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<!DOCTYPE PROOF SYSTEM "http://a3pat.ensiie.fr/pub/a3pat.dtd">
<PROOF><SIGNATURE><SYMBOLLIST><SYMBOL arity="2" unmarked=""><NAME>n__add</NAME></SYMBOL><SYMBOL arity="2" unmarked="add"><NAME>Marked_add</NAME></SYMBOL><SYMBOL arity="0" unmarked=""><NAME>0</NAME></SYMBOL><SYMBOL arity="2" unmarked="sel"><NAME>Marked_sel</NAME></SYMBOL><SYMBOL arity="2" unmarked=""><NAME>cons</NAME></SYMBOL><SYMBOL arity="1" unmarked=""><NAME>activate</NAME></SYMBOL><SYMBOL arity="2" unmarked=""><NAME>fib1</NAME></SYMBOL><SYMBOL arity="1" unmarked="fib"><NAME>Marked_fib</NAME></SYMBOL><SYMBOL arity="2" unmarked=""><NAME>n__fib1</NAME></SYMBOL><SYMBOL arity="1" unmarked="activate"><NAME>Marked_activate</NAME></SYMBOL><SYMBOL arity="1" unmarked=""><NAME>s</NAME></SYMBOL><SYMBOL arity="2" unmarked="fib1"><NAME>Marked_fib1</NAME></SYMBOL><SYMBOL arity="1" unmarked=""><NAME>fib</NAME></SYMBOL><SYMBOL arity="2" unmarked=""><NAME>add</NAME></SYMBOL><SYMBOL arity="2" unmarked=""><NAME>sel</NAME></SYMBOL></SYMBOLLIST><VARLIST><VAR>X2</VAR><VAR>X1</VAR><VAR>XS</VAR><VAR>Y</VAR><VAR>X</VAR><VAR>N</VAR></VARLIST></SIGNATURE><PROPERTY criterion="dp" prop="sntrs"><SYSTEM><REWSYS><RULE><LHS>fib(N)</LHS><RHS>sel(N,fib1(s(0),s(0)))</RHS></RULE><RULE><LHS>fib1(X,Y)</LHS><RHS>cons(X,n__fib1(Y,n__add(X,Y)))</RHS></RULE><RULE><LHS>add(0,X)</LHS><RHS>X</RHS></RULE><RULE><LHS>add(s(X),Y)</LHS><RHS>s(add(X,Y))</RHS></RULE><RULE><LHS>sel(0,cons(X,XS))</LHS><RHS>X</RHS></RULE><RULE><LHS>sel(s(N),cons(X,XS))</LHS><RHS>sel(N,activate(XS))</RHS></RULE><RULE><LHS>fib1(X1,X2)</LHS><RHS>n__fib1(X1,X2)</RHS></RULE><RULE><LHS>add(X1,X2)</LHS><RHS>n__add(X1,X2)</RHS></RULE><RULE><LHS>activate(n__fib1(X1,X2))</LHS><RHS>fib1(activate(X1),activate(X2))</RHS></RULE><RULE><LHS>activate(n__add(X1,X2))</LHS><RHS>add(activate(X1),activate(X2))</RHS></RULE><RULE><LHS>activate(X)</LHS><RHS>X</RHS></RULE></REWSYS></SYSTEM><CRITERION/><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>fib(N)</LHS><RHS>sel(N,fib1(s(0),s(0)))</RHS></RULE><RULE><LHS>fib1(X,Y)</LHS><RHS>cons(X,n__fib1(Y,n__add(X,Y)))</RHS></RULE><RULE><LHS>add(0,X)</LHS><RHS>X</RHS></RULE><RULE><LHS>add(s(X),Y)</LHS><RHS>s(add(X,Y))</RHS></RULE><RULE><LHS>sel(0,cons(X,XS))</LHS><RHS>X</RHS></RULE><RULE><LHS>sel(s(N),cons(X,XS))</LHS><RHS>sel(N,activate(XS))</RHS></RULE><RULE><LHS>fib1(X1,X2)</LHS><RHS>n__fib1(X1,X2)</RHS></RULE><RULE><LHS>add(X1,X2)</LHS><RHS>n__add(X1,X2)</RHS></RULE><RULE><LHS>activate(n__fib1(X1,X2))</LHS><RHS>fib1(activate(X1),activate(X2))</RHS></RULE><RULE><LHS>activate(n__add(X1,X2))</LHS><RHS>add(activate(X1),activate(X2))</RHS></RULE><RULE><LHS>activate(X)</LHS><RHS>X</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_fib(N)</LHS><RHS>Marked_sel(N,fib1(s(0),s(0)))</RHS></DPRULE><DPRULE num="1"><LHS>Marked_fib(N)</LHS><RHS>Marked_fib1(s(0),s(0))</RHS></DPRULE><DPRULE num="2"><LHS>Marked_add(s(X),Y)</LHS><RHS>Marked_add(X,Y)</RHS></DPRULE><DPRULE num="3"><LHS>Marked_sel(s(N),cons(X,XS))</LHS><RHS>Marked_sel(N,activate(XS))</RHS></DPRULE><DPRULE num="4"><LHS>Marked_sel(s(N),cons(X,XS))</LHS><RHS>Marked_activate(XS)</RHS></DPRULE><DPRULE num="5"><LHS>Marked_activate(n__fib1(X1,X2))</LHS><RHS>Marked_fib1(activate(X1),activate(X2))</RHS></DPRULE><DPRULE num="6"><LHS>Marked_activate(n__fib1(X1,X2))</LHS><RHS>Marked_activate(X1)</RHS></DPRULE><DPRULE num="7"><LHS>Marked_activate(n__fib1(X1,X2))</LHS><RHS>Marked_activate(X2)</RHS></DPRULE><DPRULE num="8"><LHS>Marked_activate(n__add(X1,X2))</LHS><RHS>Marked_add(activate(X1),activate(X2))</RHS></DPRULE><DPRULE num="9"><LHS>Marked_activate(n__add(X1,X2))</LHS><RHS>Marked_activate(X1)</RHS></DPRULE><DPRULE num="10"><LHS>Marked_activate(n__add(X1,X2))</LHS><RHS>Marked_activate(X2)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><DAG approx="simpl"><CCLIST><SCC num="0"><NODE ref="6"/><NODE ref="7"/><NODE ref="9"/><NODE ref="10"/></SCC><NONSCC num="1"><NODE ref="8"/></NONSCC><NONSCC num="2"><NODE ref="5"/></NONSCC><SCC num="3"><NODE ref="2"/></SCC><NONSCC num="4"><NODE ref="4"/></NONSCC><SCC num="5"><NODE ref="3"/></SCC><NONSCC num="6"><NODE ref="1"/></NONSCC><NONSCC num="7"><NODE ref="0"/></NONSCC></CCLIST><EDGE end="2" start="0"/><EDGE end="1" start="0"/><EDGE end="3" start="1"/><EDGE end="2" start="4"/><EDGE end="1" start="4"/><EDGE end="0" start="4"/><EDGE end="4" start="5"/><EDGE end="5" start="7"/><EDGE end="4" start="7"/></DAG></CRITERION><PROPERTY criterion="ordering" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>fib(N)</LHS><RHS>sel(N,fib1(s(0),s(0)))</RHS></RULE><RULE><LHS>fib1(X,Y)</LHS><RHS>cons(X,n__fib1(Y,n__add(X,Y)))</RHS></RULE><RULE><LHS>add(0,X)</LHS><RHS>X</RHS></RULE><RULE><LHS>add(s(X),Y)</LHS><RHS>s(add(X,Y))</RHS></RULE><RULE><LHS>sel(0,cons(X,XS))</LHS><RHS>X</RHS></RULE><RULE><LHS>sel(s(N),cons(X,XS))</LHS><RHS>sel(N,activate(XS))</RHS></RULE><RULE><LHS>fib1(X1,X2)</LHS><RHS>n__fib1(X1,X2)</RHS></RULE><RULE><LHS>add(X1,X2)</LHS><RHS>n__add(X1,X2)</RHS></RULE><RULE><LHS>activate(n__fib1(X1,X2))</LHS><RHS>fib1(activate(X1),activate(X2))</RHS></RULE><RULE><LHS>activate(n__add(X1,X2))</LHS><RHS>add(activate(X1),activate(X2))</RHS></RULE><RULE><LHS>activate(X)</LHS><RHS>X</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_sel(s(N),cons(X,XS))</LHS><RHS>Marked_sel(N,activate(XS))</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><ORDERING type="rpo"><STATUSLIST><STATUS status="lex"><SYMBOL><NAME>sel</NAME></SYMBOL></STATUS><STATUS status="lex"><SYMBOL><NAME>add</NAME></SYMBOL></STATUS><STATUS status="lex"><SYMBOL><NAME>fib</NAME></SYMBOL></STATUS><STATUS status="lex"><SYMBOL><NAME>s</NAME></SYMBOL></STATUS><STATUS status="lex"><SYMBOL><NAME>n__fib1</NAME></SYMBOL></STATUS><STATUS status="lex"><SYMBOL><NAME>fib1</NAME></SYMBOL></STATUS><STATUS status="lex"><SYMBOL><NAME>activate</NAME></SYMBOL></STATUS><STATUS status="lex"><SYMBOL><NAME>cons</NAME></SYMBOL></STATUS><STATUS status="lex"><SYMBOL><NAME>Marked_sel</NAME></SYMBOL></STATUS><STATUS status="lex"><SYMBOL><NAME>0</NAME></SYMBOL></STATUS><STATUS status="lex"><SYMBOL><NAME>n__add</NAME></SYMBOL></STATUS></STATUSLIST><PRECEDENCE><PREC><OLHS><SYMBOL><NAME>sel</NAME></SYMBOL></OLHS><ORHS><SYMBOL><NAME>fib</NAME></SYMBOL></ORHS></PREC><PREC><OLHS><SYMBOL><NAME>fib1</NAME></SYMBOL></OLHS><ORHS><SYMBOL><NAME>sel</NAME></SYMBOL></ORHS></PREC><PREC><OLHS><SYMBOL><NAME>fib1</NAME></SYMBOL></OLHS><ORHS><SYMBOL><NAME>fib</NAME></SYMBOL></ORHS></PREC><PREC><OLHS><SYMBOL><NAME>fib1</NAME></SYMBOL></OLHS><ORHS><SYMBOL><NAME>activate</NAME></SYMBOL></ORHS></PREC><PREC><OLHS><SYMBOL><NAME>fib1</NAME></SYMBOL></OLHS><ORHS><SYMBOL><NAME>Marked_sel</NAME></SYMBOL></ORHS></PREC><PREC><OLHS><SYMBOL><NAME>s</NAME></SYMBOL></OLHS><ORHS><SYMBOL><NAME>sel</NAME></SYMBOL></ORHS></PREC><PREC><OLHS><SYMBOL><NAME>s</NAME></SYMBOL></OLHS><ORHS><SYMBOL><NAME>fib</NAME></SYMBOL></ORHS></PREC><PREC><OLHS><SYMBOL><NAME>s</NAME></SYMBOL></OLHS><ORHS><SYMBOL><NAME>add</NAME></SYMBOL></ORHS></PREC><PREC><OLHS><SYMBOL><NAME>s</NAME></SYMBOL></OLHS><ORHS><SYMBOL><NAME>activate</NAME></SYMBOL></ORHS></PREC><PREC><OLHS><SYMBOL><NAME>s</NAME></SYMBOL></OLHS><ORHS><SYMBOL><NAME>Marked_sel</NAME></SYMBOL></ORHS></PREC><PREC><OLHS><SYMBOL><NAME>0</NAME></SYMBOL></OLHS><ORHS><SYMBOL><NAME>fib</NAME></SYMBOL></ORHS></PREC><PREC><OLHS><SYMBOL><NAME>cons</NAME></SYMBOL></OLHS><ORHS><SYMBOL><NAME>sel</NAME></SYMBOL></ORHS></PREC><PREC><OLHS><SYMBOL><NAME>cons</NAME></SYMBOL></OLHS><ORHS><SYMBOL><NAME>fib1</NAME></SYMBOL></ORHS></PREC><PREC><OLHS><SYMBOL><NAME>cons</NAME></SYMBOL></OLHS><ORHS><SYMBOL><NAME>fib</NAME></SYMBOL></ORHS></PREC><PREC><OLHS><SYMBOL><NAME>cons</NAME></SYMBOL></OLHS><ORHS><SYMBOL><NAME>activate</NAME></SYMBOL></ORHS></PREC><PREC><OLHS><SYMBOL><NAME>cons</NAME></SYMBOL></OLHS><ORHS><SYMBOL><NAME>Marked_sel</NAME></SYMBOL></ORHS></PREC><PREC><OLHS><SYMBOL><NAME>n__fib1</NAME></SYMBOL></OLHS><ORHS><SYMBOL><NAME>sel</NAME></SYMBOL></ORHS></PREC><PREC><OLHS><SYMBOL><NAME>n__fib1</NAME></SYMBOL></OLHS><ORHS><SYMBOL><NAME>fib1</NAME></SYMBOL></ORHS></PREC><PREC><OLHS><SYMBOL><NAME>n__fib1</NAME></SYMBOL></OLHS><ORHS><SYMBOL><NAME>fib</NAME></SYMBOL></ORHS></PREC><PREC><OLHS><SYMBOL><NAME>n__fib1</NAME></SYMBOL></OLHS><ORHS><SYMBOL><NAME>activate</NAME></SYMBOL></ORHS></PREC><PREC><OLHS><SYMBOL><NAME>n__fib1</NAME></SYMBOL></OLHS><ORHS><SYMBOL><NAME>Marked_sel</NAME></SYMBOL></ORHS></PREC><PREC><OLHS><SYMBOL><NAME>n__add</NAME></SYMBOL></OLHS><ORHS><SYMBOL><NAME>sel</NAME></SYMBOL></ORHS></PREC><PREC><OLHS><SYMBOL><NAME>n__add</NAME></SYMBOL></OLHS><ORHS><SYMBOL><NAME>fib1</NAME></SYMBOL></ORHS></PREC><PREC><OLHS><SYMBOL><NAME>n__add</NAME></SYMBOL></OLHS><ORHS><SYMBOL><NAME>fib</NAME></SYMBOL></ORHS></PREC><PREC><OLHS><SYMBOL><NAME>n__add</NAME></SYMBOL></OLHS><ORHS><SYMBOL><NAME>add</NAME></SYMBOL></ORHS></PREC><PREC><OLHS><SYMBOL><NAME>n__add</NAME></SYMBOL></OLHS><ORHS><SYMBOL><NAME>activate</NAME></SYMBOL></ORHS></PREC><PREC><OLHS><SYMBOL><NAME>n__add</NAME></SYMBOL></OLHS><ORHS><SYMBOL><NAME>Marked_sel</NAME></SYMBOL></ORHS></PREC><PREC><OLHS><SYMBOL><NAME>add</NAME></SYMBOL></OLHS><ORHS><SYMBOL><NAME>sel</NAME></SYMBOL></ORHS></PREC><PREC><OLHS><SYMBOL><NAME>add</NAME></SYMBOL></OLHS><ORHS><SYMBOL><NAME>fib</NAME></SYMBOL></ORHS></PREC><PREC><OLHS><SYMBOL><NAME>add</NAME></SYMBOL></OLHS><ORHS><SYMBOL><NAME>activate</NAME></SYMBOL></ORHS></PREC><PREC><OLHS><SYMBOL><NAME>add</NAME></SYMBOL></OLHS><ORHS><SYMBOL><NAME>Marked_sel</NAME></SYMBOL></ORHS></PREC><PREC><OLHS><SYMBOL><NAME>activate</NAME></SYMBOL></OLHS><ORHS><SYMBOL><NAME>sel</NAME></SYMBOL></ORHS></PREC><PREC><OLHS><SYMBOL><NAME>activate</NAME></SYMBOL></OLHS><ORHS><SYMBOL><NAME>fib</NAME></SYMBOL></ORHS></PREC><PREC><OLHS><SYMBOL><NAME>activate</NAME></SYMBOL></OLHS><ORHS><SYMBOL><NAME>Marked_sel</NAME></SYMBOL></ORHS></PREC></PRECEDENCE><EQUIVALENCE/></ORDERING></CRITERION></PROPERTY><PROPERTY criterion="ordering" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>fib(N)</LHS><RHS>sel(N,fib1(s(0),s(0)))</RHS></RULE><RULE><LHS>fib1(X,Y)</LHS><RHS>cons(X,n__fib1(Y,n__add(X,Y)))</RHS></RULE><RULE><LHS>add(0,X)</LHS><RHS>X</RHS></RULE><RULE><LHS>add(s(X),Y)</LHS><RHS>s(add(X,Y))</RHS></RULE><RULE><LHS>sel(0,cons(X,XS))</LHS><RHS>X</RHS></RULE><RULE><LHS>sel(s(N),cons(X,XS))</LHS><RHS>sel(N,activate(XS))</RHS></RULE><RULE><LHS>fib1(X1,X2)</LHS><RHS>n__fib1(X1,X2)</RHS></RULE><RULE><LHS>add(X1,X2)</LHS><RHS>n__add(X1,X2)</RHS></RULE><RULE><LHS>activate(n__fib1(X1,X2))</LHS><RHS>fib1(activate(X1),activate(X2))</RHS></RULE><RULE><LHS>activate(n__add(X1,X2))</LHS><RHS>add(activate(X1),activate(X2))</RHS></RULE><RULE><LHS>activate(X)</LHS><RHS>X</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_activate(n__fib1(X1,X2))</LHS><RHS>Marked_activate(X1)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_activate(n__fib1(X1,X2))</LHS><RHS>Marked_activate(X2)</RHS></DPRULE><DPRULE num="2"><LHS>Marked_activate(n__add(X1,X2))</LHS><RHS>Marked_activate(X1)</RHS></DPRULE><DPRULE num="3"><LHS>Marked_activate(n__add(X1,X2))</LHS><RHS>Marked_activate(X2)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><ORDERING type="rpo"><STATUSLIST><STATUS status="lex"><SYMBOL><NAME>sel</NAME></SYMBOL></STATUS><STATUS status="lex"><SYMBOL><NAME>add</NAME></SYMBOL></STATUS><STATUS status="lex"><SYMBOL><NAME>fib</NAME></SYMBOL></STATUS><STATUS status="lex"><SYMBOL><NAME>s</NAME></SYMBOL></STATUS><STATUS status="lex"><SYMBOL><NAME>n__fib1</NAME></SYMBOL></STATUS><STATUS status="lex"><SYMBOL><NAME>fib1</NAME></SYMBOL></STATUS><STATUS status="lex"><SYMBOL><NAME>activate</NAME></SYMBOL></STATUS><STATUS status="lex"><SYMBOL><NAME>cons</NAME></SYMBOL></STATUS><STATUS status="lex"><SYMBOL><NAME>0</NAME></SYMBOL></STATUS><STATUS status="lex"><SYMBOL><NAME>n__add</NAME></SYMBOL></STATUS></STATUSLIST><PRECEDENCE><PREC><OLHS><SYMBOL><NAME>sel</NAME></SYMBOL></OLHS><ORHS><SYMBOL><NAME>fib</NAME></SYMBOL></ORHS></PREC><PREC><OLHS><SYMBOL><NAME>fib1</NAME></SYMBOL></OLHS><ORHS><SYMBOL><NAME>sel</NAME></SYMBOL></ORHS></PREC><PREC><OLHS><SYMBOL><NAME>fib1</NAME></SYMBOL></OLHS><ORHS><SYMBOL><NAME>fib</NAME></SYMBOL></ORHS></PREC><PREC><OLHS><SYMBOL><NAME>fib1</NAME></SYMBOL></OLHS><ORHS><SYMBOL><NAME>activate</NAME></SYMBOL></ORHS></PREC><PREC><OLHS><SYMBOL><NAME>s</NAME></SYMBOL></OLHS><ORHS><SYMBOL><NAME>sel</NAME></SYMBOL></ORHS></PREC><PREC><OLHS><SYMBOL><NAME>s</NAME></SYMBOL></OLHS><ORHS><SYMBOL><NAME>fib</NAME></SYMBOL></ORHS></PREC><PREC><OLHS><SYMBOL><NAME>s</NAME></SYMBOL></OLHS><ORHS><SYMBOL><NAME>add</NAME></SYMBOL></ORHS></PREC><PREC><OLHS><SYMBOL><NAME>s</NAME></SYMBOL></OLHS><ORHS><SYMBOL><NAME>activate</NAME></SYMBOL></ORHS></PREC><PREC><OLHS><SYMBOL><NAME>0</NAME></SYMBOL></OLHS><ORHS><SYMBOL><NAME>fib</NAME></SYMBOL></ORHS></PREC><PREC><OLHS><SYMBOL><NAME>cons</NAME></SYMBOL></OLHS><ORHS><SYMBOL><NAME>sel</NAME></SYMBOL></ORHS></PREC><PREC><OLHS><SYMBOL><NAME>cons</NAME></SYMBOL></OLHS><ORHS><SYMBOL><NAME>fib1</NAME></SYMBOL></ORHS></PREC><PREC><OLHS><SYMBOL><NAME>cons</NAME></SYMBOL></OLHS><ORHS><SYMBOL><NAME>fib</NAME></SYMBOL></ORHS></PREC><PREC><OLHS><SYMBOL><NAME>cons</NAME></SYMBOL></OLHS><ORHS><SYMBOL><NAME>activate</NAME></SYMBOL></ORHS></PREC><PREC><OLHS><SYMBOL><NAME>n__fib1</NAME></SYMBOL></OLHS><ORHS><SYMBOL><NAME>sel</NAME></SYMBOL></ORHS></PREC><PREC><OLHS><SYMBOL><NAME>n__fib1</NAME></SYMBOL></OLHS><ORHS><SYMBOL><NAME>fib1</NAME></SYMBOL></ORHS></PREC><PREC><OLHS><SYMBOL><NAME>n__fib1</NAME></SYMBOL></OLHS><ORHS><SYMBOL><NAME>fib</NAME></SYMBOL></ORHS></PREC><PREC><OLHS><SYMBOL><NAME>n__fib1</NAME></SYMBOL></OLHS><ORHS><SYMBOL><NAME>activate</NAME></SYMBOL></ORHS></PREC><PREC><OLHS><SYMBOL><NAME>n__add</NAME></SYMBOL></OLHS><ORHS><SYMBOL><NAME>sel</NAME></SYMBOL></ORHS></PREC><PREC><OLHS><SYMBOL><NAME>n__add</NAME></SYMBOL></OLHS><ORHS><SYMBOL><NAME>fib1</NAME></SYMBOL></ORHS></PREC><PREC><OLHS><SYMBOL><NAME>n__add</NAME></SYMBOL></OLHS><ORHS><SYMBOL><NAME>fib</NAME></SYMBOL></ORHS></PREC><PREC><OLHS><SYMBOL><NAME>n__add</NAME></SYMBOL></OLHS><ORHS><SYMBOL><NAME>add</NAME></SYMBOL></ORHS></PREC><PREC><OLHS><SYMBOL><NAME>n__add</NAME></SYMBOL></OLHS><ORHS><SYMBOL><NAME>activate</NAME></SYMBOL></ORHS></PREC><PREC><OLHS><SYMBOL><NAME>add</NAME></SYMBOL></OLHS><ORHS><SYMBOL><NAME>sel</NAME></SYMBOL></ORHS></PREC><PREC><OLHS><SYMBOL><NAME>add</NAME></SYMBOL></OLHS><ORHS><SYMBOL><NAME>fib</NAME></SYMBOL></ORHS></PREC><PREC><OLHS><SYMBOL><NAME>add</NAME></SYMBOL></OLHS><ORHS><SYMBOL><NAME>activate</NAME></SYMBOL></ORHS></PREC><PREC><OLHS><SYMBOL><NAME>activate</NAME></SYMBOL></OLHS><ORHS><SYMBOL><NAME>sel</NAME></SYMBOL></ORHS></PREC><PREC><OLHS><SYMBOL><NAME>activate</NAME></SYMBOL></OLHS><ORHS><SYMBOL><NAME>fib</NAME></SYMBOL></ORHS></PREC></PRECEDENCE><EQUIVALENCE/></ORDERING></CRITERION></PROPERTY><PROPERTY criterion="ordering" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>fib(N)</LHS><RHS>sel(N,fib1(s(0),s(0)))</RHS></RULE><RULE><LHS>fib1(X,Y)</LHS><RHS>cons(X,n__fib1(Y,n__add(X,Y)))</RHS></RULE><RULE><LHS>add(0,X)</LHS><RHS>X</RHS></RULE><RULE><LHS>add(s(X),Y)</LHS><RHS>s(add(X,Y))</RHS></RULE><RULE><LHS>sel(0,cons(X,XS))</LHS><RHS>X</RHS></RULE><RULE><LHS>sel(s(N),cons(X,XS))</LHS><RHS>sel(N,activate(XS))</RHS></RULE><RULE><LHS>fib1(X1,X2)</LHS><RHS>n__fib1(X1,X2)</RHS></RULE><RULE><LHS>add(X1,X2)</LHS><RHS>n__add(X1,X2)</RHS></RULE><RULE><LHS>activate(n__fib1(X1,X2))</LHS><RHS>fib1(activate(X1),activate(X2))</RHS></RULE><RULE><LHS>activate(n__add(X1,X2))</LHS><RHS>add(activate(X1),activate(X2))</RHS></RULE><RULE><LHS>activate(X)</LHS><RHS>X</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_add(s(X),Y)</LHS><RHS>Marked_add(X,Y)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><ORDERING type="rpo"><STATUSLIST><STATUS status="lex"><SYMBOL><NAME>sel</NAME></SYMBOL></STATUS><STATUS status="lex"><SYMBOL><NAME>add</NAME></SYMBOL></STATUS><STATUS status="lex"><SYMBOL><NAME>fib</NAME></SYMBOL></STATUS><STATUS status="lex"><SYMBOL><NAME>s</NAME></SYMBOL></STATUS><STATUS status="lex"><SYMBOL><NAME>n__fib1</NAME></SYMBOL></STATUS><STATUS status="lex"><SYMBOL><NAME>fib1</NAME></SYMBOL></STATUS><STATUS status="lex"><SYMBOL><NAME>activate</NAME></SYMBOL></STATUS><STATUS status="lex"><SYMBOL><NAME>cons</NAME></SYMBOL></STATUS><STATUS status="lex"><SYMBOL><NAME>0</NAME></SYMBOL></STATUS><STATUS status="lex"><SYMBOL><NAME>n__add</NAME></SYMBOL></STATUS></STATUSLIST><PRECEDENCE><PREC><OLHS><SYMBOL><NAME>sel</NAME></SYMBOL></OLHS><ORHS><SYMBOL><NAME>fib</NAME></SYMBOL></ORHS></PREC><PREC><OLHS><SYMBOL><NAME>fib1</NAME></SYMBOL></OLHS><ORHS><SYMBOL><NAME>sel</NAME></SYMBOL></ORHS></PREC><PREC><OLHS><SYMBOL><NAME>fib1</NAME></SYMBOL></OLHS><ORHS><SYMBOL><NAME>fib</NAME></SYMBOL></ORHS></PREC><PREC><OLHS><SYMBOL><NAME>fib1</NAME></SYMBOL></OLHS><ORHS><SYMBOL><NAME>activate</NAME></SYMBOL></ORHS></PREC><PREC><OLHS><SYMBOL><NAME>s</NAME></SYMBOL></OLHS><ORHS><SYMBOL><NAME>sel</NAME></SYMBOL></ORHS></PREC><PREC><OLHS><SYMBOL><NAME>s</NAME></SYMBOL></OLHS><ORHS><SYMBOL><NAME>fib</NAME></SYMBOL></ORHS></PREC><PREC><OLHS><SYMBOL><NAME>s</NAME></SYMBOL></OLHS><ORHS><SYMBOL><NAME>add</NAME></SYMBOL></ORHS></PREC><PREC><OLHS><SYMBOL><NAME>s</NAME></SYMBOL></OLHS><ORHS><SYMBOL><NAME>activate</NAME></SYMBOL></ORHS></PREC><PREC><OLHS><SYMBOL><NAME>0</NAME></SYMBOL></OLHS><ORHS><SYMBOL><NAME>fib</NAME></SYMBOL></ORHS></PREC><PREC><OLHS><SYMBOL><NAME>cons</NAME></SYMBOL></OLHS><ORHS><SYMBOL><NAME>sel</NAME></SYMBOL></ORHS></PREC><PREC><OLHS><SYMBOL><NAME>cons</NAME></SYMBOL></OLHS><ORHS><SYMBOL><NAME>fib1</NAME></SYMBOL></ORHS></PREC><PREC><OLHS><SYMBOL><NAME>cons</NAME></SYMBOL></OLHS><ORHS><SYMBOL><NAME>fib</NAME></SYMBOL></ORHS></PREC><PREC><OLHS><SYMBOL><NAME>cons</NAME></SYMBOL></OLHS><ORHS><SYMBOL><NAME>activate</NAME></SYMBOL></ORHS></PREC><PREC><OLHS><SYMBOL><NAME>n__fib1</NAME></SYMBOL></OLHS><ORHS><SYMBOL><NAME>sel</NAME></SYMBOL></ORHS></PREC><PREC><OLHS><SYMBOL><NAME>n__fib1</NAME></SYMBOL></OLHS><ORHS><SYMBOL><NAME>fib1</NAME></SYMBOL></ORHS></PREC><PREC><OLHS><SYMBOL><NAME>n__fib1</NAME></SYMBOL></OLHS><ORHS><SYMBOL><NAME>fib</NAME></SYMBOL></ORHS></PREC><PREC><OLHS><SYMBOL><NAME>n__fib1</NAME></SYMBOL></OLHS><ORHS><SYMBOL><NAME>activate</NAME></SYMBOL></ORHS></PREC><PREC><OLHS><SYMBOL><NAME>n__add</NAME></SYMBOL></OLHS><ORHS><SYMBOL><NAME>sel</NAME></SYMBOL></ORHS></PREC><PREC><OLHS><SYMBOL><NAME>n__add</NAME></SYMBOL></OLHS><ORHS><SYMBOL><NAME>fib1</NAME></SYMBOL></ORHS></PREC><PREC><OLHS><SYMBOL><NAME>n__add</NAME></SYMBOL></OLHS><ORHS><SYMBOL><NAME>fib</NAME></SYMBOL></ORHS></PREC><PREC><OLHS><SYMBOL><NAME>n__add</NAME></SYMBOL></OLHS><ORHS><SYMBOL><NAME>add</NAME></SYMBOL></ORHS></PREC><PREC><OLHS><SYMBOL><NAME>n__add</NAME></SYMBOL></OLHS><ORHS><SYMBOL><NAME>activate</NAME></SYMBOL></ORHS></PREC><PREC><OLHS><SYMBOL><NAME>add</NAME></SYMBOL></OLHS><ORHS><SYMBOL><NAME>sel</NAME></SYMBOL></ORHS></PREC><PREC><OLHS><SYMBOL><NAME>add</NAME></SYMBOL></OLHS><ORHS><SYMBOL><NAME>fib</NAME></SYMBOL></ORHS></PREC><PREC><OLHS><SYMBOL><NAME>add</NAME></SYMBOL></OLHS><ORHS><SYMBOL><NAME>activate</NAME></SYMBOL></ORHS></PREC><PREC><OLHS><SYMBOL><NAME>activate</NAME></SYMBOL></OLHS><ORHS><SYMBOL><NAME>sel</NAME></SYMBOL></ORHS></PREC><PREC><OLHS><SYMBOL><NAME>activate</NAME></SYMBOL></OLHS><ORHS><SYMBOL><NAME>fib</NAME></SYMBOL></ORHS></PREC></PRECEDENCE><EQUIVALENCE/></ORDERING></CRITERION></PROPERTY></PROPERTY></PROPERTY></PROOF>
