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<!DOCTYPE PROOF SYSTEM "http://a3pat.ensiie.fr/pub/a3pat.dtd">
<PROOF><SIGNATURE><SYMBOLLIST><SYMBOL arity="2" unmarked=""><NAME>add</NAME></SYMBOL><SYMBOL arity="2" unmarked="add"><NAME>Marked_add</NAME></SYMBOL><SYMBOL arity="1" unmarked=""><NAME>terms</NAME></SYMBOL><SYMBOL arity="1" unmarked="sqr"><NAME>Marked_sqr</NAME></SYMBOL><SYMBOL arity="0" unmarked=""><NAME>s</NAME></SYMBOL><SYMBOL arity="2" unmarked=""><NAME>first</NAME></SYMBOL><SYMBOL arity="1" unmarked=""><NAME>recip</NAME></SYMBOL><SYMBOL arity="1" unmarked="terms"><NAME>Marked_terms</NAME></SYMBOL><SYMBOL arity="1" unmarked=""><NAME>dbl</NAME></SYMBOL><SYMBOL arity="2" unmarked="first"><NAME>Marked_first</NAME></SYMBOL><SYMBOL arity="1" unmarked=""><NAME>sqr</NAME></SYMBOL><SYMBOL arity="1" unmarked="dbl"><NAME>Marked_dbl</NAME></SYMBOL><SYMBOL arity="0" unmarked=""><NAME>0</NAME></SYMBOL><SYMBOL arity="0" unmarked=""><NAME>nil</NAME></SYMBOL><SYMBOL arity="1" unmarked=""><NAME>cons</NAME></SYMBOL></SYMBOLLIST><VARLIST><VAR>Y</VAR><VAR>X</VAR><VAR>N</VAR></VARLIST></SIGNATURE><PROPERTY criterion="dp" prop="sntrs"><SYSTEM><REWSYS><RULE><LHS>terms(N)</LHS><RHS>cons(recip(sqr(N)))</RHS></RULE><RULE><LHS>sqr(0)</LHS><RHS>0</RHS></RULE><RULE><LHS>sqr(s)</LHS><RHS>s</RHS></RULE><RULE><LHS>dbl(0)</LHS><RHS>0</RHS></RULE><RULE><LHS>dbl(s)</LHS><RHS>s</RHS></RULE><RULE><LHS>add(0,X)</LHS><RHS>X</RHS></RULE><RULE><LHS>add(s,Y)</LHS><RHS>s</RHS></RULE><RULE><LHS>first(0,X)</LHS><RHS>nil</RHS></RULE><RULE><LHS>first(s,cons(Y))</LHS><RHS>cons(Y)</RHS></RULE></REWSYS></SYSTEM><CRITERION/><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>terms(N)</LHS><RHS>cons(recip(sqr(N)))</RHS></RULE><RULE><LHS>sqr(0)</LHS><RHS>0</RHS></RULE><RULE><LHS>sqr(s)</LHS><RHS>s</RHS></RULE><RULE><LHS>dbl(0)</LHS><RHS>0</RHS></RULE><RULE><LHS>dbl(s)</LHS><RHS>s</RHS></RULE><RULE><LHS>add(0,X)</LHS><RHS>X</RHS></RULE><RULE><LHS>add(s,Y)</LHS><RHS>s</RHS></RULE><RULE><LHS>first(0,X)</LHS><RHS>nil</RHS></RULE><RULE><LHS>first(s,cons(Y))</LHS><RHS>cons(Y)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_terms(N)</LHS><RHS>Marked_sqr(N)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><DAG approx="simpl"><CCLIST><NONSCC num="0"><NODE ref="0"/></NONSCC></CCLIST></DAG></CRITERION></PROPERTY></PROPERTY></PROOF>
