MAYBE 1084.53/297.03 MAYBE 1084.53/297.03 1084.53/297.03 We are left with following problem, upon which TcT provides the 1084.53/297.03 certificate MAYBE. 1084.53/297.03 1084.53/297.03 Strict Trs: 1084.53/297.03 { a__f(X) -> cons(mark(X), f(g(X))) 1084.53/297.03 , a__f(X) -> f(X) 1084.53/297.03 , mark(cons(X1, X2)) -> cons(mark(X1), X2) 1084.53/297.03 , mark(f(X)) -> a__f(mark(X)) 1084.53/297.03 , mark(g(X)) -> a__g(mark(X)) 1084.53/297.03 , mark(0()) -> 0() 1084.53/297.03 , mark(s(X)) -> s(mark(X)) 1084.53/297.03 , mark(sel(X1, X2)) -> a__sel(mark(X1), mark(X2)) 1084.53/297.03 , a__g(X) -> g(X) 1084.53/297.03 , a__g(0()) -> s(0()) 1084.53/297.03 , a__g(s(X)) -> s(s(a__g(mark(X)))) 1084.53/297.03 , a__sel(X1, X2) -> sel(X1, X2) 1084.53/297.03 , a__sel(0(), cons(X, Y)) -> mark(X) 1084.53/297.03 , a__sel(s(X), cons(Y, Z)) -> a__sel(mark(X), mark(Z)) } 1084.53/297.03 Obligation: 1084.53/297.03 runtime complexity 1084.53/297.03 Answer: 1084.53/297.03 MAYBE 1084.53/297.03 1084.53/297.03 None of the processors succeeded. 1084.53/297.03 1084.53/297.03 Details of failed attempt(s): 1084.53/297.03 ----------------------------- 1084.53/297.03 1) 'With Problem ... (timeout of 297 seconds)' failed due to the 1084.53/297.03 following reason: 1084.53/297.03 1084.53/297.03 Computation stopped due to timeout after 297.0 seconds. 1084.53/297.03 1084.53/297.03 2) 'Best' failed due to the following reason: 1084.53/297.03 1084.53/297.03 None of the processors succeeded. 1084.53/297.03 1084.53/297.03 Details of failed attempt(s): 1084.53/297.03 ----------------------------- 1084.53/297.03 1) 'With Problem ... (timeout of 148 seconds) (timeout of 297 1084.53/297.03 seconds)' failed due to the following reason: 1084.53/297.03 1084.53/297.03 None of the processors succeeded. 1084.53/297.03 1084.53/297.03 Details of failed attempt(s): 1084.53/297.03 ----------------------------- 1084.53/297.03 1) 'empty' failed due to the following reason: 1084.53/297.03 1084.53/297.03 Empty strict component of the problem is NOT empty. 1084.53/297.03 1084.53/297.03 2) 'With Problem ...' failed due to the following reason: 1084.53/297.03 1084.53/297.03 None of the processors succeeded. 1084.53/297.03 1084.53/297.03 Details of failed attempt(s): 1084.53/297.03 ----------------------------- 1084.53/297.03 1) 'empty' failed due to the following reason: 1084.53/297.03 1084.53/297.03 Empty strict component of the problem is NOT empty. 1084.53/297.03 1084.53/297.03 2) 'Fastest' failed due to the following reason: 1084.53/297.03 1084.53/297.03 None of the processors succeeded. 1084.53/297.03 1084.53/297.03 Details of failed attempt(s): 1084.53/297.03 ----------------------------- 1084.53/297.03 1) 'With Problem ...' failed due to the following reason: 1084.53/297.03 1084.53/297.03 None of the processors succeeded. 1084.53/297.03 1084.53/297.03 Details of failed attempt(s): 1084.53/297.03 ----------------------------- 1084.53/297.03 1) 'empty' failed due to the following reason: 1084.53/297.03 1084.53/297.03 Empty strict component of the problem is NOT empty. 1084.53/297.03 1084.53/297.03 2) 'With Problem ...' failed due to the following reason: 1084.53/297.03 1084.53/297.03 None of the processors succeeded. 1084.53/297.03 1084.53/297.03 Details of failed attempt(s): 1084.53/297.03 ----------------------------- 1084.53/297.03 1) 'empty' failed due to the following reason: 1084.53/297.03 1084.53/297.03 Empty strict component of the problem is NOT empty. 1084.53/297.03 1084.53/297.03 2) 'With Problem ...' failed due to the following reason: 1084.53/297.03 1084.53/297.03 None of the processors succeeded. 1084.53/297.03 1084.53/297.03 Details of failed attempt(s): 1084.53/297.03 ----------------------------- 1084.53/297.03 1) 'empty' failed due to the following reason: 1084.53/297.03 1084.53/297.03 Empty strict component of the problem is NOT empty. 1084.53/297.03 1084.53/297.03 2) 'With Problem ...' failed due to the following reason: 1084.53/297.03 1084.53/297.03 Empty strict component of the problem is NOT empty. 1084.53/297.03 1084.53/297.03 1084.53/297.03 1084.53/297.03 1084.53/297.03 2) 'With Problem ...' failed due to the following reason: 1084.53/297.03 1084.53/297.03 None of the processors succeeded. 1084.53/297.03 1084.53/297.03 Details of failed attempt(s): 1084.53/297.03 ----------------------------- 1084.53/297.03 1) 'empty' failed due to the following reason: 1084.53/297.03 1084.53/297.03 Empty strict component of the problem is NOT empty. 1084.53/297.03 1084.53/297.03 2) 'With Problem ...' failed due to the following reason: 1084.53/297.03 1084.53/297.03 Empty strict component of the problem is NOT empty. 1084.53/297.03 1084.53/297.03 1084.53/297.03 1084.53/297.03 1084.53/297.03 1084.53/297.03 2) 'Best' failed due to the following reason: 1084.53/297.03 1084.53/297.03 None of the processors succeeded. 1084.53/297.03 1084.53/297.03 Details of failed attempt(s): 1084.53/297.03 ----------------------------- 1084.53/297.03 1) 'bsearch-popstar (timeout of 297 seconds)' failed due to the 1084.53/297.03 following reason: 1084.53/297.03 1084.53/297.03 The processor is inapplicable, reason: 1084.53/297.03 Processor only applicable for innermost runtime complexity analysis 1084.53/297.03 1084.53/297.03 2) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due 1084.53/297.03 to the following reason: 1084.53/297.03 1084.53/297.03 The processor is inapplicable, reason: 1084.53/297.03 Processor only applicable for innermost runtime complexity analysis 1084.53/297.03 1084.53/297.03 1084.53/297.03 3) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)' 1084.53/297.03 failed due to the following reason: 1084.53/297.03 1084.53/297.03 None of the processors succeeded. 1084.53/297.03 1084.53/297.03 Details of failed attempt(s): 1084.53/297.03 ----------------------------- 1084.53/297.03 1) 'Bounds with minimal-enrichment and initial automaton 'match'' 1084.53/297.03 failed due to the following reason: 1084.53/297.03 1084.53/297.03 match-boundness of the problem could not be verified. 1084.53/297.03 1084.53/297.03 2) 'Bounds with perSymbol-enrichment and initial automaton 'match'' 1084.53/297.03 failed due to the following reason: 1084.53/297.03 1084.53/297.03 match-boundness of the problem could not be verified. 1084.53/297.03 1084.53/297.03 1084.53/297.03 1084.53/297.03 3) 'Weak Dependency Pairs (timeout of 297 seconds)' failed due to 1084.53/297.03 the following reason: 1084.53/297.03 1084.53/297.03 We add the following weak dependency pairs: 1084.53/297.03 1084.53/297.03 Strict DPs: 1084.53/297.03 { a__f^#(X) -> c_1(mark^#(X), X) 1084.53/297.03 , a__f^#(X) -> c_2(X) 1084.53/297.03 , mark^#(cons(X1, X2)) -> c_3(mark^#(X1), X2) 1084.53/297.03 , mark^#(f(X)) -> c_4(a__f^#(mark(X))) 1084.53/297.03 , mark^#(g(X)) -> c_5(a__g^#(mark(X))) 1084.53/297.03 , mark^#(0()) -> c_6() 1084.53/297.03 , mark^#(s(X)) -> c_7(mark^#(X)) 1084.53/297.03 , mark^#(sel(X1, X2)) -> c_8(a__sel^#(mark(X1), mark(X2))) 1084.53/297.03 , a__g^#(X) -> c_9(X) 1084.53/297.03 , a__g^#(0()) -> c_10() 1084.53/297.03 , a__g^#(s(X)) -> c_11(a__g^#(mark(X))) 1084.53/297.03 , a__sel^#(X1, X2) -> c_12(X1, X2) 1084.53/297.03 , a__sel^#(0(), cons(X, Y)) -> c_13(mark^#(X)) 1084.53/297.03 , a__sel^#(s(X), cons(Y, Z)) -> c_14(a__sel^#(mark(X), mark(Z))) } 1084.53/297.03 1084.53/297.03 and mark the set of starting terms. 1084.53/297.03 1084.53/297.03 We are left with following problem, upon which TcT provides the 1084.53/297.03 certificate MAYBE. 1084.53/297.03 1084.53/297.03 Strict DPs: 1084.53/297.03 { a__f^#(X) -> c_1(mark^#(X), X) 1084.53/297.03 , a__f^#(X) -> c_2(X) 1084.53/297.03 , mark^#(cons(X1, X2)) -> c_3(mark^#(X1), X2) 1084.53/297.03 , mark^#(f(X)) -> c_4(a__f^#(mark(X))) 1084.53/297.03 , mark^#(g(X)) -> c_5(a__g^#(mark(X))) 1084.53/297.03 , mark^#(0()) -> c_6() 1084.53/297.03 , mark^#(s(X)) -> c_7(mark^#(X)) 1084.53/297.03 , mark^#(sel(X1, X2)) -> c_8(a__sel^#(mark(X1), mark(X2))) 1084.53/297.03 , a__g^#(X) -> c_9(X) 1084.53/297.03 , a__g^#(0()) -> c_10() 1084.53/297.03 , a__g^#(s(X)) -> c_11(a__g^#(mark(X))) 1084.53/297.03 , a__sel^#(X1, X2) -> c_12(X1, X2) 1084.53/297.03 , a__sel^#(0(), cons(X, Y)) -> c_13(mark^#(X)) 1084.53/297.03 , a__sel^#(s(X), cons(Y, Z)) -> c_14(a__sel^#(mark(X), mark(Z))) } 1084.53/297.03 Strict Trs: 1084.53/297.03 { a__f(X) -> cons(mark(X), f(g(X))) 1084.53/297.03 , a__f(X) -> f(X) 1084.53/297.03 , mark(cons(X1, X2)) -> cons(mark(X1), X2) 1084.53/297.03 , mark(f(X)) -> a__f(mark(X)) 1084.53/297.03 , mark(g(X)) -> a__g(mark(X)) 1084.53/297.03 , mark(0()) -> 0() 1084.53/297.03 , mark(s(X)) -> s(mark(X)) 1084.53/297.03 , mark(sel(X1, X2)) -> a__sel(mark(X1), mark(X2)) 1084.53/297.03 , a__g(X) -> g(X) 1084.53/297.03 , a__g(0()) -> s(0()) 1084.53/297.03 , a__g(s(X)) -> s(s(a__g(mark(X)))) 1084.53/297.03 , a__sel(X1, X2) -> sel(X1, X2) 1084.53/297.03 , a__sel(0(), cons(X, Y)) -> mark(X) 1084.53/297.03 , a__sel(s(X), cons(Y, Z)) -> a__sel(mark(X), mark(Z)) } 1084.53/297.03 Obligation: 1084.53/297.03 runtime complexity 1084.53/297.03 Answer: 1084.53/297.03 MAYBE 1084.53/297.03 1084.53/297.03 We estimate the number of application of {6,10} by applications of 1084.53/297.03 Pre({6,10}) = {1,2,3,5,7,9,11,12,13}. Here rules are labeled as 1084.53/297.03 follows: 1084.53/297.03 1084.53/297.03 DPs: 1084.53/297.03 { 1: a__f^#(X) -> c_1(mark^#(X), X) 1084.53/297.03 , 2: a__f^#(X) -> c_2(X) 1084.53/297.03 , 3: mark^#(cons(X1, X2)) -> c_3(mark^#(X1), X2) 1084.53/297.03 , 4: mark^#(f(X)) -> c_4(a__f^#(mark(X))) 1084.53/297.03 , 5: mark^#(g(X)) -> c_5(a__g^#(mark(X))) 1084.53/297.03 , 6: mark^#(0()) -> c_6() 1084.53/297.03 , 7: mark^#(s(X)) -> c_7(mark^#(X)) 1084.53/297.03 , 8: mark^#(sel(X1, X2)) -> c_8(a__sel^#(mark(X1), mark(X2))) 1084.53/297.03 , 9: a__g^#(X) -> c_9(X) 1084.53/297.03 , 10: a__g^#(0()) -> c_10() 1084.53/297.03 , 11: a__g^#(s(X)) -> c_11(a__g^#(mark(X))) 1084.53/297.03 , 12: a__sel^#(X1, X2) -> c_12(X1, X2) 1084.53/297.03 , 13: a__sel^#(0(), cons(X, Y)) -> c_13(mark^#(X)) 1084.53/297.03 , 14: a__sel^#(s(X), cons(Y, Z)) -> 1084.53/297.03 c_14(a__sel^#(mark(X), mark(Z))) } 1084.53/297.03 1084.53/297.03 We are left with following problem, upon which TcT provides the 1084.53/297.03 certificate MAYBE. 1084.53/297.03 1084.53/297.03 Strict DPs: 1084.53/297.03 { a__f^#(X) -> c_1(mark^#(X), X) 1084.53/297.03 , a__f^#(X) -> c_2(X) 1084.53/297.03 , mark^#(cons(X1, X2)) -> c_3(mark^#(X1), X2) 1084.53/297.03 , mark^#(f(X)) -> c_4(a__f^#(mark(X))) 1084.53/297.03 , mark^#(g(X)) -> c_5(a__g^#(mark(X))) 1084.53/297.03 , mark^#(s(X)) -> c_7(mark^#(X)) 1084.53/297.03 , mark^#(sel(X1, X2)) -> c_8(a__sel^#(mark(X1), mark(X2))) 1084.53/297.03 , a__g^#(X) -> c_9(X) 1084.53/297.03 , a__g^#(s(X)) -> c_11(a__g^#(mark(X))) 1084.53/297.03 , a__sel^#(X1, X2) -> c_12(X1, X2) 1084.53/297.03 , a__sel^#(0(), cons(X, Y)) -> c_13(mark^#(X)) 1084.53/297.03 , a__sel^#(s(X), cons(Y, Z)) -> c_14(a__sel^#(mark(X), mark(Z))) } 1084.53/297.03 Strict Trs: 1084.53/297.03 { a__f(X) -> cons(mark(X), f(g(X))) 1084.53/297.03 , a__f(X) -> f(X) 1084.53/297.03 , mark(cons(X1, X2)) -> cons(mark(X1), X2) 1084.53/297.03 , mark(f(X)) -> a__f(mark(X)) 1084.53/297.03 , mark(g(X)) -> a__g(mark(X)) 1084.53/297.03 , mark(0()) -> 0() 1084.53/297.03 , mark(s(X)) -> s(mark(X)) 1084.53/297.03 , mark(sel(X1, X2)) -> a__sel(mark(X1), mark(X2)) 1084.53/297.03 , a__g(X) -> g(X) 1084.53/297.03 , a__g(0()) -> s(0()) 1084.53/297.03 , a__g(s(X)) -> s(s(a__g(mark(X)))) 1084.53/297.03 , a__sel(X1, X2) -> sel(X1, X2) 1084.53/297.03 , a__sel(0(), cons(X, Y)) -> mark(X) 1084.53/297.03 , a__sel(s(X), cons(Y, Z)) -> a__sel(mark(X), mark(Z)) } 1084.53/297.03 Weak DPs: 1084.53/297.03 { mark^#(0()) -> c_6() 1084.53/297.03 , a__g^#(0()) -> c_10() } 1084.53/297.03 Obligation: 1084.53/297.03 runtime complexity 1084.53/297.03 Answer: 1084.53/297.03 MAYBE 1084.53/297.03 1084.53/297.03 Empty strict component of the problem is NOT empty. 1084.53/297.03 1084.53/297.03 1084.53/297.03 Arrrr.. 1084.87/297.35 EOF