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