<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE PROOF SYSTEM "http://a3pat.ensiie.fr/pub/a3pat.dtd">
<PROOF><SIGNATURE><SYMBOLLIST><SYMBOL arity="1" unmarked=""><NAME>p</NAME></SYMBOL><SYMBOL arity="1" unmarked="p"><NAME>Marked_p</NAME></SYMBOL><SYMBOL arity="1" unmarked=""><NAME>f</NAME></SYMBOL><SYMBOL arity="1" unmarked=""><NAME>g</NAME></SYMBOL><SYMBOL arity="1" unmarked="q"><NAME>Marked_q</NAME></SYMBOL><SYMBOL arity="1" unmarked=""><NAME>q</NAME></SYMBOL></SYMBOLLIST><VARLIST><VAR>x</VAR></VARLIST></SIGNATURE><PROPERTY criterion="dp" prop="sntrs"><SYSTEM><REWSYS><RULE><LHS>p(f(f(x)))</LHS><RHS>q(f(g(x)))</RHS></RULE><RULE><LHS>p(g(g(x)))</LHS><RHS>q(g(f(x)))</RHS></RULE><RULE><LHS>q(f(f(x)))</LHS><RHS>p(f(g(x)))</RHS></RULE><RULE><LHS>q(g(g(x)))</LHS><RHS>p(g(f(x)))</RHS></RULE></REWSYS></SYSTEM><CRITERION/><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>p(f(f(x)))</LHS><RHS>q(f(g(x)))</RHS></RULE><RULE><LHS>p(g(g(x)))</LHS><RHS>q(g(f(x)))</RHS></RULE><RULE><LHS>q(f(f(x)))</LHS><RHS>p(f(g(x)))</RHS></RULE><RULE><LHS>q(g(g(x)))</LHS><RHS>p(g(f(x)))</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_p(f(f(x)))</LHS><RHS>Marked_q(f(g(x)))</RHS></DPRULE><DPRULE num="1"><LHS>Marked_p(g(g(x)))</LHS><RHS>Marked_q(g(f(x)))</RHS></DPRULE><DPRULE num="2"><LHS>Marked_q(f(f(x)))</LHS><RHS>Marked_p(f(g(x)))</RHS></DPRULE><DPRULE num="3"><LHS>Marked_q(g(g(x)))</LHS><RHS>Marked_p(g(f(x)))</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><DAG approx="simpl"><CCLIST><NONSCC num="0"><NODE ref="3"/></NONSCC><NONSCC num="1"><NODE ref="2"/></NONSCC><NONSCC num="2"><NODE ref="1"/></NONSCC><NONSCC num="3"><NODE ref="0"/></NONSCC></CCLIST></DAG></CRITERION></PROPERTY></PROPERTY></PROOF>
