MAYBE 1062.26/297.78 MAYBE 1062.26/297.78 1062.26/297.78 We are left with following problem, upon which TcT provides the 1062.26/297.78 certificate MAYBE. 1062.26/297.78 1062.26/297.78 Strict Trs: 1062.26/297.78 { a__fib(N) -> a__sel(mark(N), a__fib1(s(0()), s(0()))) 1062.26/297.78 , a__fib(X) -> fib(X) 1062.26/297.78 , a__sel(X1, X2) -> sel(X1, X2) 1062.26/297.78 , a__sel(s(N), cons(X, XS)) -> a__sel(mark(N), mark(XS)) 1062.26/297.78 , a__sel(0(), cons(X, XS)) -> mark(X) 1062.26/297.78 , mark(s(X)) -> s(mark(X)) 1062.26/297.78 , mark(0()) -> 0() 1062.26/297.78 , mark(cons(X1, X2)) -> cons(mark(X1), X2) 1062.26/297.78 , mark(fib1(X1, X2)) -> a__fib1(mark(X1), mark(X2)) 1062.26/297.78 , mark(add(X1, X2)) -> a__add(mark(X1), mark(X2)) 1062.26/297.78 , mark(fib(X)) -> a__fib(mark(X)) 1062.26/297.78 , mark(sel(X1, X2)) -> a__sel(mark(X1), mark(X2)) 1062.26/297.78 , a__fib1(X, Y) -> cons(mark(X), fib1(Y, add(X, Y))) 1062.26/297.78 , a__fib1(X1, X2) -> fib1(X1, X2) 1062.26/297.78 , a__add(X1, X2) -> add(X1, X2) 1062.26/297.78 , a__add(s(X), Y) -> s(a__add(mark(X), mark(Y))) 1062.26/297.78 , a__add(0(), X) -> mark(X) } 1062.26/297.78 Obligation: 1062.26/297.78 runtime complexity 1062.26/297.78 Answer: 1062.26/297.78 MAYBE 1062.26/297.78 1062.26/297.78 None of the processors succeeded. 1062.26/297.78 1062.26/297.78 Details of failed attempt(s): 1062.26/297.78 ----------------------------- 1062.26/297.78 1) 'With Problem ... (timeout of 297 seconds)' failed due to the 1062.26/297.78 following reason: 1062.26/297.78 1062.26/297.78 Computation stopped due to timeout after 297.0 seconds. 1062.26/297.78 1062.26/297.78 2) 'Best' failed due to the following reason: 1062.26/297.78 1062.26/297.78 None of the processors succeeded. 1062.26/297.78 1062.26/297.78 Details of failed attempt(s): 1062.26/297.78 ----------------------------- 1062.26/297.78 1) 'With Problem ... (timeout of 148 seconds) (timeout of 297 1062.26/297.78 seconds)' failed due to the following reason: 1062.26/297.78 1062.26/297.78 Computation stopped due to timeout after 148.0 seconds. 1062.26/297.78 1062.26/297.78 2) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)' 1062.26/297.78 failed due to the following reason: 1062.26/297.78 1062.26/297.78 None of the processors succeeded. 1062.26/297.78 1062.26/297.78 Details of failed attempt(s): 1062.26/297.78 ----------------------------- 1062.26/297.78 1) 'Bounds with minimal-enrichment and initial automaton 'match'' 1062.26/297.78 failed due to the following reason: 1062.26/297.78 1062.26/297.78 match-boundness of the problem could not be verified. 1062.26/297.78 1062.26/297.78 2) 'Bounds with perSymbol-enrichment and initial automaton 'match'' 1062.26/297.78 failed due to the following reason: 1062.26/297.78 1062.26/297.78 match-boundness of the problem could not be verified. 1062.26/297.78 1062.26/297.78 1062.26/297.78 3) 'Best' failed due to the following reason: 1062.26/297.78 1062.26/297.78 None of the processors succeeded. 1062.26/297.78 1062.26/297.78 Details of failed attempt(s): 1062.26/297.78 ----------------------------- 1062.26/297.78 1) 'bsearch-popstar (timeout of 297 seconds)' failed due to the 1062.26/297.78 following reason: 1062.26/297.78 1062.26/297.78 The processor is inapplicable, reason: 1062.26/297.78 Processor only applicable for innermost runtime complexity analysis 1062.26/297.78 1062.26/297.78 2) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due 1062.26/297.78 to the following reason: 1062.26/297.78 1062.26/297.78 The processor is inapplicable, reason: 1062.26/297.78 Processor only applicable for innermost runtime complexity analysis 1062.26/297.78 1062.26/297.78 1062.26/297.78 1062.26/297.78 3) 'Weak Dependency Pairs (timeout of 297 seconds)' failed due to 1062.26/297.78 the following reason: 1062.26/297.78 1062.26/297.78 We add the following weak dependency pairs: 1062.26/297.78 1062.26/297.78 Strict DPs: 1062.26/297.78 { a__fib^#(N) -> c_1(a__sel^#(mark(N), a__fib1(s(0()), s(0())))) 1062.26/297.78 , a__fib^#(X) -> c_2(X) 1062.26/297.78 , a__sel^#(X1, X2) -> c_3(X1, X2) 1062.26/297.78 , a__sel^#(s(N), cons(X, XS)) -> c_4(a__sel^#(mark(N), mark(XS))) 1062.26/297.78 , a__sel^#(0(), cons(X, XS)) -> c_5(mark^#(X)) 1062.26/297.78 , mark^#(s(X)) -> c_6(mark^#(X)) 1062.26/297.78 , mark^#(0()) -> c_7() 1062.26/297.78 , mark^#(cons(X1, X2)) -> c_8(mark^#(X1), X2) 1062.26/297.78 , mark^#(fib1(X1, X2)) -> c_9(a__fib1^#(mark(X1), mark(X2))) 1062.26/297.78 , mark^#(add(X1, X2)) -> c_10(a__add^#(mark(X1), mark(X2))) 1062.26/297.78 , mark^#(fib(X)) -> c_11(a__fib^#(mark(X))) 1062.26/297.78 , mark^#(sel(X1, X2)) -> c_12(a__sel^#(mark(X1), mark(X2))) 1062.26/297.78 , a__fib1^#(X, Y) -> c_13(mark^#(X), Y, X, Y) 1062.26/297.78 , a__fib1^#(X1, X2) -> c_14(X1, X2) 1062.26/297.78 , a__add^#(X1, X2) -> c_15(X1, X2) 1062.26/297.78 , a__add^#(s(X), Y) -> c_16(a__add^#(mark(X), mark(Y))) 1062.26/297.78 , a__add^#(0(), X) -> c_17(mark^#(X)) } 1062.26/297.78 1062.26/297.78 and mark the set of starting terms. 1062.26/297.78 1062.26/297.78 We are left with following problem, upon which TcT provides the 1062.26/297.78 certificate MAYBE. 1062.26/297.78 1062.26/297.78 Strict DPs: 1062.26/297.78 { a__fib^#(N) -> c_1(a__sel^#(mark(N), a__fib1(s(0()), s(0())))) 1062.26/297.78 , a__fib^#(X) -> c_2(X) 1062.26/297.78 , a__sel^#(X1, X2) -> c_3(X1, X2) 1062.26/297.78 , a__sel^#(s(N), cons(X, XS)) -> c_4(a__sel^#(mark(N), mark(XS))) 1062.26/297.78 , a__sel^#(0(), cons(X, XS)) -> c_5(mark^#(X)) 1062.26/297.78 , mark^#(s(X)) -> c_6(mark^#(X)) 1062.26/297.78 , mark^#(0()) -> c_7() 1062.26/297.78 , mark^#(cons(X1, X2)) -> c_8(mark^#(X1), X2) 1062.26/297.78 , mark^#(fib1(X1, X2)) -> c_9(a__fib1^#(mark(X1), mark(X2))) 1062.26/297.78 , mark^#(add(X1, X2)) -> c_10(a__add^#(mark(X1), mark(X2))) 1062.26/297.78 , mark^#(fib(X)) -> c_11(a__fib^#(mark(X))) 1062.26/297.78 , mark^#(sel(X1, X2)) -> c_12(a__sel^#(mark(X1), mark(X2))) 1062.26/297.78 , a__fib1^#(X, Y) -> c_13(mark^#(X), Y, X, Y) 1062.26/297.78 , a__fib1^#(X1, X2) -> c_14(X1, X2) 1062.26/297.78 , a__add^#(X1, X2) -> c_15(X1, X2) 1062.26/297.78 , a__add^#(s(X), Y) -> c_16(a__add^#(mark(X), mark(Y))) 1062.26/297.78 , a__add^#(0(), X) -> c_17(mark^#(X)) } 1062.26/297.78 Strict Trs: 1062.26/297.78 { a__fib(N) -> a__sel(mark(N), a__fib1(s(0()), s(0()))) 1062.26/297.78 , a__fib(X) -> fib(X) 1062.26/297.78 , a__sel(X1, X2) -> sel(X1, X2) 1062.26/297.78 , a__sel(s(N), cons(X, XS)) -> a__sel(mark(N), mark(XS)) 1062.26/297.78 , a__sel(0(), cons(X, XS)) -> mark(X) 1062.26/297.78 , mark(s(X)) -> s(mark(X)) 1062.26/297.78 , mark(0()) -> 0() 1062.26/297.78 , mark(cons(X1, X2)) -> cons(mark(X1), X2) 1062.26/297.78 , mark(fib1(X1, X2)) -> a__fib1(mark(X1), mark(X2)) 1062.26/297.78 , mark(add(X1, X2)) -> a__add(mark(X1), mark(X2)) 1062.26/297.78 , mark(fib(X)) -> a__fib(mark(X)) 1062.26/297.78 , mark(sel(X1, X2)) -> a__sel(mark(X1), mark(X2)) 1062.26/297.78 , a__fib1(X, Y) -> cons(mark(X), fib1(Y, add(X, Y))) 1062.26/297.78 , a__fib1(X1, X2) -> fib1(X1, X2) 1062.26/297.78 , a__add(X1, X2) -> add(X1, X2) 1062.26/297.78 , a__add(s(X), Y) -> s(a__add(mark(X), mark(Y))) 1062.26/297.78 , a__add(0(), X) -> mark(X) } 1062.26/297.78 Obligation: 1062.26/297.78 runtime complexity 1062.26/297.78 Answer: 1062.26/297.78 MAYBE 1062.26/297.78 1062.26/297.78 We estimate the number of application of {7} by applications of 1062.26/297.78 Pre({7}) = {2,3,5,6,8,13,14,15,17}. Here rules are labeled as 1062.26/297.78 follows: 1062.26/297.78 1062.26/297.78 DPs: 1062.26/297.78 { 1: a__fib^#(N) -> c_1(a__sel^#(mark(N), a__fib1(s(0()), s(0())))) 1062.26/297.78 , 2: a__fib^#(X) -> c_2(X) 1062.26/297.78 , 3: a__sel^#(X1, X2) -> c_3(X1, X2) 1062.26/297.78 , 4: a__sel^#(s(N), cons(X, XS)) -> 1062.26/297.78 c_4(a__sel^#(mark(N), mark(XS))) 1062.26/297.78 , 5: a__sel^#(0(), cons(X, XS)) -> c_5(mark^#(X)) 1062.26/297.78 , 6: mark^#(s(X)) -> c_6(mark^#(X)) 1062.26/297.78 , 7: mark^#(0()) -> c_7() 1062.26/297.78 , 8: mark^#(cons(X1, X2)) -> c_8(mark^#(X1), X2) 1062.26/297.78 , 9: mark^#(fib1(X1, X2)) -> c_9(a__fib1^#(mark(X1), mark(X2))) 1062.26/297.78 , 10: mark^#(add(X1, X2)) -> c_10(a__add^#(mark(X1), mark(X2))) 1062.26/297.78 , 11: mark^#(fib(X)) -> c_11(a__fib^#(mark(X))) 1062.26/297.78 , 12: mark^#(sel(X1, X2)) -> c_12(a__sel^#(mark(X1), mark(X2))) 1062.26/297.78 , 13: a__fib1^#(X, Y) -> c_13(mark^#(X), Y, X, Y) 1062.26/297.78 , 14: a__fib1^#(X1, X2) -> c_14(X1, X2) 1062.26/297.78 , 15: a__add^#(X1, X2) -> c_15(X1, X2) 1062.26/297.78 , 16: a__add^#(s(X), Y) -> c_16(a__add^#(mark(X), mark(Y))) 1062.26/297.78 , 17: a__add^#(0(), X) -> c_17(mark^#(X)) } 1062.26/297.78 1062.26/297.78 We are left with following problem, upon which TcT provides the 1062.26/297.78 certificate MAYBE. 1062.26/297.78 1062.26/297.78 Strict DPs: 1062.26/297.78 { a__fib^#(N) -> c_1(a__sel^#(mark(N), a__fib1(s(0()), s(0())))) 1062.26/297.78 , a__fib^#(X) -> c_2(X) 1062.26/297.78 , a__sel^#(X1, X2) -> c_3(X1, X2) 1062.26/297.78 , a__sel^#(s(N), cons(X, XS)) -> c_4(a__sel^#(mark(N), mark(XS))) 1062.26/297.78 , a__sel^#(0(), cons(X, XS)) -> c_5(mark^#(X)) 1062.26/297.78 , mark^#(s(X)) -> c_6(mark^#(X)) 1062.26/297.78 , mark^#(cons(X1, X2)) -> c_8(mark^#(X1), X2) 1062.26/297.78 , mark^#(fib1(X1, X2)) -> c_9(a__fib1^#(mark(X1), mark(X2))) 1062.26/297.78 , mark^#(add(X1, X2)) -> c_10(a__add^#(mark(X1), mark(X2))) 1062.26/297.78 , mark^#(fib(X)) -> c_11(a__fib^#(mark(X))) 1062.26/297.78 , mark^#(sel(X1, X2)) -> c_12(a__sel^#(mark(X1), mark(X2))) 1062.26/297.78 , a__fib1^#(X, Y) -> c_13(mark^#(X), Y, X, Y) 1062.26/297.78 , a__fib1^#(X1, X2) -> c_14(X1, X2) 1062.26/297.78 , a__add^#(X1, X2) -> c_15(X1, X2) 1062.26/297.78 , a__add^#(s(X), Y) -> c_16(a__add^#(mark(X), mark(Y))) 1062.26/297.78 , a__add^#(0(), X) -> c_17(mark^#(X)) } 1062.26/297.78 Strict Trs: 1062.26/297.78 { a__fib(N) -> a__sel(mark(N), a__fib1(s(0()), s(0()))) 1062.26/297.78 , a__fib(X) -> fib(X) 1062.26/297.78 , a__sel(X1, X2) -> sel(X1, X2) 1062.26/297.78 , a__sel(s(N), cons(X, XS)) -> a__sel(mark(N), mark(XS)) 1062.26/297.78 , a__sel(0(), cons(X, XS)) -> mark(X) 1062.26/297.78 , mark(s(X)) -> s(mark(X)) 1062.26/297.78 , mark(0()) -> 0() 1062.26/297.78 , mark(cons(X1, X2)) -> cons(mark(X1), X2) 1062.26/297.78 , mark(fib1(X1, X2)) -> a__fib1(mark(X1), mark(X2)) 1062.26/297.78 , mark(add(X1, X2)) -> a__add(mark(X1), mark(X2)) 1062.26/297.78 , mark(fib(X)) -> a__fib(mark(X)) 1062.26/297.78 , mark(sel(X1, X2)) -> a__sel(mark(X1), mark(X2)) 1062.26/297.78 , a__fib1(X, Y) -> cons(mark(X), fib1(Y, add(X, Y))) 1062.26/297.78 , a__fib1(X1, X2) -> fib1(X1, X2) 1062.26/297.78 , a__add(X1, X2) -> add(X1, X2) 1062.26/297.78 , a__add(s(X), Y) -> s(a__add(mark(X), mark(Y))) 1062.26/297.78 , a__add(0(), X) -> mark(X) } 1062.26/297.78 Weak DPs: { mark^#(0()) -> c_7() } 1062.26/297.78 Obligation: 1062.26/297.78 runtime complexity 1062.26/297.78 Answer: 1062.26/297.78 MAYBE 1062.26/297.78 1062.26/297.78 Empty strict component of the problem is NOT empty. 1062.26/297.78 1062.26/297.78 1062.26/297.78 Arrrr.. 1063.41/298.63 EOF