS>+(+(x,y),z)</LHS><RHS>+(x,+(y,z))</RHS></RULE><RULE><LHS>s(h)</LHS><RHS>1</RHS></RULE><RULE><LHS> *(h,x)</LHS><RHS>h</RHS></RULE><RULE><LHS> *(x,h)</LHS><RHS>h</RHS></RULE><RULE><LHS> *(s(x),s(y))</LHS><RHS>s(+(+( *(x,y),x),y))</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,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><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><DPRULE num="2"><LHS>Marked_+(s(x),s(y))</LHS><RHS>Marked_+(x,y)</RHS></DPRULE></DPLIST></STRICTPAIRS><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>a(h,h,h,x)</LHS><RHS>s(x)</RHS></RULE><RULE><LHS>a(l,x,s(y),h)</LHS><RHS>a(l,x,y,s(h))</RHS></RULE><RULE><LHS>a(l,x,s(y),s(z))</LHS><RHS>a(l,x,y,a(l,x,s(y),z))</RHS></RULE><RULE><LHS>a(l,s(x),h,z)</LHS><RHS>a(l,x,z,z)</RHS></RULE><RULE><LHS>a(s(l),h,h,z)</LHS><RHS>a(l,z,h,z)</RHS></RULE><RULE><LHS>+(x,h)</LHS><RHS>x</RHS></RULE><RULE><LHS>+(h,x)</LHS><RHS>x</RHS></RULE><RULE><LHS>+(s(x),s(y))</LHS><RHS>s(s(+(x,y)))</RHS></RULE><RULE><LHS>+(+(x,y),z)</LHS><RHS>+(x,+(y,z))</RHS></RULE><RULE><LHS>s(h)</LHS><RHS>1</RHS></RULE><RULE><LHS> *(h,x)</LHS><RHS>h</RHS></RULE><RULE><LHS> *(x,h)</LHS><RHS>h</RHS></RULE><RULE><LHS> *(s(x),s(y))</LHS><RHS>s(+(+( *(x,y),x),y))</RHS></RULE></REWSYS><DPLIST/></DPSYS></SYSTEM><CRITERION><DAG approx="simpl"><CCLIST/></DAG></CRITERION></PROPERTY></PROPERTY></PROPERTY></PROPERTY></PROOF>
