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<!DOCTYPE PROOF SYSTEM "http://a3pat.ensiie.fr/pub/a3pat.dtd">
<PROOF><SIGNATURE><SYMBOLLIST><SYMBOL arity="0" unmarked=""><NAME>b'</NAME></SYMBOL><SYMBOL arity="0" unmarked=""><NAME>d</NAME></SYMBOL><SYMBOL arity="2" unmarked=""><NAME>.</NAME></SYMBOL><SYMBOL arity="2" unmarked="f"><NAME>Marked_f</NAME></SYMBOL><SYMBOL arity="0" unmarked=""><NAME>c</NAME></SYMBOL><SYMBOL arity="3" unmarked=""><NAME>i</NAME></SYMBOL><SYMBOL arity="0" unmarked=""><NAME>e</NAME></SYMBOL><SYMBOL arity="0" unmarked=""><NAME>d'</NAME></SYMBOL><SYMBOL arity="0" unmarked=""><NAME>a</NAME></SYMBOL><SYMBOL arity="2" unmarked=""><NAME>f</NAME></SYMBOL><SYMBOL arity="2" unmarked=""><NAME>h</NAME></SYMBOL><SYMBOL arity="0" unmarked=""><NAME>b</NAME></SYMBOL><SYMBOL arity="2" unmarked=""><NAME>g</NAME></SYMBOL><SYMBOL arity="3" unmarked=""><NAME>if</NAME></SYMBOL></SYMBOLLIST><VARLIST/></SIGNATURE><PROPERTY criterion="dp" prop="sntrs"><SYSTEM><REWSYS><RULE><LHS>f(g(i(a,b,b'),c),d)</LHS><RHS>if(e,f(.(b,c),d'),f(.(b',c),d'))</RHS></RULE><RULE><LHS>f(g(h(a,b),c),d)</LHS><RHS>if(e,f(.(b,g(h(a,b),c)),d),f(c,d'))</RHS></RULE></REWSYS></SYSTEM><CRITERION/><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>f(g(i(a,b,b'),c),d)</LHS><RHS>if(e,f(.(b,c),d'),f(.(b',c),d'))</RHS></RULE><RULE><LHS>f(g(h(a,b),c),d)</LHS><RHS>if(e,f(.(b,g(h(a,b),c)),d),f(c,d'))</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_f(g(i(a,b,b'),c),d)</LHS><RHS>Marked_f(.(b,c),d')</RHS></DPRULE><DPRULE num="1"><LHS>Marked_f(g(i(a,b,b'),c),d)</LHS><RHS>Marked_f(.(b',c),d')</RHS></DPRULE><DPRULE num="2"><LHS>Marked_f(g(h(a,b),c),d)</LHS><RHS>Marked_f(.(b,g(h(a,b),c)),d)</RHS></DPRULE><DPRULE num="3"><LHS>Marked_f(g(h(a,b),c),d)</LHS><RHS>Marked_f(c,d')</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>
