MAYBE 1184.17/297.09 MAYBE 1184.17/297.09 1184.17/297.09 We are left with following problem, upon which TcT provides the 1184.17/297.09 certificate MAYBE. 1184.17/297.09 1184.17/297.09 Strict Trs: 1184.17/297.09 { a__fst(X1, X2) -> fst(X1, X2) 1184.17/297.09 , a__fst(0(), Z) -> nil() 1184.17/297.09 , a__fst(s(X), cons(Y, Z)) -> cons(mark(Y), fst(X, Z)) 1184.17/297.09 , mark(0()) -> 0() 1184.17/297.09 , mark(nil()) -> nil() 1184.17/297.09 , mark(s(X)) -> s(X) 1184.17/297.09 , mark(cons(X1, X2)) -> cons(mark(X1), X2) 1184.17/297.09 , mark(fst(X1, X2)) -> a__fst(mark(X1), mark(X2)) 1184.17/297.09 , mark(from(X)) -> a__from(mark(X)) 1184.17/297.09 , mark(add(X1, X2)) -> a__add(mark(X1), mark(X2)) 1184.17/297.09 , mark(len(X)) -> a__len(mark(X)) 1184.17/297.09 , a__from(X) -> cons(mark(X), from(s(X))) 1184.17/297.09 , a__from(X) -> from(X) 1184.17/297.09 , a__add(X1, X2) -> add(X1, X2) 1184.17/297.09 , a__add(0(), X) -> mark(X) 1184.17/297.09 , a__add(s(X), Y) -> s(add(X, Y)) 1184.17/297.09 , a__len(X) -> len(X) 1184.17/297.09 , a__len(nil()) -> 0() 1184.17/297.09 , a__len(cons(X, Z)) -> s(len(Z)) } 1184.17/297.09 Obligation: 1184.17/297.09 runtime complexity 1184.17/297.09 Answer: 1184.17/297.09 MAYBE 1184.17/297.09 1184.17/297.09 None of the processors succeeded. 1184.17/297.09 1184.17/297.09 Details of failed attempt(s): 1184.17/297.09 ----------------------------- 1184.17/297.09 1) 'With Problem ... (timeout of 297 seconds)' failed due to the 1184.17/297.09 following reason: 1184.17/297.09 1184.17/297.09 Computation stopped due to timeout after 297.0 seconds. 1184.17/297.09 1184.17/297.09 2) 'Best' failed due to the following reason: 1184.17/297.09 1184.17/297.09 None of the processors succeeded. 1184.17/297.09 1184.17/297.09 Details of failed attempt(s): 1184.17/297.09 ----------------------------- 1184.17/297.09 1) 'With Problem ... (timeout of 148 seconds) (timeout of 297 1184.17/297.09 seconds)' failed due to the following reason: 1184.17/297.09 1184.17/297.09 None of the processors succeeded. 1184.17/297.09 1184.17/297.09 Details of failed attempt(s): 1184.17/297.09 ----------------------------- 1184.17/297.09 1) 'empty' failed due to the following reason: 1184.17/297.09 1184.17/297.09 Empty strict component of the problem is NOT empty. 1184.17/297.09 1184.17/297.09 2) 'With Problem ...' failed due to the following reason: 1184.17/297.09 1184.17/297.09 None of the processors succeeded. 1184.17/297.09 1184.17/297.09 Details of failed attempt(s): 1184.17/297.09 ----------------------------- 1184.17/297.09 1) 'empty' failed due to the following reason: 1184.17/297.09 1184.17/297.09 Empty strict component of the problem is NOT empty. 1184.17/297.09 1184.17/297.09 2) 'Fastest' failed due to the following reason: 1184.17/297.09 1184.17/297.09 None of the processors succeeded. 1184.17/297.09 1184.17/297.09 Details of failed attempt(s): 1184.17/297.09 ----------------------------- 1184.17/297.09 1) 'With Problem ...' failed due to the following reason: 1184.17/297.09 1184.17/297.09 None of the processors succeeded. 1184.17/297.09 1184.17/297.09 Details of failed attempt(s): 1184.17/297.09 ----------------------------- 1184.17/297.09 1) 'empty' failed due to the following reason: 1184.17/297.09 1184.17/297.09 Empty strict component of the problem is NOT empty. 1184.17/297.09 1184.17/297.09 2) 'With Problem ...' failed due to the following reason: 1184.17/297.09 1184.17/297.09 None of the processors succeeded. 1184.17/297.09 1184.17/297.09 Details of failed attempt(s): 1184.17/297.09 ----------------------------- 1184.17/297.09 1) 'empty' failed due to the following reason: 1184.17/297.09 1184.17/297.09 Empty strict component of the problem is NOT empty. 1184.17/297.09 1184.17/297.09 2) 'With Problem ...' failed due to the following reason: 1184.17/297.09 1184.17/297.09 None of the processors succeeded. 1184.17/297.09 1184.17/297.09 Details of failed attempt(s): 1184.17/297.09 ----------------------------- 1184.17/297.09 1) 'empty' failed due to the following reason: 1184.17/297.09 1184.17/297.09 Empty strict component of the problem is NOT empty. 1184.17/297.09 1184.17/297.09 2) 'With Problem ...' failed due to the following reason: 1184.17/297.09 1184.17/297.09 Empty strict component of the problem is NOT empty. 1184.17/297.09 1184.17/297.09 1184.17/297.09 1184.17/297.09 1184.17/297.09 2) 'With Problem ...' failed due to the following reason: 1184.17/297.09 1184.17/297.09 None of the processors succeeded. 1184.17/297.09 1184.17/297.09 Details of failed attempt(s): 1184.17/297.09 ----------------------------- 1184.17/297.09 1) 'empty' failed due to the following reason: 1184.17/297.09 1184.17/297.09 Empty strict component of the problem is NOT empty. 1184.17/297.09 1184.17/297.09 2) 'With Problem ...' failed due to the following reason: 1184.17/297.09 1184.17/297.09 Empty strict component of the problem is NOT empty. 1184.17/297.09 1184.17/297.09 1184.17/297.09 1184.17/297.09 1184.17/297.09 1184.17/297.09 2) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)' 1184.17/297.09 failed due to the following reason: 1184.17/297.09 1184.17/297.09 None of the processors succeeded. 1184.17/297.09 1184.17/297.09 Details of failed attempt(s): 1184.17/297.09 ----------------------------- 1184.17/297.09 1) 'Bounds with minimal-enrichment and initial automaton 'match'' 1184.17/297.09 failed due to the following reason: 1184.17/297.09 1184.17/297.09 match-boundness of the problem could not be verified. 1184.17/297.09 1184.17/297.09 2) 'Bounds with perSymbol-enrichment and initial automaton 'match'' 1184.17/297.09 failed due to the following reason: 1184.17/297.09 1184.17/297.09 match-boundness of the problem could not be verified. 1184.17/297.09 1184.17/297.09 1184.17/297.09 3) 'Best' failed due to the following reason: 1184.17/297.09 1184.17/297.09 None of the processors succeeded. 1184.17/297.09 1184.17/297.09 Details of failed attempt(s): 1184.17/297.09 ----------------------------- 1184.17/297.09 1) 'bsearch-popstar (timeout of 297 seconds)' failed due to the 1184.17/297.09 following reason: 1184.17/297.09 1184.17/297.09 The processor is inapplicable, reason: 1184.17/297.09 Processor only applicable for innermost runtime complexity analysis 1184.17/297.09 1184.17/297.09 2) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due 1184.17/297.09 to the following reason: 1184.17/297.09 1184.17/297.09 The processor is inapplicable, reason: 1184.17/297.09 Processor only applicable for innermost runtime complexity analysis 1184.17/297.09 1184.17/297.09 1184.17/297.09 1184.17/297.09 3) 'Weak Dependency Pairs (timeout of 297 seconds)' failed due to 1184.17/297.09 the following reason: 1184.17/297.09 1184.17/297.09 We add the following weak dependency pairs: 1184.17/297.09 1184.17/297.09 Strict DPs: 1184.17/297.09 { a__fst^#(X1, X2) -> c_1(X1, X2) 1184.17/297.09 , a__fst^#(0(), Z) -> c_2() 1184.17/297.09 , a__fst^#(s(X), cons(Y, Z)) -> c_3(mark^#(Y), X, Z) 1184.17/297.09 , mark^#(0()) -> c_4() 1184.17/297.09 , mark^#(nil()) -> c_5() 1184.17/297.09 , mark^#(s(X)) -> c_6(X) 1184.17/297.09 , mark^#(cons(X1, X2)) -> c_7(mark^#(X1), X2) 1184.17/297.09 , mark^#(fst(X1, X2)) -> c_8(a__fst^#(mark(X1), mark(X2))) 1184.17/297.09 , mark^#(from(X)) -> c_9(a__from^#(mark(X))) 1184.17/297.09 , mark^#(add(X1, X2)) -> c_10(a__add^#(mark(X1), mark(X2))) 1184.17/297.09 , mark^#(len(X)) -> c_11(a__len^#(mark(X))) 1184.17/297.09 , a__from^#(X) -> c_12(mark^#(X), X) 1184.17/297.09 , a__from^#(X) -> c_13(X) 1184.17/297.09 , a__add^#(X1, X2) -> c_14(X1, X2) 1184.17/297.09 , a__add^#(0(), X) -> c_15(mark^#(X)) 1184.17/297.09 , a__add^#(s(X), Y) -> c_16(X, Y) 1184.17/297.09 , a__len^#(X) -> c_17(X) 1184.17/297.09 , a__len^#(nil()) -> c_18() 1184.17/297.09 , a__len^#(cons(X, Z)) -> c_19(Z) } 1184.17/297.09 1184.17/297.09 and mark the set of starting terms. 1184.17/297.09 1184.17/297.09 We are left with following problem, upon which TcT provides the 1184.17/297.09 certificate MAYBE. 1184.17/297.09 1184.17/297.09 Strict DPs: 1184.17/297.09 { a__fst^#(X1, X2) -> c_1(X1, X2) 1184.17/297.09 , a__fst^#(0(), Z) -> c_2() 1184.17/297.09 , a__fst^#(s(X), cons(Y, Z)) -> c_3(mark^#(Y), X, Z) 1184.17/297.09 , mark^#(0()) -> c_4() 1184.17/297.09 , mark^#(nil()) -> c_5() 1184.17/297.09 , mark^#(s(X)) -> c_6(X) 1184.17/297.09 , mark^#(cons(X1, X2)) -> c_7(mark^#(X1), X2) 1184.17/297.09 , mark^#(fst(X1, X2)) -> c_8(a__fst^#(mark(X1), mark(X2))) 1184.17/297.09 , mark^#(from(X)) -> c_9(a__from^#(mark(X))) 1184.17/297.09 , mark^#(add(X1, X2)) -> c_10(a__add^#(mark(X1), mark(X2))) 1184.17/297.09 , mark^#(len(X)) -> c_11(a__len^#(mark(X))) 1184.17/297.09 , a__from^#(X) -> c_12(mark^#(X), X) 1184.17/297.09 , a__from^#(X) -> c_13(X) 1184.17/297.09 , a__add^#(X1, X2) -> c_14(X1, X2) 1184.17/297.09 , a__add^#(0(), X) -> c_15(mark^#(X)) 1184.17/297.09 , a__add^#(s(X), Y) -> c_16(X, Y) 1184.17/297.09 , a__len^#(X) -> c_17(X) 1184.17/297.09 , a__len^#(nil()) -> c_18() 1184.17/297.09 , a__len^#(cons(X, Z)) -> c_19(Z) } 1184.17/297.09 Strict Trs: 1184.17/297.09 { a__fst(X1, X2) -> fst(X1, X2) 1184.17/297.09 , a__fst(0(), Z) -> nil() 1184.17/297.09 , a__fst(s(X), cons(Y, Z)) -> cons(mark(Y), fst(X, Z)) 1184.17/297.09 , mark(0()) -> 0() 1184.17/297.09 , mark(nil()) -> nil() 1184.17/297.09 , mark(s(X)) -> s(X) 1184.17/297.09 , mark(cons(X1, X2)) -> cons(mark(X1), X2) 1184.17/297.09 , mark(fst(X1, X2)) -> a__fst(mark(X1), mark(X2)) 1184.17/297.09 , mark(from(X)) -> a__from(mark(X)) 1184.17/297.09 , mark(add(X1, X2)) -> a__add(mark(X1), mark(X2)) 1184.17/297.09 , mark(len(X)) -> a__len(mark(X)) 1184.17/297.09 , a__from(X) -> cons(mark(X), from(s(X))) 1184.17/297.09 , a__from(X) -> from(X) 1184.17/297.09 , a__add(X1, X2) -> add(X1, X2) 1184.17/297.09 , a__add(0(), X) -> mark(X) 1184.17/297.09 , a__add(s(X), Y) -> s(add(X, Y)) 1184.17/297.09 , a__len(X) -> len(X) 1184.17/297.09 , a__len(nil()) -> 0() 1184.17/297.09 , a__len(cons(X, Z)) -> s(len(Z)) } 1184.17/297.09 Obligation: 1184.17/297.09 runtime complexity 1184.17/297.09 Answer: 1184.17/297.09 MAYBE 1184.17/297.09 1184.17/297.09 We estimate the number of application of {2,4,5,18} by applications 1184.17/297.09 of Pre({2,4,5,18}) = {1,3,6,7,8,11,12,13,14,15,16,17,19}. Here 1184.17/297.09 rules are labeled as follows: 1184.17/297.09 1184.17/297.09 DPs: 1184.17/297.09 { 1: a__fst^#(X1, X2) -> c_1(X1, X2) 1184.17/297.09 , 2: a__fst^#(0(), Z) -> c_2() 1184.17/297.09 , 3: a__fst^#(s(X), cons(Y, Z)) -> c_3(mark^#(Y), X, Z) 1184.17/297.09 , 4: mark^#(0()) -> c_4() 1184.17/297.09 , 5: mark^#(nil()) -> c_5() 1184.17/297.09 , 6: mark^#(s(X)) -> c_6(X) 1184.17/297.09 , 7: mark^#(cons(X1, X2)) -> c_7(mark^#(X1), X2) 1184.17/297.09 , 8: mark^#(fst(X1, X2)) -> c_8(a__fst^#(mark(X1), mark(X2))) 1184.17/297.09 , 9: mark^#(from(X)) -> c_9(a__from^#(mark(X))) 1184.17/297.09 , 10: mark^#(add(X1, X2)) -> c_10(a__add^#(mark(X1), mark(X2))) 1184.17/297.09 , 11: mark^#(len(X)) -> c_11(a__len^#(mark(X))) 1184.17/297.09 , 12: a__from^#(X) -> c_12(mark^#(X), X) 1184.17/297.09 , 13: a__from^#(X) -> c_13(X) 1184.17/297.09 , 14: a__add^#(X1, X2) -> c_14(X1, X2) 1184.17/297.09 , 15: a__add^#(0(), X) -> c_15(mark^#(X)) 1184.17/297.09 , 16: a__add^#(s(X), Y) -> c_16(X, Y) 1184.17/297.09 , 17: a__len^#(X) -> c_17(X) 1184.17/297.09 , 18: a__len^#(nil()) -> c_18() 1184.17/297.09 , 19: a__len^#(cons(X, Z)) -> c_19(Z) } 1184.17/297.09 1184.17/297.09 We are left with following problem, upon which TcT provides the 1184.17/297.09 certificate MAYBE. 1184.17/297.09 1184.17/297.09 Strict DPs: 1184.17/297.09 { a__fst^#(X1, X2) -> c_1(X1, X2) 1184.17/297.09 , a__fst^#(s(X), cons(Y, Z)) -> c_3(mark^#(Y), X, Z) 1184.17/297.09 , mark^#(s(X)) -> c_6(X) 1184.17/297.09 , mark^#(cons(X1, X2)) -> c_7(mark^#(X1), X2) 1184.17/297.09 , mark^#(fst(X1, X2)) -> c_8(a__fst^#(mark(X1), mark(X2))) 1184.17/297.09 , mark^#(from(X)) -> c_9(a__from^#(mark(X))) 1184.17/297.09 , mark^#(add(X1, X2)) -> c_10(a__add^#(mark(X1), mark(X2))) 1184.17/297.09 , mark^#(len(X)) -> c_11(a__len^#(mark(X))) 1184.17/297.09 , a__from^#(X) -> c_12(mark^#(X), X) 1184.17/297.09 , a__from^#(X) -> c_13(X) 1184.17/297.09 , a__add^#(X1, X2) -> c_14(X1, X2) 1184.17/297.09 , a__add^#(0(), X) -> c_15(mark^#(X)) 1184.17/297.09 , a__add^#(s(X), Y) -> c_16(X, Y) 1184.17/297.09 , a__len^#(X) -> c_17(X) 1184.17/297.09 , a__len^#(cons(X, Z)) -> c_19(Z) } 1184.17/297.09 Strict Trs: 1184.17/297.09 { a__fst(X1, X2) -> fst(X1, X2) 1184.17/297.09 , a__fst(0(), Z) -> nil() 1184.17/297.09 , a__fst(s(X), cons(Y, Z)) -> cons(mark(Y), fst(X, Z)) 1184.17/297.09 , mark(0()) -> 0() 1184.17/297.09 , mark(nil()) -> nil() 1184.17/297.09 , mark(s(X)) -> s(X) 1184.17/297.09 , mark(cons(X1, X2)) -> cons(mark(X1), X2) 1184.17/297.09 , mark(fst(X1, X2)) -> a__fst(mark(X1), mark(X2)) 1184.17/297.09 , mark(from(X)) -> a__from(mark(X)) 1184.17/297.09 , mark(add(X1, X2)) -> a__add(mark(X1), mark(X2)) 1184.17/297.09 , mark(len(X)) -> a__len(mark(X)) 1184.17/297.09 , a__from(X) -> cons(mark(X), from(s(X))) 1184.17/297.09 , a__from(X) -> from(X) 1184.17/297.09 , a__add(X1, X2) -> add(X1, X2) 1184.17/297.09 , a__add(0(), X) -> mark(X) 1184.17/297.09 , a__add(s(X), Y) -> s(add(X, Y)) 1184.17/297.09 , a__len(X) -> len(X) 1184.17/297.09 , a__len(nil()) -> 0() 1184.17/297.09 , a__len(cons(X, Z)) -> s(len(Z)) } 1184.17/297.09 Weak DPs: 1184.17/297.09 { a__fst^#(0(), Z) -> c_2() 1184.17/297.09 , mark^#(0()) -> c_4() 1184.17/297.09 , mark^#(nil()) -> c_5() 1184.17/297.09 , a__len^#(nil()) -> c_18() } 1184.17/297.09 Obligation: 1184.17/297.09 runtime complexity 1184.17/297.09 Answer: 1184.17/297.09 MAYBE 1184.17/297.09 1184.17/297.09 Empty strict component of the problem is NOT empty. 1184.17/297.09 1184.17/297.09 1184.17/297.09 Arrrr.. 1185.02/297.67 EOF