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<!DOCTYPE PROOF SYSTEM "http://a3pat.ensiie.fr/pub/a3pat.dtd">
<PROOF><SIGNATURE><SYMBOLLIST><SYMBOL arity="3" unmarked="if"><NAME>Marked_if</NAME></SYMBOL><SYMBOL arity="3" unmarked=""><NAME>if</NAME></SYMBOL></SYMBOLLIST><VARLIST><VAR>v</VAR><VAR>u</VAR><VAR>z</VAR><VAR>y</VAR><VAR>x</VAR></VARLIST></SIGNATURE><PROPERTY criterion="dp" prop="sntrs"><SYSTEM><REWSYS><RULE><LHS>if(if(x,y,z),u,v)</LHS><RHS>if(x,if(y,u,v),if(z,u,v))</RHS></RULE></REWSYS></SYSTEM><CRITERION/><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>if(if(x,y,z),u,v)</LHS><RHS>if(x,if(y,u,v),if(z,u,v))</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_if(if(x,y,z),u,v)</LHS><RHS>Marked_if(x,if(y,u,v),if(z,u,v))</RHS></DPRULE><DPRULE num="1"><LHS>Marked_if(if(x,y,z),u,v)</LHS><RHS>Marked_if(y,u,v)</RHS></DPRULE><DPRULE num="2"><LHS>Marked_if(if(x,y,z),u,v)</LHS><RHS>Marked_if(z,u,v)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><DAG approx="simpl"><CCLIST><SCC num="0"><NODE ref="0"/><NODE ref="1"/><NODE ref="2"/></SCC></CCLIST></DAG></CRITERION><PROPERTY criterion="sterm" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>if(if(x,y,z),u,v)</LHS><RHS>if(x,if(y,u,v),if(z,u,v))</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_if(if(x,y,z),u,v)</LHS><RHS>Marked_if(x,if(y,u,v),if(z,u,v))</RHS></DPRULE><DPRULE num="1"><LHS>Marked_if(if(x,y,z),u,v)</LHS><RHS>Marked_if(y,u,v)</RHS></DPRULE><DPRULE num="2"><LHS>Marked_if(if(x,y,z),u,v)</LHS><RHS>Marked_if(z,u,v)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><PROJECTION><PROJ><SYMBOL><NAME>Marked_if</NAME></SYMBOL><INT>1</INT></PROJ></PROJECTION><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_if(if(x,y,z),u,v)</LHS><RHS>Marked_if(z,u,v)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_if(if(x,y,z),u,v)</LHS><RHS>Marked_if(y,u,v)</RHS></DPRULE><DPRULE num="2"><LHS>Marked_if(if(x,y,z),u,v)</LHS><RHS>Marked_if(x,if(y,u,v),if(z,u,v))</RHS></DPRULE></DPLIST></STRICTPAIRS><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>if(if(x,y,z),u,v)</LHS><RHS>if(x,if(y,u,v),if(z,u,v))</RHS></RULE></REWSYS><DPLIST/></DPSYS></SYSTEM><CRITERION><DAG approx="simpl"><CCLIST/></DAG></CRITERION></PROPERTY></PROPERTY></PROPERTY></PROPERTY></PROOF>
