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<!DOCTYPE PROOF SYSTEM "http://a3pat.ensiie.fr/pub/a3pat.dtd">
<PROOF><SIGNATURE><SYMBOLLIST><SYMBOL arity="2" unmarked=""><NAME>&lt;</NAME></SYMBOL><SYMBOL arity="2" unmarked=""><NAME>-</NAME></SYMBOL><SYMBOL arity="0" unmarked=""><NAME>0</NAME></SYMBOL><SYMBOL arity="2" unmarked="gcd"><NAME>Marked_gcd</NAME></SYMBOL><SYMBOL arity="3" unmarked=""><NAME>if</NAME></SYMBOL><SYMBOL arity="1" unmarked=""><NAME>s</NAME></SYMBOL><SYMBOL arity="2" unmarked=""><NAME>gcd</NAME></SYMBOL></SYMBOLLIST><VARLIST><VAR>z</VAR><VAR>y</VAR><VAR>x</VAR></VARLIST></SIGNATURE><PROPERTY criterion="dp" prop="sntrs"><SYSTEM><REWSYS><RULE><LHS>gcd(x,0)</LHS><RHS>x</RHS></RULE><RULE><LHS>gcd(0,y)</LHS><RHS>y</RHS></RULE><RULE><LHS>gcd(s(x),s(y))</LHS><RHS>if(&lt;(x,y),gcd(s(x),-(y,x)),gcd(-(x,y),s(y)))</RHS></RULE></REWSYS></SYSTEM><CRITERION/><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>gcd(x,0)</LHS><RHS>x</RHS></RULE><RULE><LHS>gcd(0,y)</LHS><RHS>y</RHS></RULE><RULE><LHS>gcd(s(x),s(y))</LHS><RHS>if(&lt;(x,y),gcd(s(x),-(y,x)),gcd(-(x,y),s(y)))</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_gcd(s(x),s(y))</LHS><RHS>Marked_gcd(s(x),-(y,x))</RHS></DPRULE><DPRULE num="1"><LHS>Marked_gcd(s(x),s(y))</LHS><RHS>Marked_gcd(-(x,y),s(y))</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><DAG approx="simpl"><CCLIST><NONSCC num="0"><NODE ref="1"/></NONSCC><NONSCC num="1"><NODE ref="0"/></NONSCC></CCLIST></DAG></CRITERION></PROPERTY></PROPERTY></PROOF>
