MAYBE 1171.86/297.06 MAYBE 1171.86/297.06 1171.86/297.06 We are left with following problem, upon which TcT provides the 1171.86/297.06 certificate MAYBE. 1171.86/297.06 1171.86/297.06 Strict Trs: 1171.86/297.06 { t(N) -> cs(r(q(N)), nt(ns(N))) 1171.86/297.06 , t(X) -> nt(X) 1171.86/297.06 , q(0()) -> 0() 1171.86/297.06 , q(s(X)) -> s(p(q(X), d(X))) 1171.86/297.06 , s(X) -> ns(X) 1171.86/297.06 , p(X, 0()) -> X 1171.86/297.06 , p(0(), X) -> X 1171.86/297.06 , p(s(X), s(Y)) -> s(s(p(X, Y))) 1171.86/297.06 , d(0()) -> 0() 1171.86/297.06 , d(s(X)) -> s(s(d(X))) 1171.86/297.06 , f(X1, X2) -> nf(X1, X2) 1171.86/297.06 , f(0(), X) -> nil() 1171.86/297.06 , f(s(X), cs(Y, Z)) -> cs(Y, nf(X, a(Z))) 1171.86/297.06 , a(X) -> X 1171.86/297.06 , a(nt(X)) -> t(a(X)) 1171.86/297.06 , a(ns(X)) -> s(a(X)) 1171.86/297.06 , a(nf(X1, X2)) -> f(a(X1), a(X2)) } 1171.86/297.06 Obligation: 1171.86/297.06 runtime complexity 1171.86/297.06 Answer: 1171.86/297.06 MAYBE 1171.86/297.06 1171.86/297.06 None of the processors succeeded. 1171.86/297.06 1171.86/297.06 Details of failed attempt(s): 1171.86/297.06 ----------------------------- 1171.86/297.06 1) 'With Problem ... (timeout of 297 seconds)' failed due to the 1171.86/297.06 following reason: 1171.86/297.06 1171.86/297.06 Computation stopped due to timeout after 297.0 seconds. 1171.86/297.06 1171.86/297.06 2) 'Best' failed due to the following reason: 1171.86/297.06 1171.86/297.06 None of the processors succeeded. 1171.86/297.06 1171.86/297.06 Details of failed attempt(s): 1171.86/297.06 ----------------------------- 1171.86/297.06 1) 'With Problem ... (timeout of 148 seconds) (timeout of 297 1171.86/297.06 seconds)' failed due to the following reason: 1171.86/297.06 1171.86/297.06 Computation stopped due to timeout after 148.0 seconds. 1171.86/297.06 1171.86/297.06 2) 'Best' failed due to the following reason: 1171.86/297.06 1171.86/297.06 None of the processors succeeded. 1171.86/297.06 1171.86/297.06 Details of failed attempt(s): 1171.86/297.06 ----------------------------- 1171.86/297.06 1) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due 1171.86/297.06 to the following reason: 1171.86/297.06 1171.86/297.06 The processor is inapplicable, reason: 1171.86/297.06 Processor only applicable for innermost runtime complexity analysis 1171.86/297.06 1171.86/297.06 2) 'bsearch-popstar (timeout of 297 seconds)' failed due to the 1171.86/297.06 following reason: 1171.86/297.06 1171.86/297.06 The processor is inapplicable, reason: 1171.86/297.06 Processor only applicable for innermost runtime complexity analysis 1171.86/297.06 1171.86/297.06 1171.86/297.06 3) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)' 1171.86/297.06 failed due to the following reason: 1171.86/297.06 1171.86/297.06 None of the processors succeeded. 1171.86/297.06 1171.86/297.06 Details of failed attempt(s): 1171.86/297.06 ----------------------------- 1171.86/297.06 1) 'Bounds with perSymbol-enrichment and initial automaton 'match'' 1171.86/297.06 failed due to the following reason: 1171.86/297.06 1171.86/297.06 match-boundness of the problem could not be verified. 1171.86/297.06 1171.86/297.06 2) 'Bounds with minimal-enrichment and initial automaton 'match'' 1171.86/297.06 failed due to the following reason: 1171.86/297.06 1171.86/297.06 match-boundness of the problem could not be verified. 1171.86/297.06 1171.86/297.06 1171.86/297.06 1171.86/297.06 3) 'Weak Dependency Pairs (timeout of 297 seconds)' failed due to 1171.86/297.06 the following reason: 1171.86/297.06 1171.86/297.06 We add the following weak dependency pairs: 1171.86/297.06 1171.86/297.06 Strict DPs: 1171.86/297.06 { t^#(N) -> c_1(q^#(N), N) 1171.86/297.06 , t^#(X) -> c_2(X) 1171.86/297.06 , q^#(0()) -> c_3() 1171.86/297.06 , q^#(s(X)) -> c_4(s^#(p(q(X), d(X)))) 1171.86/297.06 , s^#(X) -> c_5(X) 1171.86/297.06 , p^#(X, 0()) -> c_6(X) 1171.86/297.06 , p^#(0(), X) -> c_7(X) 1171.86/297.06 , p^#(s(X), s(Y)) -> c_8(s^#(s(p(X, Y)))) 1171.86/297.06 , d^#(0()) -> c_9() 1171.86/297.06 , d^#(s(X)) -> c_10(s^#(s(d(X)))) 1171.86/297.06 , f^#(X1, X2) -> c_11(X1, X2) 1171.86/297.06 , f^#(0(), X) -> c_12() 1171.86/297.06 , f^#(s(X), cs(Y, Z)) -> c_13(Y, X, a^#(Z)) 1171.86/297.06 , a^#(X) -> c_14(X) 1171.86/297.06 , a^#(nt(X)) -> c_15(t^#(a(X))) 1171.86/297.06 , a^#(ns(X)) -> c_16(s^#(a(X))) 1171.86/297.06 , a^#(nf(X1, X2)) -> c_17(f^#(a(X1), a(X2))) } 1171.86/297.06 1171.86/297.06 and mark the set of starting terms. 1171.86/297.06 1171.86/297.06 We are left with following problem, upon which TcT provides the 1171.86/297.06 certificate MAYBE. 1171.86/297.06 1171.86/297.06 Strict DPs: 1171.86/297.06 { t^#(N) -> c_1(q^#(N), N) 1171.86/297.06 , t^#(X) -> c_2(X) 1171.86/297.06 , q^#(0()) -> c_3() 1171.86/297.06 , q^#(s(X)) -> c_4(s^#(p(q(X), d(X)))) 1171.86/297.06 , s^#(X) -> c_5(X) 1171.86/297.06 , p^#(X, 0()) -> c_6(X) 1171.86/297.06 , p^#(0(), X) -> c_7(X) 1171.86/297.06 , p^#(s(X), s(Y)) -> c_8(s^#(s(p(X, Y)))) 1171.86/297.06 , d^#(0()) -> c_9() 1171.86/297.06 , d^#(s(X)) -> c_10(s^#(s(d(X)))) 1171.86/297.06 , f^#(X1, X2) -> c_11(X1, X2) 1171.86/297.06 , f^#(0(), X) -> c_12() 1171.86/297.06 , f^#(s(X), cs(Y, Z)) -> c_13(Y, X, a^#(Z)) 1171.86/297.06 , a^#(X) -> c_14(X) 1171.86/297.06 , a^#(nt(X)) -> c_15(t^#(a(X))) 1171.86/297.06 , a^#(ns(X)) -> c_16(s^#(a(X))) 1171.86/297.06 , a^#(nf(X1, X2)) -> c_17(f^#(a(X1), a(X2))) } 1171.86/297.06 Strict Trs: 1171.86/297.06 { t(N) -> cs(r(q(N)), nt(ns(N))) 1171.86/297.06 , t(X) -> nt(X) 1171.86/297.06 , q(0()) -> 0() 1171.86/297.06 , q(s(X)) -> s(p(q(X), d(X))) 1171.86/297.06 , s(X) -> ns(X) 1171.86/297.06 , p(X, 0()) -> X 1171.86/297.06 , p(0(), X) -> X 1171.86/297.06 , p(s(X), s(Y)) -> s(s(p(X, Y))) 1171.86/297.06 , d(0()) -> 0() 1171.86/297.06 , d(s(X)) -> s(s(d(X))) 1171.86/297.06 , f(X1, X2) -> nf(X1, X2) 1171.86/297.06 , f(0(), X) -> nil() 1171.86/297.06 , f(s(X), cs(Y, Z)) -> cs(Y, nf(X, a(Z))) 1171.86/297.06 , a(X) -> X 1171.86/297.06 , a(nt(X)) -> t(a(X)) 1171.86/297.06 , a(ns(X)) -> s(a(X)) 1171.86/297.06 , a(nf(X1, X2)) -> f(a(X1), a(X2)) } 1171.86/297.06 Obligation: 1171.86/297.06 runtime complexity 1171.86/297.06 Answer: 1171.86/297.06 MAYBE 1171.86/297.06 1171.86/297.06 We estimate the number of application of {3,9,12} by applications 1171.86/297.06 of Pre({3,9,12}) = {1,2,5,6,7,11,13,14,17}. Here rules are labeled 1171.86/297.06 as follows: 1171.86/297.06 1171.86/297.06 DPs: 1171.86/297.06 { 1: t^#(N) -> c_1(q^#(N), N) 1171.86/297.06 , 2: t^#(X) -> c_2(X) 1171.86/297.06 , 3: q^#(0()) -> c_3() 1171.86/297.06 , 4: q^#(s(X)) -> c_4(s^#(p(q(X), d(X)))) 1171.86/297.06 , 5: s^#(X) -> c_5(X) 1171.86/297.06 , 6: p^#(X, 0()) -> c_6(X) 1171.86/297.06 , 7: p^#(0(), X) -> c_7(X) 1171.86/297.06 , 8: p^#(s(X), s(Y)) -> c_8(s^#(s(p(X, Y)))) 1171.86/297.06 , 9: d^#(0()) -> c_9() 1171.86/297.06 , 10: d^#(s(X)) -> c_10(s^#(s(d(X)))) 1171.86/297.06 , 11: f^#(X1, X2) -> c_11(X1, X2) 1171.86/297.06 , 12: f^#(0(), X) -> c_12() 1171.86/297.06 , 13: f^#(s(X), cs(Y, Z)) -> c_13(Y, X, a^#(Z)) 1171.86/297.06 , 14: a^#(X) -> c_14(X) 1171.86/297.06 , 15: a^#(nt(X)) -> c_15(t^#(a(X))) 1171.86/297.06 , 16: a^#(ns(X)) -> c_16(s^#(a(X))) 1171.86/297.06 , 17: a^#(nf(X1, X2)) -> c_17(f^#(a(X1), a(X2))) } 1171.86/297.06 1171.86/297.06 We are left with following problem, upon which TcT provides the 1171.86/297.06 certificate MAYBE. 1171.86/297.06 1171.86/297.06 Strict DPs: 1171.86/297.06 { t^#(N) -> c_1(q^#(N), N) 1171.86/297.06 , t^#(X) -> c_2(X) 1171.86/297.06 , q^#(s(X)) -> c_4(s^#(p(q(X), d(X)))) 1171.86/297.06 , s^#(X) -> c_5(X) 1171.86/297.06 , p^#(X, 0()) -> c_6(X) 1171.86/297.06 , p^#(0(), X) -> c_7(X) 1171.86/297.06 , p^#(s(X), s(Y)) -> c_8(s^#(s(p(X, Y)))) 1171.86/297.06 , d^#(s(X)) -> c_10(s^#(s(d(X)))) 1171.86/297.06 , f^#(X1, X2) -> c_11(X1, X2) 1171.86/297.06 , f^#(s(X), cs(Y, Z)) -> c_13(Y, X, a^#(Z)) 1171.86/297.06 , a^#(X) -> c_14(X) 1171.86/297.06 , a^#(nt(X)) -> c_15(t^#(a(X))) 1171.86/297.06 , a^#(ns(X)) -> c_16(s^#(a(X))) 1171.86/297.06 , a^#(nf(X1, X2)) -> c_17(f^#(a(X1), a(X2))) } 1171.86/297.06 Strict Trs: 1171.86/297.06 { t(N) -> cs(r(q(N)), nt(ns(N))) 1171.86/297.06 , t(X) -> nt(X) 1171.86/297.06 , q(0()) -> 0() 1171.86/297.06 , q(s(X)) -> s(p(q(X), d(X))) 1171.86/297.06 , s(X) -> ns(X) 1171.86/297.06 , p(X, 0()) -> X 1171.86/297.06 , p(0(), X) -> X 1171.86/297.06 , p(s(X), s(Y)) -> s(s(p(X, Y))) 1171.86/297.06 , d(0()) -> 0() 1171.86/297.06 , d(s(X)) -> s(s(d(X))) 1171.86/297.06 , f(X1, X2) -> nf(X1, X2) 1171.86/297.06 , f(0(), X) -> nil() 1171.86/297.06 , f(s(X), cs(Y, Z)) -> cs(Y, nf(X, a(Z))) 1171.86/297.06 , a(X) -> X 1171.86/297.06 , a(nt(X)) -> t(a(X)) 1171.86/297.06 , a(ns(X)) -> s(a(X)) 1171.86/297.06 , a(nf(X1, X2)) -> f(a(X1), a(X2)) } 1171.86/297.06 Weak DPs: 1171.86/297.06 { q^#(0()) -> c_3() 1171.86/297.06 , d^#(0()) -> c_9() 1171.86/297.06 , f^#(0(), X) -> c_12() } 1171.86/297.06 Obligation: 1171.86/297.06 runtime complexity 1171.86/297.06 Answer: 1171.86/297.06 MAYBE 1171.86/297.06 1171.86/297.06 Empty strict component of the problem is NOT empty. 1171.86/297.06 1171.86/297.06 1171.86/297.06 Arrrr.. 1172.90/297.90 EOF