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<!DOCTYPE PROOF SYSTEM "http://a3pat.ensiie.fr/pub/a3pat.dtd">
<PROOF><SIGNATURE><SYMBOLLIST><SYMBOL arity="1" unmarked="i"><NAME>Marked_i</NAME></SYMBOL><SYMBOL arity="0" unmarked=""><NAME>1</NAME></SYMBOL><SYMBOL arity="1" unmarked=""><NAME>i</NAME></SYMBOL><SYMBOL arity="2" unmarked="."><NAME>Marked_.</NAME></SYMBOL><SYMBOL arity="2" unmarked=""><NAME>.</NAME></SYMBOL></SYMBOLLIST><VARLIST><VAR>z</VAR><VAR>y</VAR><VAR>x</VAR></VARLIST></SIGNATURE><PROPERTY criterion="dp" prop="sntrs"><SYSTEM><REWSYS><RULE><LHS>.(1,x)</LHS><RHS>x</RHS></RULE><RULE><LHS>.(x,1)</LHS><RHS>x</RHS></RULE><RULE><LHS>.(i(x),x)</LHS><RHS>1</RHS></RULE><RULE><LHS>.(x,i(x))</LHS><RHS>1</RHS></RULE><RULE><LHS>i(1)</LHS><RHS>1</RHS></RULE><RULE><LHS>i(i(x))</LHS><RHS>x</RHS></RULE><RULE><LHS>.(i(y),.(y,z))</LHS><RHS>z</RHS></RULE><RULE><LHS>.(y,.(i(y),z))</LHS><RHS>z</RHS></RULE><RULE><LHS>.(.(x,y),z)</LHS><RHS>.(x,.(y,z))</RHS></RULE><RULE><LHS>i(.(x,y))</LHS><RHS>.(i(y),i(x))</RHS></RULE></REWSYS></SYSTEM><CRITERION/><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>.(1,x)</LHS><RHS>x</RHS></RULE><RULE><LHS>.(x,1)</LHS><RHS>x</RHS></RULE><RULE><LHS>.(i(x),x)</LHS><RHS>1</RHS></RULE><RULE><LHS>.(x,i(x))</LHS><RHS>1</RHS></RULE><RULE><LHS>i(1)</LHS><RHS>1</RHS></RULE><RULE><LHS>i(i(x))</LHS><RHS>x</RHS></RULE><RULE><LHS>.(i(y),.(y,z))</LHS><RHS>z</RHS></RULE><RULE><LHS>.(y,.(i(y),z))</LHS><RHS>z</RHS></RULE><RULE><LHS>.(.(x,y),z)</LHS><RHS>.(x,.(y,z))</RHS></RULE><RULE><LHS>i(.(x,y))</LHS><RHS>.(i(y),i(x))</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_.(.(x,y),z)</LHS><RHS>Marked_.(x,.(y,z))</RHS></DPRULE><DPRULE num="1"><LHS>Marked_.(.(x,y),z)</LHS><RHS>Marked_.(y,z)</RHS></DPRULE><DPRULE num="2"><LHS>Marked_i(.(x,y))</LHS><RHS>Marked_.(i(y),i(x))</RHS></DPRULE><DPRULE num="3"><LHS>Marked_i(.(x,y))</LHS><RHS>Marked_i(y)</RHS></DPRULE><DPRULE num="4"><LHS>Marked_i(.(x,y))</LHS><RHS>Marked_i(x)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><DAG approx="simpl"><CCLIST><SCC num="0"><NODE ref="3"/><NODE ref="4"/></SCC><NONSCC num="1"><NODE ref="2"/></NONSCC><SCC num="2"><NODE ref="0"/><NODE ref="1"/></SCC></CCLIST><EDGE end="1" start="0"/><EDGE end="2" start="1"/></DAG></CRITERION><PROPERTY criterion="sterm" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>.(1,x)</LHS><RHS>x</RHS></RULE><RULE><LHS>.(x,1)</LHS><RHS>x</RHS></RULE><RULE><LHS>.(i(x),x)</LHS><RHS>1</RHS></RULE><RULE><LHS>.(x,i(x))</LHS><RHS>1</RHS></RULE><RULE><LHS>i(1)</LHS><RHS>1</RHS></RULE><RULE><LHS>i(i(x))</LHS><RHS>x</RHS></RULE><RULE><LHS>.(i(y),.(y,z))</LHS><RHS>z</RHS></RULE><RULE><LHS>.(y,.(i(y),z))</LHS><RHS>z</RHS></RULE><RULE><LHS>.(.(x,y),z)</LHS><RHS>.(x,.(y,z))</RHS></RULE><RULE><LHS>i(.(x,y))</LHS><RHS>.(i(y),i(x))</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_i(.(x,y))</LHS><RHS>Marked_i(y)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_i(.(x,y))</LHS><RHS>Marked_i(x)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><PROJECTION><PROJ><SYMBOL><NAME>Marked_i</NAME></SYMBOL><INT>1</INT></PROJ></PROJECTION><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_i(.(x,y))</LHS><RHS>Marked_i(x)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_i(.(x,y))</LHS><RHS>Marked_i(y)</RHS></DPRULE></DPLIST></STRICTPAIRS><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>.(1,x)</LHS><RHS>x</RHS></RULE><RULE><LHS>.(x,1)</LHS><RHS>x</RHS></RULE><RULE><LHS>.(i(x),x)</LHS><RHS>1</RHS></RULE><RULE><LHS>.(x,i(x))</LHS><RHS>1</RHS></RULE><RULE><LHS>i(1)</LHS><RHS>1</RHS></RULE><RULE><LHS>i(i(x))</LHS><RHS>x</RHS></RULE><RULE><LHS>.(i(y),.(y,z))</LHS><RHS>z</RHS></RULE><RULE><LHS>.(y,.(i(y),z))</LHS><RHS>z</RHS></RULE><RULE><LHS>.(.(x,y),z)</LHS><RHS>.(x,.(y,z))</RHS></RULE><RULE><LHS>i(.(x,y))</LHS><RHS>.(i(y),i(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>.(1,x)</LHS><RHS>x</RHS></RULE><RULE><LHS>.(x,1)</LHS><RHS>x</RHS></RULE><RULE><LHS>.(i(x),x)</LHS><RHS>1</RHS></RULE><RULE><LHS>.(x,i(x))</LHS><RHS>1</RHS></RULE><RULE><LHS>i(1)</LHS><RHS>1</RHS></RULE><RULE><LHS>i(i(x))</LHS><RHS>x</RHS></RULE><RULE><LHS>.(i(y),.(y,z))</LHS><RHS>z</RHS></RULE><RULE><LHS>.(y,.(i(y),z))</LHS><RHS>z</RHS></RULE><RULE><LHS>.(.(x,y),z)</LHS><RHS>.(x,.(y,z))</RHS></RULE><RULE><LHS>i(.(x,y))</LHS><RHS>.(i(y),i(x))</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_.(.(x,y),z)</LHS><RHS>Marked_.(x,.(y,z))</RHS></DPRULE><DPRULE num="1"><LHS>Marked_.(.(x,y),z)</LHS><RHS>Marked_.(y,z)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><PROJECTION><PROJ><SYMBOL><NAME>Marked_.</NAME></SYMBOL><INT>1</INT></PROJ></PROJECTION><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_.(.(x,y),z)</LHS><RHS>Marked_.(y,z)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_.(.(x,y),z)</LHS><RHS>Marked_.(x,.(y,z))</RHS></DPRULE></DPLIST></STRICTPAIRS><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>.(1,x)</LHS><RHS>x</RHS></RULE><RULE><LHS>.(x,1)</LHS><RHS>x</RHS></RULE><RULE><LHS>.(i(x),x)</LHS><RHS>1</RHS></RULE><RULE><LHS>.(x,i(x))</LHS><RHS>1</RHS></RULE><RULE><LHS>i(1)</LHS><RHS>1</RHS></RULE><RULE><LHS>i(i(x))</LHS><RHS>x</RHS></RULE><RULE><LHS>.(i(y),.(y,z))</LHS><RHS>z</RHS></RULE><RULE><LHS>.(y,.(i(y),z))</LHS><RHS>z</RHS></RULE><RULE><LHS>.(.(x,y),z)</LHS><RHS>.(x,.(y,z))</RHS></RULE><RULE><LHS>i(.(x,y))</LHS><RHS>.(i(y),i(x))</RHS></RULE></REWSYS><DPLIST/></DPSYS></SYSTEM><CRITERION><DAG approx="simpl"><CCLIST/></DAG></CRITERION></PROPERTY></PROPERTY></PROPERTY></PROPERTY></PROOF>
