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<!DOCTYPE PROOF SYSTEM "http://a3pat.ensiie.fr/pub/a3pat.dtd">
<PROOF><SIGNATURE><SYMBOLLIST><SYMBOL arity="1" unmarked=""><NAME>s</NAME></SYMBOL><SYMBOL arity="2" unmarked="cons"><NAME>Marked_cons</NAME></SYMBOL><SYMBOL arity="2" unmarked=""><NAME>n__cons</NAME></SYMBOL><SYMBOL arity="1" unmarked=""><NAME>n__s</NAME></SYMBOL><SYMBOL arity="1" unmarked="s"><NAME>Marked_s</NAME></SYMBOL><SYMBOL arity="1" unmarked=""><NAME>2nd</NAME></SYMBOL><SYMBOL arity="1" unmarked=""><NAME>from</NAME></SYMBOL><SYMBOL arity="1" unmarked="from"><NAME>Marked_from</NAME></SYMBOL><SYMBOL arity="2" unmarked=""><NAME>cons</NAME></SYMBOL><SYMBOL arity="1" unmarked="2nd"><NAME>Marked_2nd</NAME></SYMBOL><SYMBOL arity="1" unmarked=""><NAME>n__from</NAME></SYMBOL><SYMBOL arity="1" unmarked="activate"><NAME>Marked_activate</NAME></SYMBOL><SYMBOL arity="1" unmarked=""><NAME>activate</NAME></SYMBOL></SYMBOLLIST><VARLIST><VAR>X2</VAR><VAR>X1</VAR><VAR>Z</VAR><VAR>Y</VAR><VAR>X</VAR></VARLIST></SIGNATURE><PROPERTY criterion="dp" prop="sntrs"><SYSTEM><REWSYS><RULE><LHS>2nd(cons(X,n__cons(Y,Z)))</LHS><RHS>activate(Y)</RHS></RULE><RULE><LHS>from(X)</LHS><RHS>cons(X,n__from(n__s(X)))</RHS></RULE><RULE><LHS>cons(X1,X2)</LHS><RHS>n__cons(X1,X2)</RHS></RULE><RULE><LHS>from(X)</LHS><RHS>n__from(X)</RHS></RULE><RULE><LHS>s(X)</LHS><RHS>n__s(X)</RHS></RULE><RULE><LHS>activate(n__cons(X1,X2))</LHS><RHS>cons(activate(X1),X2)</RHS></RULE><RULE><LHS>activate(n__from(X))</LHS><RHS>from(activate(X))</RHS></RULE><RULE><LHS>activate(n__s(X))</LHS><RHS>s(activate(X))</RHS></RULE><RULE><LHS>activate(X)</LHS><RHS>X</RHS></RULE></REWSYS></SYSTEM><CRITERION/><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>2nd(cons(X,n__cons(Y,Z)))</LHS><RHS>activate(Y)</RHS></RULE><RULE><LHS>from(X)</LHS><RHS>cons(X,n__from(n__s(X)))</RHS></RULE><RULE><LHS>cons(X1,X2)</LHS><RHS>n__cons(X1,X2)</RHS></RULE><RULE><LHS>from(X)</LHS><RHS>n__from(X)</RHS></RULE><RULE><LHS>s(X)</LHS><RHS>n__s(X)</RHS></RULE><RULE><LHS>activate(n__cons(X1,X2))</LHS><RHS>cons(activate(X1),X2)</RHS></RULE><RULE><LHS>activate(n__from(X))</LHS><RHS>from(activate(X))</RHS></RULE><RULE><LHS>activate(n__s(X))</LHS><RHS>s(activate(X))</RHS></RULE><RULE><LHS>activate(X)</LHS><RHS>X</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_2nd(cons(X,n__cons(Y,Z)))</LHS><RHS>Marked_activate(Y)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_from(X)</LHS><RHS>Marked_cons(X,n__from(n__s(X)))</RHS></DPRULE><DPRULE num="2"><LHS>Marked_activate(n__cons(X1,X2))</LHS><RHS>Marked_cons(activate(X1),X2)</RHS></DPRULE><DPRULE num="3"><LHS>Marked_activate(n__cons(X1,X2))</LHS><RHS>Marked_activate(X1)</RHS></DPRULE><DPRULE num="4"><LHS>Marked_activate(n__from(X))</LHS><RHS>Marked_from(activate(X))</RHS></DPRULE><DPRULE num="5"><LHS>Marked_activate(n__from(X))</LHS><RHS>Marked_activate(X)</RHS></DPRULE><DPRULE num="6"><LHS>Marked_activate(n__s(X))</LHS><RHS>Marked_s(activate(X))</RHS></DPRULE><DPRULE num="7"><LHS>Marked_activate(n__s(X))</LHS><RHS>Marked_activate(X)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><DAG approx="simpl"><CCLIST><SCC num="0"><NODE ref="3"/><NODE ref="5"/><NODE ref="7"/></SCC><NONSCC num="1"><NODE ref="6"/></NONSCC><NONSCC num="2"><NODE ref="4"/></NONSCC><NONSCC num="3"><NODE ref="2"/></NONSCC><NONSCC num="4"><NODE ref="1"/></NONSCC><NONSCC num="5"><NODE ref="0"/></NONSCC></CCLIST><EDGE end="3" start="0"/><EDGE end="2" start="0"/><EDGE end="1" start="0"/><EDGE end="4" start="2"/><EDGE end="3" start="5"/><EDGE end="2" start="5"/><EDGE end="1" start="5"/><EDGE end="0" start="5"/></DAG></CRITERION><PROPERTY criterion="sterm" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>2nd(cons(X,n__cons(Y,Z)))</LHS><RHS>activate(Y)</RHS></RULE><RULE><LHS>from(X)</LHS><RHS>cons(X,n__from(n__s(X)))</RHS></RULE><RULE><LHS>cons(X1,X2)</LHS><RHS>n__cons(X1,X2)</RHS></RULE><RULE><LHS>from(X)</LHS><RHS>n__from(X)</RHS></RULE><RULE><LHS>s(X)</LHS><RHS>n__s(X)</RHS></RULE><RULE><LHS>activate(n__cons(X1,X2))</LHS><RHS>cons(activate(X1),X2)</RHS></RULE><RULE><LHS>activate(n__from(X))</LHS><RHS>from(activate(X))</RHS></RULE><RULE><LHS>activate(n__s(X))</LHS><RHS>s(activate(X))</RHS></RULE><RULE><LHS>activate(X)</LHS><RHS>X</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_activate(n__cons(X1,X2))</LHS><RHS>Marked_activate(X1)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_activate(n__from(X))</LHS><RHS>Marked_activate(X)</RHS></DPRULE><DPRULE num="2"><LHS>Marked_activate(n__s(X))</LHS><RHS>Marked_activate(X)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><PROJECTION><PROJ><SYMBOL><NAME>Marked_activate</NAME></SYMBOL><INT>1</INT></PROJ></PROJECTION><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_activate(n__s(X))</LHS><RHS>Marked_activate(X)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_activate(n__from(X))</LHS><RHS>Marked_activate(X)</RHS></DPRULE><DPRULE num="2"><LHS>Marked_activate(n__cons(X1,X2))</LHS><RHS>Marked_activate(X1)</RHS></DPRULE></DPLIST></STRICTPAIRS><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>2nd(cons(X,n__cons(Y,Z)))</LHS><RHS>activate(Y)</RHS></RULE><RULE><LHS>from(X)</LHS><RHS>cons(X,n__from(n__s(X)))</RHS></RULE><RULE><LHS>cons(X1,X2)</LHS><RHS>n__cons(X1,X2)</RHS></RULE><RULE><LHS>from(X)</LHS><RHS>n__from(X)</RHS></RULE><RULE><LHS>s(X)</LHS><RHS>n__s(X)</RHS></RULE><RULE><LHS>activate(n__cons(X1,X2))</LHS><RHS>cons(activate(X1),X2)</RHS></RULE><RULE><LHS>activate(n__from(X))</LHS><RHS>from(activate(X))</RHS></RULE><RULE><LHS>activate(n__s(X))</LHS><RHS>s(activate(X))</RHS></RULE><RULE><LHS>activate(X)</LHS><RHS>X</RHS></RULE></REWSYS><DPLIST/></DPSYS></SYSTEM><CRITERION><DAG approx="simpl"><CCLIST/></DAG></CRITERION></PROPERTY></PROPERTY></PROPERTY></PROPERTY></PROOF>
