<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE PROOF SYSTEM "http://a3pat.ensiie.fr/pub/a3pat.dtd">
<PROOF><SIGNATURE><SYMBOLLIST><SYMBOL arity="1" unmarked="mark"><NAME>Marked_mark</NAME></SYMBOL><SYMBOL arity="0" unmarked=""><NAME>a</NAME></SYMBOL><SYMBOL arity="1" unmarked=""><NAME>mark</NAME></SYMBOL><SYMBOL arity="1" unmarked=""><NAME>f</NAME></SYMBOL><SYMBOL arity="1" unmarked="a__f"><NAME>Marked_a__f</NAME></SYMBOL><SYMBOL arity="1" unmarked=""><NAME>g</NAME></SYMBOL><SYMBOL arity="1" unmarked=""><NAME>a__f</NAME></SYMBOL><SYMBOL arity="1" unmarked=""><NAME>c</NAME></SYMBOL></SYMBOLLIST><VARLIST><VAR>X</VAR></VARLIST></SIGNATURE><PROPERTY criterion="dp" prop="sntrs"><SYSTEM><REWSYS><RULE><LHS>a__f(f(a))</LHS><RHS>c(f(g(f(a))))</RHS></RULE><RULE><LHS>mark(f(X))</LHS><RHS>a__f(mark(X))</RHS></RULE><RULE><LHS>mark(a)</LHS><RHS>a</RHS></RULE><RULE><LHS>mark(c(X))</LHS><RHS>c(X)</RHS></RULE><RULE><LHS>mark(g(X))</LHS><RHS>g(mark(X))</RHS></RULE><RULE><LHS>a__f(X)</LHS><RHS>f(X)</RHS></RULE></REWSYS></SYSTEM><CRITERION/><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>a__f(f(a))</LHS><RHS>c(f(g(f(a))))</RHS></RULE><RULE><LHS>mark(f(X))</LHS><RHS>a__f(mark(X))</RHS></RULE><RULE><LHS>mark(a)</LHS><RHS>a</RHS></RULE><RULE><LHS>mark(c(X))</LHS><RHS>c(X)</RHS></RULE><RULE><LHS>mark(g(X))</LHS><RHS>g(mark(X))</RHS></RULE><RULE><LHS>a__f(X)</LHS><RHS>f(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_mark(f(X))</LHS><RHS>Marked_a__f(mark(X))</RHS></DPRULE><DPRULE num="1"><LHS>Marked_mark(f(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="2"><LHS>Marked_mark(g(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><DAG approx="simpl"><CCLIST><SCC num="0"><NODE ref="1"/><NODE ref="2"/></SCC><NONSCC num="1"><NODE ref="0"/></NONSCC></CCLIST><EDGE end="1" start="0"/></DAG></CRITERION><PROPERTY criterion="sterm" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>a__f(f(a))</LHS><RHS>c(f(g(f(a))))</RHS></RULE><RULE><LHS>mark(f(X))</LHS><RHS>a__f(mark(X))</RHS></RULE><RULE><LHS>mark(a)</LHS><RHS>a</RHS></RULE><RULE><LHS>mark(c(X))</LHS><RHS>c(X)</RHS></RULE><RULE><LHS>mark(g(X))</LHS><RHS>g(mark(X))</RHS></RULE><RULE><LHS>a__f(X)</LHS><RHS>f(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_mark(f(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_mark(g(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><PROJECTION><PROJ><SYMBOL><NAME>Marked_mark</NAME></SYMBOL><INT>1</INT></PROJ></PROJECTION><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_mark(g(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_mark(f(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE></DPLIST></STRICTPAIRS><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>a__f(f(a))</LHS><RHS>c(f(g(f(a))))</RHS></RULE><RULE><LHS>mark(f(X))</LHS><RHS>a__f(mark(X))</RHS></RULE><RULE><LHS>mark(a)</LHS><RHS>a</RHS></RULE><RULE><LHS>mark(c(X))</LHS><RHS>c(X)</RHS></RULE><RULE><LHS>mark(g(X))</LHS><RHS>g(mark(X))</RHS></RULE><RULE><LHS>a__f(X)</LHS><RHS>f(X)</RHS></RULE></REWSYS><DPLIST/></DPSYS></SYSTEM><CRITERION><DAG approx="simpl"><CCLIST/></DAG></CRITERION></PROPERTY></PROPERTY></PROPERTY></PROPERTY></PROOF>
