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<!DOCTYPE PROOF SYSTEM "http://a3pat.ensiie.fr/pub/a3pat.dtd">
<PROOF><SIGNATURE><SYMBOLLIST><SYMBOL arity="3" unmarked="if"><NAME>Marked_if</NAME></SYMBOL><SYMBOL arity="1" unmarked=""><NAME>f</NAME></SYMBOL><SYMBOL arity="1" unmarked=""><NAME>active</NAME></SYMBOL><SYMBOL arity="1" unmarked="mark"><NAME>Marked_mark</NAME></SYMBOL><SYMBOL arity="3" unmarked=""><NAME>if</NAME></SYMBOL><SYMBOL arity="0" unmarked=""><NAME>false</NAME></SYMBOL><SYMBOL arity="1" unmarked="active"><NAME>Marked_active</NAME></SYMBOL><SYMBOL arity="0" unmarked=""><NAME>c</NAME></SYMBOL><SYMBOL arity="0" unmarked=""><NAME>true</NAME></SYMBOL><SYMBOL arity="1" unmarked="f"><NAME>Marked_f</NAME></SYMBOL><SYMBOL arity="1" unmarked=""><NAME>mark</NAME></SYMBOL></SYMBOLLIST><VARLIST><VAR>X3</VAR><VAR>X2</VAR><VAR>X1</VAR><VAR>Y</VAR><VAR>X</VAR></VARLIST></SIGNATURE><PROPERTY criterion="dp" prop="sntrs"><SYSTEM><REWSYS><RULE><LHS>active(f(X))</LHS><RHS>mark(if(X,c,f(true)))</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>mark(f(X))</LHS><RHS>active(f(mark(X)))</RHS></RULE><RULE><LHS>mark(if(X1,X2,X3))</LHS><RHS>active(if(mark(X1),mark(X2),X3))</RHS></RULE><RULE><LHS>mark(c)</LHS><RHS>active(c)</RHS></RULE><RULE><LHS>mark(true)</LHS><RHS>active(true)</RHS></RULE><RULE><LHS>mark(false)</LHS><RHS>active(false)</RHS></RULE><RULE><LHS>f(mark(X))</LHS><RHS>f(X)</RHS></RULE><RULE><LHS>f(active(X))</LHS><RHS>f(X)</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></REWSYS></SYSTEM><CRITERION/><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(f(X))</LHS><RHS>mark(if(X,c,f(true)))</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>mark(f(X))</LHS><RHS>active(f(mark(X)))</RHS></RULE><RULE><LHS>mark(if(X1,X2,X3))</LHS><RHS>active(if(mark(X1),mark(X2),X3))</RHS></RULE><RULE><LHS>mark(c)</LHS><RHS>active(c)</RHS></RULE><RULE><LHS>mark(true)</LHS><RHS>active(true)</RHS></RULE><RULE><LHS>mark(false)</LHS><RHS>active(false)</RHS></RULE><RULE><LHS>f(mark(X))</LHS><RHS>f(X)</RHS></RULE><RULE><LHS>f(active(X))</LHS><RHS>f(X)</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></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_active(f(X))</LHS><RHS>Marked_mark(if(X,c,f(true)))</RHS></DPRULE><DPRULE num="1"><LHS>Marked_active(f(X))</LHS><RHS>Marked_if(X,c,f(true))</RHS></DPRULE><DPRULE num="2"><LHS>Marked_active(f(X))</LHS><RHS>Marked_f(true)</RHS></DPRULE><DPRULE num="3"><LHS>Marked_active(if(true,X,Y))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="4"><LHS>Marked_active(if(false,X,Y))</LHS><RHS>Marked_mark(Y)</RHS></DPRULE><DPRULE num="5"><LHS>Marked_mark(f(X))</LHS><RHS>Marked_active(f(mark(X)))</RHS></DPRULE><DPRULE num="6"><LHS>Marked_mark(f(X))</LHS><RHS>Marked_f(mark(X))</RHS></DPRULE><DPRULE num="7"><LHS>Marked_mark(f(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="8"><LHS>Marked_mark(if(X1,X2,X3))</LHS><RHS>Marked_active(if(mark(X1),mark(X2),X3))</RHS></DPRULE><DPRULE num="9"><LHS>Marked_mark(if(X1,X2,X3))</LHS><RHS>Marked_if(mark(X1),mark(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(if(X1,X2,X3))</LHS><RHS>Marked_mark(X2)</RHS></DPRULE><DPRULE num="12"><LHS>Marked_mark(c)</LHS><RHS>Marked_active(c)</RHS></DPRULE><DPRULE num="13"><LHS>Marked_mark(true)</LHS><RHS>Marked_active(true)</RHS></DPRULE><DPRULE num="14"><LHS>Marked_mark(false)</LHS><RHS>Marked_active(false)</RHS></DPRULE><DPRULE num="15"><LHS>Marked_f(mark(X))</LHS><RHS>Marked_f(X)</RHS></DPRULE><DPRULE num="16"><LHS>Marked_f(active(X))</LHS><RHS>Marked_f(X)</RHS></DPRULE><DPRULE num="17"><LHS>Marked_if(mark(X1),X2,X3)</LHS><RHS>Marked_if(X1,X2,X3)</RHS></DPRULE><DPRULE num="18"><LHS>Marked_if(X1,mark(X2),X3)</LHS><RHS>Marked_if(X1,X2,X3)</RHS></DPRULE><DPRULE num="19"><LHS>Marked_if(X1,X2,mark(X3))</LHS><RHS>Marked_if(X1,X2,X3)</RHS></DPRULE><DPRULE num="20"><LHS>Marked_if(active(X1),X2,X3)</LHS><RHS>Marked_if(X1,X2,X3)</RHS></DPRULE><DPRULE num="21"><LHS>Marked_if(X1,active(X2),X3)</LHS><RHS>Marked_if(X1,X2,X3)</RHS></DPRULE><DPRULE num="22"><LHS>Marked_if(X1,X2,active(X3))</LHS><RHS>Marked_if(X1,X2,X3)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><DAG approx="simpl"><CCLIST><SCC num="0"><NODE ref="17"/><NODE ref="18"/><NODE ref="19"/><NODE ref="20"/><NODE ref="21"/><NODE ref="22"/></SCC><SCC num="1"><NODE ref="15"/><NODE ref="16"/></SCC><NONSCC num="2"><NODE ref="14"/></NONSCC><NONSCC num="3"><NODE ref="13"/></NONSCC><NONSCC num="4"><NODE ref="12"/></NONSCC><SCC num="5"><NODE ref="0"/><NODE ref="3"/><NODE ref="4"/><NODE ref="5"/><NODE ref="7"/><NODE ref="8"/><NODE ref="10"/><NODE ref="11"/></SCC><NONSCC num="6"><NODE ref="9"/></NONSCC><NONSCC num="7"><NODE ref="6"/></NONSCC><NONSCC num="8"><NODE ref="2"/></NONSCC><NONSCC num="9"><NODE ref="1"/></NONSCC></CCLIST><EDGE end="9" start="5"/><EDGE end="8" start="5"/><EDGE end="7" start="5"/><EDGE end="6" start="5"/><EDGE end="4" start="5"/><EDGE end="3" start="5"/><EDGE end="2" start="5"/><EDGE end="0" start="6"/><EDGE end="1" start="7"/><EDGE end="0" start="9"/></DAG></CRITERION><PROPERTY criterion="stronggraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(f(X))</LHS><RHS>mark(if(X,c,f(true)))</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>mark(f(X))</LHS><RHS>active(f(mark(X)))</RHS></RULE><RULE><LHS>mark(if(X1,X2,X3))</LHS><RHS>active(if(mark(X1),mark(X2),X3))</RHS></RULE><RULE><LHS>mark(c)</LHS><RHS>active(c)</RHS></RULE><RULE><LHS>mark(true)</LHS><RHS>active(true)</RHS></RULE><RULE><LHS>mark(false)</LHS><RHS>active(false)</RHS></RULE><RULE><LHS>f(mark(X))</LHS><RHS>f(X)</RHS></RULE><RULE><LHS>f(active(X))</LHS><RHS>f(X)</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></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_active(f(X))</LHS><RHS>Marked_mark(if(X,c,f(true)))</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_mark(f(X))</LHS><RHS>Marked_active(f(mark(X)))</RHS></DPRULE><DPRULE num="4"><LHS>Marked_mark(f(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="5"><LHS>Marked_mark(if(X1,X2,X3))</LHS><RHS>Marked_active(if(mark(X1),mark(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(if(X1,X2,X3))</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>true</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>c</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>Marked_active</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>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>false</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>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_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>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>f</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB></ORDERING><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_active(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(f(X))</LHS><RHS>mark(if(X,c,f(true)))</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>mark(f(X))</LHS><RHS>active(f(mark(X)))</RHS></RULE><RULE><LHS>mark(if(X1,X2,X3))</LHS><RHS>active(if(mark(X1),mark(X2),X3))</RHS></RULE><RULE><LHS>mark(c)</LHS><RHS>active(c)</RHS></RULE><RULE><LHS>mark(true)</LHS><RHS>active(true)</RHS></RULE><RULE><LHS>mark(false)</LHS><RHS>active(false)</RHS></RULE><RULE><LHS>f(mark(X))</LHS><RHS>f(X)</RHS></RULE><RULE><LHS>f(active(X))</LHS><RHS>f(X)</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></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_active(f(X))</LHS><RHS>Marked_mark(if(X,c,f(true)))</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(f(X))</LHS><RHS>Marked_active(f(mark(X)))</RHS></DPRULE><DPRULE num="3"><LHS>Marked_mark(f(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="4"><LHS>Marked_mark(if(X1,X2,X3))</LHS><RHS>Marked_active(if(mark(X1),mark(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(if(X1,X2,X3))</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"/></SCC></CCLIST></DAG></CRITERION><PROPERTY criterion="stronggraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(f(X))</LHS><RHS>mark(if(X,c,f(true)))</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>mark(f(X))</LHS><RHS>active(f(mark(X)))</RHS></RULE><RULE><LHS>mark(if(X1,X2,X3))</LHS><RHS>active(if(mark(X1),mark(X2),X3))</RHS></RULE><RULE><LHS>mark(c)</LHS><RHS>active(c)</RHS></RULE><RULE><LHS>mark(true)</LHS><RHS>active(true)</RHS></RULE><RULE><LHS>mark(false)</LHS><RHS>active(false)</RHS></RULE><RULE><LHS>f(mark(X))</LHS><RHS>f(X)</RHS></RULE><RULE><LHS>f(active(X))</LHS><RHS>f(X)</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></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_active(f(X))</LHS><RHS>Marked_mark(if(X,c,f(true)))</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(f(X))</LHS><RHS>Marked_active(f(mark(X)))</RHS></DPRULE><DPRULE num="3"><LHS>Marked_mark(f(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="4"><LHS>Marked_mark(if(X1,X2,X3))</LHS><RHS>Marked_active(if(mark(X1),mark(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(if(X1,X2,X3))</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>true</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>c</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>Marked_active</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>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>false</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_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>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>f</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></ORDERING><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_mark(f(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE></DPLIST></STRICTPAIRS></CRITERION><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(f(X))</LHS><RHS>mark(if(X,c,f(true)))</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>mark(f(X))</LHS><RHS>active(f(mark(X)))</RHS></RULE><RULE><LHS>mark(if(X1,X2,X3))</LHS><RHS>active(if(mark(X1),mark(X2),X3))</RHS></RULE><RULE><LHS>mark(c)</LHS><RHS>active(c)</RHS></RULE><RULE><LHS>mark(true)</LHS><RHS>active(true)</RHS></RULE><RULE><LHS>mark(false)</LHS><RHS>active(false)</RHS></RULE><RULE><LHS>f(mark(X))</LHS><RHS>f(X)</RHS></RULE><RULE><LHS>f(active(X))</LHS><RHS>f(X)</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></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_active(f(X))</LHS><RHS>Marked_mark(if(X,c,f(true)))</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(f(X))</LHS><RHS>Marked_active(f(mark(X)))</RHS></DPRULE><DPRULE num="3"><LHS>Marked_mark(if(X1,X2,X3))</LHS><RHS>Marked_active(if(mark(X1),mark(X2),X3))</RHS></DPRULE><DPRULE num="4"><LHS>Marked_mark(if(X1,X2,X3))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="5"><LHS>Marked_mark(if(X1,X2,X3))</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"/></SCC></CCLIST></DAG></CRITERION><PROPERTY criterion="stronggraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(f(X))</LHS><RHS>mark(if(X,c,f(true)))</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>mark(f(X))</LHS><RHS>active(f(mark(X)))</RHS></RULE><RULE><LHS>mark(if(X1,X2,X3))</LHS><RHS>active(if(mark(X1),mark(X2),X3))</RHS></RULE><RULE><LHS>mark(c)</LHS><RHS>active(c)</RHS></RULE><RULE><LHS>mark(true)</LHS><RHS>active(true)</RHS></RULE><RULE><LHS>mark(false)</LHS><RHS>active(false)</RHS></RULE><RULE><LHS>f(mark(X))</LHS><RHS>f(X)</RHS></RULE><RULE><LHS>f(active(X))</LHS><RHS>f(X)</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></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_active(f(X))</LHS><RHS>Marked_mark(if(X,c,f(true)))</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(f(X))</LHS><RHS>Marked_active(f(mark(X)))</RHS></DPRULE><DPRULE num="3"><LHS>Marked_mark(if(X1,X2,X3))</LHS><RHS>Marked_active(if(mark(X1),mark(X2),X3))</RHS></DPRULE><DPRULE num="4"><LHS>Marked_mark(if(X1,X2,X3))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="5"><LHS>Marked_mark(if(X1,X2,X3))</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>true</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>c</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>Marked_active</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>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>false</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>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>2</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/><ARG degree="1" num="2"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>Marked_mark</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>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>f</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB></ORDERING><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_active(f(X))</LHS><RHS>Marked_mark(if(X,c,f(true)))</RHS></DPRULE></DPLIST></STRICTPAIRS></CRITERION><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(f(X))</LHS><RHS>mark(if(X,c,f(true)))</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>mark(f(X))</LHS><RHS>active(f(mark(X)))</RHS></RULE><RULE><LHS>mark(if(X1,X2,X3))</LHS><RHS>active(if(mark(X1),mark(X2),X3))</RHS></RULE><RULE><LHS>mark(c)</LHS><RHS>active(c)</RHS></RULE><RULE><LHS>mark(true)</LHS><RHS>active(true)</RHS></RULE><RULE><LHS>mark(false)</LHS><RHS>active(false)</RHS></RULE><RULE><LHS>f(mark(X))</LHS><RHS>f(X)</RHS></RULE><RULE><LHS>f(active(X))</LHS><RHS>f(X)</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></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_active(if(true,X,Y))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_mark(f(X))</LHS><RHS>Marked_active(f(mark(X)))</RHS></DPRULE><DPRULE num="2"><LHS>Marked_mark(if(X1,X2,X3))</LHS><RHS>Marked_active(if(mark(X1),mark(X2),X3))</RHS></DPRULE><DPRULE num="3"><LHS>Marked_mark(if(X1,X2,X3))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="4"><LHS>Marked_mark(if(X1,X2,X3))</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"/></SCC></CCLIST></DAG></CRITERION><PROPERTY criterion="stronggraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(f(X))</LHS><RHS>mark(if(X,c,f(true)))</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>mark(f(X))</LHS><RHS>active(f(mark(X)))</RHS></RULE><RULE><LHS>mark(if(X1,X2,X3))</LHS><RHS>active(if(mark(X1),mark(X2),X3))</RHS></RULE><RULE><LHS>mark(c)</LHS><RHS>active(c)</RHS></RULE><RULE><LHS>mark(true)</LHS><RHS>active(true)</RHS></RULE><RULE><LHS>mark(false)</LHS><RHS>active(false)</RHS></RULE><RULE><LHS>f(mark(X))</LHS><RHS>f(X)</RHS></RULE><RULE><LHS>f(active(X))</LHS><RHS>f(X)</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></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_active(if(true,X,Y))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_mark(f(X))</LHS><RHS>Marked_active(f(mark(X)))</RHS></DPRULE><DPRULE num="2"><LHS>Marked_mark(if(X1,X2,X3))</LHS><RHS>Marked_active(if(mark(X1),mark(X2),X3))</RHS></DPRULE><DPRULE num="3"><LHS>Marked_mark(if(X1,X2,X3))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="4"><LHS>Marked_mark(if(X1,X2,X3))</LHS><RHS>Marked_mark(X2)</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>true</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>c</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>Marked_active</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>false</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></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>Marked_mark</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>active</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>f</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB></ORDERING><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_mark(f(X))</LHS><RHS>Marked_active(f(mark(X)))</RHS></DPRULE></DPLIST></STRICTPAIRS></CRITERION><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(f(X))</LHS><RHS>mark(if(X,c,f(true)))</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>mark(f(X))</LHS><RHS>active(f(mark(X)))</RHS></RULE><RULE><LHS>mark(if(X1,X2,X3))</LHS><RHS>active(if(mark(X1),mark(X2),X3))</RHS></RULE><RULE><LHS>mark(c)</LHS><RHS>active(c)</RHS></RULE><RULE><LHS>mark(true)</LHS><RHS>active(true)</RHS></RULE><RULE><LHS>mark(false)</LHS><RHS>active(false)</RHS></RULE><RULE><LHS>f(mark(X))</LHS><RHS>f(X)</RHS></RULE><RULE><LHS>f(active(X))</LHS><RHS>f(X)</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></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_active(if(true,X,Y))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_mark(if(X1,X2,X3))</LHS><RHS>Marked_active(if(mark(X1),mark(X2),X3))</RHS></DPRULE><DPRULE num="2"><LHS>Marked_mark(if(X1,X2,X3))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="3"><LHS>Marked_mark(if(X1,X2,X3))</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"/></SCC></CCLIST></DAG></CRITERION><PROPERTY criterion="stronggraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(f(X))</LHS><RHS>mark(if(X,c,f(true)))</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>mark(f(X))</LHS><RHS>active(f(mark(X)))</RHS></RULE><RULE><LHS>mark(if(X1,X2,X3))</LHS><RHS>active(if(mark(X1),mark(X2),X3))</RHS></RULE><RULE><LHS>mark(c)</LHS><RHS>active(c)</RHS></RULE><RULE><LHS>mark(true)</LHS><RHS>active(true)</RHS></RULE><RULE><LHS>mark(false)</LHS><RHS>active(false)</RHS></RULE><RULE><LHS>f(mark(X))</LHS><RHS>f(X)</RHS></RULE><RULE><LHS>f(active(X))</LHS><RHS>f(X)</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></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_active(if(true,X,Y))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_mark(if(X1,X2,X3))</LHS><RHS>Marked_active(if(mark(X1),mark(X2),X3))</RHS></DPRULE><DPRULE num="2"><LHS>Marked_mark(if(X1,X2,X3))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="3"><LHS>Marked_mark(if(X1,X2,X3))</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>true</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>c</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>Marked_active</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><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>if</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>2</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/><ARG degree="1" num="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_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>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>f</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB></ORDERING><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_active(if(true,X,Y))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_mark(if(X1,X2,X3))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="2"><LHS>Marked_mark(if(X1,X2,X3))</LHS><RHS>Marked_mark(X2)</RHS></DPRULE></DPLIST></STRICTPAIRS></CRITERION><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(f(X))</LHS><RHS>mark(if(X,c,f(true)))</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>mark(f(X))</LHS><RHS>active(f(mark(X)))</RHS></RULE><RULE><LHS>mark(if(X1,X2,X3))</LHS><RHS>active(if(mark(X1),mark(X2),X3))</RHS></RULE><RULE><LHS>mark(c)</LHS><RHS>active(c)</RHS></RULE><RULE><LHS>mark(true)</LHS><RHS>active(true)</RHS></RULE><RULE><LHS>mark(false)</LHS><RHS>active(false)</RHS></RULE><RULE><LHS>f(mark(X))</LHS><RHS>f(X)</RHS></RULE><RULE><LHS>f(active(X))</LHS><RHS>f(X)</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></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_mark(if(X1,X2,X3))</LHS><RHS>Marked_active(if(mark(X1),mark(X2),X3))</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><DAG approx="simpl"><CCLIST><NONSCC num="0"><NODE ref="0"/></NONSCC></CCLIST></DAG></CRITERION></PROPERTY></PROPERTY></PROPERTY></PROPERTY></PROPERTY></PROPERTY></PROPERTY></PROPERTY></PROPERTY></PROPERTY><PROPERTY criterion="sterm" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(f(X))</LHS><RHS>mark(if(X,c,f(true)))</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>mark(f(X))</LHS><RHS>active(f(mark(X)))</RHS></RULE><RULE><LHS>mark(if(X1,X2,X3))</LHS><RHS>active(if(mark(X1),mark(X2),X3))</RHS></RULE><RULE><LHS>mark(c)</LHS><RHS>active(c)</RHS></RULE><RULE><LHS>mark(true)</LHS><RHS>active(true)</RHS></RULE><RULE><LHS>mark(false)</LHS><RHS>active(false)</RHS></RULE><RULE><LHS>f(mark(X))</LHS><RHS>f(X)</RHS></RULE><RULE><LHS>f(active(X))</LHS><RHS>f(X)</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></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_f(mark(X))</LHS><RHS>Marked_f(X)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_f(active(X))</LHS><RHS>Marked_f(X)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><PROJECTION><PROJ><SYMBOL><NAME>Marked_f</NAME></SYMBOL><INT>1</INT></PROJ></PROJECTION><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_f(active(X))</LHS><RHS>Marked_f(X)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_f(mark(X))</LHS><RHS>Marked_f(X)</RHS></DPRULE></DPLIST></STRICTPAIRS><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(f(X))</LHS><RHS>mark(if(X,c,f(true)))</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>mark(f(X))</LHS><RHS>active(f(mark(X)))</RHS></RULE><RULE><LHS>mark(if(X1,X2,X3))</LHS><RHS>active(if(mark(X1),mark(X2),X3))</RHS></RULE><RULE><LHS>mark(c)</LHS><RHS>active(c)</RHS></RULE><RULE><LHS>mark(true)</LHS><RHS>active(true)</RHS></RULE><RULE><LHS>mark(false)</LHS><RHS>active(false)</RHS></RULE><RULE><LHS>f(mark(X))</LHS><RHS>f(X)</RHS></RULE><RULE><LHS>f(active(X))</LHS><RHS>f(X)</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></REWSYS><DPLIST/></DPSYS></SYSTEM><CRITERION><DAG approx="simpl"><CCLIST/></DAG></CRITERION></PROPERTY></PROPERTY><PROPERTY criterion="sterm" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(f(X))</LHS><RHS>mark(if(X,c,f(true)))</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>mark(f(X))</LHS><RHS>active(f(mark(X)))</RHS></RULE><RULE><LHS>mark(if(X1,X2,X3))</LHS><RHS>active(if(mark(X1),mark(X2),X3))</RHS></RULE><RULE><LHS>mark(c)</LHS><RHS>active(c)</RHS></RULE><RULE><LHS>mark(true)</LHS><RHS>active(true)</RHS></RULE><RULE><LHS>mark(false)</LHS><RHS>active(false)</RHS></RULE><RULE><LHS>f(mark(X))</LHS><RHS>f(X)</RHS></RULE><RULE><LHS>f(active(X))</LHS><RHS>f(X)</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></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(f(X))</LHS><RHS>mark(if(X,c,f(true)))</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>mark(f(X))</LHS><RHS>active(f(mark(X)))</RHS></RULE><RULE><LHS>mark(if(X1,X2,X3))</LHS><RHS>active(if(mark(X1),mark(X2),X3))</RHS></RULE><RULE><LHS>mark(c)</LHS><RHS>active(c)</RHS></RULE><RULE><LHS>mark(true)</LHS><RHS>active(true)</RHS></RULE><RULE><LHS>mark(false)</LHS><RHS>active(false)</RHS></RULE><RULE><LHS>f(mark(X))</LHS><RHS>f(X)</RHS></RULE><RULE><LHS>f(active(X))</LHS><RHS>f(X)</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></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(f(X))</LHS><RHS>mark(if(X,c,f(true)))</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>mark(f(X))</LHS><RHS>active(f(mark(X)))</RHS></RULE><RULE><LHS>mark(if(X1,X2,X3))</LHS><RHS>active(if(mark(X1),mark(X2),X3))</RHS></RULE><RULE><LHS>mark(c)</LHS><RHS>active(c)</RHS></RULE><RULE><LHS>mark(true)</LHS><RHS>active(true)</RHS></RULE><RULE><LHS>mark(false)</LHS><RHS>active(false)</RHS></RULE><RULE><LHS>f(mark(X))</LHS><RHS>f(X)</RHS></RULE><RULE><LHS>f(active(X))</LHS><RHS>f(X)</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></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(f(X))</LHS><RHS>mark(if(X,c,f(true)))</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>mark(f(X))</LHS><RHS>active(f(mark(X)))</RHS></RULE><RULE><LHS>mark(if(X1,X2,X3))</LHS><RHS>active(if(mark(X1),mark(X2),X3))</RHS></RULE><RULE><LHS>mark(c)</LHS><RHS>active(c)</RHS></RULE><RULE><LHS>mark(true)</LHS><RHS>active(true)</RHS></RULE><RULE><LHS>mark(false)</LHS><RHS>active(false)</RHS></RULE><RULE><LHS>f(mark(X))</LHS><RHS>f(X)</RHS></RULE><RULE><LHS>f(active(X))</LHS><RHS>f(X)</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></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(f(X))</LHS><RHS>mark(if(X,c,f(true)))</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>mark(f(X))</LHS><RHS>active(f(mark(X)))</RHS></RULE><RULE><LHS>mark(if(X1,X2,X3))</LHS><RHS>active(if(mark(X1),mark(X2),X3))</RHS></RULE><RULE><LHS>mark(c)</LHS><RHS>active(c)</RHS></RULE><RULE><LHS>mark(true)</LHS><RHS>active(true)</RHS></RULE><RULE><LHS>mark(false)</LHS><RHS>active(false)</RHS></RULE><RULE><LHS>f(mark(X))</LHS><RHS>f(X)</RHS></RULE><RULE><LHS>f(active(X))</LHS><RHS>f(X)</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></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(f(X))</LHS><RHS>mark(if(X,c,f(true)))</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>mark(f(X))</LHS><RHS>active(f(mark(X)))</RHS></RULE><RULE><LHS>mark(if(X1,X2,X3))</LHS><RHS>active(if(mark(X1),mark(X2),X3))</RHS></RULE><RULE><LHS>mark(c)</LHS><RHS>active(c)</RHS></RULE><RULE><LHS>mark(true)</LHS><RHS>active(true)</RHS></RULE><RULE><LHS>mark(false)</LHS><RHS>active(false)</RHS></RULE><RULE><LHS>f(mark(X))</LHS><RHS>f(X)</RHS></RULE><RULE><LHS>f(active(X))</LHS><RHS>f(X)</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></REWSYS><DPLIST/></DPSYS></SYSTEM><CRITERION><DAG approx="simpl"><CCLIST/></DAG></CRITERION></PROPERTY></PROPERTY></PROPERTY></PROPERTY></PROPERTY></PROPERTY></PROPERTY></PROPERTY></PROOF>
