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<!DOCTYPE PROOF SYSTEM "http://a3pat.ensiie.fr/pub/a3pat.dtd">
<PROOF><SIGNATURE><SYMBOLLIST><SYMBOL arity="2" unmarked="first"><NAME>Marked_first</NAME></SYMBOL><SYMBOL arity="0" unmarked=""><NAME>0</NAME></SYMBOL><SYMBOL arity="2" unmarked=""><NAME>cons</NAME></SYMBOL><SYMBOL arity="2" unmarked="and"><NAME>Marked_and</NAME></SYMBOL><SYMBOL arity="0" unmarked=""><NAME>true</NAME></SYMBOL><SYMBOL arity="1" unmarked="from"><NAME>Marked_from</NAME></SYMBOL><SYMBOL arity="1" unmarked="active"><NAME>Marked_active</NAME></SYMBOL><SYMBOL arity="3" unmarked=""><NAME>if</NAME></SYMBOL><SYMBOL arity="0" unmarked=""><NAME>nil</NAME></SYMBOL><SYMBOL arity="2" unmarked="add"><NAME>Marked_add</NAME></SYMBOL><SYMBOL arity="1" unmarked=""><NAME>active</NAME></SYMBOL><SYMBOL arity="2" unmarked="cons"><NAME>Marked_cons</NAME></SYMBOL><SYMBOL arity="2" unmarked=""><NAME>add</NAME></SYMBOL><SYMBOL arity="2" unmarked=""><NAME>first</NAME></SYMBOL><SYMBOL arity="3" unmarked="if"><NAME>Marked_if</NAME></SYMBOL><SYMBOL arity="2" unmarked=""><NAME>and</NAME></SYMBOL><SYMBOL arity="1" unmarked=""><NAME>from</NAME></SYMBOL><SYMBOL arity="1" unmarked="mark"><NAME>Marked_mark</NAME></SYMBOL><SYMBOL arity="0" unmarked=""><NAME>false</NAME></SYMBOL><SYMBOL arity="1" unmarked=""><NAME>s</NAME></SYMBOL><SYMBOL arity="1" unmarked="s"><NAME>Marked_s</NAME></SYMBOL><SYMBOL arity="1" unmarked=""><NAME>mark</NAME></SYMBOL></SYMBOLLIST><VARLIST><VAR>X3</VAR><VAR>X2</VAR><VAR>X1</VAR><VAR>Z</VAR><VAR>Y</VAR><VAR>X</VAR></VARLIST></SIGNATURE><PROPERTY criterion="dp" prop="sntrs"><SYSTEM><REWSYS><RULE><LHS>active(and(true,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(and(false,Y))</LHS><RHS>mark(false)</RHS></RULE><RULE><LHS>active(if(true,X,Y))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(if(false,X,Y))</LHS><RHS>mark(Y)</RHS></RULE><RULE><LHS>active(add(0,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(add(s(X),Y))</LHS><RHS>mark(s(add(X,Y)))</RHS></RULE><RULE><LHS>active(first(0,X))</LHS><RHS>mark(nil)</RHS></RULE><RULE><LHS>active(first(s(X),cons(Y,Z)))</LHS><RHS>mark(cons(Y,first(X,Z)))</RHS></RULE><RULE><LHS>active(from(X))</LHS><RHS>mark(cons(X,from(s(X))))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(true)</LHS><RHS>active(true)</RHS></RULE><RULE><LHS>mark(false)</LHS><RHS>active(false)</RHS></RULE><RULE><LHS>mark(if(X1,X2,X3))</LHS><RHS>active(if(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(add(X1,X2))</LHS><RHS>active(add(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(X))</RHS></RULE><RULE><LHS>mark(first(X1,X2))</LHS><RHS>active(first(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(nil)</LHS><RHS>active(nil)</RHS></RULE><RULE><LHS>mark(cons(X1,X2))</LHS><RHS>active(cons(X1,X2))</RHS></RULE><RULE><LHS>mark(from(X))</LHS><RHS>active(from(X))</RHS></RULE><RULE><LHS>and(mark(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,mark(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(active(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,active(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>if(mark(X1),X2,X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,mark(X2),X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,X2,mark(X3))</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(active(X1),X2,X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,active(X2),X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,X2,active(X3))</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>add(mark(X1),X2)</LHS><RHS>add(X1,X2)</RHS></RULE><RULE><LHS>add(X1,mark(X2))</LHS><RHS>add(X1,X2)</RHS></RULE><RULE><LHS>add(active(X1),X2)</LHS><RHS>add(X1,X2)</RHS></RULE><RULE><LHS>add(X1,active(X2))</LHS><RHS>add(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>first(mark(X1),X2)</LHS><RHS>first(X1,X2)</RHS></RULE><RULE><LHS>first(X1,mark(X2))</LHS><RHS>first(X1,X2)</RHS></RULE><RULE><LHS>first(active(X1),X2)</LHS><RHS>first(X1,X2)</RHS></RULE><RULE><LHS>first(X1,active(X2))</LHS><RHS>first(X1,X2)</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>from(mark(X))</LHS><RHS>from(X)</RHS></RULE><RULE><LHS>from(active(X))</LHS><RHS>from(X)</RHS></RULE></REWSYS></SYSTEM><CRITERION/><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(and(true,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(and(false,Y))</LHS><RHS>mark(false)</RHS></RULE><RULE><LHS>active(if(true,X,Y))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(if(false,X,Y))</LHS><RHS>mark(Y)</RHS></RULE><RULE><LHS>active(add(0,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(add(s(X),Y))</LHS><RHS>mark(s(add(X,Y)))</RHS></RULE><RULE><LHS>active(first(0,X))</LHS><RHS>mark(nil)</RHS></RULE><RULE><LHS>active(first(s(X),cons(Y,Z)))</LHS><RHS>mark(cons(Y,first(X,Z)))</RHS></RULE><RULE><LHS>active(from(X))</LHS><RHS>mark(cons(X,from(s(X))))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(true)</LHS><RHS>active(true)</RHS></RULE><RULE><LHS>mark(false)</LHS><RHS>active(false)</RHS></RULE><RULE><LHS>mark(if(X1,X2,X3))</LHS><RHS>active(if(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(add(X1,X2))</LHS><RHS>active(add(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(X))</RHS></RULE><RULE><LHS>mark(first(X1,X2))</LHS><RHS>active(first(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(nil)</LHS><RHS>active(nil)</RHS></RULE><RULE><LHS>mark(cons(X1,X2))</LHS><RHS>active(cons(X1,X2))</RHS></RULE><RULE><LHS>mark(from(X))</LHS><RHS>active(from(X))</RHS></RULE><RULE><LHS>and(mark(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,mark(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(active(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,active(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>if(mark(X1),X2,X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,mark(X2),X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,X2,mark(X3))</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(active(X1),X2,X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,active(X2),X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,X2,active(X3))</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>add(mark(X1),X2)</LHS><RHS>add(X1,X2)</RHS></RULE><RULE><LHS>add(X1,mark(X2))</LHS><RHS>add(X1,X2)</RHS></RULE><RULE><LHS>add(active(X1),X2)</LHS><RHS>add(X1,X2)</RHS></RULE><RULE><LHS>add(X1,active(X2))</LHS><RHS>add(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>first(mark(X1),X2)</LHS><RHS>first(X1,X2)</RHS></RULE><RULE><LHS>first(X1,mark(X2))</LHS><RHS>first(X1,X2)</RHS></RULE><RULE><LHS>first(active(X1),X2)</LHS><RHS>first(X1,X2)</RHS></RULE><RULE><LHS>first(X1,active(X2))</LHS><RHS>first(X1,X2)</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>from(mark(X))</LHS><RHS>from(X)</RHS></RULE><RULE><LHS>from(active(X))</LHS><RHS>from(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_active(and(true,X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_active(and(false,Y))</LHS><RHS>Marked_mark(false)</RHS></DPRULE><DPRULE num="2"><LHS>Marked_active(if(true,X,Y))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="3"><LHS>Marked_active(if(false,X,Y))</LHS><RHS>Marked_mark(Y)</RHS></DPRULE><DPRULE num="4"><LHS>Marked_active(add(0,X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="5"><LHS>Marked_active(add(s(X),Y))</LHS><RHS>Marked_mark(s(add(X,Y)))</RHS></DPRULE><DPRULE num="6"><LHS>Marked_active(add(s(X),Y))</LHS><RHS>Marked_s(add(X,Y))</RHS></DPRULE><DPRULE num="7"><LHS>Marked_active(add(s(X),Y))</LHS><RHS>Marked_add(X,Y)</RHS></DPRULE><DPRULE num="8"><LHS>Marked_active(first(0,X))</LHS><RHS>Marked_mark(nil)</RHS></DPRULE><DPRULE num="9"><LHS>Marked_active(first(s(X),cons(Y,Z)))</LHS><RHS>Marked_mark(cons(Y,first(X,Z)))</RHS></DPRULE><DPRULE num="10"><LHS>Marked_active(first(s(X),cons(Y,Z)))</LHS><RHS>Marked_cons(Y,first(X,Z))</RHS></DPRULE><DPRULE num="11"><LHS>Marked_active(first(s(X),cons(Y,Z)))</LHS><RHS>Marked_first(X,Z)</RHS></DPRULE><DPRULE num="12"><LHS>Marked_active(from(X))</LHS><RHS>Marked_mark(cons(X,from(s(X))))</RHS></DPRULE><DPRULE num="13"><LHS>Marked_active(from(X))</LHS><RHS>Marked_cons(X,from(s(X)))</RHS></DPRULE><DPRULE num="14"><LHS>Marked_active(from(X))</LHS><RHS>Marked_from(s(X))</RHS></DPRULE><DPRULE num="15"><LHS>Marked_active(from(X))</LHS><RHS>Marked_s(X)</RHS></DPRULE><DPRULE num="16"><LHS>Marked_mark(and(X1,X2))</LHS><RHS>Marked_active(and(mark(X1),X2))</RHS></DPRULE><DPRULE num="17"><LHS>Marked_mark(and(X1,X2))</LHS><RHS>Marked_and(mark(X1),X2)</RHS></DPRULE><DPRULE num="18"><LHS>Marked_mark(and(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="19"><LHS>Marked_mark(true)</LHS><RHS>Marked_active(true)</RHS></DPRULE><DPRULE num="20"><LHS>Marked_mark(false)</LHS><RHS>Marked_active(false)</RHS></DPRULE><DPRULE num="21"><LHS>Marked_mark(if(X1,X2,X3))</LHS><RHS>Marked_active(if(mark(X1),X2,X3))</RHS></DPRULE><DPRULE num="22"><LHS>Marked_mark(if(X1,X2,X3))</LHS><RHS>Marked_if(mark(X1),X2,X3)</RHS></DPRULE><DPRULE num="23"><LHS>Marked_mark(if(X1,X2,X3))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="24"><LHS>Marked_mark(add(X1,X2))</LHS><RHS>Marked_active(add(mark(X1),X2))</RHS></DPRULE><DPRULE num="25"><LHS>Marked_mark(add(X1,X2))</LHS><RHS>Marked_add(mark(X1),X2)</RHS></DPRULE><DPRULE num="26"><LHS>Marked_mark(add(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="27"><LHS>Marked_mark(0)</LHS><RHS>Marked_active(0)</RHS></DPRULE><DPRULE num="28"><LHS>Marked_mark(s(X))</LHS><RHS>Marked_active(s(X))</RHS></DPRULE><DPRULE num="29"><LHS>Marked_mark(first(X1,X2))</LHS><RHS>Marked_active(first(mark(X1),mark(X2)))</RHS></DPRULE><DPRULE num="30"><LHS>Marked_mark(first(X1,X2))</LHS><RHS>Marked_first(mark(X1),mark(X2))</RHS></DPRULE><DPRULE num="31"><LHS>Marked_mark(first(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="32"><LHS>Marked_mark(first(X1,X2))</LHS><RHS>Marked_mark(X2)</RHS></DPRULE><DPRULE num="33"><LHS>Marked_mark(nil)</LHS><RHS>Marked_active(nil)</RHS></DPRULE><DPRULE num="34"><LHS>Marked_mark(cons(X1,X2))</LHS><RHS>Marked_active(cons(X1,X2))</RHS></DPRULE><DPRULE num="35"><LHS>Marked_mark(from(X))</LHS><RHS>Marked_active(from(X))</RHS></DPRULE><DPRULE num="36"><LHS>Marked_and(mark(X1),X2)</LHS><RHS>Marked_and(X1,X2)</RHS></DPRULE><DPRULE num="37"><LHS>Marked_and(X1,mark(X2))</LHS><RHS>Marked_and(X1,X2)</RHS></DPRULE><DPRULE num="38"><LHS>Marked_and(active(X1),X2)</LHS><RHS>Marked_and(X1,X2)</RHS></DPRULE><DPRULE num="39"><LHS>Marked_and(X1,active(X2))</LHS><RHS>Marked_and(X1,X2)</RHS></DPRULE><DPRULE num="40"><LHS>Marked_if(mark(X1),X2,X3)</LHS><RHS>Marked_if(X1,X2,X3)</RHS></DPRULE><DPRULE num="41"><LHS>Marked_if(X1,mark(X2),X3)</LHS><RHS>Marked_if(X1,X2,X3)</RHS></DPRULE><DPRULE num="42"><LHS>Marked_if(X1,X2,mark(X3))</LHS><RHS>Marked_if(X1,X2,X3)</RHS></DPRULE><DPRULE num="43"><LHS>Marked_if(active(X1),X2,X3)</LHS><RHS>Marked_if(X1,X2,X3)</RHS></DPRULE><DPRULE num="44"><LHS>Marked_if(X1,active(X2),X3)</LHS><RHS>Marked_if(X1,X2,X3)</RHS></DPRULE><DPRULE num="45"><LHS>Marked_if(X1,X2,active(X3))</LHS><RHS>Marked_if(X1,X2,X3)</RHS></DPRULE><DPRULE num="46"><LHS>Marked_add(mark(X1),X2)</LHS><RHS>Marked_add(X1,X2)</RHS></DPRULE><DPRULE num="47"><LHS>Marked_add(X1,mark(X2))</LHS><RHS>Marked_add(X1,X2)</RHS></DPRULE><DPRULE num="48"><LHS>Marked_add(active(X1),X2)</LHS><RHS>Marked_add(X1,X2)</RHS></DPRULE><DPRULE num="49"><LHS>Marked_add(X1,active(X2))</LHS><RHS>Marked_add(X1,X2)</RHS></DPRULE><DPRULE num="50"><LHS>Marked_s(mark(X))</LHS><RHS>Marked_s(X)</RHS></DPRULE><DPRULE num="51"><LHS>Marked_s(active(X))</LHS><RHS>Marked_s(X)</RHS></DPRULE><DPRULE num="52"><LHS>Marked_first(mark(X1),X2)</LHS><RHS>Marked_first(X1,X2)</RHS></DPRULE><DPRULE num="53"><LHS>Marked_first(X1,mark(X2))</LHS><RHS>Marked_first(X1,X2)</RHS></DPRULE><DPRULE num="54"><LHS>Marked_first(active(X1),X2)</LHS><RHS>Marked_first(X1,X2)</RHS></DPRULE><DPRULE num="55"><LHS>Marked_first(X1,active(X2))</LHS><RHS>Marked_first(X1,X2)</RHS></DPRULE><DPRULE num="56"><LHS>Marked_cons(mark(X1),X2)</LHS><RHS>Marked_cons(X1,X2)</RHS></DPRULE><DPRULE num="57"><LHS>Marked_cons(X1,mark(X2))</LHS><RHS>Marked_cons(X1,X2)</RHS></DPRULE><DPRULE num="58"><LHS>Marked_cons(active(X1),X2)</LHS><RHS>Marked_cons(X1,X2)</RHS></DPRULE><DPRULE num="59"><LHS>Marked_cons(X1,active(X2))</LHS><RHS>Marked_cons(X1,X2)</RHS></DPRULE><DPRULE num="60"><LHS>Marked_from(mark(X))</LHS><RHS>Marked_from(X)</RHS></DPRULE><DPRULE num="61"><LHS>Marked_from(active(X))</LHS><RHS>Marked_from(X)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><DAG approx="simpl"><CCLIST><SCC num="0"><NODE ref="60"/><NODE ref="61"/></SCC><SCC num="1"><NODE ref="56"/><NODE ref="57"/><NODE ref="58"/><NODE ref="59"/></SCC><SCC num="2"><NODE ref="52"/><NODE ref="53"/><NODE ref="54"/><NODE ref="55"/></SCC><SCC num="3"><NODE ref="50"/><NODE ref="51"/></SCC><SCC num="4"><NODE ref="46"/><NODE ref="47"/><NODE ref="48"/><NODE ref="49"/></SCC><SCC num="5"><NODE ref="40"/><NODE ref="41"/><NODE ref="42"/><NODE ref="43"/><NODE ref="44"/><NODE ref="45"/></SCC><SCC num="6"><NODE ref="36"/><NODE ref="37"/><NODE ref="38"/><NODE ref="39"/></SCC><SCC num="7"><NODE ref="0"/><NODE ref="2"/><NODE ref="3"/><NODE ref="4"/><NODE ref="5"/><NODE ref="9"/><NODE ref="12"/><NODE ref="16"/><NODE ref="18"/><NODE ref="21"/><NODE ref="23"/><NODE ref="24"/><NODE ref="26"/><NODE ref="28"/><NODE ref="29"/><NODE ref="31"/><NODE ref="32"/><NODE ref="34"/><NODE ref="35"/></SCC><NONSCC num="8"><NODE ref="15"/></NONSCC><NONSCC num="9"><NODE ref="14"/></NONSCC><NONSCC num="10"><NODE ref="13"/></NONSCC><NONSCC num="11"><NODE ref="11"/></NONSCC><NONSCC num="12"><NODE ref="10"/></NONSCC><NONSCC num="13"><NODE ref="8"/></NONSCC><NONSCC num="14"><NODE ref="7"/></NONSCC><NONSCC num="15"><NODE ref="6"/></NONSCC><NONSCC num="16"><NODE ref="1"/></NONSCC><NONSCC num="17"><NODE ref="33"/></NONSCC><NONSCC num="18"><NODE ref="30"/></NONSCC><NONSCC num="19"><NODE ref="27"/></NONSCC><NONSCC num="20"><NODE ref="25"/></NONSCC><NONSCC num="21"><NODE ref="22"/></NONSCC><NONSCC num="22"><NODE ref="20"/></NONSCC><NONSCC num="23"><NODE ref="19"/></NONSCC><NONSCC num="24"><NODE ref="17"/></NONSCC></CCLIST><EDGE end="24" start="7"/><EDGE end="23" start="7"/><EDGE end="22" start="7"/><EDGE end="21" start="7"/><EDGE end="20" start="7"/><EDGE end="19" start="7"/><EDGE end="18" start="7"/><EDGE end="17" start="7"/><EDGE end="16" start="7"/><EDGE end="15" start="7"/><EDGE end="14" start="7"/><EDGE end="13" start="7"/><EDGE end="12" start="7"/><EDGE end="11" start="7"/><EDGE end="10" start="7"/><EDGE end="9" start="7"/><EDGE end="8" start="7"/><EDGE end="3" start="8"/><EDGE end="0" start="9"/><EDGE end="1" start="10"/><EDGE end="2" start="11"/><EDGE end="1" start="12"/><EDGE end="17" start="13"/><EDGE end="4" start="14"/><EDGE end="3" start="15"/><EDGE end="22" start="16"/><EDGE end="2" start="18"/><EDGE end="4" start="20"/><EDGE end="5" start="21"/><EDGE end="6" start="24"/></DAG></CRITERION><PROPERTY criterion="stronggraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(and(true,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(and(false,Y))</LHS><RHS>mark(false)</RHS></RULE><RULE><LHS>active(if(true,X,Y))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(if(false,X,Y))</LHS><RHS>mark(Y)</RHS></RULE><RULE><LHS>active(add(0,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(add(s(X),Y))</LHS><RHS>mark(s(add(X,Y)))</RHS></RULE><RULE><LHS>active(first(0,X))</LHS><RHS>mark(nil)</RHS></RULE><RULE><LHS>active(first(s(X),cons(Y,Z)))</LHS><RHS>mark(cons(Y,first(X,Z)))</RHS></RULE><RULE><LHS>active(from(X))</LHS><RHS>mark(cons(X,from(s(X))))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(true)</LHS><RHS>active(true)</RHS></RULE><RULE><LHS>mark(false)</LHS><RHS>active(false)</RHS></RULE><RULE><LHS>mark(if(X1,X2,X3))</LHS><RHS>active(if(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(add(X1,X2))</LHS><RHS>active(add(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(X))</RHS></RULE><RULE><LHS>mark(first(X1,X2))</LHS><RHS>active(first(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(nil)</LHS><RHS>active(nil)</RHS></RULE><RULE><LHS>mark(cons(X1,X2))</LHS><RHS>active(cons(X1,X2))</RHS></RULE><RULE><LHS>mark(from(X))</LHS><RHS>active(from(X))</RHS></RULE><RULE><LHS>and(mark(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,mark(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(active(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,active(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>if(mark(X1),X2,X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,mark(X2),X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,X2,mark(X3))</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(active(X1),X2,X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,active(X2),X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,X2,active(X3))</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>add(mark(X1),X2)</LHS><RHS>add(X1,X2)</RHS></RULE><RULE><LHS>add(X1,mark(X2))</LHS><RHS>add(X1,X2)</RHS></RULE><RULE><LHS>add(active(X1),X2)</LHS><RHS>add(X1,X2)</RHS></RULE><RULE><LHS>add(X1,active(X2))</LHS><RHS>add(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>first(mark(X1),X2)</LHS><RHS>first(X1,X2)</RHS></RULE><RULE><LHS>first(X1,mark(X2))</LHS><RHS>first(X1,X2)</RHS></RULE><RULE><LHS>first(active(X1),X2)</LHS><RHS>first(X1,X2)</RHS></RULE><RULE><LHS>first(X1,active(X2))</LHS><RHS>first(X1,X2)</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>from(mark(X))</LHS><RHS>from(X)</RHS></RULE><RULE><LHS>from(active(X))</LHS><RHS>from(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_active(and(true,X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_active(if(true,X,Y))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="2"><LHS>Marked_active(if(false,X,Y))</LHS><RHS>Marked_mark(Y)</RHS></DPRULE><DPRULE num="3"><LHS>Marked_active(add(0,X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="4"><LHS>Marked_active(add(s(X),Y))</LHS><RHS>Marked_mark(s(add(X,Y)))</RHS></DPRULE><DPRULE num="5"><LHS>Marked_active(first(s(X),cons(Y,Z)))</LHS><RHS>Marked_mark(cons(Y,first(X,Z)))</RHS></DPRULE><DPRULE num="6"><LHS>Marked_active(from(X))</LHS><RHS>Marked_mark(cons(X,from(s(X))))</RHS></DPRULE><DPRULE num="7"><LHS>Marked_mark(and(X1,X2))</LHS><RHS>Marked_active(and(mark(X1),X2))</RHS></DPRULE><DPRULE num="8"><LHS>Marked_mark(and(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="9"><LHS>Marked_mark(if(X1,X2,X3))</LHS><RHS>Marked_active(if(mark(X1),X2,X3))</RHS></DPRULE><DPRULE num="10"><LHS>Marked_mark(if(X1,X2,X3))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="11"><LHS>Marked_mark(add(X1,X2))</LHS><RHS>Marked_active(add(mark(X1),X2))</RHS></DPRULE><DPRULE num="12"><LHS>Marked_mark(add(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="13"><LHS>Marked_mark(s(X))</LHS><RHS>Marked_active(s(X))</RHS></DPRULE><DPRULE num="14"><LHS>Marked_mark(first(X1,X2))</LHS><RHS>Marked_active(first(mark(X1),mark(X2)))</RHS></DPRULE><DPRULE num="15"><LHS>Marked_mark(first(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="16"><LHS>Marked_mark(first(X1,X2))</LHS><RHS>Marked_mark(X2)</RHS></DPRULE><DPRULE num="17"><LHS>Marked_mark(cons(X1,X2))</LHS><RHS>Marked_active(cons(X1,X2))</RHS></DPRULE><DPRULE num="18"><LHS>Marked_mark(from(X))</LHS><RHS>Marked_active(from(X))</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><ORDERING type="poly"><POLYSYMB><SYMBOL><NAME>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>s</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>false</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><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>from</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>and</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>3</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>first</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>add</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>3</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></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>nil</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>if</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="2"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></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><POLYSYMB><SYMBOL><NAME>true</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>cons</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>0</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB></ORDERING><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_active(if(false,X,Y))</LHS><RHS>Marked_mark(Y)</RHS></DPRULE></DPLIST></STRICTPAIRS></CRITERION><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(and(true,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(and(false,Y))</LHS><RHS>mark(false)</RHS></RULE><RULE><LHS>active(if(true,X,Y))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(if(false,X,Y))</LHS><RHS>mark(Y)</RHS></RULE><RULE><LHS>active(add(0,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(add(s(X),Y))</LHS><RHS>mark(s(add(X,Y)))</RHS></RULE><RULE><LHS>active(first(0,X))</LHS><RHS>mark(nil)</RHS></RULE><RULE><LHS>active(first(s(X),cons(Y,Z)))</LHS><RHS>mark(cons(Y,first(X,Z)))</RHS></RULE><RULE><LHS>active(from(X))</LHS><RHS>mark(cons(X,from(s(X))))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(true)</LHS><RHS>active(true)</RHS></RULE><RULE><LHS>mark(false)</LHS><RHS>active(false)</RHS></RULE><RULE><LHS>mark(if(X1,X2,X3))</LHS><RHS>active(if(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(add(X1,X2))</LHS><RHS>active(add(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(X))</RHS></RULE><RULE><LHS>mark(first(X1,X2))</LHS><RHS>active(first(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(nil)</LHS><RHS>active(nil)</RHS></RULE><RULE><LHS>mark(cons(X1,X2))</LHS><RHS>active(cons(X1,X2))</RHS></RULE><RULE><LHS>mark(from(X))</LHS><RHS>active(from(X))</RHS></RULE><RULE><LHS>and(mark(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,mark(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(active(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,active(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>if(mark(X1),X2,X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,mark(X2),X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,X2,mark(X3))</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(active(X1),X2,X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,active(X2),X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,X2,active(X3))</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>add(mark(X1),X2)</LHS><RHS>add(X1,X2)</RHS></RULE><RULE><LHS>add(X1,mark(X2))</LHS><RHS>add(X1,X2)</RHS></RULE><RULE><LHS>add(active(X1),X2)</LHS><RHS>add(X1,X2)</RHS></RULE><RULE><LHS>add(X1,active(X2))</LHS><RHS>add(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>first(mark(X1),X2)</LHS><RHS>first(X1,X2)</RHS></RULE><RULE><LHS>first(X1,mark(X2))</LHS><RHS>first(X1,X2)</RHS></RULE><RULE><LHS>first(active(X1),X2)</LHS><RHS>first(X1,X2)</RHS></RULE><RULE><LHS>first(X1,active(X2))</LHS><RHS>first(X1,X2)</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>from(mark(X))</LHS><RHS>from(X)</RHS></RULE><RULE><LHS>from(active(X))</LHS><RHS>from(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_active(and(true,X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_active(if(true,X,Y))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="2"><LHS>Marked_active(add(0,X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="3"><LHS>Marked_active(add(s(X),Y))</LHS><RHS>Marked_mark(s(add(X,Y)))</RHS></DPRULE><DPRULE num="4"><LHS>Marked_active(first(s(X),cons(Y,Z)))</LHS><RHS>Marked_mark(cons(Y,first(X,Z)))</RHS></DPRULE><DPRULE num="5"><LHS>Marked_active(from(X))</LHS><RHS>Marked_mark(cons(X,from(s(X))))</RHS></DPRULE><DPRULE num="6"><LHS>Marked_mark(and(X1,X2))</LHS><RHS>Marked_active(and(mark(X1),X2))</RHS></DPRULE><DPRULE num="7"><LHS>Marked_mark(and(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="8"><LHS>Marked_mark(if(X1,X2,X3))</LHS><RHS>Marked_active(if(mark(X1),X2,X3))</RHS></DPRULE><DPRULE num="9"><LHS>Marked_mark(if(X1,X2,X3))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="10"><LHS>Marked_mark(add(X1,X2))</LHS><RHS>Marked_active(add(mark(X1),X2))</RHS></DPRULE><DPRULE num="11"><LHS>Marked_mark(add(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="12"><LHS>Marked_mark(s(X))</LHS><RHS>Marked_active(s(X))</RHS></DPRULE><DPRULE num="13"><LHS>Marked_mark(first(X1,X2))</LHS><RHS>Marked_active(first(mark(X1),mark(X2)))</RHS></DPRULE><DPRULE num="14"><LHS>Marked_mark(first(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="15"><LHS>Marked_mark(first(X1,X2))</LHS><RHS>Marked_mark(X2)</RHS></DPRULE><DPRULE num="16"><LHS>Marked_mark(cons(X1,X2))</LHS><RHS>Marked_active(cons(X1,X2))</RHS></DPRULE><DPRULE num="17"><LHS>Marked_mark(from(X))</LHS><RHS>Marked_active(from(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"/><NODE ref="15"/><NODE ref="16"/><NODE ref="17"/></SCC></CCLIST></DAG></CRITERION><PROPERTY criterion="stronggraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(and(true,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(and(false,Y))</LHS><RHS>mark(false)</RHS></RULE><RULE><LHS>active(if(true,X,Y))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(if(false,X,Y))</LHS><RHS>mark(Y)</RHS></RULE><RULE><LHS>active(add(0,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(add(s(X),Y))</LHS><RHS>mark(s(add(X,Y)))</RHS></RULE><RULE><LHS>active(first(0,X))</LHS><RHS>mark(nil)</RHS></RULE><RULE><LHS>active(first(s(X),cons(Y,Z)))</LHS><RHS>mark(cons(Y,first(X,Z)))</RHS></RULE><RULE><LHS>active(from(X))</LHS><RHS>mark(cons(X,from(s(X))))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(true)</LHS><RHS>active(true)</RHS></RULE><RULE><LHS>mark(false)</LHS><RHS>active(false)</RHS></RULE><RULE><LHS>mark(if(X1,X2,X3))</LHS><RHS>active(if(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(add(X1,X2))</LHS><RHS>active(add(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(X))</RHS></RULE><RULE><LHS>mark(first(X1,X2))</LHS><RHS>active(first(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(nil)</LHS><RHS>active(nil)</RHS></RULE><RULE><LHS>mark(cons(X1,X2))</LHS><RHS>active(cons(X1,X2))</RHS></RULE><RULE><LHS>mark(from(X))</LHS><RHS>active(from(X))</RHS></RULE><RULE><LHS>and(mark(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,mark(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(active(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,active(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>if(mark(X1),X2,X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,mark(X2),X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,X2,mark(X3))</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(active(X1),X2,X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,active(X2),X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,X2,active(X3))</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>add(mark(X1),X2)</LHS><RHS>add(X1,X2)</RHS></RULE><RULE><LHS>add(X1,mark(X2))</LHS><RHS>add(X1,X2)</RHS></RULE><RULE><LHS>add(active(X1),X2)</LHS><RHS>add(X1,X2)</RHS></RULE><RULE><LHS>add(X1,active(X2))</LHS><RHS>add(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>first(mark(X1),X2)</LHS><RHS>first(X1,X2)</RHS></RULE><RULE><LHS>first(X1,mark(X2))</LHS><RHS>first(X1,X2)</RHS></RULE><RULE><LHS>first(active(X1),X2)</LHS><RHS>first(X1,X2)</RHS></RULE><RULE><LHS>first(X1,active(X2))</LHS><RHS>first(X1,X2)</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>from(mark(X))</LHS><RHS>from(X)</RHS></RULE><RULE><LHS>from(active(X))</LHS><RHS>from(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_active(and(true,X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_active(if(true,X,Y))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="2"><LHS>Marked_active(add(0,X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="3"><LHS>Marked_active(add(s(X),Y))</LHS><RHS>Marked_mark(s(add(X,Y)))</RHS></DPRULE><DPRULE num="4"><LHS>Marked_active(first(s(X),cons(Y,Z)))</LHS><RHS>Marked_mark(cons(Y,first(X,Z)))</RHS></DPRULE><DPRULE num="5"><LHS>Marked_active(from(X))</LHS><RHS>Marked_mark(cons(X,from(s(X))))</RHS></DPRULE><DPRULE num="6"><LHS>Marked_mark(and(X1,X2))</LHS><RHS>Marked_active(and(mark(X1),X2))</RHS></DPRULE><DPRULE num="7"><LHS>Marked_mark(and(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="8"><LHS>Marked_mark(if(X1,X2,X3))</LHS><RHS>Marked_active(if(mark(X1),X2,X3))</RHS></DPRULE><DPRULE num="9"><LHS>Marked_mark(if(X1,X2,X3))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="10"><LHS>Marked_mark(add(X1,X2))</LHS><RHS>Marked_active(add(mark(X1),X2))</RHS></DPRULE><DPRULE num="11"><LHS>Marked_mark(add(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="12"><LHS>Marked_mark(s(X))</LHS><RHS>Marked_active(s(X))</RHS></DPRULE><DPRULE num="13"><LHS>Marked_mark(first(X1,X2))</LHS><RHS>Marked_active(first(mark(X1),mark(X2)))</RHS></DPRULE><DPRULE num="14"><LHS>Marked_mark(first(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="15"><LHS>Marked_mark(first(X1,X2))</LHS><RHS>Marked_mark(X2)</RHS></DPRULE><DPRULE num="16"><LHS>Marked_mark(cons(X1,X2))</LHS><RHS>Marked_active(cons(X1,X2))</RHS></DPRULE><DPRULE num="17"><LHS>Marked_mark(from(X))</LHS><RHS>Marked_active(from(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>s</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>false</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>Marked_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>from</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>and</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>first</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>add</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>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>nil</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>if</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="2"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></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><POLYSYMB><SYMBOL><NAME>true</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>cons</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>0</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB></ORDERING><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_active(from(X))</LHS><RHS>Marked_mark(cons(X,from(s(X))))</RHS></DPRULE></DPLIST></STRICTPAIRS></CRITERION><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(and(true,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(and(false,Y))</LHS><RHS>mark(false)</RHS></RULE><RULE><LHS>active(if(true,X,Y))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(if(false,X,Y))</LHS><RHS>mark(Y)</RHS></RULE><RULE><LHS>active(add(0,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(add(s(X),Y))</LHS><RHS>mark(s(add(X,Y)))</RHS></RULE><RULE><LHS>active(first(0,X))</LHS><RHS>mark(nil)</RHS></RULE><RULE><LHS>active(first(s(X),cons(Y,Z)))</LHS><RHS>mark(cons(Y,first(X,Z)))</RHS></RULE><RULE><LHS>active(from(X))</LHS><RHS>mark(cons(X,from(s(X))))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(true)</LHS><RHS>active(true)</RHS></RULE><RULE><LHS>mark(false)</LHS><RHS>active(false)</RHS></RULE><RULE><LHS>mark(if(X1,X2,X3))</LHS><RHS>active(if(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(add(X1,X2))</LHS><RHS>active(add(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(X))</RHS></RULE><RULE><LHS>mark(first(X1,X2))</LHS><RHS>active(first(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(nil)</LHS><RHS>active(nil)</RHS></RULE><RULE><LHS>mark(cons(X1,X2))</LHS><RHS>active(cons(X1,X2))</RHS></RULE><RULE><LHS>mark(from(X))</LHS><RHS>active(from(X))</RHS></RULE><RULE><LHS>and(mark(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,mark(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(active(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,active(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>if(mark(X1),X2,X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,mark(X2),X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,X2,mark(X3))</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(active(X1),X2,X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,active(X2),X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,X2,active(X3))</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>add(mark(X1),X2)</LHS><RHS>add(X1,X2)</RHS></RULE><RULE><LHS>add(X1,mark(X2))</LHS><RHS>add(X1,X2)</RHS></RULE><RULE><LHS>add(active(X1),X2)</LHS><RHS>add(X1,X2)</RHS></RULE><RULE><LHS>add(X1,active(X2))</LHS><RHS>add(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>first(mark(X1),X2)</LHS><RHS>first(X1,X2)</RHS></RULE><RULE><LHS>first(X1,mark(X2))</LHS><RHS>first(X1,X2)</RHS></RULE><RULE><LHS>first(active(X1),X2)</LHS><RHS>first(X1,X2)</RHS></RULE><RULE><LHS>first(X1,active(X2))</LHS><RHS>first(X1,X2)</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>from(mark(X))</LHS><RHS>from(X)</RHS></RULE><RULE><LHS>from(active(X))</LHS><RHS>from(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_active(and(true,X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_active(if(true,X,Y))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="2"><LHS>Marked_active(add(0,X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="3"><LHS>Marked_active(add(s(X),Y))</LHS><RHS>Marked_mark(s(add(X,Y)))</RHS></DPRULE><DPRULE num="4"><LHS>Marked_active(first(s(X),cons(Y,Z)))</LHS><RHS>Marked_mark(cons(Y,first(X,Z)))</RHS></DPRULE><DPRULE num="5"><LHS>Marked_mark(and(X1,X2))</LHS><RHS>Marked_active(and(mark(X1),X2))</RHS></DPRULE><DPRULE num="6"><LHS>Marked_mark(and(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="7"><LHS>Marked_mark(if(X1,X2,X3))</LHS><RHS>Marked_active(if(mark(X1),X2,X3))</RHS></DPRULE><DPRULE num="8"><LHS>Marked_mark(if(X1,X2,X3))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="9"><LHS>Marked_mark(add(X1,X2))</LHS><RHS>Marked_active(add(mark(X1),X2))</RHS></DPRULE><DPRULE num="10"><LHS>Marked_mark(add(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="11"><LHS>Marked_mark(s(X))</LHS><RHS>Marked_active(s(X))</RHS></DPRULE><DPRULE num="12"><LHS>Marked_mark(first(X1,X2))</LHS><RHS>Marked_active(first(mark(X1),mark(X2)))</RHS></DPRULE><DPRULE num="13"><LHS>Marked_mark(first(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="14"><LHS>Marked_mark(first(X1,X2))</LHS><RHS>Marked_mark(X2)</RHS></DPRULE><DPRULE num="15"><LHS>Marked_mark(cons(X1,X2))</LHS><RHS>Marked_active(cons(X1,X2))</RHS></DPRULE><DPRULE num="16"><LHS>Marked_mark(from(X))</LHS><RHS>Marked_active(from(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"/><NODE ref="15"/><NODE ref="16"/></SCC></CCLIST></DAG></CRITERION><PROPERTY criterion="stronggraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(and(true,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(and(false,Y))</LHS><RHS>mark(false)</RHS></RULE><RULE><LHS>active(if(true,X,Y))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(if(false,X,Y))</LHS><RHS>mark(Y)</RHS></RULE><RULE><LHS>active(add(0,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(add(s(X),Y))</LHS><RHS>mark(s(add(X,Y)))</RHS></RULE><RULE><LHS>active(first(0,X))</LHS><RHS>mark(nil)</RHS></RULE><RULE><LHS>active(first(s(X),cons(Y,Z)))</LHS><RHS>mark(cons(Y,first(X,Z)))</RHS></RULE><RULE><LHS>active(from(X))</LHS><RHS>mark(cons(X,from(s(X))))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(true)</LHS><RHS>active(true)</RHS></RULE><RULE><LHS>mark(false)</LHS><RHS>active(false)</RHS></RULE><RULE><LHS>mark(if(X1,X2,X3))</LHS><RHS>active(if(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(add(X1,X2))</LHS><RHS>active(add(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(X))</RHS></RULE><RULE><LHS>mark(first(X1,X2))</LHS><RHS>active(first(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(nil)</LHS><RHS>active(nil)</RHS></RULE><RULE><LHS>mark(cons(X1,X2))</LHS><RHS>active(cons(X1,X2))</RHS></RULE><RULE><LHS>mark(from(X))</LHS><RHS>active(from(X))</RHS></RULE><RULE><LHS>and(mark(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,mark(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(active(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,active(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>if(mark(X1),X2,X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,mark(X2),X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,X2,mark(X3))</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(active(X1),X2,X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,active(X2),X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,X2,active(X3))</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>add(mark(X1),X2)</LHS><RHS>add(X1,X2)</RHS></RULE><RULE><LHS>add(X1,mark(X2))</LHS><RHS>add(X1,X2)</RHS></RULE><RULE><LHS>add(active(X1),X2)</LHS><RHS>add(X1,X2)</RHS></RULE><RULE><LHS>add(X1,active(X2))</LHS><RHS>add(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>first(mark(X1),X2)</LHS><RHS>first(X1,X2)</RHS></RULE><RULE><LHS>first(X1,mark(X2))</LHS><RHS>first(X1,X2)</RHS></RULE><RULE><LHS>first(active(X1),X2)</LHS><RHS>first(X1,X2)</RHS></RULE><RULE><LHS>first(X1,active(X2))</LHS><RHS>first(X1,X2)</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>from(mark(X))</LHS><RHS>from(X)</RHS></RULE><RULE><LHS>from(active(X))</LHS><RHS>from(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_active(and(true,X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_active(if(true,X,Y))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="2"><LHS>Marked_active(add(0,X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="3"><LHS>Marked_active(add(s(X),Y))</LHS><RHS>Marked_mark(s(add(X,Y)))</RHS></DPRULE><DPRULE num="4"><LHS>Marked_active(first(s(X),cons(Y,Z)))</LHS><RHS>Marked_mark(cons(Y,first(X,Z)))</RHS></DPRULE><DPRULE num="5"><LHS>Marked_mark(and(X1,X2))</LHS><RHS>Marked_active(and(mark(X1),X2))</RHS></DPRULE><DPRULE num="6"><LHS>Marked_mark(and(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="7"><LHS>Marked_mark(if(X1,X2,X3))</LHS><RHS>Marked_active(if(mark(X1),X2,X3))</RHS></DPRULE><DPRULE num="8"><LHS>Marked_mark(if(X1,X2,X3))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="9"><LHS>Marked_mark(add(X1,X2))</LHS><RHS>Marked_active(add(mark(X1),X2))</RHS></DPRULE><DPRULE num="10"><LHS>Marked_mark(add(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="11"><LHS>Marked_mark(s(X))</LHS><RHS>Marked_active(s(X))</RHS></DPRULE><DPRULE num="12"><LHS>Marked_mark(first(X1,X2))</LHS><RHS>Marked_active(first(mark(X1),mark(X2)))</RHS></DPRULE><DPRULE num="13"><LHS>Marked_mark(first(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="14"><LHS>Marked_mark(first(X1,X2))</LHS><RHS>Marked_mark(X2)</RHS></DPRULE><DPRULE num="15"><LHS>Marked_mark(cons(X1,X2))</LHS><RHS>Marked_active(cons(X1,X2))</RHS></DPRULE><DPRULE num="16"><LHS>Marked_mark(from(X))</LHS><RHS>Marked_active(from(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>s</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>false</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>Marked_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>from</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>and</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>first</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>add</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>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>nil</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>if</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>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>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><POLYSYMB><SYMBOL><NAME>true</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>cons</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>0</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB></ORDERING><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_active(add(0,X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE></DPLIST></STRICTPAIRS></CRITERION><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(and(true,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(and(false,Y))</LHS><RHS>mark(false)</RHS></RULE><RULE><LHS>active(if(true,X,Y))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(if(false,X,Y))</LHS><RHS>mark(Y)</RHS></RULE><RULE><LHS>active(add(0,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(add(s(X),Y))</LHS><RHS>mark(s(add(X,Y)))</RHS></RULE><RULE><LHS>active(first(0,X))</LHS><RHS>mark(nil)</RHS></RULE><RULE><LHS>active(first(s(X),cons(Y,Z)))</LHS><RHS>mark(cons(Y,first(X,Z)))</RHS></RULE><RULE><LHS>active(from(X))</LHS><RHS>mark(cons(X,from(s(X))))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(true)</LHS><RHS>active(true)</RHS></RULE><RULE><LHS>mark(false)</LHS><RHS>active(false)</RHS></RULE><RULE><LHS>mark(if(X1,X2,X3))</LHS><RHS>active(if(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(add(X1,X2))</LHS><RHS>active(add(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(X))</RHS></RULE><RULE><LHS>mark(first(X1,X2))</LHS><RHS>active(first(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(nil)</LHS><RHS>active(nil)</RHS></RULE><RULE><LHS>mark(cons(X1,X2))</LHS><RHS>active(cons(X1,X2))</RHS></RULE><RULE><LHS>mark(from(X))</LHS><RHS>active(from(X))</RHS></RULE><RULE><LHS>and(mark(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,mark(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(active(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,active(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>if(mark(X1),X2,X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,mark(X2),X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,X2,mark(X3))</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(active(X1),X2,X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,active(X2),X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,X2,active(X3))</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>add(mark(X1),X2)</LHS><RHS>add(X1,X2)</RHS></RULE><RULE><LHS>add(X1,mark(X2))</LHS><RHS>add(X1,X2)</RHS></RULE><RULE><LHS>add(active(X1),X2)</LHS><RHS>add(X1,X2)</RHS></RULE><RULE><LHS>add(X1,active(X2))</LHS><RHS>add(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>first(mark(X1),X2)</LHS><RHS>first(X1,X2)</RHS></RULE><RULE><LHS>first(X1,mark(X2))</LHS><RHS>first(X1,X2)</RHS></RULE><RULE><LHS>first(active(X1),X2)</LHS><RHS>first(X1,X2)</RHS></RULE><RULE><LHS>first(X1,active(X2))</LHS><RHS>first(X1,X2)</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>from(mark(X))</LHS><RHS>from(X)</RHS></RULE><RULE><LHS>from(active(X))</LHS><RHS>from(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_active(and(true,X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_active(if(true,X,Y))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="2"><LHS>Marked_active(add(s(X),Y))</LHS><RHS>Marked_mark(s(add(X,Y)))</RHS></DPRULE><DPRULE num="3"><LHS>Marked_active(first(s(X),cons(Y,Z)))</LHS><RHS>Marked_mark(cons(Y,first(X,Z)))</RHS></DPRULE><DPRULE num="4"><LHS>Marked_mark(and(X1,X2))</LHS><RHS>Marked_active(and(mark(X1),X2))</RHS></DPRULE><DPRULE num="5"><LHS>Marked_mark(and(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="6"><LHS>Marked_mark(if(X1,X2,X3))</LHS><RHS>Marked_active(if(mark(X1),X2,X3))</RHS></DPRULE><DPRULE num="7"><LHS>Marked_mark(if(X1,X2,X3))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="8"><LHS>Marked_mark(add(X1,X2))</LHS><RHS>Marked_active(add(mark(X1),X2))</RHS></DPRULE><DPRULE num="9"><LHS>Marked_mark(add(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="10"><LHS>Marked_mark(s(X))</LHS><RHS>Marked_active(s(X))</RHS></DPRULE><DPRULE num="11"><LHS>Marked_mark(first(X1,X2))</LHS><RHS>Marked_active(first(mark(X1),mark(X2)))</RHS></DPRULE><DPRULE num="12"><LHS>Marked_mark(first(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="13"><LHS>Marked_mark(first(X1,X2))</LHS><RHS>Marked_mark(X2)</RHS></DPRULE><DPRULE num="14"><LHS>Marked_mark(cons(X1,X2))</LHS><RHS>Marked_active(cons(X1,X2))</RHS></DPRULE><DPRULE num="15"><LHS>Marked_mark(from(X))</LHS><RHS>Marked_active(from(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"/><NODE ref="15"/></SCC></CCLIST></DAG></CRITERION><PROPERTY criterion="stronggraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(and(true,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(and(false,Y))</LHS><RHS>mark(false)</RHS></RULE><RULE><LHS>active(if(true,X,Y))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(if(false,X,Y))</LHS><RHS>mark(Y)</RHS></RULE><RULE><LHS>active(add(0,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(add(s(X),Y))</LHS><RHS>mark(s(add(X,Y)))</RHS></RULE><RULE><LHS>active(first(0,X))</LHS><RHS>mark(nil)</RHS></RULE><RULE><LHS>active(first(s(X),cons(Y,Z)))</LHS><RHS>mark(cons(Y,first(X,Z)))</RHS></RULE><RULE><LHS>active(from(X))</LHS><RHS>mark(cons(X,from(s(X))))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(true)</LHS><RHS>active(true)</RHS></RULE><RULE><LHS>mark(false)</LHS><RHS>active(false)</RHS></RULE><RULE><LHS>mark(if(X1,X2,X3))</LHS><RHS>active(if(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(add(X1,X2))</LHS><RHS>active(add(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(X))</RHS></RULE><RULE><LHS>mark(first(X1,X2))</LHS><RHS>active(first(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(nil)</LHS><RHS>active(nil)</RHS></RULE><RULE><LHS>mark(cons(X1,X2))</LHS><RHS>active(cons(X1,X2))</RHS></RULE><RULE><LHS>mark(from(X))</LHS><RHS>active(from(X))</RHS></RULE><RULE><LHS>and(mark(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,mark(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(active(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,active(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>if(mark(X1),X2,X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,mark(X2),X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,X2,mark(X3))</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(active(X1),X2,X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,active(X2),X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,X2,active(X3))</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>add(mark(X1),X2)</LHS><RHS>add(X1,X2)</RHS></RULE><RULE><LHS>add(X1,mark(X2))</LHS><RHS>add(X1,X2)</RHS></RULE><RULE><LHS>add(active(X1),X2)</LHS><RHS>add(X1,X2)</RHS></RULE><RULE><LHS>add(X1,active(X2))</LHS><RHS>add(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>first(mark(X1),X2)</LHS><RHS>first(X1,X2)</RHS></RULE><RULE><LHS>first(X1,mark(X2))</LHS><RHS>first(X1,X2)</RHS></RULE><RULE><LHS>first(active(X1),X2)</LHS><RHS>first(X1,X2)</RHS></RULE><RULE><LHS>first(X1,active(X2))</LHS><RHS>first(X1,X2)</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>from(mark(X))</LHS><RHS>from(X)</RHS></RULE><RULE><LHS>from(active(X))</LHS><RHS>from(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_active(and(true,X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_active(if(true,X,Y))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="2"><LHS>Marked_active(add(s(X),Y))</LHS><RHS>Marked_mark(s(add(X,Y)))</RHS></DPRULE><DPRULE num="3"><LHS>Marked_active(first(s(X),cons(Y,Z)))</LHS><RHS>Marked_mark(cons(Y,first(X,Z)))</RHS></DPRULE><DPRULE num="4"><LHS>Marked_mark(and(X1,X2))</LHS><RHS>Marked_active(and(mark(X1),X2))</RHS></DPRULE><DPRULE num="5"><LHS>Marked_mark(and(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="6"><LHS>Marked_mark(if(X1,X2,X3))</LHS><RHS>Marked_active(if(mark(X1),X2,X3))</RHS></DPRULE><DPRULE num="7"><LHS>Marked_mark(if(X1,X2,X3))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="8"><LHS>Marked_mark(add(X1,X2))</LHS><RHS>Marked_active(add(mark(X1),X2))</RHS></DPRULE><DPRULE num="9"><LHS>Marked_mark(add(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="10"><LHS>Marked_mark(s(X))</LHS><RHS>Marked_active(s(X))</RHS></DPRULE><DPRULE num="11"><LHS>Marked_mark(first(X1,X2))</LHS><RHS>Marked_active(first(mark(X1),mark(X2)))</RHS></DPRULE><DPRULE num="12"><LHS>Marked_mark(first(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="13"><LHS>Marked_mark(first(X1,X2))</LHS><RHS>Marked_mark(X2)</RHS></DPRULE><DPRULE num="14"><LHS>Marked_mark(cons(X1,X2))</LHS><RHS>Marked_active(cons(X1,X2))</RHS></DPRULE><DPRULE num="15"><LHS>Marked_mark(from(X))</LHS><RHS>Marked_active(from(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>s</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>false</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>Marked_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>from</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>and</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>first</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>add</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><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>nil</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>if</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><POLYSYMB><SYMBOL><NAME>true</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>cons</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>0</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB></ORDERING><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_mark(s(X))</LHS><RHS>Marked_active(s(X))</RHS></DPRULE><DPRULE num="1"><LHS>Marked_mark(cons(X1,X2))</LHS><RHS>Marked_active(cons(X1,X2))</RHS></DPRULE><DPRULE num="2"><LHS>Marked_mark(from(X))</LHS><RHS>Marked_active(from(X))</RHS></DPRULE></DPLIST></STRICTPAIRS></CRITERION><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(and(true,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(and(false,Y))</LHS><RHS>mark(false)</RHS></RULE><RULE><LHS>active(if(true,X,Y))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(if(false,X,Y))</LHS><RHS>mark(Y)</RHS></RULE><RULE><LHS>active(add(0,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(add(s(X),Y))</LHS><RHS>mark(s(add(X,Y)))</RHS></RULE><RULE><LHS>active(first(0,X))</LHS><RHS>mark(nil)</RHS></RULE><RULE><LHS>active(first(s(X),cons(Y,Z)))</LHS><RHS>mark(cons(Y,first(X,Z)))</RHS></RULE><RULE><LHS>active(from(X))</LHS><RHS>mark(cons(X,from(s(X))))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(true)</LHS><RHS>active(true)</RHS></RULE><RULE><LHS>mark(false)</LHS><RHS>active(false)</RHS></RULE><RULE><LHS>mark(if(X1,X2,X3))</LHS><RHS>active(if(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(add(X1,X2))</LHS><RHS>active(add(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(X))</RHS></RULE><RULE><LHS>mark(first(X1,X2))</LHS><RHS>active(first(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(nil)</LHS><RHS>active(nil)</RHS></RULE><RULE><LHS>mark(cons(X1,X2))</LHS><RHS>active(cons(X1,X2))</RHS></RULE><RULE><LHS>mark(from(X))</LHS><RHS>active(from(X))</RHS></RULE><RULE><LHS>and(mark(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,mark(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(active(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,active(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>if(mark(X1),X2,X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,mark(X2),X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,X2,mark(X3))</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(active(X1),X2,X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,active(X2),X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,X2,active(X3))</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>add(mark(X1),X2)</LHS><RHS>add(X1,X2)</RHS></RULE><RULE><LHS>add(X1,mark(X2))</LHS><RHS>add(X1,X2)</RHS></RULE><RULE><LHS>add(active(X1),X2)</LHS><RHS>add(X1,X2)</RHS></RULE><RULE><LHS>add(X1,active(X2))</LHS><RHS>add(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>first(mark(X1),X2)</LHS><RHS>first(X1,X2)</RHS></RULE><RULE><LHS>first(X1,mark(X2))</LHS><RHS>first(X1,X2)</RHS></RULE><RULE><LHS>first(active(X1),X2)</LHS><RHS>first(X1,X2)</RHS></RULE><RULE><LHS>first(X1,active(X2))</LHS><RHS>first(X1,X2)</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>from(mark(X))</LHS><RHS>from(X)</RHS></RULE><RULE><LHS>from(active(X))</LHS><RHS>from(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_active(and(true,X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_active(if(true,X,Y))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="2"><LHS>Marked_active(add(s(X),Y))</LHS><RHS>Marked_mark(s(add(X,Y)))</RHS></DPRULE><DPRULE num="3"><LHS>Marked_active(first(s(X),cons(Y,Z)))</LHS><RHS>Marked_mark(cons(Y,first(X,Z)))</RHS></DPRULE><DPRULE num="4"><LHS>Marked_mark(and(X1,X2))</LHS><RHS>Marked_active(and(mark(X1),X2))</RHS></DPRULE><DPRULE num="5"><LHS>Marked_mark(and(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="6"><LHS>Marked_mark(if(X1,X2,X3))</LHS><RHS>Marked_active(if(mark(X1),X2,X3))</RHS></DPRULE><DPRULE num="7"><LHS>Marked_mark(if(X1,X2,X3))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="8"><LHS>Marked_mark(add(X1,X2))</LHS><RHS>Marked_active(add(mark(X1),X2))</RHS></DPRULE><DPRULE num="9"><LHS>Marked_mark(add(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="10"><LHS>Marked_mark(first(X1,X2))</LHS><RHS>Marked_active(first(mark(X1),mark(X2)))</RHS></DPRULE><DPRULE num="11"><LHS>Marked_mark(first(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="12"><LHS>Marked_mark(first(X1,X2))</LHS><RHS>Marked_mark(X2)</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(and(true,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(and(false,Y))</LHS><RHS>mark(false)</RHS></RULE><RULE><LHS>active(if(true,X,Y))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(if(false,X,Y))</LHS><RHS>mark(Y)</RHS></RULE><RULE><LHS>active(add(0,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(add(s(X),Y))</LHS><RHS>mark(s(add(X,Y)))</RHS></RULE><RULE><LHS>active(first(0,X))</LHS><RHS>mark(nil)</RHS></RULE><RULE><LHS>active(first(s(X),cons(Y,Z)))</LHS><RHS>mark(cons(Y,first(X,Z)))</RHS></RULE><RULE><LHS>active(from(X))</LHS><RHS>mark(cons(X,from(s(X))))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(true)</LHS><RHS>active(true)</RHS></RULE><RULE><LHS>mark(false)</LHS><RHS>active(false)</RHS></RULE><RULE><LHS>mark(if(X1,X2,X3))</LHS><RHS>active(if(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(add(X1,X2))</LHS><RHS>active(add(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(X))</RHS></RULE><RULE><LHS>mark(first(X1,X2))</LHS><RHS>active(first(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(nil)</LHS><RHS>active(nil)</RHS></RULE><RULE><LHS>mark(cons(X1,X2))</LHS><RHS>active(cons(X1,X2))</RHS></RULE><RULE><LHS>mark(from(X))</LHS><RHS>active(from(X))</RHS></RULE><RULE><LHS>and(mark(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,mark(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(active(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,active(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>if(mark(X1),X2,X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,mark(X2),X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,X2,mark(X3))</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(active(X1),X2,X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,active(X2),X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,X2,active(X3))</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>add(mark(X1),X2)</LHS><RHS>add(X1,X2)</RHS></RULE><RULE><LHS>add(X1,mark(X2))</LHS><RHS>add(X1,X2)</RHS></RULE><RULE><LHS>add(active(X1),X2)</LHS><RHS>add(X1,X2)</RHS></RULE><RULE><LHS>add(X1,active(X2))</LHS><RHS>add(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>first(mark(X1),X2)</LHS><RHS>first(X1,X2)</RHS></RULE><RULE><LHS>first(X1,mark(X2))</LHS><RHS>first(X1,X2)</RHS></RULE><RULE><LHS>first(active(X1),X2)</LHS><RHS>first(X1,X2)</RHS></RULE><RULE><LHS>first(X1,active(X2))</LHS><RHS>first(X1,X2)</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>from(mark(X))</LHS><RHS>from(X)</RHS></RULE><RULE><LHS>from(active(X))</LHS><RHS>from(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_active(and(true,X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_active(if(true,X,Y))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="2"><LHS>Marked_active(add(s(X),Y))</LHS><RHS>Marked_mark(s(add(X,Y)))</RHS></DPRULE><DPRULE num="3"><LHS>Marked_active(first(s(X),cons(Y,Z)))</LHS><RHS>Marked_mark(cons(Y,first(X,Z)))</RHS></DPRULE><DPRULE num="4"><LHS>Marked_mark(and(X1,X2))</LHS><RHS>Marked_active(and(mark(X1),X2))</RHS></DPRULE><DPRULE num="5"><LHS>Marked_mark(and(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="6"><LHS>Marked_mark(if(X1,X2,X3))</LHS><RHS>Marked_active(if(mark(X1),X2,X3))</RHS></DPRULE><DPRULE num="7"><LHS>Marked_mark(if(X1,X2,X3))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="8"><LHS>Marked_mark(add(X1,X2))</LHS><RHS>Marked_active(add(mark(X1),X2))</RHS></DPRULE><DPRULE num="9"><LHS>Marked_mark(add(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="10"><LHS>Marked_mark(first(X1,X2))</LHS><RHS>Marked_active(first(mark(X1),mark(X2)))</RHS></DPRULE><DPRULE num="11"><LHS>Marked_mark(first(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="12"><LHS>Marked_mark(first(X1,X2))</LHS><RHS>Marked_mark(X2)</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>s</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>false</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>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>from</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>and</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>first</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>add</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></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>nil</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>if</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>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>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><POLYSYMB><SYMBOL><NAME>true</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>cons</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>0</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB></ORDERING><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_active(first(s(X),cons(Y,Z)))</LHS><RHS>Marked_mark(cons(Y,first(X,Z)))</RHS></DPRULE></DPLIST></STRICTPAIRS></CRITERION><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(and(true,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(and(false,Y))</LHS><RHS>mark(false)</RHS></RULE><RULE><LHS>active(if(true,X,Y))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(if(false,X,Y))</LHS><RHS>mark(Y)</RHS></RULE><RULE><LHS>active(add(0,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(add(s(X),Y))</LHS><RHS>mark(s(add(X,Y)))</RHS></RULE><RULE><LHS>active(first(0,X))</LHS><RHS>mark(nil)</RHS></RULE><RULE><LHS>active(first(s(X),cons(Y,Z)))</LHS><RHS>mark(cons(Y,first(X,Z)))</RHS></RULE><RULE><LHS>active(from(X))</LHS><RHS>mark(cons(X,from(s(X))))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(true)</LHS><RHS>active(true)</RHS></RULE><RULE><LHS>mark(false)</LHS><RHS>active(false)</RHS></RULE><RULE><LHS>mark(if(X1,X2,X3))</LHS><RHS>active(if(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(add(X1,X2))</LHS><RHS>active(add(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(X))</RHS></RULE><RULE><LHS>mark(first(X1,X2))</LHS><RHS>active(first(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(nil)</LHS><RHS>active(nil)</RHS></RULE><RULE><LHS>mark(cons(X1,X2))</LHS><RHS>active(cons(X1,X2))</RHS></RULE><RULE><LHS>mark(from(X))</LHS><RHS>active(from(X))</RHS></RULE><RULE><LHS>and(mark(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,mark(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(active(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,active(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>if(mark(X1),X2,X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,mark(X2),X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,X2,mark(X3))</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(active(X1),X2,X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,active(X2),X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,X2,active(X3))</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>add(mark(X1),X2)</LHS><RHS>add(X1,X2)</RHS></RULE><RULE><LHS>add(X1,mark(X2))</LHS><RHS>add(X1,X2)</RHS></RULE><RULE><LHS>add(active(X1),X2)</LHS><RHS>add(X1,X2)</RHS></RULE><RULE><LHS>add(X1,active(X2))</LHS><RHS>add(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>first(mark(X1),X2)</LHS><RHS>first(X1,X2)</RHS></RULE><RULE><LHS>first(X1,mark(X2))</LHS><RHS>first(X1,X2)</RHS></RULE><RULE><LHS>first(active(X1),X2)</LHS><RHS>first(X1,X2)</RHS></RULE><RULE><LHS>first(X1,active(X2))</LHS><RHS>first(X1,X2)</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>from(mark(X))</LHS><RHS>from(X)</RHS></RULE><RULE><LHS>from(active(X))</LHS><RHS>from(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_active(and(true,X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_active(if(true,X,Y))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="2"><LHS>Marked_active(add(s(X),Y))</LHS><RHS>Marked_mark(s(add(X,Y)))</RHS></DPRULE><DPRULE num="3"><LHS>Marked_mark(and(X1,X2))</LHS><RHS>Marked_active(and(mark(X1),X2))</RHS></DPRULE><DPRULE num="4"><LHS>Marked_mark(and(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="5"><LHS>Marked_mark(if(X1,X2,X3))</LHS><RHS>Marked_active(if(mark(X1),X2,X3))</RHS></DPRULE><DPRULE num="6"><LHS>Marked_mark(if(X1,X2,X3))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="7"><LHS>Marked_mark(add(X1,X2))</LHS><RHS>Marked_active(add(mark(X1),X2))</RHS></DPRULE><DPRULE num="8"><LHS>Marked_mark(add(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="9"><LHS>Marked_mark(first(X1,X2))</LHS><RHS>Marked_active(first(mark(X1),mark(X2)))</RHS></DPRULE><DPRULE num="10"><LHS>Marked_mark(first(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="11"><LHS>Marked_mark(first(X1,X2))</LHS><RHS>Marked_mark(X2)</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"/></SCC></CCLIST></DAG></CRITERION><PROPERTY criterion="stronggraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(and(true,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(and(false,Y))</LHS><RHS>mark(false)</RHS></RULE><RULE><LHS>active(if(true,X,Y))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(if(false,X,Y))</LHS><RHS>mark(Y)</RHS></RULE><RULE><LHS>active(add(0,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(add(s(X),Y))</LHS><RHS>mark(s(add(X,Y)))</RHS></RULE><RULE><LHS>active(first(0,X))</LHS><RHS>mark(nil)</RHS></RULE><RULE><LHS>active(first(s(X),cons(Y,Z)))</LHS><RHS>mark(cons(Y,first(X,Z)))</RHS></RULE><RULE><LHS>active(from(X))</LHS><RHS>mark(cons(X,from(s(X))))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(true)</LHS><RHS>active(true)</RHS></RULE><RULE><LHS>mark(false)</LHS><RHS>active(false)</RHS></RULE><RULE><LHS>mark(if(X1,X2,X3))</LHS><RHS>active(if(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(add(X1,X2))</LHS><RHS>active(add(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(X))</RHS></RULE><RULE><LHS>mark(first(X1,X2))</LHS><RHS>active(first(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(nil)</LHS><RHS>active(nil)</RHS></RULE><RULE><LHS>mark(cons(X1,X2))</LHS><RHS>active(cons(X1,X2))</RHS></RULE><RULE><LHS>mark(from(X))</LHS><RHS>active(from(X))</RHS></RULE><RULE><LHS>and(mark(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,mark(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(active(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,active(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>if(mark(X1),X2,X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,mark(X2),X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,X2,mark(X3))</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(active(X1),X2,X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,active(X2),X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,X2,active(X3))</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>add(mark(X1),X2)</LHS><RHS>add(X1,X2)</RHS></RULE><RULE><LHS>add(X1,mark(X2))</LHS><RHS>add(X1,X2)</RHS></RULE><RULE><LHS>add(active(X1),X2)</LHS><RHS>add(X1,X2)</RHS></RULE><RULE><LHS>add(X1,active(X2))</LHS><RHS>add(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>first(mark(X1),X2)</LHS><RHS>first(X1,X2)</RHS></RULE><RULE><LHS>first(X1,mark(X2))</LHS><RHS>first(X1,X2)</RHS></RULE><RULE><LHS>first(active(X1),X2)</LHS><RHS>first(X1,X2)</RHS></RULE><RULE><LHS>first(X1,active(X2))</LHS><RHS>first(X1,X2)</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>from(mark(X))</LHS><RHS>from(X)</RHS></RULE><RULE><LHS>from(active(X))</LHS><RHS>from(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_active(and(true,X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_active(if(true,X,Y))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="2"><LHS>Marked_active(add(s(X),Y))</LHS><RHS>Marked_mark(s(add(X,Y)))</RHS></DPRULE><DPRULE num="3"><LHS>Marked_mark(and(X1,X2))</LHS><RHS>Marked_active(and(mark(X1),X2))</RHS></DPRULE><DPRULE num="4"><LHS>Marked_mark(and(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="5"><LHS>Marked_mark(if(X1,X2,X3))</LHS><RHS>Marked_active(if(mark(X1),X2,X3))</RHS></DPRULE><DPRULE num="6"><LHS>Marked_mark(if(X1,X2,X3))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="7"><LHS>Marked_mark(add(X1,X2))</LHS><RHS>Marked_active(add(mark(X1),X2))</RHS></DPRULE><DPRULE num="8"><LHS>Marked_mark(add(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="9"><LHS>Marked_mark(first(X1,X2))</LHS><RHS>Marked_active(first(mark(X1),mark(X2)))</RHS></DPRULE><DPRULE num="10"><LHS>Marked_mark(first(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="11"><LHS>Marked_mark(first(X1,X2))</LHS><RHS>Marked_mark(X2)</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>s</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>false</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>2</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>from</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>and</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>first</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>add</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>3</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>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>nil</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>if</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>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>Marked_active</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>true</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>cons</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>0</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB></ORDERING><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_active(add(s(X),Y))</LHS><RHS>Marked_mark(s(add(X,Y)))</RHS></DPRULE><DPRULE num="1"><LHS>Marked_mark(add(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE></DPLIST></STRICTPAIRS></CRITERION><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(and(true,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(and(false,Y))</LHS><RHS>mark(false)</RHS></RULE><RULE><LHS>active(if(true,X,Y))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(if(false,X,Y))</LHS><RHS>mark(Y)</RHS></RULE><RULE><LHS>active(add(0,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(add(s(X),Y))</LHS><RHS>mark(s(add(X,Y)))</RHS></RULE><RULE><LHS>active(first(0,X))</LHS><RHS>mark(nil)</RHS></RULE><RULE><LHS>active(first(s(X),cons(Y,Z)))</LHS><RHS>mark(cons(Y,first(X,Z)))</RHS></RULE><RULE><LHS>active(from(X))</LHS><RHS>mark(cons(X,from(s(X))))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(true)</LHS><RHS>active(true)</RHS></RULE><RULE><LHS>mark(false)</LHS><RHS>active(false)</RHS></RULE><RULE><LHS>mark(if(X1,X2,X3))</LHS><RHS>active(if(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(add(X1,X2))</LHS><RHS>active(add(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(X))</RHS></RULE><RULE><LHS>mark(first(X1,X2))</LHS><RHS>active(first(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(nil)</LHS><RHS>active(nil)</RHS></RULE><RULE><LHS>mark(cons(X1,X2))</LHS><RHS>active(cons(X1,X2))</RHS></RULE><RULE><LHS>mark(from(X))</LHS><RHS>active(from(X))</RHS></RULE><RULE><LHS>and(mark(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,mark(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(active(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,active(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>if(mark(X1),X2,X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,mark(X2),X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,X2,mark(X3))</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(active(X1),X2,X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,active(X2),X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,X2,active(X3))</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>add(mark(X1),X2)</LHS><RHS>add(X1,X2)</RHS></RULE><RULE><LHS>add(X1,mark(X2))</LHS><RHS>add(X1,X2)</RHS></RULE><RULE><LHS>add(active(X1),X2)</LHS><RHS>add(X1,X2)</RHS></RULE><RULE><LHS>add(X1,active(X2))</LHS><RHS>add(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>first(mark(X1),X2)</LHS><RHS>first(X1,X2)</RHS></RULE><RULE><LHS>first(X1,mark(X2))</LHS><RHS>first(X1,X2)</RHS></RULE><RULE><LHS>first(active(X1),X2)</LHS><RHS>first(X1,X2)</RHS></RULE><RULE><LHS>first(X1,active(X2))</LHS><RHS>first(X1,X2)</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>from(mark(X))</LHS><RHS>from(X)</RHS></RULE><RULE><LHS>from(active(X))</LHS><RHS>from(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_active(and(true,X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_active(if(true,X,Y))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="2"><LHS>Marked_mark(and(X1,X2))</LHS><RHS>Marked_active(and(mark(X1),X2))</RHS></DPRULE><DPRULE num="3"><LHS>Marked_mark(and(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="4"><LHS>Marked_mark(if(X1,X2,X3))</LHS><RHS>Marked_active(if(mark(X1),X2,X3))</RHS></DPRULE><DPRULE num="5"><LHS>Marked_mark(if(X1,X2,X3))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="6"><LHS>Marked_mark(add(X1,X2))</LHS><RHS>Marked_active(add(mark(X1),X2))</RHS></DPRULE><DPRULE num="7"><LHS>Marked_mark(first(X1,X2))</LHS><RHS>Marked_active(first(mark(X1),mark(X2)))</RHS></DPRULE><DPRULE num="8"><LHS>Marked_mark(first(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="9"><LHS>Marked_mark(first(X1,X2))</LHS><RHS>Marked_mark(X2)</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(and(true,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(and(false,Y))</LHS><RHS>mark(false)</RHS></RULE><RULE><LHS>active(if(true,X,Y))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(if(false,X,Y))</LHS><RHS>mark(Y)</RHS></RULE><RULE><LHS>active(add(0,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(add(s(X),Y))</LHS><RHS>mark(s(add(X,Y)))</RHS></RULE><RULE><LHS>active(first(0,X))</LHS><RHS>mark(nil)</RHS></RULE><RULE><LHS>active(first(s(X),cons(Y,Z)))</LHS><RHS>mark(cons(Y,first(X,Z)))</RHS></RULE><RULE><LHS>active(from(X))</LHS><RHS>mark(cons(X,from(s(X))))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(true)</LHS><RHS>active(true)</RHS></RULE><RULE><LHS>mark(false)</LHS><RHS>active(false)</RHS></RULE><RULE><LHS>mark(if(X1,X2,X3))</LHS><RHS>active(if(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(add(X1,X2))</LHS><RHS>active(add(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(X))</RHS></RULE><RULE><LHS>mark(first(X1,X2))</LHS><RHS>active(first(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(nil)</LHS><RHS>active(nil)</RHS></RULE><RULE><LHS>mark(cons(X1,X2))</LHS><RHS>active(cons(X1,X2))</RHS></RULE><RULE><LHS>mark(from(X))</LHS><RHS>active(from(X))</RHS></RULE><RULE><LHS>and(mark(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,mark(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(active(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,active(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>if(mark(X1),X2,X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,mark(X2),X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,X2,mark(X3))</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(active(X1),X2,X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,active(X2),X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,X2,active(X3))</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>add(mark(X1),X2)</LHS><RHS>add(X1,X2)</RHS></RULE><RULE><LHS>add(X1,mark(X2))</LHS><RHS>add(X1,X2)</RHS></RULE><RULE><LHS>add(active(X1),X2)</LHS><RHS>add(X1,X2)</RHS></RULE><RULE><LHS>add(X1,active(X2))</LHS><RHS>add(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>first(mark(X1),X2)</LHS><RHS>first(X1,X2)</RHS></RULE><RULE><LHS>first(X1,mark(X2))</LHS><RHS>first(X1,X2)</RHS></RULE><RULE><LHS>first(active(X1),X2)</LHS><RHS>first(X1,X2)</RHS></RULE><RULE><LHS>first(X1,active(X2))</LHS><RHS>first(X1,X2)</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>from(mark(X))</LHS><RHS>from(X)</RHS></RULE><RULE><LHS>from(active(X))</LHS><RHS>from(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_active(and(true,X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_active(if(true,X,Y))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="2"><LHS>Marked_mark(and(X1,X2))</LHS><RHS>Marked_active(and(mark(X1),X2))</RHS></DPRULE><DPRULE num="3"><LHS>Marked_mark(and(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="4"><LHS>Marked_mark(if(X1,X2,X3))</LHS><RHS>Marked_active(if(mark(X1),X2,X3))</RHS></DPRULE><DPRULE num="5"><LHS>Marked_mark(if(X1,X2,X3))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="6"><LHS>Marked_mark(add(X1,X2))</LHS><RHS>Marked_active(add(mark(X1),X2))</RHS></DPRULE><DPRULE num="7"><LHS>Marked_mark(first(X1,X2))</LHS><RHS>Marked_active(first(mark(X1),mark(X2)))</RHS></DPRULE><DPRULE num="8"><LHS>Marked_mark(first(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="9"><LHS>Marked_mark(first(X1,X2))</LHS><RHS>Marked_mark(X2)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><ORDERING type="poly"><POLYSYMB><SYMBOL><NAME>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>s</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>false</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>Marked_mark</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>from</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>and</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>3</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>first</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>add</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="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></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>nil</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>if</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>3</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>3</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><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></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>Marked_active</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>true</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>0</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB></ORDERING><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_active(and(true,X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_active(if(true,X,Y))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="2"><LHS>Marked_mark(and(X1,X2))</LHS><RHS>Marked_active(and(mark(X1),X2))</RHS></DPRULE><DPRULE num="3"><LHS>Marked_mark(and(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="4"><LHS>Marked_mark(if(X1,X2,X3))</LHS><RHS>Marked_active(if(mark(X1),X2,X3))</RHS></DPRULE><DPRULE num="5"><LHS>Marked_mark(if(X1,X2,X3))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="6"><LHS>Marked_mark(add(X1,X2))</LHS><RHS>Marked_active(add(mark(X1),X2))</RHS></DPRULE></DPLIST></STRICTPAIRS></CRITERION><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(and(true,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(and(false,Y))</LHS><RHS>mark(false)</RHS></RULE><RULE><LHS>active(if(true,X,Y))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(if(false,X,Y))</LHS><RHS>mark(Y)</RHS></RULE><RULE><LHS>active(add(0,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(add(s(X),Y))</LHS><RHS>mark(s(add(X,Y)))</RHS></RULE><RULE><LHS>active(first(0,X))</LHS><RHS>mark(nil)</RHS></RULE><RULE><LHS>active(first(s(X),cons(Y,Z)))</LHS><RHS>mark(cons(Y,first(X,Z)))</RHS></RULE><RULE><LHS>active(from(X))</LHS><RHS>mark(cons(X,from(s(X))))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(true)</LHS><RHS>active(true)</RHS></RULE><RULE><LHS>mark(false)</LHS><RHS>active(false)</RHS></RULE><RULE><LHS>mark(if(X1,X2,X3))</LHS><RHS>active(if(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(add(X1,X2))</LHS><RHS>active(add(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(X))</RHS></RULE><RULE><LHS>mark(first(X1,X2))</LHS><RHS>active(first(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(nil)</LHS><RHS>active(nil)</RHS></RULE><RULE><LHS>mark(cons(X1,X2))</LHS><RHS>active(cons(X1,X2))</RHS></RULE><RULE><LHS>mark(from(X))</LHS><RHS>active(from(X))</RHS></RULE><RULE><LHS>and(mark(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,mark(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(active(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,active(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>if(mark(X1),X2,X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,mark(X2),X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,X2,mark(X3))</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(active(X1),X2,X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,active(X2),X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,X2,active(X3))</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>add(mark(X1),X2)</LHS><RHS>add(X1,X2)</RHS></RULE><RULE><LHS>add(X1,mark(X2))</LHS><RHS>add(X1,X2)</RHS></RULE><RULE><LHS>add(active(X1),X2)</LHS><RHS>add(X1,X2)</RHS></RULE><RULE><LHS>add(X1,active(X2))</LHS><RHS>add(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>first(mark(X1),X2)</LHS><RHS>first(X1,X2)</RHS></RULE><RULE><LHS>first(X1,mark(X2))</LHS><RHS>first(X1,X2)</RHS></RULE><RULE><LHS>first(active(X1),X2)</LHS><RHS>first(X1,X2)</RHS></RULE><RULE><LHS>first(X1,active(X2))</LHS><RHS>first(X1,X2)</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>from(mark(X))</LHS><RHS>from(X)</RHS></RULE><RULE><LHS>from(active(X))</LHS><RHS>from(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_mark(first(X1,X2))</LHS><RHS>Marked_active(first(mark(X1),mark(X2)))</RHS></DPRULE><DPRULE num="1"><LHS>Marked_mark(first(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="2"><LHS>Marked_mark(first(X1,X2))</LHS><RHS>Marked_mark(X2)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><DAG approx="simpl"><CCLIST><SCC num="0"><NODE ref="1"/><NODE ref="2"/></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(and(true,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(and(false,Y))</LHS><RHS>mark(false)</RHS></RULE><RULE><LHS>active(if(true,X,Y))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(if(false,X,Y))</LHS><RHS>mark(Y)</RHS></RULE><RULE><LHS>active(add(0,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(add(s(X),Y))</LHS><RHS>mark(s(add(X,Y)))</RHS></RULE><RULE><LHS>active(first(0,X))</LHS><RHS>mark(nil)</RHS></RULE><RULE><LHS>active(first(s(X),cons(Y,Z)))</LHS><RHS>mark(cons(Y,first(X,Z)))</RHS></RULE><RULE><LHS>active(from(X))</LHS><RHS>mark(cons(X,from(s(X))))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(true)</LHS><RHS>active(true)</RHS></RULE><RULE><LHS>mark(false)</LHS><RHS>active(false)</RHS></RULE><RULE><LHS>mark(if(X1,X2,X3))</LHS><RHS>active(if(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(add(X1,X2))</LHS><RHS>active(add(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(X))</RHS></RULE><RULE><LHS>mark(first(X1,X2))</LHS><RHS>active(first(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(nil)</LHS><RHS>active(nil)</RHS></RULE><RULE><LHS>mark(cons(X1,X2))</LHS><RHS>active(cons(X1,X2))</RHS></RULE><RULE><LHS>mark(from(X))</LHS><RHS>active(from(X))</RHS></RULE><RULE><LHS>and(mark(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,mark(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(active(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,active(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>if(mark(X1),X2,X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,mark(X2),X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,X2,mark(X3))</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(active(X1),X2,X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,active(X2),X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,X2,active(X3))</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>add(mark(X1),X2)</LHS><RHS>add(X1,X2)</RHS></RULE><RULE><LHS>add(X1,mark(X2))</LHS><RHS>add(X1,X2)</RHS></RULE><RULE><LHS>add(active(X1),X2)</LHS><RHS>add(X1,X2)</RHS></RULE><RULE><LHS>add(X1,active(X2))</LHS><RHS>add(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>first(mark(X1),X2)</LHS><RHS>first(X1,X2)</RHS></RULE><RULE><LHS>first(X1,mark(X2))</LHS><RHS>first(X1,X2)</RHS></RULE><RULE><LHS>first(active(X1),X2)</LHS><RHS>first(X1,X2)</RHS></RULE><RULE><LHS>first(X1,active(X2))</LHS><RHS>first(X1,X2)</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>from(mark(X))</LHS><RHS>from(X)</RHS></RULE><RULE><LHS>from(active(X))</LHS><RHS>from(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_mark(first(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_mark(first(X1,X2))</LHS><RHS>Marked_mark(X2)</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(first(X1,X2))</LHS><RHS>Marked_mark(X2)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_mark(first(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE></DPLIST></STRICTPAIRS><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(and(true,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(and(false,Y))</LHS><RHS>mark(false)</RHS></RULE><RULE><LHS>active(if(true,X,Y))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(if(false,X,Y))</LHS><RHS>mark(Y)</RHS></RULE><RULE><LHS>active(add(0,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(add(s(X),Y))</LHS><RHS>mark(s(add(X,Y)))</RHS></RULE><RULE><LHS>active(first(0,X))</LHS><RHS>mark(nil)</RHS></RULE><RULE><LHS>active(first(s(X),cons(Y,Z)))</LHS><RHS>mark(cons(Y,first(X,Z)))</RHS></RULE><RULE><LHS>active(from(X))</LHS><RHS>mark(cons(X,from(s(X))))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(true)</LHS><RHS>active(true)</RHS></RULE><RULE><LHS>mark(false)</LHS><RHS>active(false)</RHS></RULE><RULE><LHS>mark(if(X1,X2,X3))</LHS><RHS>active(if(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(add(X1,X2))</LHS><RHS>active(add(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(X))</RHS></RULE><RULE><LHS>mark(first(X1,X2))</LHS><RHS>active(first(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(nil)</LHS><RHS>active(nil)</RHS></RULE><RULE><LHS>mark(cons(X1,X2))</LHS><RHS>active(cons(X1,X2))</RHS></RULE><RULE><LHS>mark(from(X))</LHS><RHS>active(from(X))</RHS></RULE><RULE><LHS>and(mark(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,mark(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(active(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,active(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>if(mark(X1),X2,X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,mark(X2),X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,X2,mark(X3))</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(active(X1),X2,X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,active(X2),X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,X2,active(X3))</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>add(mark(X1),X2)</LHS><RHS>add(X1,X2)</RHS></RULE><RULE><LHS>add(X1,mark(X2))</LHS><RHS>add(X1,X2)</RHS></RULE><RULE><LHS>add(active(X1),X2)</LHS><RHS>add(X1,X2)</RHS></RULE><RULE><LHS>add(X1,active(X2))</LHS><RHS>add(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>first(mark(X1),X2)</LHS><RHS>first(X1,X2)</RHS></RULE><RULE><LHS>first(X1,mark(X2))</LHS><RHS>first(X1,X2)</RHS></RULE><RULE><LHS>first(active(X1),X2)</LHS><RHS>first(X1,X2)</RHS></RULE><RULE><LHS>first(X1,active(X2))</LHS><RHS>first(X1,X2)</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>from(mark(X))</LHS><RHS>from(X)</RHS></RULE><RULE><LHS>from(active(X))</LHS><RHS>from(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(and(true,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(and(false,Y))</LHS><RHS>mark(false)</RHS></RULE><RULE><LHS>active(if(true,X,Y))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(if(false,X,Y))</LHS><RHS>mark(Y)</RHS></RULE><RULE><LHS>active(add(0,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(add(s(X),Y))</LHS><RHS>mark(s(add(X,Y)))</RHS></RULE><RULE><LHS>active(first(0,X))</LHS><RHS>mark(nil)</RHS></RULE><RULE><LHS>active(first(s(X),cons(Y,Z)))</LHS><RHS>mark(cons(Y,first(X,Z)))</RHS></RULE><RULE><LHS>active(from(X))</LHS><RHS>mark(cons(X,from(s(X))))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(true)</LHS><RHS>active(true)</RHS></RULE><RULE><LHS>mark(false)</LHS><RHS>active(false)</RHS></RULE><RULE><LHS>mark(if(X1,X2,X3))</LHS><RHS>active(if(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(add(X1,X2))</LHS><RHS>active(add(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(X))</RHS></RULE><RULE><LHS>mark(first(X1,X2))</LHS><RHS>active(first(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(nil)</LHS><RHS>active(nil)</RHS></RULE><RULE><LHS>mark(cons(X1,X2))</LHS><RHS>active(cons(X1,X2))</RHS></RULE><RULE><LHS>mark(from(X))</LHS><RHS>active(from(X))</RHS></RULE><RULE><LHS>and(mark(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,mark(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(active(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,active(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>if(mark(X1),X2,X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,mark(X2),X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,X2,mark(X3))</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(active(X1),X2,X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,active(X2),X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,X2,active(X3))</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>add(mark(X1),X2)</LHS><RHS>add(X1,X2)</RHS></RULE><RULE><LHS>add(X1,mark(X2))</LHS><RHS>add(X1,X2)</RHS></RULE><RULE><LHS>add(active(X1),X2)</LHS><RHS>add(X1,X2)</RHS></RULE><RULE><LHS>add(X1,active(X2))</LHS><RHS>add(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>first(mark(X1),X2)</LHS><RHS>first(X1,X2)</RHS></RULE><RULE><LHS>first(X1,mark(X2))</LHS><RHS>first(X1,X2)</RHS></RULE><RULE><LHS>first(active(X1),X2)</LHS><RHS>first(X1,X2)</RHS></RULE><RULE><LHS>first(X1,active(X2))</LHS><RHS>first(X1,X2)</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>from(mark(X))</LHS><RHS>from(X)</RHS></RULE><RULE><LHS>from(active(X))</LHS><RHS>from(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_and(mark(X1),X2)</LHS><RHS>Marked_and(X1,X2)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_and(X1,mark(X2))</LHS><RHS>Marked_and(X1,X2)</RHS></DPRULE><DPRULE num="2"><LHS>Marked_and(active(X1),X2)</LHS><RHS>Marked_and(X1,X2)</RHS></DPRULE><DPRULE num="3"><LHS>Marked_and(X1,active(X2))</LHS><RHS>Marked_and(X1,X2)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><PROJECTION><PROJ><SYMBOL><NAME>Marked_and</NAME></SYMBOL><INT>2</INT></PROJ></PROJECTION><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_and(X1,active(X2))</LHS><RHS>Marked_and(X1,X2)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_and(X1,mark(X2))</LHS><RHS>Marked_and(X1,X2)</RHS></DPRULE></DPLIST></STRICTPAIRS><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(and(true,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(and(false,Y))</LHS><RHS>mark(false)</RHS></RULE><RULE><LHS>active(if(true,X,Y))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(if(false,X,Y))</LHS><RHS>mark(Y)</RHS></RULE><RULE><LHS>active(add(0,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(add(s(X),Y))</LHS><RHS>mark(s(add(X,Y)))</RHS></RULE><RULE><LHS>active(first(0,X))</LHS><RHS>mark(nil)</RHS></RULE><RULE><LHS>active(first(s(X),cons(Y,Z)))</LHS><RHS>mark(cons(Y,first(X,Z)))</RHS></RULE><RULE><LHS>active(from(X))</LHS><RHS>mark(cons(X,from(s(X))))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(true)</LHS><RHS>active(true)</RHS></RULE><RULE><LHS>mark(false)</LHS><RHS>active(false)</RHS></RULE><RULE><LHS>mark(if(X1,X2,X3))</LHS><RHS>active(if(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(add(X1,X2))</LHS><RHS>active(add(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(X))</RHS></RULE><RULE><LHS>mark(first(X1,X2))</LHS><RHS>active(first(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(nil)</LHS><RHS>active(nil)</RHS></RULE><RULE><LHS>mark(cons(X1,X2))</LHS><RHS>active(cons(X1,X2))</RHS></RULE><RULE><LHS>mark(from(X))</LHS><RHS>active(from(X))</RHS></RULE><RULE><LHS>and(mark(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,mark(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(active(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,active(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>if(mark(X1),X2,X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,mark(X2),X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,X2,mark(X3))</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(active(X1),X2,X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,active(X2),X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,X2,active(X3))</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>add(mark(X1),X2)</LHS><RHS>add(X1,X2)</RHS></RULE><RULE><LHS>add(X1,mark(X2))</LHS><RHS>add(X1,X2)</RHS></RULE><RULE><LHS>add(active(X1),X2)</LHS><RHS>add(X1,X2)</RHS></RULE><RULE><LHS>add(X1,active(X2))</LHS><RHS>add(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>first(mark(X1),X2)</LHS><RHS>first(X1,X2)</RHS></RULE><RULE><LHS>first(X1,mark(X2))</LHS><RHS>first(X1,X2)</RHS></RULE><RULE><LHS>first(active(X1),X2)</LHS><RHS>first(X1,X2)</RHS></RULE><RULE><LHS>first(X1,active(X2))</LHS><RHS>first(X1,X2)</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>from(mark(X))</LHS><RHS>from(X)</RHS></RULE><RULE><LHS>from(active(X))</LHS><RHS>from(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_and(active(X1),X2)</LHS><RHS>Marked_and(X1,X2)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_and(mark(X1),X2)</LHS><RHS>Marked_and(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(and(true,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(and(false,Y))</LHS><RHS>mark(false)</RHS></RULE><RULE><LHS>active(if(true,X,Y))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(if(false,X,Y))</LHS><RHS>mark(Y)</RHS></RULE><RULE><LHS>active(add(0,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(add(s(X),Y))</LHS><RHS>mark(s(add(X,Y)))</RHS></RULE><RULE><LHS>active(first(0,X))</LHS><RHS>mark(nil)</RHS></RULE><RULE><LHS>active(first(s(X),cons(Y,Z)))</LHS><RHS>mark(cons(Y,first(X,Z)))</RHS></RULE><RULE><LHS>active(from(X))</LHS><RHS>mark(cons(X,from(s(X))))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(true)</LHS><RHS>active(true)</RHS></RULE><RULE><LHS>mark(false)</LHS><RHS>active(false)</RHS></RULE><RULE><LHS>mark(if(X1,X2,X3))</LHS><RHS>active(if(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(add(X1,X2))</LHS><RHS>active(add(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(X))</RHS></RULE><RULE><LHS>mark(first(X1,X2))</LHS><RHS>active(first(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(nil)</LHS><RHS>active(nil)</RHS></RULE><RULE><LHS>mark(cons(X1,X2))</LHS><RHS>active(cons(X1,X2))</RHS></RULE><RULE><LHS>mark(from(X))</LHS><RHS>active(from(X))</RHS></RULE><RULE><LHS>and(mark(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,mark(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(active(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,active(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>if(mark(X1),X2,X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,mark(X2),X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,X2,mark(X3))</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(active(X1),X2,X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,active(X2),X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,X2,active(X3))</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>add(mark(X1),X2)</LHS><RHS>add(X1,X2)</RHS></RULE><RULE><LHS>add(X1,mark(X2))</LHS><RHS>add(X1,X2)</RHS></RULE><RULE><LHS>add(active(X1),X2)</LHS><RHS>add(X1,X2)</RHS></RULE><RULE><LHS>add(X1,active(X2))</LHS><RHS>add(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>first(mark(X1),X2)</LHS><RHS>first(X1,X2)</RHS></RULE><RULE><LHS>first(X1,mark(X2))</LHS><RHS>first(X1,X2)</RHS></RULE><RULE><LHS>first(active(X1),X2)</LHS><RHS>first(X1,X2)</RHS></RULE><RULE><LHS>first(X1,active(X2))</LHS><RHS>first(X1,X2)</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>from(mark(X))</LHS><RHS>from(X)</RHS></RULE><RULE><LHS>from(active(X))</LHS><RHS>from(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_and(active(X1),X2)</LHS><RHS>Marked_and(X1,X2)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_and(mark(X1),X2)</LHS><RHS>Marked_and(X1,X2)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><PROJECTION><PROJ><SYMBOL><NAME>Marked_and</NAME></SYMBOL><INT>1</INT></PROJ></PROJECTION><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_and(mark(X1),X2)</LHS><RHS>Marked_and(X1,X2)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_and(active(X1),X2)</LHS><RHS>Marked_and(X1,X2)</RHS></DPRULE></DPLIST></STRICTPAIRS><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(and(true,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(and(false,Y))</LHS><RHS>mark(false)</RHS></RULE><RULE><LHS>active(if(true,X,Y))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(if(false,X,Y))</LHS><RHS>mark(Y)</RHS></RULE><RULE><LHS>active(add(0,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(add(s(X),Y))</LHS><RHS>mark(s(add(X,Y)))</RHS></RULE><RULE><LHS>active(first(0,X))</LHS><RHS>mark(nil)</RHS></RULE><RULE><LHS>active(first(s(X),cons(Y,Z)))</LHS><RHS>mark(cons(Y,first(X,Z)))</RHS></RULE><RULE><LHS>active(from(X))</LHS><RHS>mark(cons(X,from(s(X))))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(true)</LHS><RHS>active(true)</RHS></RULE><RULE><LHS>mark(false)</LHS><RHS>active(false)</RHS></RULE><RULE><LHS>mark(if(X1,X2,X3))</LHS><RHS>active(if(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(add(X1,X2))</LHS><RHS>active(add(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(X))</RHS></RULE><RULE><LHS>mark(first(X1,X2))</LHS><RHS>active(first(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(nil)</LHS><RHS>active(nil)</RHS></RULE><RULE><LHS>mark(cons(X1,X2))</LHS><RHS>active(cons(X1,X2))</RHS></RULE><RULE><LHS>mark(from(X))</LHS><RHS>active(from(X))</RHS></RULE><RULE><LHS>and(mark(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,mark(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(active(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,active(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>if(mark(X1),X2,X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,mark(X2),X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,X2,mark(X3))</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(active(X1),X2,X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,active(X2),X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,X2,active(X3))</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>add(mark(X1),X2)</LHS><RHS>add(X1,X2)</RHS></RULE><RULE><LHS>add(X1,mark(X2))</LHS><RHS>add(X1,X2)</RHS></RULE><RULE><LHS>add(active(X1),X2)</LHS><RHS>add(X1,X2)</RHS></RULE><RULE><LHS>add(X1,active(X2))</LHS><RHS>add(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>first(mark(X1),X2)</LHS><RHS>first(X1,X2)</RHS></RULE><RULE><LHS>first(X1,mark(X2))</LHS><RHS>first(X1,X2)</RHS></RULE><RULE><LHS>first(active(X1),X2)</LHS><RHS>first(X1,X2)</RHS></RULE><RULE><LHS>first(X1,active(X2))</LHS><RHS>first(X1,X2)</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>from(mark(X))</LHS><RHS>from(X)</RHS></RULE><RULE><LHS>from(active(X))</LHS><RHS>from(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(and(true,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(and(false,Y))</LHS><RHS>mark(false)</RHS></RULE><RULE><LHS>active(if(true,X,Y))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(if(false,X,Y))</LHS><RHS>mark(Y)</RHS></RULE><RULE><LHS>active(add(0,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(add(s(X),Y))</LHS><RHS>mark(s(add(X,Y)))</RHS></RULE><RULE><LHS>active(first(0,X))</LHS><RHS>mark(nil)</RHS></RULE><RULE><LHS>active(first(s(X),cons(Y,Z)))</LHS><RHS>mark(cons(Y,first(X,Z)))</RHS></RULE><RULE><LHS>active(from(X))</LHS><RHS>mark(cons(X,from(s(X))))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(true)</LHS><RHS>active(true)</RHS></RULE><RULE><LHS>mark(false)</LHS><RHS>active(false)</RHS></RULE><RULE><LHS>mark(if(X1,X2,X3))</LHS><RHS>active(if(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(add(X1,X2))</LHS><RHS>active(add(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(X))</RHS></RULE><RULE><LHS>mark(first(X1,X2))</LHS><RHS>active(first(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(nil)</LHS><RHS>active(nil)</RHS></RULE><RULE><LHS>mark(cons(X1,X2))</LHS><RHS>active(cons(X1,X2))</RHS></RULE><RULE><LHS>mark(from(X))</LHS><RHS>active(from(X))</RHS></RULE><RULE><LHS>and(mark(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,mark(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(active(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,active(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>if(mark(X1),X2,X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,mark(X2),X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,X2,mark(X3))</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(active(X1),X2,X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,active(X2),X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,X2,active(X3))</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>add(mark(X1),X2)</LHS><RHS>add(X1,X2)</RHS></RULE><RULE><LHS>add(X1,mark(X2))</LHS><RHS>add(X1,X2)</RHS></RULE><RULE><LHS>add(active(X1),X2)</LHS><RHS>add(X1,X2)</RHS></RULE><RULE><LHS>add(X1,active(X2))</LHS><RHS>add(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>first(mark(X1),X2)</LHS><RHS>first(X1,X2)</RHS></RULE><RULE><LHS>first(X1,mark(X2))</LHS><RHS>first(X1,X2)</RHS></RULE><RULE><LHS>first(active(X1),X2)</LHS><RHS>first(X1,X2)</RHS></RULE><RULE><LHS>first(X1,active(X2))</LHS><RHS>first(X1,X2)</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>from(mark(X))</LHS><RHS>from(X)</RHS></RULE><RULE><LHS>from(active(X))</LHS><RHS>from(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_if(mark(X1),X2,X3)</LHS><RHS>Marked_if(X1,X2,X3)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_if(X1,mark(X2),X3)</LHS><RHS>Marked_if(X1,X2,X3)</RHS></DPRULE><DPRULE num="2"><LHS>Marked_if(X1,X2,mark(X3))</LHS><RHS>Marked_if(X1,X2,X3)</RHS></DPRULE><DPRULE num="3"><LHS>Marked_if(active(X1),X2,X3)</LHS><RHS>Marked_if(X1,X2,X3)</RHS></DPRULE><DPRULE num="4"><LHS>Marked_if(X1,active(X2),X3)</LHS><RHS>Marked_if(X1,X2,X3)</RHS></DPRULE><DPRULE num="5"><LHS>Marked_if(X1,X2,active(X3))</LHS><RHS>Marked_if(X1,X2,X3)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><PROJECTION><PROJ><SYMBOL><NAME>Marked_if</NAME></SYMBOL><INT>3</INT></PROJ></PROJECTION><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_if(X1,X2,active(X3))</LHS><RHS>Marked_if(X1,X2,X3)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_if(X1,X2,mark(X3))</LHS><RHS>Marked_if(X1,X2,X3)</RHS></DPRULE></DPLIST></STRICTPAIRS><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(and(true,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(and(false,Y))</LHS><RHS>mark(false)</RHS></RULE><RULE><LHS>active(if(true,X,Y))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(if(false,X,Y))</LHS><RHS>mark(Y)</RHS></RULE><RULE><LHS>active(add(0,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(add(s(X),Y))</LHS><RHS>mark(s(add(X,Y)))</RHS></RULE><RULE><LHS>active(first(0,X))</LHS><RHS>mark(nil)</RHS></RULE><RULE><LHS>active(first(s(X),cons(Y,Z)))</LHS><RHS>mark(cons(Y,first(X,Z)))</RHS></RULE><RULE><LHS>active(from(X))</LHS><RHS>mark(cons(X,from(s(X))))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(true)</LHS><RHS>active(true)</RHS></RULE><RULE><LHS>mark(false)</LHS><RHS>active(false)</RHS></RULE><RULE><LHS>mark(if(X1,X2,X3))</LHS><RHS>active(if(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(add(X1,X2))</LHS><RHS>active(add(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(X))</RHS></RULE><RULE><LHS>mark(first(X1,X2))</LHS><RHS>active(first(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(nil)</LHS><RHS>active(nil)</RHS></RULE><RULE><LHS>mark(cons(X1,X2))</LHS><RHS>active(cons(X1,X2))</RHS></RULE><RULE><LHS>mark(from(X))</LHS><RHS>active(from(X))</RHS></RULE><RULE><LHS>and(mark(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,mark(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(active(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,active(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>if(mark(X1),X2,X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,mark(X2),X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,X2,mark(X3))</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(active(X1),X2,X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,active(X2),X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,X2,active(X3))</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>add(mark(X1),X2)</LHS><RHS>add(X1,X2)</RHS></RULE><RULE><LHS>add(X1,mark(X2))</LHS><RHS>add(X1,X2)</RHS></RULE><RULE><LHS>add(active(X1),X2)</LHS><RHS>add(X1,X2)</RHS></RULE><RULE><LHS>add(X1,active(X2))</LHS><RHS>add(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>first(mark(X1),X2)</LHS><RHS>first(X1,X2)</RHS></RULE><RULE><LHS>first(X1,mark(X2))</LHS><RHS>first(X1,X2)</RHS></RULE><RULE><LHS>first(active(X1),X2)</LHS><RHS>first(X1,X2)</RHS></RULE><RULE><LHS>first(X1,active(X2))</LHS><RHS>first(X1,X2)</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>from(mark(X))</LHS><RHS>from(X)</RHS></RULE><RULE><LHS>from(active(X))</LHS><RHS>from(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_if(X1,active(X2),X3)</LHS><RHS>Marked_if(X1,X2,X3)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_if(active(X1),X2,X3)</LHS><RHS>Marked_if(X1,X2,X3)</RHS></DPRULE><DPRULE num="2"><LHS>Marked_if(X1,mark(X2),X3)</LHS><RHS>Marked_if(X1,X2,X3)</RHS></DPRULE><DPRULE num="3"><LHS>Marked_if(mark(X1),X2,X3)</LHS><RHS>Marked_if(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(and(true,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(and(false,Y))</LHS><RHS>mark(false)</RHS></RULE><RULE><LHS>active(if(true,X,Y))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(if(false,X,Y))</LHS><RHS>mark(Y)</RHS></RULE><RULE><LHS>active(add(0,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(add(s(X),Y))</LHS><RHS>mark(s(add(X,Y)))</RHS></RULE><RULE><LHS>active(first(0,X))</LHS><RHS>mark(nil)</RHS></RULE><RULE><LHS>active(first(s(X),cons(Y,Z)))</LHS><RHS>mark(cons(Y,first(X,Z)))</RHS></RULE><RULE><LHS>active(from(X))</LHS><RHS>mark(cons(X,from(s(X))))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(true)</LHS><RHS>active(true)</RHS></RULE><RULE><LHS>mark(false)</LHS><RHS>active(false)</RHS></RULE><RULE><LHS>mark(if(X1,X2,X3))</LHS><RHS>active(if(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(add(X1,X2))</LHS><RHS>active(add(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(X))</RHS></RULE><RULE><LHS>mark(first(X1,X2))</LHS><RHS>active(first(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(nil)</LHS><RHS>active(nil)</RHS></RULE><RULE><LHS>mark(cons(X1,X2))</LHS><RHS>active(cons(X1,X2))</RHS></RULE><RULE><LHS>mark(from(X))</LHS><RHS>active(from(X))</RHS></RULE><RULE><LHS>and(mark(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,mark(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(active(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,active(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>if(mark(X1),X2,X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,mark(X2),X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,X2,mark(X3))</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(active(X1),X2,X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,active(X2),X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,X2,active(X3))</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>add(mark(X1),X2)</LHS><RHS>add(X1,X2)</RHS></RULE><RULE><LHS>add(X1,mark(X2))</LHS><RHS>add(X1,X2)</RHS></RULE><RULE><LHS>add(active(X1),X2)</LHS><RHS>add(X1,X2)</RHS></RULE><RULE><LHS>add(X1,active(X2))</LHS><RHS>add(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>first(mark(X1),X2)</LHS><RHS>first(X1,X2)</RHS></RULE><RULE><LHS>first(X1,mark(X2))</LHS><RHS>first(X1,X2)</RHS></RULE><RULE><LHS>first(active(X1),X2)</LHS><RHS>first(X1,X2)</RHS></RULE><RULE><LHS>first(X1,active(X2))</LHS><RHS>first(X1,X2)</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>from(mark(X))</LHS><RHS>from(X)</RHS></RULE><RULE><LHS>from(active(X))</LHS><RHS>from(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_if(X1,active(X2),X3)</LHS><RHS>Marked_if(X1,X2,X3)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_if(active(X1),X2,X3)</LHS><RHS>Marked_if(X1,X2,X3)</RHS></DPRULE><DPRULE num="2"><LHS>Marked_if(X1,mark(X2),X3)</LHS><RHS>Marked_if(X1,X2,X3)</RHS></DPRULE><DPRULE num="3"><LHS>Marked_if(mark(X1),X2,X3)</LHS><RHS>Marked_if(X1,X2,X3)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><PROJECTION><PROJ><SYMBOL><NAME>Marked_if</NAME></SYMBOL><INT>2</INT></PROJ></PROJECTION><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_if(X1,mark(X2),X3)</LHS><RHS>Marked_if(X1,X2,X3)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_if(X1,active(X2),X3)</LHS><RHS>Marked_if(X1,X2,X3)</RHS></DPRULE></DPLIST></STRICTPAIRS><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(and(true,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(and(false,Y))</LHS><RHS>mark(false)</RHS></RULE><RULE><LHS>active(if(true,X,Y))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(if(false,X,Y))</LHS><RHS>mark(Y)</RHS></RULE><RULE><LHS>active(add(0,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(add(s(X),Y))</LHS><RHS>mark(s(add(X,Y)))</RHS></RULE><RULE><LHS>active(first(0,X))</LHS><RHS>mark(nil)</RHS></RULE><RULE><LHS>active(first(s(X),cons(Y,Z)))</LHS><RHS>mark(cons(Y,first(X,Z)))</RHS></RULE><RULE><LHS>active(from(X))</LHS><RHS>mark(cons(X,from(s(X))))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(true)</LHS><RHS>active(true)</RHS></RULE><RULE><LHS>mark(false)</LHS><RHS>active(false)</RHS></RULE><RULE><LHS>mark(if(X1,X2,X3))</LHS><RHS>active(if(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(add(X1,X2))</LHS><RHS>active(add(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(X))</RHS></RULE><RULE><LHS>mark(first(X1,X2))</LHS><RHS>active(first(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(nil)</LHS><RHS>active(nil)</RHS></RULE><RULE><LHS>mark(cons(X1,X2))</LHS><RHS>active(cons(X1,X2))</RHS></RULE><RULE><LHS>mark(from(X))</LHS><RHS>active(from(X))</RHS></RULE><RULE><LHS>and(mark(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,mark(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(active(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,active(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>if(mark(X1),X2,X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,mark(X2),X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,X2,mark(X3))</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(active(X1),X2,X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,active(X2),X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,X2,active(X3))</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>add(mark(X1),X2)</LHS><RHS>add(X1,X2)</RHS></RULE><RULE><LHS>add(X1,mark(X2))</LHS><RHS>add(X1,X2)</RHS></RULE><RULE><LHS>add(active(X1),X2)</LHS><RHS>add(X1,X2)</RHS></RULE><RULE><LHS>add(X1,active(X2))</LHS><RHS>add(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>first(mark(X1),X2)</LHS><RHS>first(X1,X2)</RHS></RULE><RULE><LHS>first(X1,mark(X2))</LHS><RHS>first(X1,X2)</RHS></RULE><RULE><LHS>first(active(X1),X2)</LHS><RHS>first(X1,X2)</RHS></RULE><RULE><LHS>first(X1,active(X2))</LHS><RHS>first(X1,X2)</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>from(mark(X))</LHS><RHS>from(X)</RHS></RULE><RULE><LHS>from(active(X))</LHS><RHS>from(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_if(mark(X1),X2,X3)</LHS><RHS>Marked_if(X1,X2,X3)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_if(active(X1),X2,X3)</LHS><RHS>Marked_if(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(and(true,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(and(false,Y))</LHS><RHS>mark(false)</RHS></RULE><RULE><LHS>active(if(true,X,Y))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(if(false,X,Y))</LHS><RHS>mark(Y)</RHS></RULE><RULE><LHS>active(add(0,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(add(s(X),Y))</LHS><RHS>mark(s(add(X,Y)))</RHS></RULE><RULE><LHS>active(first(0,X))</LHS><RHS>mark(nil)</RHS></RULE><RULE><LHS>active(first(s(X),cons(Y,Z)))</LHS><RHS>mark(cons(Y,first(X,Z)))</RHS></RULE><RULE><LHS>active(from(X))</LHS><RHS>mark(cons(X,from(s(X))))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(true)</LHS><RHS>active(true)</RHS></RULE><RULE><LHS>mark(false)</LHS><RHS>active(false)</RHS></RULE><RULE><LHS>mark(if(X1,X2,X3))</LHS><RHS>active(if(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(add(X1,X2))</LHS><RHS>active(add(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(X))</RHS></RULE><RULE><LHS>mark(first(X1,X2))</LHS><RHS>active(first(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(nil)</LHS><RHS>active(nil)</RHS></RULE><RULE><LHS>mark(cons(X1,X2))</LHS><RHS>active(cons(X1,X2))</RHS></RULE><RULE><LHS>mark(from(X))</LHS><RHS>active(from(X))</RHS></RULE><RULE><LHS>and(mark(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,mark(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(active(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,active(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>if(mark(X1),X2,X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,mark(X2),X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,X2,mark(X3))</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(active(X1),X2,X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,active(X2),X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,X2,active(X3))</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>add(mark(X1),X2)</LHS><RHS>add(X1,X2)</RHS></RULE><RULE><LHS>add(X1,mark(X2))</LHS><RHS>add(X1,X2)</RHS></RULE><RULE><LHS>add(active(X1),X2)</LHS><RHS>add(X1,X2)</RHS></RULE><RULE><LHS>add(X1,active(X2))</LHS><RHS>add(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>first(mark(X1),X2)</LHS><RHS>first(X1,X2)</RHS></RULE><RULE><LHS>first(X1,mark(X2))</LHS><RHS>first(X1,X2)</RHS></RULE><RULE><LHS>first(active(X1),X2)</LHS><RHS>first(X1,X2)</RHS></RULE><RULE><LHS>first(X1,active(X2))</LHS><RHS>first(X1,X2)</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>from(mark(X))</LHS><RHS>from(X)</RHS></RULE><RULE><LHS>from(active(X))</LHS><RHS>from(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_if(mark(X1),X2,X3)</LHS><RHS>Marked_if(X1,X2,X3)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_if(active(X1),X2,X3)</LHS><RHS>Marked_if(X1,X2,X3)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><PROJECTION><PROJ><SYMBOL><NAME>Marked_if</NAME></SYMBOL><INT>1</INT></PROJ></PROJECTION><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_if(active(X1),X2,X3)</LHS><RHS>Marked_if(X1,X2,X3)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_if(mark(X1),X2,X3)</LHS><RHS>Marked_if(X1,X2,X3)</RHS></DPRULE></DPLIST></STRICTPAIRS><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(and(true,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(and(false,Y))</LHS><RHS>mark(false)</RHS></RULE><RULE><LHS>active(if(true,X,Y))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(if(false,X,Y))</LHS><RHS>mark(Y)</RHS></RULE><RULE><LHS>active(add(0,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(add(s(X),Y))</LHS><RHS>mark(s(add(X,Y)))</RHS></RULE><RULE><LHS>active(first(0,X))</LHS><RHS>mark(nil)</RHS></RULE><RULE><LHS>active(first(s(X),cons(Y,Z)))</LHS><RHS>mark(cons(Y,first(X,Z)))</RHS></RULE><RULE><LHS>active(from(X))</LHS><RHS>mark(cons(X,from(s(X))))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(true)</LHS><RHS>active(true)</RHS></RULE><RULE><LHS>mark(false)</LHS><RHS>active(false)</RHS></RULE><RULE><LHS>mark(if(X1,X2,X3))</LHS><RHS>active(if(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(add(X1,X2))</LHS><RHS>active(add(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(X))</RHS></RULE><RULE><LHS>mark(first(X1,X2))</LHS><RHS>active(first(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(nil)</LHS><RHS>active(nil)</RHS></RULE><RULE><LHS>mark(cons(X1,X2))</LHS><RHS>active(cons(X1,X2))</RHS></RULE><RULE><LHS>mark(from(X))</LHS><RHS>active(from(X))</RHS></RULE><RULE><LHS>and(mark(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,mark(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(active(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,active(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>if(mark(X1),X2,X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,mark(X2),X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,X2,mark(X3))</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(active(X1),X2,X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,active(X2),X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,X2,active(X3))</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>add(mark(X1),X2)</LHS><RHS>add(X1,X2)</RHS></RULE><RULE><LHS>add(X1,mark(X2))</LHS><RHS>add(X1,X2)</RHS></RULE><RULE><LHS>add(active(X1),X2)</LHS><RHS>add(X1,X2)</RHS></RULE><RULE><LHS>add(X1,active(X2))</LHS><RHS>add(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>first(mark(X1),X2)</LHS><RHS>first(X1,X2)</RHS></RULE><RULE><LHS>first(X1,mark(X2))</LHS><RHS>first(X1,X2)</RHS></RULE><RULE><LHS>first(active(X1),X2)</LHS><RHS>first(X1,X2)</RHS></RULE><RULE><LHS>first(X1,active(X2))</LHS><RHS>first(X1,X2)</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>from(mark(X))</LHS><RHS>from(X)</RHS></RULE><RULE><LHS>from(active(X))</LHS><RHS>from(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(and(true,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(and(false,Y))</LHS><RHS>mark(false)</RHS></RULE><RULE><LHS>active(if(true,X,Y))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(if(false,X,Y))</LHS><RHS>mark(Y)</RHS></RULE><RULE><LHS>active(add(0,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(add(s(X),Y))</LHS><RHS>mark(s(add(X,Y)))</RHS></RULE><RULE><LHS>active(first(0,X))</LHS><RHS>mark(nil)</RHS></RULE><RULE><LHS>active(first(s(X),cons(Y,Z)))</LHS><RHS>mark(cons(Y,first(X,Z)))</RHS></RULE><RULE><LHS>active(from(X))</LHS><RHS>mark(cons(X,from(s(X))))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(true)</LHS><RHS>active(true)</RHS></RULE><RULE><LHS>mark(false)</LHS><RHS>active(false)</RHS></RULE><RULE><LHS>mark(if(X1,X2,X3))</LHS><RHS>active(if(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(add(X1,X2))</LHS><RHS>active(add(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(X))</RHS></RULE><RULE><LHS>mark(first(X1,X2))</LHS><RHS>active(first(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(nil)</LHS><RHS>active(nil)</RHS></RULE><RULE><LHS>mark(cons(X1,X2))</LHS><RHS>active(cons(X1,X2))</RHS></RULE><RULE><LHS>mark(from(X))</LHS><RHS>active(from(X))</RHS></RULE><RULE><LHS>and(mark(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,mark(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(active(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,active(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>if(mark(X1),X2,X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,mark(X2),X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,X2,mark(X3))</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(active(X1),X2,X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,active(X2),X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,X2,active(X3))</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>add(mark(X1),X2)</LHS><RHS>add(X1,X2)</RHS></RULE><RULE><LHS>add(X1,mark(X2))</LHS><RHS>add(X1,X2)</RHS></RULE><RULE><LHS>add(active(X1),X2)</LHS><RHS>add(X1,X2)</RHS></RULE><RULE><LHS>add(X1,active(X2))</LHS><RHS>add(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>first(mark(X1),X2)</LHS><RHS>first(X1,X2)</RHS></RULE><RULE><LHS>first(X1,mark(X2))</LHS><RHS>first(X1,X2)</RHS></RULE><RULE><LHS>first(active(X1),X2)</LHS><RHS>first(X1,X2)</RHS></RULE><RULE><LHS>first(X1,active(X2))</LHS><RHS>first(X1,X2)</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>from(mark(X))</LHS><RHS>from(X)</RHS></RULE><RULE><LHS>from(active(X))</LHS><RHS>from(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_add(mark(X1),X2)</LHS><RHS>Marked_add(X1,X2)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_add(X1,mark(X2))</LHS><RHS>Marked_add(X1,X2)</RHS></DPRULE><DPRULE num="2"><LHS>Marked_add(active(X1),X2)</LHS><RHS>Marked_add(X1,X2)</RHS></DPRULE><DPRULE num="3"><LHS>Marked_add(X1,active(X2))</LHS><RHS>Marked_add(X1,X2)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><PROJECTION><PROJ><SYMBOL><NAME>Marked_add</NAME></SYMBOL><INT>2</INT></PROJ></PROJECTION><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_add(X1,active(X2))</LHS><RHS>Marked_add(X1,X2)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_add(X1,mark(X2))</LHS><RHS>Marked_add(X1,X2)</RHS></DPRULE></DPLIST></STRICTPAIRS><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(and(true,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(and(false,Y))</LHS><RHS>mark(false)</RHS></RULE><RULE><LHS>active(if(true,X,Y))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(if(false,X,Y))</LHS><RHS>mark(Y)</RHS></RULE><RULE><LHS>active(add(0,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(add(s(X),Y))</LHS><RHS>mark(s(add(X,Y)))</RHS></RULE><RULE><LHS>active(first(0,X))</LHS><RHS>mark(nil)</RHS></RULE><RULE><LHS>active(first(s(X),cons(Y,Z)))</LHS><RHS>mark(cons(Y,first(X,Z)))</RHS></RULE><RULE><LHS>active(from(X))</LHS><RHS>mark(cons(X,from(s(X))))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(true)</LHS><RHS>active(true)</RHS></RULE><RULE><LHS>mark(false)</LHS><RHS>active(false)</RHS></RULE><RULE><LHS>mark(if(X1,X2,X3))</LHS><RHS>active(if(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(add(X1,X2))</LHS><RHS>active(add(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(X))</RHS></RULE><RULE><LHS>mark(first(X1,X2))</LHS><RHS>active(first(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(nil)</LHS><RHS>active(nil)</RHS></RULE><RULE><LHS>mark(cons(X1,X2))</LHS><RHS>active(cons(X1,X2))</RHS></RULE><RULE><LHS>mark(from(X))</LHS><RHS>active(from(X))</RHS></RULE><RULE><LHS>and(mark(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,mark(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(active(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,active(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>if(mark(X1),X2,X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,mark(X2),X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,X2,mark(X3))</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(active(X1),X2,X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,active(X2),X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,X2,active(X3))</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>add(mark(X1),X2)</LHS><RHS>add(X1,X2)</RHS></RULE><RULE><LHS>add(X1,mark(X2))</LHS><RHS>add(X1,X2)</RHS></RULE><RULE><LHS>add(active(X1),X2)</LHS><RHS>add(X1,X2)</RHS></RULE><RULE><LHS>add(X1,active(X2))</LHS><RHS>add(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>first(mark(X1),X2)</LHS><RHS>first(X1,X2)</RHS></RULE><RULE><LHS>first(X1,mark(X2))</LHS><RHS>first(X1,X2)</RHS></RULE><RULE><LHS>first(active(X1),X2)</LHS><RHS>first(X1,X2)</RHS></RULE><RULE><LHS>first(X1,active(X2))</LHS><RHS>first(X1,X2)</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>from(mark(X))</LHS><RHS>from(X)</RHS></RULE><RULE><LHS>from(active(X))</LHS><RHS>from(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_add(active(X1),X2)</LHS><RHS>Marked_add(X1,X2)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_add(mark(X1),X2)</LHS><RHS>Marked_add(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(and(true,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(and(false,Y))</LHS><RHS>mark(false)</RHS></RULE><RULE><LHS>active(if(true,X,Y))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(if(false,X,Y))</LHS><RHS>mark(Y)</RHS></RULE><RULE><LHS>active(add(0,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(add(s(X),Y))</LHS><RHS>mark(s(add(X,Y)))</RHS></RULE><RULE><LHS>active(first(0,X))</LHS><RHS>mark(nil)</RHS></RULE><RULE><LHS>active(first(s(X),cons(Y,Z)))</LHS><RHS>mark(cons(Y,first(X,Z)))</RHS></RULE><RULE><LHS>active(from(X))</LHS><RHS>mark(cons(X,from(s(X))))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(true)</LHS><RHS>active(true)</RHS></RULE><RULE><LHS>mark(false)</LHS><RHS>active(false)</RHS></RULE><RULE><LHS>mark(if(X1,X2,X3))</LHS><RHS>active(if(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(add(X1,X2))</LHS><RHS>active(add(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(X))</RHS></RULE><RULE><LHS>mark(first(X1,X2))</LHS><RHS>active(first(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(nil)</LHS><RHS>active(nil)</RHS></RULE><RULE><LHS>mark(cons(X1,X2))</LHS><RHS>active(cons(X1,X2))</RHS></RULE><RULE><LHS>mark(from(X))</LHS><RHS>active(from(X))</RHS></RULE><RULE><LHS>and(mark(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,mark(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(active(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,active(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>if(mark(X1),X2,X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,mark(X2),X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,X2,mark(X3))</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(active(X1),X2,X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,active(X2),X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,X2,active(X3))</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>add(mark(X1),X2)</LHS><RHS>add(X1,X2)</RHS></RULE><RULE><LHS>add(X1,mark(X2))</LHS><RHS>add(X1,X2)</RHS></RULE><RULE><LHS>add(active(X1),X2)</LHS><RHS>add(X1,X2)</RHS></RULE><RULE><LHS>add(X1,active(X2))</LHS><RHS>add(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>first(mark(X1),X2)</LHS><RHS>first(X1,X2)</RHS></RULE><RULE><LHS>first(X1,mark(X2))</LHS><RHS>first(X1,X2)</RHS></RULE><RULE><LHS>first(active(X1),X2)</LHS><RHS>first(X1,X2)</RHS></RULE><RULE><LHS>first(X1,active(X2))</LHS><RHS>first(X1,X2)</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>from(mark(X))</LHS><RHS>from(X)</RHS></RULE><RULE><LHS>from(active(X))</LHS><RHS>from(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_add(active(X1),X2)</LHS><RHS>Marked_add(X1,X2)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_add(mark(X1),X2)</LHS><RHS>Marked_add(X1,X2)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><PROJECTION><PROJ><SYMBOL><NAME>Marked_add</NAME></SYMBOL><INT>1</INT></PROJ></PROJECTION><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_add(mark(X1),X2)</LHS><RHS>Marked_add(X1,X2)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_add(active(X1),X2)</LHS><RHS>Marked_add(X1,X2)</RHS></DPRULE></DPLIST></STRICTPAIRS><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(and(true,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(and(false,Y))</LHS><RHS>mark(false)</RHS></RULE><RULE><LHS>active(if(true,X,Y))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(if(false,X,Y))</LHS><RHS>mark(Y)</RHS></RULE><RULE><LHS>active(add(0,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(add(s(X),Y))</LHS><RHS>mark(s(add(X,Y)))</RHS></RULE><RULE><LHS>active(first(0,X))</LHS><RHS>mark(nil)</RHS></RULE><RULE><LHS>active(first(s(X),cons(Y,Z)))</LHS><RHS>mark(cons(Y,first(X,Z)))</RHS></RULE><RULE><LHS>active(from(X))</LHS><RHS>mark(cons(X,from(s(X))))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(true)</LHS><RHS>active(true)</RHS></RULE><RULE><LHS>mark(false)</LHS><RHS>active(false)</RHS></RULE><RULE><LHS>mark(if(X1,X2,X3))</LHS><RHS>active(if(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(add(X1,X2))</LHS><RHS>active(add(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(X))</RHS></RULE><RULE><LHS>mark(first(X1,X2))</LHS><RHS>active(first(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(nil)</LHS><RHS>active(nil)</RHS></RULE><RULE><LHS>mark(cons(X1,X2))</LHS><RHS>active(cons(X1,X2))</RHS></RULE><RULE><LHS>mark(from(X))</LHS><RHS>active(from(X))</RHS></RULE><RULE><LHS>and(mark(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,mark(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(active(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,active(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>if(mark(X1),X2,X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,mark(X2),X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,X2,mark(X3))</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(active(X1),X2,X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,active(X2),X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,X2,active(X3))</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>add(mark(X1),X2)</LHS><RHS>add(X1,X2)</RHS></RULE><RULE><LHS>add(X1,mark(X2))</LHS><RHS>add(X1,X2)</RHS></RULE><RULE><LHS>add(active(X1),X2)</LHS><RHS>add(X1,X2)</RHS></RULE><RULE><LHS>add(X1,active(X2))</LHS><RHS>add(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>first(mark(X1),X2)</LHS><RHS>first(X1,X2)</RHS></RULE><RULE><LHS>first(X1,mark(X2))</LHS><RHS>first(X1,X2)</RHS></RULE><RULE><LHS>first(active(X1),X2)</LHS><RHS>first(X1,X2)</RHS></RULE><RULE><LHS>first(X1,active(X2))</LHS><RHS>first(X1,X2)</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>from(mark(X))</LHS><RHS>from(X)</RHS></RULE><RULE><LHS>from(active(X))</LHS><RHS>from(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(and(true,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(and(false,Y))</LHS><RHS>mark(false)</RHS></RULE><RULE><LHS>active(if(true,X,Y))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(if(false,X,Y))</LHS><RHS>mark(Y)</RHS></RULE><RULE><LHS>active(add(0,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(add(s(X),Y))</LHS><RHS>mark(s(add(X,Y)))</RHS></RULE><RULE><LHS>active(first(0,X))</LHS><RHS>mark(nil)</RHS></RULE><RULE><LHS>active(first(s(X),cons(Y,Z)))</LHS><RHS>mark(cons(Y,first(X,Z)))</RHS></RULE><RULE><LHS>active(from(X))</LHS><RHS>mark(cons(X,from(s(X))))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(true)</LHS><RHS>active(true)</RHS></RULE><RULE><LHS>mark(false)</LHS><RHS>active(false)</RHS></RULE><RULE><LHS>mark(if(X1,X2,X3))</LHS><RHS>active(if(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(add(X1,X2))</LHS><RHS>active(add(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(X))</RHS></RULE><RULE><LHS>mark(first(X1,X2))</LHS><RHS>active(first(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(nil)</LHS><RHS>active(nil)</RHS></RULE><RULE><LHS>mark(cons(X1,X2))</LHS><RHS>active(cons(X1,X2))</RHS></RULE><RULE><LHS>mark(from(X))</LHS><RHS>active(from(X))</RHS></RULE><RULE><LHS>and(mark(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,mark(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(active(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,active(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>if(mark(X1),X2,X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,mark(X2),X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,X2,mark(X3))</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(active(X1),X2,X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,active(X2),X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,X2,active(X3))</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>add(mark(X1),X2)</LHS><RHS>add(X1,X2)</RHS></RULE><RULE><LHS>add(X1,mark(X2))</LHS><RHS>add(X1,X2)</RHS></RULE><RULE><LHS>add(active(X1),X2)</LHS><RHS>add(X1,X2)</RHS></RULE><RULE><LHS>add(X1,active(X2))</LHS><RHS>add(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>first(mark(X1),X2)</LHS><RHS>first(X1,X2)</RHS></RULE><RULE><LHS>first(X1,mark(X2))</LHS><RHS>first(X1,X2)</RHS></RULE><RULE><LHS>first(active(X1),X2)</LHS><RHS>first(X1,X2)</RHS></RULE><RULE><LHS>first(X1,active(X2))</LHS><RHS>first(X1,X2)</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>from(mark(X))</LHS><RHS>from(X)</RHS></RULE><RULE><LHS>from(active(X))</LHS><RHS>from(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(and(true,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(and(false,Y))</LHS><RHS>mark(false)</RHS></RULE><RULE><LHS>active(if(true,X,Y))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(if(false,X,Y))</LHS><RHS>mark(Y)</RHS></RULE><RULE><LHS>active(add(0,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(add(s(X),Y))</LHS><RHS>mark(s(add(X,Y)))</RHS></RULE><RULE><LHS>active(first(0,X))</LHS><RHS>mark(nil)</RHS></RULE><RULE><LHS>active(first(s(X),cons(Y,Z)))</LHS><RHS>mark(cons(Y,first(X,Z)))</RHS></RULE><RULE><LHS>active(from(X))</LHS><RHS>mark(cons(X,from(s(X))))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(true)</LHS><RHS>active(true)</RHS></RULE><RULE><LHS>mark(false)</LHS><RHS>active(false)</RHS></RULE><RULE><LHS>mark(if(X1,X2,X3))</LHS><RHS>active(if(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(add(X1,X2))</LHS><RHS>active(add(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(X))</RHS></RULE><RULE><LHS>mark(first(X1,X2))</LHS><RHS>active(first(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(nil)</LHS><RHS>active(nil)</RHS></RULE><RULE><LHS>mark(cons(X1,X2))</LHS><RHS>active(cons(X1,X2))</RHS></RULE><RULE><LHS>mark(from(X))</LHS><RHS>active(from(X))</RHS></RULE><RULE><LHS>and(mark(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,mark(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(active(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,active(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>if(mark(X1),X2,X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,mark(X2),X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,X2,mark(X3))</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(active(X1),X2,X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,active(X2),X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,X2,active(X3))</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>add(mark(X1),X2)</LHS><RHS>add(X1,X2)</RHS></RULE><RULE><LHS>add(X1,mark(X2))</LHS><RHS>add(X1,X2)</RHS></RULE><RULE><LHS>add(active(X1),X2)</LHS><RHS>add(X1,X2)</RHS></RULE><RULE><LHS>add(X1,active(X2))</LHS><RHS>add(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>first(mark(X1),X2)</LHS><RHS>first(X1,X2)</RHS></RULE><RULE><LHS>first(X1,mark(X2))</LHS><RHS>first(X1,X2)</RHS></RULE><RULE><LHS>first(active(X1),X2)</LHS><RHS>first(X1,X2)</RHS></RULE><RULE><LHS>first(X1,active(X2))</LHS><RHS>first(X1,X2)</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>from(mark(X))</LHS><RHS>from(X)</RHS></RULE><RULE><LHS>from(active(X))</LHS><RHS>from(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(and(true,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(and(false,Y))</LHS><RHS>mark(false)</RHS></RULE><RULE><LHS>active(if(true,X,Y))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(if(false,X,Y))</LHS><RHS>mark(Y)</RHS></RULE><RULE><LHS>active(add(0,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(add(s(X),Y))</LHS><RHS>mark(s(add(X,Y)))</RHS></RULE><RULE><LHS>active(first(0,X))</LHS><RHS>mark(nil)</RHS></RULE><RULE><LHS>active(first(s(X),cons(Y,Z)))</LHS><RHS>mark(cons(Y,first(X,Z)))</RHS></RULE><RULE><LHS>active(from(X))</LHS><RHS>mark(cons(X,from(s(X))))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(true)</LHS><RHS>active(true)</RHS></RULE><RULE><LHS>mark(false)</LHS><RHS>active(false)</RHS></RULE><RULE><LHS>mark(if(X1,X2,X3))</LHS><RHS>active(if(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(add(X1,X2))</LHS><RHS>active(add(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(X))</RHS></RULE><RULE><LHS>mark(first(X1,X2))</LHS><RHS>active(first(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(nil)</LHS><RHS>active(nil)</RHS></RULE><RULE><LHS>mark(cons(X1,X2))</LHS><RHS>active(cons(X1,X2))</RHS></RULE><RULE><LHS>mark(from(X))</LHS><RHS>active(from(X))</RHS></RULE><RULE><LHS>and(mark(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,mark(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(active(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,active(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>if(mark(X1),X2,X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,mark(X2),X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,X2,mark(X3))</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(active(X1),X2,X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,active(X2),X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,X2,active(X3))</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>add(mark(X1),X2)</LHS><RHS>add(X1,X2)</RHS></RULE><RULE><LHS>add(X1,mark(X2))</LHS><RHS>add(X1,X2)</RHS></RULE><RULE><LHS>add(active(X1),X2)</LHS><RHS>add(X1,X2)</RHS></RULE><RULE><LHS>add(X1,active(X2))</LHS><RHS>add(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>first(mark(X1),X2)</LHS><RHS>first(X1,X2)</RHS></RULE><RULE><LHS>first(X1,mark(X2))</LHS><RHS>first(X1,X2)</RHS></RULE><RULE><LHS>first(active(X1),X2)</LHS><RHS>first(X1,X2)</RHS></RULE><RULE><LHS>first(X1,active(X2))</LHS><RHS>first(X1,X2)</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>from(mark(X))</LHS><RHS>from(X)</RHS></RULE><RULE><LHS>from(active(X))</LHS><RHS>from(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_first(mark(X1),X2)</LHS><RHS>Marked_first(X1,X2)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_first(X1,mark(X2))</LHS><RHS>Marked_first(X1,X2)</RHS></DPRULE><DPRULE num="2"><LHS>Marked_first(active(X1),X2)</LHS><RHS>Marked_first(X1,X2)</RHS></DPRULE><DPRULE num="3"><LHS>Marked_first(X1,active(X2))</LHS><RHS>Marked_first(X1,X2)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><PROJECTION><PROJ><SYMBOL><NAME>Marked_first</NAME></SYMBOL><INT>2</INT></PROJ></PROJECTION><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_first(X1,active(X2))</LHS><RHS>Marked_first(X1,X2)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_first(X1,mark(X2))</LHS><RHS>Marked_first(X1,X2)</RHS></DPRULE></DPLIST></STRICTPAIRS><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(and(true,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(and(false,Y))</LHS><RHS>mark(false)</RHS></RULE><RULE><LHS>active(if(true,X,Y))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(if(false,X,Y))</LHS><RHS>mark(Y)</RHS></RULE><RULE><LHS>active(add(0,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(add(s(X),Y))</LHS><RHS>mark(s(add(X,Y)))</RHS></RULE><RULE><LHS>active(first(0,X))</LHS><RHS>mark(nil)</RHS></RULE><RULE><LHS>active(first(s(X),cons(Y,Z)))</LHS><RHS>mark(cons(Y,first(X,Z)))</RHS></RULE><RULE><LHS>active(from(X))</LHS><RHS>mark(cons(X,from(s(X))))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(true)</LHS><RHS>active(true)</RHS></RULE><RULE><LHS>mark(false)</LHS><RHS>active(false)</RHS></RULE><RULE><LHS>mark(if(X1,X2,X3))</LHS><RHS>active(if(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(add(X1,X2))</LHS><RHS>active(add(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(X))</RHS></RULE><RULE><LHS>mark(first(X1,X2))</LHS><RHS>active(first(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(nil)</LHS><RHS>active(nil)</RHS></RULE><RULE><LHS>mark(cons(X1,X2))</LHS><RHS>active(cons(X1,X2))</RHS></RULE><RULE><LHS>mark(from(X))</LHS><RHS>active(from(X))</RHS></RULE><RULE><LHS>and(mark(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,mark(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(active(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,active(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>if(mark(X1),X2,X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,mark(X2),X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,X2,mark(X3))</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(active(X1),X2,X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,active(X2),X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,X2,active(X3))</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>add(mark(X1),X2)</LHS><RHS>add(X1,X2)</RHS></RULE><RULE><LHS>add(X1,mark(X2))</LHS><RHS>add(X1,X2)</RHS></RULE><RULE><LHS>add(active(X1),X2)</LHS><RHS>add(X1,X2)</RHS></RULE><RULE><LHS>add(X1,active(X2))</LHS><RHS>add(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>first(mark(X1),X2)</LHS><RHS>first(X1,X2)</RHS></RULE><RULE><LHS>first(X1,mark(X2))</LHS><RHS>first(X1,X2)</RHS></RULE><RULE><LHS>first(active(X1),X2)</LHS><RHS>first(X1,X2)</RHS></RULE><RULE><LHS>first(X1,active(X2))</LHS><RHS>first(X1,X2)</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>from(mark(X))</LHS><RHS>from(X)</RHS></RULE><RULE><LHS>from(active(X))</LHS><RHS>from(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_first(active(X1),X2)</LHS><RHS>Marked_first(X1,X2)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_first(mark(X1),X2)</LHS><RHS>Marked_first(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(and(true,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(and(false,Y))</LHS><RHS>mark(false)</RHS></RULE><RULE><LHS>active(if(true,X,Y))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(if(false,X,Y))</LHS><RHS>mark(Y)</RHS></RULE><RULE><LHS>active(add(0,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(add(s(X),Y))</LHS><RHS>mark(s(add(X,Y)))</RHS></RULE><RULE><LHS>active(first(0,X))</LHS><RHS>mark(nil)</RHS></RULE><RULE><LHS>active(first(s(X),cons(Y,Z)))</LHS><RHS>mark(cons(Y,first(X,Z)))</RHS></RULE><RULE><LHS>active(from(X))</LHS><RHS>mark(cons(X,from(s(X))))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(true)</LHS><RHS>active(true)</RHS></RULE><RULE><LHS>mark(false)</LHS><RHS>active(false)</RHS></RULE><RULE><LHS>mark(if(X1,X2,X3))</LHS><RHS>active(if(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(add(X1,X2))</LHS><RHS>active(add(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(X))</RHS></RULE><RULE><LHS>mark(first(X1,X2))</LHS><RHS>active(first(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(nil)</LHS><RHS>active(nil)</RHS></RULE><RULE><LHS>mark(cons(X1,X2))</LHS><RHS>active(cons(X1,X2))</RHS></RULE><RULE><LHS>mark(from(X))</LHS><RHS>active(from(X))</RHS></RULE><RULE><LHS>and(mark(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,mark(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(active(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,active(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>if(mark(X1),X2,X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,mark(X2),X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,X2,mark(X3))</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(active(X1),X2,X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,active(X2),X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,X2,active(X3))</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>add(mark(X1),X2)</LHS><RHS>add(X1,X2)</RHS></RULE><RULE><LHS>add(X1,mark(X2))</LHS><RHS>add(X1,X2)</RHS></RULE><RULE><LHS>add(active(X1),X2)</LHS><RHS>add(X1,X2)</RHS></RULE><RULE><LHS>add(X1,active(X2))</LHS><RHS>add(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>first(mark(X1),X2)</LHS><RHS>first(X1,X2)</RHS></RULE><RULE><LHS>first(X1,mark(X2))</LHS><RHS>first(X1,X2)</RHS></RULE><RULE><LHS>first(active(X1),X2)</LHS><RHS>first(X1,X2)</RHS></RULE><RULE><LHS>first(X1,active(X2))</LHS><RHS>first(X1,X2)</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>from(mark(X))</LHS><RHS>from(X)</RHS></RULE><RULE><LHS>from(active(X))</LHS><RHS>from(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_first(active(X1),X2)</LHS><RHS>Marked_first(X1,X2)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_first(mark(X1),X2)</LHS><RHS>Marked_first(X1,X2)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><PROJECTION><PROJ><SYMBOL><NAME>Marked_first</NAME></SYMBOL><INT>1</INT></PROJ></PROJECTION><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_first(mark(X1),X2)</LHS><RHS>Marked_first(X1,X2)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_first(active(X1),X2)</LHS><RHS>Marked_first(X1,X2)</RHS></DPRULE></DPLIST></STRICTPAIRS><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(and(true,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(and(false,Y))</LHS><RHS>mark(false)</RHS></RULE><RULE><LHS>active(if(true,X,Y))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(if(false,X,Y))</LHS><RHS>mark(Y)</RHS></RULE><RULE><LHS>active(add(0,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(add(s(X),Y))</LHS><RHS>mark(s(add(X,Y)))</RHS></RULE><RULE><LHS>active(first(0,X))</LHS><RHS>mark(nil)</RHS></RULE><RULE><LHS>active(first(s(X),cons(Y,Z)))</LHS><RHS>mark(cons(Y,first(X,Z)))</RHS></RULE><RULE><LHS>active(from(X))</LHS><RHS>mark(cons(X,from(s(X))))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(true)</LHS><RHS>active(true)</RHS></RULE><RULE><LHS>mark(false)</LHS><RHS>active(false)</RHS></RULE><RULE><LHS>mark(if(X1,X2,X3))</LHS><RHS>active(if(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(add(X1,X2))</LHS><RHS>active(add(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(X))</RHS></RULE><RULE><LHS>mark(first(X1,X2))</LHS><RHS>active(first(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(nil)</LHS><RHS>active(nil)</RHS></RULE><RULE><LHS>mark(cons(X1,X2))</LHS><RHS>active(cons(X1,X2))</RHS></RULE><RULE><LHS>mark(from(X))</LHS><RHS>active(from(X))</RHS></RULE><RULE><LHS>and(mark(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,mark(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(active(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,active(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>if(mark(X1),X2,X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,mark(X2),X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,X2,mark(X3))</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(active(X1),X2,X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,active(X2),X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,X2,active(X3))</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>add(mark(X1),X2)</LHS><RHS>add(X1,X2)</RHS></RULE><RULE><LHS>add(X1,mark(X2))</LHS><RHS>add(X1,X2)</RHS></RULE><RULE><LHS>add(active(X1),X2)</LHS><RHS>add(X1,X2)</RHS></RULE><RULE><LHS>add(X1,active(X2))</LHS><RHS>add(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>first(mark(X1),X2)</LHS><RHS>first(X1,X2)</RHS></RULE><RULE><LHS>first(X1,mark(X2))</LHS><RHS>first(X1,X2)</RHS></RULE><RULE><LHS>first(active(X1),X2)</LHS><RHS>first(X1,X2)</RHS></RULE><RULE><LHS>first(X1,active(X2))</LHS><RHS>first(X1,X2)</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>from(mark(X))</LHS><RHS>from(X)</RHS></RULE><RULE><LHS>from(active(X))</LHS><RHS>from(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(and(true,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(and(false,Y))</LHS><RHS>mark(false)</RHS></RULE><RULE><LHS>active(if(true,X,Y))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(if(false,X,Y))</LHS><RHS>mark(Y)</RHS></RULE><RULE><LHS>active(add(0,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(add(s(X),Y))</LHS><RHS>mark(s(add(X,Y)))</RHS></RULE><RULE><LHS>active(first(0,X))</LHS><RHS>mark(nil)</RHS></RULE><RULE><LHS>active(first(s(X),cons(Y,Z)))</LHS><RHS>mark(cons(Y,first(X,Z)))</RHS></RULE><RULE><LHS>active(from(X))</LHS><RHS>mark(cons(X,from(s(X))))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(true)</LHS><RHS>active(true)</RHS></RULE><RULE><LHS>mark(false)</LHS><RHS>active(false)</RHS></RULE><RULE><LHS>mark(if(X1,X2,X3))</LHS><RHS>active(if(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(add(X1,X2))</LHS><RHS>active(add(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(X))</RHS></RULE><RULE><LHS>mark(first(X1,X2))</LHS><RHS>active(first(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(nil)</LHS><RHS>active(nil)</RHS></RULE><RULE><LHS>mark(cons(X1,X2))</LHS><RHS>active(cons(X1,X2))</RHS></RULE><RULE><LHS>mark(from(X))</LHS><RHS>active(from(X))</RHS></RULE><RULE><LHS>and(mark(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,mark(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(active(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,active(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>if(mark(X1),X2,X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,mark(X2),X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,X2,mark(X3))</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(active(X1),X2,X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,active(X2),X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,X2,active(X3))</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>add(mark(X1),X2)</LHS><RHS>add(X1,X2)</RHS></RULE><RULE><LHS>add(X1,mark(X2))</LHS><RHS>add(X1,X2)</RHS></RULE><RULE><LHS>add(active(X1),X2)</LHS><RHS>add(X1,X2)</RHS></RULE><RULE><LHS>add(X1,active(X2))</LHS><RHS>add(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>first(mark(X1),X2)</LHS><RHS>first(X1,X2)</RHS></RULE><RULE><LHS>first(X1,mark(X2))</LHS><RHS>first(X1,X2)</RHS></RULE><RULE><LHS>first(active(X1),X2)</LHS><RHS>first(X1,X2)</RHS></RULE><RULE><LHS>first(X1,active(X2))</LHS><RHS>first(X1,X2)</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>from(mark(X))</LHS><RHS>from(X)</RHS></RULE><RULE><LHS>from(active(X))</LHS><RHS>from(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(and(true,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(and(false,Y))</LHS><RHS>mark(false)</RHS></RULE><RULE><LHS>active(if(true,X,Y))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(if(false,X,Y))</LHS><RHS>mark(Y)</RHS></RULE><RULE><LHS>active(add(0,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(add(s(X),Y))</LHS><RHS>mark(s(add(X,Y)))</RHS></RULE><RULE><LHS>active(first(0,X))</LHS><RHS>mark(nil)</RHS></RULE><RULE><LHS>active(first(s(X),cons(Y,Z)))</LHS><RHS>mark(cons(Y,first(X,Z)))</RHS></RULE><RULE><LHS>active(from(X))</LHS><RHS>mark(cons(X,from(s(X))))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(true)</LHS><RHS>active(true)</RHS></RULE><RULE><LHS>mark(false)</LHS><RHS>active(false)</RHS></RULE><RULE><LHS>mark(if(X1,X2,X3))</LHS><RHS>active(if(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(add(X1,X2))</LHS><RHS>active(add(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(X))</RHS></RULE><RULE><LHS>mark(first(X1,X2))</LHS><RHS>active(first(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(nil)</LHS><RHS>active(nil)</RHS></RULE><RULE><LHS>mark(cons(X1,X2))</LHS><RHS>active(cons(X1,X2))</RHS></RULE><RULE><LHS>mark(from(X))</LHS><RHS>active(from(X))</RHS></RULE><RULE><LHS>and(mark(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,mark(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(active(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,active(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>if(mark(X1),X2,X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,mark(X2),X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,X2,mark(X3))</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(active(X1),X2,X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,active(X2),X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,X2,active(X3))</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>add(mark(X1),X2)</LHS><RHS>add(X1,X2)</RHS></RULE><RULE><LHS>add(X1,mark(X2))</LHS><RHS>add(X1,X2)</RHS></RULE><RULE><LHS>add(active(X1),X2)</LHS><RHS>add(X1,X2)</RHS></RULE><RULE><LHS>add(X1,active(X2))</LHS><RHS>add(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>first(mark(X1),X2)</LHS><RHS>first(X1,X2)</RHS></RULE><RULE><LHS>first(X1,mark(X2))</LHS><RHS>first(X1,X2)</RHS></RULE><RULE><LHS>first(active(X1),X2)</LHS><RHS>first(X1,X2)</RHS></RULE><RULE><LHS>first(X1,active(X2))</LHS><RHS>first(X1,X2)</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>from(mark(X))</LHS><RHS>from(X)</RHS></RULE><RULE><LHS>from(active(X))</LHS><RHS>from(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(and(true,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(and(false,Y))</LHS><RHS>mark(false)</RHS></RULE><RULE><LHS>active(if(true,X,Y))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(if(false,X,Y))</LHS><RHS>mark(Y)</RHS></RULE><RULE><LHS>active(add(0,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(add(s(X),Y))</LHS><RHS>mark(s(add(X,Y)))</RHS></RULE><RULE><LHS>active(first(0,X))</LHS><RHS>mark(nil)</RHS></RULE><RULE><LHS>active(first(s(X),cons(Y,Z)))</LHS><RHS>mark(cons(Y,first(X,Z)))</RHS></RULE><RULE><LHS>active(from(X))</LHS><RHS>mark(cons(X,from(s(X))))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(true)</LHS><RHS>active(true)</RHS></RULE><RULE><LHS>mark(false)</LHS><RHS>active(false)</RHS></RULE><RULE><LHS>mark(if(X1,X2,X3))</LHS><RHS>active(if(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(add(X1,X2))</LHS><RHS>active(add(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(X))</RHS></RULE><RULE><LHS>mark(first(X1,X2))</LHS><RHS>active(first(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(nil)</LHS><RHS>active(nil)</RHS></RULE><RULE><LHS>mark(cons(X1,X2))</LHS><RHS>active(cons(X1,X2))</RHS></RULE><RULE><LHS>mark(from(X))</LHS><RHS>active(from(X))</RHS></RULE><RULE><LHS>and(mark(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,mark(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(active(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,active(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>if(mark(X1),X2,X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,mark(X2),X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,X2,mark(X3))</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(active(X1),X2,X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,active(X2),X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,X2,active(X3))</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>add(mark(X1),X2)</LHS><RHS>add(X1,X2)</RHS></RULE><RULE><LHS>add(X1,mark(X2))</LHS><RHS>add(X1,X2)</RHS></RULE><RULE><LHS>add(active(X1),X2)</LHS><RHS>add(X1,X2)</RHS></RULE><RULE><LHS>add(X1,active(X2))</LHS><RHS>add(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>first(mark(X1),X2)</LHS><RHS>first(X1,X2)</RHS></RULE><RULE><LHS>first(X1,mark(X2))</LHS><RHS>first(X1,X2)</RHS></RULE><RULE><LHS>first(active(X1),X2)</LHS><RHS>first(X1,X2)</RHS></RULE><RULE><LHS>first(X1,active(X2))</LHS><RHS>first(X1,X2)</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>from(mark(X))</LHS><RHS>from(X)</RHS></RULE><RULE><LHS>from(active(X))</LHS><RHS>from(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(and(true,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(and(false,Y))</LHS><RHS>mark(false)</RHS></RULE><RULE><LHS>active(if(true,X,Y))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(if(false,X,Y))</LHS><RHS>mark(Y)</RHS></RULE><RULE><LHS>active(add(0,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(add(s(X),Y))</LHS><RHS>mark(s(add(X,Y)))</RHS></RULE><RULE><LHS>active(first(0,X))</LHS><RHS>mark(nil)</RHS></RULE><RULE><LHS>active(first(s(X),cons(Y,Z)))</LHS><RHS>mark(cons(Y,first(X,Z)))</RHS></RULE><RULE><LHS>active(from(X))</LHS><RHS>mark(cons(X,from(s(X))))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(true)</LHS><RHS>active(true)</RHS></RULE><RULE><LHS>mark(false)</LHS><RHS>active(false)</RHS></RULE><RULE><LHS>mark(if(X1,X2,X3))</LHS><RHS>active(if(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(add(X1,X2))</LHS><RHS>active(add(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(X))</RHS></RULE><RULE><LHS>mark(first(X1,X2))</LHS><RHS>active(first(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(nil)</LHS><RHS>active(nil)</RHS></RULE><RULE><LHS>mark(cons(X1,X2))</LHS><RHS>active(cons(X1,X2))</RHS></RULE><RULE><LHS>mark(from(X))</LHS><RHS>active(from(X))</RHS></RULE><RULE><LHS>and(mark(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,mark(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(active(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,active(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>if(mark(X1),X2,X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,mark(X2),X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,X2,mark(X3))</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(active(X1),X2,X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,active(X2),X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,X2,active(X3))</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>add(mark(X1),X2)</LHS><RHS>add(X1,X2)</RHS></RULE><RULE><LHS>add(X1,mark(X2))</LHS><RHS>add(X1,X2)</RHS></RULE><RULE><LHS>add(active(X1),X2)</LHS><RHS>add(X1,X2)</RHS></RULE><RULE><LHS>add(X1,active(X2))</LHS><RHS>add(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>first(mark(X1),X2)</LHS><RHS>first(X1,X2)</RHS></RULE><RULE><LHS>first(X1,mark(X2))</LHS><RHS>first(X1,X2)</RHS></RULE><RULE><LHS>first(active(X1),X2)</LHS><RHS>first(X1,X2)</RHS></RULE><RULE><LHS>first(X1,active(X2))</LHS><RHS>first(X1,X2)</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>from(mark(X))</LHS><RHS>from(X)</RHS></RULE><RULE><LHS>from(active(X))</LHS><RHS>from(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(and(true,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(and(false,Y))</LHS><RHS>mark(false)</RHS></RULE><RULE><LHS>active(if(true,X,Y))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(if(false,X,Y))</LHS><RHS>mark(Y)</RHS></RULE><RULE><LHS>active(add(0,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(add(s(X),Y))</LHS><RHS>mark(s(add(X,Y)))</RHS></RULE><RULE><LHS>active(first(0,X))</LHS><RHS>mark(nil)</RHS></RULE><RULE><LHS>active(first(s(X),cons(Y,Z)))</LHS><RHS>mark(cons(Y,first(X,Z)))</RHS></RULE><RULE><LHS>active(from(X))</LHS><RHS>mark(cons(X,from(s(X))))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(true)</LHS><RHS>active(true)</RHS></RULE><RULE><LHS>mark(false)</LHS><RHS>active(false)</RHS></RULE><RULE><LHS>mark(if(X1,X2,X3))</LHS><RHS>active(if(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(add(X1,X2))</LHS><RHS>active(add(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(X))</RHS></RULE><RULE><LHS>mark(first(X1,X2))</LHS><RHS>active(first(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(nil)</LHS><RHS>active(nil)</RHS></RULE><RULE><LHS>mark(cons(X1,X2))</LHS><RHS>active(cons(X1,X2))</RHS></RULE><RULE><LHS>mark(from(X))</LHS><RHS>active(from(X))</RHS></RULE><RULE><LHS>and(mark(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,mark(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(active(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,active(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>if(mark(X1),X2,X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,mark(X2),X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,X2,mark(X3))</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(active(X1),X2,X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,active(X2),X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,X2,active(X3))</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>add(mark(X1),X2)</LHS><RHS>add(X1,X2)</RHS></RULE><RULE><LHS>add(X1,mark(X2))</LHS><RHS>add(X1,X2)</RHS></RULE><RULE><LHS>add(active(X1),X2)</LHS><RHS>add(X1,X2)</RHS></RULE><RULE><LHS>add(X1,active(X2))</LHS><RHS>add(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>first(mark(X1),X2)</LHS><RHS>first(X1,X2)</RHS></RULE><RULE><LHS>first(X1,mark(X2))</LHS><RHS>first(X1,X2)</RHS></RULE><RULE><LHS>first(active(X1),X2)</LHS><RHS>first(X1,X2)</RHS></RULE><RULE><LHS>first(X1,active(X2))</LHS><RHS>first(X1,X2)</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>from(mark(X))</LHS><RHS>from(X)</RHS></RULE><RULE><LHS>from(active(X))</LHS><RHS>from(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_from(mark(X))</LHS><RHS>Marked_from(X)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_from(active(X))</LHS><RHS>Marked_from(X)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><PROJECTION><PROJ><SYMBOL><NAME>Marked_from</NAME></SYMBOL><INT>1</INT></PROJ></PROJECTION><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_from(active(X))</LHS><RHS>Marked_from(X)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_from(mark(X))</LHS><RHS>Marked_from(X)</RHS></DPRULE></DPLIST></STRICTPAIRS><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(and(true,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(and(false,Y))</LHS><RHS>mark(false)</RHS></RULE><RULE><LHS>active(if(true,X,Y))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(if(false,X,Y))</LHS><RHS>mark(Y)</RHS></RULE><RULE><LHS>active(add(0,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(add(s(X),Y))</LHS><RHS>mark(s(add(X,Y)))</RHS></RULE><RULE><LHS>active(first(0,X))</LHS><RHS>mark(nil)</RHS></RULE><RULE><LHS>active(first(s(X),cons(Y,Z)))</LHS><RHS>mark(cons(Y,first(X,Z)))</RHS></RULE><RULE><LHS>active(from(X))</LHS><RHS>mark(cons(X,from(s(X))))</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(true)</LHS><RHS>active(true)</RHS></RULE><RULE><LHS>mark(false)</LHS><RHS>active(false)</RHS></RULE><RULE><LHS>mark(if(X1,X2,X3))</LHS><RHS>active(if(mark(X1),X2,X3))</RHS></RULE><RULE><LHS>mark(add(X1,X2))</LHS><RHS>active(add(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(0)</LHS><RHS>active(0)</RHS></RULE><RULE><LHS>mark(s(X))</LHS><RHS>active(s(X))</RHS></RULE><RULE><LHS>mark(first(X1,X2))</LHS><RHS>active(first(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(nil)</LHS><RHS>active(nil)</RHS></RULE><RULE><LHS>mark(cons(X1,X2))</LHS><RHS>active(cons(X1,X2))</RHS></RULE><RULE><LHS>mark(from(X))</LHS><RHS>active(from(X))</RHS></RULE><RULE><LHS>and(mark(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,mark(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(active(X1),X2)</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>and(X1,active(X2))</LHS><RHS>and(X1,X2)</RHS></RULE><RULE><LHS>if(mark(X1),X2,X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,mark(X2),X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,X2,mark(X3))</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(active(X1),X2,X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,active(X2),X3)</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>if(X1,X2,active(X3))</LHS><RHS>if(X1,X2,X3)</RHS></RULE><RULE><LHS>add(mark(X1),X2)</LHS><RHS>add(X1,X2)</RHS></RULE><RULE><LHS>add(X1,mark(X2))</LHS><RHS>add(X1,X2)</RHS></RULE><RULE><LHS>add(active(X1),X2)</LHS><RHS>add(X1,X2)</RHS></RULE><RULE><LHS>add(X1,active(X2))</LHS><RHS>add(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>first(mark(X1),X2)</LHS><RHS>first(X1,X2)</RHS></RULE><RULE><LHS>first(X1,mark(X2))</LHS><RHS>first(X1,X2)</RHS></RULE><RULE><LHS>first(active(X1),X2)</LHS><RHS>first(X1,X2)</RHS></RULE><RULE><LHS>first(X1,active(X2))</LHS><RHS>first(X1,X2)</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>from(mark(X))</LHS><RHS>from(X)</RHS></RULE><RULE><LHS>from(active(X))</LHS><RHS>from(X)</RHS></RULE></REWSYS><DPLIST/></DPSYS></SYSTEM><CRITERION><DAG approx="simpl"><CCLIST/></DAG></CRITERION></PROPERTY></PROPERTY></PROPERTY></PROPERTY></PROOF>
