<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE PROOF SYSTEM "http://a3pat.ensiie.fr/pub/a3pat.dtd">
<PROOF><SIGNATURE><SYMBOLLIST><SYMBOL arity="0" unmarked=""><NAME>tl</NAME></SYMBOL><SYMBOL arity="2" unmarked="app"><NAME>Marked_app</NAME></SYMBOL><SYMBOL arity="0" unmarked=""><NAME>nil</NAME></SYMBOL><SYMBOL arity="0" unmarked=""><NAME>cons</NAME></SYMBOL><SYMBOL arity="0" unmarked=""><NAME>init</NAME></SYMBOL><SYMBOL arity="0" unmarked=""><NAME>compose</NAME></SYMBOL><SYMBOL arity="0" unmarked=""><NAME>hd</NAME></SYMBOL><SYMBOL arity="0" unmarked="init"><NAME>Marked_init</NAME></SYMBOL><SYMBOL arity="0" unmarked=""><NAME>reverse2</NAME></SYMBOL><SYMBOL arity="0" unmarked="last"><NAME>Marked_last</NAME></SYMBOL><SYMBOL arity="0" unmarked=""><NAME>reverse</NAME></SYMBOL><SYMBOL arity="0" unmarked=""><NAME>last</NAME></SYMBOL><SYMBOL arity="2" unmarked=""><NAME>app</NAME></SYMBOL></SYMBOLLIST><VARLIST><VAR>xs</VAR><VAR>l</VAR><VAR>x</VAR><VAR>g</VAR><VAR>f</VAR></VARLIST></SIGNATURE><PROPERTY criterion="dp" prop="sntrs"><SYSTEM><REWSYS><RULE><LHS>app(app(app(compose,f),g),x)</LHS><RHS>app(g,app(f,x))</RHS></RULE><RULE><LHS>app(reverse,l)</LHS><RHS>app(app(reverse2,l),nil)</RHS></RULE><RULE><LHS>app(app(reverse2,nil),l)</LHS><RHS>l</RHS></RULE><RULE><LHS>app(app(reverse2,app(app(cons,x),xs)),l)</LHS><RHS>app(app(reverse2,xs),app(app(cons,x),l))</RHS></RULE><RULE><LHS>app(hd,app(app(cons,x),xs))</LHS><RHS>x</RHS></RULE><RULE><LHS>app(tl,app(app(cons,x),xs))</LHS><RHS>xs</RHS></RULE><RULE><LHS>last</LHS><RHS>app(app(compose,hd),reverse)</RHS></RULE><RULE><LHS>init</LHS><RHS>app(app(compose,reverse),app(app(compose,tl),reverse))</RHS></RULE></REWSYS></SYSTEM><CRITERION/><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>app(app(app(compose,f),g),x)</LHS><RHS>app(g,app(f,x))</RHS></RULE><RULE><LHS>app(reverse,l)</LHS><RHS>app(app(reverse2,l),nil)</RHS></RULE><RULE><LHS>app(app(reverse2,nil),l)</LHS><RHS>l</RHS></RULE><RULE><LHS>app(app(reverse2,app(app(cons,x),xs)),l)</LHS><RHS>app(app(reverse2,xs),app(app(cons,x),l))</RHS></RULE><RULE><LHS>app(hd,app(app(cons,x),xs))</LHS><RHS>x</RHS></RULE><RULE><LHS>app(tl,app(app(cons,x),xs))</LHS><RHS>xs</RHS></RULE><RULE><LHS>last</LHS><RHS>app(app(compose,hd),reverse)</RHS></RULE><RULE><LHS>init</LHS><RHS>app(app(compose,reverse),app(app(compose,tl),reverse))</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_app(app(app(compose,f),g),x)</LHS><RHS>Marked_app(g,app(f,x))</RHS></DPRULE><DPRULE num="1"><LHS>Marked_app(app(app(compose,f),g),x)</LHS><RHS>Marked_app(f,x)</RHS></DPRULE><DPRULE num="2"><LHS>Marked_app(reverse,l)</LHS><RHS>Marked_app(app(reverse2,l),nil)</RHS></DPRULE><DPRULE num="3"><LHS>Marked_app(reverse,l)</LHS><RHS>Marked_app(reverse2,l)</RHS></DPRULE><DPRULE num="4"><LHS>Marked_app(app(reverse2,app(app(cons,x),xs)),l)</LHS><RHS>Marked_app(app(reverse2,xs),app(app(cons,x),l))</RHS></DPRULE><DPRULE num="5"><LHS>Marked_app(app(reverse2,app(app(cons,x),xs)),l)</LHS><RHS>Marked_app(reverse2,xs)</RHS></DPRULE><DPRULE num="6"><LHS>Marked_app(app(reverse2,app(app(cons,x),xs)),l)</LHS><RHS>Marked_app(app(cons,x),l)</RHS></DPRULE><DPRULE num="7"><LHS>Marked_last</LHS><RHS>Marked_app(app(compose,hd),reverse)</RHS></DPRULE><DPRULE num="8"><LHS>Marked_last</LHS><RHS>Marked_app(compose,hd)</RHS></DPRULE><DPRULE num="9"><LHS>Marked_init</LHS><RHS>Marked_app(app(compose,reverse),app(app(compose,tl),reverse))</RHS></DPRULE><DPRULE num="10"><LHS>Marked_init</LHS><RHS>Marked_app(compose,reverse)</RHS></DPRULE><DPRULE num="11"><LHS>Marked_init</LHS><RHS>Marked_app(app(compose,tl),reverse)</RHS></DPRULE><DPRULE num="12"><LHS>Marked_init</LHS><RHS>Marked_app(compose,tl)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><DAG approx="simpl"><CCLIST><NONSCC num="0"><NODE ref="12"/></NONSCC><NONSCC num="1"><NODE ref="11"/></NONSCC><SCC num="2"><NODE ref="0"/><NODE ref="1"/><NODE ref="2"/><NODE ref="4"/><NODE ref="6"/></SCC><NONSCC num="3"><NODE ref="5"/></NONSCC><NONSCC num="4"><NODE ref="3"/></NONSCC><NONSCC num="5"><NODE ref="10"/></NONSCC><NONSCC num="6"><NODE ref="9"/></NONSCC><NONSCC num="7"><NODE ref="8"/></NONSCC><NONSCC num="8"><NODE ref="7"/></NONSCC></CCLIST><EDGE end="4" start="1"/><EDGE end="3" start="1"/><EDGE end="2" start="1"/><EDGE end="4" start="2"/><EDGE end="3" start="2"/><EDGE end="4" start="6"/><EDGE end="3" start="6"/><EDGE end="2" start="6"/><EDGE end="4" start="8"/><EDGE end="3" start="8"/><EDGE end="2" start="8"/></DAG></CRITERION><PROPERTY criterion="stronggraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>app(app(app(compose,f),g),x)</LHS><RHS>app(g,app(f,x))</RHS></RULE><RULE><LHS>app(reverse,l)</LHS><RHS>app(app(reverse2,l),nil)</RHS></RULE><RULE><LHS>app(app(reverse2,nil),l)</LHS><RHS>l</RHS></RULE><RULE><LHS>app(app(reverse2,app(app(cons,x),xs)),l)</LHS><RHS>app(app(reverse2,xs),app(app(cons,x),l))</RHS></RULE><RULE><LHS>app(hd,app(app(cons,x),xs))</LHS><RHS>x</RHS></RULE><RULE><LHS>app(tl,app(app(cons,x),xs))</LHS><RHS>xs</RHS></RULE><RULE><LHS>last</LHS><RHS>app(app(compose,hd),reverse)</RHS></RULE><RULE><LHS>init</LHS><RHS>app(app(compose,reverse),app(app(compose,tl),reverse))</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_app(app(app(compose,f),g),x)</LHS><RHS>Marked_app(g,app(f,x))</RHS></DPRULE><DPRULE num="1"><LHS>Marked_app(app(app(compose,f),g),x)</LHS><RHS>Marked_app(f,x)</RHS></DPRULE><DPRULE num="2"><LHS>Marked_app(reverse,l)</LHS><RHS>Marked_app(app(reverse2,l),nil)</RHS></DPRULE><DPRULE num="3"><LHS>Marked_app(app(reverse2,app(app(cons,x),xs)),l)</LHS><RHS>Marked_app(app(reverse2,xs),app(app(cons,x),l))</RHS></DPRULE><DPRULE num="4"><LHS>Marked_app(app(reverse2,app(app(cons,x),xs)),l)</LHS><RHS>Marked_app(app(cons,x),l)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><ORDERING type="poly"><POLYSYMB><SYMBOL><NAME>app</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>last</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>3</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>reverse</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>reverse2</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>hd</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>compose</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>init</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>3</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>cons</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>nil</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>Marked_app</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>tl</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB></ORDERING><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_app(reverse,l)</LHS><RHS>Marked_app(app(reverse2,l),nil)</RHS></DPRULE></DPLIST></STRICTPAIRS></CRITERION><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>app(app(app(compose,f),g),x)</LHS><RHS>app(g,app(f,x))</RHS></RULE><RULE><LHS>app(reverse,l)</LHS><RHS>app(app(reverse2,l),nil)</RHS></RULE><RULE><LHS>app(app(reverse2,nil),l)</LHS><RHS>l</RHS></RULE><RULE><LHS>app(app(reverse2,app(app(cons,x),xs)),l)</LHS><RHS>app(app(reverse2,xs),app(app(cons,x),l))</RHS></RULE><RULE><LHS>app(hd,app(app(cons,x),xs))</LHS><RHS>x</RHS></RULE><RULE><LHS>app(tl,app(app(cons,x),xs))</LHS><RHS>xs</RHS></RULE><RULE><LHS>last</LHS><RHS>app(app(compose,hd),reverse)</RHS></RULE><RULE><LHS>init</LHS><RHS>app(app(compose,reverse),app(app(compose,tl),reverse))</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_app(app(app(compose,f),g),x)</LHS><RHS>Marked_app(g,app(f,x))</RHS></DPRULE><DPRULE num="1"><LHS>Marked_app(app(app(compose,f),g),x)</LHS><RHS>Marked_app(f,x)</RHS></DPRULE><DPRULE num="2"><LHS>Marked_app(app(reverse2,app(app(cons,x),xs)),l)</LHS><RHS>Marked_app(app(reverse2,xs),app(app(cons,x),l))</RHS></DPRULE><DPRULE num="3"><LHS>Marked_app(app(reverse2,app(app(cons,x),xs)),l)</LHS><RHS>Marked_app(app(cons,x),l)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><DAG approx="simpl"><CCLIST><SCC num="0"><NODE ref="0"/><NODE ref="1"/><NODE ref="2"/><NODE ref="3"/></SCC></CCLIST></DAG></CRITERION><PROPERTY criterion="stronggraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>app(app(app(compose,f),g),x)</LHS><RHS>app(g,app(f,x))</RHS></RULE><RULE><LHS>app(reverse,l)</LHS><RHS>app(app(reverse2,l),nil)</RHS></RULE><RULE><LHS>app(app(reverse2,nil),l)</LHS><RHS>l</RHS></RULE><RULE><LHS>app(app(reverse2,app(app(cons,x),xs)),l)</LHS><RHS>app(app(reverse2,xs),app(app(cons,x),l))</RHS></RULE><RULE><LHS>app(hd,app(app(cons,x),xs))</LHS><RHS>x</RHS></RULE><RULE><LHS>app(tl,app(app(cons,x),xs))</LHS><RHS>xs</RHS></RULE><RULE><LHS>last</LHS><RHS>app(app(compose,hd),reverse)</RHS></RULE><RULE><LHS>init</LHS><RHS>app(app(compose,reverse),app(app(compose,tl),reverse))</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_app(app(app(compose,f),g),x)</LHS><RHS>Marked_app(g,app(f,x))</RHS></DPRULE><DPRULE num="1"><LHS>Marked_app(app(app(compose,f),g),x)</LHS><RHS>Marked_app(f,x)</RHS></DPRULE><DPRULE num="2"><LHS>Marked_app(app(reverse2,app(app(cons,x),xs)),l)</LHS><RHS>Marked_app(app(reverse2,xs),app(app(cons,x),l))</RHS></DPRULE><DPRULE num="3"><LHS>Marked_app(app(reverse2,app(app(cons,x),xs)),l)</LHS><RHS>Marked_app(app(cons,x),l)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><ORDERING type="poly"><POLYSYMB><SYMBOL><NAME>app</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>last</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>reverse</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>reverse2</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>hd</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>compose</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>init</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>cons</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>nil</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>Marked_app</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>tl</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB></ORDERING><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_app(app(reverse2,app(app(cons,x),xs)),l)</LHS><RHS>Marked_app(app(reverse2,xs),app(app(cons,x),l))</RHS></DPRULE></DPLIST></STRICTPAIRS></CRITERION><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>app(app(app(compose,f),g),x)</LHS><RHS>app(g,app(f,x))</RHS></RULE><RULE><LHS>app(reverse,l)</LHS><RHS>app(app(reverse2,l),nil)</RHS></RULE><RULE><LHS>app(app(reverse2,nil),l)</LHS><RHS>l</RHS></RULE><RULE><LHS>app(app(reverse2,app(app(cons,x),xs)),l)</LHS><RHS>app(app(reverse2,xs),app(app(cons,x),l))</RHS></RULE><RULE><LHS>app(hd,app(app(cons,x),xs))</LHS><RHS>x</RHS></RULE><RULE><LHS>app(tl,app(app(cons,x),xs))</LHS><RHS>xs</RHS></RULE><RULE><LHS>last</LHS><RHS>app(app(compose,hd),reverse)</RHS></RULE><RULE><LHS>init</LHS><RHS>app(app(compose,reverse),app(app(compose,tl),reverse))</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_app(app(app(compose,f),g),x)</LHS><RHS>Marked_app(g,app(f,x))</RHS></DPRULE><DPRULE num="1"><LHS>Marked_app(app(app(compose,f),g),x)</LHS><RHS>Marked_app(f,x)</RHS></DPRULE><DPRULE num="2"><LHS>Marked_app(app(reverse2,app(app(cons,x),xs)),l)</LHS><RHS>Marked_app(app(cons,x),l)</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="stronggraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>app(app(app(compose,f),g),x)</LHS><RHS>app(g,app(f,x))</RHS></RULE><RULE><LHS>app(reverse,l)</LHS><RHS>app(app(reverse2,l),nil)</RHS></RULE><RULE><LHS>app(app(reverse2,nil),l)</LHS><RHS>l</RHS></RULE><RULE><LHS>app(app(reverse2,app(app(cons,x),xs)),l)</LHS><RHS>app(app(reverse2,xs),app(app(cons,x),l))</RHS></RULE><RULE><LHS>app(hd,app(app(cons,x),xs))</LHS><RHS>x</RHS></RULE><RULE><LHS>app(tl,app(app(cons,x),xs))</LHS><RHS>xs</RHS></RULE><RULE><LHS>last</LHS><RHS>app(app(compose,hd),reverse)</RHS></RULE><RULE><LHS>init</LHS><RHS>app(app(compose,reverse),app(app(compose,tl),reverse))</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_app(app(app(compose,f),g),x)</LHS><RHS>Marked_app(g,app(f,x))</RHS></DPRULE><DPRULE num="1"><LHS>Marked_app(app(app(compose,f),g),x)</LHS><RHS>Marked_app(f,x)</RHS></DPRULE><DPRULE num="2"><LHS>Marked_app(app(reverse2,app(app(cons,x),xs)),l)</LHS><RHS>Marked_app(app(cons,x),l)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><ORDERING type="poly"><POLYSYMB><SYMBOL><NAME>app</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>last</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>3</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>reverse</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>reverse2</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>hd</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>compose</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>init</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>3</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>cons</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>nil</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>Marked_app</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>3</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>tl</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB></ORDERING><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_app(app(reverse2,app(app(cons,x),xs)),l)</LHS><RHS>Marked_app(app(cons,x),l)</RHS></DPRULE></DPLIST></STRICTPAIRS></CRITERION><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>app(app(app(compose,f),g),x)</LHS><RHS>app(g,app(f,x))</RHS></RULE><RULE><LHS>app(reverse,l)</LHS><RHS>app(app(reverse2,l),nil)</RHS></RULE><RULE><LHS>app(app(reverse2,nil),l)</LHS><RHS>l</RHS></RULE><RULE><LHS>app(app(reverse2,app(app(cons,x),xs)),l)</LHS><RHS>app(app(reverse2,xs),app(app(cons,x),l))</RHS></RULE><RULE><LHS>app(hd,app(app(cons,x),xs))</LHS><RHS>x</RHS></RULE><RULE><LHS>app(tl,app(app(cons,x),xs))</LHS><RHS>xs</RHS></RULE><RULE><LHS>last</LHS><RHS>app(app(compose,hd),reverse)</RHS></RULE><RULE><LHS>init</LHS><RHS>app(app(compose,reverse),app(app(compose,tl),reverse))</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_app(app(app(compose,f),g),x)</LHS><RHS>Marked_app(g,app(f,x))</RHS></DPRULE><DPRULE num="1"><LHS>Marked_app(app(app(compose,f),g),x)</LHS><RHS>Marked_app(f,x)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><DAG approx="simpl"><CCLIST><SCC num="0"><NODE ref="0"/><NODE ref="1"/></SCC></CCLIST></DAG></CRITERION><PROPERTY criterion="ordering" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>app(app(app(compose,f),g),x)</LHS><RHS>app(g,app(f,x))</RHS></RULE><RULE><LHS>app(reverse,l)</LHS><RHS>app(app(reverse2,l),nil)</RHS></RULE><RULE><LHS>app(app(reverse2,nil),l)</LHS><RHS>l</RHS></RULE><RULE><LHS>app(app(reverse2,app(app(cons,x),xs)),l)</LHS><RHS>app(app(reverse2,xs),app(app(cons,x),l))</RHS></RULE><RULE><LHS>app(hd,app(app(cons,x),xs))</LHS><RHS>x</RHS></RULE><RULE><LHS>app(tl,app(app(cons,x),xs))</LHS><RHS>xs</RHS></RULE><RULE><LHS>last</LHS><RHS>app(app(compose,hd),reverse)</RHS></RULE><RULE><LHS>init</LHS><RHS>app(app(compose,reverse),app(app(compose,tl),reverse))</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_app(app(app(compose,f),g),x)</LHS><RHS>Marked_app(g,app(f,x))</RHS></DPRULE><DPRULE num="1"><LHS>Marked_app(app(app(compose,f),g),x)</LHS><RHS>Marked_app(f,x)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><ORDERING type="poly"><POLYSYMB><SYMBOL><NAME>app</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>last</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>3</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>reverse</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>reverse2</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>hd</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>compose</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>init</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>3</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>cons</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>3</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>nil</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>Marked_app</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>3</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>3</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>tl</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB></ORDERING></CRITERION></PROPERTY></PROPERTY></PROPERTY></PROPERTY></PROPERTY></PROPERTY></PROPERTY></PROPERTY></PROPERTY></PROOF>
