<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE PROOF SYSTEM "http://a3pat.ensiie.fr/pub/a3pat.dtd">
<PROOF><SIGNATURE><SYMBOLLIST><SYMBOL arity="1" unmarked="active"><NAME>Marked_active</NAME></SYMBOL><SYMBOL arity="1" unmarked=""><NAME>nats</NAME></SYMBOL><SYMBOL arity="1" unmarked="s"><NAME>Marked_s</NAME></SYMBOL><SYMBOL arity="3" unmarked=""><NAME>filter</NAME></SYMBOL><SYMBOL arity="3" unmarked="filter"><NAME>Marked_filter</NAME></SYMBOL><SYMBOL arity="1" unmarked=""><NAME>s</NAME></SYMBOL><SYMBOL arity="1" unmarked="nats"><NAME>Marked_nats</NAME></SYMBOL><SYMBOL arity="2" unmarked=""><NAME>cons</NAME></SYMBOL><SYMBOL arity="1" unmarked="mark"><NAME>Marked_mark</NAME></SYMBOL><SYMBOL arity="1" unmarked=""><NAME>sieve</NAME></SYMBOL><SYMBOL arity="1" unmarked="sieve"><NAME>Marked_sieve</NAME></SYMBOL><SYMBOL arity="0" unmarked=""><NAME>0</NAME></SYMBOL><SYMBOL arity="2" unmarked="cons"><NAME>Marked_cons</NAME></SYMBOL><SYMBOL arity="1" unmarked=""><NAME>active</NAME></SYMBOL><SYMBOL arity="0" unmarked=""><NAME>zprimes</NAME></SYMBOL><SYMBOL arity="1" unmarked=""><NAME>mark</NAME></SYMBOL></SYMBOLLIST><VARLIST><VAR>X3</VAR><VAR>X2</VAR><VAR>X1</VAR><VAR>N</VAR><VAR>M</VAR><VAR>Y</VAR><VAR>X</VAR></VARLIST></SIGNATURE><PROPERTY criterion="dp" prop="sntrs"><SYSTEM><REWSYS><RULE><LHS>active(filter(cons(X,Y),0,M))</LHS><RHS>mark(cons(0,filter(Y,M,M)))</RHS></RULE><RULE><LHS>active(filter(cons(X,Y),s(N),M))</LHS><RHS>mark(cons(X,filter(Y,N,M)))</RHS></RULE><RULE><LHS>active(sieve(cons(0,Y)))</LHS><RHS>mark(cons(0,sieve(Y)))</RHS></RULE><RULE><LHS>active(sieve(cons(s(N),Y)))</LHS><RHS>mark(cons(s(N),sieve(filter(Y,N,N))))</RHS></RULE><RULE><LHS>active(nats(N))</LHS><RHS>mark(cons(N,nats(s(N))))</RHS></RULE><RULE><LHS>active(zprimes)</LHS><RHS>mark(sieve(nats(s(s(0)))))</RHS></RULE><RULE><LHS>mark(filter(X1,X2,X3))</LHS><RHS>active(filter(mark(X1),mark(X2),mark(X3)))</RHS></RULE><RULE><LHS>mark(cons(X1,X2))</LHS><RHS>active(cons(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(mark(X)))</RHS></RULE><RULE><LHS>mark(sieve(X))</LHS><RHS>active(sieve(mark(X)))</RHS></RULE><RULE><LHS>mark(nats(X))</LHS><RHS>active(nats(mark(X)))</RHS></RULE><RULE><LHS>mark(zprimes)</LHS><RHS>active(zprimes)</RHS></RULE><RULE><LHS>filter(mark(X1),X2,X3)</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(X1,mark(X2),X3)</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(X1,X2,mark(X3))</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(active(X1),X2,X3)</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(X1,active(X2),X3)</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(X1,X2,active(X3))</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>cons(mark(X1),X2)</LHS><RHS>cons(X1,X2)</RHS></RULE><RULE><LHS>cons(X1,mark(X2))</LHS><RHS>cons(X1,X2)</RHS></RULE><RULE><LHS>cons(active(X1),X2)</LHS><RHS>cons(X1,X2)</RHS></RULE><RULE><LHS>cons(X1,active(X2))</LHS><RHS>cons(X1,X2)</RHS></RULE><RULE><LHS>s(mark(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>s(active(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>sieve(mark(X))</LHS><RHS>sieve(X)</RHS></RULE><RULE><LHS>sieve(active(X))</LHS><RHS>sieve(X)</RHS></RULE><RULE><LHS>nats(mark(X))</LHS><RHS>nats(X)</RHS></RULE><RULE><LHS>nats(active(X))</LHS><RHS>nats(X)</RHS></RULE></REWSYS></SYSTEM><CRITERION/><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(filter(cons(X,Y),0,M))</LHS><RHS>mark(cons(0,filter(Y,M,M)))</RHS></RULE><RULE><LHS>active(filter(cons(X,Y),s(N),M))</LHS><RHS>mark(cons(X,filter(Y,N,M)))</RHS></RULE><RULE><LHS>active(sieve(cons(0,Y)))</LHS><RHS>mark(cons(0,sieve(Y)))</RHS></RULE><RULE><LHS>active(sieve(cons(s(N),Y)))</LHS><RHS>mark(cons(s(N),sieve(filter(Y,N,N))))</RHS></RULE><RULE><LHS>active(nats(N))</LHS><RHS>mark(cons(N,nats(s(N))))</RHS></RULE><RULE><LHS>active(zprimes)</LHS><RHS>mark(sieve(nats(s(s(0)))))</RHS></RULE><RULE><LHS>mark(filter(X1,X2,X3))</LHS><RHS>active(filter(mark(X1),mark(X2),mark(X3)))</RHS></RULE><RULE><LHS>mark(cons(X1,X2))</LHS><RHS>active(cons(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(mark(X)))</RHS></RULE><RULE><LHS>mark(sieve(X))</LHS><RHS>active(sieve(mark(X)))</RHS></RULE><RULE><LHS>mark(nats(X))</LHS><RHS>active(nats(mark(X)))</RHS></RULE><RULE><LHS>mark(zprimes)</LHS><RHS>active(zprimes)</RHS></RULE><RULE><LHS>filter(mark(X1),X2,X3)</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(X1,mark(X2),X3)</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(X1,X2,mark(X3))</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(active(X1),X2,X3)</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(X1,active(X2),X3)</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(X1,X2,active(X3))</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>cons(mark(X1),X2)</LHS><RHS>cons(X1,X2)</RHS></RULE><RULE><LHS>cons(X1,mark(X2))</LHS><RHS>cons(X1,X2)</RHS></RULE><RULE><LHS>cons(active(X1),X2)</LHS><RHS>cons(X1,X2)</RHS></RULE><RULE><LHS>cons(X1,active(X2))</LHS><RHS>cons(X1,X2)</RHS></RULE><RULE><LHS>s(mark(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>s(active(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>sieve(mark(X))</LHS><RHS>sieve(X)</RHS></RULE><RULE><LHS>sieve(active(X))</LHS><RHS>sieve(X)</RHS></RULE><RULE><LHS>nats(mark(X))</LHS><RHS>nats(X)</RHS></RULE><RULE><LHS>nats(active(X))</LHS><RHS>nats(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_active(filter(cons(X,Y),0,M))</LHS><RHS>Marked_mark(cons(0,filter(Y,M,M)))</RHS></DPRULE><DPRULE num="1"><LHS>Marked_active(filter(cons(X,Y),0,M))</LHS><RHS>Marked_cons(0,filter(Y,M,M))</RHS></DPRULE><DPRULE num="2"><LHS>Marked_active(filter(cons(X,Y),0,M))</LHS><RHS>Marked_filter(Y,M,M)</RHS></DPRULE><DPRULE num="3"><LHS>Marked_active(filter(cons(X,Y),s(N),M))</LHS><RHS>Marked_mark(cons(X,filter(Y,N,M)))</RHS></DPRULE><DPRULE num="4"><LHS>Marked_active(filter(cons(X,Y),s(N),M))</LHS><RHS>Marked_cons(X,filter(Y,N,M))</RHS></DPRULE><DPRULE num="5"><LHS>Marked_active(filter(cons(X,Y),s(N),M))</LHS><RHS>Marked_filter(Y,N,M)</RHS></DPRULE><DPRULE num="6"><LHS>Marked_active(sieve(cons(0,Y)))</LHS><RHS>Marked_mark(cons(0,sieve(Y)))</RHS></DPRULE><DPRULE num="7"><LHS>Marked_active(sieve(cons(0,Y)))</LHS><RHS>Marked_cons(0,sieve(Y))</RHS></DPRULE><DPRULE num="8"><LHS>Marked_active(sieve(cons(0,Y)))</LHS><RHS>Marked_sieve(Y)</RHS></DPRULE><DPRULE num="9"><LHS>Marked_active(sieve(cons(s(N),Y)))</LHS><RHS>Marked_mark(cons(s(N),sieve(filter(Y,N,N))))</RHS></DPRULE><DPRULE num="10"><LHS>Marked_active(sieve(cons(s(N),Y)))</LHS><RHS>Marked_cons(s(N),sieve(filter(Y,N,N)))</RHS></DPRULE><DPRULE num="11"><LHS>Marked_active(sieve(cons(s(N),Y)))</LHS><RHS>Marked_sieve(filter(Y,N,N))</RHS></DPRULE><DPRULE num="12"><LHS>Marked_active(sieve(cons(s(N),Y)))</LHS><RHS>Marked_filter(Y,N,N)</RHS></DPRULE><DPRULE num="13"><LHS>Marked_active(nats(N))</LHS><RHS>Marked_mark(cons(N,nats(s(N))))</RHS></DPRULE><DPRULE num="14"><LHS>Marked_active(nats(N))</LHS><RHS>Marked_cons(N,nats(s(N)))</RHS></DPRULE><DPRULE num="15"><LHS>Marked_active(nats(N))</LHS><RHS>Marked_nats(s(N))</RHS></DPRULE><DPRULE num="16"><LHS>Marked_active(nats(N))</LHS><RHS>Marked_s(N)</RHS></DPRULE><DPRULE num="17"><LHS>Marked_active(zprimes)</LHS><RHS>Marked_mark(sieve(nats(s(s(0)))))</RHS></DPRULE><DPRULE num="18"><LHS>Marked_active(zprimes)</LHS><RHS>Marked_sieve(nats(s(s(0))))</RHS></DPRULE><DPRULE num="19"><LHS>Marked_active(zprimes)</LHS><RHS>Marked_nats(s(s(0)))</RHS></DPRULE><DPRULE num="20"><LHS>Marked_active(zprimes)</LHS><RHS>Marked_s(s(0))</RHS></DPRULE><DPRULE num="21"><LHS>Marked_active(zprimes)</LHS><RHS>Marked_s(0)</RHS></DPRULE><DPRULE num="22"><LHS>Marked_mark(filter(X1,X2,X3))</LHS><RHS>Marked_active(filter(mark(X1),mark(X2),mark(X3)))</RHS></DPRULE><DPRULE num="23"><LHS>Marked_mark(filter(X1,X2,X3))</LHS><RHS>Marked_filter(mark(X1),mark(X2),mark(X3))</RHS></DPRULE><DPRULE num="24"><LHS>Marked_mark(filter(X1,X2,X3))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="25"><LHS>Marked_mark(filter(X1,X2,X3))</LHS><RHS>Marked_mark(X2)</RHS></DPRULE><DPRULE num="26"><LHS>Marked_mark(filter(X1,X2,X3))</LHS><RHS>Marked_mark(X3)</RHS></DPRULE><DPRULE num="27"><LHS>Marked_mark(cons(X1,X2))</LHS><RHS>Marked_active(cons(mark(X1),X2))</RHS></DPRULE><DPRULE num="28"><LHS>Marked_mark(cons(X1,X2))</LHS><RHS>Marked_cons(mark(X1),X2)</RHS></DPRULE><DPRULE num="29"><LHS>Marked_mark(cons(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="30"><LHS>Marked_mark(0)</LHS><RHS>Marked_active(0)</RHS></DPRULE><DPRULE num="31"><LHS>Marked_mark(s(X))</LHS><RHS>Marked_active(s(mark(X)))</RHS></DPRULE><DPRULE num="32"><LHS>Marked_mark(s(X))</LHS><RHS>Marked_s(mark(X))</RHS></DPRULE><DPRULE num="33"><LHS>Marked_mark(s(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="34"><LHS>Marked_mark(sieve(X))</LHS><RHS>Marked_active(sieve(mark(X)))</RHS></DPRULE><DPRULE num="35"><LHS>Marked_mark(sieve(X))</LHS><RHS>Marked_sieve(mark(X))</RHS></DPRULE><DPRULE num="36"><LHS>Marked_mark(sieve(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="37"><LHS>Marked_mark(nats(X))</LHS><RHS>Marked_active(nats(mark(X)))</RHS></DPRULE><DPRULE num="38"><LHS>Marked_mark(nats(X))</LHS><RHS>Marked_nats(mark(X))</RHS></DPRULE><DPRULE num="39"><LHS>Marked_mark(nats(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="40"><LHS>Marked_mark(zprimes)</LHS><RHS>Marked_active(zprimes)</RHS></DPRULE><DPRULE num="41"><LHS>Marked_filter(mark(X1),X2,X3)</LHS><RHS>Marked_filter(X1,X2,X3)</RHS></DPRULE><DPRULE num="42"><LHS>Marked_filter(X1,mark(X2),X3)</LHS><RHS>Marked_filter(X1,X2,X3)</RHS></DPRULE><DPRULE num="43"><LHS>Marked_filter(X1,X2,mark(X3))</LHS><RHS>Marked_filter(X1,X2,X3)</RHS></DPRULE><DPRULE num="44"><LHS>Marked_filter(active(X1),X2,X3)</LHS><RHS>Marked_filter(X1,X2,X3)</RHS></DPRULE><DPRULE num="45"><LHS>Marked_filter(X1,active(X2),X3)</LHS><RHS>Marked_filter(X1,X2,X3)</RHS></DPRULE><DPRULE num="46"><LHS>Marked_filter(X1,X2,active(X3))</LHS><RHS>Marked_filter(X1,X2,X3)</RHS></DPRULE><DPRULE num="47"><LHS>Marked_cons(mark(X1),X2)</LHS><RHS>Marked_cons(X1,X2)</RHS></DPRULE><DPRULE num="48"><LHS>Marked_cons(X1,mark(X2))</LHS><RHS>Marked_cons(X1,X2)</RHS></DPRULE><DPRULE num="49"><LHS>Marked_cons(active(X1),X2)</LHS><RHS>Marked_cons(X1,X2)</RHS></DPRULE><DPRULE num="50"><LHS>Marked_cons(X1,active(X2))</LHS><RHS>Marked_cons(X1,X2)</RHS></DPRULE><DPRULE num="51"><LHS>Marked_s(mark(X))</LHS><RHS>Marked_s(X)</RHS></DPRULE><DPRULE num="52"><LHS>Marked_s(active(X))</LHS><RHS>Marked_s(X)</RHS></DPRULE><DPRULE num="53"><LHS>Marked_sieve(mark(X))</LHS><RHS>Marked_sieve(X)</RHS></DPRULE><DPRULE num="54"><LHS>Marked_sieve(active(X))</LHS><RHS>Marked_sieve(X)</RHS></DPRULE><DPRULE num="55"><LHS>Marked_nats(mark(X))</LHS><RHS>Marked_nats(X)</RHS></DPRULE><DPRULE num="56"><LHS>Marked_nats(active(X))</LHS><RHS>Marked_nats(X)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><DAG approx="simpl"><CCLIST><SCC num="0"><NODE ref="55"/><NODE ref="56"/></SCC><SCC num="1"><NODE ref="53"/><NODE ref="54"/></SCC><SCC num="2"><NODE ref="51"/><NODE ref="52"/></SCC><SCC num="3"><NODE ref="47"/><NODE ref="48"/><NODE ref="49"/><NODE ref="50"/></SCC><SCC num="4"><NODE ref="41"/><NODE ref="42"/><NODE ref="43"/><NODE ref="44"/><NODE ref="45"/><NODE ref="46"/></SCC><SCC num="5"><NODE ref="0"/><NODE ref="3"/><NODE ref="6"/><NODE ref="9"/><NODE ref="13"/><NODE ref="17"/><NODE ref="22"/><NODE ref="24"/><NODE ref="25"/><NODE ref="26"/><NODE ref="27"/><NODE ref="29"/><NODE ref="31"/><NODE ref="33"/><NODE ref="34"/><NODE ref="36"/><NODE ref="37"/><NODE ref="39"/><NODE ref="40"/></SCC><NONSCC num="6"><NODE ref="21"/></NONSCC><NONSCC num="7"><NODE ref="20"/></NONSCC><NONSCC num="8"><NODE ref="19"/></NONSCC><NONSCC num="9"><NODE ref="18"/></NONSCC><NONSCC num="10"><NODE ref="38"/></NONSCC><NONSCC num="11"><NODE ref="35"/></NONSCC><NONSCC num="12"><NODE ref="32"/></NONSCC><NONSCC num="13"><NODE ref="30"/></NONSCC><NONSCC num="14"><NODE ref="28"/></NONSCC><NONSCC num="15"><NODE ref="23"/></NONSCC><NONSCC num="16"><NODE ref="16"/></NONSCC><NONSCC num="17"><NODE ref="15"/></NONSCC><NONSCC num="18"><NODE ref="14"/></NONSCC><NONSCC num="19"><NODE ref="12"/></NONSCC><NONSCC num="20"><NODE ref="11"/></NONSCC><NONSCC num="21"><NODE ref="10"/></NONSCC><NONSCC num="22"><NODE ref="8"/></NONSCC><NONSCC num="23"><NODE ref="7"/></NONSCC><NONSCC num="24"><NODE ref="5"/></NONSCC><NONSCC num="25"><NODE ref="4"/></NONSCC><NONSCC num="26"><NODE ref="2"/></NONSCC><NONSCC num="27"><NODE ref="1"/></NONSCC></CCLIST><EDGE end="27" start="5"/><EDGE end="26" start="5"/><EDGE end="25" start="5"/><EDGE end="24" start="5"/><EDGE end="23" start="5"/><EDGE end="22" start="5"/><EDGE end="21" start="5"/><EDGE end="20" start="5"/><EDGE end="19" start="5"/><EDGE end="18" start="5"/><EDGE end="17" start="5"/><EDGE end="16" start="5"/><EDGE end="15" start="5"/><EDGE end="14" start="5"/><EDGE end="13" start="5"/><EDGE end="12" start="5"/><EDGE end="11" start="5"/><EDGE end="10" start="5"/><EDGE end="9" start="5"/><EDGE end="8" start="5"/><EDGE end="7" start="5"/><EDGE end="6" start="5"/><EDGE end="2" start="7"/><EDGE end="0" start="8"/><EDGE end="1" start="9"/><EDGE end="0" start="10"/><EDGE end="1" start="11"/><EDGE end="2" start="12"/><EDGE end="3" start="14"/><EDGE end="4" start="15"/><EDGE end="2" start="16"/><EDGE end="0" start="17"/><EDGE end="3" start="18"/><EDGE end="4" start="19"/><EDGE end="1" start="20"/><EDGE end="3" start="21"/><EDGE end="1" start="22"/><EDGE end="3" start="23"/><EDGE end="4" start="24"/><EDGE end="3" start="25"/><EDGE end="4" start="26"/><EDGE end="3" start="27"/></DAG></CRITERION><PROPERTY criterion="stronggraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(filter(cons(X,Y),0,M))</LHS><RHS>mark(cons(0,filter(Y,M,M)))</RHS></RULE><RULE><LHS>active(filter(cons(X,Y),s(N),M))</LHS><RHS>mark(cons(X,filter(Y,N,M)))</RHS></RULE><RULE><LHS>active(sieve(cons(0,Y)))</LHS><RHS>mark(cons(0,sieve(Y)))</RHS></RULE><RULE><LHS>active(sieve(cons(s(N),Y)))</LHS><RHS>mark(cons(s(N),sieve(filter(Y,N,N))))</RHS></RULE><RULE><LHS>active(nats(N))</LHS><RHS>mark(cons(N,nats(s(N))))</RHS></RULE><RULE><LHS>active(zprimes)</LHS><RHS>mark(sieve(nats(s(s(0)))))</RHS></RULE><RULE><LHS>mark(filter(X1,X2,X3))</LHS><RHS>active(filter(mark(X1),mark(X2),mark(X3)))</RHS></RULE><RULE><LHS>mark(cons(X1,X2))</LHS><RHS>active(cons(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(mark(X)))</RHS></RULE><RULE><LHS>mark(sieve(X))</LHS><RHS>active(sieve(mark(X)))</RHS></RULE><RULE><LHS>mark(nats(X))</LHS><RHS>active(nats(mark(X)))</RHS></RULE><RULE><LHS>mark(zprimes)</LHS><RHS>active(zprimes)</RHS></RULE><RULE><LHS>filter(mark(X1),X2,X3)</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(X1,mark(X2),X3)</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(X1,X2,mark(X3))</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(active(X1),X2,X3)</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(X1,active(X2),X3)</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(X1,X2,active(X3))</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>cons(mark(X1),X2)</LHS><RHS>cons(X1,X2)</RHS></RULE><RULE><LHS>cons(X1,mark(X2))</LHS><RHS>cons(X1,X2)</RHS></RULE><RULE><LHS>cons(active(X1),X2)</LHS><RHS>cons(X1,X2)</RHS></RULE><RULE><LHS>cons(X1,active(X2))</LHS><RHS>cons(X1,X2)</RHS></RULE><RULE><LHS>s(mark(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>s(active(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>sieve(mark(X))</LHS><RHS>sieve(X)</RHS></RULE><RULE><LHS>sieve(active(X))</LHS><RHS>sieve(X)</RHS></RULE><RULE><LHS>nats(mark(X))</LHS><RHS>nats(X)</RHS></RULE><RULE><LHS>nats(active(X))</LHS><RHS>nats(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_active(filter(cons(X,Y),0,M))</LHS><RHS>Marked_mark(cons(0,filter(Y,M,M)))</RHS></DPRULE><DPRULE num="1"><LHS>Marked_active(filter(cons(X,Y),s(N),M))</LHS><RHS>Marked_mark(cons(X,filter(Y,N,M)))</RHS></DPRULE><DPRULE num="2"><LHS>Marked_active(sieve(cons(0,Y)))</LHS><RHS>Marked_mark(cons(0,sieve(Y)))</RHS></DPRULE><DPRULE num="3"><LHS>Marked_active(sieve(cons(s(N),Y)))</LHS><RHS>Marked_mark(cons(s(N),sieve(filter(Y,N,N))))</RHS></DPRULE><DPRULE num="4"><LHS>Marked_active(nats(N))</LHS><RHS>Marked_mark(cons(N,nats(s(N))))</RHS></DPRULE><DPRULE num="5"><LHS>Marked_active(zprimes)</LHS><RHS>Marked_mark(sieve(nats(s(s(0)))))</RHS></DPRULE><DPRULE num="6"><LHS>Marked_mark(filter(X1,X2,X3))</LHS><RHS>Marked_active(filter(mark(X1),mark(X2),mark(X3)))</RHS></DPRULE><DPRULE num="7"><LHS>Marked_mark(filter(X1,X2,X3))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="8"><LHS>Marked_mark(filter(X1,X2,X3))</LHS><RHS>Marked_mark(X2)</RHS></DPRULE><DPRULE num="9"><LHS>Marked_mark(filter(X1,X2,X3))</LHS><RHS>Marked_mark(X3)</RHS></DPRULE><DPRULE num="10"><LHS>Marked_mark(cons(X1,X2))</LHS><RHS>Marked_active(cons(mark(X1),X2))</RHS></DPRULE><DPRULE num="11"><LHS>Marked_mark(cons(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="12"><LHS>Marked_mark(s(X))</LHS><RHS>Marked_active(s(mark(X)))</RHS></DPRULE><DPRULE num="13"><LHS>Marked_mark(s(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="14"><LHS>Marked_mark(sieve(X))</LHS><RHS>Marked_active(sieve(mark(X)))</RHS></DPRULE><DPRULE num="15"><LHS>Marked_mark(sieve(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="16"><LHS>Marked_mark(nats(X))</LHS><RHS>Marked_active(nats(mark(X)))</RHS></DPRULE><DPRULE num="17"><LHS>Marked_mark(nats(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="18"><LHS>Marked_mark(zprimes)</LHS><RHS>Marked_active(zprimes)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><ORDERING type="poly"><POLYSYMB><SYMBOL><NAME>mark</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>zprimes</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>active</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>0</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>sieve</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>Marked_mark</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>cons</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>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>filter</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><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></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>nats</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>Marked_active</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></ORDERING><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_active(zprimes)</LHS><RHS>Marked_mark(sieve(nats(s(s(0)))))</RHS></DPRULE></DPLIST></STRICTPAIRS></CRITERION><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(filter(cons(X,Y),0,M))</LHS><RHS>mark(cons(0,filter(Y,M,M)))</RHS></RULE><RULE><LHS>active(filter(cons(X,Y),s(N),M))</LHS><RHS>mark(cons(X,filter(Y,N,M)))</RHS></RULE><RULE><LHS>active(sieve(cons(0,Y)))</LHS><RHS>mark(cons(0,sieve(Y)))</RHS></RULE><RULE><LHS>active(sieve(cons(s(N),Y)))</LHS><RHS>mark(cons(s(N),sieve(filter(Y,N,N))))</RHS></RULE><RULE><LHS>active(nats(N))</LHS><RHS>mark(cons(N,nats(s(N))))</RHS></RULE><RULE><LHS>active(zprimes)</LHS><RHS>mark(sieve(nats(s(s(0)))))</RHS></RULE><RULE><LHS>mark(filter(X1,X2,X3))</LHS><RHS>active(filter(mark(X1),mark(X2),mark(X3)))</RHS></RULE><RULE><LHS>mark(cons(X1,X2))</LHS><RHS>active(cons(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(mark(X)))</RHS></RULE><RULE><LHS>mark(sieve(X))</LHS><RHS>active(sieve(mark(X)))</RHS></RULE><RULE><LHS>mark(nats(X))</LHS><RHS>active(nats(mark(X)))</RHS></RULE><RULE><LHS>mark(zprimes)</LHS><RHS>active(zprimes)</RHS></RULE><RULE><LHS>filter(mark(X1),X2,X3)</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(X1,mark(X2),X3)</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(X1,X2,mark(X3))</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(active(X1),X2,X3)</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(X1,active(X2),X3)</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(X1,X2,active(X3))</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>cons(mark(X1),X2)</LHS><RHS>cons(X1,X2)</RHS></RULE><RULE><LHS>cons(X1,mark(X2))</LHS><RHS>cons(X1,X2)</RHS></RULE><RULE><LHS>cons(active(X1),X2)</LHS><RHS>cons(X1,X2)</RHS></RULE><RULE><LHS>cons(X1,active(X2))</LHS><RHS>cons(X1,X2)</RHS></RULE><RULE><LHS>s(mark(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>s(active(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>sieve(mark(X))</LHS><RHS>sieve(X)</RHS></RULE><RULE><LHS>sieve(active(X))</LHS><RHS>sieve(X)</RHS></RULE><RULE><LHS>nats(mark(X))</LHS><RHS>nats(X)</RHS></RULE><RULE><LHS>nats(active(X))</LHS><RHS>nats(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_active(filter(cons(X,Y),0,M))</LHS><RHS>Marked_mark(cons(0,filter(Y,M,M)))</RHS></DPRULE><DPRULE num="1"><LHS>Marked_active(filter(cons(X,Y),s(N),M))</LHS><RHS>Marked_mark(cons(X,filter(Y,N,M)))</RHS></DPRULE><DPRULE num="2"><LHS>Marked_active(sieve(cons(0,Y)))</LHS><RHS>Marked_mark(cons(0,sieve(Y)))</RHS></DPRULE><DPRULE num="3"><LHS>Marked_active(sieve(cons(s(N),Y)))</LHS><RHS>Marked_mark(cons(s(N),sieve(filter(Y,N,N))))</RHS></DPRULE><DPRULE num="4"><LHS>Marked_active(nats(N))</LHS><RHS>Marked_mark(cons(N,nats(s(N))))</RHS></DPRULE><DPRULE num="5"><LHS>Marked_mark(filter(X1,X2,X3))</LHS><RHS>Marked_active(filter(mark(X1),mark(X2),mark(X3)))</RHS></DPRULE><DPRULE num="6"><LHS>Marked_mark(filter(X1,X2,X3))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="7"><LHS>Marked_mark(filter(X1,X2,X3))</LHS><RHS>Marked_mark(X2)</RHS></DPRULE><DPRULE num="8"><LHS>Marked_mark(filter(X1,X2,X3))</LHS><RHS>Marked_mark(X3)</RHS></DPRULE><DPRULE num="9"><LHS>Marked_mark(cons(X1,X2))</LHS><RHS>Marked_active(cons(mark(X1),X2))</RHS></DPRULE><DPRULE num="10"><LHS>Marked_mark(cons(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="11"><LHS>Marked_mark(s(X))</LHS><RHS>Marked_active(s(mark(X)))</RHS></DPRULE><DPRULE num="12"><LHS>Marked_mark(s(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="13"><LHS>Marked_mark(sieve(X))</LHS><RHS>Marked_active(sieve(mark(X)))</RHS></DPRULE><DPRULE num="14"><LHS>Marked_mark(sieve(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="15"><LHS>Marked_mark(nats(X))</LHS><RHS>Marked_active(nats(mark(X)))</RHS></DPRULE><DPRULE num="16"><LHS>Marked_mark(nats(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="17"><LHS>Marked_mark(zprimes)</LHS><RHS>Marked_active(zprimes)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><DAG approx="simpl"><CCLIST><NONSCC num="0"><NODE ref="17"/></NONSCC><SCC num="1"><NODE ref="0"/><NODE ref="1"/><NODE ref="2"/><NODE ref="3"/><NODE ref="4"/><NODE ref="5"/><NODE ref="6"/><NODE ref="7"/><NODE ref="8"/><NODE ref="9"/><NODE ref="10"/><NODE ref="11"/><NODE ref="12"/><NODE ref="13"/><NODE ref="14"/><NODE ref="15"/><NODE ref="16"/></SCC></CCLIST><EDGE end="0" start="1"/></DAG></CRITERION><PROPERTY criterion="stronggraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(filter(cons(X,Y),0,M))</LHS><RHS>mark(cons(0,filter(Y,M,M)))</RHS></RULE><RULE><LHS>active(filter(cons(X,Y),s(N),M))</LHS><RHS>mark(cons(X,filter(Y,N,M)))</RHS></RULE><RULE><LHS>active(sieve(cons(0,Y)))</LHS><RHS>mark(cons(0,sieve(Y)))</RHS></RULE><RULE><LHS>active(sieve(cons(s(N),Y)))</LHS><RHS>mark(cons(s(N),sieve(filter(Y,N,N))))</RHS></RULE><RULE><LHS>active(nats(N))</LHS><RHS>mark(cons(N,nats(s(N))))</RHS></RULE><RULE><LHS>active(zprimes)</LHS><RHS>mark(sieve(nats(s(s(0)))))</RHS></RULE><RULE><LHS>mark(filter(X1,X2,X3))</LHS><RHS>active(filter(mark(X1),mark(X2),mark(X3)))</RHS></RULE><RULE><LHS>mark(cons(X1,X2))</LHS><RHS>active(cons(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(mark(X)))</RHS></RULE><RULE><LHS>mark(sieve(X))</LHS><RHS>active(sieve(mark(X)))</RHS></RULE><RULE><LHS>mark(nats(X))</LHS><RHS>active(nats(mark(X)))</RHS></RULE><RULE><LHS>mark(zprimes)</LHS><RHS>active(zprimes)</RHS></RULE><RULE><LHS>filter(mark(X1),X2,X3)</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(X1,mark(X2),X3)</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(X1,X2,mark(X3))</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(active(X1),X2,X3)</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(X1,active(X2),X3)</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(X1,X2,active(X3))</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>cons(mark(X1),X2)</LHS><RHS>cons(X1,X2)</RHS></RULE><RULE><LHS>cons(X1,mark(X2))</LHS><RHS>cons(X1,X2)</RHS></RULE><RULE><LHS>cons(active(X1),X2)</LHS><RHS>cons(X1,X2)</RHS></RULE><RULE><LHS>cons(X1,active(X2))</LHS><RHS>cons(X1,X2)</RHS></RULE><RULE><LHS>s(mark(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>s(active(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>sieve(mark(X))</LHS><RHS>sieve(X)</RHS></RULE><RULE><LHS>sieve(active(X))</LHS><RHS>sieve(X)</RHS></RULE><RULE><LHS>nats(mark(X))</LHS><RHS>nats(X)</RHS></RULE><RULE><LHS>nats(active(X))</LHS><RHS>nats(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_active(filter(cons(X,Y),0,M))</LHS><RHS>Marked_mark(cons(0,filter(Y,M,M)))</RHS></DPRULE><DPRULE num="1"><LHS>Marked_active(filter(cons(X,Y),s(N),M))</LHS><RHS>Marked_mark(cons(X,filter(Y,N,M)))</RHS></DPRULE><DPRULE num="2"><LHS>Marked_active(sieve(cons(0,Y)))</LHS><RHS>Marked_mark(cons(0,sieve(Y)))</RHS></DPRULE><DPRULE num="3"><LHS>Marked_active(sieve(cons(s(N),Y)))</LHS><RHS>Marked_mark(cons(s(N),sieve(filter(Y,N,N))))</RHS></DPRULE><DPRULE num="4"><LHS>Marked_active(nats(N))</LHS><RHS>Marked_mark(cons(N,nats(s(N))))</RHS></DPRULE><DPRULE num="5"><LHS>Marked_mark(filter(X1,X2,X3))</LHS><RHS>Marked_active(filter(mark(X1),mark(X2),mark(X3)))</RHS></DPRULE><DPRULE num="6"><LHS>Marked_mark(filter(X1,X2,X3))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="7"><LHS>Marked_mark(filter(X1,X2,X3))</LHS><RHS>Marked_mark(X2)</RHS></DPRULE><DPRULE num="8"><LHS>Marked_mark(filter(X1,X2,X3))</LHS><RHS>Marked_mark(X3)</RHS></DPRULE><DPRULE num="9"><LHS>Marked_mark(cons(X1,X2))</LHS><RHS>Marked_active(cons(mark(X1),X2))</RHS></DPRULE><DPRULE num="10"><LHS>Marked_mark(cons(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="11"><LHS>Marked_mark(s(X))</LHS><RHS>Marked_active(s(mark(X)))</RHS></DPRULE><DPRULE num="12"><LHS>Marked_mark(s(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="13"><LHS>Marked_mark(sieve(X))</LHS><RHS>Marked_active(sieve(mark(X)))</RHS></DPRULE><DPRULE num="14"><LHS>Marked_mark(sieve(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="15"><LHS>Marked_mark(nats(X))</LHS><RHS>Marked_active(nats(mark(X)))</RHS></DPRULE><DPRULE num="16"><LHS>Marked_mark(nats(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><ORDERING type="poly"><POLYSYMB><SYMBOL><NAME>mark</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>zprimes</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>active</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>sieve</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>Marked_mark</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>cons</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>filter</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>nats</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>Marked_active</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></ORDERING><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_mark(cons(X1,X2))</LHS><RHS>Marked_active(cons(mark(X1),X2))</RHS></DPRULE><DPRULE num="1"><LHS>Marked_mark(s(X))</LHS><RHS>Marked_active(s(mark(X)))</RHS></DPRULE></DPLIST></STRICTPAIRS></CRITERION><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(filter(cons(X,Y),0,M))</LHS><RHS>mark(cons(0,filter(Y,M,M)))</RHS></RULE><RULE><LHS>active(filter(cons(X,Y),s(N),M))</LHS><RHS>mark(cons(X,filter(Y,N,M)))</RHS></RULE><RULE><LHS>active(sieve(cons(0,Y)))</LHS><RHS>mark(cons(0,sieve(Y)))</RHS></RULE><RULE><LHS>active(sieve(cons(s(N),Y)))</LHS><RHS>mark(cons(s(N),sieve(filter(Y,N,N))))</RHS></RULE><RULE><LHS>active(nats(N))</LHS><RHS>mark(cons(N,nats(s(N))))</RHS></RULE><RULE><LHS>active(zprimes)</LHS><RHS>mark(sieve(nats(s(s(0)))))</RHS></RULE><RULE><LHS>mark(filter(X1,X2,X3))</LHS><RHS>active(filter(mark(X1),mark(X2),mark(X3)))</RHS></RULE><RULE><LHS>mark(cons(X1,X2))</LHS><RHS>active(cons(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(mark(X)))</RHS></RULE><RULE><LHS>mark(sieve(X))</LHS><RHS>active(sieve(mark(X)))</RHS></RULE><RULE><LHS>mark(nats(X))</LHS><RHS>active(nats(mark(X)))</RHS></RULE><RULE><LHS>mark(zprimes)</LHS><RHS>active(zprimes)</RHS></RULE><RULE><LHS>filter(mark(X1),X2,X3)</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(X1,mark(X2),X3)</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(X1,X2,mark(X3))</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(active(X1),X2,X3)</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(X1,active(X2),X3)</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(X1,X2,active(X3))</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>cons(mark(X1),X2)</LHS><RHS>cons(X1,X2)</RHS></RULE><RULE><LHS>cons(X1,mark(X2))</LHS><RHS>cons(X1,X2)</RHS></RULE><RULE><LHS>cons(active(X1),X2)</LHS><RHS>cons(X1,X2)</RHS></RULE><RULE><LHS>cons(X1,active(X2))</LHS><RHS>cons(X1,X2)</RHS></RULE><RULE><LHS>s(mark(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>s(active(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>sieve(mark(X))</LHS><RHS>sieve(X)</RHS></RULE><RULE><LHS>sieve(active(X))</LHS><RHS>sieve(X)</RHS></RULE><RULE><LHS>nats(mark(X))</LHS><RHS>nats(X)</RHS></RULE><RULE><LHS>nats(active(X))</LHS><RHS>nats(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_active(filter(cons(X,Y),0,M))</LHS><RHS>Marked_mark(cons(0,filter(Y,M,M)))</RHS></DPRULE><DPRULE num="1"><LHS>Marked_active(filter(cons(X,Y),s(N),M))</LHS><RHS>Marked_mark(cons(X,filter(Y,N,M)))</RHS></DPRULE><DPRULE num="2"><LHS>Marked_active(sieve(cons(0,Y)))</LHS><RHS>Marked_mark(cons(0,sieve(Y)))</RHS></DPRULE><DPRULE num="3"><LHS>Marked_active(sieve(cons(s(N),Y)))</LHS><RHS>Marked_mark(cons(s(N),sieve(filter(Y,N,N))))</RHS></DPRULE><DPRULE num="4"><LHS>Marked_active(nats(N))</LHS><RHS>Marked_mark(cons(N,nats(s(N))))</RHS></DPRULE><DPRULE num="5"><LHS>Marked_mark(filter(X1,X2,X3))</LHS><RHS>Marked_active(filter(mark(X1),mark(X2),mark(X3)))</RHS></DPRULE><DPRULE num="6"><LHS>Marked_mark(filter(X1,X2,X3))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="7"><LHS>Marked_mark(filter(X1,X2,X3))</LHS><RHS>Marked_mark(X2)</RHS></DPRULE><DPRULE num="8"><LHS>Marked_mark(filter(X1,X2,X3))</LHS><RHS>Marked_mark(X3)</RHS></DPRULE><DPRULE num="9"><LHS>Marked_mark(cons(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="10"><LHS>Marked_mark(s(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="11"><LHS>Marked_mark(sieve(X))</LHS><RHS>Marked_active(sieve(mark(X)))</RHS></DPRULE><DPRULE num="12"><LHS>Marked_mark(sieve(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="13"><LHS>Marked_mark(nats(X))</LHS><RHS>Marked_active(nats(mark(X)))</RHS></DPRULE><DPRULE num="14"><LHS>Marked_mark(nats(X))</LHS><RHS>Marked_mark(X)</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"/><NODE ref="7"/><NODE ref="8"/><NODE ref="9"/><NODE ref="10"/><NODE ref="11"/><NODE ref="12"/><NODE ref="13"/><NODE ref="14"/></SCC></CCLIST></DAG></CRITERION><PROPERTY criterion="stronggraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(filter(cons(X,Y),0,M))</LHS><RHS>mark(cons(0,filter(Y,M,M)))</RHS></RULE><RULE><LHS>active(filter(cons(X,Y),s(N),M))</LHS><RHS>mark(cons(X,filter(Y,N,M)))</RHS></RULE><RULE><LHS>active(sieve(cons(0,Y)))</LHS><RHS>mark(cons(0,sieve(Y)))</RHS></RULE><RULE><LHS>active(sieve(cons(s(N),Y)))</LHS><RHS>mark(cons(s(N),sieve(filter(Y,N,N))))</RHS></RULE><RULE><LHS>active(nats(N))</LHS><RHS>mark(cons(N,nats(s(N))))</RHS></RULE><RULE><LHS>active(zprimes)</LHS><RHS>mark(sieve(nats(s(s(0)))))</RHS></RULE><RULE><LHS>mark(filter(X1,X2,X3))</LHS><RHS>active(filter(mark(X1),mark(X2),mark(X3)))</RHS></RULE><RULE><LHS>mark(cons(X1,X2))</LHS><RHS>active(cons(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(mark(X)))</RHS></RULE><RULE><LHS>mark(sieve(X))</LHS><RHS>active(sieve(mark(X)))</RHS></RULE><RULE><LHS>mark(nats(X))</LHS><RHS>active(nats(mark(X)))</RHS></RULE><RULE><LHS>mark(zprimes)</LHS><RHS>active(zprimes)</RHS></RULE><RULE><LHS>filter(mark(X1),X2,X3)</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(X1,mark(X2),X3)</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(X1,X2,mark(X3))</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(active(X1),X2,X3)</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(X1,active(X2),X3)</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(X1,X2,active(X3))</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>cons(mark(X1),X2)</LHS><RHS>cons(X1,X2)</RHS></RULE><RULE><LHS>cons(X1,mark(X2))</LHS><RHS>cons(X1,X2)</RHS></RULE><RULE><LHS>cons(active(X1),X2)</LHS><RHS>cons(X1,X2)</RHS></RULE><RULE><LHS>cons(X1,active(X2))</LHS><RHS>cons(X1,X2)</RHS></RULE><RULE><LHS>s(mark(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>s(active(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>sieve(mark(X))</LHS><RHS>sieve(X)</RHS></RULE><RULE><LHS>sieve(active(X))</LHS><RHS>sieve(X)</RHS></RULE><RULE><LHS>nats(mark(X))</LHS><RHS>nats(X)</RHS></RULE><RULE><LHS>nats(active(X))</LHS><RHS>nats(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_active(filter(cons(X,Y),0,M))</LHS><RHS>Marked_mark(cons(0,filter(Y,M,M)))</RHS></DPRULE><DPRULE num="1"><LHS>Marked_active(filter(cons(X,Y),s(N),M))</LHS><RHS>Marked_mark(cons(X,filter(Y,N,M)))</RHS></DPRULE><DPRULE num="2"><LHS>Marked_active(sieve(cons(0,Y)))</LHS><RHS>Marked_mark(cons(0,sieve(Y)))</RHS></DPRULE><DPRULE num="3"><LHS>Marked_active(sieve(cons(s(N),Y)))</LHS><RHS>Marked_mark(cons(s(N),sieve(filter(Y,N,N))))</RHS></DPRULE><DPRULE num="4"><LHS>Marked_active(nats(N))</LHS><RHS>Marked_mark(cons(N,nats(s(N))))</RHS></DPRULE><DPRULE num="5"><LHS>Marked_mark(filter(X1,X2,X3))</LHS><RHS>Marked_active(filter(mark(X1),mark(X2),mark(X3)))</RHS></DPRULE><DPRULE num="6"><LHS>Marked_mark(filter(X1,X2,X3))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="7"><LHS>Marked_mark(filter(X1,X2,X3))</LHS><RHS>Marked_mark(X2)</RHS></DPRULE><DPRULE num="8"><LHS>Marked_mark(filter(X1,X2,X3))</LHS><RHS>Marked_mark(X3)</RHS></DPRULE><DPRULE num="9"><LHS>Marked_mark(cons(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="10"><LHS>Marked_mark(s(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="11"><LHS>Marked_mark(sieve(X))</LHS><RHS>Marked_active(sieve(mark(X)))</RHS></DPRULE><DPRULE num="12"><LHS>Marked_mark(sieve(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="13"><LHS>Marked_mark(nats(X))</LHS><RHS>Marked_active(nats(mark(X)))</RHS></DPRULE><DPRULE num="14"><LHS>Marked_mark(nats(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><ORDERING type="poly"><POLYSYMB><SYMBOL><NAME>mark</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>zprimes</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>active</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>0</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>sieve</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>Marked_mark</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>cons</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>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>filter</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><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>nats</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><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>Marked_active</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></ORDERING><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_active(nats(N))</LHS><RHS>Marked_mark(cons(N,nats(s(N))))</RHS></DPRULE><DPRULE num="1"><LHS>Marked_mark(nats(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE></DPLIST></STRICTPAIRS></CRITERION><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(filter(cons(X,Y),0,M))</LHS><RHS>mark(cons(0,filter(Y,M,M)))</RHS></RULE><RULE><LHS>active(filter(cons(X,Y),s(N),M))</LHS><RHS>mark(cons(X,filter(Y,N,M)))</RHS></RULE><RULE><LHS>active(sieve(cons(0,Y)))</LHS><RHS>mark(cons(0,sieve(Y)))</RHS></RULE><RULE><LHS>active(sieve(cons(s(N),Y)))</LHS><RHS>mark(cons(s(N),sieve(filter(Y,N,N))))</RHS></RULE><RULE><LHS>active(nats(N))</LHS><RHS>mark(cons(N,nats(s(N))))</RHS></RULE><RULE><LHS>active(zprimes)</LHS><RHS>mark(sieve(nats(s(s(0)))))</RHS></RULE><RULE><LHS>mark(filter(X1,X2,X3))</LHS><RHS>active(filter(mark(X1),mark(X2),mark(X3)))</RHS></RULE><RULE><LHS>mark(cons(X1,X2))</LHS><RHS>active(cons(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(mark(X)))</RHS></RULE><RULE><LHS>mark(sieve(X))</LHS><RHS>active(sieve(mark(X)))</RHS></RULE><RULE><LHS>mark(nats(X))</LHS><RHS>active(nats(mark(X)))</RHS></RULE><RULE><LHS>mark(zprimes)</LHS><RHS>active(zprimes)</RHS></RULE><RULE><LHS>filter(mark(X1),X2,X3)</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(X1,mark(X2),X3)</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(X1,X2,mark(X3))</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(active(X1),X2,X3)</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(X1,active(X2),X3)</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(X1,X2,active(X3))</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>cons(mark(X1),X2)</LHS><RHS>cons(X1,X2)</RHS></RULE><RULE><LHS>cons(X1,mark(X2))</LHS><RHS>cons(X1,X2)</RHS></RULE><RULE><LHS>cons(active(X1),X2)</LHS><RHS>cons(X1,X2)</RHS></RULE><RULE><LHS>cons(X1,active(X2))</LHS><RHS>cons(X1,X2)</RHS></RULE><RULE><LHS>s(mark(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>s(active(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>sieve(mark(X))</LHS><RHS>sieve(X)</RHS></RULE><RULE><LHS>sieve(active(X))</LHS><RHS>sieve(X)</RHS></RULE><RULE><LHS>nats(mark(X))</LHS><RHS>nats(X)</RHS></RULE><RULE><LHS>nats(active(X))</LHS><RHS>nats(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_active(filter(cons(X,Y),0,M))</LHS><RHS>Marked_mark(cons(0,filter(Y,M,M)))</RHS></DPRULE><DPRULE num="1"><LHS>Marked_active(filter(cons(X,Y),s(N),M))</LHS><RHS>Marked_mark(cons(X,filter(Y,N,M)))</RHS></DPRULE><DPRULE num="2"><LHS>Marked_active(sieve(cons(0,Y)))</LHS><RHS>Marked_mark(cons(0,sieve(Y)))</RHS></DPRULE><DPRULE num="3"><LHS>Marked_active(sieve(cons(s(N),Y)))</LHS><RHS>Marked_mark(cons(s(N),sieve(filter(Y,N,N))))</RHS></DPRULE><DPRULE num="4"><LHS>Marked_mark(filter(X1,X2,X3))</LHS><RHS>Marked_active(filter(mark(X1),mark(X2),mark(X3)))</RHS></DPRULE><DPRULE num="5"><LHS>Marked_mark(filter(X1,X2,X3))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="6"><LHS>Marked_mark(filter(X1,X2,X3))</LHS><RHS>Marked_mark(X2)</RHS></DPRULE><DPRULE num="7"><LHS>Marked_mark(filter(X1,X2,X3))</LHS><RHS>Marked_mark(X3)</RHS></DPRULE><DPRULE num="8"><LHS>Marked_mark(cons(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="9"><LHS>Marked_mark(s(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="10"><LHS>Marked_mark(sieve(X))</LHS><RHS>Marked_active(sieve(mark(X)))</RHS></DPRULE><DPRULE num="11"><LHS>Marked_mark(sieve(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="12"><LHS>Marked_mark(nats(X))</LHS><RHS>Marked_active(nats(mark(X)))</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"/><NODE ref="7"/><NODE ref="8"/><NODE ref="9"/><NODE ref="10"/><NODE ref="11"/><NODE ref="12"/></SCC></CCLIST></DAG></CRITERION><PROPERTY criterion="stronggraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(filter(cons(X,Y),0,M))</LHS><RHS>mark(cons(0,filter(Y,M,M)))</RHS></RULE><RULE><LHS>active(filter(cons(X,Y),s(N),M))</LHS><RHS>mark(cons(X,filter(Y,N,M)))</RHS></RULE><RULE><LHS>active(sieve(cons(0,Y)))</LHS><RHS>mark(cons(0,sieve(Y)))</RHS></RULE><RULE><LHS>active(sieve(cons(s(N),Y)))</LHS><RHS>mark(cons(s(N),sieve(filter(Y,N,N))))</RHS></RULE><RULE><LHS>active(nats(N))</LHS><RHS>mark(cons(N,nats(s(N))))</RHS></RULE><RULE><LHS>active(zprimes)</LHS><RHS>mark(sieve(nats(s(s(0)))))</RHS></RULE><RULE><LHS>mark(filter(X1,X2,X3))</LHS><RHS>active(filter(mark(X1),mark(X2),mark(X3)))</RHS></RULE><RULE><LHS>mark(cons(X1,X2))</LHS><RHS>active(cons(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(mark(X)))</RHS></RULE><RULE><LHS>mark(sieve(X))</LHS><RHS>active(sieve(mark(X)))</RHS></RULE><RULE><LHS>mark(nats(X))</LHS><RHS>active(nats(mark(X)))</RHS></RULE><RULE><LHS>mark(zprimes)</LHS><RHS>active(zprimes)</RHS></RULE><RULE><LHS>filter(mark(X1),X2,X3)</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(X1,mark(X2),X3)</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(X1,X2,mark(X3))</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(active(X1),X2,X3)</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(X1,active(X2),X3)</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(X1,X2,active(X3))</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>cons(mark(X1),X2)</LHS><RHS>cons(X1,X2)</RHS></RULE><RULE><LHS>cons(X1,mark(X2))</LHS><RHS>cons(X1,X2)</RHS></RULE><RULE><LHS>cons(active(X1),X2)</LHS><RHS>cons(X1,X2)</RHS></RULE><RULE><LHS>cons(X1,active(X2))</LHS><RHS>cons(X1,X2)</RHS></RULE><RULE><LHS>s(mark(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>s(active(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>sieve(mark(X))</LHS><RHS>sieve(X)</RHS></RULE><RULE><LHS>sieve(active(X))</LHS><RHS>sieve(X)</RHS></RULE><RULE><LHS>nats(mark(X))</LHS><RHS>nats(X)</RHS></RULE><RULE><LHS>nats(active(X))</LHS><RHS>nats(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_active(filter(cons(X,Y),0,M))</LHS><RHS>Marked_mark(cons(0,filter(Y,M,M)))</RHS></DPRULE><DPRULE num="1"><LHS>Marked_active(filter(cons(X,Y),s(N),M))</LHS><RHS>Marked_mark(cons(X,filter(Y,N,M)))</RHS></DPRULE><DPRULE num="2"><LHS>Marked_active(sieve(cons(0,Y)))</LHS><RHS>Marked_mark(cons(0,sieve(Y)))</RHS></DPRULE><DPRULE num="3"><LHS>Marked_active(sieve(cons(s(N),Y)))</LHS><RHS>Marked_mark(cons(s(N),sieve(filter(Y,N,N))))</RHS></DPRULE><DPRULE num="4"><LHS>Marked_mark(filter(X1,X2,X3))</LHS><RHS>Marked_active(filter(mark(X1),mark(X2),mark(X3)))</RHS></DPRULE><DPRULE num="5"><LHS>Marked_mark(filter(X1,X2,X3))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="6"><LHS>Marked_mark(filter(X1,X2,X3))</LHS><RHS>Marked_mark(X2)</RHS></DPRULE><DPRULE num="7"><LHS>Marked_mark(filter(X1,X2,X3))</LHS><RHS>Marked_mark(X3)</RHS></DPRULE><DPRULE num="8"><LHS>Marked_mark(cons(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="9"><LHS>Marked_mark(s(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="10"><LHS>Marked_mark(sieve(X))</LHS><RHS>Marked_active(sieve(mark(X)))</RHS></DPRULE><DPRULE num="11"><LHS>Marked_mark(sieve(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="12"><LHS>Marked_mark(nats(X))</LHS><RHS>Marked_active(nats(mark(X)))</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><ORDERING type="poly"><POLYSYMB><SYMBOL><NAME>mark</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>zprimes</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>active</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>0</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>sieve</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><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>Marked_mark</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>cons</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>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>filter</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><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></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>nats</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>Marked_active</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></ORDERING><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_active(sieve(cons(0,Y)))</LHS><RHS>Marked_mark(cons(0,sieve(Y)))</RHS></DPRULE><DPRULE num="1"><LHS>Marked_active(sieve(cons(s(N),Y)))</LHS><RHS>Marked_mark(cons(s(N),sieve(filter(Y,N,N))))</RHS></DPRULE><DPRULE num="2"><LHS>Marked_mark(sieve(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE></DPLIST></STRICTPAIRS></CRITERION><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(filter(cons(X,Y),0,M))</LHS><RHS>mark(cons(0,filter(Y,M,M)))</RHS></RULE><RULE><LHS>active(filter(cons(X,Y),s(N),M))</LHS><RHS>mark(cons(X,filter(Y,N,M)))</RHS></RULE><RULE><LHS>active(sieve(cons(0,Y)))</LHS><RHS>mark(cons(0,sieve(Y)))</RHS></RULE><RULE><LHS>active(sieve(cons(s(N),Y)))</LHS><RHS>mark(cons(s(N),sieve(filter(Y,N,N))))</RHS></RULE><RULE><LHS>active(nats(N))</LHS><RHS>mark(cons(N,nats(s(N))))</RHS></RULE><RULE><LHS>active(zprimes)</LHS><RHS>mark(sieve(nats(s(s(0)))))</RHS></RULE><RULE><LHS>mark(filter(X1,X2,X3))</LHS><RHS>active(filter(mark(X1),mark(X2),mark(X3)))</RHS></RULE><RULE><LHS>mark(cons(X1,X2))</LHS><RHS>active(cons(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(mark(X)))</RHS></RULE><RULE><LHS>mark(sieve(X))</LHS><RHS>active(sieve(mark(X)))</RHS></RULE><RULE><LHS>mark(nats(X))</LHS><RHS>active(nats(mark(X)))</RHS></RULE><RULE><LHS>mark(zprimes)</LHS><RHS>active(zprimes)</RHS></RULE><RULE><LHS>filter(mark(X1),X2,X3)</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(X1,mark(X2),X3)</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(X1,X2,mark(X3))</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(active(X1),X2,X3)</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(X1,active(X2),X3)</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(X1,X2,active(X3))</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>cons(mark(X1),X2)</LHS><RHS>cons(X1,X2)</RHS></RULE><RULE><LHS>cons(X1,mark(X2))</LHS><RHS>cons(X1,X2)</RHS></RULE><RULE><LHS>cons(active(X1),X2)</LHS><RHS>cons(X1,X2)</RHS></RULE><RULE><LHS>cons(X1,active(X2))</LHS><RHS>cons(X1,X2)</RHS></RULE><RULE><LHS>s(mark(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>s(active(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>sieve(mark(X))</LHS><RHS>sieve(X)</RHS></RULE><RULE><LHS>sieve(active(X))</LHS><RHS>sieve(X)</RHS></RULE><RULE><LHS>nats(mark(X))</LHS><RHS>nats(X)</RHS></RULE><RULE><LHS>nats(active(X))</LHS><RHS>nats(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_active(filter(cons(X,Y),0,M))</LHS><RHS>Marked_mark(cons(0,filter(Y,M,M)))</RHS></DPRULE><DPRULE num="1"><LHS>Marked_active(filter(cons(X,Y),s(N),M))</LHS><RHS>Marked_mark(cons(X,filter(Y,N,M)))</RHS></DPRULE><DPRULE num="2"><LHS>Marked_mark(filter(X1,X2,X3))</LHS><RHS>Marked_active(filter(mark(X1),mark(X2),mark(X3)))</RHS></DPRULE><DPRULE num="3"><LHS>Marked_mark(filter(X1,X2,X3))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="4"><LHS>Marked_mark(filter(X1,X2,X3))</LHS><RHS>Marked_mark(X2)</RHS></DPRULE><DPRULE num="5"><LHS>Marked_mark(filter(X1,X2,X3))</LHS><RHS>Marked_mark(X3)</RHS></DPRULE><DPRULE num="6"><LHS>Marked_mark(cons(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="7"><LHS>Marked_mark(s(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="8"><LHS>Marked_mark(sieve(X))</LHS><RHS>Marked_active(sieve(mark(X)))</RHS></DPRULE><DPRULE num="9"><LHS>Marked_mark(nats(X))</LHS><RHS>Marked_active(nats(mark(X)))</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"/><NODE ref="7"/><NODE ref="8"/><NODE ref="9"/></SCC></CCLIST></DAG></CRITERION><PROPERTY criterion="stronggraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(filter(cons(X,Y),0,M))</LHS><RHS>mark(cons(0,filter(Y,M,M)))</RHS></RULE><RULE><LHS>active(filter(cons(X,Y),s(N),M))</LHS><RHS>mark(cons(X,filter(Y,N,M)))</RHS></RULE><RULE><LHS>active(sieve(cons(0,Y)))</LHS><RHS>mark(cons(0,sieve(Y)))</RHS></RULE><RULE><LHS>active(sieve(cons(s(N),Y)))</LHS><RHS>mark(cons(s(N),sieve(filter(Y,N,N))))</RHS></RULE><RULE><LHS>active(nats(N))</LHS><RHS>mark(cons(N,nats(s(N))))</RHS></RULE><RULE><LHS>active(zprimes)</LHS><RHS>mark(sieve(nats(s(s(0)))))</RHS></RULE><RULE><LHS>mark(filter(X1,X2,X3))</LHS><RHS>active(filter(mark(X1),mark(X2),mark(X3)))</RHS></RULE><RULE><LHS>mark(cons(X1,X2))</LHS><RHS>active(cons(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(mark(X)))</RHS></RULE><RULE><LHS>mark(sieve(X))</LHS><RHS>active(sieve(mark(X)))</RHS></RULE><RULE><LHS>mark(nats(X))</LHS><RHS>active(nats(mark(X)))</RHS></RULE><RULE><LHS>mark(zprimes)</LHS><RHS>active(zprimes)</RHS></RULE><RULE><LHS>filter(mark(X1),X2,X3)</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(X1,mark(X2),X3)</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(X1,X2,mark(X3))</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(active(X1),X2,X3)</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(X1,active(X2),X3)</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(X1,X2,active(X3))</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>cons(mark(X1),X2)</LHS><RHS>cons(X1,X2)</RHS></RULE><RULE><LHS>cons(X1,mark(X2))</LHS><RHS>cons(X1,X2)</RHS></RULE><RULE><LHS>cons(active(X1),X2)</LHS><RHS>cons(X1,X2)</RHS></RULE><RULE><LHS>cons(X1,active(X2))</LHS><RHS>cons(X1,X2)</RHS></RULE><RULE><LHS>s(mark(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>s(active(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>sieve(mark(X))</LHS><RHS>sieve(X)</RHS></RULE><RULE><LHS>sieve(active(X))</LHS><RHS>sieve(X)</RHS></RULE><RULE><LHS>nats(mark(X))</LHS><RHS>nats(X)</RHS></RULE><RULE><LHS>nats(active(X))</LHS><RHS>nats(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_active(filter(cons(X,Y),0,M))</LHS><RHS>Marked_mark(cons(0,filter(Y,M,M)))</RHS></DPRULE><DPRULE num="1"><LHS>Marked_active(filter(cons(X,Y),s(N),M))</LHS><RHS>Marked_mark(cons(X,filter(Y,N,M)))</RHS></DPRULE><DPRULE num="2"><LHS>Marked_mark(filter(X1,X2,X3))</LHS><RHS>Marked_active(filter(mark(X1),mark(X2),mark(X3)))</RHS></DPRULE><DPRULE num="3"><LHS>Marked_mark(filter(X1,X2,X3))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="4"><LHS>Marked_mark(filter(X1,X2,X3))</LHS><RHS>Marked_mark(X2)</RHS></DPRULE><DPRULE num="5"><LHS>Marked_mark(filter(X1,X2,X3))</LHS><RHS>Marked_mark(X3)</RHS></DPRULE><DPRULE num="6"><LHS>Marked_mark(cons(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="7"><LHS>Marked_mark(s(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="8"><LHS>Marked_mark(sieve(X))</LHS><RHS>Marked_active(sieve(mark(X)))</RHS></DPRULE><DPRULE num="9"><LHS>Marked_mark(nats(X))</LHS><RHS>Marked_active(nats(mark(X)))</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><ORDERING type="poly"><POLYSYMB><SYMBOL><NAME>mark</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>zprimes</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>active</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>sieve</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>Marked_mark</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><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>filter</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>nats</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>Marked_active</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></ORDERING><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_mark(sieve(X))</LHS><RHS>Marked_active(sieve(mark(X)))</RHS></DPRULE><DPRULE num="1"><LHS>Marked_mark(nats(X))</LHS><RHS>Marked_active(nats(mark(X)))</RHS></DPRULE></DPLIST></STRICTPAIRS></CRITERION><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(filter(cons(X,Y),0,M))</LHS><RHS>mark(cons(0,filter(Y,M,M)))</RHS></RULE><RULE><LHS>active(filter(cons(X,Y),s(N),M))</LHS><RHS>mark(cons(X,filter(Y,N,M)))</RHS></RULE><RULE><LHS>active(sieve(cons(0,Y)))</LHS><RHS>mark(cons(0,sieve(Y)))</RHS></RULE><RULE><LHS>active(sieve(cons(s(N),Y)))</LHS><RHS>mark(cons(s(N),sieve(filter(Y,N,N))))</RHS></RULE><RULE><LHS>active(nats(N))</LHS><RHS>mark(cons(N,nats(s(N))))</RHS></RULE><RULE><LHS>active(zprimes)</LHS><RHS>mark(sieve(nats(s(s(0)))))</RHS></RULE><RULE><LHS>mark(filter(X1,X2,X3))</LHS><RHS>active(filter(mark(X1),mark(X2),mark(X3)))</RHS></RULE><RULE><LHS>mark(cons(X1,X2))</LHS><RHS>active(cons(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(mark(X)))</RHS></RULE><RULE><LHS>mark(sieve(X))</LHS><RHS>active(sieve(mark(X)))</RHS></RULE><RULE><LHS>mark(nats(X))</LHS><RHS>active(nats(mark(X)))</RHS></RULE><RULE><LHS>mark(zprimes)</LHS><RHS>active(zprimes)</RHS></RULE><RULE><LHS>filter(mark(X1),X2,X3)</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(X1,mark(X2),X3)</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(X1,X2,mark(X3))</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(active(X1),X2,X3)</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(X1,active(X2),X3)</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(X1,X2,active(X3))</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>cons(mark(X1),X2)</LHS><RHS>cons(X1,X2)</RHS></RULE><RULE><LHS>cons(X1,mark(X2))</LHS><RHS>cons(X1,X2)</RHS></RULE><RULE><LHS>cons(active(X1),X2)</LHS><RHS>cons(X1,X2)</RHS></RULE><RULE><LHS>cons(X1,active(X2))</LHS><RHS>cons(X1,X2)</RHS></RULE><RULE><LHS>s(mark(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>s(active(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>sieve(mark(X))</LHS><RHS>sieve(X)</RHS></RULE><RULE><LHS>sieve(active(X))</LHS><RHS>sieve(X)</RHS></RULE><RULE><LHS>nats(mark(X))</LHS><RHS>nats(X)</RHS></RULE><RULE><LHS>nats(active(X))</LHS><RHS>nats(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_active(filter(cons(X,Y),0,M))</LHS><RHS>Marked_mark(cons(0,filter(Y,M,M)))</RHS></DPRULE><DPRULE num="1"><LHS>Marked_active(filter(cons(X,Y),s(N),M))</LHS><RHS>Marked_mark(cons(X,filter(Y,N,M)))</RHS></DPRULE><DPRULE num="2"><LHS>Marked_mark(filter(X1,X2,X3))</LHS><RHS>Marked_active(filter(mark(X1),mark(X2),mark(X3)))</RHS></DPRULE><DPRULE num="3"><LHS>Marked_mark(filter(X1,X2,X3))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="4"><LHS>Marked_mark(filter(X1,X2,X3))</LHS><RHS>Marked_mark(X2)</RHS></DPRULE><DPRULE num="5"><LHS>Marked_mark(filter(X1,X2,X3))</LHS><RHS>Marked_mark(X3)</RHS></DPRULE><DPRULE num="6"><LHS>Marked_mark(cons(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="7"><LHS>Marked_mark(s(X))</LHS><RHS>Marked_mark(X)</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"/><NODE ref="7"/></SCC></CCLIST></DAG></CRITERION><PROPERTY criterion="stronggraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(filter(cons(X,Y),0,M))</LHS><RHS>mark(cons(0,filter(Y,M,M)))</RHS></RULE><RULE><LHS>active(filter(cons(X,Y),s(N),M))</LHS><RHS>mark(cons(X,filter(Y,N,M)))</RHS></RULE><RULE><LHS>active(sieve(cons(0,Y)))</LHS><RHS>mark(cons(0,sieve(Y)))</RHS></RULE><RULE><LHS>active(sieve(cons(s(N),Y)))</LHS><RHS>mark(cons(s(N),sieve(filter(Y,N,N))))</RHS></RULE><RULE><LHS>active(nats(N))</LHS><RHS>mark(cons(N,nats(s(N))))</RHS></RULE><RULE><LHS>active(zprimes)</LHS><RHS>mark(sieve(nats(s(s(0)))))</RHS></RULE><RULE><LHS>mark(filter(X1,X2,X3))</LHS><RHS>active(filter(mark(X1),mark(X2),mark(X3)))</RHS></RULE><RULE><LHS>mark(cons(X1,X2))</LHS><RHS>active(cons(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(mark(X)))</RHS></RULE><RULE><LHS>mark(sieve(X))</LHS><RHS>active(sieve(mark(X)))</RHS></RULE><RULE><LHS>mark(nats(X))</LHS><RHS>active(nats(mark(X)))</RHS></RULE><RULE><LHS>mark(zprimes)</LHS><RHS>active(zprimes)</RHS></RULE><RULE><LHS>filter(mark(X1),X2,X3)</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(X1,mark(X2),X3)</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(X1,X2,mark(X3))</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(active(X1),X2,X3)</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(X1,active(X2),X3)</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(X1,X2,active(X3))</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>cons(mark(X1),X2)</LHS><RHS>cons(X1,X2)</RHS></RULE><RULE><LHS>cons(X1,mark(X2))</LHS><RHS>cons(X1,X2)</RHS></RULE><RULE><LHS>cons(active(X1),X2)</LHS><RHS>cons(X1,X2)</RHS></RULE><RULE><LHS>cons(X1,active(X2))</LHS><RHS>cons(X1,X2)</RHS></RULE><RULE><LHS>s(mark(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>s(active(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>sieve(mark(X))</LHS><RHS>sieve(X)</RHS></RULE><RULE><LHS>sieve(active(X))</LHS><RHS>sieve(X)</RHS></RULE><RULE><LHS>nats(mark(X))</LHS><RHS>nats(X)</RHS></RULE><RULE><LHS>nats(active(X))</LHS><RHS>nats(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_active(filter(cons(X,Y),0,M))</LHS><RHS>Marked_mark(cons(0,filter(Y,M,M)))</RHS></DPRULE><DPRULE num="1"><LHS>Marked_active(filter(cons(X,Y),s(N),M))</LHS><RHS>Marked_mark(cons(X,filter(Y,N,M)))</RHS></DPRULE><DPRULE num="2"><LHS>Marked_mark(filter(X1,X2,X3))</LHS><RHS>Marked_active(filter(mark(X1),mark(X2),mark(X3)))</RHS></DPRULE><DPRULE num="3"><LHS>Marked_mark(filter(X1,X2,X3))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="4"><LHS>Marked_mark(filter(X1,X2,X3))</LHS><RHS>Marked_mark(X2)</RHS></DPRULE><DPRULE num="5"><LHS>Marked_mark(filter(X1,X2,X3))</LHS><RHS>Marked_mark(X3)</RHS></DPRULE><DPRULE num="6"><LHS>Marked_mark(cons(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="7"><LHS>Marked_mark(s(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><ORDERING type="poly"><POLYSYMB><SYMBOL><NAME>mark</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>zprimes</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>active</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>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>sieve</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>Marked_mark</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><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="0"/></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>filter</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>1</INT></COEF><ARG degree="1" num="2"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>nats</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>Marked_active</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><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB></ORDERING><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_active(filter(cons(X,Y),0,M))</LHS><RHS>Marked_mark(cons(0,filter(Y,M,M)))</RHS></DPRULE></DPLIST></STRICTPAIRS></CRITERION><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(filter(cons(X,Y),0,M))</LHS><RHS>mark(cons(0,filter(Y,M,M)))</RHS></RULE><RULE><LHS>active(filter(cons(X,Y),s(N),M))</LHS><RHS>mark(cons(X,filter(Y,N,M)))</RHS></RULE><RULE><LHS>active(sieve(cons(0,Y)))</LHS><RHS>mark(cons(0,sieve(Y)))</RHS></RULE><RULE><LHS>active(sieve(cons(s(N),Y)))</LHS><RHS>mark(cons(s(N),sieve(filter(Y,N,N))))</RHS></RULE><RULE><LHS>active(nats(N))</LHS><RHS>mark(cons(N,nats(s(N))))</RHS></RULE><RULE><LHS>active(zprimes)</LHS><RHS>mark(sieve(nats(s(s(0)))))</RHS></RULE><RULE><LHS>mark(filter(X1,X2,X3))</LHS><RHS>active(filter(mark(X1),mark(X2),mark(X3)))</RHS></RULE><RULE><LHS>mark(cons(X1,X2))</LHS><RHS>active(cons(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(mark(X)))</RHS></RULE><RULE><LHS>mark(sieve(X))</LHS><RHS>active(sieve(mark(X)))</RHS></RULE><RULE><LHS>mark(nats(X))</LHS><RHS>active(nats(mark(X)))</RHS></RULE><RULE><LHS>mark(zprimes)</LHS><RHS>active(zprimes)</RHS></RULE><RULE><LHS>filter(mark(X1),X2,X3)</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(X1,mark(X2),X3)</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(X1,X2,mark(X3))</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(active(X1),X2,X3)</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(X1,active(X2),X3)</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(X1,X2,active(X3))</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>cons(mark(X1),X2)</LHS><RHS>cons(X1,X2)</RHS></RULE><RULE><LHS>cons(X1,mark(X2))</LHS><RHS>cons(X1,X2)</RHS></RULE><RULE><LHS>cons(active(X1),X2)</LHS><RHS>cons(X1,X2)</RHS></RULE><RULE><LHS>cons(X1,active(X2))</LHS><RHS>cons(X1,X2)</RHS></RULE><RULE><LHS>s(mark(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>s(active(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>sieve(mark(X))</LHS><RHS>sieve(X)</RHS></RULE><RULE><LHS>sieve(active(X))</LHS><RHS>sieve(X)</RHS></RULE><RULE><LHS>nats(mark(X))</LHS><RHS>nats(X)</RHS></RULE><RULE><LHS>nats(active(X))</LHS><RHS>nats(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_active(filter(cons(X,Y),s(N),M))</LHS><RHS>Marked_mark(cons(X,filter(Y,N,M)))</RHS></DPRULE><DPRULE num="1"><LHS>Marked_mark(filter(X1,X2,X3))</LHS><RHS>Marked_active(filter(mark(X1),mark(X2),mark(X3)))</RHS></DPRULE><DPRULE num="2"><LHS>Marked_mark(filter(X1,X2,X3))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="3"><LHS>Marked_mark(filter(X1,X2,X3))</LHS><RHS>Marked_mark(X2)</RHS></DPRULE><DPRULE num="4"><LHS>Marked_mark(filter(X1,X2,X3))</LHS><RHS>Marked_mark(X3)</RHS></DPRULE><DPRULE num="5"><LHS>Marked_mark(cons(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="6"><LHS>Marked_mark(s(X))</LHS><RHS>Marked_mark(X)</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>active(filter(cons(X,Y),0,M))</LHS><RHS>mark(cons(0,filter(Y,M,M)))</RHS></RULE><RULE><LHS>active(filter(cons(X,Y),s(N),M))</LHS><RHS>mark(cons(X,filter(Y,N,M)))</RHS></RULE><RULE><LHS>active(sieve(cons(0,Y)))</LHS><RHS>mark(cons(0,sieve(Y)))</RHS></RULE><RULE><LHS>active(sieve(cons(s(N),Y)))</LHS><RHS>mark(cons(s(N),sieve(filter(Y,N,N))))</RHS></RULE><RULE><LHS>active(nats(N))</LHS><RHS>mark(cons(N,nats(s(N))))</RHS></RULE><RULE><LHS>active(zprimes)</LHS><RHS>mark(sieve(nats(s(s(0)))))</RHS></RULE><RULE><LHS>mark(filter(X1,X2,X3))</LHS><RHS>active(filter(mark(X1),mark(X2),mark(X3)))</RHS></RULE><RULE><LHS>mark(cons(X1,X2))</LHS><RHS>active(cons(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(mark(X)))</RHS></RULE><RULE><LHS>mark(sieve(X))</LHS><RHS>active(sieve(mark(X)))</RHS></RULE><RULE><LHS>mark(nats(X))</LHS><RHS>active(nats(mark(X)))</RHS></RULE><RULE><LHS>mark(zprimes)</LHS><RHS>active(zprimes)</RHS></RULE><RULE><LHS>filter(mark(X1),X2,X3)</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(X1,mark(X2),X3)</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(X1,X2,mark(X3))</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(active(X1),X2,X3)</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(X1,active(X2),X3)</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(X1,X2,active(X3))</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>cons(mark(X1),X2)</LHS><RHS>cons(X1,X2)</RHS></RULE><RULE><LHS>cons(X1,mark(X2))</LHS><RHS>cons(X1,X2)</RHS></RULE><RULE><LHS>cons(active(X1),X2)</LHS><RHS>cons(X1,X2)</RHS></RULE><RULE><LHS>cons(X1,active(X2))</LHS><RHS>cons(X1,X2)</RHS></RULE><RULE><LHS>s(mark(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>s(active(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>sieve(mark(X))</LHS><RHS>sieve(X)</RHS></RULE><RULE><LHS>sieve(active(X))</LHS><RHS>sieve(X)</RHS></RULE><RULE><LHS>nats(mark(X))</LHS><RHS>nats(X)</RHS></RULE><RULE><LHS>nats(active(X))</LHS><RHS>nats(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_active(filter(cons(X,Y),s(N),M))</LHS><RHS>Marked_mark(cons(X,filter(Y,N,M)))</RHS></DPRULE><DPRULE num="1"><LHS>Marked_mark(filter(X1,X2,X3))</LHS><RHS>Marked_active(filter(mark(X1),mark(X2),mark(X3)))</RHS></DPRULE><DPRULE num="2"><LHS>Marked_mark(filter(X1,X2,X3))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="3"><LHS>Marked_mark(filter(X1,X2,X3))</LHS><RHS>Marked_mark(X2)</RHS></DPRULE><DPRULE num="4"><LHS>Marked_mark(filter(X1,X2,X3))</LHS><RHS>Marked_mark(X3)</RHS></DPRULE><DPRULE num="5"><LHS>Marked_mark(cons(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="6"><LHS>Marked_mark(s(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><ORDERING type="poly"><POLYSYMB><SYMBOL><NAME>mark</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>zprimes</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>active</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>0</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>sieve</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>Marked_mark</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>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="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></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>filter</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><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>nats</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_active</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></ORDERING><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_active(filter(cons(X,Y),s(N),M))</LHS><RHS>Marked_mark(cons(X,filter(Y,N,M)))</RHS></DPRULE><DPRULE num="1"><LHS>Marked_mark(cons(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE></DPLIST></STRICTPAIRS></CRITERION><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(filter(cons(X,Y),0,M))</LHS><RHS>mark(cons(0,filter(Y,M,M)))</RHS></RULE><RULE><LHS>active(filter(cons(X,Y),s(N),M))</LHS><RHS>mark(cons(X,filter(Y,N,M)))</RHS></RULE><RULE><LHS>active(sieve(cons(0,Y)))</LHS><RHS>mark(cons(0,sieve(Y)))</RHS></RULE><RULE><LHS>active(sieve(cons(s(N),Y)))</LHS><RHS>mark(cons(s(N),sieve(filter(Y,N,N))))</RHS></RULE><RULE><LHS>active(nats(N))</LHS><RHS>mark(cons(N,nats(s(N))))</RHS></RULE><RULE><LHS>active(zprimes)</LHS><RHS>mark(sieve(nats(s(s(0)))))</RHS></RULE><RULE><LHS>mark(filter(X1,X2,X3))</LHS><RHS>active(filter(mark(X1),mark(X2),mark(X3)))</RHS></RULE><RULE><LHS>mark(cons(X1,X2))</LHS><RHS>active(cons(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(mark(X)))</RHS></RULE><RULE><LHS>mark(sieve(X))</LHS><RHS>active(sieve(mark(X)))</RHS></RULE><RULE><LHS>mark(nats(X))</LHS><RHS>active(nats(mark(X)))</RHS></RULE><RULE><LHS>mark(zprimes)</LHS><RHS>active(zprimes)</RHS></RULE><RULE><LHS>filter(mark(X1),X2,X3)</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(X1,mark(X2),X3)</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(X1,X2,mark(X3))</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(active(X1),X2,X3)</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(X1,active(X2),X3)</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(X1,X2,active(X3))</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>cons(mark(X1),X2)</LHS><RHS>cons(X1,X2)</RHS></RULE><RULE><LHS>cons(X1,mark(X2))</LHS><RHS>cons(X1,X2)</RHS></RULE><RULE><LHS>cons(active(X1),X2)</LHS><RHS>cons(X1,X2)</RHS></RULE><RULE><LHS>cons(X1,active(X2))</LHS><RHS>cons(X1,X2)</RHS></RULE><RULE><LHS>s(mark(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>s(active(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>sieve(mark(X))</LHS><RHS>sieve(X)</RHS></RULE><RULE><LHS>sieve(active(X))</LHS><RHS>sieve(X)</RHS></RULE><RULE><LHS>nats(mark(X))</LHS><RHS>nats(X)</RHS></RULE><RULE><LHS>nats(active(X))</LHS><RHS>nats(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_mark(filter(X1,X2,X3))</LHS><RHS>Marked_active(filter(mark(X1),mark(X2),mark(X3)))</RHS></DPRULE><DPRULE num="1"><LHS>Marked_mark(filter(X1,X2,X3))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="2"><LHS>Marked_mark(filter(X1,X2,X3))</LHS><RHS>Marked_mark(X2)</RHS></DPRULE><DPRULE num="3"><LHS>Marked_mark(filter(X1,X2,X3))</LHS><RHS>Marked_mark(X3)</RHS></DPRULE><DPRULE num="4"><LHS>Marked_mark(s(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><DAG approx="simpl"><CCLIST><SCC num="0"><NODE ref="1"/><NODE ref="2"/><NODE ref="3"/><NODE ref="4"/></SCC><NONSCC num="1"><NODE ref="0"/></NONSCC></CCLIST><EDGE end="1" start="0"/></DAG></CRITERION><PROPERTY criterion="sterm" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(filter(cons(X,Y),0,M))</LHS><RHS>mark(cons(0,filter(Y,M,M)))</RHS></RULE><RULE><LHS>active(filter(cons(X,Y),s(N),M))</LHS><RHS>mark(cons(X,filter(Y,N,M)))</RHS></RULE><RULE><LHS>active(sieve(cons(0,Y)))</LHS><RHS>mark(cons(0,sieve(Y)))</RHS></RULE><RULE><LHS>active(sieve(cons(s(N),Y)))</LHS><RHS>mark(cons(s(N),sieve(filter(Y,N,N))))</RHS></RULE><RULE><LHS>active(nats(N))</LHS><RHS>mark(cons(N,nats(s(N))))</RHS></RULE><RULE><LHS>active(zprimes)</LHS><RHS>mark(sieve(nats(s(s(0)))))</RHS></RULE><RULE><LHS>mark(filter(X1,X2,X3))</LHS><RHS>active(filter(mark(X1),mark(X2),mark(X3)))</RHS></RULE><RULE><LHS>mark(cons(X1,X2))</LHS><RHS>active(cons(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(mark(X)))</RHS></RULE><RULE><LHS>mark(sieve(X))</LHS><RHS>active(sieve(mark(X)))</RHS></RULE><RULE><LHS>mark(nats(X))</LHS><RHS>active(nats(mark(X)))</RHS></RULE><RULE><LHS>mark(zprimes)</LHS><RHS>active(zprimes)</RHS></RULE><RULE><LHS>filter(mark(X1),X2,X3)</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(X1,mark(X2),X3)</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(X1,X2,mark(X3))</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(active(X1),X2,X3)</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(X1,active(X2),X3)</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(X1,X2,active(X3))</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>cons(mark(X1),X2)</LHS><RHS>cons(X1,X2)</RHS></RULE><RULE><LHS>cons(X1,mark(X2))</LHS><RHS>cons(X1,X2)</RHS></RULE><RULE><LHS>cons(active(X1),X2)</LHS><RHS>cons(X1,X2)</RHS></RULE><RULE><LHS>cons(X1,active(X2))</LHS><RHS>cons(X1,X2)</RHS></RULE><RULE><LHS>s(mark(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>s(active(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>sieve(mark(X))</LHS><RHS>sieve(X)</RHS></RULE><RULE><LHS>sieve(active(X))</LHS><RHS>sieve(X)</RHS></RULE><RULE><LHS>nats(mark(X))</LHS><RHS>nats(X)</RHS></RULE><RULE><LHS>nats(active(X))</LHS><RHS>nats(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_mark(filter(X1,X2,X3))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_mark(filter(X1,X2,X3))</LHS><RHS>Marked_mark(X2)</RHS></DPRULE><DPRULE num="2"><LHS>Marked_mark(filter(X1,X2,X3))</LHS><RHS>Marked_mark(X3)</RHS></DPRULE><DPRULE num="3"><LHS>Marked_mark(s(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><PROJECTION><PROJ><SYMBOL><NAME>Marked_mark</NAME></SYMBOL><INT>1</INT></PROJ></PROJECTION><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_mark(s(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_mark(filter(X1,X2,X3))</LHS><RHS>Marked_mark(X3)</RHS></DPRULE><DPRULE num="2"><LHS>Marked_mark(filter(X1,X2,X3))</LHS><RHS>Marked_mark(X2)</RHS></DPRULE><DPRULE num="3"><LHS>Marked_mark(filter(X1,X2,X3))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE></DPLIST></STRICTPAIRS><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(filter(cons(X,Y),0,M))</LHS><RHS>mark(cons(0,filter(Y,M,M)))</RHS></RULE><RULE><LHS>active(filter(cons(X,Y),s(N),M))</LHS><RHS>mark(cons(X,filter(Y,N,M)))</RHS></RULE><RULE><LHS>active(sieve(cons(0,Y)))</LHS><RHS>mark(cons(0,sieve(Y)))</RHS></RULE><RULE><LHS>active(sieve(cons(s(N),Y)))</LHS><RHS>mark(cons(s(N),sieve(filter(Y,N,N))))</RHS></RULE><RULE><LHS>active(nats(N))</LHS><RHS>mark(cons(N,nats(s(N))))</RHS></RULE><RULE><LHS>active(zprimes)</LHS><RHS>mark(sieve(nats(s(s(0)))))</RHS></RULE><RULE><LHS>mark(filter(X1,X2,X3))</LHS><RHS>active(filter(mark(X1),mark(X2),mark(X3)))</RHS></RULE><RULE><LHS>mark(cons(X1,X2))</LHS><RHS>active(cons(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(mark(X)))</RHS></RULE><RULE><LHS>mark(sieve(X))</LHS><RHS>active(sieve(mark(X)))</RHS></RULE><RULE><LHS>mark(nats(X))</LHS><RHS>active(nats(mark(X)))</RHS></RULE><RULE><LHS>mark(zprimes)</LHS><RHS>active(zprimes)</RHS></RULE><RULE><LHS>filter(mark(X1),X2,X3)</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(X1,mark(X2),X3)</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(X1,X2,mark(X3))</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(active(X1),X2,X3)</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(X1,active(X2),X3)</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(X1,X2,active(X3))</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>cons(mark(X1),X2)</LHS><RHS>cons(X1,X2)</RHS></RULE><RULE><LHS>cons(X1,mark(X2))</LHS><RHS>cons(X1,X2)</RHS></RULE><RULE><LHS>cons(active(X1),X2)</LHS><RHS>cons(X1,X2)</RHS></RULE><RULE><LHS>cons(X1,active(X2))</LHS><RHS>cons(X1,X2)</RHS></RULE><RULE><LHS>s(mark(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>s(active(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>sieve(mark(X))</LHS><RHS>sieve(X)</RHS></RULE><RULE><LHS>sieve(active(X))</LHS><RHS>sieve(X)</RHS></RULE><RULE><LHS>nats(mark(X))</LHS><RHS>nats(X)</RHS></RULE><RULE><LHS>nats(active(X))</LHS><RHS>nats(X)</RHS></RULE></REWSYS><DPLIST/></DPSYS></SYSTEM><CRITERION><DAG approx="simpl"><CCLIST/></DAG></CRITERION></PROPERTY></PROPERTY></PROPERTY></PROPERTY></PROPERTY></PROPERTY></PROPERTY></PROPERTY></PROPERTY></PROPERTY></PROPERTY></PROPERTY></PROPERTY></PROPERTY></PROPERTY></PROPERTY><PROPERTY criterion="sterm" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(filter(cons(X,Y),0,M))</LHS><RHS>mark(cons(0,filter(Y,M,M)))</RHS></RULE><RULE><LHS>active(filter(cons(X,Y),s(N),M))</LHS><RHS>mark(cons(X,filter(Y,N,M)))</RHS></RULE><RULE><LHS>active(sieve(cons(0,Y)))</LHS><RHS>mark(cons(0,sieve(Y)))</RHS></RULE><RULE><LHS>active(sieve(cons(s(N),Y)))</LHS><RHS>mark(cons(s(N),sieve(filter(Y,N,N))))</RHS></RULE><RULE><LHS>active(nats(N))</LHS><RHS>mark(cons(N,nats(s(N))))</RHS></RULE><RULE><LHS>active(zprimes)</LHS><RHS>mark(sieve(nats(s(s(0)))))</RHS></RULE><RULE><LHS>mark(filter(X1,X2,X3))</LHS><RHS>active(filter(mark(X1),mark(X2),mark(X3)))</RHS></RULE><RULE><LHS>mark(cons(X1,X2))</LHS><RHS>active(cons(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(mark(X)))</RHS></RULE><RULE><LHS>mark(sieve(X))</LHS><RHS>active(sieve(mark(X)))</RHS></RULE><RULE><LHS>mark(nats(X))</LHS><RHS>active(nats(mark(X)))</RHS></RULE><RULE><LHS>mark(zprimes)</LHS><RHS>active(zprimes)</RHS></RULE><RULE><LHS>filter(mark(X1),X2,X3)</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(X1,mark(X2),X3)</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(X1,X2,mark(X3))</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(active(X1),X2,X3)</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(X1,active(X2),X3)</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(X1,X2,active(X3))</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>cons(mark(X1),X2)</LHS><RHS>cons(X1,X2)</RHS></RULE><RULE><LHS>cons(X1,mark(X2))</LHS><RHS>cons(X1,X2)</RHS></RULE><RULE><LHS>cons(active(X1),X2)</LHS><RHS>cons(X1,X2)</RHS></RULE><RULE><LHS>cons(X1,active(X2))</LHS><RHS>cons(X1,X2)</RHS></RULE><RULE><LHS>s(mark(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>s(active(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>sieve(mark(X))</LHS><RHS>sieve(X)</RHS></RULE><RULE><LHS>sieve(active(X))</LHS><RHS>sieve(X)</RHS></RULE><RULE><LHS>nats(mark(X))</LHS><RHS>nats(X)</RHS></RULE><RULE><LHS>nats(active(X))</LHS><RHS>nats(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_filter(mark(X1),X2,X3)</LHS><RHS>Marked_filter(X1,X2,X3)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_filter(X1,mark(X2),X3)</LHS><RHS>Marked_filter(X1,X2,X3)</RHS></DPRULE><DPRULE num="2"><LHS>Marked_filter(X1,X2,mark(X3))</LHS><RHS>Marked_filter(X1,X2,X3)</RHS></DPRULE><DPRULE num="3"><LHS>Marked_filter(active(X1),X2,X3)</LHS><RHS>Marked_filter(X1,X2,X3)</RHS></DPRULE><DPRULE num="4"><LHS>Marked_filter(X1,active(X2),X3)</LHS><RHS>Marked_filter(X1,X2,X3)</RHS></DPRULE><DPRULE num="5"><LHS>Marked_filter(X1,X2,active(X3))</LHS><RHS>Marked_filter(X1,X2,X3)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><PROJECTION><PROJ><SYMBOL><NAME>Marked_filter</NAME></SYMBOL><INT>3</INT></PROJ></PROJECTION><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_filter(X1,X2,active(X3))</LHS><RHS>Marked_filter(X1,X2,X3)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_filter(X1,X2,mark(X3))</LHS><RHS>Marked_filter(X1,X2,X3)</RHS></DPRULE></DPLIST></STRICTPAIRS><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(filter(cons(X,Y),0,M))</LHS><RHS>mark(cons(0,filter(Y,M,M)))</RHS></RULE><RULE><LHS>active(filter(cons(X,Y),s(N),M))</LHS><RHS>mark(cons(X,filter(Y,N,M)))</RHS></RULE><RULE><LHS>active(sieve(cons(0,Y)))</LHS><RHS>mark(cons(0,sieve(Y)))</RHS></RULE><RULE><LHS>active(sieve(cons(s(N),Y)))</LHS><RHS>mark(cons(s(N),sieve(filter(Y,N,N))))</RHS></RULE><RULE><LHS>active(nats(N))</LHS><RHS>mark(cons(N,nats(s(N))))</RHS></RULE><RULE><LHS>active(zprimes)</LHS><RHS>mark(sieve(nats(s(s(0)))))</RHS></RULE><RULE><LHS>mark(filter(X1,X2,X3))</LHS><RHS>active(filter(mark(X1),mark(X2),mark(X3)))</RHS></RULE><RULE><LHS>mark(cons(X1,X2))</LHS><RHS>active(cons(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(mark(X)))</RHS></RULE><RULE><LHS>mark(sieve(X))</LHS><RHS>active(sieve(mark(X)))</RHS></RULE><RULE><LHS>mark(nats(X))</LHS><RHS>active(nats(mark(X)))</RHS></RULE><RULE><LHS>mark(zprimes)</LHS><RHS>active(zprimes)</RHS></RULE><RULE><LHS>filter(mark(X1),X2,X3)</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(X1,mark(X2),X3)</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(X1,X2,mark(X3))</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(active(X1),X2,X3)</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(X1,active(X2),X3)</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(X1,X2,active(X3))</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>cons(mark(X1),X2)</LHS><RHS>cons(X1,X2)</RHS></RULE><RULE><LHS>cons(X1,mark(X2))</LHS><RHS>cons(X1,X2)</RHS></RULE><RULE><LHS>cons(active(X1),X2)</LHS><RHS>cons(X1,X2)</RHS></RULE><RULE><LHS>cons(X1,active(X2))</LHS><RHS>cons(X1,X2)</RHS></RULE><RULE><LHS>s(mark(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>s(active(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>sieve(mark(X))</LHS><RHS>sieve(X)</RHS></RULE><RULE><LHS>sieve(active(X))</LHS><RHS>sieve(X)</RHS></RULE><RULE><LHS>nats(mark(X))</LHS><RHS>nats(X)</RHS></RULE><RULE><LHS>nats(active(X))</LHS><RHS>nats(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_filter(X1,active(X2),X3)</LHS><RHS>Marked_filter(X1,X2,X3)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_filter(active(X1),X2,X3)</LHS><RHS>Marked_filter(X1,X2,X3)</RHS></DPRULE><DPRULE num="2"><LHS>Marked_filter(X1,mark(X2),X3)</LHS><RHS>Marked_filter(X1,X2,X3)</RHS></DPRULE><DPRULE num="3"><LHS>Marked_filter(mark(X1),X2,X3)</LHS><RHS>Marked_filter(X1,X2,X3)</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="sterm" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(filter(cons(X,Y),0,M))</LHS><RHS>mark(cons(0,filter(Y,M,M)))</RHS></RULE><RULE><LHS>active(filter(cons(X,Y),s(N),M))</LHS><RHS>mark(cons(X,filter(Y,N,M)))</RHS></RULE><RULE><LHS>active(sieve(cons(0,Y)))</LHS><RHS>mark(cons(0,sieve(Y)))</RHS></RULE><RULE><LHS>active(sieve(cons(s(N),Y)))</LHS><RHS>mark(cons(s(N),sieve(filter(Y,N,N))))</RHS></RULE><RULE><LHS>active(nats(N))</LHS><RHS>mark(cons(N,nats(s(N))))</RHS></RULE><RULE><LHS>active(zprimes)</LHS><RHS>mark(sieve(nats(s(s(0)))))</RHS></RULE><RULE><LHS>mark(filter(X1,X2,X3))</LHS><RHS>active(filter(mark(X1),mark(X2),mark(X3)))</RHS></RULE><RULE><LHS>mark(cons(X1,X2))</LHS><RHS>active(cons(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(mark(X)))</RHS></RULE><RULE><LHS>mark(sieve(X))</LHS><RHS>active(sieve(mark(X)))</RHS></RULE><RULE><LHS>mark(nats(X))</LHS><RHS>active(nats(mark(X)))</RHS></RULE><RULE><LHS>mark(zprimes)</LHS><RHS>active(zprimes)</RHS></RULE><RULE><LHS>filter(mark(X1),X2,X3)</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(X1,mark(X2),X3)</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(X1,X2,mark(X3))</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(active(X1),X2,X3)</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(X1,active(X2),X3)</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(X1,X2,active(X3))</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>cons(mark(X1),X2)</LHS><RHS>cons(X1,X2)</RHS></RULE><RULE><LHS>cons(X1,mark(X2))</LHS><RHS>cons(X1,X2)</RHS></RULE><RULE><LHS>cons(active(X1),X2)</LHS><RHS>cons(X1,X2)</RHS></RULE><RULE><LHS>cons(X1,active(X2))</LHS><RHS>cons(X1,X2)</RHS></RULE><RULE><LHS>s(mark(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>s(active(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>sieve(mark(X))</LHS><RHS>sieve(X)</RHS></RULE><RULE><LHS>sieve(active(X))</LHS><RHS>sieve(X)</RHS></RULE><RULE><LHS>nats(mark(X))</LHS><RHS>nats(X)</RHS></RULE><RULE><LHS>nats(active(X))</LHS><RHS>nats(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_filter(X1,active(X2),X3)</LHS><RHS>Marked_filter(X1,X2,X3)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_filter(active(X1),X2,X3)</LHS><RHS>Marked_filter(X1,X2,X3)</RHS></DPRULE><DPRULE num="2"><LHS>Marked_filter(X1,mark(X2),X3)</LHS><RHS>Marked_filter(X1,X2,X3)</RHS></DPRULE><DPRULE num="3"><LHS>Marked_filter(mark(X1),X2,X3)</LHS><RHS>Marked_filter(X1,X2,X3)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><PROJECTION><PROJ><SYMBOL><NAME>Marked_filter</NAME></SYMBOL><INT>2</INT></PROJ></PROJECTION><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_filter(X1,mark(X2),X3)</LHS><RHS>Marked_filter(X1,X2,X3)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_filter(X1,active(X2),X3)</LHS><RHS>Marked_filter(X1,X2,X3)</RHS></DPRULE></DPLIST></STRICTPAIRS><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(filter(cons(X,Y),0,M))</LHS><RHS>mark(cons(0,filter(Y,M,M)))</RHS></RULE><RULE><LHS>active(filter(cons(X,Y),s(N),M))</LHS><RHS>mark(cons(X,filter(Y,N,M)))</RHS></RULE><RULE><LHS>active(sieve(cons(0,Y)))</LHS><RHS>mark(cons(0,sieve(Y)))</RHS></RULE><RULE><LHS>active(sieve(cons(s(N),Y)))</LHS><RHS>mark(cons(s(N),sieve(filter(Y,N,N))))</RHS></RULE><RULE><LHS>active(nats(N))</LHS><RHS>mark(cons(N,nats(s(N))))</RHS></RULE><RULE><LHS>active(zprimes)</LHS><RHS>mark(sieve(nats(s(s(0)))))</RHS></RULE><RULE><LHS>mark(filter(X1,X2,X3))</LHS><RHS>active(filter(mark(X1),mark(X2),mark(X3)))</RHS></RULE><RULE><LHS>mark(cons(X1,X2))</LHS><RHS>active(cons(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(mark(X)))</RHS></RULE><RULE><LHS>mark(sieve(X))</LHS><RHS>active(sieve(mark(X)))</RHS></RULE><RULE><LHS>mark(nats(X))</LHS><RHS>active(nats(mark(X)))</RHS></RULE><RULE><LHS>mark(zprimes)</LHS><RHS>active(zprimes)</RHS></RULE><RULE><LHS>filter(mark(X1),X2,X3)</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(X1,mark(X2),X3)</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(X1,X2,mark(X3))</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(active(X1),X2,X3)</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(X1,active(X2),X3)</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(X1,X2,active(X3))</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>cons(mark(X1),X2)</LHS><RHS>cons(X1,X2)</RHS></RULE><RULE><LHS>cons(X1,mark(X2))</LHS><RHS>cons(X1,X2)</RHS></RULE><RULE><LHS>cons(active(X1),X2)</LHS><RHS>cons(X1,X2)</RHS></RULE><RULE><LHS>cons(X1,active(X2))</LHS><RHS>cons(X1,X2)</RHS></RULE><RULE><LHS>s(mark(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>s(active(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>sieve(mark(X))</LHS><RHS>sieve(X)</RHS></RULE><RULE><LHS>sieve(active(X))</LHS><RHS>sieve(X)</RHS></RULE><RULE><LHS>nats(mark(X))</LHS><RHS>nats(X)</RHS></RULE><RULE><LHS>nats(active(X))</LHS><RHS>nats(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_filter(mark(X1),X2,X3)</LHS><RHS>Marked_filter(X1,X2,X3)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_filter(active(X1),X2,X3)</LHS><RHS>Marked_filter(X1,X2,X3)</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="sterm" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(filter(cons(X,Y),0,M))</LHS><RHS>mark(cons(0,filter(Y,M,M)))</RHS></RULE><RULE><LHS>active(filter(cons(X,Y),s(N),M))</LHS><RHS>mark(cons(X,filter(Y,N,M)))</RHS></RULE><RULE><LHS>active(sieve(cons(0,Y)))</LHS><RHS>mark(cons(0,sieve(Y)))</RHS></RULE><RULE><LHS>active(sieve(cons(s(N),Y)))</LHS><RHS>mark(cons(s(N),sieve(filter(Y,N,N))))</RHS></RULE><RULE><LHS>active(nats(N))</LHS><RHS>mark(cons(N,nats(s(N))))</RHS></RULE><RULE><LHS>active(zprimes)</LHS><RHS>mark(sieve(nats(s(s(0)))))</RHS></RULE><RULE><LHS>mark(filter(X1,X2,X3))</LHS><RHS>active(filter(mark(X1),mark(X2),mark(X3)))</RHS></RULE><RULE><LHS>mark(cons(X1,X2))</LHS><RHS>active(cons(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(mark(X)))</RHS></RULE><RULE><LHS>mark(sieve(X))</LHS><RHS>active(sieve(mark(X)))</RHS></RULE><RULE><LHS>mark(nats(X))</LHS><RHS>active(nats(mark(X)))</RHS></RULE><RULE><LHS>mark(zprimes)</LHS><RHS>active(zprimes)</RHS></RULE><RULE><LHS>filter(mark(X1),X2,X3)</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(X1,mark(X2),X3)</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(X1,X2,mark(X3))</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(active(X1),X2,X3)</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(X1,active(X2),X3)</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(X1,X2,active(X3))</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>cons(mark(X1),X2)</LHS><RHS>cons(X1,X2)</RHS></RULE><RULE><LHS>cons(X1,mark(X2))</LHS><RHS>cons(X1,X2)</RHS></RULE><RULE><LHS>cons(active(X1),X2)</LHS><RHS>cons(X1,X2)</RHS></RULE><RULE><LHS>cons(X1,active(X2))</LHS><RHS>cons(X1,X2)</RHS></RULE><RULE><LHS>s(mark(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>s(active(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>sieve(mark(X))</LHS><RHS>sieve(X)</RHS></RULE><RULE><LHS>sieve(active(X))</LHS><RHS>sieve(X)</RHS></RULE><RULE><LHS>nats(mark(X))</LHS><RHS>nats(X)</RHS></RULE><RULE><LHS>nats(active(X))</LHS><RHS>nats(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_filter(mark(X1),X2,X3)</LHS><RHS>Marked_filter(X1,X2,X3)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_filter(active(X1),X2,X3)</LHS><RHS>Marked_filter(X1,X2,X3)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><PROJECTION><PROJ><SYMBOL><NAME>Marked_filter</NAME></SYMBOL><INT>1</INT></PROJ></PROJECTION><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_filter(active(X1),X2,X3)</LHS><RHS>Marked_filter(X1,X2,X3)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_filter(mark(X1),X2,X3)</LHS><RHS>Marked_filter(X1,X2,X3)</RHS></DPRULE></DPLIST></STRICTPAIRS><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(filter(cons(X,Y),0,M))</LHS><RHS>mark(cons(0,filter(Y,M,M)))</RHS></RULE><RULE><LHS>active(filter(cons(X,Y),s(N),M))</LHS><RHS>mark(cons(X,filter(Y,N,M)))</RHS></RULE><RULE><LHS>active(sieve(cons(0,Y)))</LHS><RHS>mark(cons(0,sieve(Y)))</RHS></RULE><RULE><LHS>active(sieve(cons(s(N),Y)))</LHS><RHS>mark(cons(s(N),sieve(filter(Y,N,N))))</RHS></RULE><RULE><LHS>active(nats(N))</LHS><RHS>mark(cons(N,nats(s(N))))</RHS></RULE><RULE><LHS>active(zprimes)</LHS><RHS>mark(sieve(nats(s(s(0)))))</RHS></RULE><RULE><LHS>mark(filter(X1,X2,X3))</LHS><RHS>active(filter(mark(X1),mark(X2),mark(X3)))</RHS></RULE><RULE><LHS>mark(cons(X1,X2))</LHS><RHS>active(cons(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(mark(X)))</RHS></RULE><RULE><LHS>mark(sieve(X))</LHS><RHS>active(sieve(mark(X)))</RHS></RULE><RULE><LHS>mark(nats(X))</LHS><RHS>active(nats(mark(X)))</RHS></RULE><RULE><LHS>mark(zprimes)</LHS><RHS>active(zprimes)</RHS></RULE><RULE><LHS>filter(mark(X1),X2,X3)</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(X1,mark(X2),X3)</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(X1,X2,mark(X3))</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(active(X1),X2,X3)</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(X1,active(X2),X3)</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(X1,X2,active(X3))</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>cons(mark(X1),X2)</LHS><RHS>cons(X1,X2)</RHS></RULE><RULE><LHS>cons(X1,mark(X2))</LHS><RHS>cons(X1,X2)</RHS></RULE><RULE><LHS>cons(active(X1),X2)</LHS><RHS>cons(X1,X2)</RHS></RULE><RULE><LHS>cons(X1,active(X2))</LHS><RHS>cons(X1,X2)</RHS></RULE><RULE><LHS>s(mark(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>s(active(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>sieve(mark(X))</LHS><RHS>sieve(X)</RHS></RULE><RULE><LHS>sieve(active(X))</LHS><RHS>sieve(X)</RHS></RULE><RULE><LHS>nats(mark(X))</LHS><RHS>nats(X)</RHS></RULE><RULE><LHS>nats(active(X))</LHS><RHS>nats(X)</RHS></RULE></REWSYS><DPLIST/></DPSYS></SYSTEM><CRITERION><DAG approx="simpl"><CCLIST/></DAG></CRITERION></PROPERTY></PROPERTY></PROPERTY></PROPERTY></PROPERTY></PROPERTY><PROPERTY criterion="sterm" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(filter(cons(X,Y),0,M))</LHS><RHS>mark(cons(0,filter(Y,M,M)))</RHS></RULE><RULE><LHS>active(filter(cons(X,Y),s(N),M))</LHS><RHS>mark(cons(X,filter(Y,N,M)))</RHS></RULE><RULE><LHS>active(sieve(cons(0,Y)))</LHS><RHS>mark(cons(0,sieve(Y)))</RHS></RULE><RULE><LHS>active(sieve(cons(s(N),Y)))</LHS><RHS>mark(cons(s(N),sieve(filter(Y,N,N))))</RHS></RULE><RULE><LHS>active(nats(N))</LHS><RHS>mark(cons(N,nats(s(N))))</RHS></RULE><RULE><LHS>active(zprimes)</LHS><RHS>mark(sieve(nats(s(s(0)))))</RHS></RULE><RULE><LHS>mark(filter(X1,X2,X3))</LHS><RHS>active(filter(mark(X1),mark(X2),mark(X3)))</RHS></RULE><RULE><LHS>mark(cons(X1,X2))</LHS><RHS>active(cons(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(mark(X)))</RHS></RULE><RULE><LHS>mark(sieve(X))</LHS><RHS>active(sieve(mark(X)))</RHS></RULE><RULE><LHS>mark(nats(X))</LHS><RHS>active(nats(mark(X)))</RHS></RULE><RULE><LHS>mark(zprimes)</LHS><RHS>active(zprimes)</RHS></RULE><RULE><LHS>filter(mark(X1),X2,X3)</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(X1,mark(X2),X3)</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(X1,X2,mark(X3))</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(active(X1),X2,X3)</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(X1,active(X2),X3)</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(X1,X2,active(X3))</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>cons(mark(X1),X2)</LHS><RHS>cons(X1,X2)</RHS></RULE><RULE><LHS>cons(X1,mark(X2))</LHS><RHS>cons(X1,X2)</RHS></RULE><RULE><LHS>cons(active(X1),X2)</LHS><RHS>cons(X1,X2)</RHS></RULE><RULE><LHS>cons(X1,active(X2))</LHS><RHS>cons(X1,X2)</RHS></RULE><RULE><LHS>s(mark(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>s(active(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>sieve(mark(X))</LHS><RHS>sieve(X)</RHS></RULE><RULE><LHS>sieve(active(X))</LHS><RHS>sieve(X)</RHS></RULE><RULE><LHS>nats(mark(X))</LHS><RHS>nats(X)</RHS></RULE><RULE><LHS>nats(active(X))</LHS><RHS>nats(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_cons(mark(X1),X2)</LHS><RHS>Marked_cons(X1,X2)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_cons(X1,mark(X2))</LHS><RHS>Marked_cons(X1,X2)</RHS></DPRULE><DPRULE num="2"><LHS>Marked_cons(active(X1),X2)</LHS><RHS>Marked_cons(X1,X2)</RHS></DPRULE><DPRULE num="3"><LHS>Marked_cons(X1,active(X2))</LHS><RHS>Marked_cons(X1,X2)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><PROJECTION><PROJ><SYMBOL><NAME>Marked_cons</NAME></SYMBOL><INT>2</INT></PROJ></PROJECTION><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_cons(X1,active(X2))</LHS><RHS>Marked_cons(X1,X2)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_cons(X1,mark(X2))</LHS><RHS>Marked_cons(X1,X2)</RHS></DPRULE></DPLIST></STRICTPAIRS><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(filter(cons(X,Y),0,M))</LHS><RHS>mark(cons(0,filter(Y,M,M)))</RHS></RULE><RULE><LHS>active(filter(cons(X,Y),s(N),M))</LHS><RHS>mark(cons(X,filter(Y,N,M)))</RHS></RULE><RULE><LHS>active(sieve(cons(0,Y)))</LHS><RHS>mark(cons(0,sieve(Y)))</RHS></RULE><RULE><LHS>active(sieve(cons(s(N),Y)))</LHS><RHS>mark(cons(s(N),sieve(filter(Y,N,N))))</RHS></RULE><RULE><LHS>active(nats(N))</LHS><RHS>mark(cons(N,nats(s(N))))</RHS></RULE><RULE><LHS>active(zprimes)</LHS><RHS>mark(sieve(nats(s(s(0)))))</RHS></RULE><RULE><LHS>mark(filter(X1,X2,X3))</LHS><RHS>active(filter(mark(X1),mark(X2),mark(X3)))</RHS></RULE><RULE><LHS>mark(cons(X1,X2))</LHS><RHS>active(cons(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(mark(X)))</RHS></RULE><RULE><LHS>mark(sieve(X))</LHS><RHS>active(sieve(mark(X)))</RHS></RULE><RULE><LHS>mark(nats(X))</LHS><RHS>active(nats(mark(X)))</RHS></RULE><RULE><LHS>mark(zprimes)</LHS><RHS>active(zprimes)</RHS></RULE><RULE><LHS>filter(mark(X1),X2,X3)</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(X1,mark(X2),X3)</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(X1,X2,mark(X3))</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(active(X1),X2,X3)</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(X1,active(X2),X3)</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(X1,X2,active(X3))</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>cons(mark(X1),X2)</LHS><RHS>cons(X1,X2)</RHS></RULE><RULE><LHS>cons(X1,mark(X2))</LHS><RHS>cons(X1,X2)</RHS></RULE><RULE><LHS>cons(active(X1),X2)</LHS><RHS>cons(X1,X2)</RHS></RULE><RULE><LHS>cons(X1,active(X2))</LHS><RHS>cons(X1,X2)</RHS></RULE><RULE><LHS>s(mark(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>s(active(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>sieve(mark(X))</LHS><RHS>sieve(X)</RHS></RULE><RULE><LHS>sieve(active(X))</LHS><RHS>sieve(X)</RHS></RULE><RULE><LHS>nats(mark(X))</LHS><RHS>nats(X)</RHS></RULE><RULE><LHS>nats(active(X))</LHS><RHS>nats(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_cons(active(X1),X2)</LHS><RHS>Marked_cons(X1,X2)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_cons(mark(X1),X2)</LHS><RHS>Marked_cons(X1,X2)</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="sterm" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(filter(cons(X,Y),0,M))</LHS><RHS>mark(cons(0,filter(Y,M,M)))</RHS></RULE><RULE><LHS>active(filter(cons(X,Y),s(N),M))</LHS><RHS>mark(cons(X,filter(Y,N,M)))</RHS></RULE><RULE><LHS>active(sieve(cons(0,Y)))</LHS><RHS>mark(cons(0,sieve(Y)))</RHS></RULE><RULE><LHS>active(sieve(cons(s(N),Y)))</LHS><RHS>mark(cons(s(N),sieve(filter(Y,N,N))))</RHS></RULE><RULE><LHS>active(nats(N))</LHS><RHS>mark(cons(N,nats(s(N))))</RHS></RULE><RULE><LHS>active(zprimes)</LHS><RHS>mark(sieve(nats(s(s(0)))))</RHS></RULE><RULE><LHS>mark(filter(X1,X2,X3))</LHS><RHS>active(filter(mark(X1),mark(X2),mark(X3)))</RHS></RULE><RULE><LHS>mark(cons(X1,X2))</LHS><RHS>active(cons(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(mark(X)))</RHS></RULE><RULE><LHS>mark(sieve(X))</LHS><RHS>active(sieve(mark(X)))</RHS></RULE><RULE><LHS>mark(nats(X))</LHS><RHS>active(nats(mark(X)))</RHS></RULE><RULE><LHS>mark(zprimes)</LHS><RHS>active(zprimes)</RHS></RULE><RULE><LHS>filter(mark(X1),X2,X3)</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(X1,mark(X2),X3)</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(X1,X2,mark(X3))</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(active(X1),X2,X3)</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(X1,active(X2),X3)</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(X1,X2,active(X3))</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>cons(mark(X1),X2)</LHS><RHS>cons(X1,X2)</RHS></RULE><RULE><LHS>cons(X1,mark(X2))</LHS><RHS>cons(X1,X2)</RHS></RULE><RULE><LHS>cons(active(X1),X2)</LHS><RHS>cons(X1,X2)</RHS></RULE><RULE><LHS>cons(X1,active(X2))</LHS><RHS>cons(X1,X2)</RHS></RULE><RULE><LHS>s(mark(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>s(active(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>sieve(mark(X))</LHS><RHS>sieve(X)</RHS></RULE><RULE><LHS>sieve(active(X))</LHS><RHS>sieve(X)</RHS></RULE><RULE><LHS>nats(mark(X))</LHS><RHS>nats(X)</RHS></RULE><RULE><LHS>nats(active(X))</LHS><RHS>nats(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_cons(active(X1),X2)</LHS><RHS>Marked_cons(X1,X2)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_cons(mark(X1),X2)</LHS><RHS>Marked_cons(X1,X2)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><PROJECTION><PROJ><SYMBOL><NAME>Marked_cons</NAME></SYMBOL><INT>1</INT></PROJ></PROJECTION><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_cons(mark(X1),X2)</LHS><RHS>Marked_cons(X1,X2)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_cons(active(X1),X2)</LHS><RHS>Marked_cons(X1,X2)</RHS></DPRULE></DPLIST></STRICTPAIRS><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(filter(cons(X,Y),0,M))</LHS><RHS>mark(cons(0,filter(Y,M,M)))</RHS></RULE><RULE><LHS>active(filter(cons(X,Y),s(N),M))</LHS><RHS>mark(cons(X,filter(Y,N,M)))</RHS></RULE><RULE><LHS>active(sieve(cons(0,Y)))</LHS><RHS>mark(cons(0,sieve(Y)))</RHS></RULE><RULE><LHS>active(sieve(cons(s(N),Y)))</LHS><RHS>mark(cons(s(N),sieve(filter(Y,N,N))))</RHS></RULE><RULE><LHS>active(nats(N))</LHS><RHS>mark(cons(N,nats(s(N))))</RHS></RULE><RULE><LHS>active(zprimes)</LHS><RHS>mark(sieve(nats(s(s(0)))))</RHS></RULE><RULE><LHS>mark(filter(X1,X2,X3))</LHS><RHS>active(filter(mark(X1),mark(X2),mark(X3)))</RHS></RULE><RULE><LHS>mark(cons(X1,X2))</LHS><RHS>active(cons(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(mark(X)))</RHS></RULE><RULE><LHS>mark(sieve(X))</LHS><RHS>active(sieve(mark(X)))</RHS></RULE><RULE><LHS>mark(nats(X))</LHS><RHS>active(nats(mark(X)))</RHS></RULE><RULE><LHS>mark(zprimes)</LHS><RHS>active(zprimes)</RHS></RULE><RULE><LHS>filter(mark(X1),X2,X3)</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(X1,mark(X2),X3)</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(X1,X2,mark(X3))</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(active(X1),X2,X3)</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(X1,active(X2),X3)</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(X1,X2,active(X3))</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>cons(mark(X1),X2)</LHS><RHS>cons(X1,X2)</RHS></RULE><RULE><LHS>cons(X1,mark(X2))</LHS><RHS>cons(X1,X2)</RHS></RULE><RULE><LHS>cons(active(X1),X2)</LHS><RHS>cons(X1,X2)</RHS></RULE><RULE><LHS>cons(X1,active(X2))</LHS><RHS>cons(X1,X2)</RHS></RULE><RULE><LHS>s(mark(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>s(active(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>sieve(mark(X))</LHS><RHS>sieve(X)</RHS></RULE><RULE><LHS>sieve(active(X))</LHS><RHS>sieve(X)</RHS></RULE><RULE><LHS>nats(mark(X))</LHS><RHS>nats(X)</RHS></RULE><RULE><LHS>nats(active(X))</LHS><RHS>nats(X)</RHS></RULE></REWSYS><DPLIST/></DPSYS></SYSTEM><CRITERION><DAG approx="simpl"><CCLIST/></DAG></CRITERION></PROPERTY></PROPERTY></PROPERTY></PROPERTY><PROPERTY criterion="sterm" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(filter(cons(X,Y),0,M))</LHS><RHS>mark(cons(0,filter(Y,M,M)))</RHS></RULE><RULE><LHS>active(filter(cons(X,Y),s(N),M))</LHS><RHS>mark(cons(X,filter(Y,N,M)))</RHS></RULE><RULE><LHS>active(sieve(cons(0,Y)))</LHS><RHS>mark(cons(0,sieve(Y)))</RHS></RULE><RULE><LHS>active(sieve(cons(s(N),Y)))</LHS><RHS>mark(cons(s(N),sieve(filter(Y,N,N))))</RHS></RULE><RULE><LHS>active(nats(N))</LHS><RHS>mark(cons(N,nats(s(N))))</RHS></RULE><RULE><LHS>active(zprimes)</LHS><RHS>mark(sieve(nats(s(s(0)))))</RHS></RULE><RULE><LHS>mark(filter(X1,X2,X3))</LHS><RHS>active(filter(mark(X1),mark(X2),mark(X3)))</RHS></RULE><RULE><LHS>mark(cons(X1,X2))</LHS><RHS>active(cons(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(mark(X)))</RHS></RULE><RULE><LHS>mark(sieve(X))</LHS><RHS>active(sieve(mark(X)))</RHS></RULE><RULE><LHS>mark(nats(X))</LHS><RHS>active(nats(mark(X)))</RHS></RULE><RULE><LHS>mark(zprimes)</LHS><RHS>active(zprimes)</RHS></RULE><RULE><LHS>filter(mark(X1),X2,X3)</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(X1,mark(X2),X3)</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(X1,X2,mark(X3))</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(active(X1),X2,X3)</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(X1,active(X2),X3)</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(X1,X2,active(X3))</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>cons(mark(X1),X2)</LHS><RHS>cons(X1,X2)</RHS></RULE><RULE><LHS>cons(X1,mark(X2))</LHS><RHS>cons(X1,X2)</RHS></RULE><RULE><LHS>cons(active(X1),X2)</LHS><RHS>cons(X1,X2)</RHS></RULE><RULE><LHS>cons(X1,active(X2))</LHS><RHS>cons(X1,X2)</RHS></RULE><RULE><LHS>s(mark(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>s(active(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>sieve(mark(X))</LHS><RHS>sieve(X)</RHS></RULE><RULE><LHS>sieve(active(X))</LHS><RHS>sieve(X)</RHS></RULE><RULE><LHS>nats(mark(X))</LHS><RHS>nats(X)</RHS></RULE><RULE><LHS>nats(active(X))</LHS><RHS>nats(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_s(mark(X))</LHS><RHS>Marked_s(X)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_s(active(X))</LHS><RHS>Marked_s(X)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><PROJECTION><PROJ><SYMBOL><NAME>Marked_s</NAME></SYMBOL><INT>1</INT></PROJ></PROJECTION><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_s(active(X))</LHS><RHS>Marked_s(X)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_s(mark(X))</LHS><RHS>Marked_s(X)</RHS></DPRULE></DPLIST></STRICTPAIRS><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(filter(cons(X,Y),0,M))</LHS><RHS>mark(cons(0,filter(Y,M,M)))</RHS></RULE><RULE><LHS>active(filter(cons(X,Y),s(N),M))</LHS><RHS>mark(cons(X,filter(Y,N,M)))</RHS></RULE><RULE><LHS>active(sieve(cons(0,Y)))</LHS><RHS>mark(cons(0,sieve(Y)))</RHS></RULE><RULE><LHS>active(sieve(cons(s(N),Y)))</LHS><RHS>mark(cons(s(N),sieve(filter(Y,N,N))))</RHS></RULE><RULE><LHS>active(nats(N))</LHS><RHS>mark(cons(N,nats(s(N))))</RHS></RULE><RULE><LHS>active(zprimes)</LHS><RHS>mark(sieve(nats(s(s(0)))))</RHS></RULE><RULE><LHS>mark(filter(X1,X2,X3))</LHS><RHS>active(filter(mark(X1),mark(X2),mark(X3)))</RHS></RULE><RULE><LHS>mark(cons(X1,X2))</LHS><RHS>active(cons(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(mark(X)))</RHS></RULE><RULE><LHS>mark(sieve(X))</LHS><RHS>active(sieve(mark(X)))</RHS></RULE><RULE><LHS>mark(nats(X))</LHS><RHS>active(nats(mark(X)))</RHS></RULE><RULE><LHS>mark(zprimes)</LHS><RHS>active(zprimes)</RHS></RULE><RULE><LHS>filter(mark(X1),X2,X3)</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(X1,mark(X2),X3)</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(X1,X2,mark(X3))</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(active(X1),X2,X3)</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(X1,active(X2),X3)</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(X1,X2,active(X3))</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>cons(mark(X1),X2)</LHS><RHS>cons(X1,X2)</RHS></RULE><RULE><LHS>cons(X1,mark(X2))</LHS><RHS>cons(X1,X2)</RHS></RULE><RULE><LHS>cons(active(X1),X2)</LHS><RHS>cons(X1,X2)</RHS></RULE><RULE><LHS>cons(X1,active(X2))</LHS><RHS>cons(X1,X2)</RHS></RULE><RULE><LHS>s(mark(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>s(active(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>sieve(mark(X))</LHS><RHS>sieve(X)</RHS></RULE><RULE><LHS>sieve(active(X))</LHS><RHS>sieve(X)</RHS></RULE><RULE><LHS>nats(mark(X))</LHS><RHS>nats(X)</RHS></RULE><RULE><LHS>nats(active(X))</LHS><RHS>nats(X)</RHS></RULE></REWSYS><DPLIST/></DPSYS></SYSTEM><CRITERION><DAG approx="simpl"><CCLIST/></DAG></CRITERION></PROPERTY></PROPERTY><PROPERTY criterion="sterm" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(filter(cons(X,Y),0,M))</LHS><RHS>mark(cons(0,filter(Y,M,M)))</RHS></RULE><RULE><LHS>active(filter(cons(X,Y),s(N),M))</LHS><RHS>mark(cons(X,filter(Y,N,M)))</RHS></RULE><RULE><LHS>active(sieve(cons(0,Y)))</LHS><RHS>mark(cons(0,sieve(Y)))</RHS></RULE><RULE><LHS>active(sieve(cons(s(N),Y)))</LHS><RHS>mark(cons(s(N),sieve(filter(Y,N,N))))</RHS></RULE><RULE><LHS>active(nats(N))</LHS><RHS>mark(cons(N,nats(s(N))))</RHS></RULE><RULE><LHS>active(zprimes)</LHS><RHS>mark(sieve(nats(s(s(0)))))</RHS></RULE><RULE><LHS>mark(filter(X1,X2,X3))</LHS><RHS>active(filter(mark(X1),mark(X2),mark(X3)))</RHS></RULE><RULE><LHS>mark(cons(X1,X2))</LHS><RHS>active(cons(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(mark(X)))</RHS></RULE><RULE><LHS>mark(sieve(X))</LHS><RHS>active(sieve(mark(X)))</RHS></RULE><RULE><LHS>mark(nats(X))</LHS><RHS>active(nats(mark(X)))</RHS></RULE><RULE><LHS>mark(zprimes)</LHS><RHS>active(zprimes)</RHS></RULE><RULE><LHS>filter(mark(X1),X2,X3)</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(X1,mark(X2),X3)</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(X1,X2,mark(X3))</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(active(X1),X2,X3)</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(X1,active(X2),X3)</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(X1,X2,active(X3))</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>cons(mark(X1),X2)</LHS><RHS>cons(X1,X2)</RHS></RULE><RULE><LHS>cons(X1,mark(X2))</LHS><RHS>cons(X1,X2)</RHS></RULE><RULE><LHS>cons(active(X1),X2)</LHS><RHS>cons(X1,X2)</RHS></RULE><RULE><LHS>cons(X1,active(X2))</LHS><RHS>cons(X1,X2)</RHS></RULE><RULE><LHS>s(mark(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>s(active(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>sieve(mark(X))</LHS><RHS>sieve(X)</RHS></RULE><RULE><LHS>sieve(active(X))</LHS><RHS>sieve(X)</RHS></RULE><RULE><LHS>nats(mark(X))</LHS><RHS>nats(X)</RHS></RULE><RULE><LHS>nats(active(X))</LHS><RHS>nats(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_sieve(mark(X))</LHS><RHS>Marked_sieve(X)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_sieve(active(X))</LHS><RHS>Marked_sieve(X)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><PROJECTION><PROJ><SYMBOL><NAME>Marked_sieve</NAME></SYMBOL><INT>1</INT></PROJ></PROJECTION><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_sieve(active(X))</LHS><RHS>Marked_sieve(X)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_sieve(mark(X))</LHS><RHS>Marked_sieve(X)</RHS></DPRULE></DPLIST></STRICTPAIRS><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(filter(cons(X,Y),0,M))</LHS><RHS>mark(cons(0,filter(Y,M,M)))</RHS></RULE><RULE><LHS>active(filter(cons(X,Y),s(N),M))</LHS><RHS>mark(cons(X,filter(Y,N,M)))</RHS></RULE><RULE><LHS>active(sieve(cons(0,Y)))</LHS><RHS>mark(cons(0,sieve(Y)))</RHS></RULE><RULE><LHS>active(sieve(cons(s(N),Y)))</LHS><RHS>mark(cons(s(N),sieve(filter(Y,N,N))))</RHS></RULE><RULE><LHS>active(nats(N))</LHS><RHS>mark(cons(N,nats(s(N))))</RHS></RULE><RULE><LHS>active(zprimes)</LHS><RHS>mark(sieve(nats(s(s(0)))))</RHS></RULE><RULE><LHS>mark(filter(X1,X2,X3))</LHS><RHS>active(filter(mark(X1),mark(X2),mark(X3)))</RHS></RULE><RULE><LHS>mark(cons(X1,X2))</LHS><RHS>active(cons(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(mark(X)))</RHS></RULE><RULE><LHS>mark(sieve(X))</LHS><RHS>active(sieve(mark(X)))</RHS></RULE><RULE><LHS>mark(nats(X))</LHS><RHS>active(nats(mark(X)))</RHS></RULE><RULE><LHS>mark(zprimes)</LHS><RHS>active(zprimes)</RHS></RULE><RULE><LHS>filter(mark(X1),X2,X3)</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(X1,mark(X2),X3)</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(X1,X2,mark(X3))</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(active(X1),X2,X3)</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(X1,active(X2),X3)</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(X1,X2,active(X3))</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>cons(mark(X1),X2)</LHS><RHS>cons(X1,X2)</RHS></RULE><RULE><LHS>cons(X1,mark(X2))</LHS><RHS>cons(X1,X2)</RHS></RULE><RULE><LHS>cons(active(X1),X2)</LHS><RHS>cons(X1,X2)</RHS></RULE><RULE><LHS>cons(X1,active(X2))</LHS><RHS>cons(X1,X2)</RHS></RULE><RULE><LHS>s(mark(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>s(active(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>sieve(mark(X))</LHS><RHS>sieve(X)</RHS></RULE><RULE><LHS>sieve(active(X))</LHS><RHS>sieve(X)</RHS></RULE><RULE><LHS>nats(mark(X))</LHS><RHS>nats(X)</RHS></RULE><RULE><LHS>nats(active(X))</LHS><RHS>nats(X)</RHS></RULE></REWSYS><DPLIST/></DPSYS></SYSTEM><CRITERION><DAG approx="simpl"><CCLIST/></DAG></CRITERION></PROPERTY></PROPERTY><PROPERTY criterion="sterm" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(filter(cons(X,Y),0,M))</LHS><RHS>mark(cons(0,filter(Y,M,M)))</RHS></RULE><RULE><LHS>active(filter(cons(X,Y),s(N),M))</LHS><RHS>mark(cons(X,filter(Y,N,M)))</RHS></RULE><RULE><LHS>active(sieve(cons(0,Y)))</LHS><RHS>mark(cons(0,sieve(Y)))</RHS></RULE><RULE><LHS>active(sieve(cons(s(N),Y)))</LHS><RHS>mark(cons(s(N),sieve(filter(Y,N,N))))</RHS></RULE><RULE><LHS>active(nats(N))</LHS><RHS>mark(cons(N,nats(s(N))))</RHS></RULE><RULE><LHS>active(zprimes)</LHS><RHS>mark(sieve(nats(s(s(0)))))</RHS></RULE><RULE><LHS>mark(filter(X1,X2,X3))</LHS><RHS>active(filter(mark(X1),mark(X2),mark(X3)))</RHS></RULE><RULE><LHS>mark(cons(X1,X2))</LHS><RHS>active(cons(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(mark(X)))</RHS></RULE><RULE><LHS>mark(sieve(X))</LHS><RHS>active(sieve(mark(X)))</RHS></RULE><RULE><LHS>mark(nats(X))</LHS><RHS>active(nats(mark(X)))</RHS></RULE><RULE><LHS>mark(zprimes)</LHS><RHS>active(zprimes)</RHS></RULE><RULE><LHS>filter(mark(X1),X2,X3)</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(X1,mark(X2),X3)</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(X1,X2,mark(X3))</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(active(X1),X2,X3)</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(X1,active(X2),X3)</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(X1,X2,active(X3))</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>cons(mark(X1),X2)</LHS><RHS>cons(X1,X2)</RHS></RULE><RULE><LHS>cons(X1,mark(X2))</LHS><RHS>cons(X1,X2)</RHS></RULE><RULE><LHS>cons(active(X1),X2)</LHS><RHS>cons(X1,X2)</RHS></RULE><RULE><LHS>cons(X1,active(X2))</LHS><RHS>cons(X1,X2)</RHS></RULE><RULE><LHS>s(mark(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>s(active(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>sieve(mark(X))</LHS><RHS>sieve(X)</RHS></RULE><RULE><LHS>sieve(active(X))</LHS><RHS>sieve(X)</RHS></RULE><RULE><LHS>nats(mark(X))</LHS><RHS>nats(X)</RHS></RULE><RULE><LHS>nats(active(X))</LHS><RHS>nats(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_nats(mark(X))</LHS><RHS>Marked_nats(X)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_nats(active(X))</LHS><RHS>Marked_nats(X)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><PROJECTION><PROJ><SYMBOL><NAME>Marked_nats</NAME></SYMBOL><INT>1</INT></PROJ></PROJECTION><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_nats(active(X))</LHS><RHS>Marked_nats(X)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_nats(mark(X))</LHS><RHS>Marked_nats(X)</RHS></DPRULE></DPLIST></STRICTPAIRS><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(filter(cons(X,Y),0,M))</LHS><RHS>mark(cons(0,filter(Y,M,M)))</RHS></RULE><RULE><LHS>active(filter(cons(X,Y),s(N),M))</LHS><RHS>mark(cons(X,filter(Y,N,M)))</RHS></RULE><RULE><LHS>active(sieve(cons(0,Y)))</LHS><RHS>mark(cons(0,sieve(Y)))</RHS></RULE><RULE><LHS>active(sieve(cons(s(N),Y)))</LHS><RHS>mark(cons(s(N),sieve(filter(Y,N,N))))</RHS></RULE><RULE><LHS>active(nats(N))</LHS><RHS>mark(cons(N,nats(s(N))))</RHS></RULE><RULE><LHS>active(zprimes)</LHS><RHS>mark(sieve(nats(s(s(0)))))</RHS></RULE><RULE><LHS>mark(filter(X1,X2,X3))</LHS><RHS>active(filter(mark(X1),mark(X2),mark(X3)))</RHS></RULE><RULE><LHS>mark(cons(X1,X2))</LHS><RHS>active(cons(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(mark(X)))</RHS></RULE><RULE><LHS>mark(sieve(X))</LHS><RHS>active(sieve(mark(X)))</RHS></RULE><RULE><LHS>mark(nats(X))</LHS><RHS>active(nats(mark(X)))</RHS></RULE><RULE><LHS>mark(zprimes)</LHS><RHS>active(zprimes)</RHS></RULE><RULE><LHS>filter(mark(X1),X2,X3)</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(X1,mark(X2),X3)</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(X1,X2,mark(X3))</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(active(X1),X2,X3)</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(X1,active(X2),X3)</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>filter(X1,X2,active(X3))</LHS><RHS>filter(X1,X2,X3)</RHS></RULE><RULE><LHS>cons(mark(X1),X2)</LHS><RHS>cons(X1,X2)</RHS></RULE><RULE><LHS>cons(X1,mark(X2))</LHS><RHS>cons(X1,X2)</RHS></RULE><RULE><LHS>cons(active(X1),X2)</LHS><RHS>cons(X1,X2)</RHS></RULE><RULE><LHS>cons(X1,active(X2))</LHS><RHS>cons(X1,X2)</RHS></RULE><RULE><LHS>s(mark(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>s(active(X))</LHS><RHS>s(X)</RHS></RULE><RULE><LHS>sieve(mark(X))</LHS><RHS>sieve(X)</RHS></RULE><RULE><LHS>sieve(active(X))</LHS><RHS>sieve(X)</RHS></RULE><RULE><LHS>nats(mark(X))</LHS><RHS>nats(X)</RHS></RULE><RULE><LHS>nats(active(X))</LHS><RHS>nats(X)</RHS></RULE></REWSYS><DPLIST/></DPSYS></SYSTEM><CRITERION><DAG approx="simpl"><CCLIST/></DAG></CRITERION></PROPERTY></PROPERTY></PROPERTY></PROPERTY></PROOF>
