<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE PROOF SYSTEM "http://a3pat.ensiie.fr/pub/a3pat.dtd">
<PROOF><SIGNATURE><SYMBOLLIST><SYMBOL arity="0" unmarked="zeros"><NAME>Marked_zeros</NAME></SYMBOL><SYMBOL arity="0" unmarked=""><NAME>zeros</NAME></SYMBOL><SYMBOL arity="1" unmarked=""><NAME>tail</NAME></SYMBOL><SYMBOL arity="0" unmarked=""><NAME>0</NAME></SYMBOL><SYMBOL arity="1" unmarked="activate"><NAME>Marked_activate</NAME></SYMBOL><SYMBOL arity="0" unmarked=""><NAME>n__zeros</NAME></SYMBOL><SYMBOL arity="1" unmarked=""><NAME>activate</NAME></SYMBOL><SYMBOL arity="1" unmarked="tail"><NAME>Marked_tail</NAME></SYMBOL><SYMBOL arity="2" unmarked=""><NAME>cons</NAME></SYMBOL></SYMBOLLIST><VARLIST><VAR>XS</VAR><VAR>X</VAR></VARLIST></SIGNATURE><PROPERTY criterion="dp" prop="sntrs"><SYSTEM><REWSYS><RULE><LHS>zeros</LHS><RHS>cons(0,n__zeros)</RHS></RULE><RULE><LHS>tail(cons(X,XS))</LHS><RHS>activate(XS)</RHS></RULE><RULE><LHS>zeros</LHS><RHS>n__zeros</RHS></RULE><RULE><LHS>activate(n__zeros)</LHS><RHS>zeros</RHS></RULE><RULE><LHS>activate(X)</LHS><RHS>X</RHS></RULE></REWSYS></SYSTEM><CRITERION/><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>zeros</LHS><RHS>cons(0,n__zeros)</RHS></RULE><RULE><LHS>tail(cons(X,XS))</LHS><RHS>activate(XS)</RHS></RULE><RULE><LHS>zeros</LHS><RHS>n__zeros</RHS></RULE><RULE><LHS>activate(n__zeros)</LHS><RHS>zeros</RHS></RULE><RULE><LHS>activate(X)</LHS><RHS>X</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_tail(cons(X,XS))</LHS><RHS>Marked_activate(XS)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_activate(n__zeros)</LHS><RHS>Marked_zeros</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><DAG approx="simpl"><CCLIST><NONSCC num="0"><NODE ref="1"/></NONSCC><NONSCC num="1"><NODE ref="0"/></NONSCC></CCLIST><EDGE end="0" start="1"/></DAG></CRITERION></PROPERTY></PROPERTY></PROOF>
