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