MAYBE 1185.63/297.55 MAYBE 1185.63/297.55 1185.63/297.55 We are left with following problem, upon which TcT provides the 1185.63/297.55 certificate MAYBE. 1185.63/297.55 1185.63/297.55 Strict Trs: 1185.63/297.55 { a__fact(X) -> 1185.63/297.55 a__if(a__zero(mark(X)), s(0()), prod(X, fact(p(X)))) 1185.63/297.55 , a__fact(X) -> fact(X) 1185.63/297.55 , a__if(X1, X2, X3) -> if(X1, X2, X3) 1185.63/297.55 , a__if(true(), X, Y) -> mark(X) 1185.63/297.55 , a__if(false(), X, Y) -> mark(Y) 1185.63/297.55 , a__zero(X) -> zero(X) 1185.63/297.55 , a__zero(s(X)) -> false() 1185.63/297.55 , a__zero(0()) -> true() 1185.63/297.55 , mark(s(X)) -> s(mark(X)) 1185.63/297.55 , mark(0()) -> 0() 1185.63/297.55 , mark(prod(X1, X2)) -> a__prod(mark(X1), mark(X2)) 1185.63/297.55 , mark(fact(X)) -> a__fact(mark(X)) 1185.63/297.55 , mark(p(X)) -> a__p(mark(X)) 1185.63/297.55 , mark(true()) -> true() 1185.63/297.55 , mark(false()) -> false() 1185.63/297.55 , mark(if(X1, X2, X3)) -> a__if(mark(X1), X2, X3) 1185.63/297.55 , mark(zero(X)) -> a__zero(mark(X)) 1185.63/297.55 , mark(add(X1, X2)) -> a__add(mark(X1), mark(X2)) 1185.63/297.55 , a__add(X1, X2) -> add(X1, X2) 1185.63/297.55 , a__add(s(X), Y) -> s(a__add(mark(X), mark(Y))) 1185.63/297.55 , a__add(0(), X) -> mark(X) 1185.63/297.55 , a__prod(X1, X2) -> prod(X1, X2) 1185.63/297.55 , a__prod(s(X), Y) -> a__add(mark(Y), a__prod(mark(X), mark(Y))) 1185.63/297.55 , a__prod(0(), X) -> 0() 1185.63/297.55 , a__p(X) -> p(X) 1185.63/297.55 , a__p(s(X)) -> mark(X) } 1185.63/297.55 Obligation: 1185.63/297.55 runtime complexity 1185.63/297.55 Answer: 1185.63/297.55 MAYBE 1185.63/297.55 1185.63/297.55 None of the processors succeeded. 1185.63/297.55 1185.63/297.55 Details of failed attempt(s): 1185.63/297.55 ----------------------------- 1185.63/297.55 1) 'With Problem ... (timeout of 297 seconds)' failed due to the 1185.63/297.55 following reason: 1185.63/297.55 1185.63/297.55 Computation stopped due to timeout after 297.0 seconds. 1185.63/297.55 1185.63/297.55 2) 'Best' failed due to the following reason: 1185.63/297.55 1185.63/297.55 None of the processors succeeded. 1185.63/297.55 1185.63/297.55 Details of failed attempt(s): 1185.63/297.55 ----------------------------- 1185.63/297.55 1) 'With Problem ... (timeout of 148 seconds) (timeout of 297 1185.63/297.55 seconds)' failed due to the following reason: 1185.63/297.55 1185.63/297.55 Computation stopped due to timeout after 148.0 seconds. 1185.63/297.55 1185.63/297.55 2) 'Best' failed due to the following reason: 1185.63/297.55 1185.63/297.55 None of the processors succeeded. 1185.63/297.55 1185.63/297.55 Details of failed attempt(s): 1185.63/297.55 ----------------------------- 1185.63/297.55 1) 'bsearch-popstar (timeout of 297 seconds)' failed due to the 1185.63/297.55 following reason: 1185.63/297.55 1185.63/297.55 The processor is inapplicable, reason: 1185.63/297.55 Processor only applicable for innermost runtime complexity analysis 1185.63/297.55 1185.63/297.55 2) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due 1185.63/297.55 to the following reason: 1185.63/297.55 1185.63/297.55 The processor is inapplicable, reason: 1185.63/297.55 Processor only applicable for innermost runtime complexity analysis 1185.63/297.55 1185.63/297.55 1185.63/297.55 3) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)' 1185.63/297.55 failed due to the following reason: 1185.63/297.55 1185.63/297.55 None of the processors succeeded. 1185.63/297.55 1185.63/297.55 Details of failed attempt(s): 1185.63/297.55 ----------------------------- 1185.63/297.55 1) 'Bounds with perSymbol-enrichment and initial automaton 'match'' 1185.63/297.55 failed due to the following reason: 1185.63/297.55 1185.63/297.55 match-boundness of the problem could not be verified. 1185.63/297.55 1185.63/297.55 2) 'Bounds with minimal-enrichment and initial automaton 'match'' 1185.63/297.55 failed due to the following reason: 1185.63/297.55 1185.63/297.55 match-boundness of the problem could not be verified. 1185.63/297.55 1185.63/297.55 1185.63/297.55 1185.63/297.55 3) 'Weak Dependency Pairs (timeout of 297 seconds)' failed due to 1185.63/297.55 the following reason: 1185.63/297.55 1185.63/297.55 We add the following weak dependency pairs: 1185.63/297.55 1185.63/297.55 Strict DPs: 1185.63/297.55 { a__fact^#(X) -> 1185.63/297.55 c_1(a__if^#(a__zero(mark(X)), s(0()), prod(X, fact(p(X))))) 1185.63/297.55 , a__fact^#(X) -> c_2(X) 1185.63/297.55 , a__if^#(X1, X2, X3) -> c_3(X1, X2, X3) 1185.63/297.55 , a__if^#(true(), X, Y) -> c_4(mark^#(X)) 1185.63/297.55 , a__if^#(false(), X, Y) -> c_5(mark^#(Y)) 1185.63/297.55 , mark^#(s(X)) -> c_9(mark^#(X)) 1185.63/297.55 , mark^#(0()) -> c_10() 1185.63/297.55 , mark^#(prod(X1, X2)) -> c_11(a__prod^#(mark(X1), mark(X2))) 1185.63/297.55 , mark^#(fact(X)) -> c_12(a__fact^#(mark(X))) 1185.63/297.55 , mark^#(p(X)) -> c_13(a__p^#(mark(X))) 1185.63/297.55 , mark^#(true()) -> c_14() 1185.63/297.55 , mark^#(false()) -> c_15() 1185.63/297.55 , mark^#(if(X1, X2, X3)) -> c_16(a__if^#(mark(X1), X2, X3)) 1185.63/297.55 , mark^#(zero(X)) -> c_17(a__zero^#(mark(X))) 1185.63/297.55 , mark^#(add(X1, X2)) -> c_18(a__add^#(mark(X1), mark(X2))) 1185.63/297.55 , a__zero^#(X) -> c_6(X) 1185.63/297.55 , a__zero^#(s(X)) -> c_7() 1185.63/297.55 , a__zero^#(0()) -> c_8() 1185.63/297.55 , a__prod^#(X1, X2) -> c_22(X1, X2) 1185.63/297.55 , a__prod^#(s(X), Y) -> 1185.63/297.55 c_23(a__add^#(mark(Y), a__prod(mark(X), mark(Y)))) 1185.63/297.55 , a__prod^#(0(), X) -> c_24() 1185.63/297.55 , a__p^#(X) -> c_25(X) 1185.63/297.55 , a__p^#(s(X)) -> c_26(mark^#(X)) 1185.63/297.55 , a__add^#(X1, X2) -> c_19(X1, X2) 1185.63/297.55 , a__add^#(s(X), Y) -> c_20(a__add^#(mark(X), mark(Y))) 1185.63/297.55 , a__add^#(0(), X) -> c_21(mark^#(X)) } 1185.63/297.55 1185.63/297.55 and mark the set of starting terms. 1185.63/297.55 1185.63/297.55 We are left with following problem, upon which TcT provides the 1185.63/297.55 certificate MAYBE. 1185.63/297.55 1185.63/297.55 Strict DPs: 1185.63/297.55 { a__fact^#(X) -> 1185.63/297.55 c_1(a__if^#(a__zero(mark(X)), s(0()), prod(X, fact(p(X))))) 1185.63/297.55 , a__fact^#(X) -> c_2(X) 1185.63/297.55 , a__if^#(X1, X2, X3) -> c_3(X1, X2, X3) 1185.63/297.55 , a__if^#(true(), X, Y) -> c_4(mark^#(X)) 1185.63/297.55 , a__if^#(false(), X, Y) -> c_5(mark^#(Y)) 1185.63/297.55 , mark^#(s(X)) -> c_9(mark^#(X)) 1185.63/297.55 , mark^#(0()) -> c_10() 1185.63/297.55 , mark^#(prod(X1, X2)) -> c_11(a__prod^#(mark(X1), mark(X2))) 1185.63/297.55 , mark^#(fact(X)) -> c_12(a__fact^#(mark(X))) 1185.63/297.55 , mark^#(p(X)) -> c_13(a__p^#(mark(X))) 1185.63/297.55 , mark^#(true()) -> c_14() 1185.63/297.55 , mark^#(false()) -> c_15() 1185.63/297.55 , mark^#(if(X1, X2, X3)) -> c_16(a__if^#(mark(X1), X2, X3)) 1185.63/297.55 , mark^#(zero(X)) -> c_17(a__zero^#(mark(X))) 1185.63/297.55 , mark^#(add(X1, X2)) -> c_18(a__add^#(mark(X1), mark(X2))) 1185.63/297.55 , a__zero^#(X) -> c_6(X) 1185.63/297.55 , a__zero^#(s(X)) -> c_7() 1185.63/297.55 , a__zero^#(0()) -> c_8() 1185.63/297.55 , a__prod^#(X1, X2) -> c_22(X1, X2) 1185.63/297.55 , a__prod^#(s(X), Y) -> 1185.63/297.55 c_23(a__add^#(mark(Y), a__prod(mark(X), mark(Y)))) 1185.63/297.55 , a__prod^#(0(), X) -> c_24() 1185.63/297.55 , a__p^#(X) -> c_25(X) 1185.63/297.55 , a__p^#(s(X)) -> c_26(mark^#(X)) 1185.63/297.55 , a__add^#(X1, X2) -> c_19(X1, X2) 1185.63/297.55 , a__add^#(s(X), Y) -> c_20(a__add^#(mark(X), mark(Y))) 1185.63/297.55 , a__add^#(0(), X) -> c_21(mark^#(X)) } 1185.63/297.55 Strict Trs: 1185.63/297.55 { a__fact(X) -> 1185.63/297.55 a__if(a__zero(mark(X)), s(0()), prod(X, fact(p(X)))) 1185.63/297.55 , a__fact(X) -> fact(X) 1185.63/297.55 , a__if(X1, X2, X3) -> if(X1, X2, X3) 1185.63/297.55 , a__if(true(), X, Y) -> mark(X) 1185.63/297.55 , a__if(false(), X, Y) -> mark(Y) 1185.63/297.55 , a__zero(X) -> zero(X) 1185.63/297.55 , a__zero(s(X)) -> false() 1185.63/297.55 , a__zero(0()) -> true() 1185.63/297.55 , mark(s(X)) -> s(mark(X)) 1185.63/297.55 , mark(0()) -> 0() 1185.63/297.55 , mark(prod(X1, X2)) -> a__prod(mark(X1), mark(X2)) 1185.63/297.55 , mark(fact(X)) -> a__fact(mark(X)) 1185.63/297.55 , mark(p(X)) -> a__p(mark(X)) 1185.63/297.55 , mark(true()) -> true() 1185.63/297.55 , mark(false()) -> false() 1185.63/297.55 , mark(if(X1, X2, X3)) -> a__if(mark(X1), X2, X3) 1185.63/297.55 , mark(zero(X)) -> a__zero(mark(X)) 1185.63/297.55 , mark(add(X1, X2)) -> a__add(mark(X1), mark(X2)) 1185.63/297.55 , a__add(X1, X2) -> add(X1, X2) 1185.63/297.55 , a__add(s(X), Y) -> s(a__add(mark(X), mark(Y))) 1185.63/297.55 , a__add(0(), X) -> mark(X) 1185.63/297.55 , a__prod(X1, X2) -> prod(X1, X2) 1185.63/297.55 , a__prod(s(X), Y) -> a__add(mark(Y), a__prod(mark(X), mark(Y))) 1185.63/297.55 , a__prod(0(), X) -> 0() 1185.63/297.55 , a__p(X) -> p(X) 1185.63/297.55 , a__p(s(X)) -> mark(X) } 1185.63/297.55 Obligation: 1185.63/297.55 runtime complexity 1185.63/297.55 Answer: 1185.63/297.55 MAYBE 1185.63/297.55 1185.63/297.55 We estimate the number of application of {7,11,12,17,18,21} by 1185.63/297.55 applications of Pre({7,11,12,17,18,21}) = 1185.63/297.55 {2,3,4,5,6,8,14,16,19,22,23,24,26}. Here rules are labeled as 1185.63/297.55 follows: 1185.63/297.55 1185.63/297.55 DPs: 1185.63/297.55 { 1: a__fact^#(X) -> 1185.63/297.55 c_1(a__if^#(a__zero(mark(X)), s(0()), prod(X, fact(p(X))))) 1185.63/297.55 , 2: a__fact^#(X) -> c_2(X) 1185.63/297.55 , 3: a__if^#(X1, X2, X3) -> c_3(X1, X2, X3) 1185.63/297.55 , 4: a__if^#(true(), X, Y) -> c_4(mark^#(X)) 1185.63/297.55 , 5: a__if^#(false(), X, Y) -> c_5(mark^#(Y)) 1185.63/297.55 , 6: mark^#(s(X)) -> c_9(mark^#(X)) 1185.63/297.55 , 7: mark^#(0()) -> c_10() 1185.63/297.55 , 8: mark^#(prod(X1, X2)) -> c_11(a__prod^#(mark(X1), mark(X2))) 1185.63/297.55 , 9: mark^#(fact(X)) -> c_12(a__fact^#(mark(X))) 1185.63/297.55 , 10: mark^#(p(X)) -> c_13(a__p^#(mark(X))) 1185.63/297.55 , 11: mark^#(true()) -> c_14() 1185.63/297.55 , 12: mark^#(false()) -> c_15() 1185.63/297.55 , 13: mark^#(if(X1, X2, X3)) -> c_16(a__if^#(mark(X1), X2, X3)) 1185.63/297.55 , 14: mark^#(zero(X)) -> c_17(a__zero^#(mark(X))) 1185.63/297.55 , 15: mark^#(add(X1, X2)) -> c_18(a__add^#(mark(X1), mark(X2))) 1185.63/297.55 , 16: a__zero^#(X) -> c_6(X) 1185.63/297.55 , 17: a__zero^#(s(X)) -> c_7() 1185.63/297.55 , 18: a__zero^#(0()) -> c_8() 1185.63/297.55 , 19: a__prod^#(X1, X2) -> c_22(X1, X2) 1185.63/297.55 , 20: a__prod^#(s(X), Y) -> 1185.63/297.55 c_23(a__add^#(mark(Y), a__prod(mark(X), mark(Y)))) 1185.63/297.55 , 21: a__prod^#(0(), X) -> c_24() 1185.63/297.55 , 22: a__p^#(X) -> c_25(X) 1185.63/297.55 , 23: a__p^#(s(X)) -> c_26(mark^#(X)) 1185.63/297.55 , 24: a__add^#(X1, X2) -> c_19(X1, X2) 1185.63/297.55 , 25: a__add^#(s(X), Y) -> c_20(a__add^#(mark(X), mark(Y))) 1185.63/297.55 , 26: a__add^#(0(), X) -> c_21(mark^#(X)) } 1185.63/297.55 1185.63/297.55 We are left with following problem, upon which TcT provides the 1185.63/297.55 certificate MAYBE. 1185.63/297.55 1185.63/297.55 Strict DPs: 1185.63/297.55 { a__fact^#(X) -> 1185.63/297.55 c_1(a__if^#(a__zero(mark(X)), s(0()), prod(X, fact(p(X))))) 1185.63/297.55 , a__fact^#(X) -> c_2(X) 1185.63/297.55 , a__if^#(X1, X2, X3) -> c_3(X1, X2, X3) 1185.63/297.55 , a__if^#(true(), X, Y) -> c_4(mark^#(X)) 1185.63/297.55 , a__if^#(false(), X, Y) -> c_5(mark^#(Y)) 1185.63/297.55 , mark^#(s(X)) -> c_9(mark^#(X)) 1185.63/297.55 , mark^#(prod(X1, X2)) -> c_11(a__prod^#(mark(X1), mark(X2))) 1185.63/297.55 , mark^#(fact(X)) -> c_12(a__fact^#(mark(X))) 1185.63/297.55 , mark^#(p(X)) -> c_13(a__p^#(mark(X))) 1185.63/297.55 , mark^#(if(X1, X2, X3)) -> c_16(a__if^#(mark(X1), X2, X3)) 1185.63/297.55 , mark^#(zero(X)) -> c_17(a__zero^#(mark(X))) 1185.63/297.55 , mark^#(add(X1, X2)) -> c_18(a__add^#(mark(X1), mark(X2))) 1185.63/297.55 , a__zero^#(X) -> c_6(X) 1185.63/297.55 , a__prod^#(X1, X2) -> c_22(X1, X2) 1185.63/297.55 , a__prod^#(s(X), Y) -> 1185.63/297.55 c_23(a__add^#(mark(Y), a__prod(mark(X), mark(Y)))) 1185.63/297.55 , a__p^#(X) -> c_25(X) 1185.63/297.55 , a__p^#(s(X)) -> c_26(mark^#(X)) 1185.63/297.55 , a__add^#(X1, X2) -> c_19(X1, X2) 1185.63/297.55 , a__add^#(s(X), Y) -> c_20(a__add^#(mark(X), mark(Y))) 1185.63/297.55 , a__add^#(0(), X) -> c_21(mark^#(X)) } 1185.63/297.55 Strict Trs: 1185.63/297.55 { a__fact(X) -> 1185.63/297.55 a__if(a__zero(mark(X)), s(0()), prod(X, fact(p(X)))) 1185.63/297.55 , a__fact(X) -> fact(X) 1185.63/297.55 , a__if(X1, X2, X3) -> if(X1, X2, X3) 1185.63/297.55 , a__if(true(), X, Y) -> mark(X) 1185.63/297.55 , a__if(false(), X, Y) -> mark(Y) 1185.63/297.55 , a__zero(X) -> zero(X) 1185.63/297.55 , a__zero(s(X)) -> false() 1185.63/297.55 , a__zero(0()) -> true() 1185.63/297.55 , mark(s(X)) -> s(mark(X)) 1185.63/297.55 , mark(0()) -> 0() 1185.63/297.55 , mark(prod(X1, X2)) -> a__prod(mark(X1), mark(X2)) 1185.63/297.55 , mark(fact(X)) -> a__fact(mark(X)) 1185.63/297.55 , mark(p(X)) -> a__p(mark(X)) 1185.63/297.55 , mark(true()) -> true() 1185.63/297.55 , mark(false()) -> false() 1185.63/297.55 , mark(if(X1, X2, X3)) -> a__if(mark(X1), X2, X3) 1185.63/297.55 , mark(zero(X)) -> a__zero(mark(X)) 1185.63/297.55 , mark(add(X1, X2)) -> a__add(mark(X1), mark(X2)) 1185.63/297.55 , a__add(X1, X2) -> add(X1, X2) 1185.63/297.55 , a__add(s(X), Y) -> s(a__add(mark(X), mark(Y))) 1185.63/297.55 , a__add(0(), X) -> mark(X) 1185.63/297.55 , a__prod(X1, X2) -> prod(X1, X2) 1185.63/297.55 , a__prod(s(X), Y) -> a__add(mark(Y), a__prod(mark(X), mark(Y))) 1185.63/297.55 , a__prod(0(), X) -> 0() 1185.63/297.55 , a__p(X) -> p(X) 1185.63/297.55 , a__p(s(X)) -> mark(X) } 1185.63/297.55 Weak DPs: 1185.63/297.55 { mark^#(0()) -> c_10() 1185.63/297.55 , mark^#(true()) -> c_14() 1185.63/297.55 , mark^#(false()) -> c_15() 1185.63/297.55 , a__zero^#(s(X)) -> c_7() 1185.63/297.55 , a__zero^#(0()) -> c_8() 1185.63/297.55 , a__prod^#(0(), X) -> c_24() } 1185.63/297.55 Obligation: 1185.63/297.55 runtime complexity 1185.63/297.55 Answer: 1185.63/297.55 MAYBE 1185.63/297.55 1185.63/297.55 Empty strict component of the problem is NOT empty. 1185.63/297.55 1185.63/297.55 1185.63/297.55 Arrrr.. 1186.71/298.42 EOF