<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE PROOF SYSTEM "http://a3pat.ensiie.fr/pub/a3pat.dtd">
<PROOF><SIGNATURE><SYMBOLLIST><SYMBOL arity="2" unmarked="mem"><NAME>Marked_mem</NAME></SYMBOL><SYMBOL arity="0" unmarked=""><NAME>nil</NAME></SYMBOL><SYMBOL arity="2" unmarked=""><NAME>inter</NAME></SYMBOL><SYMBOL arity="3" unmarked="if"><NAME>Marked_if</NAME></SYMBOL><SYMBOL arity="2" unmarked=""><NAME>eq</NAME></SYMBOL><SYMBOL arity="4" unmarked="ifinter"><NAME>Marked_ifinter</NAME></SYMBOL><SYMBOL arity="1" unmarked=""><NAME>s</NAME></SYMBOL><SYMBOL arity="2" unmarked=""><NAME>mem</NAME></SYMBOL><SYMBOL arity="3" unmarked="ifmem"><NAME>Marked_ifmem</NAME></SYMBOL><SYMBOL arity="0" unmarked=""><NAME>true</NAME></SYMBOL><SYMBOL arity="2" unmarked="inter"><NAME>Marked_inter</NAME></SYMBOL><SYMBOL arity="2" unmarked=""><NAME>app</NAME></SYMBOL><SYMBOL arity="3" unmarked=""><NAME>ifmem</NAME></SYMBOL><SYMBOL arity="2" unmarked="eq"><NAME>Marked_eq</NAME></SYMBOL><SYMBOL arity="0" unmarked=""><NAME>false</NAME></SYMBOL><SYMBOL arity="4" unmarked=""><NAME>ifinter</NAME></SYMBOL><SYMBOL arity="0" unmarked=""><NAME>0</NAME></SYMBOL><SYMBOL arity="2" unmarked=""><NAME>cons</NAME></SYMBOL><SYMBOL arity="2" unmarked="app"><NAME>Marked_app</NAME></SYMBOL><SYMBOL arity="3" unmarked=""><NAME>if</NAME></SYMBOL></SYMBOLLIST><VARLIST><VAR>x</VAR><VAR>y</VAR><VAR>l</VAR><VAR>l1</VAR><VAR>l2</VAR><VAR>l3</VAR></VARLIST></SIGNATURE><PROPERTY criterion="dp" prop="sntrs"><SYSTEM><REWSYS><RULE><LHS>if(true,x,y)</LHS><RHS>x</RHS></RULE><RULE><LHS>if(false,x,y)</LHS><RHS>y</RHS></RULE><RULE><LHS>eq(0,0)</LHS><RHS>true</RHS></RULE><RULE><LHS>eq(0,s(x))</LHS><RHS>false</RHS></RULE><RULE><LHS>eq(s(x),0)</LHS><RHS>false</RHS></RULE><RULE><LHS>eq(s(x),s(y))</LHS><RHS>eq(x,y)</RHS></RULE><RULE><LHS>app(nil,l)</LHS><RHS>l</RHS></RULE><RULE><LHS>app(cons(x,l1),l2)</LHS><RHS>cons(x,app(l1,l2))</RHS></RULE><RULE><LHS>app(app(l1,l2),l3)</LHS><RHS>app(l1,app(l2,l3))</RHS></RULE><RULE><LHS>mem(x,nil)</LHS><RHS>false</RHS></RULE><RULE><LHS>mem(x,cons(y,l))</LHS><RHS>ifmem(eq(x,y),x,l)</RHS></RULE><RULE><LHS>ifmem(true,x,l)</LHS><RHS>true</RHS></RULE><RULE><LHS>ifmem(false,x,l)</LHS><RHS>mem(x,l)</RHS></RULE><RULE><LHS>inter(x,nil)</LHS><RHS>nil</RHS></RULE><RULE><LHS>inter(nil,x)</LHS><RHS>nil</RHS></RULE><RULE><LHS>inter(app(l1,l2),l3)</LHS><RHS>app(inter(l1,l3),inter(l2,l3))</RHS></RULE><RULE><LHS>inter(l1,app(l2,l3))</LHS><RHS>app(inter(l1,l2),inter(l1,l3))</RHS></RULE><RULE><LHS>inter(cons(x,l1),l2)</LHS><RHS>ifinter(mem(x,l2),x,l1,l2)</RHS></RULE><RULE><LHS>inter(l1,cons(x,l2))</LHS><RHS>ifinter(mem(x,l1),x,l2,l1)</RHS></RULE><RULE><LHS>ifinter(true,x,l1,l2)</LHS><RHS>cons(x,inter(l1,l2))</RHS></RULE><RULE><LHS>ifinter(false,x,l1,l2)</LHS><RHS>inter(l1,l2)</RHS></RULE></REWSYS></SYSTEM><CRITERION/><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>if(true,x,y)</LHS><RHS>x</RHS></RULE><RULE><LHS>if(false,x,y)</LHS><RHS>y</RHS></RULE><RULE><LHS>eq(0,0)</LHS><RHS>true</RHS></RULE><RULE><LHS>eq(0,s(x))</LHS><RHS>false</RHS></RULE><RULE><LHS>eq(s(x),0)</LHS><RHS>false</RHS></RULE><RULE><LHS>eq(s(x),s(y))</LHS><RHS>eq(x,y)</RHS></RULE><RULE><LHS>app(nil,l)</LHS><RHS>l</RHS></RULE><RULE><LHS>app(cons(x,l1),l2)</LHS><RHS>cons(x,app(l1,l2))</RHS></RULE><RULE><LHS>app(app(l1,l2),l3)</LHS><RHS>app(l1,app(l2,l3))</RHS></RULE><RULE><LHS>mem(x,nil)</LHS><RHS>false</RHS></RULE><RULE><LHS>mem(x,cons(y,l))</LHS><RHS>ifmem(eq(x,y),x,l)</RHS></RULE><RULE><LHS>ifmem(true,x,l)</LHS><RHS>true</RHS></RULE><RULE><LHS>ifmem(false,x,l)</LHS><RHS>mem(x,l)</RHS></RULE><RULE><LHS>inter(x,nil)</LHS><RHS>nil</RHS></RULE><RULE><LHS>inter(nil,x)</LHS><RHS>nil</RHS></RULE><RULE><LHS>inter(app(l1,l2),l3)</LHS><RHS>app(inter(l1,l3),inter(l2,l3))</RHS></RULE><RULE><LHS>inter(l1,app(l2,l3))</LHS><RHS>app(inter(l1,l2),inter(l1,l3))</RHS></RULE><RULE><LHS>inter(cons(x,l1),l2)</LHS><RHS>ifinter(mem(x,l2),x,l1,l2)</RHS></RULE><RULE><LHS>inter(l1,cons(x,l2))</LHS><RHS>ifinter(mem(x,l1),x,l2,l1)</RHS></RULE><RULE><LHS>ifinter(true,x,l1,l2)</LHS><RHS>cons(x,inter(l1,l2))</RHS></RULE><RULE><LHS>ifinter(false,x,l1,l2)</LHS><RHS>inter(l1,l2)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_eq(s(x),s(y))</LHS><RHS>Marked_eq(x,y)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_app(cons(x,l1),l2)</LHS><RHS>Marked_app(l1,l2)</RHS></DPRULE><DPRULE num="2"><LHS>Marked_app(app(l1,l2),l3)</LHS><RHS>Marked_app(l1,app(l2,l3))</RHS></DPRULE><DPRULE num="3"><LHS>Marked_app(app(l1,l2),l3)</LHS><RHS>Marked_app(l2,l3)</RHS></DPRULE><DPRULE num="4"><LHS>Marked_mem(x,cons(y,l))</LHS><RHS>Marked_ifmem(eq(x,y),x,l)</RHS></DPRULE><DPRULE num="5"><LHS>Marked_mem(x,cons(y,l))</LHS><RHS>Marked_eq(x,y)</RHS></DPRULE><DPRULE num="6"><LHS>Marked_ifmem(false,x,l)</LHS><RHS>Marked_mem(x,l)</RHS></DPRULE><DPRULE num="7"><LHS>Marked_inter(app(l1,l2),l3)</LHS><RHS>Marked_app(inter(l1,l3),inter(l2,l3))</RHS></DPRULE><DPRULE num="8"><LHS>Marked_inter(app(l1,l2),l3)</LHS><RHS>Marked_inter(l1,l3)</RHS></DPRULE><DPRULE num="9"><LHS>Marked_inter(app(l1,l2),l3)</LHS><RHS>Marked_inter(l2,l3)</RHS></DPRULE><DPRULE num="10"><LHS>Marked_inter(l1,app(l2,l3))</LHS><RHS>Marked_app(inter(l1,l2),inter(l1,l3))</RHS></DPRULE><DPRULE num="11"><LHS>Marked_inter(l1,app(l2,l3))</LHS><RHS>Marked_inter(l1,l2)</RHS></DPRULE><DPRULE num="12"><LHS>Marked_inter(l1,app(l2,l3))</LHS><RHS>Marked_inter(l1,l3)</RHS></DPRULE><DPRULE num="13"><LHS>Marked_inter(cons(x,l1),l2)</LHS><RHS>Marked_ifinter(mem(x,l2),x,l1,l2)</RHS></DPRULE><DPRULE num="14"><LHS>Marked_inter(cons(x,l1),l2)</LHS><RHS>Marked_mem(x,l2)</RHS></DPRULE><DPRULE num="15"><LHS>Marked_inter(l1,cons(x,l2))</LHS><RHS>Marked_ifinter(mem(x,l1),x,l2,l1)</RHS></DPRULE><DPRULE num="16"><LHS>Marked_inter(l1,cons(x,l2))</LHS><RHS>Marked_mem(x,l1)</RHS></DPRULE><DPRULE num="17"><LHS>Marked_ifinter(true,x,l1,l2)</LHS><RHS>Marked_inter(l1,l2)</RHS></DPRULE><DPRULE num="18"><LHS>Marked_ifinter(false,x,l1,l2)</LHS><RHS>Marked_inter(l1,l2)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><DAG approx="simpl"><CCLIST><SCC num="0"><NODE ref="8"/><NODE ref="9"/><NODE ref="11"/><NODE ref="12"/><NODE ref="13"/><NODE ref="15"/><NODE ref="17"/><NODE ref="18"/></SCC><NONSCC num="1"><NODE ref="16"/></NONSCC><NONSCC num="2"><NODE ref="14"/></NONSCC><NONSCC num="3"><NODE ref="10"/></NONSCC><NONSCC num="4"><NODE ref="7"/></NONSCC><NONSCC num="5"><NODE ref="5"/></NONSCC><SCC num="6"><NODE ref="4"/><NODE ref="6"/></SCC><SCC num="7"><NODE ref="1"/><NODE ref="2"/><NODE ref="3"/></SCC><SCC num="8"><NODE ref="0"/></SCC></CCLIST><EDGE end="4" start="0"/><EDGE end="3" start="0"/><EDGE end="2" start="0"/><EDGE end="1" start="0"/><EDGE end="6" start="1"/><EDGE end="5" start="1"/><EDGE end="6" start="2"/><EDGE end="5" start="2"/><EDGE end="7" start="3"/><EDGE end="7" start="4"/><EDGE end="8" start="5"/><EDGE end="5" start="6"/></DAG></CRITERION><PROPERTY criterion="stronggraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>if(true,x,y)</LHS><RHS>x</RHS></RULE><RULE><LHS>if(false,x,y)</LHS><RHS>y</RHS></RULE><RULE><LHS>eq(0,0)</LHS><RHS>true</RHS></RULE><RULE><LHS>eq(0,s(x))</LHS><RHS>false</RHS></RULE><RULE><LHS>eq(s(x),0)</LHS><RHS>false</RHS></RULE><RULE><LHS>eq(s(x),s(y))</LHS><RHS>eq(x,y)</RHS></RULE><RULE><LHS>app(nil,l)</LHS><RHS>l</RHS></RULE><RULE><LHS>app(cons(x,l1),l2)</LHS><RHS>cons(x,app(l1,l2))</RHS></RULE><RULE><LHS>app(app(l1,l2),l3)</LHS><RHS>app(l1,app(l2,l3))</RHS></RULE><RULE><LHS>mem(x,nil)</LHS><RHS>false</RHS></RULE><RULE><LHS>mem(x,cons(y,l))</LHS><RHS>ifmem(eq(x,y),x,l)</RHS></RULE><RULE><LHS>ifmem(true,x,l)</LHS><RHS>true</RHS></RULE><RULE><LHS>ifmem(false,x,l)</LHS><RHS>mem(x,l)</RHS></RULE><RULE><LHS>inter(x,nil)</LHS><RHS>nil</RHS></RULE><RULE><LHS>inter(nil,x)</LHS><RHS>nil</RHS></RULE><RULE><LHS>inter(app(l1,l2),l3)</LHS><RHS>app(inter(l1,l3),inter(l2,l3))</RHS></RULE><RULE><LHS>inter(l1,app(l2,l3))</LHS><RHS>app(inter(l1,l2),inter(l1,l3))</RHS></RULE><RULE><LHS>inter(cons(x,l1),l2)</LHS><RHS>ifinter(mem(x,l2),x,l1,l2)</RHS></RULE><RULE><LHS>inter(l1,cons(x,l2))</LHS><RHS>ifinter(mem(x,l1),x,l2,l1)</RHS></RULE><RULE><LHS>ifinter(true,x,l1,l2)</LHS><RHS>cons(x,inter(l1,l2))</RHS></RULE><RULE><LHS>ifinter(false,x,l1,l2)</LHS><RHS>inter(l1,l2)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_inter(app(l1,l2),l3)</LHS><RHS>Marked_inter(l1,l3)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_inter(app(l1,l2),l3)</LHS><RHS>Marked_inter(l2,l3)</RHS></DPRULE><DPRULE num="2"><LHS>Marked_inter(l1,app(l2,l3))</LHS><RHS>Marked_inter(l1,l2)</RHS></DPRULE><DPRULE num="3"><LHS>Marked_inter(l1,app(l2,l3))</LHS><RHS>Marked_inter(l1,l3)</RHS></DPRULE><DPRULE num="4"><LHS>Marked_inter(cons(x,l1),l2)</LHS><RHS>Marked_ifinter(mem(x,l2),x,l1,l2)</RHS></DPRULE><DPRULE num="5"><LHS>Marked_inter(l1,cons(x,l2))</LHS><RHS>Marked_ifinter(mem(x,l1),x,l2,l1)</RHS></DPRULE><DPRULE num="6"><LHS>Marked_ifinter(true,x,l1,l2)</LHS><RHS>Marked_inter(l1,l2)</RHS></DPRULE><DPRULE num="7"><LHS>Marked_ifinter(false,x,l1,l2)</LHS><RHS>Marked_inter(l1,l2)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><ORDERING type="poly"><POLYSYMB><SYMBOL><NAME>if</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</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><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="0"/><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="0"/><ARG degree="1" num="2"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="1"/><ARG degree="1" num="2"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="0"/><ARG degree="1" num="1"/><ARG degree="1" num="2"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>cons</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF></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>0</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>ifinter</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="2"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="3"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="2"/><ARG degree="1" num="3"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>false</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>ifmem</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="2"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>app</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF></MONOME></POLYNOMIAL><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></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>Marked_inter</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="0"/><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>true</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>mem</NAME></SYMBOL><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></POLYSYMB><POLYSYMB><SYMBOL><NAME>s</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF></MONOME></POLYNOMIAL><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></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>Marked_ifinter</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="2"/><ARG degree="1" num="3"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>eq</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</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>inter</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><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="0"/><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>nil</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></ORDERING><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_ifinter(false,x,l1,l2)</LHS><RHS>Marked_inter(l1,l2)</RHS></DPRULE></DPLIST></STRICTPAIRS></CRITERION><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>if(true,x,y)</LHS><RHS>x</RHS></RULE><RULE><LHS>if(false,x,y)</LHS><RHS>y</RHS></RULE><RULE><LHS>eq(0,0)</LHS><RHS>true</RHS></RULE><RULE><LHS>eq(0,s(x))</LHS><RHS>false</RHS></RULE><RULE><LHS>eq(s(x),0)</LHS><RHS>false</RHS></RULE><RULE><LHS>eq(s(x),s(y))</LHS><RHS>eq(x,y)</RHS></RULE><RULE><LHS>app(nil,l)</LHS><RHS>l</RHS></RULE><RULE><LHS>app(cons(x,l1),l2)</LHS><RHS>cons(x,app(l1,l2))</RHS></RULE><RULE><LHS>app(app(l1,l2),l3)</LHS><RHS>app(l1,app(l2,l3))</RHS></RULE><RULE><LHS>mem(x,nil)</LHS><RHS>false</RHS></RULE><RULE><LHS>mem(x,cons(y,l))</LHS><RHS>ifmem(eq(x,y),x,l)</RHS></RULE><RULE><LHS>ifmem(true,x,l)</LHS><RHS>true</RHS></RULE><RULE><LHS>ifmem(false,x,l)</LHS><RHS>mem(x,l)</RHS></RULE><RULE><LHS>inter(x,nil)</LHS><RHS>nil</RHS></RULE><RULE><LHS>inter(nil,x)</LHS><RHS>nil</RHS></RULE><RULE><LHS>inter(app(l1,l2),l3)</LHS><RHS>app(inter(l1,l3),inter(l2,l3))</RHS></RULE><RULE><LHS>inter(l1,app(l2,l3))</LHS><RHS>app(inter(l1,l2),inter(l1,l3))</RHS></RULE><RULE><LHS>inter(cons(x,l1),l2)</LHS><RHS>ifinter(mem(x,l2),x,l1,l2)</RHS></RULE><RULE><LHS>inter(l1,cons(x,l2))</LHS><RHS>ifinter(mem(x,l1),x,l2,l1)</RHS></RULE><RULE><LHS>ifinter(true,x,l1,l2)</LHS><RHS>cons(x,inter(l1,l2))</RHS></RULE><RULE><LHS>ifinter(false,x,l1,l2)</LHS><RHS>inter(l1,l2)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_inter(app(l1,l2),l3)</LHS><RHS>Marked_inter(l1,l3)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_inter(app(l1,l2),l3)</LHS><RHS>Marked_inter(l2,l3)</RHS></DPRULE><DPRULE num="2"><LHS>Marked_inter(l1,app(l2,l3))</LHS><RHS>Marked_inter(l1,l2)</RHS></DPRULE><DPRULE num="3"><LHS>Marked_inter(l1,app(l2,l3))</LHS><RHS>Marked_inter(l1,l3)</RHS></DPRULE><DPRULE num="4"><LHS>Marked_inter(cons(x,l1),l2)</LHS><RHS>Marked_ifinter(mem(x,l2),x,l1,l2)</RHS></DPRULE><DPRULE num="5"><LHS>Marked_inter(l1,cons(x,l2))</LHS><RHS>Marked_ifinter(mem(x,l1),x,l2,l1)</RHS></DPRULE><DPRULE num="6"><LHS>Marked_ifinter(true,x,l1,l2)</LHS><RHS>Marked_inter(l1,l2)</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"/><NODE ref="4"/><NODE ref="5"/><NODE ref="6"/></SCC></CCLIST></DAG></CRITERION><PROPERTY criterion="stronggraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>if(true,x,y)</LHS><RHS>x</RHS></RULE><RULE><LHS>if(false,x,y)</LHS><RHS>y</RHS></RULE><RULE><LHS>eq(0,0)</LHS><RHS>true</RHS></RULE><RULE><LHS>eq(0,s(x))</LHS><RHS>false</RHS></RULE><RULE><LHS>eq(s(x),0)</LHS><RHS>false</RHS></RULE><RULE><LHS>eq(s(x),s(y))</LHS><RHS>eq(x,y)</RHS></RULE><RULE><LHS>app(nil,l)</LHS><RHS>l</RHS></RULE><RULE><LHS>app(cons(x,l1),l2)</LHS><RHS>cons(x,app(l1,l2))</RHS></RULE><RULE><LHS>app(app(l1,l2),l3)</LHS><RHS>app(l1,app(l2,l3))</RHS></RULE><RULE><LHS>mem(x,nil)</LHS><RHS>false</RHS></RULE><RULE><LHS>mem(x,cons(y,l))</LHS><RHS>ifmem(eq(x,y),x,l)</RHS></RULE><RULE><LHS>ifmem(true,x,l)</LHS><RHS>true</RHS></RULE><RULE><LHS>ifmem(false,x,l)</LHS><RHS>mem(x,l)</RHS></RULE><RULE><LHS>inter(x,nil)</LHS><RHS>nil</RHS></RULE><RULE><LHS>inter(nil,x)</LHS><RHS>nil</RHS></RULE><RULE><LHS>inter(app(l1,l2),l3)</LHS><RHS>app(inter(l1,l3),inter(l2,l3))</RHS></RULE><RULE><LHS>inter(l1,app(l2,l3))</LHS><RHS>app(inter(l1,l2),inter(l1,l3))</RHS></RULE><RULE><LHS>inter(cons(x,l1),l2)</LHS><RHS>ifinter(mem(x,l2),x,l1,l2)</RHS></RULE><RULE><LHS>inter(l1,cons(x,l2))</LHS><RHS>ifinter(mem(x,l1),x,l2,l1)</RHS></RULE><RULE><LHS>ifinter(true,x,l1,l2)</LHS><RHS>cons(x,inter(l1,l2))</RHS></RULE><RULE><LHS>ifinter(false,x,l1,l2)</LHS><RHS>inter(l1,l2)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_inter(app(l1,l2),l3)</LHS><RHS>Marked_inter(l1,l3)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_inter(app(l1,l2),l3)</LHS><RHS>Marked_inter(l2,l3)</RHS></DPRULE><DPRULE num="2"><LHS>Marked_inter(l1,app(l2,l3))</LHS><RHS>Marked_inter(l1,l2)</RHS></DPRULE><DPRULE num="3"><LHS>Marked_inter(l1,app(l2,l3))</LHS><RHS>Marked_inter(l1,l3)</RHS></DPRULE><DPRULE num="4"><LHS>Marked_inter(cons(x,l1),l2)</LHS><RHS>Marked_ifinter(mem(x,l2),x,l1,l2)</RHS></DPRULE><DPRULE num="5"><LHS>Marked_inter(l1,cons(x,l2))</LHS><RHS>Marked_ifinter(mem(x,l1),x,l2,l1)</RHS></DPRULE><DPRULE num="6"><LHS>Marked_ifinter(true,x,l1,l2)</LHS><RHS>Marked_inter(l1,l2)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><ORDERING type="poly"><POLYSYMB><SYMBOL><NAME>if</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><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="2"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="1"/><ARG degree="1" num="2"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="0"/><ARG degree="1" num="1"/><ARG degree="1" num="2"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>cons</NAME></SYMBOL><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></POLYSYMB><POLYSYMB><SYMBOL><NAME>0</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>ifinter</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="2"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="3"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="2"/><ARG degree="1" num="3"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>false</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>ifmem</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>app</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</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></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>Marked_inter</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>true</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>mem</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>s</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>Marked_ifinter</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="2"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="3"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>eq</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>inter</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><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="0"/><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>nil</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB></ORDERING><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_inter(app(l1,l2),l3)</LHS><RHS>Marked_inter(l1,l3)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_inter(app(l1,l2),l3)</LHS><RHS>Marked_inter(l2,l3)</RHS></DPRULE><DPRULE num="2"><LHS>Marked_inter(l1,app(l2,l3))</LHS><RHS>Marked_inter(l1,l2)</RHS></DPRULE><DPRULE num="3"><LHS>Marked_inter(l1,app(l2,l3))</LHS><RHS>Marked_inter(l1,l3)</RHS></DPRULE></DPLIST></STRICTPAIRS></CRITERION><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>if(true,x,y)</LHS><RHS>x</RHS></RULE><RULE><LHS>if(false,x,y)</LHS><RHS>y</RHS></RULE><RULE><LHS>eq(0,0)</LHS><RHS>true</RHS></RULE><RULE><LHS>eq(0,s(x))</LHS><RHS>false</RHS></RULE><RULE><LHS>eq(s(x),0)</LHS><RHS>false</RHS></RULE><RULE><LHS>eq(s(x),s(y))</LHS><RHS>eq(x,y)</RHS></RULE><RULE><LHS>app(nil,l)</LHS><RHS>l</RHS></RULE><RULE><LHS>app(cons(x,l1),l2)</LHS><RHS>cons(x,app(l1,l2))</RHS></RULE><RULE><LHS>app(app(l1,l2),l3)</LHS><RHS>app(l1,app(l2,l3))</RHS></RULE><RULE><LHS>mem(x,nil)</LHS><RHS>false</RHS></RULE><RULE><LHS>mem(x,cons(y,l))</LHS><RHS>ifmem(eq(x,y),x,l)</RHS></RULE><RULE><LHS>ifmem(true,x,l)</LHS><RHS>true</RHS></RULE><RULE><LHS>ifmem(false,x,l)</LHS><RHS>mem(x,l)</RHS></RULE><RULE><LHS>inter(x,nil)</LHS><RHS>nil</RHS></RULE><RULE><LHS>inter(nil,x)</LHS><RHS>nil</RHS></RULE><RULE><LHS>inter(app(l1,l2),l3)</LHS><RHS>app(inter(l1,l3),inter(l2,l3))</RHS></RULE><RULE><LHS>inter(l1,app(l2,l3))</LHS><RHS>app(inter(l1,l2),inter(l1,l3))</RHS></RULE><RULE><LHS>inter(cons(x,l1),l2)</LHS><RHS>ifinter(mem(x,l2),x,l1,l2)</RHS></RULE><RULE><LHS>inter(l1,cons(x,l2))</LHS><RHS>ifinter(mem(x,l1),x,l2,l1)</RHS></RULE><RULE><LHS>ifinter(true,x,l1,l2)</LHS><RHS>cons(x,inter(l1,l2))</RHS></RULE><RULE><LHS>ifinter(false,x,l1,l2)</LHS><RHS>inter(l1,l2)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_inter(cons(x,l1),l2)</LHS><RHS>Marked_ifinter(mem(x,l2),x,l1,l2)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_inter(l1,cons(x,l2))</LHS><RHS>Marked_ifinter(mem(x,l1),x,l2,l1)</RHS></DPRULE><DPRULE num="2"><LHS>Marked_ifinter(true,x,l1,l2)</LHS><RHS>Marked_inter(l1,l2)</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>if(true,x,y)</LHS><RHS>x</RHS></RULE><RULE><LHS>if(false,x,y)</LHS><RHS>y</RHS></RULE><RULE><LHS>eq(0,0)</LHS><RHS>true</RHS></RULE><RULE><LHS>eq(0,s(x))</LHS><RHS>false</RHS></RULE><RULE><LHS>eq(s(x),0)</LHS><RHS>false</RHS></RULE><RULE><LHS>eq(s(x),s(y))</LHS><RHS>eq(x,y)</RHS></RULE><RULE><LHS>app(nil,l)</LHS><RHS>l</RHS></RULE><RULE><LHS>app(cons(x,l1),l2)</LHS><RHS>cons(x,app(l1,l2))</RHS></RULE><RULE><LHS>app(app(l1,l2),l3)</LHS><RHS>app(l1,app(l2,l3))</RHS></RULE><RULE><LHS>mem(x,nil)</LHS><RHS>false</RHS></RULE><RULE><LHS>mem(x,cons(y,l))</LHS><RHS>ifmem(eq(x,y),x,l)</RHS></RULE><RULE><LHS>ifmem(true,x,l)</LHS><RHS>true</RHS></RULE><RULE><LHS>ifmem(false,x,l)</LHS><RHS>mem(x,l)</RHS></RULE><RULE><LHS>inter(x,nil)</LHS><RHS>nil</RHS></RULE><RULE><LHS>inter(nil,x)</LHS><RHS>nil</RHS></RULE><RULE><LHS>inter(app(l1,l2),l3)</LHS><RHS>app(inter(l1,l3),inter(l2,l3))</RHS></RULE><RULE><LHS>inter(l1,app(l2,l3))</LHS><RHS>app(inter(l1,l2),inter(l1,l3))</RHS></RULE><RULE><LHS>inter(cons(x,l1),l2)</LHS><RHS>ifinter(mem(x,l2),x,l1,l2)</RHS></RULE><RULE><LHS>inter(l1,cons(x,l2))</LHS><RHS>ifinter(mem(x,l1),x,l2,l1)</RHS></RULE><RULE><LHS>ifinter(true,x,l1,l2)</LHS><RHS>cons(x,inter(l1,l2))</RHS></RULE><RULE><LHS>ifinter(false,x,l1,l2)</LHS><RHS>inter(l1,l2)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_inter(cons(x,l1),l2)</LHS><RHS>Marked_ifinter(mem(x,l2),x,l1,l2)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_inter(l1,cons(x,l2))</LHS><RHS>Marked_ifinter(mem(x,l1),x,l2,l1)</RHS></DPRULE><DPRULE num="2"><LHS>Marked_ifinter(true,x,l1,l2)</LHS><RHS>Marked_inter(l1,l2)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><ORDERING type="poly"><POLYSYMB><SYMBOL><NAME>if</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="0"/><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="2"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="0"/><ARG degree="1" num="2"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>cons</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF></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>0</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>ifinter</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="2"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="3"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="2"/><ARG degree="1" num="3"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>false</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>ifmem</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>app</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF></MONOME></POLYNOMIAL><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></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>Marked_inter</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>true</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>mem</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>s</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>Marked_ifinter</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="3"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="2"/><ARG degree="1" num="3"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>eq</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>inter</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><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="0"/><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>nil</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB></ORDERING><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_inter(l1,cons(x,l2))</LHS><RHS>Marked_ifinter(mem(x,l1),x,l2,l1)</RHS></DPRULE></DPLIST></STRICTPAIRS></CRITERION><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>if(true,x,y)</LHS><RHS>x</RHS></RULE><RULE><LHS>if(false,x,y)</LHS><RHS>y</RHS></RULE><RULE><LHS>eq(0,0)</LHS><RHS>true</RHS></RULE><RULE><LHS>eq(0,s(x))</LHS><RHS>false</RHS></RULE><RULE><LHS>eq(s(x),0)</LHS><RHS>false</RHS></RULE><RULE><LHS>eq(s(x),s(y))</LHS><RHS>eq(x,y)</RHS></RULE><RULE><LHS>app(nil,l)</LHS><RHS>l</RHS></RULE><RULE><LHS>app(cons(x,l1),l2)</LHS><RHS>cons(x,app(l1,l2))</RHS></RULE><RULE><LHS>app(app(l1,l2),l3)</LHS><RHS>app(l1,app(l2,l3))</RHS></RULE><RULE><LHS>mem(x,nil)</LHS><RHS>false</RHS></RULE><RULE><LHS>mem(x,cons(y,l))</LHS><RHS>ifmem(eq(x,y),x,l)</RHS></RULE><RULE><LHS>ifmem(true,x,l)</LHS><RHS>true</RHS></RULE><RULE><LHS>ifmem(false,x,l)</LHS><RHS>mem(x,l)</RHS></RULE><RULE><LHS>inter(x,nil)</LHS><RHS>nil</RHS></RULE><RULE><LHS>inter(nil,x)</LHS><RHS>nil</RHS></RULE><RULE><LHS>inter(app(l1,l2),l3)</LHS><RHS>app(inter(l1,l3),inter(l2,l3))</RHS></RULE><RULE><LHS>inter(l1,app(l2,l3))</LHS><RHS>app(inter(l1,l2),inter(l1,l3))</RHS></RULE><RULE><LHS>inter(cons(x,l1),l2)</LHS><RHS>ifinter(mem(x,l2),x,l1,l2)</RHS></RULE><RULE><LHS>inter(l1,cons(x,l2))</LHS><RHS>ifinter(mem(x,l1),x,l2,l1)</RHS></RULE><RULE><LHS>ifinter(true,x,l1,l2)</LHS><RHS>cons(x,inter(l1,l2))</RHS></RULE><RULE><LHS>ifinter(false,x,l1,l2)</LHS><RHS>inter(l1,l2)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_inter(cons(x,l1),l2)</LHS><RHS>Marked_ifinter(mem(x,l2),x,l1,l2)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_ifinter(true,x,l1,l2)</LHS><RHS>Marked_inter(l1,l2)</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="stronggraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>if(true,x,y)</LHS><RHS>x</RHS></RULE><RULE><LHS>if(false,x,y)</LHS><RHS>y</RHS></RULE><RULE><LHS>eq(0,0)</LHS><RHS>true</RHS></RULE><RULE><LHS>eq(0,s(x))</LHS><RHS>false</RHS></RULE><RULE><LHS>eq(s(x),0)</LHS><RHS>false</RHS></RULE><RULE><LHS>eq(s(x),s(y))</LHS><RHS>eq(x,y)</RHS></RULE><RULE><LHS>app(nil,l)</LHS><RHS>l</RHS></RULE><RULE><LHS>app(cons(x,l1),l2)</LHS><RHS>cons(x,app(l1,l2))</RHS></RULE><RULE><LHS>app(app(l1,l2),l3)</LHS><RHS>app(l1,app(l2,l3))</RHS></RULE><RULE><LHS>mem(x,nil)</LHS><RHS>false</RHS></RULE><RULE><LHS>mem(x,cons(y,l))</LHS><RHS>ifmem(eq(x,y),x,l)</RHS></RULE><RULE><LHS>ifmem(true,x,l)</LHS><RHS>true</RHS></RULE><RULE><LHS>ifmem(false,x,l)</LHS><RHS>mem(x,l)</RHS></RULE><RULE><LHS>inter(x,nil)</LHS><RHS>nil</RHS></RULE><RULE><LHS>inter(nil,x)</LHS><RHS>nil</RHS></RULE><RULE><LHS>inter(app(l1,l2),l3)</LHS><RHS>app(inter(l1,l3),inter(l2,l3))</RHS></RULE><RULE><LHS>inter(l1,app(l2,l3))</LHS><RHS>app(inter(l1,l2),inter(l1,l3))</RHS></RULE><RULE><LHS>inter(cons(x,l1),l2)</LHS><RHS>ifinter(mem(x,l2),x,l1,l2)</RHS></RULE><RULE><LHS>inter(l1,cons(x,l2))</LHS><RHS>ifinter(mem(x,l1),x,l2,l1)</RHS></RULE><RULE><LHS>ifinter(true,x,l1,l2)</LHS><RHS>cons(x,inter(l1,l2))</RHS></RULE><RULE><LHS>ifinter(false,x,l1,l2)</LHS><RHS>inter(l1,l2)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_inter(cons(x,l1),l2)</LHS><RHS>Marked_ifinter(mem(x,l2),x,l1,l2)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_ifinter(true,x,l1,l2)</LHS><RHS>Marked_inter(l1,l2)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><ORDERING type="poly"><POLYSYMB><SYMBOL><NAME>if</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="2"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/><ARG degree="1" num="2"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>cons</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF></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>0</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>ifinter</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="2"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="3"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="2"/><ARG degree="1" num="3"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>false</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>ifmem</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>app</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF></MONOME></POLYNOMIAL><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></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>Marked_inter</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="0"/><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>true</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>mem</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>s</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>Marked_ifinter</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="2"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="2"/><ARG degree="1" num="3"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>eq</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>inter</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><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>nil</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB></ORDERING><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_inter(cons(x,l1),l2)</LHS><RHS>Marked_ifinter(mem(x,l2),x,l1,l2)</RHS></DPRULE></DPLIST></STRICTPAIRS></CRITERION><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>if(true,x,y)</LHS><RHS>x</RHS></RULE><RULE><LHS>if(false,x,y)</LHS><RHS>y</RHS></RULE><RULE><LHS>eq(0,0)</LHS><RHS>true</RHS></RULE><RULE><LHS>eq(0,s(x))</LHS><RHS>false</RHS></RULE><RULE><LHS>eq(s(x),0)</LHS><RHS>false</RHS></RULE><RULE><LHS>eq(s(x),s(y))</LHS><RHS>eq(x,y)</RHS></RULE><RULE><LHS>app(nil,l)</LHS><RHS>l</RHS></RULE><RULE><LHS>app(cons(x,l1),l2)</LHS><RHS>cons(x,app(l1,l2))</RHS></RULE><RULE><LHS>app(app(l1,l2),l3)</LHS><RHS>app(l1,app(l2,l3))</RHS></RULE><RULE><LHS>mem(x,nil)</LHS><RHS>false</RHS></RULE><RULE><LHS>mem(x,cons(y,l))</LHS><RHS>ifmem(eq(x,y),x,l)</RHS></RULE><RULE><LHS>ifmem(true,x,l)</LHS><RHS>true</RHS></RULE><RULE><LHS>ifmem(false,x,l)</LHS><RHS>mem(x,l)</RHS></RULE><RULE><LHS>inter(x,nil)</LHS><RHS>nil</RHS></RULE><RULE><LHS>inter(nil,x)</LHS><RHS>nil</RHS></RULE><RULE><LHS>inter(app(l1,l2),l3)</LHS><RHS>app(inter(l1,l3),inter(l2,l3))</RHS></RULE><RULE><LHS>inter(l1,app(l2,l3))</LHS><RHS>app(inter(l1,l2),inter(l1,l3))</RHS></RULE><RULE><LHS>inter(cons(x,l1),l2)</LHS><RHS>ifinter(mem(x,l2),x,l1,l2)</RHS></RULE><RULE><LHS>inter(l1,cons(x,l2))</LHS><RHS>ifinter(mem(x,l1),x,l2,l1)</RHS></RULE><RULE><LHS>ifinter(true,x,l1,l2)</LHS><RHS>cons(x,inter(l1,l2))</RHS></RULE><RULE><LHS>ifinter(false,x,l1,l2)</LHS><RHS>inter(l1,l2)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_ifinter(true,x,l1,l2)</LHS><RHS>Marked_inter(l1,l2)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><DAG approx="simpl"><CCLIST><NONSCC num="0"><NODE ref="0"/></NONSCC></CCLIST></DAG></CRITERION></PROPERTY></PROPERTY></PROPERTY></PROPERTY></PROPERTY></PROPERTY></PROPERTY></PROPERTY><PROPERTY criterion="stronggraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>if(true,x,y)</LHS><RHS>x</RHS></RULE><RULE><LHS>if(false,x,y)</LHS><RHS>y</RHS></RULE><RULE><LHS>eq(0,0)</LHS><RHS>true</RHS></RULE><RULE><LHS>eq(0,s(x))</LHS><RHS>false</RHS></RULE><RULE><LHS>eq(s(x),0)</LHS><RHS>false</RHS></RULE><RULE><LHS>eq(s(x),s(y))</LHS><RHS>eq(x,y)</RHS></RULE><RULE><LHS>app(nil,l)</LHS><RHS>l</RHS></RULE><RULE><LHS>app(cons(x,l1),l2)</LHS><RHS>cons(x,app(l1,l2))</RHS></RULE><RULE><LHS>app(app(l1,l2),l3)</LHS><RHS>app(l1,app(l2,l3))</RHS></RULE><RULE><LHS>mem(x,nil)</LHS><RHS>false</RHS></RULE><RULE><LHS>mem(x,cons(y,l))</LHS><RHS>ifmem(eq(x,y),x,l)</RHS></RULE><RULE><LHS>ifmem(true,x,l)</LHS><RHS>true</RHS></RULE><RULE><LHS>ifmem(false,x,l)</LHS><RHS>mem(x,l)</RHS></RULE><RULE><LHS>inter(x,nil)</LHS><RHS>nil</RHS></RULE><RULE><LHS>inter(nil,x)</LHS><RHS>nil</RHS></RULE><RULE><LHS>inter(app(l1,l2),l3)</LHS><RHS>app(inter(l1,l3),inter(l2,l3))</RHS></RULE><RULE><LHS>inter(l1,app(l2,l3))</LHS><RHS>app(inter(l1,l2),inter(l1,l3))</RHS></RULE><RULE><LHS>inter(cons(x,l1),l2)</LHS><RHS>ifinter(mem(x,l2),x,l1,l2)</RHS></RULE><RULE><LHS>inter(l1,cons(x,l2))</LHS><RHS>ifinter(mem(x,l1),x,l2,l1)</RHS></RULE><RULE><LHS>ifinter(true,x,l1,l2)</LHS><RHS>cons(x,inter(l1,l2))</RHS></RULE><RULE><LHS>ifinter(false,x,l1,l2)</LHS><RHS>inter(l1,l2)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_app(cons(x,l1),l2)</LHS><RHS>Marked_app(l1,l2)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_app(app(l1,l2),l3)</LHS><RHS>Marked_app(l1,app(l2,l3))</RHS></DPRULE><DPRULE num="2"><LHS>Marked_app(app(l1,l2),l3)</LHS><RHS>Marked_app(l2,l3)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><ORDERING type="poly"><POLYSYMB><SYMBOL><NAME>if</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF></MONOME></POLYNOMIAL><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><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="2"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="0"/><ARG degree="1" num="2"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="1"/><ARG degree="1" num="2"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="0"/><ARG degree="1" num="1"/><ARG degree="1" num="2"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></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><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>cons</NAME></SYMBOL><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></POLYSYMB><POLYSYMB><SYMBOL><NAME>0</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>ifinter</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="2"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="3"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="2"/><ARG degree="1" num="3"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>false</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>ifmem</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>app</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF></MONOME></POLYNOMIAL><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></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>true</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>mem</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>s</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>eq</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>inter</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><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>nil</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB></ORDERING><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_app(app(l1,l2),l3)</LHS><RHS>Marked_app(l2,l3)</RHS></DPRULE></DPLIST></STRICTPAIRS></CRITERION><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>if(true,x,y)</LHS><RHS>x</RHS></RULE><RULE><LHS>if(false,x,y)</LHS><RHS>y</RHS></RULE><RULE><LHS>eq(0,0)</LHS><RHS>true</RHS></RULE><RULE><LHS>eq(0,s(x))</LHS><RHS>false</RHS></RULE><RULE><LHS>eq(s(x),0)</LHS><RHS>false</RHS></RULE><RULE><LHS>eq(s(x),s(y))</LHS><RHS>eq(x,y)</RHS></RULE><RULE><LHS>app(nil,l)</LHS><RHS>l</RHS></RULE><RULE><LHS>app(cons(x,l1),l2)</LHS><RHS>cons(x,app(l1,l2))</RHS></RULE><RULE><LHS>app(app(l1,l2),l3)</LHS><RHS>app(l1,app(l2,l3))</RHS></RULE><RULE><LHS>mem(x,nil)</LHS><RHS>false</RHS></RULE><RULE><LHS>mem(x,cons(y,l))</LHS><RHS>ifmem(eq(x,y),x,l)</RHS></RULE><RULE><LHS>ifmem(true,x,l)</LHS><RHS>true</RHS></RULE><RULE><LHS>ifmem(false,x,l)</LHS><RHS>mem(x,l)</RHS></RULE><RULE><LHS>inter(x,nil)</LHS><RHS>nil</RHS></RULE><RULE><LHS>inter(nil,x)</LHS><RHS>nil</RHS></RULE><RULE><LHS>inter(app(l1,l2),l3)</LHS><RHS>app(inter(l1,l3),inter(l2,l3))</RHS></RULE><RULE><LHS>inter(l1,app(l2,l3))</LHS><RHS>app(inter(l1,l2),inter(l1,l3))</RHS></RULE><RULE><LHS>inter(cons(x,l1),l2)</LHS><RHS>ifinter(mem(x,l2),x,l1,l2)</RHS></RULE><RULE><LHS>inter(l1,cons(x,l2))</LHS><RHS>ifinter(mem(x,l1),x,l2,l1)</RHS></RULE><RULE><LHS>ifinter(true,x,l1,l2)</LHS><RHS>cons(x,inter(l1,l2))</RHS></RULE><RULE><LHS>ifinter(false,x,l1,l2)</LHS><RHS>inter(l1,l2)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_app(cons(x,l1),l2)</LHS><RHS>Marked_app(l1,l2)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_app(app(l1,l2),l3)</LHS><RHS>Marked_app(l1,app(l2,l3))</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>if(true,x,y)</LHS><RHS>x</RHS></RULE><RULE><LHS>if(false,x,y)</LHS><RHS>y</RHS></RULE><RULE><LHS>eq(0,0)</LHS><RHS>true</RHS></RULE><RULE><LHS>eq(0,s(x))</LHS><RHS>false</RHS></RULE><RULE><LHS>eq(s(x),0)</LHS><RHS>false</RHS></RULE><RULE><LHS>eq(s(x),s(y))</LHS><RHS>eq(x,y)</RHS></RULE><RULE><LHS>app(nil,l)</LHS><RHS>l</RHS></RULE><RULE><LHS>app(cons(x,l1),l2)</LHS><RHS>cons(x,app(l1,l2))</RHS></RULE><RULE><LHS>app(app(l1,l2),l3)</LHS><RHS>app(l1,app(l2,l3))</RHS></RULE><RULE><LHS>mem(x,nil)</LHS><RHS>false</RHS></RULE><RULE><LHS>mem(x,cons(y,l))</LHS><RHS>ifmem(eq(x,y),x,l)</RHS></RULE><RULE><LHS>ifmem(true,x,l)</LHS><RHS>true</RHS></RULE><RULE><LHS>ifmem(false,x,l)</LHS><RHS>mem(x,l)</RHS></RULE><RULE><LHS>inter(x,nil)</LHS><RHS>nil</RHS></RULE><RULE><LHS>inter(nil,x)</LHS><RHS>nil</RHS></RULE><RULE><LHS>inter(app(l1,l2),l3)</LHS><RHS>app(inter(l1,l3),inter(l2,l3))</RHS></RULE><RULE><LHS>inter(l1,app(l2,l3))</LHS><RHS>app(inter(l1,l2),inter(l1,l3))</RHS></RULE><RULE><LHS>inter(cons(x,l1),l2)</LHS><RHS>ifinter(mem(x,l2),x,l1,l2)</RHS></RULE><RULE><LHS>inter(l1,cons(x,l2))</LHS><RHS>ifinter(mem(x,l1),x,l2,l1)</RHS></RULE><RULE><LHS>ifinter(true,x,l1,l2)</LHS><RHS>cons(x,inter(l1,l2))</RHS></RULE><RULE><LHS>ifinter(false,x,l1,l2)</LHS><RHS>inter(l1,l2)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_app(cons(x,l1),l2)</LHS><RHS>Marked_app(l1,l2)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_app(app(l1,l2),l3)</LHS><RHS>Marked_app(l1,app(l2,l3))</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><ORDERING type="poly"><POLYSYMB><SYMBOL><NAME>if</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF></MONOME></POLYNOMIAL><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="0"/><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="2"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/><ARG degree="1" num="2"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="1"/><ARG degree="1" num="2"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="0"/><ARG degree="1" num="1"/><ARG degree="1" num="2"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></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>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>cons</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</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></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>0</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>ifinter</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="0"/><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="2"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="3"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="2"/><ARG degree="1" num="3"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>false</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>ifmem</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="2"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>app</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</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></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>true</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>mem</NAME></SYMBOL><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></POLYSYMB><POLYSYMB><SYMBOL><NAME>s</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>eq</NAME></SYMBOL><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></POLYSYMB><POLYSYMB><SYMBOL><NAME>inter</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><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="0"/><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>nil</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB></ORDERING></CRITERION></PROPERTY></PROPERTY></PROPERTY><PROPERTY criterion="stronggraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>if(true,x,y)</LHS><RHS>x</RHS></RULE><RULE><LHS>if(false,x,y)</LHS><RHS>y</RHS></RULE><RULE><LHS>eq(0,0)</LHS><RHS>true</RHS></RULE><RULE><LHS>eq(0,s(x))</LHS><RHS>false</RHS></RULE><RULE><LHS>eq(s(x),0)</LHS><RHS>false</RHS></RULE><RULE><LHS>eq(s(x),s(y))</LHS><RHS>eq(x,y)</RHS></RULE><RULE><LHS>app(nil,l)</LHS><RHS>l</RHS></RULE><RULE><LHS>app(cons(x,l1),l2)</LHS><RHS>cons(x,app(l1,l2))</RHS></RULE><RULE><LHS>app(app(l1,l2),l3)</LHS><RHS>app(l1,app(l2,l3))</RHS></RULE><RULE><LHS>mem(x,nil)</LHS><RHS>false</RHS></RULE><RULE><LHS>mem(x,cons(y,l))</LHS><RHS>ifmem(eq(x,y),x,l)</RHS></RULE><RULE><LHS>ifmem(true,x,l)</LHS><RHS>true</RHS></RULE><RULE><LHS>ifmem(false,x,l)</LHS><RHS>mem(x,l)</RHS></RULE><RULE><LHS>inter(x,nil)</LHS><RHS>nil</RHS></RULE><RULE><LHS>inter(nil,x)</LHS><RHS>nil</RHS></RULE><RULE><LHS>inter(app(l1,l2),l3)</LHS><RHS>app(inter(l1,l3),inter(l2,l3))</RHS></RULE><RULE><LHS>inter(l1,app(l2,l3))</LHS><RHS>app(inter(l1,l2),inter(l1,l3))</RHS></RULE><RULE><LHS>inter(cons(x,l1),l2)</LHS><RHS>ifinter(mem(x,l2),x,l1,l2)</RHS></RULE><RULE><LHS>inter(l1,cons(x,l2))</LHS><RHS>ifinter(mem(x,l1),x,l2,l1)</RHS></RULE><RULE><LHS>ifinter(true,x,l1,l2)</LHS><RHS>cons(x,inter(l1,l2))</RHS></RULE><RULE><LHS>ifinter(false,x,l1,l2)</LHS><RHS>inter(l1,l2)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_mem(x,cons(y,l))</LHS><RHS>Marked_ifmem(eq(x,y),x,l)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_ifmem(false,x,l)</LHS><RHS>Marked_mem(x,l)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><ORDERING type="poly"><POLYSYMB><SYMBOL><NAME>if</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="0"/><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="2"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="1"/><ARG degree="1" num="2"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="0"/><ARG degree="1" num="1"/><ARG degree="1" num="2"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>cons</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF></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>0</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>ifinter</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="3"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="2"/><ARG degree="1" num="3"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>false</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>ifmem</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="2"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>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>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>true</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>Marked_ifmem</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="2"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>mem</NAME></SYMBOL><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></POLYSYMB><POLYSYMB><SYMBOL><NAME>s</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>eq</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>inter</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="0"/><ARG degree="1" num="1"/></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_mem</NAME></SYMBOL><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></POLYSYMB></ORDERING><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_mem(x,cons(y,l))</LHS><RHS>Marked_ifmem(eq(x,y),x,l)</RHS></DPRULE></DPLIST></STRICTPAIRS></CRITERION><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>if(true,x,y)</LHS><RHS>x</RHS></RULE><RULE><LHS>if(false,x,y)</LHS><RHS>y</RHS></RULE><RULE><LHS>eq(0,0)</LHS><RHS>true</RHS></RULE><RULE><LHS>eq(0,s(x))</LHS><RHS>false</RHS></RULE><RULE><LHS>eq(s(x),0)</LHS><RHS>false</RHS></RULE><RULE><LHS>eq(s(x),s(y))</LHS><RHS>eq(x,y)</RHS></RULE><RULE><LHS>app(nil,l)</LHS><RHS>l</RHS></RULE><RULE><LHS>app(cons(x,l1),l2)</LHS><RHS>cons(x,app(l1,l2))</RHS></RULE><RULE><LHS>app(app(l1,l2),l3)</LHS><RHS>app(l1,app(l2,l3))</RHS></RULE><RULE><LHS>mem(x,nil)</LHS><RHS>false</RHS></RULE><RULE><LHS>mem(x,cons(y,l))</LHS><RHS>ifmem(eq(x,y),x,l)</RHS></RULE><RULE><LHS>ifmem(true,x,l)</LHS><RHS>true</RHS></RULE><RULE><LHS>ifmem(false,x,l)</LHS><RHS>mem(x,l)</RHS></RULE><RULE><LHS>inter(x,nil)</LHS><RHS>nil</RHS></RULE><RULE><LHS>inter(nil,x)</LHS><RHS>nil</RHS></RULE><RULE><LHS>inter(app(l1,l2),l3)</LHS><RHS>app(inter(l1,l3),inter(l2,l3))</RHS></RULE><RULE><LHS>inter(l1,app(l2,l3))</LHS><RHS>app(inter(l1,l2),inter(l1,l3))</RHS></RULE><RULE><LHS>inter(cons(x,l1),l2)</LHS><RHS>ifinter(mem(x,l2),x,l1,l2)</RHS></RULE><RULE><LHS>inter(l1,cons(x,l2))</LHS><RHS>ifinter(mem(x,l1),x,l2,l1)</RHS></RULE><RULE><LHS>ifinter(true,x,l1,l2)</LHS><RHS>cons(x,inter(l1,l2))</RHS></RULE><RULE><LHS>ifinter(false,x,l1,l2)</LHS><RHS>inter(l1,l2)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_ifmem(false,x,l)</LHS><RHS>Marked_mem(x,l)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><DAG approx="simpl"><CCLIST><NONSCC num="0"><NODE ref="0"/></NONSCC></CCLIST></DAG></CRITERION></PROPERTY></PROPERTY><PROPERTY criterion="ordering" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>if(true,x,y)</LHS><RHS>x</RHS></RULE><RULE><LHS>if(false,x,y)</LHS><RHS>y</RHS></RULE><RULE><LHS>eq(0,0)</LHS><RHS>true</RHS></RULE><RULE><LHS>eq(0,s(x))</LHS><RHS>false</RHS></RULE><RULE><LHS>eq(s(x),0)</LHS><RHS>false</RHS></RULE><RULE><LHS>eq(s(x),s(y))</LHS><RHS>eq(x,y)</RHS></RULE><RULE><LHS>app(nil,l)</LHS><RHS>l</RHS></RULE><RULE><LHS>app(cons(x,l1),l2)</LHS><RHS>cons(x,app(l1,l2))</RHS></RULE><RULE><LHS>app(app(l1,l2),l3)</LHS><RHS>app(l1,app(l2,l3))</RHS></RULE><RULE><LHS>mem(x,nil)</LHS><RHS>false</RHS></RULE><RULE><LHS>mem(x,cons(y,l))</LHS><RHS>ifmem(eq(x,y),x,l)</RHS></RULE><RULE><LHS>ifmem(true,x,l)</LHS><RHS>true</RHS></RULE><RULE><LHS>ifmem(false,x,l)</LHS><RHS>mem(x,l)</RHS></RULE><RULE><LHS>inter(x,nil)</LHS><RHS>nil</RHS></RULE><RULE><LHS>inter(nil,x)</LHS><RHS>nil</RHS></RULE><RULE><LHS>inter(app(l1,l2),l3)</LHS><RHS>app(inter(l1,l3),inter(l2,l3))</RHS></RULE><RULE><LHS>inter(l1,app(l2,l3))</LHS><RHS>app(inter(l1,l2),inter(l1,l3))</RHS></RULE><RULE><LHS>inter(cons(x,l1),l2)</LHS><RHS>ifinter(mem(x,l2),x,l1,l2)</RHS></RULE><RULE><LHS>inter(l1,cons(x,l2))</LHS><RHS>ifinter(mem(x,l1),x,l2,l1)</RHS></RULE><RULE><LHS>ifinter(true,x,l1,l2)</LHS><RHS>cons(x,inter(l1,l2))</RHS></RULE><RULE><LHS>ifinter(false,x,l1,l2)</LHS><RHS>inter(l1,l2)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_eq(s(x),s(y))</LHS><RHS>Marked_eq(x,y)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><ORDERING type="poly"><POLYSYMB><SYMBOL><NAME>if</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>3</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</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><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>3</INT></COEF><ARG degree="1" num="2"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>cons</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>0</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>ifinter</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>false</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>Marked_eq</NAME></SYMBOL><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></POLYSYMB><POLYSYMB><SYMBOL><NAME>ifmem</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>app</NAME></SYMBOL><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></POLYSYMB><POLYSYMB><SYMBOL><NAME>true</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>mem</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>s</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>3</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>eq</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>inter</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></ORDERING></CRITERION></PROPERTY></PROPERTY></PROPERTY></PROOF>
