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<!DOCTYPE PROOF SYSTEM "http://a3pat.ensiie.fr/pub/a3pat.dtd">
<PROOF><SIGNATURE><SYMBOLLIST><SYMBOL arity="1" unmarked="active"><NAME>Marked_active</NAME></SYMBOL><SYMBOL arity="1" unmarked=""><NAME>active</NAME></SYMBOL><SYMBOL arity="3" unmarked="f"><NAME>Marked_f</NAME></SYMBOL><SYMBOL arity="3" unmarked=""><NAME>f</NAME></SYMBOL><SYMBOL arity="1" unmarked="mark"><NAME>Marked_mark</NAME></SYMBOL><SYMBOL arity="0" unmarked=""><NAME>b</NAME></SYMBOL><SYMBOL arity="0" unmarked=""><NAME>a</NAME></SYMBOL><SYMBOL arity="1" unmarked=""><NAME>mark</NAME></SYMBOL></SYMBOLLIST><VARLIST><VAR>X3</VAR><VAR>X2</VAR><VAR>X1</VAR><VAR>X</VAR></VARLIST></SIGNATURE><PROPERTY criterion="dp" prop="sntrs"><SYSTEM><REWSYS><RULE><LHS>active(f(a,X,X))</LHS><RHS>mark(f(X,b,b))</RHS></RULE><RULE><LHS>active(b)</LHS><RHS>mark(a)</RHS></RULE><RULE><LHS>mark(f(X1,X2,X3))</LHS><RHS>active(f(X1,mark(X2),X3))</RHS></RULE><RULE><LHS>mark(a)</LHS><RHS>active(a)</RHS></RULE><RULE><LHS>mark(b)</LHS><RHS>active(b)</RHS></RULE><RULE><LHS>f(mark(X1),X2,X3)</LHS><RHS>f(X1,X2,X3)</RHS></RULE><RULE><LHS>f(X1,mark(X2),X3)</LHS><RHS>f(X1,X2,X3)</RHS></RULE><RULE><LHS>f(X1,X2,mark(X3))</LHS><RHS>f(X1,X2,X3)</RHS></RULE><RULE><LHS>f(active(X1),X2,X3)</LHS><RHS>f(X1,X2,X3)</RHS></RULE><RULE><LHS>f(X1,active(X2),X3)</LHS><RHS>f(X1,X2,X3)</RHS></RULE><RULE><LHS>f(X1,X2,active(X3))</LHS><RHS>f(X1,X2,X3)</RHS></RULE></REWSYS></SYSTEM><CRITERION/><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(f(a,X,X))</LHS><RHS>mark(f(X,b,b))</RHS></RULE><RULE><LHS>active(b)</LHS><RHS>mark(a)</RHS></RULE><RULE><LHS>mark(f(X1,X2,X3))</LHS><RHS>active(f(X1,mark(X2),X3))</RHS></RULE><RULE><LHS>mark(a)</LHS><RHS>active(a)</RHS></RULE><RULE><LHS>mark(b)</LHS><RHS>active(b)</RHS></RULE><RULE><LHS>f(mark(X1),X2,X3)</LHS><RHS>f(X1,X2,X3)</RHS></RULE><RULE><LHS>f(X1,mark(X2),X3)</LHS><RHS>f(X1,X2,X3)</RHS></RULE><RULE><LHS>f(X1,X2,mark(X3))</LHS><RHS>f(X1,X2,X3)</RHS></RULE><RULE><LHS>f(active(X1),X2,X3)</LHS><RHS>f(X1,X2,X3)</RHS></RULE><RULE><LHS>f(X1,active(X2),X3)</LHS><RHS>f(X1,X2,X3)</RHS></RULE><RULE><LHS>f(X1,X2,active(X3))</LHS><RHS>f(X1,X2,X3)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_active(f(a,X,X))</LHS><RHS>Marked_mark(f(X,b,b))</RHS></DPRULE><DPRULE num="1"><LHS>Marked_active(f(a,X,X))</LHS><RHS>Marked_f(X,b,b)</RHS></DPRULE><DPRULE num="2"><LHS>Marked_active(b)</LHS><RHS>Marked_mark(a)</RHS></DPRULE><DPRULE num="3"><LHS>Marked_mark(f(X1,X2,X3))</LHS><RHS>Marked_active(f(X1,mark(X2),X3))</RHS></DPRULE><DPRULE num="4"><LHS>Marked_mark(f(X1,X2,X3))</LHS><RHS>Marked_f(X1,mark(X2),X3)</RHS></DPRULE><DPRULE num="5"><LHS>Marked_mark(f(X1,X2,X3))</LHS><RHS>Marked_mark(X2)</RHS></DPRULE><DPRULE num="6"><LHS>Marked_mark(a)</LHS><RHS>Marked_active(a)</RHS></DPRULE><DPRULE num="7"><LHS>Marked_mark(b)</LHS><RHS>Marked_active(b)</RHS></DPRULE><DPRULE num="8"><LHS>Marked_f(mark(X1),X2,X3)</LHS><RHS>Marked_f(X1,X2,X3)</RHS></DPRULE><DPRULE num="9"><LHS>Marked_f(X1,mark(X2),X3)</LHS><RHS>Marked_f(X1,X2,X3)</RHS></DPRULE><DPRULE num="10"><LHS>Marked_f(X1,X2,mark(X3))</LHS><RHS>Marked_f(X1,X2,X3)</RHS></DPRULE><DPRULE num="11"><LHS>Marked_f(active(X1),X2,X3)</LHS><RHS>Marked_f(X1,X2,X3)</RHS></DPRULE><DPRULE num="12"><LHS>Marked_f(X1,active(X2),X3)</LHS><RHS>Marked_f(X1,X2,X3)</RHS></DPRULE><DPRULE num="13"><LHS>Marked_f(X1,X2,active(X3))</LHS><RHS>Marked_f(X1,X2,X3)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><DAG approx="simpl"><CCLIST><SCC num="0"><NODE ref="8"/><NODE ref="9"/><NODE ref="10"/><NODE ref="11"/><NODE ref="12"/><NODE ref="13"/></SCC><NONSCC num="1"><NODE ref="7"/></NONSCC><NONSCC num="2"><NODE ref="2"/></NONSCC><NONSCC num="3"><NODE ref="6"/></NONSCC><SCC num="4"><NODE ref="0"/><NODE ref="3"/><NODE ref="5"/></SCC><NONSCC num="5"><NODE ref="4"/></NONSCC><NONSCC num="6"><NODE ref="1"/></NONSCC></CCLIST><EDGE end="2" start="1"/><EDGE end="3" start="2"/><EDGE end="6" start="4"/><EDGE end="5" start="4"/><EDGE end="3" start="4"/><EDGE end="2" start="4"/><EDGE end="1" start="4"/><EDGE end="0" start="5"/><EDGE end="0" start="6"/></DAG></CRITERION><PROPERTY criterion="stronggraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(f(a,X,X))</LHS><RHS>mark(f(X,b,b))</RHS></RULE><RULE><LHS>active(b)</LHS><RHS>mark(a)</RHS></RULE><RULE><LHS>mark(f(X1,X2,X3))</LHS><RHS>active(f(X1,mark(X2),X3))</RHS></RULE><RULE><LHS>mark(a)</LHS><RHS>active(a)</RHS></RULE><RULE><LHS>mark(b)</LHS><RHS>active(b)</RHS></RULE><RULE><LHS>f(mark(X1),X2,X3)</LHS><RHS>f(X1,X2,X3)</RHS></RULE><RULE><LHS>f(X1,mark(X2),X3)</LHS><RHS>f(X1,X2,X3)</RHS></RULE><RULE><LHS>f(X1,X2,mark(X3))</LHS><RHS>f(X1,X2,X3)</RHS></RULE><RULE><LHS>f(active(X1),X2,X3)</LHS><RHS>f(X1,X2,X3)</RHS></RULE><RULE><LHS>f(X1,active(X2),X3)</LHS><RHS>f(X1,X2,X3)</RHS></RULE><RULE><LHS>f(X1,X2,active(X3))</LHS><RHS>f(X1,X2,X3)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_active(f(a,X,X))</LHS><RHS>Marked_mark(f(X,b,b))</RHS></DPRULE><DPRULE num="1"><LHS>Marked_mark(f(X1,X2,X3))</LHS><RHS>Marked_active(f(X1,mark(X2),X3))</RHS></DPRULE><DPRULE num="2"><LHS>Marked_mark(f(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>a</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>b</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>Marked_mark</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><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>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>Marked_active</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></ORDERING><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_mark(f(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(a,X,X))</LHS><RHS>mark(f(X,b,b))</RHS></RULE><RULE><LHS>active(b)</LHS><RHS>mark(a)</RHS></RULE><RULE><LHS>mark(f(X1,X2,X3))</LHS><RHS>active(f(X1,mark(X2),X3))</RHS></RULE><RULE><LHS>mark(a)</LHS><RHS>active(a)</RHS></RULE><RULE><LHS>mark(b)</LHS><RHS>active(b)</RHS></RULE><RULE><LHS>f(mark(X1),X2,X3)</LHS><RHS>f(X1,X2,X3)</RHS></RULE><RULE><LHS>f(X1,mark(X2),X3)</LHS><RHS>f(X1,X2,X3)</RHS></RULE><RULE><LHS>f(X1,X2,mark(X3))</LHS><RHS>f(X1,X2,X3)</RHS></RULE><RULE><LHS>f(active(X1),X2,X3)</LHS><RHS>f(X1,X2,X3)</RHS></RULE><RULE><LHS>f(X1,active(X2),X3)</LHS><RHS>f(X1,X2,X3)</RHS></RULE><RULE><LHS>f(X1,X2,active(X3))</LHS><RHS>f(X1,X2,X3)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_active(f(a,X,X))</LHS><RHS>Marked_mark(f(X,b,b))</RHS></DPRULE><DPRULE num="1"><LHS>Marked_mark(f(X1,X2,X3))</LHS><RHS>Marked_active(f(X1,mark(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="stronggraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(f(a,X,X))</LHS><RHS>mark(f(X,b,b))</RHS></RULE><RULE><LHS>active(b)</LHS><RHS>mark(a)</RHS></RULE><RULE><LHS>mark(f(X1,X2,X3))</LHS><RHS>active(f(X1,mark(X2),X3))</RHS></RULE><RULE><LHS>mark(a)</LHS><RHS>active(a)</RHS></RULE><RULE><LHS>mark(b)</LHS><RHS>active(b)</RHS></RULE><RULE><LHS>f(mark(X1),X2,X3)</LHS><RHS>f(X1,X2,X3)</RHS></RULE><RULE><LHS>f(X1,mark(X2),X3)</LHS><RHS>f(X1,X2,X3)</RHS></RULE><RULE><LHS>f(X1,X2,mark(X3))</LHS><RHS>f(X1,X2,X3)</RHS></RULE><RULE><LHS>f(active(X1),X2,X3)</LHS><RHS>f(X1,X2,X3)</RHS></RULE><RULE><LHS>f(X1,active(X2),X3)</LHS><RHS>f(X1,X2,X3)</RHS></RULE><RULE><LHS>f(X1,X2,active(X3))</LHS><RHS>f(X1,X2,X3)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_active(f(a,X,X))</LHS><RHS>Marked_mark(f(X,b,b))</RHS></DPRULE><DPRULE num="1"><LHS>Marked_mark(f(X1,X2,X3))</LHS><RHS>Marked_active(f(X1,mark(X2),X3))</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><ORDERING numstrictcol="1" size="3" type="matrix"><POLYSYMB><SYMBOL><NAME>mark</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><MATRIX><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN></MATRIX></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><MATRIX><COLUMN><INT>0</INT><INT>1</INT><INT>0</INT></COLUMN><COLUMN><INT>1</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>1</INT><INT>1</INT><INT>0</INT></COLUMN></MATRIX></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><MATRIX><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN></MATRIX></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>a</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><MATRIX><COLUMN><INT>1</INT><INT>1</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN></MATRIX></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><MATRIX><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN></MATRIX></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>b</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><MATRIX><COLUMN><INT>0</INT><INT>0</INT><INT>1</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN></MATRIX></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><MATRIX><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN></MATRIX></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>Marked_mark</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><MATRIX><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN></MATRIX></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><MATRIX><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>1</INT><INT>0</INT><INT>0</INT></COLUMN></MATRIX></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><MATRIX><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN></MATRIX></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>f</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><MATRIX><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN></MATRIX></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><MATRIX><COLUMN><INT>0</INT><INT>0</INT><INT>1</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>1</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN></MATRIX></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><MATRIX><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN></MATRIX></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><MATRIX><COLUMN><INT>0</INT><INT>0</INT><INT>1</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>1</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN></MATRIX></COEF><ARG degree="1" num="2"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><MATRIX><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN></MATRIX></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>active</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><MATRIX><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN></MATRIX></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><MATRIX><COLUMN><INT>0</INT><INT>1</INT><INT>0</INT></COLUMN><COLUMN><INT>1</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>1</INT><INT>1</INT><INT>0</INT></COLUMN></MATRIX></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><MATRIX><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN></MATRIX></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>Marked_active</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><MATRIX><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN></MATRIX></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><MATRIX><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>1</INT><INT>0</INT><INT>0</INT></COLUMN></MATRIX></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><MATRIX><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN></MATRIX></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB></ORDERING><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_active(f(a,X,X))</LHS><RHS>Marked_mark(f(X,b,b))</RHS></DPRULE></DPLIST></STRICTPAIRS></CRITERION><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(f(a,X,X))</LHS><RHS>mark(f(X,b,b))</RHS></RULE><RULE><LHS>active(b)</LHS><RHS>mark(a)</RHS></RULE><RULE><LHS>mark(f(X1,X2,X3))</LHS><RHS>active(f(X1,mark(X2),X3))</RHS></RULE><RULE><LHS>mark(a)</LHS><RHS>active(a)</RHS></RULE><RULE><LHS>mark(b)</LHS><RHS>active(b)</RHS></RULE><RULE><LHS>f(mark(X1),X2,X3)</LHS><RHS>f(X1,X2,X3)</RHS></RULE><RULE><LHS>f(X1,mark(X2),X3)</LHS><RHS>f(X1,X2,X3)</RHS></RULE><RULE><LHS>f(X1,X2,mark(X3))</LHS><RHS>f(X1,X2,X3)</RHS></RULE><RULE><LHS>f(active(X1),X2,X3)</LHS><RHS>f(X1,X2,X3)</RHS></RULE><RULE><LHS>f(X1,active(X2),X3)</LHS><RHS>f(X1,X2,X3)</RHS></RULE><RULE><LHS>f(X1,X2,active(X3))</LHS><RHS>f(X1,X2,X3)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_mark(f(X1,X2,X3))</LHS><RHS>Marked_active(f(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 criterion="sterm" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(f(a,X,X))</LHS><RHS>mark(f(X,b,b))</RHS></RULE><RULE><LHS>active(b)</LHS><RHS>mark(a)</RHS></RULE><RULE><LHS>mark(f(X1,X2,X3))</LHS><RHS>active(f(X1,mark(X2),X3))</RHS></RULE><RULE><LHS>mark(a)</LHS><RHS>active(a)</RHS></RULE><RULE><LHS>mark(b)</LHS><RHS>active(b)</RHS></RULE><RULE><LHS>f(mark(X1),X2,X3)</LHS><RHS>f(X1,X2,X3)</RHS></RULE><RULE><LHS>f(X1,mark(X2),X3)</LHS><RHS>f(X1,X2,X3)</RHS></RULE><RULE><LHS>f(X1,X2,mark(X3))</LHS><RHS>f(X1,X2,X3)</RHS></RULE><RULE><LHS>f(active(X1),X2,X3)</LHS><RHS>f(X1,X2,X3)</RHS></RULE><RULE><LHS>f(X1,active(X2),X3)</LHS><RHS>f(X1,X2,X3)</RHS></RULE><RULE><LHS>f(X1,X2,active(X3))</LHS><RHS>f(X1,X2,X3)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_f(mark(X1),X2,X3)</LHS><RHS>Marked_f(X1,X2,X3)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_f(X1,mark(X2),X3)</LHS><RHS>Marked_f(X1,X2,X3)</RHS></DPRULE><DPRULE num="2"><LHS>Marked_f(X1,X2,mark(X3))</LHS><RHS>Marked_f(X1,X2,X3)</RHS></DPRULE><DPRULE num="3"><LHS>Marked_f(active(X1),X2,X3)</LHS><RHS>Marked_f(X1,X2,X3)</RHS></DPRULE><DPRULE num="4"><LHS>Marked_f(X1,active(X2),X3)</LHS><RHS>Marked_f(X1,X2,X3)</RHS></DPRULE><DPRULE num="5"><LHS>Marked_f(X1,X2,active(X3))</LHS><RHS>Marked_f(X1,X2,X3)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><PROJECTION><PROJ><SYMBOL><NAME>Marked_f</NAME></SYMBOL><INT>3</INT></PROJ></PROJECTION><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_f(X1,X2,active(X3))</LHS><RHS>Marked_f(X1,X2,X3)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_f(X1,X2,mark(X3))</LHS><RHS>Marked_f(X1,X2,X3)</RHS></DPRULE></DPLIST></STRICTPAIRS><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(f(a,X,X))</LHS><RHS>mark(f(X,b,b))</RHS></RULE><RULE><LHS>active(b)</LHS><RHS>mark(a)</RHS></RULE><RULE><LHS>mark(f(X1,X2,X3))</LHS><RHS>active(f(X1,mark(X2),X3))</RHS></RULE><RULE><LHS>mark(a)</LHS><RHS>active(a)</RHS></RULE><RULE><LHS>mark(b)</LHS><RHS>active(b)</RHS></RULE><RULE><LHS>f(mark(X1),X2,X3)</LHS><RHS>f(X1,X2,X3)</RHS></RULE><RULE><LHS>f(X1,mark(X2),X3)</LHS><RHS>f(X1,X2,X3)</RHS></RULE><RULE><LHS>f(X1,X2,mark(X3))</LHS><RHS>f(X1,X2,X3)</RHS></RULE><RULE><LHS>f(active(X1),X2,X3)</LHS><RHS>f(X1,X2,X3)</RHS></RULE><RULE><LHS>f(X1,active(X2),X3)</LHS><RHS>f(X1,X2,X3)</RHS></RULE><RULE><LHS>f(X1,X2,active(X3))</LHS><RHS>f(X1,X2,X3)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_f(X1,active(X2),X3)</LHS><RHS>Marked_f(X1,X2,X3)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_f(active(X1),X2,X3)</LHS><RHS>Marked_f(X1,X2,X3)</RHS></DPRULE><DPRULE num="2"><LHS>Marked_f(X1,mark(X2),X3)</LHS><RHS>Marked_f(X1,X2,X3)</RHS></DPRULE><DPRULE num="3"><LHS>Marked_f(mark(X1),X2,X3)</LHS><RHS>Marked_f(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(a,X,X))</LHS><RHS>mark(f(X,b,b))</RHS></RULE><RULE><LHS>active(b)</LHS><RHS>mark(a)</RHS></RULE><RULE><LHS>mark(f(X1,X2,X3))</LHS><RHS>active(f(X1,mark(X2),X3))</RHS></RULE><RULE><LHS>mark(a)</LHS><RHS>active(a)</RHS></RULE><RULE><LHS>mark(b)</LHS><RHS>active(b)</RHS></RULE><RULE><LHS>f(mark(X1),X2,X3)</LHS><RHS>f(X1,X2,X3)</RHS></RULE><RULE><LHS>f(X1,mark(X2),X3)</LHS><RHS>f(X1,X2,X3)</RHS></RULE><RULE><LHS>f(X1,X2,mark(X3))</LHS><RHS>f(X1,X2,X3)</RHS></RULE><RULE><LHS>f(active(X1),X2,X3)</LHS><RHS>f(X1,X2,X3)</RHS></RULE><RULE><LHS>f(X1,active(X2),X3)</LHS><RHS>f(X1,X2,X3)</RHS></RULE><RULE><LHS>f(X1,X2,active(X3))</LHS><RHS>f(X1,X2,X3)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_f(X1,active(X2),X3)</LHS><RHS>Marked_f(X1,X2,X3)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_f(active(X1),X2,X3)</LHS><RHS>Marked_f(X1,X2,X3)</RHS></DPRULE><DPRULE num="2"><LHS>Marked_f(X1,mark(X2),X3)</LHS><RHS>Marked_f(X1,X2,X3)</RHS></DPRULE><DPRULE num="3"><LHS>Marked_f(mark(X1),X2,X3)</LHS><RHS>Marked_f(X1,X2,X3)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><PROJECTION><PROJ><SYMBOL><NAME>Marked_f</NAME></SYMBOL><INT>2</INT></PROJ></PROJECTION><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_f(X1,mark(X2),X3)</LHS><RHS>Marked_f(X1,X2,X3)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_f(X1,active(X2),X3)</LHS><RHS>Marked_f(X1,X2,X3)</RHS></DPRULE></DPLIST></STRICTPAIRS><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(f(a,X,X))</LHS><RHS>mark(f(X,b,b))</RHS></RULE><RULE><LHS>active(b)</LHS><RHS>mark(a)</RHS></RULE><RULE><LHS>mark(f(X1,X2,X3))</LHS><RHS>active(f(X1,mark(X2),X3))</RHS></RULE><RULE><LHS>mark(a)</LHS><RHS>active(a)</RHS></RULE><RULE><LHS>mark(b)</LHS><RHS>active(b)</RHS></RULE><RULE><LHS>f(mark(X1),X2,X3)</LHS><RHS>f(X1,X2,X3)</RHS></RULE><RULE><LHS>f(X1,mark(X2),X3)</LHS><RHS>f(X1,X2,X3)</RHS></RULE><RULE><LHS>f(X1,X2,mark(X3))</LHS><RHS>f(X1,X2,X3)</RHS></RULE><RULE><LHS>f(active(X1),X2,X3)</LHS><RHS>f(X1,X2,X3)</RHS></RULE><RULE><LHS>f(X1,active(X2),X3)</LHS><RHS>f(X1,X2,X3)</RHS></RULE><RULE><LHS>f(X1,X2,active(X3))</LHS><RHS>f(X1,X2,X3)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_f(mark(X1),X2,X3)</LHS><RHS>Marked_f(X1,X2,X3)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_f(active(X1),X2,X3)</LHS><RHS>Marked_f(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(a,X,X))</LHS><RHS>mark(f(X,b,b))</RHS></RULE><RULE><LHS>active(b)</LHS><RHS>mark(a)</RHS></RULE><RULE><LHS>mark(f(X1,X2,X3))</LHS><RHS>active(f(X1,mark(X2),X3))</RHS></RULE><RULE><LHS>mark(a)</LHS><RHS>active(a)</RHS></RULE><RULE><LHS>mark(b)</LHS><RHS>active(b)</RHS></RULE><RULE><LHS>f(mark(X1),X2,X3)</LHS><RHS>f(X1,X2,X3)</RHS></RULE><RULE><LHS>f(X1,mark(X2),X3)</LHS><RHS>f(X1,X2,X3)</RHS></RULE><RULE><LHS>f(X1,X2,mark(X3))</LHS><RHS>f(X1,X2,X3)</RHS></RULE><RULE><LHS>f(active(X1),X2,X3)</LHS><RHS>f(X1,X2,X3)</RHS></RULE><RULE><LHS>f(X1,active(X2),X3)</LHS><RHS>f(X1,X2,X3)</RHS></RULE><RULE><LHS>f(X1,X2,active(X3))</LHS><RHS>f(X1,X2,X3)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_f(mark(X1),X2,X3)</LHS><RHS>Marked_f(X1,X2,X3)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_f(active(X1),X2,X3)</LHS><RHS>Marked_f(X1,X2,X3)</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(X1),X2,X3)</LHS><RHS>Marked_f(X1,X2,X3)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_f(mark(X1),X2,X3)</LHS><RHS>Marked_f(X1,X2,X3)</RHS></DPRULE></DPLIST></STRICTPAIRS><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(f(a,X,X))</LHS><RHS>mark(f(X,b,b))</RHS></RULE><RULE><LHS>active(b)</LHS><RHS>mark(a)</RHS></RULE><RULE><LHS>mark(f(X1,X2,X3))</LHS><RHS>active(f(X1,mark(X2),X3))</RHS></RULE><RULE><LHS>mark(a)</LHS><RHS>active(a)</RHS></RULE><RULE><LHS>mark(b)</LHS><RHS>active(b)</RHS></RULE><RULE><LHS>f(mark(X1),X2,X3)</LHS><RHS>f(X1,X2,X3)</RHS></RULE><RULE><LHS>f(X1,mark(X2),X3)</LHS><RHS>f(X1,X2,X3)</RHS></RULE><RULE><LHS>f(X1,X2,mark(X3))</LHS><RHS>f(X1,X2,X3)</RHS></RULE><RULE><LHS>f(active(X1),X2,X3)</LHS><RHS>f(X1,X2,X3)</RHS></RULE><RULE><LHS>f(X1,active(X2),X3)</LHS><RHS>f(X1,X2,X3)</RHS></RULE><RULE><LHS>f(X1,X2,active(X3))</LHS><RHS>f(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>
