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<PROOF><SIGNATURE><SYMBOLLIST><SYMBOL arity="1" unmarked=""><NAME>tautology'i'in</NAME></SYMBOL><SYMBOL arity="1" unmarked="u'6'2"><NAME>Marked_u'6'2</NAME></SYMBOL><SYMBOL arity="1" unmarked=""><NAME>u'5'1</NAME></SYMBOL><SYMBOL arity="1" unmarked=""><NAME>u'11'1</NAME></SYMBOL><SYMBOL arity="1" unmarked="u'13'1"><NAME>Marked_u'13'1</NAME></SYMBOL><SYMBOL arity="2" unmarked=""><NAME>sequent</NAME></SYMBOL><SYMBOL arity="1" unmarked=""><NAME>u'14'1</NAME></SYMBOL><SYMBOL arity="1" unmarked="u'10'1"><NAME>Marked_u'10'1</NAME></SYMBOL><SYMBOL arity="0" unmarked=""><NAME>reduce'ii'out</NAME></SYMBOL><SYMBOL arity="1" unmarked="u'3'1"><NAME>Marked_u'3'1</NAME></SYMBOL><SYMBOL arity="1" unmarked=""><NAME>u'8'1</NAME></SYMBOL><SYMBOL arity="2" unmarked="reduce'ii'in"><NAME>Marked_reduce'ii'in</NAME></SYMBOL><SYMBOL arity="1" unmarked=""><NAME>u'1'1</NAME></SYMBOL><SYMBOL arity="1" unmarked=""><NAME>u'15'1</NAME></SYMBOL><SYMBOL arity="1" unmarked="u'8'1"><NAME>Marked_u'8'1</NAME></SYMBOL><SYMBOL arity="2" unmarked=""><NAME>x'2a</NAME></SYMBOL><SYMBOL arity="1" unmarked="u'1'1"><NAME>Marked_u'1'1</NAME></SYMBOL><SYMBOL arity="1" unmarked=""><NAME>u'10'1</NAME></SYMBOL><SYMBOL arity="2" unmarked="intersect'ii'in"><NAME>Marked_intersect'ii'in</NAME></SYMBOL><SYMBOL arity="1" unmarked=""><NAME>u'3'1</NAME></SYMBOL><SYMBOL arity="1" unmarked=""><NAME>u'12'2</NAME></SYMBOL><SYMBOL arity="5" unmarked="u'12'1"><NAME>Marked_u'12'1</NAME></SYMBOL><SYMBOL arity="1" unmarked=""><NAME>x'2d</NAME></SYMBOL><SYMBOL arity="1" unmarked="u'5'1"><NAME>Marked_u'5'1</NAME></SYMBOL><SYMBOL arity="1" unmarked=""><NAME>u'6'2</NAME></SYMBOL><SYMBOL arity="1" unmarked="u'16'1"><NAME>Marked_u'16'1</NAME></SYMBOL><SYMBOL arity="2" unmarked=""><NAME>intersect'ii'in</NAME></SYMBOL><SYMBOL arity="1" unmarked=""><NAME>u'16'1</NAME></SYMBOL><SYMBOL arity="1" unmarked="u'7'1"><NAME>Marked_u'7'1</NAME></SYMBOL><SYMBOL arity="2" unmarked=""><NAME>iff</NAME></SYMBOL><SYMBOL arity="1" unmarked=""><NAME>p</NAME></SYMBOL><SYMBOL arity="1" unmarked="u'14'1"><NAME>Marked_u'14'1</NAME></SYMBOL><SYMBOL arity="2" unmarked=""><NAME>reduce'ii'in</NAME></SYMBOL><SYMBOL arity="1" unmarked=""><NAME>u'13'1</NAME></SYMBOL><SYMBOL arity="1" unmarked="u'11'1"><NAME>Marked_u'11'1</NAME></SYMBOL><SYMBOL arity="2" unmarked=""><NAME>if</NAME></SYMBOL><SYMBOL arity="1" unmarked="u'4'1"><NAME>Marked_u'4'1</NAME></SYMBOL><SYMBOL arity="1" unmarked=""><NAME>u'7'1</NAME></SYMBOL><SYMBOL arity="1" unmarked="tautology'i'in"><NAME>Marked_tautology'i'in</NAME></SYMBOL><SYMBOL arity="2" unmarked=""><NAME>cons</NAME></SYMBOL><SYMBOL arity="0" unmarked=""><NAME>nil</NAME></SYMBOL><SYMBOL arity="1" unmarked="u'9'1"><NAME>Marked_u'9'1</NAME></SYMBOL><SYMBOL arity="1" unmarked=""><NAME>u'4'1</NAME></SYMBOL><SYMBOL arity="1" unmarked="u'2'1"><NAME>Marked_u'2'1</NAME></SYMBOL><SYMBOL arity="1" unmarked=""><NAME>u'9'1</NAME></SYMBOL><SYMBOL arity="1" unmarked="u'15'1"><NAME>Marked_u'15'1</NAME></SYMBOL><SYMBOL arity="1" unmarked=""><NAME>u'2'1</NAME></SYMBOL><SYMBOL arity="5" unmarked=""><NAME>u'12'1</NAME></SYMBOL><SYMBOL arity="1" unmarked="u'12'2"><NAME>Marked_u'12'2</NAME></SYMBOL><SYMBOL arity="2" unmarked=""><NAME>x'2b</NAME></SYMBOL><SYMBOL arity="5" unmarked="u'6'1"><NAME>Marked_u'6'1</NAME></SYMBOL><SYMBOL arity="5" unmarked=""><NAME>u'6'1</NAME></SYMBOL><SYMBOL arity="0" unmarked=""><NAME>tautology'i'out</NAME></SYMBOL><SYMBOL arity="0" unmarked=""><NAME>intersect'ii'out</NAME></SYMBOL></SYMBOLLIST><VARLIST><VAR>Ys</VAR><VAR>Xs</VAR><VAR>X1</VAR><VAR>X0</VAR><VAR>X</VAR><VAR>V</VAR><VAR>Right</VAR><VAR>NF</VAR><VAR>Left</VAR><VAR>Gs</VAR><VAR>G2</VAR><VAR>G1</VAR><VAR>Fs</VAR><VAR>F2</VAR><VAR>F1</VAR><VAR>F</VAR><VAR>B</VAR><VAR>A</VAR></VARLIST></SIGNATURE><PROPERTY criterion="dp" prop="sntrs"><SYSTEM><REWSYS><RULE><LHS>intersect'ii'in(cons(X,X0),cons(X,X1))</LHS><RHS>intersect'ii'out</RHS></RULE><RULE><LHS>intersect'ii'in(Xs,cons(X0,Ys))</LHS><RHS>u'1'1(intersect'ii'in(Xs,Ys))</RHS></RULE><RULE><LHS>u'1'1(intersect'ii'out)</LHS><RHS>intersect'ii'out</RHS></RULE><RULE><LHS>intersect'ii'in(cons(X0,Xs),Ys)</LHS><RHS>u'2'1(intersect'ii'in(Xs,Ys))</RHS></RULE><RULE><LHS>u'2'1(intersect'ii'out)</LHS><RHS>intersect'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(cons(if(A,B),Fs),Gs),NF)</LHS><RHS>u'3'1(reduce'ii'in(sequent(cons(x'2b(x'2d(B),A),Fs),Gs),NF))</RHS></RULE><RULE><LHS>u'3'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(cons(iff(A,B),Fs),Gs),NF)</LHS><RHS>u'4'1(reduce'ii'in(sequent(cons(x'2a(if(A,B),if(B,A)),Fs),Gs),NF))</RHS></RULE><RULE><LHS>u'4'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(cons(x'2a(F1,F2),Fs),Gs),NF)</LHS><RHS>u'5'1(reduce'ii'in(sequent(cons(F1,cons(F2,Fs)),Gs),NF))</RHS></RULE><RULE><LHS>u'5'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(cons(x'2b(F1,F2),Fs),Gs),NF)</LHS><RHS>u'6'1(reduce'ii'in(sequent(cons(F1,Fs),Gs),NF),F2,Fs,Gs,NF)</RHS></RULE><RULE><LHS>u'6'1(reduce'ii'out,F2,Fs,Gs,NF)</LHS><RHS>u'6'2(reduce'ii'in(sequent(cons(F2,Fs),Gs),NF))</RHS></RULE><RULE><LHS>u'6'2(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(cons(x'2d(F1),Fs),Gs),NF)</LHS><RHS>u'7'1(reduce'ii'in(sequent(Fs,cons(F1,Gs)),NF))</RHS></RULE><RULE><LHS>u'7'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(Fs,cons(if(A,B),Gs)),NF)</LHS><RHS>u'8'1(reduce'ii'in(sequent(Fs,cons(x'2b(x'2d(B),A),Gs)),NF))</RHS></RULE><RULE><LHS>u'8'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(Fs,cons(iff(A,B),Gs)),NF)</LHS><RHS>u'9'1(reduce'ii'in(sequent(Fs,cons(x'2a(if(A,B),if(B,A)),Gs)),NF))</RHS></RULE><RULE><LHS>u'9'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(cons(p(V),Fs),Gs),sequent(Left,Right))</LHS><RHS>u'10'1(reduce'ii'in(sequent(Fs,Gs),sequent(cons(p(V),Left),Right)))</RHS></RULE><RULE><LHS>u'10'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(Fs,cons(x'2b(G1,G2),Gs)),NF)</LHS><RHS>u'11'1(reduce'ii'in(sequent(Fs,cons(G1,cons(G2,Gs))),NF))</RHS></RULE><RULE><LHS>u'11'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(Fs,cons(x'2a(G1,G2),Gs)),NF)</LHS><RHS>u'12'1(reduce'ii'in(sequent(Fs,cons(G1,Gs)),NF),Fs,G2,Gs,NF)</RHS></RULE><RULE><LHS>u'12'1(reduce'ii'out,Fs,G2,Gs,NF)</LHS><RHS>u'12'2(reduce'ii'in(sequent(Fs,cons(G2,Gs)),NF))</RHS></RULE><RULE><LHS>u'12'2(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(Fs,cons(x'2d(G1),Gs)),NF)</LHS><RHS>u'13'1(reduce'ii'in(sequent(cons(G1,Fs),Gs),NF))</RHS></RULE><RULE><LHS>u'13'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(nil,cons(p(V),Gs)),sequent(Left,Right))</LHS><RHS>u'14'1(reduce'ii'in(sequent(nil,Gs),sequent(Left,cons(p(V),Right))))</RHS></RULE><RULE><LHS>u'14'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(nil,nil),sequent(F1,F2))</LHS><RHS>u'15'1(intersect'ii'in(F1,F2))</RHS></RULE><RULE><LHS>u'15'1(intersect'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>tautology'i'in(F)</LHS><RHS>u'16'1(reduce'ii'in(sequent(nil,cons(F,nil)),sequent(nil,nil)))</RHS></RULE><RULE><LHS>u'16'1(reduce'ii'out)</LHS><RHS>tautology'i'out</RHS></RULE></REWSYS></SYSTEM><CRITERION/><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>intersect'ii'in(cons(X,X0),cons(X,X1))</LHS><RHS>intersect'ii'out</RHS></RULE><RULE><LHS>intersect'ii'in(Xs,cons(X0,Ys))</LHS><RHS>u'1'1(intersect'ii'in(Xs,Ys))</RHS></RULE><RULE><LHS>u'1'1(intersect'ii'out)</LHS><RHS>intersect'ii'out</RHS></RULE><RULE><LHS>intersect'ii'in(cons(X0,Xs),Ys)</LHS><RHS>u'2'1(intersect'ii'in(Xs,Ys))</RHS></RULE><RULE><LHS>u'2'1(intersect'ii'out)</LHS><RHS>intersect'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(cons(if(A,B),Fs),Gs),NF)</LHS><RHS>u'3'1(reduce'ii'in(sequent(cons(x'2b(x'2d(B),A),Fs),Gs),NF))</RHS></RULE><RULE><LHS>u'3'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(cons(iff(A,B),Fs),Gs),NF)</LHS><RHS>u'4'1(reduce'ii'in(sequent(cons(x'2a(if(A,B),if(B,A)),Fs),Gs),NF))</RHS></RULE><RULE><LHS>u'4'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(cons(x'2a(F1,F2),Fs),Gs),NF)</LHS><RHS>u'5'1(reduce'ii'in(sequent(cons(F1,cons(F2,Fs)),Gs),NF))</RHS></RULE><RULE><LHS>u'5'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(cons(x'2b(F1,F2),Fs),Gs),NF)</LHS><RHS>u'6'1(reduce'ii'in(sequent(cons(F1,Fs),Gs),NF),F2,Fs,Gs,NF)</RHS></RULE><RULE><LHS>u'6'1(reduce'ii'out,F2,Fs,Gs,NF)</LHS><RHS>u'6'2(reduce'ii'in(sequent(cons(F2,Fs),Gs),NF))</RHS></RULE><RULE><LHS>u'6'2(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(cons(x'2d(F1),Fs),Gs),NF)</LHS><RHS>u'7'1(reduce'ii'in(sequent(Fs,cons(F1,Gs)),NF))</RHS></RULE><RULE><LHS>u'7'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(Fs,cons(if(A,B),Gs)),NF)</LHS><RHS>u'8'1(reduce'ii'in(sequent(Fs,cons(x'2b(x'2d(B),A),Gs)),NF))</RHS></RULE><RULE><LHS>u'8'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(Fs,cons(iff(A,B),Gs)),NF)</LHS><RHS>u'9'1(reduce'ii'in(sequent(Fs,cons(x'2a(if(A,B),if(B,A)),Gs)),NF))</RHS></RULE><RULE><LHS>u'9'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(cons(p(V),Fs),Gs),sequent(Left,Right))</LHS><RHS>u'10'1(reduce'ii'in(sequent(Fs,Gs),sequent(cons(p(V),Left),Right)))</RHS></RULE><RULE><LHS>u'10'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(Fs,cons(x'2b(G1,G2),Gs)),NF)</LHS><RHS>u'11'1(reduce'ii'in(sequent(Fs,cons(G1,cons(G2,Gs))),NF))</RHS></RULE><RULE><LHS>u'11'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(Fs,cons(x'2a(G1,G2),Gs)),NF)</LHS><RHS>u'12'1(reduce'ii'in(sequent(Fs,cons(G1,Gs)),NF),Fs,G2,Gs,NF)</RHS></RULE><RULE><LHS>u'12'1(reduce'ii'out,Fs,G2,Gs,NF)</LHS><RHS>u'12'2(reduce'ii'in(sequent(Fs,cons(G2,Gs)),NF))</RHS></RULE><RULE><LHS>u'12'2(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(Fs,cons(x'2d(G1),Gs)),NF)</LHS><RHS>u'13'1(reduce'ii'in(sequent(cons(G1,Fs),Gs),NF))</RHS></RULE><RULE><LHS>u'13'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(nil,cons(p(V),Gs)),sequent(Left,Right))</LHS><RHS>u'14'1(reduce'ii'in(sequent(nil,Gs),sequent(Left,cons(p(V),Right))))</RHS></RULE><RULE><LHS>u'14'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(nil,nil),sequent(F1,F2))</LHS><RHS>u'15'1(intersect'ii'in(F1,F2))</RHS></RULE><RULE><LHS>u'15'1(intersect'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>tautology'i'in(F)</LHS><RHS>u'16'1(reduce'ii'in(sequent(nil,cons(F,nil)),sequent(nil,nil)))</RHS></RULE><RULE><LHS>u'16'1(reduce'ii'out)</LHS><RHS>tautology'i'out</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_intersect'ii'in(Xs,cons(X0,Ys))</LHS><RHS>Marked_u'1'1(intersect'ii'in(Xs,Ys))</RHS></DPRULE><DPRULE num="1"><LHS>Marked_intersect'ii'in(Xs,cons(X0,Ys))</LHS><RHS>Marked_intersect'ii'in(Xs,Ys)</RHS></DPRULE><DPRULE num="2"><LHS>Marked_intersect'ii'in(cons(X0,Xs),Ys)</LHS><RHS>Marked_u'2'1(intersect'ii'in(Xs,Ys))</RHS></DPRULE><DPRULE num="3"><LHS>Marked_intersect'ii'in(cons(X0,Xs),Ys)</LHS><RHS>Marked_intersect'ii'in(Xs,Ys)</RHS></DPRULE><DPRULE num="4"><LHS>Marked_reduce'ii'in(sequent(cons(if(A,B),Fs),Gs),NF)</LHS><RHS>Marked_u'3'1(reduce'ii'in(sequent(cons(x'2b(x'2d(B),A),Fs),Gs),NF))</RHS></DPRULE><DPRULE num="5"><LHS>Marked_reduce'ii'in(sequent(cons(if(A,B),Fs),Gs),NF)</LHS><RHS>Marked_reduce'ii'in(sequent(cons(x'2b(x'2d(B),A),Fs),Gs),NF)</RHS></DPRULE><DPRULE num="6"><LHS>Marked_reduce'ii'in(sequent(cons(iff(A,B),Fs),Gs),NF)</LHS><RHS>Marked_u'4'1(reduce'ii'in(sequent(cons(x'2a(if(A,B),if(B,A)),Fs),Gs),NF))</RHS></DPRULE><DPRULE num="7"><LHS>Marked_reduce'ii'in(sequent(cons(iff(A,B),Fs),Gs),NF)</LHS><RHS>Marked_reduce'ii'in(sequent(cons(x'2a(if(A,B),if(B,A)),Fs),Gs),NF)</RHS></DPRULE><DPRULE num="8"><LHS>Marked_reduce'ii'in(sequent(cons(x'2a(F1,F2),Fs),Gs),NF)</LHS><RHS>Marked_u'5'1(reduce'ii'in(sequent(cons(F1,cons(F2,Fs)),Gs),NF))</RHS></DPRULE><DPRULE num="9"><LHS>Marked_reduce'ii'in(sequent(cons(x'2a(F1,F2),Fs),Gs),NF)</LHS><RHS>Marked_reduce'ii'in(sequent(cons(F1,cons(F2,Fs)),Gs),NF)</RHS></DPRULE><DPRULE num="10"><LHS>Marked_reduce'ii'in(sequent(cons(x'2b(F1,F2),Fs),Gs),NF)</LHS><RHS>Marked_u'6'1(reduce'ii'in(sequent(cons(F1,Fs),Gs),NF),F2,Fs,Gs,NF)</RHS></DPRULE><DPRULE num="11"><LHS>Marked_reduce'ii'in(sequent(cons(x'2b(F1,F2),Fs),Gs),NF)</LHS><RHS>Marked_reduce'ii'in(sequent(cons(F1,Fs),Gs),NF)</RHS></DPRULE><DPRULE num="12"><LHS>Marked_u'6'1(reduce'ii'out,F2,Fs,Gs,NF)</LHS><RHS>Marked_u'6'2(reduce'ii'in(sequent(cons(F2,Fs),Gs),NF))</RHS></DPRULE><DPRULE num="13"><LHS>Marked_u'6'1(reduce'ii'out,F2,Fs,Gs,NF)</LHS><RHS>Marked_reduce'ii'in(sequent(cons(F2,Fs),Gs),NF)</RHS></DPRULE><DPRULE num="14"><LHS>Marked_reduce'ii'in(sequent(cons(x'2d(F1),Fs),Gs),NF)</LHS><RHS>Marked_u'7'1(reduce'ii'in(sequent(Fs,cons(F1,Gs)),NF))</RHS></DPRULE><DPRULE num="15"><LHS>Marked_reduce'ii'in(sequent(cons(x'2d(F1),Fs),Gs),NF)</LHS><RHS>Marked_reduce'ii'in(sequent(Fs,cons(F1,Gs)),NF)</RHS></DPRULE><DPRULE num="16"><LHS>Marked_reduce'ii'in(sequent(Fs,cons(if(A,B),Gs)),NF)</LHS><RHS>Marked_u'8'1(reduce'ii'in(sequent(Fs,cons(x'2b(x'2d(B),A),Gs)),NF))</RHS></DPRULE><DPRULE num="17"><LHS>Marked_reduce'ii'in(sequent(Fs,cons(if(A,B),Gs)),NF)</LHS><RHS>Marked_reduce'ii'in(sequent(Fs,cons(x'2b(x'2d(B),A),Gs)),NF)</RHS></DPRULE><DPRULE num="18"><LHS>Marked_reduce'ii'in(sequent(Fs,cons(iff(A,B),Gs)),NF)</LHS><RHS>Marked_u'9'1(reduce'ii'in(sequent(Fs,cons(x'2a(if(A,B),if(B,A)),Gs)),NF))</RHS></DPRULE><DPRULE num="19"><LHS>Marked_reduce'ii'in(sequent(Fs,cons(iff(A,B),Gs)),NF)</LHS><RHS>Marked_reduce'ii'in(sequent(Fs,cons(x'2a(if(A,B),if(B,A)),Gs)),NF)</RHS></DPRULE><DPRULE num="20"><LHS>Marked_reduce'ii'in(sequent(cons(p(V),Fs),Gs),sequent(Left,Right))</LHS><RHS>Marked_u'10'1(reduce'ii'in(sequent(Fs,Gs),sequent(cons(p(V),Left),Right)))</RHS></DPRULE><DPRULE num="21"><LHS>Marked_reduce'ii'in(sequent(cons(p(V),Fs),Gs),sequent(Left,Right))</LHS><RHS>Marked_reduce'ii'in(sequent(Fs,Gs),sequent(cons(p(V),Left),Right))</RHS></DPRULE><DPRULE num="22"><LHS>Marked_reduce'ii'in(sequent(Fs,cons(x'2b(G1,G2),Gs)),NF)</LHS><RHS>Marked_u'11'1(reduce'ii'in(sequent(Fs,cons(G1,cons(G2,Gs))),NF))</RHS></DPRULE><DPRULE num="23"><LHS>Marked_reduce'ii'in(sequent(Fs,cons(x'2b(G1,G2),Gs)),NF)</LHS><RHS>Marked_reduce'ii'in(sequent(Fs,cons(G1,cons(G2,Gs))),NF)</RHS></DPRULE><DPRULE num="24"><LHS>Marked_reduce'ii'in(sequent(Fs,cons(x'2a(G1,G2),Gs)),NF)</LHS><RHS>Marked_u'12'1(reduce'ii'in(sequent(Fs,cons(G1,Gs)),NF),Fs,G2,Gs,NF)</RHS></DPRULE><DPRULE num="25"><LHS>Marked_reduce'ii'in(sequent(Fs,cons(x'2a(G1,G2),Gs)),NF)</LHS><RHS>Marked_reduce'ii'in(sequent(Fs,cons(G1,Gs)),NF)</RHS></DPRULE><DPRULE num="26"><LHS>Marked_u'12'1(reduce'ii'out,Fs,G2,Gs,NF)</LHS><RHS>Marked_u'12'2(reduce'ii'in(sequent(Fs,cons(G2,Gs)),NF))</RHS></DPRULE><DPRULE num="27"><LHS>Marked_u'12'1(reduce'ii'out,Fs,G2,Gs,NF)</LHS><RHS>Marked_reduce'ii'in(sequent(Fs,cons(G2,Gs)),NF)</RHS></DPRULE><DPRULE num="28"><LHS>Marked_reduce'ii'in(sequent(Fs,cons(x'2d(G1),Gs)),NF)</LHS><RHS>Marked_u'13'1(reduce'ii'in(sequent(cons(G1,Fs),Gs),NF))</RHS></DPRULE><DPRULE num="29"><LHS>Marked_reduce'ii'in(sequent(Fs,cons(x'2d(G1),Gs)),NF)</LHS><RHS>Marked_reduce'ii'in(sequent(cons(G1,Fs),Gs),NF)</RHS></DPRULE><DPRULE num="30"><LHS>Marked_reduce'ii'in(sequent(nil,cons(p(V),Gs)),sequent(Left,Right))</LHS><RHS>Marked_u'14'1(reduce'ii'in(sequent(nil,Gs),sequent(Left,cons(p(V),Right))))</RHS></DPRULE><DPRULE num="31"><LHS>Marked_reduce'ii'in(sequent(nil,cons(p(V),Gs)),sequent(Left,Right))</LHS><RHS>Marked_reduce'ii'in(sequent(nil,Gs),sequent(Left,cons(p(V),Right)))</RHS></DPRULE><DPRULE num="32"><LHS>Marked_reduce'ii'in(sequent(nil,nil),sequent(F1,F2))</LHS><RHS>Marked_u'15'1(intersect'ii'in(F1,F2))</RHS></DPRULE><DPRULE num="33"><LHS>Marked_reduce'ii'in(sequent(nil,nil),sequent(F1,F2))</LHS><RHS>Marked_intersect'ii'in(F1,F2)</RHS></DPRULE><DPRULE num="34"><LHS>Marked_tautology'i'in(F)</LHS><RHS>Marked_u'16'1(reduce'ii'in(sequent(nil,cons(F,nil)),sequent(nil,nil)))</RHS></DPRULE><DPRULE num="35"><LHS>Marked_tautology'i'in(F)</LHS><RHS>Marked_reduce'ii'in(sequent(nil,cons(F,nil)),sequent(nil,nil))</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><DAG approx="simpl"><CCLIST><NONSCC num="0"><NODE ref="35"/></NONSCC><SCC num="1"><NODE ref="5"/><NODE ref="7"/><NODE ref="9"/><NODE ref="10"/><NODE ref="11"/><NODE ref="13"/><NODE ref="15"/><NODE ref="17"/><NODE ref="19"/><NODE ref="21"/><NODE ref="23"/><NODE ref="24"/><NODE ref="25"/><NODE ref="27"/><NODE ref="29"/><NODE ref="31"/></SCC><NONSCC num="2"><NODE ref="30"/></NONSCC><NONSCC num="3"><NODE ref="28"/></NONSCC><NONSCC num="4"><NODE ref="22"/></NONSCC><NONSCC num="5"><NODE ref="18"/></NONSCC><NONSCC num="6"><NODE ref="16"/></NONSCC><NONSCC num="7"><NODE ref="34"/></NONSCC><NONSCC num="8"><NODE ref="33"/></NONSCC><SCC num="9"><NODE ref="1"/><NODE ref="3"/></SCC><NONSCC num="10"><NODE ref="2"/></NONSCC><NONSCC num="11"><NODE ref="0"/></NONSCC><NONSCC num="12"><NODE ref="32"/></NONSCC><NONSCC num="13"><NODE ref="20"/></NONSCC><NONSCC num="14"><NODE ref="14"/></NONSCC><NONSCC num="15"><NODE ref="8"/></NONSCC><NONSCC num="16"><NODE ref="6"/></NONSCC><NONSCC num="17"><NODE ref="4"/></NONSCC><NONSCC num="18"><NODE ref="26"/></NONSCC><NONSCC num="19"><NODE ref="12"/></NONSCC></CCLIST><EDGE end="6" start="0"/><EDGE end="5" start="0"/><EDGE end="4" start="0"/><EDGE end="3" start="0"/><EDGE end="2" start="0"/><EDGE end="1" start="0"/><EDGE end="19" start="1"/><EDGE end="18" start="1"/><EDGE end="17" start="1"/><EDGE end="16" start="1"/><EDGE end="15" start="1"/><EDGE end="14" start="1"/><EDGE end="13" start="1"/><EDGE end="12" start="1"/><EDGE end="8" start="1"/><EDGE end="6" start="1"/><EDGE end="5" start="1"/><EDGE end="4" start="1"/><EDGE end="3" start="1"/><EDGE end="2" start="1"/><EDGE end="11" start="8"/><EDGE end="10" start="8"/><EDGE end="9" start="8"/><EDGE end="11" start="9"/><EDGE end="10" start="9"/></DAG></CRITERION><PROPERTY criterion="stronggraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>intersect'ii'in(cons(X,X0),cons(X,X1))</LHS><RHS>intersect'ii'out</RHS></RULE><RULE><LHS>intersect'ii'in(Xs,cons(X0,Ys))</LHS><RHS>u'1'1(intersect'ii'in(Xs,Ys))</RHS></RULE><RULE><LHS>u'1'1(intersect'ii'out)</LHS><RHS>intersect'ii'out</RHS></RULE><RULE><LHS>intersect'ii'in(cons(X0,Xs),Ys)</LHS><RHS>u'2'1(intersect'ii'in(Xs,Ys))</RHS></RULE><RULE><LHS>u'2'1(intersect'ii'out)</LHS><RHS>intersect'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(cons(if(A,B),Fs),Gs),NF)</LHS><RHS>u'3'1(reduce'ii'in(sequent(cons(x'2b(x'2d(B),A),Fs),Gs),NF))</RHS></RULE><RULE><LHS>u'3'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(cons(iff(A,B),Fs),Gs),NF)</LHS><RHS>u'4'1(reduce'ii'in(sequent(cons(x'2a(if(A,B),if(B,A)),Fs),Gs),NF))</RHS></RULE><RULE><LHS>u'4'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(cons(x'2a(F1,F2),Fs),Gs),NF)</LHS><RHS>u'5'1(reduce'ii'in(sequent(cons(F1,cons(F2,Fs)),Gs),NF))</RHS></RULE><RULE><LHS>u'5'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(cons(x'2b(F1,F2),Fs),Gs),NF)</LHS><RHS>u'6'1(reduce'ii'in(sequent(cons(F1,Fs),Gs),NF),F2,Fs,Gs,NF)</RHS></RULE><RULE><LHS>u'6'1(reduce'ii'out,F2,Fs,Gs,NF)</LHS><RHS>u'6'2(reduce'ii'in(sequent(cons(F2,Fs),Gs),NF))</RHS></RULE><RULE><LHS>u'6'2(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(cons(x'2d(F1),Fs),Gs),NF)</LHS><RHS>u'7'1(reduce'ii'in(sequent(Fs,cons(F1,Gs)),NF))</RHS></RULE><RULE><LHS>u'7'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(Fs,cons(if(A,B),Gs)),NF)</LHS><RHS>u'8'1(reduce'ii'in(sequent(Fs,cons(x'2b(x'2d(B),A),Gs)),NF))</RHS></RULE><RULE><LHS>u'8'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(Fs,cons(iff(A,B),Gs)),NF)</LHS><RHS>u'9'1(reduce'ii'in(sequent(Fs,cons(x'2a(if(A,B),if(B,A)),Gs)),NF))</RHS></RULE><RULE><LHS>u'9'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(cons(p(V),Fs),Gs),sequent(Left,Right))</LHS><RHS>u'10'1(reduce'ii'in(sequent(Fs,Gs),sequent(cons(p(V),Left),Right)))</RHS></RULE><RULE><LHS>u'10'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(Fs,cons(x'2b(G1,G2),Gs)),NF)</LHS><RHS>u'11'1(reduce'ii'in(sequent(Fs,cons(G1,cons(G2,Gs))),NF))</RHS></RULE><RULE><LHS>u'11'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(Fs,cons(x'2a(G1,G2),Gs)),NF)</LHS><RHS>u'12'1(reduce'ii'in(sequent(Fs,cons(G1,Gs)),NF),Fs,G2,Gs,NF)</RHS></RULE><RULE><LHS>u'12'1(reduce'ii'out,Fs,G2,Gs,NF)</LHS><RHS>u'12'2(reduce'ii'in(sequent(Fs,cons(G2,Gs)),NF))</RHS></RULE><RULE><LHS>u'12'2(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(Fs,cons(x'2d(G1),Gs)),NF)</LHS><RHS>u'13'1(reduce'ii'in(sequent(cons(G1,Fs),Gs),NF))</RHS></RULE><RULE><LHS>u'13'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(nil,cons(p(V),Gs)),sequent(Left,Right))</LHS><RHS>u'14'1(reduce'ii'in(sequent(nil,Gs),sequent(Left,cons(p(V),Right))))</RHS></RULE><RULE><LHS>u'14'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(nil,nil),sequent(F1,F2))</LHS><RHS>u'15'1(intersect'ii'in(F1,F2))</RHS></RULE><RULE><LHS>u'15'1(intersect'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>tautology'i'in(F)</LHS><RHS>u'16'1(reduce'ii'in(sequent(nil,cons(F,nil)),sequent(nil,nil)))</RHS></RULE><RULE><LHS>u'16'1(reduce'ii'out)</LHS><RHS>tautology'i'out</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_reduce'ii'in(sequent(cons(if(A,B),Fs),Gs),NF)</LHS><RHS>Marked_reduce'ii'in(sequent(cons(x'2b(x'2d(B),A),Fs),Gs),NF)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_reduce'ii'in(sequent(cons(iff(A,B),Fs),Gs),NF)</LHS><RHS>Marked_reduce'ii'in(sequent(cons(x'2a(if(A,B),if(B,A)),Fs),Gs),NF)</RHS></DPRULE><DPRULE num="2"><LHS>Marked_reduce'ii'in(sequent(cons(x'2a(F1,F2),Fs),Gs),NF)</LHS><RHS>Marked_reduce'ii'in(sequent(cons(F1,cons(F2,Fs)),Gs),NF)</RHS></DPRULE><DPRULE num="3"><LHS>Marked_reduce'ii'in(sequent(cons(x'2b(F1,F2),Fs),Gs),NF)</LHS><RHS>Marked_u'6'1(reduce'ii'in(sequent(cons(F1,Fs),Gs),NF),F2,Fs,Gs,NF)</RHS></DPRULE><DPRULE num="4"><LHS>Marked_reduce'ii'in(sequent(cons(x'2b(F1,F2),Fs),Gs),NF)</LHS><RHS>Marked_reduce'ii'in(sequent(cons(F1,Fs),Gs),NF)</RHS></DPRULE><DPRULE num="5"><LHS>Marked_u'6'1(reduce'ii'out,F2,Fs,Gs,NF)</LHS><RHS>Marked_reduce'ii'in(sequent(cons(F2,Fs),Gs),NF)</RHS></DPRULE><DPRULE num="6"><LHS>Marked_reduce'ii'in(sequent(cons(x'2d(F1),Fs),Gs),NF)</LHS><RHS>Marked_reduce'ii'in(sequent(Fs,cons(F1,Gs)),NF)</RHS></DPRULE><DPRULE num="7"><LHS>Marked_reduce'ii'in(sequent(Fs,cons(if(A,B),Gs)),NF)</LHS><RHS>Marked_reduce'ii'in(sequent(Fs,cons(x'2b(x'2d(B),A),Gs)),NF)</RHS></DPRULE><DPRULE num="8"><LHS>Marked_reduce'ii'in(sequent(Fs,cons(iff(A,B),Gs)),NF)</LHS><RHS>Marked_reduce'ii'in(sequent(Fs,cons(x'2a(if(A,B),if(B,A)),Gs)),NF)</RHS></DPRULE><DPRULE num="9"><LHS>Marked_reduce'ii'in(sequent(cons(p(V),Fs),Gs),sequent(Left,Right))</LHS><RHS>Marked_reduce'ii'in(sequent(Fs,Gs),sequent(cons(p(V),Left),Right))</RHS></DPRULE><DPRULE num="10"><LHS>Marked_reduce'ii'in(sequent(Fs,cons(x'2b(G1,G2),Gs)),NF)</LHS><RHS>Marked_reduce'ii'in(sequent(Fs,cons(G1,cons(G2,Gs))),NF)</RHS></DPRULE><DPRULE num="11"><LHS>Marked_reduce'ii'in(sequent(Fs,cons(x'2a(G1,G2),Gs)),NF)</LHS><RHS>Marked_u'12'1(reduce'ii'in(sequent(Fs,cons(G1,Gs)),NF),Fs,G2,Gs,NF)</RHS></DPRULE><DPRULE num="12"><LHS>Marked_reduce'ii'in(sequent(Fs,cons(x'2a(G1,G2),Gs)),NF)</LHS><RHS>Marked_reduce'ii'in(sequent(Fs,cons(G1,Gs)),NF)</RHS></DPRULE><DPRULE num="13"><LHS>Marked_u'12'1(reduce'ii'out,Fs,G2,Gs,NF)</LHS><RHS>Marked_reduce'ii'in(sequent(Fs,cons(G2,Gs)),NF)</RHS></DPRULE><DPRULE num="14"><LHS>Marked_reduce'ii'in(sequent(Fs,cons(x'2d(G1),Gs)),NF)</LHS><RHS>Marked_reduce'ii'in(sequent(cons(G1,Fs),Gs),NF)</RHS></DPRULE><DPRULE num="15"><LHS>Marked_reduce'ii'in(sequent(nil,cons(p(V),Gs)),sequent(Left,Right))</LHS><RHS>Marked_reduce'ii'in(sequent(nil,Gs),sequent(Left,cons(p(V),Right)))</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><ORDERING type="poly"><POLYSYMB><SYMBOL><NAME>intersect'ii'out</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>tautology'i'out</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>3</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>u'6'1</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>Marked_u'6'1</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="2"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="3"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>x'2b</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF></MONOME></POLYNOMIAL><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></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>u'12'1</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>u'2'1</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>u'9'1</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>u'4'1</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>cons</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>u'7'1</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>if</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</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><POLYSYMB><SYMBOL><NAME>u'13'1</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>reduce'ii'in</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></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><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>iff</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>3</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>3</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>u'16'1</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>3</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>intersect'ii'in</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>u'6'2</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>x'2d</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>Marked_u'12'1</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="2"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="3"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>u'12'2</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>u'3'1</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>u'10'1</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>x'2a</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>u'15'1</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>u'1'1</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>Marked_reduce'ii'in</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>u'8'1</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>reduce'ii'out</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>u'14'1</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>sequent</NAME></SYMBOL><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></POLYSYMB><POLYSYMB><SYMBOL><NAME>u'11'1</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>u'5'1</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>tautology'i'in</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>3</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></ORDERING><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_reduce'ii'in(sequent(cons(x'2b(F1,F2),Fs),Gs),NF)</LHS><RHS>Marked_u'6'1(reduce'ii'in(sequent(cons(F1,Fs),Gs),NF),F2,Fs,Gs,NF)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_reduce'ii'in(sequent(cons(x'2b(F1,F2),Fs),Gs),NF)</LHS><RHS>Marked_reduce'ii'in(sequent(cons(F1,Fs),Gs),NF)</RHS></DPRULE><DPRULE num="2"><LHS>Marked_reduce'ii'in(sequent(Fs,cons(x'2b(G1,G2),Gs)),NF)</LHS><RHS>Marked_reduce'ii'in(sequent(Fs,cons(G1,cons(G2,Gs))),NF)</RHS></DPRULE></DPLIST></STRICTPAIRS></CRITERION><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>intersect'ii'in(cons(X,X0),cons(X,X1))</LHS><RHS>intersect'ii'out</RHS></RULE><RULE><LHS>intersect'ii'in(Xs,cons(X0,Ys))</LHS><RHS>u'1'1(intersect'ii'in(Xs,Ys))</RHS></RULE><RULE><LHS>u'1'1(intersect'ii'out)</LHS><RHS>intersect'ii'out</RHS></RULE><RULE><LHS>intersect'ii'in(cons(X0,Xs),Ys)</LHS><RHS>u'2'1(intersect'ii'in(Xs,Ys))</RHS></RULE><RULE><LHS>u'2'1(intersect'ii'out)</LHS><RHS>intersect'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(cons(if(A,B),Fs),Gs),NF)</LHS><RHS>u'3'1(reduce'ii'in(sequent(cons(x'2b(x'2d(B),A),Fs),Gs),NF))</RHS></RULE><RULE><LHS>u'3'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(cons(iff(A,B),Fs),Gs),NF)</LHS><RHS>u'4'1(reduce'ii'in(sequent(cons(x'2a(if(A,B),if(B,A)),Fs),Gs),NF))</RHS></RULE><RULE><LHS>u'4'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(cons(x'2a(F1,F2),Fs),Gs),NF)</LHS><RHS>u'5'1(reduce'ii'in(sequent(cons(F1,cons(F2,Fs)),Gs),NF))</RHS></RULE><RULE><LHS>u'5'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(cons(x'2b(F1,F2),Fs),Gs),NF)</LHS><RHS>u'6'1(reduce'ii'in(sequent(cons(F1,Fs),Gs),NF),F2,Fs,Gs,NF)</RHS></RULE><RULE><LHS>u'6'1(reduce'ii'out,F2,Fs,Gs,NF)</LHS><RHS>u'6'2(reduce'ii'in(sequent(cons(F2,Fs),Gs),NF))</RHS></RULE><RULE><LHS>u'6'2(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(cons(x'2d(F1),Fs),Gs),NF)</LHS><RHS>u'7'1(reduce'ii'in(sequent(Fs,cons(F1,Gs)),NF))</RHS></RULE><RULE><LHS>u'7'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(Fs,cons(if(A,B),Gs)),NF)</LHS><RHS>u'8'1(reduce'ii'in(sequent(Fs,cons(x'2b(x'2d(B),A),Gs)),NF))</RHS></RULE><RULE><LHS>u'8'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(Fs,cons(iff(A,B),Gs)),NF)</LHS><RHS>u'9'1(reduce'ii'in(sequent(Fs,cons(x'2a(if(A,B),if(B,A)),Gs)),NF))</RHS></RULE><RULE><LHS>u'9'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(cons(p(V),Fs),Gs),sequent(Left,Right))</LHS><RHS>u'10'1(reduce'ii'in(sequent(Fs,Gs),sequent(cons(p(V),Left),Right)))</RHS></RULE><RULE><LHS>u'10'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(Fs,cons(x'2b(G1,G2),Gs)),NF)</LHS><RHS>u'11'1(reduce'ii'in(sequent(Fs,cons(G1,cons(G2,Gs))),NF))</RHS></RULE><RULE><LHS>u'11'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(Fs,cons(x'2a(G1,G2),Gs)),NF)</LHS><RHS>u'12'1(reduce'ii'in(sequent(Fs,cons(G1,Gs)),NF),Fs,G2,Gs,NF)</RHS></RULE><RULE><LHS>u'12'1(reduce'ii'out,Fs,G2,Gs,NF)</LHS><RHS>u'12'2(reduce'ii'in(sequent(Fs,cons(G2,Gs)),NF))</RHS></RULE><RULE><LHS>u'12'2(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(Fs,cons(x'2d(G1),Gs)),NF)</LHS><RHS>u'13'1(reduce'ii'in(sequent(cons(G1,Fs),Gs),NF))</RHS></RULE><RULE><LHS>u'13'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(nil,cons(p(V),Gs)),sequent(Left,Right))</LHS><RHS>u'14'1(reduce'ii'in(sequent(nil,Gs),sequent(Left,cons(p(V),Right))))</RHS></RULE><RULE><LHS>u'14'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(nil,nil),sequent(F1,F2))</LHS><RHS>u'15'1(intersect'ii'in(F1,F2))</RHS></RULE><RULE><LHS>u'15'1(intersect'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>tautology'i'in(F)</LHS><RHS>u'16'1(reduce'ii'in(sequent(nil,cons(F,nil)),sequent(nil,nil)))</RHS></RULE><RULE><LHS>u'16'1(reduce'ii'out)</LHS><RHS>tautology'i'out</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_reduce'ii'in(sequent(cons(if(A,B),Fs),Gs),NF)</LHS><RHS>Marked_reduce'ii'in(sequent(cons(x'2b(x'2d(B),A),Fs),Gs),NF)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_reduce'ii'in(sequent(cons(iff(A,B),Fs),Gs),NF)</LHS><RHS>Marked_reduce'ii'in(sequent(cons(x'2a(if(A,B),if(B,A)),Fs),Gs),NF)</RHS></DPRULE><DPRULE num="2"><LHS>Marked_reduce'ii'in(sequent(cons(x'2a(F1,F2),Fs),Gs),NF)</LHS><RHS>Marked_reduce'ii'in(sequent(cons(F1,cons(F2,Fs)),Gs),NF)</RHS></DPRULE><DPRULE num="3"><LHS>Marked_u'6'1(reduce'ii'out,F2,Fs,Gs,NF)</LHS><RHS>Marked_reduce'ii'in(sequent(cons(F2,Fs),Gs),NF)</RHS></DPRULE><DPRULE num="4"><LHS>Marked_reduce'ii'in(sequent(cons(x'2d(F1),Fs),Gs),NF)</LHS><RHS>Marked_reduce'ii'in(sequent(Fs,cons(F1,Gs)),NF)</RHS></DPRULE><DPRULE num="5"><LHS>Marked_reduce'ii'in(sequent(Fs,cons(if(A,B),Gs)),NF)</LHS><RHS>Marked_reduce'ii'in(sequent(Fs,cons(x'2b(x'2d(B),A),Gs)),NF)</RHS></DPRULE><DPRULE num="6"><LHS>Marked_reduce'ii'in(sequent(Fs,cons(iff(A,B),Gs)),NF)</LHS><RHS>Marked_reduce'ii'in(sequent(Fs,cons(x'2a(if(A,B),if(B,A)),Gs)),NF)</RHS></DPRULE><DPRULE num="7"><LHS>Marked_reduce'ii'in(sequent(cons(p(V),Fs),Gs),sequent(Left,Right))</LHS><RHS>Marked_reduce'ii'in(sequent(Fs,Gs),sequent(cons(p(V),Left),Right))</RHS></DPRULE><DPRULE num="8"><LHS>Marked_reduce'ii'in(sequent(Fs,cons(x'2a(G1,G2),Gs)),NF)</LHS><RHS>Marked_u'12'1(reduce'ii'in(sequent(Fs,cons(G1,Gs)),NF),Fs,G2,Gs,NF)</RHS></DPRULE><DPRULE num="9"><LHS>Marked_reduce'ii'in(sequent(Fs,cons(x'2a(G1,G2),Gs)),NF)</LHS><RHS>Marked_reduce'ii'in(sequent(Fs,cons(G1,Gs)),NF)</RHS></DPRULE><DPRULE num="10"><LHS>Marked_u'12'1(reduce'ii'out,Fs,G2,Gs,NF)</LHS><RHS>Marked_reduce'ii'in(sequent(Fs,cons(G2,Gs)),NF)</RHS></DPRULE><DPRULE num="11"><LHS>Marked_reduce'ii'in(sequent(Fs,cons(x'2d(G1),Gs)),NF)</LHS><RHS>Marked_reduce'ii'in(sequent(cons(G1,Fs),Gs),NF)</RHS></DPRULE><DPRULE num="12"><LHS>Marked_reduce'ii'in(sequent(nil,cons(p(V),Gs)),sequent(Left,Right))</LHS><RHS>Marked_reduce'ii'in(sequent(nil,Gs),sequent(Left,cons(p(V),Right)))</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><DAG approx="simpl"><CCLIST><SCC num="0"><NODE ref="0"/><NODE ref="1"/><NODE ref="2"/><NODE ref="4"/><NODE ref="5"/><NODE ref="6"/><NODE ref="7"/><NODE ref="8"/><NODE ref="9"/><NODE ref="10"/><NODE ref="11"/><NODE ref="12"/></SCC><NONSCC num="1"><NODE ref="3"/></NONSCC></CCLIST><EDGE end="0" start="1"/></DAG></CRITERION><PROPERTY criterion="stronggraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>intersect'ii'in(cons(X,X0),cons(X,X1))</LHS><RHS>intersect'ii'out</RHS></RULE><RULE><LHS>intersect'ii'in(Xs,cons(X0,Ys))</LHS><RHS>u'1'1(intersect'ii'in(Xs,Ys))</RHS></RULE><RULE><LHS>u'1'1(intersect'ii'out)</LHS><RHS>intersect'ii'out</RHS></RULE><RULE><LHS>intersect'ii'in(cons(X0,Xs),Ys)</LHS><RHS>u'2'1(intersect'ii'in(Xs,Ys))</RHS></RULE><RULE><LHS>u'2'1(intersect'ii'out)</LHS><RHS>intersect'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(cons(if(A,B),Fs),Gs),NF)</LHS><RHS>u'3'1(reduce'ii'in(sequent(cons(x'2b(x'2d(B),A),Fs),Gs),NF))</RHS></RULE><RULE><LHS>u'3'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(cons(iff(A,B),Fs),Gs),NF)</LHS><RHS>u'4'1(reduce'ii'in(sequent(cons(x'2a(if(A,B),if(B,A)),Fs),Gs),NF))</RHS></RULE><RULE><LHS>u'4'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(cons(x'2a(F1,F2),Fs),Gs),NF)</LHS><RHS>u'5'1(reduce'ii'in(sequent(cons(F1,cons(F2,Fs)),Gs),NF))</RHS></RULE><RULE><LHS>u'5'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(cons(x'2b(F1,F2),Fs),Gs),NF)</LHS><RHS>u'6'1(reduce'ii'in(sequent(cons(F1,Fs),Gs),NF),F2,Fs,Gs,NF)</RHS></RULE><RULE><LHS>u'6'1(reduce'ii'out,F2,Fs,Gs,NF)</LHS><RHS>u'6'2(reduce'ii'in(sequent(cons(F2,Fs),Gs),NF))</RHS></RULE><RULE><LHS>u'6'2(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(cons(x'2d(F1),Fs),Gs),NF)</LHS><RHS>u'7'1(reduce'ii'in(sequent(Fs,cons(F1,Gs)),NF))</RHS></RULE><RULE><LHS>u'7'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(Fs,cons(if(A,B),Gs)),NF)</LHS><RHS>u'8'1(reduce'ii'in(sequent(Fs,cons(x'2b(x'2d(B),A),Gs)),NF))</RHS></RULE><RULE><LHS>u'8'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(Fs,cons(iff(A,B),Gs)),NF)</LHS><RHS>u'9'1(reduce'ii'in(sequent(Fs,cons(x'2a(if(A,B),if(B,A)),Gs)),NF))</RHS></RULE><RULE><LHS>u'9'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(cons(p(V),Fs),Gs),sequent(Left,Right))</LHS><RHS>u'10'1(reduce'ii'in(sequent(Fs,Gs),sequent(cons(p(V),Left),Right)))</RHS></RULE><RULE><LHS>u'10'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(Fs,cons(x'2b(G1,G2),Gs)),NF)</LHS><RHS>u'11'1(reduce'ii'in(sequent(Fs,cons(G1,cons(G2,Gs))),NF))</RHS></RULE><RULE><LHS>u'11'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(Fs,cons(x'2a(G1,G2),Gs)),NF)</LHS><RHS>u'12'1(reduce'ii'in(sequent(Fs,cons(G1,Gs)),NF),Fs,G2,Gs,NF)</RHS></RULE><RULE><LHS>u'12'1(reduce'ii'out,Fs,G2,Gs,NF)</LHS><RHS>u'12'2(reduce'ii'in(sequent(Fs,cons(G2,Gs)),NF))</RHS></RULE><RULE><LHS>u'12'2(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(Fs,cons(x'2d(G1),Gs)),NF)</LHS><RHS>u'13'1(reduce'ii'in(sequent(cons(G1,Fs),Gs),NF))</RHS></RULE><RULE><LHS>u'13'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(nil,cons(p(V),Gs)),sequent(Left,Right))</LHS><RHS>u'14'1(reduce'ii'in(sequent(nil,Gs),sequent(Left,cons(p(V),Right))))</RHS></RULE><RULE><LHS>u'14'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(nil,nil),sequent(F1,F2))</LHS><RHS>u'15'1(intersect'ii'in(F1,F2))</RHS></RULE><RULE><LHS>u'15'1(intersect'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>tautology'i'in(F)</LHS><RHS>u'16'1(reduce'ii'in(sequent(nil,cons(F,nil)),sequent(nil,nil)))</RHS></RULE><RULE><LHS>u'16'1(reduce'ii'out)</LHS><RHS>tautology'i'out</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_reduce'ii'in(sequent(cons(if(A,B),Fs),Gs),NF)</LHS><RHS>Marked_reduce'ii'in(sequent(cons(x'2b(x'2d(B),A),Fs),Gs),NF)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_reduce'ii'in(sequent(cons(iff(A,B),Fs),Gs),NF)</LHS><RHS>Marked_reduce'ii'in(sequent(cons(x'2a(if(A,B),if(B,A)),Fs),Gs),NF)</RHS></DPRULE><DPRULE num="2"><LHS>Marked_reduce'ii'in(sequent(cons(x'2a(F1,F2),Fs),Gs),NF)</LHS><RHS>Marked_reduce'ii'in(sequent(cons(F1,cons(F2,Fs)),Gs),NF)</RHS></DPRULE><DPRULE num="3"><LHS>Marked_reduce'ii'in(sequent(cons(x'2d(F1),Fs),Gs),NF)</LHS><RHS>Marked_reduce'ii'in(sequent(Fs,cons(F1,Gs)),NF)</RHS></DPRULE><DPRULE num="4"><LHS>Marked_reduce'ii'in(sequent(Fs,cons(if(A,B),Gs)),NF)</LHS><RHS>Marked_reduce'ii'in(sequent(Fs,cons(x'2b(x'2d(B),A),Gs)),NF)</RHS></DPRULE><DPRULE num="5"><LHS>Marked_reduce'ii'in(sequent(Fs,cons(iff(A,B),Gs)),NF)</LHS><RHS>Marked_reduce'ii'in(sequent(Fs,cons(x'2a(if(A,B),if(B,A)),Gs)),NF)</RHS></DPRULE><DPRULE num="6"><LHS>Marked_reduce'ii'in(sequent(cons(p(V),Fs),Gs),sequent(Left,Right))</LHS><RHS>Marked_reduce'ii'in(sequent(Fs,Gs),sequent(cons(p(V),Left),Right))</RHS></DPRULE><DPRULE num="7"><LHS>Marked_reduce'ii'in(sequent(Fs,cons(x'2a(G1,G2),Gs)),NF)</LHS><RHS>Marked_u'12'1(reduce'ii'in(sequent(Fs,cons(G1,Gs)),NF),Fs,G2,Gs,NF)</RHS></DPRULE><DPRULE num="8"><LHS>Marked_reduce'ii'in(sequent(Fs,cons(x'2a(G1,G2),Gs)),NF)</LHS><RHS>Marked_reduce'ii'in(sequent(Fs,cons(G1,Gs)),NF)</RHS></DPRULE><DPRULE num="9"><LHS>Marked_u'12'1(reduce'ii'out,Fs,G2,Gs,NF)</LHS><RHS>Marked_reduce'ii'in(sequent(Fs,cons(G2,Gs)),NF)</RHS></DPRULE><DPRULE num="10"><LHS>Marked_reduce'ii'in(sequent(Fs,cons(x'2d(G1),Gs)),NF)</LHS><RHS>Marked_reduce'ii'in(sequent(cons(G1,Fs),Gs),NF)</RHS></DPRULE><DPRULE num="11"><LHS>Marked_reduce'ii'in(sequent(nil,cons(p(V),Gs)),sequent(Left,Right))</LHS><RHS>Marked_reduce'ii'in(sequent(nil,Gs),sequent(Left,cons(p(V),Right)))</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><ORDERING type="poly"><POLYSYMB><SYMBOL><NAME>intersect'ii'out</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>tautology'i'out</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>3</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>u'6'1</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>x'2b</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>u'12'1</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>u'2'1</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>u'9'1</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>u'4'1</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>cons</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>u'7'1</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>if</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>u'13'1</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>reduce'ii'in</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></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><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>iff</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</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>u'16'1</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>3</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>intersect'ii'in</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>u'6'2</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>x'2d</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>Marked_u'12'1</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>3</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="2"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="3"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>u'12'2</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>u'3'1</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>u'10'1</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>x'2a</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><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><POLYSYMB><SYMBOL><NAME>u'15'1</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>u'1'1</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>Marked_reduce'ii'in</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>u'8'1</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>reduce'ii'out</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>u'14'1</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>sequent</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>u'11'1</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>u'5'1</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>tautology'i'in</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>3</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></ORDERING><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_reduce'ii'in(sequent(cons(x'2a(F1,F2),Fs),Gs),NF)</LHS><RHS>Marked_reduce'ii'in(sequent(cons(F1,cons(F2,Fs)),Gs),NF)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_reduce'ii'in(sequent(Fs,cons(x'2a(G1,G2),Gs)),NF)</LHS><RHS>Marked_u'12'1(reduce'ii'in(sequent(Fs,cons(G1,Gs)),NF),Fs,G2,Gs,NF)</RHS></DPRULE><DPRULE num="2"><LHS>Marked_reduce'ii'in(sequent(Fs,cons(x'2a(G1,G2),Gs)),NF)</LHS><RHS>Marked_reduce'ii'in(sequent(Fs,cons(G1,Gs)),NF)</RHS></DPRULE><DPRULE num="3"><LHS>Marked_u'12'1(reduce'ii'out,Fs,G2,Gs,NF)</LHS><RHS>Marked_reduce'ii'in(sequent(Fs,cons(G2,Gs)),NF)</RHS></DPRULE></DPLIST></STRICTPAIRS></CRITERION><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>intersect'ii'in(cons(X,X0),cons(X,X1))</LHS><RHS>intersect'ii'out</RHS></RULE><RULE><LHS>intersect'ii'in(Xs,cons(X0,Ys))</LHS><RHS>u'1'1(intersect'ii'in(Xs,Ys))</RHS></RULE><RULE><LHS>u'1'1(intersect'ii'out)</LHS><RHS>intersect'ii'out</RHS></RULE><RULE><LHS>intersect'ii'in(cons(X0,Xs),Ys)</LHS><RHS>u'2'1(intersect'ii'in(Xs,Ys))</RHS></RULE><RULE><LHS>u'2'1(intersect'ii'out)</LHS><RHS>intersect'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(cons(if(A,B),Fs),Gs),NF)</LHS><RHS>u'3'1(reduce'ii'in(sequent(cons(x'2b(x'2d(B),A),Fs),Gs),NF))</RHS></RULE><RULE><LHS>u'3'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(cons(iff(A,B),Fs),Gs),NF)</LHS><RHS>u'4'1(reduce'ii'in(sequent(cons(x'2a(if(A,B),if(B,A)),Fs),Gs),NF))</RHS></RULE><RULE><LHS>u'4'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(cons(x'2a(F1,F2),Fs),Gs),NF)</LHS><RHS>u'5'1(reduce'ii'in(sequent(cons(F1,cons(F2,Fs)),Gs),NF))</RHS></RULE><RULE><LHS>u'5'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(cons(x'2b(F1,F2),Fs),Gs),NF)</LHS><RHS>u'6'1(reduce'ii'in(sequent(cons(F1,Fs),Gs),NF),F2,Fs,Gs,NF)</RHS></RULE><RULE><LHS>u'6'1(reduce'ii'out,F2,Fs,Gs,NF)</LHS><RHS>u'6'2(reduce'ii'in(sequent(cons(F2,Fs),Gs),NF))</RHS></RULE><RULE><LHS>u'6'2(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(cons(x'2d(F1),Fs),Gs),NF)</LHS><RHS>u'7'1(reduce'ii'in(sequent(Fs,cons(F1,Gs)),NF))</RHS></RULE><RULE><LHS>u'7'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(Fs,cons(if(A,B),Gs)),NF)</LHS><RHS>u'8'1(reduce'ii'in(sequent(Fs,cons(x'2b(x'2d(B),A),Gs)),NF))</RHS></RULE><RULE><LHS>u'8'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(Fs,cons(iff(A,B),Gs)),NF)</LHS><RHS>u'9'1(reduce'ii'in(sequent(Fs,cons(x'2a(if(A,B),if(B,A)),Gs)),NF))</RHS></RULE><RULE><LHS>u'9'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(cons(p(V),Fs),Gs),sequent(Left,Right))</LHS><RHS>u'10'1(reduce'ii'in(sequent(Fs,Gs),sequent(cons(p(V),Left),Right)))</RHS></RULE><RULE><LHS>u'10'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(Fs,cons(x'2b(G1,G2),Gs)),NF)</LHS><RHS>u'11'1(reduce'ii'in(sequent(Fs,cons(G1,cons(G2,Gs))),NF))</RHS></RULE><RULE><LHS>u'11'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(Fs,cons(x'2a(G1,G2),Gs)),NF)</LHS><RHS>u'12'1(reduce'ii'in(sequent(Fs,cons(G1,Gs)),NF),Fs,G2,Gs,NF)</RHS></RULE><RULE><LHS>u'12'1(reduce'ii'out,Fs,G2,Gs,NF)</LHS><RHS>u'12'2(reduce'ii'in(sequent(Fs,cons(G2,Gs)),NF))</RHS></RULE><RULE><LHS>u'12'2(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(Fs,cons(x'2d(G1),Gs)),NF)</LHS><RHS>u'13'1(reduce'ii'in(sequent(cons(G1,Fs),Gs),NF))</RHS></RULE><RULE><LHS>u'13'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(nil,cons(p(V),Gs)),sequent(Left,Right))</LHS><RHS>u'14'1(reduce'ii'in(sequent(nil,Gs),sequent(Left,cons(p(V),Right))))</RHS></RULE><RULE><LHS>u'14'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(nil,nil),sequent(F1,F2))</LHS><RHS>u'15'1(intersect'ii'in(F1,F2))</RHS></RULE><RULE><LHS>u'15'1(intersect'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>tautology'i'in(F)</LHS><RHS>u'16'1(reduce'ii'in(sequent(nil,cons(F,nil)),sequent(nil,nil)))</RHS></RULE><RULE><LHS>u'16'1(reduce'ii'out)</LHS><RHS>tautology'i'out</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_reduce'ii'in(sequent(cons(if(A,B),Fs),Gs),NF)</LHS><RHS>Marked_reduce'ii'in(sequent(cons(x'2b(x'2d(B),A),Fs),Gs),NF)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_reduce'ii'in(sequent(cons(iff(A,B),Fs),Gs),NF)</LHS><RHS>Marked_reduce'ii'in(sequent(cons(x'2a(if(A,B),if(B,A)),Fs),Gs),NF)</RHS></DPRULE><DPRULE num="2"><LHS>Marked_reduce'ii'in(sequent(cons(x'2d(F1),Fs),Gs),NF)</LHS><RHS>Marked_reduce'ii'in(sequent(Fs,cons(F1,Gs)),NF)</RHS></DPRULE><DPRULE num="3"><LHS>Marked_reduce'ii'in(sequent(Fs,cons(if(A,B),Gs)),NF)</LHS><RHS>Marked_reduce'ii'in(sequent(Fs,cons(x'2b(x'2d(B),A),Gs)),NF)</RHS></DPRULE><DPRULE num="4"><LHS>Marked_reduce'ii'in(sequent(Fs,cons(iff(A,B),Gs)),NF)</LHS><RHS>Marked_reduce'ii'in(sequent(Fs,cons(x'2a(if(A,B),if(B,A)),Gs)),NF)</RHS></DPRULE><DPRULE num="5"><LHS>Marked_reduce'ii'in(sequent(cons(p(V),Fs),Gs),sequent(Left,Right))</LHS><RHS>Marked_reduce'ii'in(sequent(Fs,Gs),sequent(cons(p(V),Left),Right))</RHS></DPRULE><DPRULE num="6"><LHS>Marked_reduce'ii'in(sequent(Fs,cons(x'2d(G1),Gs)),NF)</LHS><RHS>Marked_reduce'ii'in(sequent(cons(G1,Fs),Gs),NF)</RHS></DPRULE><DPRULE num="7"><LHS>Marked_reduce'ii'in(sequent(nil,cons(p(V),Gs)),sequent(Left,Right))</LHS><RHS>Marked_reduce'ii'in(sequent(nil,Gs),sequent(Left,cons(p(V),Right)))</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"/></SCC></CCLIST></DAG></CRITERION><PROPERTY criterion="stronggraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>intersect'ii'in(cons(X,X0),cons(X,X1))</LHS><RHS>intersect'ii'out</RHS></RULE><RULE><LHS>intersect'ii'in(Xs,cons(X0,Ys))</LHS><RHS>u'1'1(intersect'ii'in(Xs,Ys))</RHS></RULE><RULE><LHS>u'1'1(intersect'ii'out)</LHS><RHS>intersect'ii'out</RHS></RULE><RULE><LHS>intersect'ii'in(cons(X0,Xs),Ys)</LHS><RHS>u'2'1(intersect'ii'in(Xs,Ys))</RHS></RULE><RULE><LHS>u'2'1(intersect'ii'out)</LHS><RHS>intersect'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(cons(if(A,B),Fs),Gs),NF)</LHS><RHS>u'3'1(reduce'ii'in(sequent(cons(x'2b(x'2d(B),A),Fs),Gs),NF))</RHS></RULE><RULE><LHS>u'3'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(cons(iff(A,B),Fs),Gs),NF)</LHS><RHS>u'4'1(reduce'ii'in(sequent(cons(x'2a(if(A,B),if(B,A)),Fs),Gs),NF))</RHS></RULE><RULE><LHS>u'4'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(cons(x'2a(F1,F2),Fs),Gs),NF)</LHS><RHS>u'5'1(reduce'ii'in(sequent(cons(F1,cons(F2,Fs)),Gs),NF))</RHS></RULE><RULE><LHS>u'5'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(cons(x'2b(F1,F2),Fs),Gs),NF)</LHS><RHS>u'6'1(reduce'ii'in(sequent(cons(F1,Fs),Gs),NF),F2,Fs,Gs,NF)</RHS></RULE><RULE><LHS>u'6'1(reduce'ii'out,F2,Fs,Gs,NF)</LHS><RHS>u'6'2(reduce'ii'in(sequent(cons(F2,Fs),Gs),NF))</RHS></RULE><RULE><LHS>u'6'2(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(cons(x'2d(F1),Fs),Gs),NF)</LHS><RHS>u'7'1(reduce'ii'in(sequent(Fs,cons(F1,Gs)),NF))</RHS></RULE><RULE><LHS>u'7'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(Fs,cons(if(A,B),Gs)),NF)</LHS><RHS>u'8'1(reduce'ii'in(sequent(Fs,cons(x'2b(x'2d(B),A),Gs)),NF))</RHS></RULE><RULE><LHS>u'8'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(Fs,cons(iff(A,B),Gs)),NF)</LHS><RHS>u'9'1(reduce'ii'in(sequent(Fs,cons(x'2a(if(A,B),if(B,A)),Gs)),NF))</RHS></RULE><RULE><LHS>u'9'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(cons(p(V),Fs),Gs),sequent(Left,Right))</LHS><RHS>u'10'1(reduce'ii'in(sequent(Fs,Gs),sequent(cons(p(V),Left),Right)))</RHS></RULE><RULE><LHS>u'10'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(Fs,cons(x'2b(G1,G2),Gs)),NF)</LHS><RHS>u'11'1(reduce'ii'in(sequent(Fs,cons(G1,cons(G2,Gs))),NF))</RHS></RULE><RULE><LHS>u'11'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(Fs,cons(x'2a(G1,G2),Gs)),NF)</LHS><RHS>u'12'1(reduce'ii'in(sequent(Fs,cons(G1,Gs)),NF),Fs,G2,Gs,NF)</RHS></RULE><RULE><LHS>u'12'1(reduce'ii'out,Fs,G2,Gs,NF)</LHS><RHS>u'12'2(reduce'ii'in(sequent(Fs,cons(G2,Gs)),NF))</RHS></RULE><RULE><LHS>u'12'2(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(Fs,cons(x'2d(G1),Gs)),NF)</LHS><RHS>u'13'1(reduce'ii'in(sequent(cons(G1,Fs),Gs),NF))</RHS></RULE><RULE><LHS>u'13'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(nil,cons(p(V),Gs)),sequent(Left,Right))</LHS><RHS>u'14'1(reduce'ii'in(sequent(nil,Gs),sequent(Left,cons(p(V),Right))))</RHS></RULE><RULE><LHS>u'14'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(nil,nil),sequent(F1,F2))</LHS><RHS>u'15'1(intersect'ii'in(F1,F2))</RHS></RULE><RULE><LHS>u'15'1(intersect'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>tautology'i'in(F)</LHS><RHS>u'16'1(reduce'ii'in(sequent(nil,cons(F,nil)),sequent(nil,nil)))</RHS></RULE><RULE><LHS>u'16'1(reduce'ii'out)</LHS><RHS>tautology'i'out</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_reduce'ii'in(sequent(cons(if(A,B),Fs),Gs),NF)</LHS><RHS>Marked_reduce'ii'in(sequent(cons(x'2b(x'2d(B),A),Fs),Gs),NF)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_reduce'ii'in(sequent(cons(iff(A,B),Fs),Gs),NF)</LHS><RHS>Marked_reduce'ii'in(sequent(cons(x'2a(if(A,B),if(B,A)),Fs),Gs),NF)</RHS></DPRULE><DPRULE num="2"><LHS>Marked_reduce'ii'in(sequent(cons(x'2d(F1),Fs),Gs),NF)</LHS><RHS>Marked_reduce'ii'in(sequent(Fs,cons(F1,Gs)),NF)</RHS></DPRULE><DPRULE num="3"><LHS>Marked_reduce'ii'in(sequent(Fs,cons(if(A,B),Gs)),NF)</LHS><RHS>Marked_reduce'ii'in(sequent(Fs,cons(x'2b(x'2d(B),A),Gs)),NF)</RHS></DPRULE><DPRULE num="4"><LHS>Marked_reduce'ii'in(sequent(Fs,cons(iff(A,B),Gs)),NF)</LHS><RHS>Marked_reduce'ii'in(sequent(Fs,cons(x'2a(if(A,B),if(B,A)),Gs)),NF)</RHS></DPRULE><DPRULE num="5"><LHS>Marked_reduce'ii'in(sequent(cons(p(V),Fs),Gs),sequent(Left,Right))</LHS><RHS>Marked_reduce'ii'in(sequent(Fs,Gs),sequent(cons(p(V),Left),Right))</RHS></DPRULE><DPRULE num="6"><LHS>Marked_reduce'ii'in(sequent(Fs,cons(x'2d(G1),Gs)),NF)</LHS><RHS>Marked_reduce'ii'in(sequent(cons(G1,Fs),Gs),NF)</RHS></DPRULE><DPRULE num="7"><LHS>Marked_reduce'ii'in(sequent(nil,cons(p(V),Gs)),sequent(Left,Right))</LHS><RHS>Marked_reduce'ii'in(sequent(nil,Gs),sequent(Left,cons(p(V),Right)))</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><ORDERING type="poly"><POLYSYMB><SYMBOL><NAME>intersect'ii'out</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>tautology'i'out</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>3</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>u'6'1</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>x'2b</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>u'12'1</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>u'2'1</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>u'9'1</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>u'4'1</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>cons</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>u'7'1</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>if</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><POLYSYMB><SYMBOL><NAME>u'13'1</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>reduce'ii'in</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>p</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>iff</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><POLYSYMB><SYMBOL><NAME>u'16'1</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>3</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>intersect'ii'in</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>u'6'2</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>x'2d</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF></MONOME></POLYNOMIAL><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></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>u'12'2</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>u'3'1</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>u'10'1</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>x'2a</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>u'15'1</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>u'1'1</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>Marked_reduce'ii'in</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>u'8'1</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>reduce'ii'out</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>u'14'1</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>sequent</NAME></SYMBOL><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></POLYSYMB><POLYSYMB><SYMBOL><NAME>u'11'1</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>u'5'1</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>tautology'i'in</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>3</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></ORDERING><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_reduce'ii'in(sequent(cons(x'2d(F1),Fs),Gs),NF)</LHS><RHS>Marked_reduce'ii'in(sequent(Fs,cons(F1,Gs)),NF)</RHS></DPRULE></DPLIST></STRICTPAIRS></CRITERION><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>intersect'ii'in(cons(X,X0),cons(X,X1))</LHS><RHS>intersect'ii'out</RHS></RULE><RULE><LHS>intersect'ii'in(Xs,cons(X0,Ys))</LHS><RHS>u'1'1(intersect'ii'in(Xs,Ys))</RHS></RULE><RULE><LHS>u'1'1(intersect'ii'out)</LHS><RHS>intersect'ii'out</RHS></RULE><RULE><LHS>intersect'ii'in(cons(X0,Xs),Ys)</LHS><RHS>u'2'1(intersect'ii'in(Xs,Ys))</RHS></RULE><RULE><LHS>u'2'1(intersect'ii'out)</LHS><RHS>intersect'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(cons(if(A,B),Fs),Gs),NF)</LHS><RHS>u'3'1(reduce'ii'in(sequent(cons(x'2b(x'2d(B),A),Fs),Gs),NF))</RHS></RULE><RULE><LHS>u'3'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(cons(iff(A,B),Fs),Gs),NF)</LHS><RHS>u'4'1(reduce'ii'in(sequent(cons(x'2a(if(A,B),if(B,A)),Fs),Gs),NF))</RHS></RULE><RULE><LHS>u'4'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(cons(x'2a(F1,F2),Fs),Gs),NF)</LHS><RHS>u'5'1(reduce'ii'in(sequent(cons(F1,cons(F2,Fs)),Gs),NF))</RHS></RULE><RULE><LHS>u'5'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(cons(x'2b(F1,F2),Fs),Gs),NF)</LHS><RHS>u'6'1(reduce'ii'in(sequent(cons(F1,Fs),Gs),NF),F2,Fs,Gs,NF)</RHS></RULE><RULE><LHS>u'6'1(reduce'ii'out,F2,Fs,Gs,NF)</LHS><RHS>u'6'2(reduce'ii'in(sequent(cons(F2,Fs),Gs),NF))</RHS></RULE><RULE><LHS>u'6'2(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(cons(x'2d(F1),Fs),Gs),NF)</LHS><RHS>u'7'1(reduce'ii'in(sequent(Fs,cons(F1,Gs)),NF))</RHS></RULE><RULE><LHS>u'7'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(Fs,cons(if(A,B),Gs)),NF)</LHS><RHS>u'8'1(reduce'ii'in(sequent(Fs,cons(x'2b(x'2d(B),A),Gs)),NF))</RHS></RULE><RULE><LHS>u'8'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(Fs,cons(iff(A,B),Gs)),NF)</LHS><RHS>u'9'1(reduce'ii'in(sequent(Fs,cons(x'2a(if(A,B),if(B,A)),Gs)),NF))</RHS></RULE><RULE><LHS>u'9'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(cons(p(V),Fs),Gs),sequent(Left,Right))</LHS><RHS>u'10'1(reduce'ii'in(sequent(Fs,Gs),sequent(cons(p(V),Left),Right)))</RHS></RULE><RULE><LHS>u'10'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(Fs,cons(x'2b(G1,G2),Gs)),NF)</LHS><RHS>u'11'1(reduce'ii'in(sequent(Fs,cons(G1,cons(G2,Gs))),NF))</RHS></RULE><RULE><LHS>u'11'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(Fs,cons(x'2a(G1,G2),Gs)),NF)</LHS><RHS>u'12'1(reduce'ii'in(sequent(Fs,cons(G1,Gs)),NF),Fs,G2,Gs,NF)</RHS></RULE><RULE><LHS>u'12'1(reduce'ii'out,Fs,G2,Gs,NF)</LHS><RHS>u'12'2(reduce'ii'in(sequent(Fs,cons(G2,Gs)),NF))</RHS></RULE><RULE><LHS>u'12'2(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(Fs,cons(x'2d(G1),Gs)),NF)</LHS><RHS>u'13'1(reduce'ii'in(sequent(cons(G1,Fs),Gs),NF))</RHS></RULE><RULE><LHS>u'13'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(nil,cons(p(V),Gs)),sequent(Left,Right))</LHS><RHS>u'14'1(reduce'ii'in(sequent(nil,Gs),sequent(Left,cons(p(V),Right))))</RHS></RULE><RULE><LHS>u'14'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(nil,nil),sequent(F1,F2))</LHS><RHS>u'15'1(intersect'ii'in(F1,F2))</RHS></RULE><RULE><LHS>u'15'1(intersect'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>tautology'i'in(F)</LHS><RHS>u'16'1(reduce'ii'in(sequent(nil,cons(F,nil)),sequent(nil,nil)))</RHS></RULE><RULE><LHS>u'16'1(reduce'ii'out)</LHS><RHS>tautology'i'out</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_reduce'ii'in(sequent(cons(if(A,B),Fs),Gs),NF)</LHS><RHS>Marked_reduce'ii'in(sequent(cons(x'2b(x'2d(B),A),Fs),Gs),NF)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_reduce'ii'in(sequent(cons(iff(A,B),Fs),Gs),NF)</LHS><RHS>Marked_reduce'ii'in(sequent(cons(x'2a(if(A,B),if(B,A)),Fs),Gs),NF)</RHS></DPRULE><DPRULE num="2"><LHS>Marked_reduce'ii'in(sequent(Fs,cons(if(A,B),Gs)),NF)</LHS><RHS>Marked_reduce'ii'in(sequent(Fs,cons(x'2b(x'2d(B),A),Gs)),NF)</RHS></DPRULE><DPRULE num="3"><LHS>Marked_reduce'ii'in(sequent(Fs,cons(iff(A,B),Gs)),NF)</LHS><RHS>Marked_reduce'ii'in(sequent(Fs,cons(x'2a(if(A,B),if(B,A)),Gs)),NF)</RHS></DPRULE><DPRULE num="4"><LHS>Marked_reduce'ii'in(sequent(cons(p(V),Fs),Gs),sequent(Left,Right))</LHS><RHS>Marked_reduce'ii'in(sequent(Fs,Gs),sequent(cons(p(V),Left),Right))</RHS></DPRULE><DPRULE num="5"><LHS>Marked_reduce'ii'in(sequent(Fs,cons(x'2d(G1),Gs)),NF)</LHS><RHS>Marked_reduce'ii'in(sequent(cons(G1,Fs),Gs),NF)</RHS></DPRULE><DPRULE num="6"><LHS>Marked_reduce'ii'in(sequent(nil,cons(p(V),Gs)),sequent(Left,Right))</LHS><RHS>Marked_reduce'ii'in(sequent(nil,Gs),sequent(Left,cons(p(V),Right)))</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"/></SCC></CCLIST></DAG></CRITERION><PROPERTY criterion="stronggraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>intersect'ii'in(cons(X,X0),cons(X,X1))</LHS><RHS>intersect'ii'out</RHS></RULE><RULE><LHS>intersect'ii'in(Xs,cons(X0,Ys))</LHS><RHS>u'1'1(intersect'ii'in(Xs,Ys))</RHS></RULE><RULE><LHS>u'1'1(intersect'ii'out)</LHS><RHS>intersect'ii'out</RHS></RULE><RULE><LHS>intersect'ii'in(cons(X0,Xs),Ys)</LHS><RHS>u'2'1(intersect'ii'in(Xs,Ys))</RHS></RULE><RULE><LHS>u'2'1(intersect'ii'out)</LHS><RHS>intersect'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(cons(if(A,B),Fs),Gs),NF)</LHS><RHS>u'3'1(reduce'ii'in(sequent(cons(x'2b(x'2d(B),A),Fs),Gs),NF))</RHS></RULE><RULE><LHS>u'3'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(cons(iff(A,B),Fs),Gs),NF)</LHS><RHS>u'4'1(reduce'ii'in(sequent(cons(x'2a(if(A,B),if(B,A)),Fs),Gs),NF))</RHS></RULE><RULE><LHS>u'4'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(cons(x'2a(F1,F2),Fs),Gs),NF)</LHS><RHS>u'5'1(reduce'ii'in(sequent(cons(F1,cons(F2,Fs)),Gs),NF))</RHS></RULE><RULE><LHS>u'5'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(cons(x'2b(F1,F2),Fs),Gs),NF)</LHS><RHS>u'6'1(reduce'ii'in(sequent(cons(F1,Fs),Gs),NF),F2,Fs,Gs,NF)</RHS></RULE><RULE><LHS>u'6'1(reduce'ii'out,F2,Fs,Gs,NF)</LHS><RHS>u'6'2(reduce'ii'in(sequent(cons(F2,Fs),Gs),NF))</RHS></RULE><RULE><LHS>u'6'2(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(cons(x'2d(F1),Fs),Gs),NF)</LHS><RHS>u'7'1(reduce'ii'in(sequent(Fs,cons(F1,Gs)),NF))</RHS></RULE><RULE><LHS>u'7'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(Fs,cons(if(A,B),Gs)),NF)</LHS><RHS>u'8'1(reduce'ii'in(sequent(Fs,cons(x'2b(x'2d(B),A),Gs)),NF))</RHS></RULE><RULE><LHS>u'8'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(Fs,cons(iff(A,B),Gs)),NF)</LHS><RHS>u'9'1(reduce'ii'in(sequent(Fs,cons(x'2a(if(A,B),if(B,A)),Gs)),NF))</RHS></RULE><RULE><LHS>u'9'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(cons(p(V),Fs),Gs),sequent(Left,Right))</LHS><RHS>u'10'1(reduce'ii'in(sequent(Fs,Gs),sequent(cons(p(V),Left),Right)))</RHS></RULE><RULE><LHS>u'10'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(Fs,cons(x'2b(G1,G2),Gs)),NF)</LHS><RHS>u'11'1(reduce'ii'in(sequent(Fs,cons(G1,cons(G2,Gs))),NF))</RHS></RULE><RULE><LHS>u'11'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(Fs,cons(x'2a(G1,G2),Gs)),NF)</LHS><RHS>u'12'1(reduce'ii'in(sequent(Fs,cons(G1,Gs)),NF),Fs,G2,Gs,NF)</RHS></RULE><RULE><LHS>u'12'1(reduce'ii'out,Fs,G2,Gs,NF)</LHS><RHS>u'12'2(reduce'ii'in(sequent(Fs,cons(G2,Gs)),NF))</RHS></RULE><RULE><LHS>u'12'2(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(Fs,cons(x'2d(G1),Gs)),NF)</LHS><RHS>u'13'1(reduce'ii'in(sequent(cons(G1,Fs),Gs),NF))</RHS></RULE><RULE><LHS>u'13'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(nil,cons(p(V),Gs)),sequent(Left,Right))</LHS><RHS>u'14'1(reduce'ii'in(sequent(nil,Gs),sequent(Left,cons(p(V),Right))))</RHS></RULE><RULE><LHS>u'14'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(nil,nil),sequent(F1,F2))</LHS><RHS>u'15'1(intersect'ii'in(F1,F2))</RHS></RULE><RULE><LHS>u'15'1(intersect'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>tautology'i'in(F)</LHS><RHS>u'16'1(reduce'ii'in(sequent(nil,cons(F,nil)),sequent(nil,nil)))</RHS></RULE><RULE><LHS>u'16'1(reduce'ii'out)</LHS><RHS>tautology'i'out</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_reduce'ii'in(sequent(cons(if(A,B),Fs),Gs),NF)</LHS><RHS>Marked_reduce'ii'in(sequent(cons(x'2b(x'2d(B),A),Fs),Gs),NF)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_reduce'ii'in(sequent(cons(iff(A,B),Fs),Gs),NF)</LHS><RHS>Marked_reduce'ii'in(sequent(cons(x'2a(if(A,B),if(B,A)),Fs),Gs),NF)</RHS></DPRULE><DPRULE num="2"><LHS>Marked_reduce'ii'in(sequent(Fs,cons(if(A,B),Gs)),NF)</LHS><RHS>Marked_reduce'ii'in(sequent(Fs,cons(x'2b(x'2d(B),A),Gs)),NF)</RHS></DPRULE><DPRULE num="3"><LHS>Marked_reduce'ii'in(sequent(Fs,cons(iff(A,B),Gs)),NF)</LHS><RHS>Marked_reduce'ii'in(sequent(Fs,cons(x'2a(if(A,B),if(B,A)),Gs)),NF)</RHS></DPRULE><DPRULE num="4"><LHS>Marked_reduce'ii'in(sequent(cons(p(V),Fs),Gs),sequent(Left,Right))</LHS><RHS>Marked_reduce'ii'in(sequent(Fs,Gs),sequent(cons(p(V),Left),Right))</RHS></DPRULE><DPRULE num="5"><LHS>Marked_reduce'ii'in(sequent(Fs,cons(x'2d(G1),Gs)),NF)</LHS><RHS>Marked_reduce'ii'in(sequent(cons(G1,Fs),Gs),NF)</RHS></DPRULE><DPRULE num="6"><LHS>Marked_reduce'ii'in(sequent(nil,cons(p(V),Gs)),sequent(Left,Right))</LHS><RHS>Marked_reduce'ii'in(sequent(nil,Gs),sequent(Left,cons(p(V),Right)))</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><ORDERING type="poly"><POLYSYMB><SYMBOL><NAME>intersect'ii'out</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>tautology'i'out</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>3</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>u'6'1</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>x'2b</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><POLYSYMB><SYMBOL><NAME>u'12'1</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>u'2'1</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>u'9'1</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>u'4'1</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>cons</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>3</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>3</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>u'7'1</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>if</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>u'13'1</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>reduce'ii'in</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></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><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>iff</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><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>3</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>u'16'1</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>3</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>intersect'ii'in</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><POLYSYMB><SYMBOL><NAME>u'6'2</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>x'2d</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>u'12'2</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>u'3'1</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>u'10'1</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>x'2a</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><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>u'15'1</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>u'1'1</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>Marked_reduce'ii'in</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>u'8'1</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>reduce'ii'out</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>u'14'1</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>sequent</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><POLYSYMB><SYMBOL><NAME>u'11'1</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>u'5'1</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>tautology'i'in</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>3</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></ORDERING><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_reduce'ii'in(sequent(Fs,cons(iff(A,B),Gs)),NF)</LHS><RHS>Marked_reduce'ii'in(sequent(Fs,cons(x'2a(if(A,B),if(B,A)),Gs)),NF)</RHS></DPRULE></DPLIST></STRICTPAIRS></CRITERION><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>intersect'ii'in(cons(X,X0),cons(X,X1))</LHS><RHS>intersect'ii'out</RHS></RULE><RULE><LHS>intersect'ii'in(Xs,cons(X0,Ys))</LHS><RHS>u'1'1(intersect'ii'in(Xs,Ys))</RHS></RULE><RULE><LHS>u'1'1(intersect'ii'out)</LHS><RHS>intersect'ii'out</RHS></RULE><RULE><LHS>intersect'ii'in(cons(X0,Xs),Ys)</LHS><RHS>u'2'1(intersect'ii'in(Xs,Ys))</RHS></RULE><RULE><LHS>u'2'1(intersect'ii'out)</LHS><RHS>intersect'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(cons(if(A,B),Fs),Gs),NF)</LHS><RHS>u'3'1(reduce'ii'in(sequent(cons(x'2b(x'2d(B),A),Fs),Gs),NF))</RHS></RULE><RULE><LHS>u'3'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(cons(iff(A,B),Fs),Gs),NF)</LHS><RHS>u'4'1(reduce'ii'in(sequent(cons(x'2a(if(A,B),if(B,A)),Fs),Gs),NF))</RHS></RULE><RULE><LHS>u'4'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(cons(x'2a(F1,F2),Fs),Gs),NF)</LHS><RHS>u'5'1(reduce'ii'in(sequent(cons(F1,cons(F2,Fs)),Gs),NF))</RHS></RULE><RULE><LHS>u'5'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(cons(x'2b(F1,F2),Fs),Gs),NF)</LHS><RHS>u'6'1(reduce'ii'in(sequent(cons(F1,Fs),Gs),NF),F2,Fs,Gs,NF)</RHS></RULE><RULE><LHS>u'6'1(reduce'ii'out,F2,Fs,Gs,NF)</LHS><RHS>u'6'2(reduce'ii'in(sequent(cons(F2,Fs),Gs),NF))</RHS></RULE><RULE><LHS>u'6'2(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(cons(x'2d(F1),Fs),Gs),NF)</LHS><RHS>u'7'1(reduce'ii'in(sequent(Fs,cons(F1,Gs)),NF))</RHS></RULE><RULE><LHS>u'7'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(Fs,cons(if(A,B),Gs)),NF)</LHS><RHS>u'8'1(reduce'ii'in(sequent(Fs,cons(x'2b(x'2d(B),A),Gs)),NF))</RHS></RULE><RULE><LHS>u'8'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(Fs,cons(iff(A,B),Gs)),NF)</LHS><RHS>u'9'1(reduce'ii'in(sequent(Fs,cons(x'2a(if(A,B),if(B,A)),Gs)),NF))</RHS></RULE><RULE><LHS>u'9'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(cons(p(V),Fs),Gs),sequent(Left,Right))</LHS><RHS>u'10'1(reduce'ii'in(sequent(Fs,Gs),sequent(cons(p(V),Left),Right)))</RHS></RULE><RULE><LHS>u'10'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(Fs,cons(x'2b(G1,G2),Gs)),NF)</LHS><RHS>u'11'1(reduce'ii'in(sequent(Fs,cons(G1,cons(G2,Gs))),NF))</RHS></RULE><RULE><LHS>u'11'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(Fs,cons(x'2a(G1,G2),Gs)),NF)</LHS><RHS>u'12'1(reduce'ii'in(sequent(Fs,cons(G1,Gs)),NF),Fs,G2,Gs,NF)</RHS></RULE><RULE><LHS>u'12'1(reduce'ii'out,Fs,G2,Gs,NF)</LHS><RHS>u'12'2(reduce'ii'in(sequent(Fs,cons(G2,Gs)),NF))</RHS></RULE><RULE><LHS>u'12'2(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(Fs,cons(x'2d(G1),Gs)),NF)</LHS><RHS>u'13'1(reduce'ii'in(sequent(cons(G1,Fs),Gs),NF))</RHS></RULE><RULE><LHS>u'13'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(nil,cons(p(V),Gs)),sequent(Left,Right))</LHS><RHS>u'14'1(reduce'ii'in(sequent(nil,Gs),sequent(Left,cons(p(V),Right))))</RHS></RULE><RULE><LHS>u'14'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(nil,nil),sequent(F1,F2))</LHS><RHS>u'15'1(intersect'ii'in(F1,F2))</RHS></RULE><RULE><LHS>u'15'1(intersect'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>tautology'i'in(F)</LHS><RHS>u'16'1(reduce'ii'in(sequent(nil,cons(F,nil)),sequent(nil,nil)))</RHS></RULE><RULE><LHS>u'16'1(reduce'ii'out)</LHS><RHS>tautology'i'out</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_reduce'ii'in(sequent(cons(if(A,B),Fs),Gs),NF)</LHS><RHS>Marked_reduce'ii'in(sequent(cons(x'2b(x'2d(B),A),Fs),Gs),NF)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_reduce'ii'in(sequent(cons(iff(A,B),Fs),Gs),NF)</LHS><RHS>Marked_reduce'ii'in(sequent(cons(x'2a(if(A,B),if(B,A)),Fs),Gs),NF)</RHS></DPRULE><DPRULE num="2"><LHS>Marked_reduce'ii'in(sequent(Fs,cons(if(A,B),Gs)),NF)</LHS><RHS>Marked_reduce'ii'in(sequent(Fs,cons(x'2b(x'2d(B),A),Gs)),NF)</RHS></DPRULE><DPRULE num="3"><LHS>Marked_reduce'ii'in(sequent(cons(p(V),Fs),Gs),sequent(Left,Right))</LHS><RHS>Marked_reduce'ii'in(sequent(Fs,Gs),sequent(cons(p(V),Left),Right))</RHS></DPRULE><DPRULE num="4"><LHS>Marked_reduce'ii'in(sequent(Fs,cons(x'2d(G1),Gs)),NF)</LHS><RHS>Marked_reduce'ii'in(sequent(cons(G1,Fs),Gs),NF)</RHS></DPRULE><DPRULE num="5"><LHS>Marked_reduce'ii'in(sequent(nil,cons(p(V),Gs)),sequent(Left,Right))</LHS><RHS>Marked_reduce'ii'in(sequent(nil,Gs),sequent(Left,cons(p(V),Right)))</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"/></SCC></CCLIST></DAG></CRITERION><PROPERTY criterion="stronggraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>intersect'ii'in(cons(X,X0),cons(X,X1))</LHS><RHS>intersect'ii'out</RHS></RULE><RULE><LHS>intersect'ii'in(Xs,cons(X0,Ys))</LHS><RHS>u'1'1(intersect'ii'in(Xs,Ys))</RHS></RULE><RULE><LHS>u'1'1(intersect'ii'out)</LHS><RHS>intersect'ii'out</RHS></RULE><RULE><LHS>intersect'ii'in(cons(X0,Xs),Ys)</LHS><RHS>u'2'1(intersect'ii'in(Xs,Ys))</RHS></RULE><RULE><LHS>u'2'1(intersect'ii'out)</LHS><RHS>intersect'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(cons(if(A,B),Fs),Gs),NF)</LHS><RHS>u'3'1(reduce'ii'in(sequent(cons(x'2b(x'2d(B),A),Fs),Gs),NF))</RHS></RULE><RULE><LHS>u'3'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(cons(iff(A,B),Fs),Gs),NF)</LHS><RHS>u'4'1(reduce'ii'in(sequent(cons(x'2a(if(A,B),if(B,A)),Fs),Gs),NF))</RHS></RULE><RULE><LHS>u'4'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(cons(x'2a(F1,F2),Fs),Gs),NF)</LHS><RHS>u'5'1(reduce'ii'in(sequent(cons(F1,cons(F2,Fs)),Gs),NF))</RHS></RULE><RULE><LHS>u'5'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(cons(x'2b(F1,F2),Fs),Gs),NF)</LHS><RHS>u'6'1(reduce'ii'in(sequent(cons(F1,Fs),Gs),NF),F2,Fs,Gs,NF)</RHS></RULE><RULE><LHS>u'6'1(reduce'ii'out,F2,Fs,Gs,NF)</LHS><RHS>u'6'2(reduce'ii'in(sequent(cons(F2,Fs),Gs),NF))</RHS></RULE><RULE><LHS>u'6'2(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(cons(x'2d(F1),Fs),Gs),NF)</LHS><RHS>u'7'1(reduce'ii'in(sequent(Fs,cons(F1,Gs)),NF))</RHS></RULE><RULE><LHS>u'7'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(Fs,cons(if(A,B),Gs)),NF)</LHS><RHS>u'8'1(reduce'ii'in(sequent(Fs,cons(x'2b(x'2d(B),A),Gs)),NF))</RHS></RULE><RULE><LHS>u'8'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(Fs,cons(iff(A,B),Gs)),NF)</LHS><RHS>u'9'1(reduce'ii'in(sequent(Fs,cons(x'2a(if(A,B),if(B,A)),Gs)),NF))</RHS></RULE><RULE><LHS>u'9'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(cons(p(V),Fs),Gs),sequent(Left,Right))</LHS><RHS>u'10'1(reduce'ii'in(sequent(Fs,Gs),sequent(cons(p(V),Left),Right)))</RHS></RULE><RULE><LHS>u'10'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(Fs,cons(x'2b(G1,G2),Gs)),NF)</LHS><RHS>u'11'1(reduce'ii'in(sequent(Fs,cons(G1,cons(G2,Gs))),NF))</RHS></RULE><RULE><LHS>u'11'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(Fs,cons(x'2a(G1,G2),Gs)),NF)</LHS><RHS>u'12'1(reduce'ii'in(sequent(Fs,cons(G1,Gs)),NF),Fs,G2,Gs,NF)</RHS></RULE><RULE><LHS>u'12'1(reduce'ii'out,Fs,G2,Gs,NF)</LHS><RHS>u'12'2(reduce'ii'in(sequent(Fs,cons(G2,Gs)),NF))</RHS></RULE><RULE><LHS>u'12'2(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(Fs,cons(x'2d(G1),Gs)),NF)</LHS><RHS>u'13'1(reduce'ii'in(sequent(cons(G1,Fs),Gs),NF))</RHS></RULE><RULE><LHS>u'13'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(nil,cons(p(V),Gs)),sequent(Left,Right))</LHS><RHS>u'14'1(reduce'ii'in(sequent(nil,Gs),sequent(Left,cons(p(V),Right))))</RHS></RULE><RULE><LHS>u'14'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(nil,nil),sequent(F1,F2))</LHS><RHS>u'15'1(intersect'ii'in(F1,F2))</RHS></RULE><RULE><LHS>u'15'1(intersect'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>tautology'i'in(F)</LHS><RHS>u'16'1(reduce'ii'in(sequent(nil,cons(F,nil)),sequent(nil,nil)))</RHS></RULE><RULE><LHS>u'16'1(reduce'ii'out)</LHS><RHS>tautology'i'out</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_reduce'ii'in(sequent(cons(if(A,B),Fs),Gs),NF)</LHS><RHS>Marked_reduce'ii'in(sequent(cons(x'2b(x'2d(B),A),Fs),Gs),NF)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_reduce'ii'in(sequent(cons(iff(A,B),Fs),Gs),NF)</LHS><RHS>Marked_reduce'ii'in(sequent(cons(x'2a(if(A,B),if(B,A)),Fs),Gs),NF)</RHS></DPRULE><DPRULE num="2"><LHS>Marked_reduce'ii'in(sequent(Fs,cons(if(A,B),Gs)),NF)</LHS><RHS>Marked_reduce'ii'in(sequent(Fs,cons(x'2b(x'2d(B),A),Gs)),NF)</RHS></DPRULE><DPRULE num="3"><LHS>Marked_reduce'ii'in(sequent(cons(p(V),Fs),Gs),sequent(Left,Right))</LHS><RHS>Marked_reduce'ii'in(sequent(Fs,Gs),sequent(cons(p(V),Left),Right))</RHS></DPRULE><DPRULE num="4"><LHS>Marked_reduce'ii'in(sequent(Fs,cons(x'2d(G1),Gs)),NF)</LHS><RHS>Marked_reduce'ii'in(sequent(cons(G1,Fs),Gs),NF)</RHS></DPRULE><DPRULE num="5"><LHS>Marked_reduce'ii'in(sequent(nil,cons(p(V),Gs)),sequent(Left,Right))</LHS><RHS>Marked_reduce'ii'in(sequent(nil,Gs),sequent(Left,cons(p(V),Right)))</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><ORDERING type="poly"><POLYSYMB><SYMBOL><NAME>intersect'ii'out</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>tautology'i'out</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>3</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>u'6'1</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>x'2b</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>u'12'1</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>u'2'1</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>u'9'1</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>u'4'1</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>cons</NAME></SYMBOL><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></POLYSYMB><POLYSYMB><SYMBOL><NAME>u'7'1</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>if</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>3</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>u'13'1</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>reduce'ii'in</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>p</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>iff</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>u'16'1</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>3</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>intersect'ii'in</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><POLYSYMB><SYMBOL><NAME>u'6'2</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>x'2d</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>u'12'2</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>u'3'1</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>u'10'1</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>x'2a</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>u'15'1</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>u'1'1</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>Marked_reduce'ii'in</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><POLYSYMB><SYMBOL><NAME>u'8'1</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>reduce'ii'out</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>u'14'1</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>sequent</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><POLYSYMB><SYMBOL><NAME>u'11'1</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>u'5'1</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>tautology'i'in</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>3</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></ORDERING><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_reduce'ii'in(sequent(Fs,cons(if(A,B),Gs)),NF)</LHS><RHS>Marked_reduce'ii'in(sequent(Fs,cons(x'2b(x'2d(B),A),Gs)),NF)</RHS></DPRULE></DPLIST></STRICTPAIRS></CRITERION><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>intersect'ii'in(cons(X,X0),cons(X,X1))</LHS><RHS>intersect'ii'out</RHS></RULE><RULE><LHS>intersect'ii'in(Xs,cons(X0,Ys))</LHS><RHS>u'1'1(intersect'ii'in(Xs,Ys))</RHS></RULE><RULE><LHS>u'1'1(intersect'ii'out)</LHS><RHS>intersect'ii'out</RHS></RULE><RULE><LHS>intersect'ii'in(cons(X0,Xs),Ys)</LHS><RHS>u'2'1(intersect'ii'in(Xs,Ys))</RHS></RULE><RULE><LHS>u'2'1(intersect'ii'out)</LHS><RHS>intersect'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(cons(if(A,B),Fs),Gs),NF)</LHS><RHS>u'3'1(reduce'ii'in(sequent(cons(x'2b(x'2d(B),A),Fs),Gs),NF))</RHS></RULE><RULE><LHS>u'3'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(cons(iff(A,B),Fs),Gs),NF)</LHS><RHS>u'4'1(reduce'ii'in(sequent(cons(x'2a(if(A,B),if(B,A)),Fs),Gs),NF))</RHS></RULE><RULE><LHS>u'4'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(cons(x'2a(F1,F2),Fs),Gs),NF)</LHS><RHS>u'5'1(reduce'ii'in(sequent(cons(F1,cons(F2,Fs)),Gs),NF))</RHS></RULE><RULE><LHS>u'5'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(cons(x'2b(F1,F2),Fs),Gs),NF)</LHS><RHS>u'6'1(reduce'ii'in(sequent(cons(F1,Fs),Gs),NF),F2,Fs,Gs,NF)</RHS></RULE><RULE><LHS>u'6'1(reduce'ii'out,F2,Fs,Gs,NF)</LHS><RHS>u'6'2(reduce'ii'in(sequent(cons(F2,Fs),Gs),NF))</RHS></RULE><RULE><LHS>u'6'2(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(cons(x'2d(F1),Fs),Gs),NF)</LHS><RHS>u'7'1(reduce'ii'in(sequent(Fs,cons(F1,Gs)),NF))</RHS></RULE><RULE><LHS>u'7'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(Fs,cons(if(A,B),Gs)),NF)</LHS><RHS>u'8'1(reduce'ii'in(sequent(Fs,cons(x'2b(x'2d(B),A),Gs)),NF))</RHS></RULE><RULE><LHS>u'8'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(Fs,cons(iff(A,B),Gs)),NF)</LHS><RHS>u'9'1(reduce'ii'in(sequent(Fs,cons(x'2a(if(A,B),if(B,A)),Gs)),NF))</RHS></RULE><RULE><LHS>u'9'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(cons(p(V),Fs),Gs),sequent(Left,Right))</LHS><RHS>u'10'1(reduce'ii'in(sequent(Fs,Gs),sequent(cons(p(V),Left),Right)))</RHS></RULE><RULE><LHS>u'10'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(Fs,cons(x'2b(G1,G2),Gs)),NF)</LHS><RHS>u'11'1(reduce'ii'in(sequent(Fs,cons(G1,cons(G2,Gs))),NF))</RHS></RULE><RULE><LHS>u'11'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(Fs,cons(x'2a(G1,G2),Gs)),NF)</LHS><RHS>u'12'1(reduce'ii'in(sequent(Fs,cons(G1,Gs)),NF),Fs,G2,Gs,NF)</RHS></RULE><RULE><LHS>u'12'1(reduce'ii'out,Fs,G2,Gs,NF)</LHS><RHS>u'12'2(reduce'ii'in(sequent(Fs,cons(G2,Gs)),NF))</RHS></RULE><RULE><LHS>u'12'2(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(Fs,cons(x'2d(G1),Gs)),NF)</LHS><RHS>u'13'1(reduce'ii'in(sequent(cons(G1,Fs),Gs),NF))</RHS></RULE><RULE><LHS>u'13'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(nil,cons(p(V),Gs)),sequent(Left,Right))</LHS><RHS>u'14'1(reduce'ii'in(sequent(nil,Gs),sequent(Left,cons(p(V),Right))))</RHS></RULE><RULE><LHS>u'14'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(nil,nil),sequent(F1,F2))</LHS><RHS>u'15'1(intersect'ii'in(F1,F2))</RHS></RULE><RULE><LHS>u'15'1(intersect'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>tautology'i'in(F)</LHS><RHS>u'16'1(reduce'ii'in(sequent(nil,cons(F,nil)),sequent(nil,nil)))</RHS></RULE><RULE><LHS>u'16'1(reduce'ii'out)</LHS><RHS>tautology'i'out</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_reduce'ii'in(sequent(cons(if(A,B),Fs),Gs),NF)</LHS><RHS>Marked_reduce'ii'in(sequent(cons(x'2b(x'2d(B),A),Fs),Gs),NF)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_reduce'ii'in(sequent(cons(iff(A,B),Fs),Gs),NF)</LHS><RHS>Marked_reduce'ii'in(sequent(cons(x'2a(if(A,B),if(B,A)),Fs),Gs),NF)</RHS></DPRULE><DPRULE num="2"><LHS>Marked_reduce'ii'in(sequent(cons(p(V),Fs),Gs),sequent(Left,Right))</LHS><RHS>Marked_reduce'ii'in(sequent(Fs,Gs),sequent(cons(p(V),Left),Right))</RHS></DPRULE><DPRULE num="3"><LHS>Marked_reduce'ii'in(sequent(Fs,cons(x'2d(G1),Gs)),NF)</LHS><RHS>Marked_reduce'ii'in(sequent(cons(G1,Fs),Gs),NF)</RHS></DPRULE><DPRULE num="4"><LHS>Marked_reduce'ii'in(sequent(nil,cons(p(V),Gs)),sequent(Left,Right))</LHS><RHS>Marked_reduce'ii'in(sequent(nil,Gs),sequent(Left,cons(p(V),Right)))</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>intersect'ii'in(cons(X,X0),cons(X,X1))</LHS><RHS>intersect'ii'out</RHS></RULE><RULE><LHS>intersect'ii'in(Xs,cons(X0,Ys))</LHS><RHS>u'1'1(intersect'ii'in(Xs,Ys))</RHS></RULE><RULE><LHS>u'1'1(intersect'ii'out)</LHS><RHS>intersect'ii'out</RHS></RULE><RULE><LHS>intersect'ii'in(cons(X0,Xs),Ys)</LHS><RHS>u'2'1(intersect'ii'in(Xs,Ys))</RHS></RULE><RULE><LHS>u'2'1(intersect'ii'out)</LHS><RHS>intersect'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(cons(if(A,B),Fs),Gs),NF)</LHS><RHS>u'3'1(reduce'ii'in(sequent(cons(x'2b(x'2d(B),A),Fs),Gs),NF))</RHS></RULE><RULE><LHS>u'3'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(cons(iff(A,B),Fs),Gs),NF)</LHS><RHS>u'4'1(reduce'ii'in(sequent(cons(x'2a(if(A,B),if(B,A)),Fs),Gs),NF))</RHS></RULE><RULE><LHS>u'4'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(cons(x'2a(F1,F2),Fs),Gs),NF)</LHS><RHS>u'5'1(reduce'ii'in(sequent(cons(F1,cons(F2,Fs)),Gs),NF))</RHS></RULE><RULE><LHS>u'5'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(cons(x'2b(F1,F2),Fs),Gs),NF)</LHS><RHS>u'6'1(reduce'ii'in(sequent(cons(F1,Fs),Gs),NF),F2,Fs,Gs,NF)</RHS></RULE><RULE><LHS>u'6'1(reduce'ii'out,F2,Fs,Gs,NF)</LHS><RHS>u'6'2(reduce'ii'in(sequent(cons(F2,Fs),Gs),NF))</RHS></RULE><RULE><LHS>u'6'2(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(cons(x'2d(F1),Fs),Gs),NF)</LHS><RHS>u'7'1(reduce'ii'in(sequent(Fs,cons(F1,Gs)),NF))</RHS></RULE><RULE><LHS>u'7'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(Fs,cons(if(A,B),Gs)),NF)</LHS><RHS>u'8'1(reduce'ii'in(sequent(Fs,cons(x'2b(x'2d(B),A),Gs)),NF))</RHS></RULE><RULE><LHS>u'8'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(Fs,cons(iff(A,B),Gs)),NF)</LHS><RHS>u'9'1(reduce'ii'in(sequent(Fs,cons(x'2a(if(A,B),if(B,A)),Gs)),NF))</RHS></RULE><RULE><LHS>u'9'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(cons(p(V),Fs),Gs),sequent(Left,Right))</LHS><RHS>u'10'1(reduce'ii'in(sequent(Fs,Gs),sequent(cons(p(V),Left),Right)))</RHS></RULE><RULE><LHS>u'10'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(Fs,cons(x'2b(G1,G2),Gs)),NF)</LHS><RHS>u'11'1(reduce'ii'in(sequent(Fs,cons(G1,cons(G2,Gs))),NF))</RHS></RULE><RULE><LHS>u'11'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(Fs,cons(x'2a(G1,G2),Gs)),NF)</LHS><RHS>u'12'1(reduce'ii'in(sequent(Fs,cons(G1,Gs)),NF),Fs,G2,Gs,NF)</RHS></RULE><RULE><LHS>u'12'1(reduce'ii'out,Fs,G2,Gs,NF)</LHS><RHS>u'12'2(reduce'ii'in(sequent(Fs,cons(G2,Gs)),NF))</RHS></RULE><RULE><LHS>u'12'2(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(Fs,cons(x'2d(G1),Gs)),NF)</LHS><RHS>u'13'1(reduce'ii'in(sequent(cons(G1,Fs),Gs),NF))</RHS></RULE><RULE><LHS>u'13'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(nil,cons(p(V),Gs)),sequent(Left,Right))</LHS><RHS>u'14'1(reduce'ii'in(sequent(nil,Gs),sequent(Left,cons(p(V),Right))))</RHS></RULE><RULE><LHS>u'14'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(nil,nil),sequent(F1,F2))</LHS><RHS>u'15'1(intersect'ii'in(F1,F2))</RHS></RULE><RULE><LHS>u'15'1(intersect'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>tautology'i'in(F)</LHS><RHS>u'16'1(reduce'ii'in(sequent(nil,cons(F,nil)),sequent(nil,nil)))</RHS></RULE><RULE><LHS>u'16'1(reduce'ii'out)</LHS><RHS>tautology'i'out</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_reduce'ii'in(sequent(cons(if(A,B),Fs),Gs),NF)</LHS><RHS>Marked_reduce'ii'in(sequent(cons(x'2b(x'2d(B),A),Fs),Gs),NF)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_reduce'ii'in(sequent(cons(iff(A,B),Fs),Gs),NF)</LHS><RHS>Marked_reduce'ii'in(sequent(cons(x'2a(if(A,B),if(B,A)),Fs),Gs),NF)</RHS></DPRULE><DPRULE num="2"><LHS>Marked_reduce'ii'in(sequent(cons(p(V),Fs),Gs),sequent(Left,Right))</LHS><RHS>Marked_reduce'ii'in(sequent(Fs,Gs),sequent(cons(p(V),Left),Right))</RHS></DPRULE><DPRULE num="3"><LHS>Marked_reduce'ii'in(sequent(Fs,cons(x'2d(G1),Gs)),NF)</LHS><RHS>Marked_reduce'ii'in(sequent(cons(G1,Fs),Gs),NF)</RHS></DPRULE><DPRULE num="4"><LHS>Marked_reduce'ii'in(sequent(nil,cons(p(V),Gs)),sequent(Left,Right))</LHS><RHS>Marked_reduce'ii'in(sequent(nil,Gs),sequent(Left,cons(p(V),Right)))</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><ORDERING type="poly"><POLYSYMB><SYMBOL><NAME>intersect'ii'out</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>tautology'i'out</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>3</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>u'6'1</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>x'2b</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>u'12'1</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>u'2'1</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>u'9'1</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>u'4'1</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>cons</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF></MONOME></POLYNOMIAL><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></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>u'7'1</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>if</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>u'13'1</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>reduce'ii'in</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>p</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>iff</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>u'16'1</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>3</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>intersect'ii'in</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>u'6'2</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>x'2d</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>u'12'2</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>u'3'1</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>u'10'1</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>x'2a</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>u'15'1</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>u'1'1</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>Marked_reduce'ii'in</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><POLYSYMB><SYMBOL><NAME>u'8'1</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>reduce'ii'out</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>u'14'1</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>sequent</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>3</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>u'11'1</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>u'5'1</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>tautology'i'in</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>3</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></ORDERING><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_reduce'ii'in(sequent(cons(if(A,B),Fs),Gs),NF)</LHS><RHS>Marked_reduce'ii'in(sequent(cons(x'2b(x'2d(B),A),Fs),Gs),NF)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_reduce'ii'in(sequent(cons(p(V),Fs),Gs),sequent(Left,Right))</LHS><RHS>Marked_reduce'ii'in(sequent(Fs,Gs),sequent(cons(p(V),Left),Right))</RHS></DPRULE><DPRULE num="2"><LHS>Marked_reduce'ii'in(sequent(Fs,cons(x'2d(G1),Gs)),NF)</LHS><RHS>Marked_reduce'ii'in(sequent(cons(G1,Fs),Gs),NF)</RHS></DPRULE><DPRULE num="3"><LHS>Marked_reduce'ii'in(sequent(nil,cons(p(V),Gs)),sequent(Left,Right))</LHS><RHS>Marked_reduce'ii'in(sequent(nil,Gs),sequent(Left,cons(p(V),Right)))</RHS></DPRULE></DPLIST></STRICTPAIRS></CRITERION><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>intersect'ii'in(cons(X,X0),cons(X,X1))</LHS><RHS>intersect'ii'out</RHS></RULE><RULE><LHS>intersect'ii'in(Xs,cons(X0,Ys))</LHS><RHS>u'1'1(intersect'ii'in(Xs,Ys))</RHS></RULE><RULE><LHS>u'1'1(intersect'ii'out)</LHS><RHS>intersect'ii'out</RHS></RULE><RULE><LHS>intersect'ii'in(cons(X0,Xs),Ys)</LHS><RHS>u'2'1(intersect'ii'in(Xs,Ys))</RHS></RULE><RULE><LHS>u'2'1(intersect'ii'out)</LHS><RHS>intersect'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(cons(if(A,B),Fs),Gs),NF)</LHS><RHS>u'3'1(reduce'ii'in(sequent(cons(x'2b(x'2d(B),A),Fs),Gs),NF))</RHS></RULE><RULE><LHS>u'3'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(cons(iff(A,B),Fs),Gs),NF)</LHS><RHS>u'4'1(reduce'ii'in(sequent(cons(x'2a(if(A,B),if(B,A)),Fs),Gs),NF))</RHS></RULE><RULE><LHS>u'4'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(cons(x'2a(F1,F2),Fs),Gs),NF)</LHS><RHS>u'5'1(reduce'ii'in(sequent(cons(F1,cons(F2,Fs)),Gs),NF))</RHS></RULE><RULE><LHS>u'5'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(cons(x'2b(F1,F2),Fs),Gs),NF)</LHS><RHS>u'6'1(reduce'ii'in(sequent(cons(F1,Fs),Gs),NF),F2,Fs,Gs,NF)</RHS></RULE><RULE><LHS>u'6'1(reduce'ii'out,F2,Fs,Gs,NF)</LHS><RHS>u'6'2(reduce'ii'in(sequent(cons(F2,Fs),Gs),NF))</RHS></RULE><RULE><LHS>u'6'2(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(cons(x'2d(F1),Fs),Gs),NF)</LHS><RHS>u'7'1(reduce'ii'in(sequent(Fs,cons(F1,Gs)),NF))</RHS></RULE><RULE><LHS>u'7'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(Fs,cons(if(A,B),Gs)),NF)</LHS><RHS>u'8'1(reduce'ii'in(sequent(Fs,cons(x'2b(x'2d(B),A),Gs)),NF))</RHS></RULE><RULE><LHS>u'8'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(Fs,cons(iff(A,B),Gs)),NF)</LHS><RHS>u'9'1(reduce'ii'in(sequent(Fs,cons(x'2a(if(A,B),if(B,A)),Gs)),NF))</RHS></RULE><RULE><LHS>u'9'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(cons(p(V),Fs),Gs),sequent(Left,Right))</LHS><RHS>u'10'1(reduce'ii'in(sequent(Fs,Gs),sequent(cons(p(V),Left),Right)))</RHS></RULE><RULE><LHS>u'10'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(Fs,cons(x'2b(G1,G2),Gs)),NF)</LHS><RHS>u'11'1(reduce'ii'in(sequent(Fs,cons(G1,cons(G2,Gs))),NF))</RHS></RULE><RULE><LHS>u'11'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(Fs,cons(x'2a(G1,G2),Gs)),NF)</LHS><RHS>u'12'1(reduce'ii'in(sequent(Fs,cons(G1,Gs)),NF),Fs,G2,Gs,NF)</RHS></RULE><RULE><LHS>u'12'1(reduce'ii'out,Fs,G2,Gs,NF)</LHS><RHS>u'12'2(reduce'ii'in(sequent(Fs,cons(G2,Gs)),NF))</RHS></RULE><RULE><LHS>u'12'2(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(Fs,cons(x'2d(G1),Gs)),NF)</LHS><RHS>u'13'1(reduce'ii'in(sequent(cons(G1,Fs),Gs),NF))</RHS></RULE><RULE><LHS>u'13'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(nil,cons(p(V),Gs)),sequent(Left,Right))</LHS><RHS>u'14'1(reduce'ii'in(sequent(nil,Gs),sequent(Left,cons(p(V),Right))))</RHS></RULE><RULE><LHS>u'14'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(nil,nil),sequent(F1,F2))</LHS><RHS>u'15'1(intersect'ii'in(F1,F2))</RHS></RULE><RULE><LHS>u'15'1(intersect'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>tautology'i'in(F)</LHS><RHS>u'16'1(reduce'ii'in(sequent(nil,cons(F,nil)),sequent(nil,nil)))</RHS></RULE><RULE><LHS>u'16'1(reduce'ii'out)</LHS><RHS>tautology'i'out</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_reduce'ii'in(sequent(cons(iff(A,B),Fs),Gs),NF)</LHS><RHS>Marked_reduce'ii'in(sequent(cons(x'2a(if(A,B),if(B,A)),Fs),Gs),NF)</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></PROPERTY></PROPERTY></PROPERTY></PROPERTY></PROPERTY></PROPERTY></PROPERTY><PROPERTY criterion="ordering" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>intersect'ii'in(cons(X,X0),cons(X,X1))</LHS><RHS>intersect'ii'out</RHS></RULE><RULE><LHS>intersect'ii'in(Xs,cons(X0,Ys))</LHS><RHS>u'1'1(intersect'ii'in(Xs,Ys))</RHS></RULE><RULE><LHS>u'1'1(intersect'ii'out)</LHS><RHS>intersect'ii'out</RHS></RULE><RULE><LHS>intersect'ii'in(cons(X0,Xs),Ys)</LHS><RHS>u'2'1(intersect'ii'in(Xs,Ys))</RHS></RULE><RULE><LHS>u'2'1(intersect'ii'out)</LHS><RHS>intersect'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(cons(if(A,B),Fs),Gs),NF)</LHS><RHS>u'3'1(reduce'ii'in(sequent(cons(x'2b(x'2d(B),A),Fs),Gs),NF))</RHS></RULE><RULE><LHS>u'3'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(cons(iff(A,B),Fs),Gs),NF)</LHS><RHS>u'4'1(reduce'ii'in(sequent(cons(x'2a(if(A,B),if(B,A)),Fs),Gs),NF))</RHS></RULE><RULE><LHS>u'4'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(cons(x'2a(F1,F2),Fs),Gs),NF)</LHS><RHS>u'5'1(reduce'ii'in(sequent(cons(F1,cons(F2,Fs)),Gs),NF))</RHS></RULE><RULE><LHS>u'5'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(cons(x'2b(F1,F2),Fs),Gs),NF)</LHS><RHS>u'6'1(reduce'ii'in(sequent(cons(F1,Fs),Gs),NF),F2,Fs,Gs,NF)</RHS></RULE><RULE><LHS>u'6'1(reduce'ii'out,F2,Fs,Gs,NF)</LHS><RHS>u'6'2(reduce'ii'in(sequent(cons(F2,Fs),Gs),NF))</RHS></RULE><RULE><LHS>u'6'2(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(cons(x'2d(F1),Fs),Gs),NF)</LHS><RHS>u'7'1(reduce'ii'in(sequent(Fs,cons(F1,Gs)),NF))</RHS></RULE><RULE><LHS>u'7'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(Fs,cons(if(A,B),Gs)),NF)</LHS><RHS>u'8'1(reduce'ii'in(sequent(Fs,cons(x'2b(x'2d(B),A),Gs)),NF))</RHS></RULE><RULE><LHS>u'8'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(Fs,cons(iff(A,B),Gs)),NF)</LHS><RHS>u'9'1(reduce'ii'in(sequent(Fs,cons(x'2a(if(A,B),if(B,A)),Gs)),NF))</RHS></RULE><RULE><LHS>u'9'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(cons(p(V),Fs),Gs),sequent(Left,Right))</LHS><RHS>u'10'1(reduce'ii'in(sequent(Fs,Gs),sequent(cons(p(V),Left),Right)))</RHS></RULE><RULE><LHS>u'10'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(Fs,cons(x'2b(G1,G2),Gs)),NF)</LHS><RHS>u'11'1(reduce'ii'in(sequent(Fs,cons(G1,cons(G2,Gs))),NF))</RHS></RULE><RULE><LHS>u'11'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(Fs,cons(x'2a(G1,G2),Gs)),NF)</LHS><RHS>u'12'1(reduce'ii'in(sequent(Fs,cons(G1,Gs)),NF),Fs,G2,Gs,NF)</RHS></RULE><RULE><LHS>u'12'1(reduce'ii'out,Fs,G2,Gs,NF)</LHS><RHS>u'12'2(reduce'ii'in(sequent(Fs,cons(G2,Gs)),NF))</RHS></RULE><RULE><LHS>u'12'2(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(Fs,cons(x'2d(G1),Gs)),NF)</LHS><RHS>u'13'1(reduce'ii'in(sequent(cons(G1,Fs),Gs),NF))</RHS></RULE><RULE><LHS>u'13'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(nil,cons(p(V),Gs)),sequent(Left,Right))</LHS><RHS>u'14'1(reduce'ii'in(sequent(nil,Gs),sequent(Left,cons(p(V),Right))))</RHS></RULE><RULE><LHS>u'14'1(reduce'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>reduce'ii'in(sequent(nil,nil),sequent(F1,F2))</LHS><RHS>u'15'1(intersect'ii'in(F1,F2))</RHS></RULE><RULE><LHS>u'15'1(intersect'ii'out)</LHS><RHS>reduce'ii'out</RHS></RULE><RULE><LHS>tautology'i'in(F)</LHS><RHS>u'16'1(reduce'ii'in(sequent(nil,cons(F,nil)),sequent(nil,nil)))</RHS></RULE><RULE><LHS>u'16'1(reduce'ii'out)</LHS><RHS>tautology'i'out</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_intersect'ii'in(Xs,cons(X0,Ys))</LHS><RHS>Marked_intersect'ii'in(Xs,Ys)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_intersect'ii'in(cons(X0,Xs),Ys)</LHS><RHS>Marked_intersect'ii'in(Xs,Ys)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><ORDERING type="poly"><POLYSYMB><SYMBOL><NAME>intersect'ii'out</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>tautology'i'out</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>3</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>u'6'1</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>x'2b</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>u'12'1</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>u'2'1</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>u'9'1</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>u'4'1</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>cons</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="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>u'7'1</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>if</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>u'13'1</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>reduce'ii'in</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>p</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>iff</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>u'16'1</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>3</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>intersect'ii'in</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>u'6'2</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>x'2d</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>u'12'2</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>u'3'1</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>Marked_intersect'ii'in</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>3</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>3</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>u'10'1</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>x'2a</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>u'15'1</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>u'1'1</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>u'8'1</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>reduce'ii'out</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>u'14'1</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>sequent</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>u'11'1</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>u'5'1</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>tautology'i'in</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>3</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></ORDERING></CRITERION></PROPERTY></PROPERTY></PROPERTY></PROOF>
