MAYBE 'Pop* (timeout of 60.0 seconds)' -------------------------------- Answer: MAYBE Input Problem: innermost runtime-complexity with respect to Rules: { intersect'ii'in(cons(X, X0), cons(X, X1)) -> intersect'ii'out() , intersect'ii'in(Xs, cons(X0, Ys)) -> u'1'1(intersect'ii'in(Xs, Ys)) , u'1'1(intersect'ii'out()) -> intersect'ii'out() , intersect'ii'in(cons(X0, Xs), Ys) -> u'2'1(intersect'ii'in(Xs, Ys)) , u'2'1(intersect'ii'out()) -> intersect'ii'out() , reduce'ii'in(sequent(cons(if(A, B), Fs), Gs), NF) -> u'3'1(reduce'ii'in(sequent(cons(x'2b(x'2d(B), A), Fs), Gs), NF)) , u'3'1(reduce'ii'out()) -> reduce'ii'out() , reduce'ii'in(sequent(cons(iff(A, B), Fs), Gs), NF) -> u'4'1(reduce'ii'in(sequent(cons(x'2a(if(A, B), if(B, A)), Fs), Gs), NF)) , u'4'1(reduce'ii'out()) -> reduce'ii'out() , reduce'ii'in(sequent(cons(x'2a(F1, F2), Fs), Gs), NF) -> u'5'1(reduce'ii'in(sequent(cons(F1, cons(F2, Fs)), Gs), NF)) , u'5'1(reduce'ii'out()) -> reduce'ii'out() , reduce'ii'in(sequent(cons(x'2b(F1, F2), Fs), Gs), NF) -> u'6'1(reduce'ii'in(sequent(cons(F1, Fs), Gs), NF), F2, Fs, Gs, NF) , u'6'1(reduce'ii'out(), F2, Fs, Gs, NF) -> u'6'2(reduce'ii'in(sequent(cons(F2, Fs), Gs), NF)) , u'6'2(reduce'ii'out()) -> reduce'ii'out() , reduce'ii'in(sequent(cons(x'2d(F1), Fs), Gs), NF) -> u'7'1(reduce'ii'in(sequent(Fs, cons(F1, Gs)), NF)) , u'7'1(reduce'ii'out()) -> reduce'ii'out() , reduce'ii'in(sequent(Fs, cons(if(A, B), Gs)), NF) -> u'8'1(reduce'ii'in(sequent(Fs, cons(x'2b(x'2d(B), A), Gs)), NF)) , u'8'1(reduce'ii'out()) -> reduce'ii'out() , reduce'ii'in(sequent(Fs, cons(iff(A, B), Gs)), NF) -> u'9'1(reduce'ii'in(sequent(Fs, cons(x'2a(if(A, B), if(B, A)), Gs)), NF)) , u'9'1(reduce'ii'out()) -> reduce'ii'out() , reduce'ii'in(sequent(cons(p(V), Fs), Gs), sequent(Left, Right)) -> u'10'1(reduce'ii'in(sequent(Fs, Gs), sequent(cons(p(V), Left), Right))) , u'10'1(reduce'ii'out()) -> reduce'ii'out() , reduce'ii'in(sequent(Fs, cons(x'2b(G1, G2), Gs)), NF) -> u'11'1(reduce'ii'in(sequent(Fs, cons(G1, cons(G2, Gs))), NF)) , u'11'1(reduce'ii'out()) -> reduce'ii'out() , reduce'ii'in(sequent(Fs, cons(x'2a(G1, G2), Gs)), NF) -> u'12'1(reduce'ii'in(sequent(Fs, cons(G1, Gs)), NF), Fs, G2, Gs, NF) , u'12'1(reduce'ii'out(), Fs, G2, Gs, NF) -> u'12'2(reduce'ii'in(sequent(Fs, cons(G2, Gs)), NF)) , u'12'2(reduce'ii'out()) -> reduce'ii'out() , reduce'ii'in(sequent(Fs, cons(x'2d(G1), Gs)), NF) -> u'13'1(reduce'ii'in(sequent(cons(G1, Fs), Gs), NF)) , u'13'1(reduce'ii'out()) -> reduce'ii'out() , reduce'ii'in(sequent(nil(), cons(p(V), Gs)), sequent(Left, Right)) -> u'14'1(reduce'ii'in(sequent(nil(), Gs), sequent(Left, cons(p(V), Right)))) , u'14'1(reduce'ii'out()) -> reduce'ii'out() , reduce'ii'in(sequent(nil(), nil()), sequent(F1, F2)) -> u'15'1(intersect'ii'in(F1, F2)) , u'15'1(intersect'ii'out()) -> reduce'ii'out() , tautology'i'in(F) -> u'16'1(reduce'ii'in(sequent(nil(), cons(F, nil())), sequent(nil(), nil()))) , u'16'1(reduce'ii'out()) -> tautology'i'out()} Proof Output: The input cannot be shown compatible