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<!DOCTYPE PROOF SYSTEM "http://a3pat.ensiie.fr/pub/a3pat.dtd">
<PROOF><SIGNATURE><SYMBOLLIST><SYMBOL arity="2" unmarked=""><NAME>-</NAME></SYMBOL><SYMBOL arity="0" unmarked=""><NAME>2</NAME></SYMBOL><SYMBOL arity="0" unmarked=""><NAME>0</NAME></SYMBOL><SYMBOL arity="1" unmarked="D"><NAME>Marked_D</NAME></SYMBOL><SYMBOL arity="2" unmarked=""><NAME>+</NAME></SYMBOL><SYMBOL arity="2" unmarked=""><NAME>div</NAME></SYMBOL><SYMBOL arity="1" unmarked=""><NAME>D</NAME></SYMBOL><SYMBOL arity="2" unmarked=""><NAME> *</NAME></SYMBOL><SYMBOL arity="2" unmarked=""><NAME>pow</NAME></SYMBOL><SYMBOL arity="0" unmarked=""><NAME>t</NAME></SYMBOL><SYMBOL arity="1" unmarked=""><NAME>ln</NAME></SYMBOL><SYMBOL arity="0" unmarked=""><NAME>constant</NAME></SYMBOL><SYMBOL arity="1" unmarked=""><NAME>minus</NAME></SYMBOL><SYMBOL arity="0" unmarked=""><NAME>1</NAME></SYMBOL></SYMBOLLIST><VARLIST><VAR>y</VAR><VAR>x</VAR></VARLIST></SIGNATURE><PROPERTY criterion="dp" prop="sntrs"><SYSTEM><REWSYS><RULE><LHS>D(t)</LHS><RHS>1</RHS></RULE><RULE><LHS>D(constant)</LHS><RHS>0</RHS></RULE><RULE><LHS>D(+(x,y))</LHS><RHS>+(D(x),D(y))</RHS></RULE><RULE><LHS>D( *(x,y))</LHS><RHS>+( *(y,D(x)), *(x,D(y)))</RHS></RULE><RULE><LHS>D(-(x,y))</LHS><RHS>-(D(x),D(y))</RHS></RULE><RULE><LHS>D(minus(x))</LHS><RHS>minus(D(x))</RHS></RULE><RULE><LHS>D(div(x,y))</LHS><RHS>-(div(D(x),y),div( *(x,D(y)),pow(y,2)))</RHS></RULE><RULE><LHS>D(ln(x))</LHS><RHS>div(D(x),x)</RHS></RULE><RULE><LHS>D(pow(x,y))</LHS><RHS>+( *( *(y,pow(x,-(y,1))),D(x)), *( *(pow(x,y),ln(x)),D(y)))</RHS></RULE></REWSYS></SYSTEM><CRITERION/><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>D(t)</LHS><RHS>1</RHS></RULE><RULE><LHS>D(constant)</LHS><RHS>0</RHS></RULE><RULE><LHS>D(+(x,y))</LHS><RHS>+(D(x),D(y))</RHS></RULE><RULE><LHS>D( *(x,y))</LHS><RHS>+( *(y,D(x)), *(x,D(y)))</RHS></RULE><RULE><LHS>D(-(x,y))</LHS><RHS>-(D(x),D(y))</RHS></RULE><RULE><LHS>D(minus(x))</LHS><RHS>minus(D(x))</RHS></RULE><RULE><LHS>D(div(x,y))</LHS><RHS>-(div(D(x),y),div( *(x,D(y)),pow(y,2)))</RHS></RULE><RULE><LHS>D(ln(x))</LHS><RHS>div(D(x),x)</RHS></RULE><RULE><LHS>D(pow(x,y))</LHS><RHS>+( *( *(y,pow(x,-(y,1))),D(x)), *( *(pow(x,y),ln(x)),D(y)))</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_D(+(x,y))</LHS><RHS>Marked_D(x)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_D(+(x,y))</LHS><RHS>Marked_D(y)</RHS></DPRULE><DPRULE num="2"><LHS>Marked_D( *(x,y))</LHS><RHS>Marked_D(x)</RHS></DPRULE><DPRULE num="3"><LHS>Marked_D( *(x,y))</LHS><RHS>Marked_D(y)</RHS></DPRULE><DPRULE num="4"><LHS>Marked_D(-(x,y))</LHS><RHS>Marked_D(x)</RHS></DPRULE><DPRULE num="5"><LHS>Marked_D(-(x,y))</LHS><RHS>Marked_D(y)</RHS></DPRULE><DPRULE num="6"><LHS>Marked_D(minus(x))</LHS><RHS>Marked_D(x)</RHS></DPRULE><DPRULE num="7"><LHS>Marked_D(div(x,y))</LHS><RHS>Marked_D(x)</RHS></DPRULE><DPRULE num="8"><LHS>Marked_D(div(x,y))</LHS><RHS>Marked_D(y)</RHS></DPRULE><DPRULE num="9"><LHS>Marked_D(ln(x))</LHS><RHS>Marked_D(x)</RHS></DPRULE><DPRULE num="10"><LHS>Marked_D(pow(x,y))</LHS><RHS>Marked_D(x)</RHS></DPRULE><DPRULE num="11"><LHS>Marked_D(pow(x,y))</LHS><RHS>Marked_D(y)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><DAG approx="simpl"><CCLIST><SCC num="0"><NODE ref="0"/><NODE ref="1"/><NODE ref="2"/><NODE ref="3"/><NODE ref="4"/><NODE ref="5"/><NODE ref="6"/><NODE ref="7"/><NODE ref="8"/><NODE ref="9"/><NODE ref="10"/><NODE ref="11"/></SCC></CCLIST></DAG></CRITERION><PROPERTY criterion="sterm" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>D(t)</LHS><RHS>1</RHS></RULE><RULE><LHS>D(constant)</LHS><RHS>0</RHS></RULE><RULE><LHS>D(+(x,y))</LHS><RHS>+(D(x),D(y))</RHS></RULE><RULE><LHS>D( *(x,y))</LHS><RHS>+( *(y,D(x)), *(x,D(y)))</RHS></RULE><RULE><LHS>D(-(x,y))</LHS><RHS>-(D(x),D(y))</RHS></RULE><RULE><LHS>D(minus(x))</LHS><RHS>minus(D(x))</RHS></RULE><RULE><LHS>D(div(x,y))</LHS><RHS>-(div(D(x),y),div( *(x,D(y)),pow(y,2)))</RHS></RULE><RULE><LHS>D(ln(x))</LHS><RHS>div(D(x),x)</RHS></RULE><RULE><LHS>D(pow(x,y))</LHS><RHS>+( *( *(y,pow(x,-(y,1))),D(x)), *( *(pow(x,y),ln(x)),D(y)))</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_D(+(x,y))</LHS><RHS>Marked_D(x)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_D(+(x,y))</LHS><RHS>Marked_D(y)</RHS></DPRULE><DPRULE num="2"><LHS>Marked_D( *(x,y))</LHS><RHS>Marked_D(x)</RHS></DPRULE><DPRULE num="3"><LHS>Marked_D( *(x,y))</LHS><RHS>Marked_D(y)</RHS></DPRULE><DPRULE num="4"><LHS>Marked_D(-(x,y))</LHS><RHS>Marked_D(x)</RHS></DPRULE><DPRULE num="5"><LHS>Marked_D(-(x,y))</LHS><RHS>Marked_D(y)</RHS></DPRULE><DPRULE num="6"><LHS>Marked_D(minus(x))</LHS><RHS>Marked_D(x)</RHS></DPRULE><DPRULE num="7"><LHS>Marked_D(div(x,y))</LHS><RHS>Marked_D(x)</RHS></DPRULE><DPRULE num="8"><LHS>Marked_D(div(x,y))</LHS><RHS>Marked_D(y)</RHS></DPRULE><DPRULE num="9"><LHS>Marked_D(ln(x))</LHS><RHS>Marked_D(x)</RHS></DPRULE><DPRULE num="10"><LHS>Marked_D(pow(x,y))</LHS><RHS>Marked_D(x)</RHS></DPRULE><DPRULE num="11"><LHS>Marked_D(pow(x,y))</LHS><RHS>Marked_D(y)</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(pow(x,y))</LHS><RHS>Marked_D(y)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_D(pow(x,y))</LHS><RHS>Marked_D(x)</RHS></DPRULE><DPRULE num="2"><LHS>Marked_D(ln(x))</LHS><RHS>Marked_D(x)</RHS></DPRULE><DPRULE num="3"><LHS>Marked_D(div(x,y))</LHS><RHS>Marked_D(y)</RHS></DPRULE><DPRULE num="4"><LHS>Marked_D(div(x,y))</LHS><RHS>Marked_D(x)</RHS></DPRULE><DPRULE num="5"><LHS>Marked_D(minus(x))</LHS><RHS>Marked_D(x)</RHS></DPRULE><DPRULE num="6"><LHS>Marked_D(-(x,y))</LHS><RHS>Marked_D(y)</RHS></DPRULE><DPRULE num="7"><LHS>Marked_D(-(x,y))</LHS><RHS>Marked_D(x)</RHS></DPRULE><DPRULE num="8"><LHS>Marked_D( *(x,y))</LHS><RHS>Marked_D(y)</RHS></DPRULE><DPRULE num="9"><LHS>Marked_D( *(x,y))</LHS><RHS>Marked_D(x)</RHS></DPRULE><DPRULE num="10"><LHS>Marked_D(+(x,y))</LHS><RHS>Marked_D(y)</RHS></DPRULE><DPRULE num="11"><LHS>Marked_D(+(x,y))</LHS><RHS>Marked_D(x)</RHS></DPRULE></DPLIST></STRICTPAIRS><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>D(t)</LHS><RHS>1</RHS></RULE><RULE><LHS>D(constant)</LHS><RHS>0</RHS></RULE><RULE><LHS>D(+(x,y))</LHS><RHS>+(D(x),D(y))</RHS></RULE><RULE><LHS>D( *(x,y))</LHS><RHS>+( *(y,D(x)), *(x,D(y)))</RHS></RULE><RULE><LHS>D(-(x,y))</LHS><RHS>-(D(x),D(y))</RHS></RULE><RULE><LHS>D(minus(x))</LHS><RHS>minus(D(x))</RHS></RULE><RULE><LHS>D(div(x,y))</LHS><RHS>-(div(D(x),y),div( *(x,D(y)),pow(y,2)))</RHS></RULE><RULE><LHS>D(ln(x))</LHS><RHS>div(D(x),x)</RHS></RULE><RULE><LHS>D(pow(x,y))</LHS><RHS>+( *( *(y,pow(x,-(y,1))),D(x)), *( *(pow(x,y),ln(x)),D(y)))</RHS></RULE></REWSYS><DPLIST/></DPSYS></SYSTEM><CRITERION><DAG approx="simpl"><CCLIST/></DAG></CRITERION></PROPERTY></PROPERTY></PROPERTY></PROPERTY></PROOF>
