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<!DOCTYPE PROOF SYSTEM "http://a3pat.ensiie.fr/pub/a3pat.dtd">
<PROOF><SIGNATURE><SYMBOLLIST><SYMBOL arity="1" unmarked="isNePal"><NAME>Marked_isNePal</NAME></SYMBOL><SYMBOL arity="1" unmarked="active"><NAME>Marked_active</NAME></SYMBOL><SYMBOL arity="0" unmarked=""><NAME>nil</NAME></SYMBOL><SYMBOL arity="0" unmarked=""><NAME>tt</NAME></SYMBOL><SYMBOL arity="2" unmarked="__"><NAME>Marked___</NAME></SYMBOL><SYMBOL arity="2" unmarked=""><NAME>__</NAME></SYMBOL><SYMBOL arity="1" unmarked=""><NAME>isNePal</NAME></SYMBOL><SYMBOL arity="1" unmarked="mark"><NAME>Marked_mark</NAME></SYMBOL><SYMBOL arity="1" unmarked=""><NAME>active</NAME></SYMBOL><SYMBOL arity="2" unmarked=""><NAME>and</NAME></SYMBOL><SYMBOL arity="2" unmarked="and"><NAME>Marked_and</NAME></SYMBOL><SYMBOL arity="1" unmarked=""><NAME>mark</NAME></SYMBOL></SYMBOLLIST><VARLIST><VAR>X2</VAR><VAR>X1</VAR><VAR>P</VAR><VAR>I</VAR><VAR>Z</VAR><VAR>Y</VAR><VAR>X</VAR></VARLIST></SIGNATURE><PROPERTY criterion="dp" prop="sntrs"><SYSTEM><REWSYS><RULE><LHS>active(__(__(X,Y),Z))</LHS><RHS>mark(__(X,__(Y,Z)))</RHS></RULE><RULE><LHS>active(__(X,nil))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(__(nil,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(and(tt,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(isNePal(__(I,__(P,I))))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>mark(__(X1,X2))</LHS><RHS>active(__(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(nil)</LHS><RHS>active(nil)</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(tt)</LHS><RHS>active(tt)</RHS></RULE><RULE><LHS>mark(isNePal(X))</LHS><RHS>active(isNePal(mark(X)))</RHS></RULE><RULE><LHS>__(mark(X1),X2)</LHS><RHS>__(X1,X2)</RHS></RULE><RULE><LHS>__(X1,mark(X2))</LHS><RHS>__(X1,X2)</RHS></RULE><RULE><LHS>__(active(X1),X2)</LHS><RHS>__(X1,X2)</RHS></RULE><RULE><LHS>__(X1,active(X2))</LHS><RHS>__(X1,X2)</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>isNePal(mark(X))</LHS><RHS>isNePal(X)</RHS></RULE><RULE><LHS>isNePal(active(X))</LHS><RHS>isNePal(X)</RHS></RULE></REWSYS></SYSTEM><CRITERION/><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(__(__(X,Y),Z))</LHS><RHS>mark(__(X,__(Y,Z)))</RHS></RULE><RULE><LHS>active(__(X,nil))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(__(nil,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(and(tt,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(isNePal(__(I,__(P,I))))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>mark(__(X1,X2))</LHS><RHS>active(__(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(nil)</LHS><RHS>active(nil)</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(tt)</LHS><RHS>active(tt)</RHS></RULE><RULE><LHS>mark(isNePal(X))</LHS><RHS>active(isNePal(mark(X)))</RHS></RULE><RULE><LHS>__(mark(X1),X2)</LHS><RHS>__(X1,X2)</RHS></RULE><RULE><LHS>__(X1,mark(X2))</LHS><RHS>__(X1,X2)</RHS></RULE><RULE><LHS>__(active(X1),X2)</LHS><RHS>__(X1,X2)</RHS></RULE><RULE><LHS>__(X1,active(X2))</LHS><RHS>__(X1,X2)</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>isNePal(mark(X))</LHS><RHS>isNePal(X)</RHS></RULE><RULE><LHS>isNePal(active(X))</LHS><RHS>isNePal(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_active(__(__(X,Y),Z))</LHS><RHS>Marked_mark(__(X,__(Y,Z)))</RHS></DPRULE><DPRULE num="1"><LHS>Marked_active(__(__(X,Y),Z))</LHS><RHS>Marked___(X,__(Y,Z))</RHS></DPRULE><DPRULE num="2"><LHS>Marked_active(__(__(X,Y),Z))</LHS><RHS>Marked___(Y,Z)</RHS></DPRULE><DPRULE num="3"><LHS>Marked_active(__(X,nil))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="4"><LHS>Marked_active(__(nil,X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="5"><LHS>Marked_active(and(tt,X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="6"><LHS>Marked_active(isNePal(__(I,__(P,I))))</LHS><RHS>Marked_mark(tt)</RHS></DPRULE><DPRULE num="7"><LHS>Marked_mark(__(X1,X2))</LHS><RHS>Marked_active(__(mark(X1),mark(X2)))</RHS></DPRULE><DPRULE num="8"><LHS>Marked_mark(__(X1,X2))</LHS><RHS>Marked___(mark(X1),mark(X2))</RHS></DPRULE><DPRULE num="9"><LHS>Marked_mark(__(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="10"><LHS>Marked_mark(__(X1,X2))</LHS><RHS>Marked_mark(X2)</RHS></DPRULE><DPRULE num="11"><LHS>Marked_mark(nil)</LHS><RHS>Marked_active(nil)</RHS></DPRULE><DPRULE num="12"><LHS>Marked_mark(and(X1,X2))</LHS><RHS>Marked_active(and(mark(X1),X2))</RHS></DPRULE><DPRULE num="13"><LHS>Marked_mark(and(X1,X2))</LHS><RHS>Marked_and(mark(X1),X2)</RHS></DPRULE><DPRULE num="14"><LHS>Marked_mark(and(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="15"><LHS>Marked_mark(tt)</LHS><RHS>Marked_active(tt)</RHS></DPRULE><DPRULE num="16"><LHS>Marked_mark(isNePal(X))</LHS><RHS>Marked_active(isNePal(mark(X)))</RHS></DPRULE><DPRULE num="17"><LHS>Marked_mark(isNePal(X))</LHS><RHS>Marked_isNePal(mark(X))</RHS></DPRULE><DPRULE num="18"><LHS>Marked_mark(isNePal(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="19"><LHS>Marked___(mark(X1),X2)</LHS><RHS>Marked___(X1,X2)</RHS></DPRULE><DPRULE num="20"><LHS>Marked___(X1,mark(X2))</LHS><RHS>Marked___(X1,X2)</RHS></DPRULE><DPRULE num="21"><LHS>Marked___(active(X1),X2)</LHS><RHS>Marked___(X1,X2)</RHS></DPRULE><DPRULE num="22"><LHS>Marked___(X1,active(X2))</LHS><RHS>Marked___(X1,X2)</RHS></DPRULE><DPRULE num="23"><LHS>Marked_and(mark(X1),X2)</LHS><RHS>Marked_and(X1,X2)</RHS></DPRULE><DPRULE num="24"><LHS>Marked_and(X1,mark(X2))</LHS><RHS>Marked_and(X1,X2)</RHS></DPRULE><DPRULE num="25"><LHS>Marked_and(active(X1),X2)</LHS><RHS>Marked_and(X1,X2)</RHS></DPRULE><DPRULE num="26"><LHS>Marked_and(X1,active(X2))</LHS><RHS>Marked_and(X1,X2)</RHS></DPRULE><DPRULE num="27"><LHS>Marked_isNePal(mark(X))</LHS><RHS>Marked_isNePal(X)</RHS></DPRULE><DPRULE num="28"><LHS>Marked_isNePal(active(X))</LHS><RHS>Marked_isNePal(X)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><DAG approx="simpl"><CCLIST><SCC num="0"><NODE ref="27"/><NODE ref="28"/></SCC><SCC num="1"><NODE ref="23"/><NODE ref="24"/><NODE ref="25"/><NODE ref="26"/></SCC><SCC num="2"><NODE ref="19"/><NODE ref="20"/><NODE ref="21"/><NODE ref="22"/></SCC><SCC num="3"><NODE ref="0"/><NODE ref="3"/><NODE ref="4"/><NODE ref="5"/><NODE ref="7"/><NODE ref="9"/><NODE ref="10"/><NODE ref="12"/><NODE ref="14"/><NODE ref="16"/><NODE ref="18"/></SCC><NONSCC num="4"><NODE ref="17"/></NONSCC><NONSCC num="5"><NODE ref="15"/></NONSCC><NONSCC num="6"><NODE ref="13"/></NONSCC><NONSCC num="7"><NODE ref="11"/></NONSCC><NONSCC num="8"><NODE ref="8"/></NONSCC><NONSCC num="9"><NODE ref="6"/></NONSCC><NONSCC num="10"><NODE ref="2"/></NONSCC><NONSCC num="11"><NODE ref="1"/></NONSCC></CCLIST><EDGE end="11" start="3"/><EDGE end="10" start="3"/><EDGE end="9" start="3"/><EDGE end="8" start="3"/><EDGE end="7" start="3"/><EDGE end="6" start="3"/><EDGE end="5" start="3"/><EDGE end="4" start="3"/><EDGE end="0" start="4"/><EDGE end="1" start="6"/><EDGE end="2" start="8"/><EDGE end="5" start="9"/><EDGE end="2" start="10"/><EDGE end="2" start="11"/></DAG></CRITERION><PROPERTY criterion="stronggraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(__(__(X,Y),Z))</LHS><RHS>mark(__(X,__(Y,Z)))</RHS></RULE><RULE><LHS>active(__(X,nil))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(__(nil,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(and(tt,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(isNePal(__(I,__(P,I))))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>mark(__(X1,X2))</LHS><RHS>active(__(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(nil)</LHS><RHS>active(nil)</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(tt)</LHS><RHS>active(tt)</RHS></RULE><RULE><LHS>mark(isNePal(X))</LHS><RHS>active(isNePal(mark(X)))</RHS></RULE><RULE><LHS>__(mark(X1),X2)</LHS><RHS>__(X1,X2)</RHS></RULE><RULE><LHS>__(X1,mark(X2))</LHS><RHS>__(X1,X2)</RHS></RULE><RULE><LHS>__(active(X1),X2)</LHS><RHS>__(X1,X2)</RHS></RULE><RULE><LHS>__(X1,active(X2))</LHS><RHS>__(X1,X2)</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>isNePal(mark(X))</LHS><RHS>isNePal(X)</RHS></RULE><RULE><LHS>isNePal(active(X))</LHS><RHS>isNePal(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_active(__(__(X,Y),Z))</LHS><RHS>Marked_mark(__(X,__(Y,Z)))</RHS></DPRULE><DPRULE num="1"><LHS>Marked_active(__(X,nil))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="2"><LHS>Marked_active(__(nil,X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="3"><LHS>Marked_active(and(tt,X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="4"><LHS>Marked_mark(__(X1,X2))</LHS><RHS>Marked_active(__(mark(X1),mark(X2)))</RHS></DPRULE><DPRULE num="5"><LHS>Marked_mark(__(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="6"><LHS>Marked_mark(__(X1,X2))</LHS><RHS>Marked_mark(X2)</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(isNePal(X))</LHS><RHS>Marked_active(isNePal(mark(X)))</RHS></DPRULE><DPRULE num="10"><LHS>Marked_mark(isNePal(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><ORDERING type="poly"><POLYSYMB><SYMBOL><NAME>mark</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>and</NAME></SYMBOL><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></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_mark</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><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>isNePal</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>__</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>tt</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>nil</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>Marked_active</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>3</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB></ORDERING><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_active(__(__(X,Y),Z))</LHS><RHS>Marked_mark(__(X,__(Y,Z)))</RHS></DPRULE><DPRULE num="1"><LHS>Marked_active(__(X,nil))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="2"><LHS>Marked_active(__(nil,X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="3"><LHS>Marked_active(and(tt,X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="4"><LHS>Marked_mark(__(X1,X2))</LHS><RHS>Marked_active(__(mark(X1),mark(X2)))</RHS></DPRULE><DPRULE num="5"><LHS>Marked_mark(__(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="6"><LHS>Marked_mark(__(X1,X2))</LHS><RHS>Marked_mark(X2)</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(isNePal(X))</LHS><RHS>Marked_active(isNePal(mark(X)))</RHS></DPRULE></DPLIST></STRICTPAIRS></CRITERION><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(__(__(X,Y),Z))</LHS><RHS>mark(__(X,__(Y,Z)))</RHS></RULE><RULE><LHS>active(__(X,nil))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(__(nil,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(and(tt,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(isNePal(__(I,__(P,I))))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>mark(__(X1,X2))</LHS><RHS>active(__(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(nil)</LHS><RHS>active(nil)</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(tt)</LHS><RHS>active(tt)</RHS></RULE><RULE><LHS>mark(isNePal(X))</LHS><RHS>active(isNePal(mark(X)))</RHS></RULE><RULE><LHS>__(mark(X1),X2)</LHS><RHS>__(X1,X2)</RHS></RULE><RULE><LHS>__(X1,mark(X2))</LHS><RHS>__(X1,X2)</RHS></RULE><RULE><LHS>__(active(X1),X2)</LHS><RHS>__(X1,X2)</RHS></RULE><RULE><LHS>__(X1,active(X2))</LHS><RHS>__(X1,X2)</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>isNePal(mark(X))</LHS><RHS>isNePal(X)</RHS></RULE><RULE><LHS>isNePal(active(X))</LHS><RHS>isNePal(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_mark(and(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_mark(isNePal(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><DAG approx="simpl"><CCLIST><SCC num="0"><NODE ref="0"/><NODE ref="1"/></SCC></CCLIST></DAG></CRITERION><PROPERTY criterion="sterm" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(__(__(X,Y),Z))</LHS><RHS>mark(__(X,__(Y,Z)))</RHS></RULE><RULE><LHS>active(__(X,nil))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(__(nil,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(and(tt,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(isNePal(__(I,__(P,I))))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>mark(__(X1,X2))</LHS><RHS>active(__(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(nil)</LHS><RHS>active(nil)</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(tt)</LHS><RHS>active(tt)</RHS></RULE><RULE><LHS>mark(isNePal(X))</LHS><RHS>active(isNePal(mark(X)))</RHS></RULE><RULE><LHS>__(mark(X1),X2)</LHS><RHS>__(X1,X2)</RHS></RULE><RULE><LHS>__(X1,mark(X2))</LHS><RHS>__(X1,X2)</RHS></RULE><RULE><LHS>__(active(X1),X2)</LHS><RHS>__(X1,X2)</RHS></RULE><RULE><LHS>__(X1,active(X2))</LHS><RHS>__(X1,X2)</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>isNePal(mark(X))</LHS><RHS>isNePal(X)</RHS></RULE><RULE><LHS>isNePal(active(X))</LHS><RHS>isNePal(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_mark(and(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_mark(isNePal(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><PROJECTION><PROJ><SYMBOL><NAME>Marked_mark</NAME></SYMBOL><INT>1</INT></PROJ></PROJECTION><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_mark(isNePal(X))</LHS><RHS>Marked_mark(X)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_mark(and(X1,X2))</LHS><RHS>Marked_mark(X1)</RHS></DPRULE></DPLIST></STRICTPAIRS><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(__(__(X,Y),Z))</LHS><RHS>mark(__(X,__(Y,Z)))</RHS></RULE><RULE><LHS>active(__(X,nil))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(__(nil,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(and(tt,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(isNePal(__(I,__(P,I))))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>mark(__(X1,X2))</LHS><RHS>active(__(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(nil)</LHS><RHS>active(nil)</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(tt)</LHS><RHS>active(tt)</RHS></RULE><RULE><LHS>mark(isNePal(X))</LHS><RHS>active(isNePal(mark(X)))</RHS></RULE><RULE><LHS>__(mark(X1),X2)</LHS><RHS>__(X1,X2)</RHS></RULE><RULE><LHS>__(X1,mark(X2))</LHS><RHS>__(X1,X2)</RHS></RULE><RULE><LHS>__(active(X1),X2)</LHS><RHS>__(X1,X2)</RHS></RULE><RULE><LHS>__(X1,active(X2))</LHS><RHS>__(X1,X2)</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>isNePal(mark(X))</LHS><RHS>isNePal(X)</RHS></RULE><RULE><LHS>isNePal(active(X))</LHS><RHS>isNePal(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(__(__(X,Y),Z))</LHS><RHS>mark(__(X,__(Y,Z)))</RHS></RULE><RULE><LHS>active(__(X,nil))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(__(nil,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(and(tt,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(isNePal(__(I,__(P,I))))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>mark(__(X1,X2))</LHS><RHS>active(__(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(nil)</LHS><RHS>active(nil)</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(tt)</LHS><RHS>active(tt)</RHS></RULE><RULE><LHS>mark(isNePal(X))</LHS><RHS>active(isNePal(mark(X)))</RHS></RULE><RULE><LHS>__(mark(X1),X2)</LHS><RHS>__(X1,X2)</RHS></RULE><RULE><LHS>__(X1,mark(X2))</LHS><RHS>__(X1,X2)</RHS></RULE><RULE><LHS>__(active(X1),X2)</LHS><RHS>__(X1,X2)</RHS></RULE><RULE><LHS>__(X1,active(X2))</LHS><RHS>__(X1,X2)</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>isNePal(mark(X))</LHS><RHS>isNePal(X)</RHS></RULE><RULE><LHS>isNePal(active(X))</LHS><RHS>isNePal(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked___(mark(X1),X2)</LHS><RHS>Marked___(X1,X2)</RHS></DPRULE><DPRULE num="1"><LHS>Marked___(X1,mark(X2))</LHS><RHS>Marked___(X1,X2)</RHS></DPRULE><DPRULE num="2"><LHS>Marked___(active(X1),X2)</LHS><RHS>Marked___(X1,X2)</RHS></DPRULE><DPRULE num="3"><LHS>Marked___(X1,active(X2))</LHS><RHS>Marked___(X1,X2)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><PROJECTION><PROJ><SYMBOL><NAME>Marked___</NAME></SYMBOL><INT>2</INT></PROJ></PROJECTION><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked___(X1,active(X2))</LHS><RHS>Marked___(X1,X2)</RHS></DPRULE><DPRULE num="1"><LHS>Marked___(X1,mark(X2))</LHS><RHS>Marked___(X1,X2)</RHS></DPRULE></DPLIST></STRICTPAIRS><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(__(__(X,Y),Z))</LHS><RHS>mark(__(X,__(Y,Z)))</RHS></RULE><RULE><LHS>active(__(X,nil))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(__(nil,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(and(tt,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(isNePal(__(I,__(P,I))))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>mark(__(X1,X2))</LHS><RHS>active(__(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(nil)</LHS><RHS>active(nil)</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(tt)</LHS><RHS>active(tt)</RHS></RULE><RULE><LHS>mark(isNePal(X))</LHS><RHS>active(isNePal(mark(X)))</RHS></RULE><RULE><LHS>__(mark(X1),X2)</LHS><RHS>__(X1,X2)</RHS></RULE><RULE><LHS>__(X1,mark(X2))</LHS><RHS>__(X1,X2)</RHS></RULE><RULE><LHS>__(active(X1),X2)</LHS><RHS>__(X1,X2)</RHS></RULE><RULE><LHS>__(X1,active(X2))</LHS><RHS>__(X1,X2)</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>isNePal(mark(X))</LHS><RHS>isNePal(X)</RHS></RULE><RULE><LHS>isNePal(active(X))</LHS><RHS>isNePal(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked___(active(X1),X2)</LHS><RHS>Marked___(X1,X2)</RHS></DPRULE><DPRULE num="1"><LHS>Marked___(mark(X1),X2)</LHS><RHS>Marked___(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(__(__(X,Y),Z))</LHS><RHS>mark(__(X,__(Y,Z)))</RHS></RULE><RULE><LHS>active(__(X,nil))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(__(nil,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(and(tt,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(isNePal(__(I,__(P,I))))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>mark(__(X1,X2))</LHS><RHS>active(__(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(nil)</LHS><RHS>active(nil)</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(tt)</LHS><RHS>active(tt)</RHS></RULE><RULE><LHS>mark(isNePal(X))</LHS><RHS>active(isNePal(mark(X)))</RHS></RULE><RULE><LHS>__(mark(X1),X2)</LHS><RHS>__(X1,X2)</RHS></RULE><RULE><LHS>__(X1,mark(X2))</LHS><RHS>__(X1,X2)</RHS></RULE><RULE><LHS>__(active(X1),X2)</LHS><RHS>__(X1,X2)</RHS></RULE><RULE><LHS>__(X1,active(X2))</LHS><RHS>__(X1,X2)</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>isNePal(mark(X))</LHS><RHS>isNePal(X)</RHS></RULE><RULE><LHS>isNePal(active(X))</LHS><RHS>isNePal(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked___(active(X1),X2)</LHS><RHS>Marked___(X1,X2)</RHS></DPRULE><DPRULE num="1"><LHS>Marked___(mark(X1),X2)</LHS><RHS>Marked___(X1,X2)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><PROJECTION><PROJ><SYMBOL><NAME>Marked___</NAME></SYMBOL><INT>1</INT></PROJ></PROJECTION><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked___(mark(X1),X2)</LHS><RHS>Marked___(X1,X2)</RHS></DPRULE><DPRULE num="1"><LHS>Marked___(active(X1),X2)</LHS><RHS>Marked___(X1,X2)</RHS></DPRULE></DPLIST></STRICTPAIRS><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(__(__(X,Y),Z))</LHS><RHS>mark(__(X,__(Y,Z)))</RHS></RULE><RULE><LHS>active(__(X,nil))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(__(nil,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(and(tt,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(isNePal(__(I,__(P,I))))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>mark(__(X1,X2))</LHS><RHS>active(__(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(nil)</LHS><RHS>active(nil)</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(tt)</LHS><RHS>active(tt)</RHS></RULE><RULE><LHS>mark(isNePal(X))</LHS><RHS>active(isNePal(mark(X)))</RHS></RULE><RULE><LHS>__(mark(X1),X2)</LHS><RHS>__(X1,X2)</RHS></RULE><RULE><LHS>__(X1,mark(X2))</LHS><RHS>__(X1,X2)</RHS></RULE><RULE><LHS>__(active(X1),X2)</LHS><RHS>__(X1,X2)</RHS></RULE><RULE><LHS>__(X1,active(X2))</LHS><RHS>__(X1,X2)</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>isNePal(mark(X))</LHS><RHS>isNePal(X)</RHS></RULE><RULE><LHS>isNePal(active(X))</LHS><RHS>isNePal(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(__(__(X,Y),Z))</LHS><RHS>mark(__(X,__(Y,Z)))</RHS></RULE><RULE><LHS>active(__(X,nil))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(__(nil,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(and(tt,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(isNePal(__(I,__(P,I))))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>mark(__(X1,X2))</LHS><RHS>active(__(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(nil)</LHS><RHS>active(nil)</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(tt)</LHS><RHS>active(tt)</RHS></RULE><RULE><LHS>mark(isNePal(X))</LHS><RHS>active(isNePal(mark(X)))</RHS></RULE><RULE><LHS>__(mark(X1),X2)</LHS><RHS>__(X1,X2)</RHS></RULE><RULE><LHS>__(X1,mark(X2))</LHS><RHS>__(X1,X2)</RHS></RULE><RULE><LHS>__(active(X1),X2)</LHS><RHS>__(X1,X2)</RHS></RULE><RULE><LHS>__(X1,active(X2))</LHS><RHS>__(X1,X2)</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>isNePal(mark(X))</LHS><RHS>isNePal(X)</RHS></RULE><RULE><LHS>isNePal(active(X))</LHS><RHS>isNePal(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(__(__(X,Y),Z))</LHS><RHS>mark(__(X,__(Y,Z)))</RHS></RULE><RULE><LHS>active(__(X,nil))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(__(nil,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(and(tt,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(isNePal(__(I,__(P,I))))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>mark(__(X1,X2))</LHS><RHS>active(__(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(nil)</LHS><RHS>active(nil)</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(tt)</LHS><RHS>active(tt)</RHS></RULE><RULE><LHS>mark(isNePal(X))</LHS><RHS>active(isNePal(mark(X)))</RHS></RULE><RULE><LHS>__(mark(X1),X2)</LHS><RHS>__(X1,X2)</RHS></RULE><RULE><LHS>__(X1,mark(X2))</LHS><RHS>__(X1,X2)</RHS></RULE><RULE><LHS>__(active(X1),X2)</LHS><RHS>__(X1,X2)</RHS></RULE><RULE><LHS>__(X1,active(X2))</LHS><RHS>__(X1,X2)</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>isNePal(mark(X))</LHS><RHS>isNePal(X)</RHS></RULE><RULE><LHS>isNePal(active(X))</LHS><RHS>isNePal(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(__(__(X,Y),Z))</LHS><RHS>mark(__(X,__(Y,Z)))</RHS></RULE><RULE><LHS>active(__(X,nil))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(__(nil,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(and(tt,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(isNePal(__(I,__(P,I))))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>mark(__(X1,X2))</LHS><RHS>active(__(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(nil)</LHS><RHS>active(nil)</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(tt)</LHS><RHS>active(tt)</RHS></RULE><RULE><LHS>mark(isNePal(X))</LHS><RHS>active(isNePal(mark(X)))</RHS></RULE><RULE><LHS>__(mark(X1),X2)</LHS><RHS>__(X1,X2)</RHS></RULE><RULE><LHS>__(X1,mark(X2))</LHS><RHS>__(X1,X2)</RHS></RULE><RULE><LHS>__(active(X1),X2)</LHS><RHS>__(X1,X2)</RHS></RULE><RULE><LHS>__(X1,active(X2))</LHS><RHS>__(X1,X2)</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>isNePal(mark(X))</LHS><RHS>isNePal(X)</RHS></RULE><RULE><LHS>isNePal(active(X))</LHS><RHS>isNePal(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(__(__(X,Y),Z))</LHS><RHS>mark(__(X,__(Y,Z)))</RHS></RULE><RULE><LHS>active(__(X,nil))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(__(nil,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(and(tt,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(isNePal(__(I,__(P,I))))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>mark(__(X1,X2))</LHS><RHS>active(__(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(nil)</LHS><RHS>active(nil)</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(tt)</LHS><RHS>active(tt)</RHS></RULE><RULE><LHS>mark(isNePal(X))</LHS><RHS>active(isNePal(mark(X)))</RHS></RULE><RULE><LHS>__(mark(X1),X2)</LHS><RHS>__(X1,X2)</RHS></RULE><RULE><LHS>__(X1,mark(X2))</LHS><RHS>__(X1,X2)</RHS></RULE><RULE><LHS>__(active(X1),X2)</LHS><RHS>__(X1,X2)</RHS></RULE><RULE><LHS>__(X1,active(X2))</LHS><RHS>__(X1,X2)</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>isNePal(mark(X))</LHS><RHS>isNePal(X)</RHS></RULE><RULE><LHS>isNePal(active(X))</LHS><RHS>isNePal(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(__(__(X,Y),Z))</LHS><RHS>mark(__(X,__(Y,Z)))</RHS></RULE><RULE><LHS>active(__(X,nil))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(__(nil,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(and(tt,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(isNePal(__(I,__(P,I))))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>mark(__(X1,X2))</LHS><RHS>active(__(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(nil)</LHS><RHS>active(nil)</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(tt)</LHS><RHS>active(tt)</RHS></RULE><RULE><LHS>mark(isNePal(X))</LHS><RHS>active(isNePal(mark(X)))</RHS></RULE><RULE><LHS>__(mark(X1),X2)</LHS><RHS>__(X1,X2)</RHS></RULE><RULE><LHS>__(X1,mark(X2))</LHS><RHS>__(X1,X2)</RHS></RULE><RULE><LHS>__(active(X1),X2)</LHS><RHS>__(X1,X2)</RHS></RULE><RULE><LHS>__(X1,active(X2))</LHS><RHS>__(X1,X2)</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>isNePal(mark(X))</LHS><RHS>isNePal(X)</RHS></RULE><RULE><LHS>isNePal(active(X))</LHS><RHS>isNePal(X)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_isNePal(mark(X))</LHS><RHS>Marked_isNePal(X)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_isNePal(active(X))</LHS><RHS>Marked_isNePal(X)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><PROJECTION><PROJ><SYMBOL><NAME>Marked_isNePal</NAME></SYMBOL><INT>1</INT></PROJ></PROJECTION><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_isNePal(active(X))</LHS><RHS>Marked_isNePal(X)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_isNePal(mark(X))</LHS><RHS>Marked_isNePal(X)</RHS></DPRULE></DPLIST></STRICTPAIRS><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>active(__(__(X,Y),Z))</LHS><RHS>mark(__(X,__(Y,Z)))</RHS></RULE><RULE><LHS>active(__(X,nil))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(__(nil,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(and(tt,X))</LHS><RHS>mark(X)</RHS></RULE><RULE><LHS>active(isNePal(__(I,__(P,I))))</LHS><RHS>mark(tt)</RHS></RULE><RULE><LHS>mark(__(X1,X2))</LHS><RHS>active(__(mark(X1),mark(X2)))</RHS></RULE><RULE><LHS>mark(nil)</LHS><RHS>active(nil)</RHS></RULE><RULE><LHS>mark(and(X1,X2))</LHS><RHS>active(and(mark(X1),X2))</RHS></RULE><RULE><LHS>mark(tt)</LHS><RHS>active(tt)</RHS></RULE><RULE><LHS>mark(isNePal(X))</LHS><RHS>active(isNePal(mark(X)))</RHS></RULE><RULE><LHS>__(mark(X1),X2)</LHS><RHS>__(X1,X2)</RHS></RULE><RULE><LHS>__(X1,mark(X2))</LHS><RHS>__(X1,X2)</RHS></RULE><RULE><LHS>__(active(X1),X2)</LHS><RHS>__(X1,X2)</RHS></RULE><RULE><LHS>__(X1,active(X2))</LHS><RHS>__(X1,X2)</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>isNePal(mark(X))</LHS><RHS>isNePal(X)</RHS></RULE><RULE><LHS>isNePal(active(X))</LHS><RHS>isNePal(X)</RHS></RULE></REWSYS><DPLIST/></DPSYS></SYSTEM><CRITERION><DAG approx="simpl"><CCLIST/></DAG></CRITERION></PROPERTY></PROPERTY></PROPERTY></PROPERTY></PROOF>
