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<!DOCTYPE PROOF SYSTEM "http://a3pat.ensiie.fr/pub/a3pat.dtd">
<PROOF><SIGNATURE><SYMBOLLIST><SYMBOL arity="2" unmarked="f"><NAME>Marked_f</NAME></SYMBOL><SYMBOL arity="1" unmarked=""><NAME>s</NAME></SYMBOL><SYMBOL arity="2" unmarked=""><NAME>f</NAME></SYMBOL><SYMBOL arity="1" unmarked="d"><NAME>Marked_d</NAME></SYMBOL><SYMBOL arity="1" unmarked=""><NAME>nt</NAME></SYMBOL><SYMBOL arity="1" unmarked=""><NAME>a</NAME></SYMBOL><SYMBOL arity="1" unmarked=""><NAME>t</NAME></SYMBOL><SYMBOL arity="1" unmarked=""><NAME>d</NAME></SYMBOL><SYMBOL arity="1" unmarked="t"><NAME>Marked_t</NAME></SYMBOL><SYMBOL arity="1" unmarked=""><NAME>r</NAME></SYMBOL><SYMBOL arity="1" unmarked="a"><NAME>Marked_a</NAME></SYMBOL><SYMBOL arity="0" unmarked=""><NAME>0</NAME></SYMBOL><SYMBOL arity="0" unmarked=""><NAME>nil</NAME></SYMBOL><SYMBOL arity="2" unmarked="p"><NAME>Marked_p</NAME></SYMBOL><SYMBOL arity="1" unmarked=""><NAME>q</NAME></SYMBOL><SYMBOL arity="2" unmarked=""><NAME>nf</NAME></SYMBOL><SYMBOL arity="1" unmarked="q"><NAME>Marked_q</NAME></SYMBOL><SYMBOL arity="1" unmarked=""><NAME>ns</NAME></SYMBOL><SYMBOL arity="2" unmarked=""><NAME>p</NAME></SYMBOL><SYMBOL arity="1" unmarked="s"><NAME>Marked_s</NAME></SYMBOL><SYMBOL arity="2" unmarked=""><NAME>cs</NAME></SYMBOL></SYMBOLLIST><VARLIST><VAR>z</VAR><VAR>y</VAR><VAR>x</VAR><VAR>X2</VAR><VAR>X1</VAR><VAR>Z</VAR><VAR>Y</VAR><VAR>X</VAR><VAR>N</VAR></VARLIST></SIGNATURE><PROPERTY criterion="dp" prop="sntrs"><SYSTEM><REWSYS><RULE><LHS>t(N)</LHS><RHS>cs(r(q(N)),nt(ns(N)))</RHS></RULE><RULE><LHS>q(0)</LHS><RHS>0</RHS></RULE><RULE><LHS>q(s(X))</LHS><RHS>s(p(q(X),d(X)))</RHS></RULE><RULE><LHS>d(0)</LHS><RHS>0</RHS></RULE><RULE><LHS>d(s(X))</LHS><RHS>s(s(d(X)))</RHS></RULE><RULE><LHS>p(0,X)</LHS><RHS>X</RHS></RULE><RULE><LHS>p(X,0)</LHS><RHS>X</RHS></RULE><RULE><LHS>p(s(X),s(Y))</LHS><RHS>s(s(p(X,Y)))</RHS></RULE><RULE><LHS>f(0,X)</LHS><RHS>nil</RHS></RULE><RULE><LHS>f(s(X),cs(Y,Z))</LHS><RHS>cs(Y,nf(X,a(Z)))</RHS></RULE><RULE><LHS>t(X)</LHS><RHS>nt(X)</RHS></RULE><RULE><LHS>s(X)</LHS><RHS>ns(X)</RHS></RULE><RULE><LHS>f(X1,X2)</LHS><RHS>nf(X1,X2)</RHS></RULE><RULE><LHS>a(nt(X))</LHS><RHS>t(a(X))</RHS></RULE><RULE><LHS>a(ns(X))</LHS><RHS>s(a(X))</RHS></RULE><RULE><LHS>a(nf(X1,X2))</LHS><RHS>f(a(X1),a(X2))</RHS></RULE><RULE><LHS>a(X)</LHS><RHS>X</RHS></RULE></REWSYS></SYSTEM><CRITERION/><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>t(N)</LHS><RHS>cs(r(q(N)),nt(ns(N)))</RHS></RULE><RULE><LHS>q(0)</LHS><RHS>0</RHS></RULE><RULE><LHS>q(s(X))</LHS><RHS>s(p(q(X),d(X)))</RHS></RULE><RULE><LHS>d(0)</LHS><RHS>0</RHS></RULE><RULE><LHS>d(s(X))</LHS><RHS>s(s(d(X)))</RHS></RULE><RULE><LHS>p(0,X)</LHS><RHS>X</RHS></RULE><RULE><LHS>p(X,0)</LHS><RHS>X</RHS></RULE><RULE><LHS>p(s(X),s(Y))</LHS><RHS>s(s(p(X,Y)))</RHS></RULE><RULE><LHS>f(0,X)</LHS><RHS>nil</RHS></RULE><RULE><LHS>f(s(X),cs(Y,Z))</LHS><RHS>cs(Y,nf(X,a(Z)))</RHS></RULE><RULE><LHS>t(X)</LHS><RHS>nt(X)</RHS></RULE><RULE><LHS>s(X)</LHS><RHS>ns(X)</RHS></RULE><RULE><LHS>f(X1,X2)</LHS><RHS>nf(X1,X2)</RHS></RULE><RULE><LHS>a(nt(X))</LHS><RHS>t(a(X))</RHS></RULE><RULE><LHS>a(ns(X))</LHS><RHS>s(a(X))</RHS></RULE><RULE><LHS>a(nf(X1,X2))</LHS><RHS>f(a(X1),a(X2))</RHS></RULE><RULE><LHS>a(X)</LHS><RHS>X</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_t(N)</LHS><RHS>Marked_q(N)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_q(s(X))</LHS><RHS>Marked_s(p(q(X),d(X)))</RHS></DPRULE><DPRULE num="2"><LHS>Marked_q(s(X))</LHS><RHS>Marked_p(q(X),d(X))</RHS></DPRULE><DPRULE num="3"><LHS>Marked_q(s(X))</LHS><RHS>Marked_q(X)</RHS></DPRULE><DPRULE num="4"><LHS>Marked_q(s(X))</LHS><RHS>Marked_d(X)</RHS></DPRULE><DPRULE num="5"><LHS>Marked_d(s(X))</LHS><RHS>Marked_s(s(d(X)))</RHS></DPRULE><DPRULE num="6"><LHS>Marked_d(s(X))</LHS><RHS>Marked_s(d(X))</RHS></DPRULE><DPRULE num="7"><LHS>Marked_d(s(X))</LHS><RHS>Marked_d(X)</RHS></DPRULE><DPRULE num="8"><LHS>Marked_p(s(X),s(Y))</LHS><RHS>Marked_s(s(p(X,Y)))</RHS></DPRULE><DPRULE num="9"><LHS>Marked_p(s(X),s(Y))</LHS><RHS>Marked_s(p(X,Y))</RHS></DPRULE><DPRULE num="10"><LHS>Marked_p(s(X),s(Y))</LHS><RHS>Marked_p(X,Y)</RHS></DPRULE><DPRULE num="11"><LHS>Marked_f(s(X),cs(Y,Z))</LHS><RHS>Marked_a(Z)</RHS></DPRULE><DPRULE num="12"><LHS>Marked_a(nt(X))</LHS><RHS>Marked_t(a(X))</RHS></DPRULE><DPRULE num="13"><LHS>Marked_a(nt(X))</LHS><RHS>Marked_a(X)</RHS></DPRULE><DPRULE num="14"><LHS>Marked_a(ns(X))</LHS><RHS>Marked_s(a(X))</RHS></DPRULE><DPRULE num="15"><LHS>Marked_a(ns(X))</LHS><RHS>Marked_a(X)</RHS></DPRULE><DPRULE num="16"><LHS>Marked_a(nf(X1,X2))</LHS><RHS>Marked_f(a(X1),a(X2))</RHS></DPRULE><DPRULE num="17"><LHS>Marked_a(nf(X1,X2))</LHS><RHS>Marked_a(X1)</RHS></DPRULE><DPRULE num="18"><LHS>Marked_a(nf(X1,X2))</LHS><RHS>Marked_a(X2)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><DAG approx="simpl"><CCLIST><SCC num="0"><NODE ref="11"/><NODE ref="13"/><NODE ref="15"/><NODE ref="16"/><NODE ref="17"/><NODE ref="18"/></SCC><NONSCC num="1"><NODE ref="14"/></NONSCC><NONSCC num="2"><NODE ref="12"/></NONSCC><NONSCC num="3"><NODE ref="0"/></NONSCC><SCC num="4"><NODE ref="10"/></SCC><NONSCC num="5"><NODE ref="9"/></NONSCC><NONSCC num="6"><NODE ref="8"/></NONSCC><SCC num="7"><NODE ref="7"/></SCC><NONSCC num="8"><NODE ref="6"/></NONSCC><NONSCC num="9"><NODE ref="5"/></NONSCC><NONSCC num="10"><NODE ref="4"/></NONSCC><SCC num="11"><NODE ref="3"/></SCC><NONSCC num="12"><NODE ref="2"/></NONSCC><NONSCC num="13"><NODE ref="1"/></NONSCC></CCLIST><EDGE end="2" start="0"/><EDGE end="1" start="0"/><EDGE end="3" start="2"/><EDGE end="13" start="3"/><EDGE end="12" start="3"/><EDGE end="11" start="3"/><EDGE end="10" start="3"/><EDGE end="6" start="4"/><EDGE end="5" start="4"/><EDGE end="9" start="7"/><EDGE end="8" start="7"/><EDGE end="9" start="10"/><EDGE end="8" start="10"/><EDGE end="7" start="10"/><EDGE end="13" start="11"/><EDGE end="12" start="11"/><EDGE end="10" start="11"/><EDGE end="6" start="12"/><EDGE end="5" start="12"/><EDGE end="4" start="12"/></DAG></CRITERION><PROPERTY criterion="stronggraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>t(N)</LHS><RHS>cs(r(q(N)),nt(ns(N)))</RHS></RULE><RULE><LHS>q(0)</LHS><RHS>0</RHS></RULE><RULE><LHS>q(s(X))</LHS><RHS>s(p(q(X),d(X)))</RHS></RULE><RULE><LHS>d(0)</LHS><RHS>0</RHS></RULE><RULE><LHS>d(s(X))</LHS><RHS>s(s(d(X)))</RHS></RULE><RULE><LHS>p(0,X)</LHS><RHS>X</RHS></RULE><RULE><LHS>p(X,0)</LHS><RHS>X</RHS></RULE><RULE><LHS>p(s(X),s(Y))</LHS><RHS>s(s(p(X,Y)))</RHS></RULE><RULE><LHS>f(0,X)</LHS><RHS>nil</RHS></RULE><RULE><LHS>f(s(X),cs(Y,Z))</LHS><RHS>cs(Y,nf(X,a(Z)))</RHS></RULE><RULE><LHS>t(X)</LHS><RHS>nt(X)</RHS></RULE><RULE><LHS>s(X)</LHS><RHS>ns(X)</RHS></RULE><RULE><LHS>f(X1,X2)</LHS><RHS>nf(X1,X2)</RHS></RULE><RULE><LHS>a(nt(X))</LHS><RHS>t(a(X))</RHS></RULE><RULE><LHS>a(ns(X))</LHS><RHS>s(a(X))</RHS></RULE><RULE><LHS>a(nf(X1,X2))</LHS><RHS>f(a(X1),a(X2))</RHS></RULE><RULE><LHS>a(X)</LHS><RHS>X</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_f(s(X),cs(Y,Z))</LHS><RHS>Marked_a(Z)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_a(nt(X))</LHS><RHS>Marked_a(X)</RHS></DPRULE><DPRULE num="2"><LHS>Marked_a(ns(X))</LHS><RHS>Marked_a(X)</RHS></DPRULE><DPRULE num="3"><LHS>Marked_a(nf(X1,X2))</LHS><RHS>Marked_f(a(X1),a(X2))</RHS></DPRULE><DPRULE num="4"><LHS>Marked_a(nf(X1,X2))</LHS><RHS>Marked_a(X1)</RHS></DPRULE><DPRULE num="5"><LHS>Marked_a(nf(X1,X2))</LHS><RHS>Marked_a(X2)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><ORDERING type="poly"><POLYSYMB><SYMBOL><NAME>cs</NAME></SYMBOL><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></POLYSYMB><POLYSYMB><SYMBOL><NAME>p</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>ns</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>nf</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>q</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>nil</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>0</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>Marked_a</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>r</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>d</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>t</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>a</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>nt</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>f</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>s</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>Marked_f</NAME></SYMBOL><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></POLYSYMB></ORDERING><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_a(nt(X))</LHS><RHS>Marked_a(X)</RHS></DPRULE></DPLIST></STRICTPAIRS></CRITERION><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>t(N)</LHS><RHS>cs(r(q(N)),nt(ns(N)))</RHS></RULE><RULE><LHS>q(0)</LHS><RHS>0</RHS></RULE><RULE><LHS>q(s(X))</LHS><RHS>s(p(q(X),d(X)))</RHS></RULE><RULE><LHS>d(0)</LHS><RHS>0</RHS></RULE><RULE><LHS>d(s(X))</LHS><RHS>s(s(d(X)))</RHS></RULE><RULE><LHS>p(0,X)</LHS><RHS>X</RHS></RULE><RULE><LHS>p(X,0)</LHS><RHS>X</RHS></RULE><RULE><LHS>p(s(X),s(Y))</LHS><RHS>s(s(p(X,Y)))</RHS></RULE><RULE><LHS>f(0,X)</LHS><RHS>nil</RHS></RULE><RULE><LHS>f(s(X),cs(Y,Z))</LHS><RHS>cs(Y,nf(X,a(Z)))</RHS></RULE><RULE><LHS>t(X)</LHS><RHS>nt(X)</RHS></RULE><RULE><LHS>s(X)</LHS><RHS>ns(X)</RHS></RULE><RULE><LHS>f(X1,X2)</LHS><RHS>nf(X1,X2)</RHS></RULE><RULE><LHS>a(nt(X))</LHS><RHS>t(a(X))</RHS></RULE><RULE><LHS>a(ns(X))</LHS><RHS>s(a(X))</RHS></RULE><RULE><LHS>a(nf(X1,X2))</LHS><RHS>f(a(X1),a(X2))</RHS></RULE><RULE><LHS>a(X)</LHS><RHS>X</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_f(s(X),cs(Y,Z))</LHS><RHS>Marked_a(Z)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_a(ns(X))</LHS><RHS>Marked_a(X)</RHS></DPRULE><DPRULE num="2"><LHS>Marked_a(nf(X1,X2))</LHS><RHS>Marked_f(a(X1),a(X2))</RHS></DPRULE><DPRULE num="3"><LHS>Marked_a(nf(X1,X2))</LHS><RHS>Marked_a(X1)</RHS></DPRULE><DPRULE num="4"><LHS>Marked_a(nf(X1,X2))</LHS><RHS>Marked_a(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>t(N)</LHS><RHS>cs(r(q(N)),nt(ns(N)))</RHS></RULE><RULE><LHS>q(0)</LHS><RHS>0</RHS></RULE><RULE><LHS>q(s(X))</LHS><RHS>s(p(q(X),d(X)))</RHS></RULE><RULE><LHS>d(0)</LHS><RHS>0</RHS></RULE><RULE><LHS>d(s(X))</LHS><RHS>s(s(d(X)))</RHS></RULE><RULE><LHS>p(0,X)</LHS><RHS>X</RHS></RULE><RULE><LHS>p(X,0)</LHS><RHS>X</RHS></RULE><RULE><LHS>p(s(X),s(Y))</LHS><RHS>s(s(p(X,Y)))</RHS></RULE><RULE><LHS>f(0,X)</LHS><RHS>nil</RHS></RULE><RULE><LHS>f(s(X),cs(Y,Z))</LHS><RHS>cs(Y,nf(X,a(Z)))</RHS></RULE><RULE><LHS>t(X)</LHS><RHS>nt(X)</RHS></RULE><RULE><LHS>s(X)</LHS><RHS>ns(X)</RHS></RULE><RULE><LHS>f(X1,X2)</LHS><RHS>nf(X1,X2)</RHS></RULE><RULE><LHS>a(nt(X))</LHS><RHS>t(a(X))</RHS></RULE><RULE><LHS>a(ns(X))</LHS><RHS>s(a(X))</RHS></RULE><RULE><LHS>a(nf(X1,X2))</LHS><RHS>f(a(X1),a(X2))</RHS></RULE><RULE><LHS>a(X)</LHS><RHS>X</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_f(s(X),cs(Y,Z))</LHS><RHS>Marked_a(Z)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_a(ns(X))</LHS><RHS>Marked_a(X)</RHS></DPRULE><DPRULE num="2"><LHS>Marked_a(nf(X1,X2))</LHS><RHS>Marked_f(a(X1),a(X2))</RHS></DPRULE><DPRULE num="3"><LHS>Marked_a(nf(X1,X2))</LHS><RHS>Marked_a(X1)</RHS></DPRULE><DPRULE num="4"><LHS>Marked_a(nf(X1,X2))</LHS><RHS>Marked_a(X2)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><ORDERING type="poly"><POLYSYMB><SYMBOL><NAME>cs</NAME></SYMBOL><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></POLYSYMB><POLYSYMB><SYMBOL><NAME>p</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>ns</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>nf</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>q</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>nil</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>0</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>Marked_a</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>r</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>d</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>t</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>a</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>nt</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></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="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>s</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>Marked_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="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB></ORDERING><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_f(s(X),cs(Y,Z))</LHS><RHS>Marked_a(Z)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_a(nf(X1,X2))</LHS><RHS>Marked_f(a(X1),a(X2))</RHS></DPRULE><DPRULE num="2"><LHS>Marked_a(nf(X1,X2))</LHS><RHS>Marked_a(X1)</RHS></DPRULE><DPRULE num="3"><LHS>Marked_a(nf(X1,X2))</LHS><RHS>Marked_a(X2)</RHS></DPRULE></DPLIST></STRICTPAIRS></CRITERION><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>t(N)</LHS><RHS>cs(r(q(N)),nt(ns(N)))</RHS></RULE><RULE><LHS>q(0)</LHS><RHS>0</RHS></RULE><RULE><LHS>q(s(X))</LHS><RHS>s(p(q(X),d(X)))</RHS></RULE><RULE><LHS>d(0)</LHS><RHS>0</RHS></RULE><RULE><LHS>d(s(X))</LHS><RHS>s(s(d(X)))</RHS></RULE><RULE><LHS>p(0,X)</LHS><RHS>X</RHS></RULE><RULE><LHS>p(X,0)</LHS><RHS>X</RHS></RULE><RULE><LHS>p(s(X),s(Y))</LHS><RHS>s(s(p(X,Y)))</RHS></RULE><RULE><LHS>f(0,X)</LHS><RHS>nil</RHS></RULE><RULE><LHS>f(s(X),cs(Y,Z))</LHS><RHS>cs(Y,nf(X,a(Z)))</RHS></RULE><RULE><LHS>t(X)</LHS><RHS>nt(X)</RHS></RULE><RULE><LHS>s(X)</LHS><RHS>ns(X)</RHS></RULE><RULE><LHS>f(X1,X2)</LHS><RHS>nf(X1,X2)</RHS></RULE><RULE><LHS>a(nt(X))</LHS><RHS>t(a(X))</RHS></RULE><RULE><LHS>a(ns(X))</LHS><RHS>s(a(X))</RHS></RULE><RULE><LHS>a(nf(X1,X2))</LHS><RHS>f(a(X1),a(X2))</RHS></RULE><RULE><LHS>a(X)</LHS><RHS>X</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_a(ns(X))</LHS><RHS>Marked_a(X)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><DAG approx="simpl"><CCLIST><SCC num="0"><NODE ref="0"/></SCC></CCLIST></DAG></CRITERION><PROPERTY criterion="sterm" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>t(N)</LHS><RHS>cs(r(q(N)),nt(ns(N)))</RHS></RULE><RULE><LHS>q(0)</LHS><RHS>0</RHS></RULE><RULE><LHS>q(s(X))</LHS><RHS>s(p(q(X),d(X)))</RHS></RULE><RULE><LHS>d(0)</LHS><RHS>0</RHS></RULE><RULE><LHS>d(s(X))</LHS><RHS>s(s(d(X)))</RHS></RULE><RULE><LHS>p(0,X)</LHS><RHS>X</RHS></RULE><RULE><LHS>p(X,0)</LHS><RHS>X</RHS></RULE><RULE><LHS>p(s(X),s(Y))</LHS><RHS>s(s(p(X,Y)))</RHS></RULE><RULE><LHS>f(0,X)</LHS><RHS>nil</RHS></RULE><RULE><LHS>f(s(X),cs(Y,Z))</LHS><RHS>cs(Y,nf(X,a(Z)))</RHS></RULE><RULE><LHS>t(X)</LHS><RHS>nt(X)</RHS></RULE><RULE><LHS>s(X)</LHS><RHS>ns(X)</RHS></RULE><RULE><LHS>f(X1,X2)</LHS><RHS>nf(X1,X2)</RHS></RULE><RULE><LHS>a(nt(X))</LHS><RHS>t(a(X))</RHS></RULE><RULE><LHS>a(ns(X))</LHS><RHS>s(a(X))</RHS></RULE><RULE><LHS>a(nf(X1,X2))</LHS><RHS>f(a(X1),a(X2))</RHS></RULE><RULE><LHS>a(X)</LHS><RHS>X</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_a(ns(X))</LHS><RHS>Marked_a(X)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><PROJECTION><PROJ><SYMBOL><NAME>Marked_a</NAME></SYMBOL><INT>1</INT></PROJ></PROJECTION><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_a(ns(X))</LHS><RHS>Marked_a(X)</RHS></DPRULE></DPLIST></STRICTPAIRS><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>t(N)</LHS><RHS>cs(r(q(N)),nt(ns(N)))</RHS></RULE><RULE><LHS>q(0)</LHS><RHS>0</RHS></RULE><RULE><LHS>q(s(X))</LHS><RHS>s(p(q(X),d(X)))</RHS></RULE><RULE><LHS>d(0)</LHS><RHS>0</RHS></RULE><RULE><LHS>d(s(X))</LHS><RHS>s(s(d(X)))</RHS></RULE><RULE><LHS>p(0,X)</LHS><RHS>X</RHS></RULE><RULE><LHS>p(X,0)</LHS><RHS>X</RHS></RULE><RULE><LHS>p(s(X),s(Y))</LHS><RHS>s(s(p(X,Y)))</RHS></RULE><RULE><LHS>f(0,X)</LHS><RHS>nil</RHS></RULE><RULE><LHS>f(s(X),cs(Y,Z))</LHS><RHS>cs(Y,nf(X,a(Z)))</RHS></RULE><RULE><LHS>t(X)</LHS><RHS>nt(X)</RHS></RULE><RULE><LHS>s(X)</LHS><RHS>ns(X)</RHS></RULE><RULE><LHS>f(X1,X2)</LHS><RHS>nf(X1,X2)</RHS></RULE><RULE><LHS>a(nt(X))</LHS><RHS>t(a(X))</RHS></RULE><RULE><LHS>a(ns(X))</LHS><RHS>s(a(X))</RHS></RULE><RULE><LHS>a(nf(X1,X2))</LHS><RHS>f(a(X1),a(X2))</RHS></RULE><RULE><LHS>a(X)</LHS><RHS>X</RHS></RULE></REWSYS><DPLIST/></DPSYS></SYSTEM><CRITERION><DAG approx="simpl"><CCLIST/></DAG></CRITERION></PROPERTY></PROPERTY></PROPERTY></PROPERTY></PROPERTY></PROPERTY><PROPERTY criterion="sterm" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>t(N)</LHS><RHS>cs(r(q(N)),nt(ns(N)))</RHS></RULE><RULE><LHS>q(0)</LHS><RHS>0</RHS></RULE><RULE><LHS>q(s(X))</LHS><RHS>s(p(q(X),d(X)))</RHS></RULE><RULE><LHS>d(0)</LHS><RHS>0</RHS></RULE><RULE><LHS>d(s(X))</LHS><RHS>s(s(d(X)))</RHS></RULE><RULE><LHS>p(0,X)</LHS><RHS>X</RHS></RULE><RULE><LHS>p(X,0)</LHS><RHS>X</RHS></RULE><RULE><LHS>p(s(X),s(Y))</LHS><RHS>s(s(p(X,Y)))</RHS></RULE><RULE><LHS>f(0,X)</LHS><RHS>nil</RHS></RULE><RULE><LHS>f(s(X),cs(Y,Z))</LHS><RHS>cs(Y,nf(X,a(Z)))</RHS></RULE><RULE><LHS>t(X)</LHS><RHS>nt(X)</RHS></RULE><RULE><LHS>s(X)</LHS><RHS>ns(X)</RHS></RULE><RULE><LHS>f(X1,X2)</LHS><RHS>nf(X1,X2)</RHS></RULE><RULE><LHS>a(nt(X))</LHS><RHS>t(a(X))</RHS></RULE><RULE><LHS>a(ns(X))</LHS><RHS>s(a(X))</RHS></RULE><RULE><LHS>a(nf(X1,X2))</LHS><RHS>f(a(X1),a(X2))</RHS></RULE><RULE><LHS>a(X)</LHS><RHS>X</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_q(s(X))</LHS><RHS>Marked_q(X)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><PROJECTION><PROJ><SYMBOL><NAME>Marked_q</NAME></SYMBOL><INT>1</INT></PROJ></PROJECTION><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_q(s(X))</LHS><RHS>Marked_q(X)</RHS></DPRULE></DPLIST></STRICTPAIRS><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>t(N)</LHS><RHS>cs(r(q(N)),nt(ns(N)))</RHS></RULE><RULE><LHS>q(0)</LHS><RHS>0</RHS></RULE><RULE><LHS>q(s(X))</LHS><RHS>s(p(q(X),d(X)))</RHS></RULE><RULE><LHS>d(0)</LHS><RHS>0</RHS></RULE><RULE><LHS>d(s(X))</LHS><RHS>s(s(d(X)))</RHS></RULE><RULE><LHS>p(0,X)</LHS><RHS>X</RHS></RULE><RULE><LHS>p(X,0)</LHS><RHS>X</RHS></RULE><RULE><LHS>p(s(X),s(Y))</LHS><RHS>s(s(p(X,Y)))</RHS></RULE><RULE><LHS>f(0,X)</LHS><RHS>nil</RHS></RULE><RULE><LHS>f(s(X),cs(Y,Z))</LHS><RHS>cs(Y,nf(X,a(Z)))</RHS></RULE><RULE><LHS>t(X)</LHS><RHS>nt(X)</RHS></RULE><RULE><LHS>s(X)</LHS><RHS>ns(X)</RHS></RULE><RULE><LHS>f(X1,X2)</LHS><RHS>nf(X1,X2)</RHS></RULE><RULE><LHS>a(nt(X))</LHS><RHS>t(a(X))</RHS></RULE><RULE><LHS>a(ns(X))</LHS><RHS>s(a(X))</RHS></RULE><RULE><LHS>a(nf(X1,X2))</LHS><RHS>f(a(X1),a(X2))</RHS></RULE><RULE><LHS>a(X)</LHS><RHS>X</RHS></RULE></REWSYS><DPLIST/></DPSYS></SYSTEM><CRITERION><DAG approx="simpl"><CCLIST/></DAG></CRITERION></PROPERTY></PROPERTY><PROPERTY criterion="sterm" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>t(N)</LHS><RHS>cs(r(q(N)),nt(ns(N)))</RHS></RULE><RULE><LHS>q(0)</LHS><RHS>0</RHS></RULE><RULE><LHS>q(s(X))</LHS><RHS>s(p(q(X),d(X)))</RHS></RULE><RULE><LHS>d(0)</LHS><RHS>0</RHS></RULE><RULE><LHS>d(s(X))</LHS><RHS>s(s(d(X)))</RHS></RULE><RULE><LHS>p(0,X)</LHS><RHS>X</RHS></RULE><RULE><LHS>p(X,0)</LHS><RHS>X</RHS></RULE><RULE><LHS>p(s(X),s(Y))</LHS><RHS>s(s(p(X,Y)))</RHS></RULE><RULE><LHS>f(0,X)</LHS><RHS>nil</RHS></RULE><RULE><LHS>f(s(X),cs(Y,Z))</LHS><RHS>cs(Y,nf(X,a(Z)))</RHS></RULE><RULE><LHS>t(X)</LHS><RHS>nt(X)</RHS></RULE><RULE><LHS>s(X)</LHS><RHS>ns(X)</RHS></RULE><RULE><LHS>f(X1,X2)</LHS><RHS>nf(X1,X2)</RHS></RULE><RULE><LHS>a(nt(X))</LHS><RHS>t(a(X))</RHS></RULE><RULE><LHS>a(ns(X))</LHS><RHS>s(a(X))</RHS></RULE><RULE><LHS>a(nf(X1,X2))</LHS><RHS>f(a(X1),a(X2))</RHS></RULE><RULE><LHS>a(X)</LHS><RHS>X</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_p(s(X),s(Y))</LHS><RHS>Marked_p(X,Y)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><PROJECTION><PROJ><SYMBOL><NAME>Marked_p</NAME></SYMBOL><INT>1</INT></PROJ></PROJECTION><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_p(s(X),s(Y))</LHS><RHS>Marked_p(X,Y)</RHS></DPRULE></DPLIST></STRICTPAIRS><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>t(N)</LHS><RHS>cs(r(q(N)),nt(ns(N)))</RHS></RULE><RULE><LHS>q(0)</LHS><RHS>0</RHS></RULE><RULE><LHS>q(s(X))</LHS><RHS>s(p(q(X),d(X)))</RHS></RULE><RULE><LHS>d(0)</LHS><RHS>0</RHS></RULE><RULE><LHS>d(s(X))</LHS><RHS>s(s(d(X)))</RHS></RULE><RULE><LHS>p(0,X)</LHS><RHS>X</RHS></RULE><RULE><LHS>p(X,0)</LHS><RHS>X</RHS></RULE><RULE><LHS>p(s(X),s(Y))</LHS><RHS>s(s(p(X,Y)))</RHS></RULE><RULE><LHS>f(0,X)</LHS><RHS>nil</RHS></RULE><RULE><LHS>f(s(X),cs(Y,Z))</LHS><RHS>cs(Y,nf(X,a(Z)))</RHS></RULE><RULE><LHS>t(X)</LHS><RHS>nt(X)</RHS></RULE><RULE><LHS>s(X)</LHS><RHS>ns(X)</RHS></RULE><RULE><LHS>f(X1,X2)</LHS><RHS>nf(X1,X2)</RHS></RULE><RULE><LHS>a(nt(X))</LHS><RHS>t(a(X))</RHS></RULE><RULE><LHS>a(ns(X))</LHS><RHS>s(a(X))</RHS></RULE><RULE><LHS>a(nf(X1,X2))</LHS><RHS>f(a(X1),a(X2))</RHS></RULE><RULE><LHS>a(X)</LHS><RHS>X</RHS></RULE></REWSYS><DPLIST/></DPSYS></SYSTEM><CRITERION><DAG approx="simpl"><CCLIST/></DAG></CRITERION></PROPERTY></PROPERTY><PROPERTY criterion="sterm" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>t(N)</LHS><RHS>cs(r(q(N)),nt(ns(N)))</RHS></RULE><RULE><LHS>q(0)</LHS><RHS>0</RHS></RULE><RULE><LHS>q(s(X))</LHS><RHS>s(p(q(X),d(X)))</RHS></RULE><RULE><LHS>d(0)</LHS><RHS>0</RHS></RULE><RULE><LHS>d(s(X))</LHS><RHS>s(s(d(X)))</RHS></RULE><RULE><LHS>p(0,X)</LHS><RHS>X</RHS></RULE><RULE><LHS>p(X,0)</LHS><RHS>X</RHS></RULE><RULE><LHS>p(s(X),s(Y))</LHS><RHS>s(s(p(X,Y)))</RHS></RULE><RULE><LHS>f(0,X)</LHS><RHS>nil</RHS></RULE><RULE><LHS>f(s(X),cs(Y,Z))</LHS><RHS>cs(Y,nf(X,a(Z)))</RHS></RULE><RULE><LHS>t(X)</LHS><RHS>nt(X)</RHS></RULE><RULE><LHS>s(X)</LHS><RHS>ns(X)</RHS></RULE><RULE><LHS>f(X1,X2)</LHS><RHS>nf(X1,X2)</RHS></RULE><RULE><LHS>a(nt(X))</LHS><RHS>t(a(X))</RHS></RULE><RULE><LHS>a(ns(X))</LHS><RHS>s(a(X))</RHS></RULE><RULE><LHS>a(nf(X1,X2))</LHS><RHS>f(a(X1),a(X2))</RHS></RULE><RULE><LHS>a(X)</LHS><RHS>X</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_d(s(X))</LHS><RHS>Marked_d(X)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><PROJECTION><PROJ><SYMBOL><NAME>Marked_d</NAME></SYMBOL><INT>1</INT></PROJ></PROJECTION><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_d(s(X))</LHS><RHS>Marked_d(X)</RHS></DPRULE></DPLIST></STRICTPAIRS><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>t(N)</LHS><RHS>cs(r(q(N)),nt(ns(N)))</RHS></RULE><RULE><LHS>q(0)</LHS><RHS>0</RHS></RULE><RULE><LHS>q(s(X))</LHS><RHS>s(p(q(X),d(X)))</RHS></RULE><RULE><LHS>d(0)</LHS><RHS>0</RHS></RULE><RULE><LHS>d(s(X))</LHS><RHS>s(s(d(X)))</RHS></RULE><RULE><LHS>p(0,X)</LHS><RHS>X</RHS></RULE><RULE><LHS>p(X,0)</LHS><RHS>X</RHS></RULE><RULE><LHS>p(s(X),s(Y))</LHS><RHS>s(s(p(X,Y)))</RHS></RULE><RULE><LHS>f(0,X)</LHS><RHS>nil</RHS></RULE><RULE><LHS>f(s(X),cs(Y,Z))</LHS><RHS>cs(Y,nf(X,a(Z)))</RHS></RULE><RULE><LHS>t(X)</LHS><RHS>nt(X)</RHS></RULE><RULE><LHS>s(X)</LHS><RHS>ns(X)</RHS></RULE><RULE><LHS>f(X1,X2)</LHS><RHS>nf(X1,X2)</RHS></RULE><RULE><LHS>a(nt(X))</LHS><RHS>t(a(X))</RHS></RULE><RULE><LHS>a(ns(X))</LHS><RHS>s(a(X))</RHS></RULE><RULE><LHS>a(nf(X1,X2))</LHS><RHS>f(a(X1),a(X2))</RHS></RULE><RULE><LHS>a(X)</LHS><RHS>X</RHS></RULE></REWSYS><DPLIST/></DPSYS></SYSTEM><CRITERION><DAG approx="simpl"><CCLIST/></DAG></CRITERION></PROPERTY></PROPERTY></PROPERTY></PROPERTY></PROOF>
