MAYBE 1185.78/297.60 MAYBE 1185.78/297.60 1185.78/297.60 We are left with following problem, upon which TcT provides the 1185.78/297.60 certificate MAYBE. 1185.78/297.60 1185.78/297.60 Strict Trs: 1185.78/297.60 { a__from(X) -> cons(mark(X), from(s(X))) 1185.78/297.60 , a__from(X) -> from(X) 1185.78/297.60 , mark(cons(X1, X2)) -> cons(mark(X1), X2) 1185.78/297.60 , mark(from(X)) -> a__from(mark(X)) 1185.78/297.60 , mark(s(X)) -> s(mark(X)) 1185.78/297.60 , mark(0()) -> 0() 1185.78/297.60 , mark(nil()) -> nil() 1185.78/297.60 , mark(zWquot(X1, X2)) -> a__zWquot(mark(X1), mark(X2)) 1185.78/297.60 , mark(sel(X1, X2)) -> a__sel(mark(X1), mark(X2)) 1185.78/297.60 , mark(minus(X1, X2)) -> a__minus(mark(X1), mark(X2)) 1185.78/297.60 , mark(quot(X1, X2)) -> a__quot(mark(X1), mark(X2)) 1185.78/297.60 , a__sel(X1, X2) -> sel(X1, X2) 1185.78/297.60 , a__sel(s(N), cons(X, XS)) -> a__sel(mark(N), mark(XS)) 1185.78/297.60 , a__sel(0(), cons(X, XS)) -> mark(X) 1185.78/297.60 , a__minus(X1, X2) -> minus(X1, X2) 1185.78/297.60 , a__minus(X, 0()) -> 0() 1185.78/297.60 , a__minus(s(X), s(Y)) -> a__minus(mark(X), mark(Y)) 1185.78/297.60 , a__quot(X1, X2) -> quot(X1, X2) 1185.78/297.60 , a__quot(s(X), s(Y)) -> 1185.78/297.60 s(a__quot(a__minus(mark(X), mark(Y)), s(mark(Y)))) 1185.78/297.60 , a__quot(0(), s(Y)) -> 0() 1185.78/297.60 , a__zWquot(X1, X2) -> zWquot(X1, X2) 1185.78/297.60 , a__zWquot(XS, nil()) -> nil() 1185.78/297.60 , a__zWquot(cons(X, XS), cons(Y, YS)) -> 1185.78/297.60 cons(a__quot(mark(X), mark(Y)), zWquot(XS, YS)) 1185.78/297.60 , a__zWquot(nil(), XS) -> nil() } 1185.78/297.60 Obligation: 1185.78/297.60 runtime complexity 1185.78/297.60 Answer: 1185.78/297.60 MAYBE 1185.78/297.60 1185.78/297.60 None of the processors succeeded. 1185.78/297.60 1185.78/297.60 Details of failed attempt(s): 1185.78/297.60 ----------------------------- 1185.78/297.60 1) 'With Problem ... (timeout of 297 seconds)' failed due to the 1185.78/297.60 following reason: 1185.78/297.60 1185.78/297.60 Computation stopped due to timeout after 297.0 seconds. 1185.78/297.60 1185.78/297.60 2) 'Best' failed due to the following reason: 1185.78/297.60 1185.78/297.60 None of the processors succeeded. 1185.78/297.60 1185.78/297.60 Details of failed attempt(s): 1185.78/297.60 ----------------------------- 1185.78/297.60 1) 'With Problem ... (timeout of 148 seconds) (timeout of 297 1185.78/297.60 seconds)' failed due to the following reason: 1185.78/297.60 1185.78/297.60 Computation stopped due to timeout after 148.0 seconds. 1185.78/297.60 1185.78/297.60 2) 'Best' failed due to the following reason: 1185.78/297.60 1185.78/297.60 None of the processors succeeded. 1185.78/297.60 1185.78/297.60 Details of failed attempt(s): 1185.78/297.60 ----------------------------- 1185.78/297.60 1) 'bsearch-popstar (timeout of 297 seconds)' failed due to the 1185.78/297.60 following reason: 1185.78/297.60 1185.78/297.60 The processor is inapplicable, reason: 1185.78/297.60 Processor only applicable for innermost runtime complexity analysis 1185.78/297.60 1185.78/297.60 2) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due 1185.78/297.60 to the following reason: 1185.78/297.60 1185.78/297.60 The processor is inapplicable, reason: 1185.78/297.60 Processor only applicable for innermost runtime complexity analysis 1185.78/297.60 1185.78/297.60 1185.78/297.60 3) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)' 1185.78/297.60 failed due to the following reason: 1185.78/297.60 1185.78/297.60 None of the processors succeeded. 1185.78/297.60 1185.78/297.60 Details of failed attempt(s): 1185.78/297.60 ----------------------------- 1185.78/297.60 1) 'Bounds with minimal-enrichment and initial automaton 'match'' 1185.78/297.60 failed due to the following reason: 1185.78/297.60 1185.78/297.60 match-boundness of the problem could not be verified. 1185.78/297.60 1185.78/297.60 2) 'Bounds with perSymbol-enrichment and initial automaton 'match'' 1185.78/297.60 failed due to the following reason: 1185.78/297.60 1185.78/297.60 match-boundness of the problem could not be verified. 1185.78/297.60 1185.78/297.60 1185.78/297.60 1185.78/297.60 3) 'Weak Dependency Pairs (timeout of 297 seconds)' failed due to 1185.78/297.60 the following reason: 1185.78/297.60 1185.78/297.60 We add the following weak dependency pairs: 1185.78/297.60 1185.78/297.60 Strict DPs: 1185.78/297.60 { a__from^#(X) -> c_1(mark^#(X), X) 1185.78/297.60 , a__from^#(X) -> c_2(X) 1185.78/297.60 , mark^#(cons(X1, X2)) -> c_3(mark^#(X1), X2) 1185.78/297.60 , mark^#(from(X)) -> c_4(a__from^#(mark(X))) 1185.78/297.60 , mark^#(s(X)) -> c_5(mark^#(X)) 1185.78/297.60 , mark^#(0()) -> c_6() 1185.78/297.60 , mark^#(nil()) -> c_7() 1185.78/297.60 , mark^#(zWquot(X1, X2)) -> c_8(a__zWquot^#(mark(X1), mark(X2))) 1185.78/297.60 , mark^#(sel(X1, X2)) -> c_9(a__sel^#(mark(X1), mark(X2))) 1185.78/297.60 , mark^#(minus(X1, X2)) -> c_10(a__minus^#(mark(X1), mark(X2))) 1185.78/297.60 , mark^#(quot(X1, X2)) -> c_11(a__quot^#(mark(X1), mark(X2))) 1185.78/297.60 , a__zWquot^#(X1, X2) -> c_21(X1, X2) 1185.78/297.60 , a__zWquot^#(XS, nil()) -> c_22() 1185.78/297.60 , a__zWquot^#(cons(X, XS), cons(Y, YS)) -> 1185.78/297.60 c_23(a__quot^#(mark(X), mark(Y)), XS, YS) 1185.78/297.60 , a__zWquot^#(nil(), XS) -> c_24() 1185.78/297.60 , a__sel^#(X1, X2) -> c_12(X1, X2) 1185.78/297.60 , a__sel^#(s(N), cons(X, XS)) -> c_13(a__sel^#(mark(N), mark(XS))) 1186.21/297.60 , a__sel^#(0(), cons(X, XS)) -> c_14(mark^#(X)) 1186.21/297.60 , a__minus^#(X1, X2) -> c_15(X1, X2) 1186.21/297.60 , a__minus^#(X, 0()) -> c_16() 1186.21/297.60 , a__minus^#(s(X), s(Y)) -> c_17(a__minus^#(mark(X), mark(Y))) 1186.21/297.60 , a__quot^#(X1, X2) -> c_18(X1, X2) 1186.21/297.60 , a__quot^#(s(X), s(Y)) -> 1186.21/297.60 c_19(a__quot^#(a__minus(mark(X), mark(Y)), s(mark(Y)))) 1186.21/297.60 , a__quot^#(0(), s(Y)) -> c_20() } 1186.21/297.60 1186.21/297.60 and mark the set of starting terms. 1186.21/297.60 1186.21/297.60 We are left with following problem, upon which TcT provides the 1186.21/297.60 certificate MAYBE. 1186.21/297.60 1186.21/297.60 Strict DPs: 1186.21/297.60 { a__from^#(X) -> c_1(mark^#(X), X) 1186.21/297.60 , a__from^#(X) -> c_2(X) 1186.21/297.60 , mark^#(cons(X1, X2)) -> c_3(mark^#(X1), X2) 1186.21/297.60 , mark^#(from(X)) -> c_4(a__from^#(mark(X))) 1186.21/297.60 , mark^#(s(X)) -> c_5(mark^#(X)) 1186.21/297.60 , mark^#(0()) -> c_6() 1186.21/297.60 , mark^#(nil()) -> c_7() 1186.21/297.60 , mark^#(zWquot(X1, X2)) -> c_8(a__zWquot^#(mark(X1), mark(X2))) 1186.21/297.60 , mark^#(sel(X1, X2)) -> c_9(a__sel^#(mark(X1), mark(X2))) 1186.21/297.60 , mark^#(minus(X1, X2)) -> c_10(a__minus^#(mark(X1), mark(X2))) 1186.21/297.60 , mark^#(quot(X1, X2)) -> c_11(a__quot^#(mark(X1), mark(X2))) 1186.21/297.60 , a__zWquot^#(X1, X2) -> c_21(X1, X2) 1186.21/297.60 , a__zWquot^#(XS, nil()) -> c_22() 1186.21/297.60 , a__zWquot^#(cons(X, XS), cons(Y, YS)) -> 1186.21/297.60 c_23(a__quot^#(mark(X), mark(Y)), XS, YS) 1186.21/297.60 , a__zWquot^#(nil(), XS) -> c_24() 1186.21/297.60 , a__sel^#(X1, X2) -> c_12(X1, X2) 1186.21/297.60 , a__sel^#(s(N), cons(X, XS)) -> c_13(a__sel^#(mark(N), mark(XS))) 1186.21/297.60 , a__sel^#(0(), cons(X, XS)) -> c_14(mark^#(X)) 1186.21/297.60 , a__minus^#(X1, X2) -> c_15(X1, X2) 1186.21/297.60 , a__minus^#(X, 0()) -> c_16() 1186.21/297.60 , a__minus^#(s(X), s(Y)) -> c_17(a__minus^#(mark(X), mark(Y))) 1186.21/297.60 , a__quot^#(X1, X2) -> c_18(X1, X2) 1186.21/297.60 , a__quot^#(s(X), s(Y)) -> 1186.21/297.60 c_19(a__quot^#(a__minus(mark(X), mark(Y)), s(mark(Y)))) 1186.21/297.60 , a__quot^#(0(), s(Y)) -> c_20() } 1186.21/297.60 Strict Trs: 1186.21/297.60 { a__from(X) -> cons(mark(X), from(s(X))) 1186.21/297.60 , a__from(X) -> from(X) 1186.21/297.60 , mark(cons(X1, X2)) -> cons(mark(X1), X2) 1186.21/297.60 , mark(from(X)) -> a__from(mark(X)) 1186.21/297.60 , mark(s(X)) -> s(mark(X)) 1186.21/297.60 , mark(0()) -> 0() 1186.21/297.60 , mark(nil()) -> nil() 1186.21/297.60 , mark(zWquot(X1, X2)) -> a__zWquot(mark(X1), mark(X2)) 1186.21/297.60 , mark(sel(X1, X2)) -> a__sel(mark(X1), mark(X2)) 1186.21/297.60 , mark(minus(X1, X2)) -> a__minus(mark(X1), mark(X2)) 1186.21/297.60 , mark(quot(X1, X2)) -> a__quot(mark(X1), mark(X2)) 1186.21/297.60 , a__sel(X1, X2) -> sel(X1, X2) 1186.21/297.60 , a__sel(s(N), cons(X, XS)) -> a__sel(mark(N), mark(XS)) 1186.21/297.60 , a__sel(0(), cons(X, XS)) -> mark(X) 1186.21/297.60 , a__minus(X1, X2) -> minus(X1, X2) 1186.21/297.60 , a__minus(X, 0()) -> 0() 1186.21/297.60 , a__minus(s(X), s(Y)) -> a__minus(mark(X), mark(Y)) 1186.21/297.60 , a__quot(X1, X2) -> quot(X1, X2) 1186.21/297.60 , a__quot(s(X), s(Y)) -> 1186.21/297.60 s(a__quot(a__minus(mark(X), mark(Y)), s(mark(Y)))) 1186.21/297.60 , a__quot(0(), s(Y)) -> 0() 1186.21/297.60 , a__zWquot(X1, X2) -> zWquot(X1, X2) 1186.21/297.60 , a__zWquot(XS, nil()) -> nil() 1186.21/297.60 , a__zWquot(cons(X, XS), cons(Y, YS)) -> 1186.21/297.60 cons(a__quot(mark(X), mark(Y)), zWquot(XS, YS)) 1186.21/297.60 , a__zWquot(nil(), XS) -> nil() } 1186.21/297.60 Obligation: 1186.21/297.60 runtime complexity 1186.21/297.60 Answer: 1186.21/297.60 MAYBE 1186.21/297.60 1186.21/297.60 We estimate the number of application of {6,7,13,15,20,24} by 1186.21/297.60 applications of Pre({6,7,13,15,20,24}) = 1186.21/297.60 {1,2,3,5,8,10,11,12,14,16,18,19,21,22,23}. Here rules are labeled 1186.21/297.60 as follows: 1186.21/297.60 1186.21/297.60 DPs: 1186.21/297.60 { 1: a__from^#(X) -> c_1(mark^#(X), X) 1186.21/297.60 , 2: a__from^#(X) -> c_2(X) 1186.21/297.60 , 3: mark^#(cons(X1, X2)) -> c_3(mark^#(X1), X2) 1186.21/297.60 , 4: mark^#(from(X)) -> c_4(a__from^#(mark(X))) 1186.21/297.60 , 5: mark^#(s(X)) -> c_5(mark^#(X)) 1186.21/297.60 , 6: mark^#(0()) -> c_6() 1186.21/297.60 , 7: mark^#(nil()) -> c_7() 1186.21/297.60 , 8: mark^#(zWquot(X1, X2)) -> c_8(a__zWquot^#(mark(X1), mark(X2))) 1186.21/297.60 , 9: mark^#(sel(X1, X2)) -> c_9(a__sel^#(mark(X1), mark(X2))) 1186.21/297.60 , 10: mark^#(minus(X1, X2)) -> c_10(a__minus^#(mark(X1), mark(X2))) 1186.21/297.60 , 11: mark^#(quot(X1, X2)) -> c_11(a__quot^#(mark(X1), mark(X2))) 1186.21/297.60 , 12: a__zWquot^#(X1, X2) -> c_21(X1, X2) 1186.21/297.60 , 13: a__zWquot^#(XS, nil()) -> c_22() 1186.21/297.60 , 14: a__zWquot^#(cons(X, XS), cons(Y, YS)) -> 1186.21/297.60 c_23(a__quot^#(mark(X), mark(Y)), XS, YS) 1186.21/297.62 , 15: a__zWquot^#(nil(), XS) -> c_24() 1186.21/297.62 , 16: a__sel^#(X1, X2) -> c_12(X1, X2) 1186.21/297.62 , 17: a__sel^#(s(N), cons(X, XS)) -> 1186.21/297.62 c_13(a__sel^#(mark(N), mark(XS))) 1186.21/297.62 , 18: a__sel^#(0(), cons(X, XS)) -> c_14(mark^#(X)) 1186.21/297.62 , 19: a__minus^#(X1, X2) -> c_15(X1, X2) 1186.21/297.62 , 20: a__minus^#(X, 0()) -> c_16() 1186.21/297.62 , 21: a__minus^#(s(X), s(Y)) -> c_17(a__minus^#(mark(X), mark(Y))) 1186.21/297.62 , 22: a__quot^#(X1, X2) -> c_18(X1, X2) 1186.21/297.62 , 23: a__quot^#(s(X), s(Y)) -> 1186.21/297.62 c_19(a__quot^#(a__minus(mark(X), mark(Y)), s(mark(Y)))) 1186.21/297.62 , 24: a__quot^#(0(), s(Y)) -> c_20() } 1186.21/297.62 1186.21/297.62 We are left with following problem, upon which TcT provides the 1186.21/297.62 certificate MAYBE. 1186.21/297.62 1186.21/297.62 Strict DPs: 1186.21/297.62 { a__from^#(X) -> c_1(mark^#(X), X) 1186.21/297.62 , a__from^#(X) -> c_2(X) 1186.21/297.62 , mark^#(cons(X1, X2)) -> c_3(mark^#(X1), X2) 1186.21/297.62 , mark^#(from(X)) -> c_4(a__from^#(mark(X))) 1186.21/297.62 , mark^#(s(X)) -> c_5(mark^#(X)) 1186.21/297.62 , mark^#(zWquot(X1, X2)) -> c_8(a__zWquot^#(mark(X1), mark(X2))) 1186.21/297.62 , mark^#(sel(X1, X2)) -> c_9(a__sel^#(mark(X1), mark(X2))) 1186.21/297.62 , mark^#(minus(X1, X2)) -> c_10(a__minus^#(mark(X1), mark(X2))) 1186.21/297.62 , mark^#(quot(X1, X2)) -> c_11(a__quot^#(mark(X1), mark(X2))) 1186.21/297.62 , a__zWquot^#(X1, X2) -> c_21(X1, X2) 1186.21/297.62 , a__zWquot^#(cons(X, XS), cons(Y, YS)) -> 1186.21/297.62 c_23(a__quot^#(mark(X), mark(Y)), XS, YS) 1186.21/297.62 , a__sel^#(X1, X2) -> c_12(X1, X2) 1186.21/297.62 , a__sel^#(s(N), cons(X, XS)) -> c_13(a__sel^#(mark(N), mark(XS))) 1186.21/297.62 , a__sel^#(0(), cons(X, XS)) -> c_14(mark^#(X)) 1186.21/297.62 , a__minus^#(X1, X2) -> c_15(X1, X2) 1186.21/297.62 , a__minus^#(s(X), s(Y)) -> c_17(a__minus^#(mark(X), mark(Y))) 1186.21/297.62 , a__quot^#(X1, X2) -> c_18(X1, X2) 1186.21/297.62 , a__quot^#(s(X), s(Y)) -> 1186.21/297.62 c_19(a__quot^#(a__minus(mark(X), mark(Y)), s(mark(Y)))) } 1186.21/297.62 Strict Trs: 1186.21/297.62 { a__from(X) -> cons(mark(X), from(s(X))) 1186.21/297.62 , a__from(X) -> from(X) 1186.21/297.62 , mark(cons(X1, X2)) -> cons(mark(X1), X2) 1186.21/297.62 , mark(from(X)) -> a__from(mark(X)) 1186.21/297.62 , mark(s(X)) -> s(mark(X)) 1186.21/297.62 , mark(0()) -> 0() 1186.21/297.62 , mark(nil()) -> nil() 1186.21/297.62 , mark(zWquot(X1, X2)) -> a__zWquot(mark(X1), mark(X2)) 1186.21/297.62 , mark(sel(X1, X2)) -> a__sel(mark(X1), mark(X2)) 1186.21/297.62 , mark(minus(X1, X2)) -> a__minus(mark(X1), mark(X2)) 1186.21/297.62 , mark(quot(X1, X2)) -> a__quot(mark(X1), mark(X2)) 1186.21/297.62 , a__sel(X1, X2) -> sel(X1, X2) 1186.21/297.62 , a__sel(s(N), cons(X, XS)) -> a__sel(mark(N), mark(XS)) 1186.21/297.62 , a__sel(0(), cons(X, XS)) -> mark(X) 1186.21/297.62 , a__minus(X1, X2) -> minus(X1, X2) 1186.21/297.62 , a__minus(X, 0()) -> 0() 1186.21/297.62 , a__minus(s(X), s(Y)) -> a__minus(mark(X), mark(Y)) 1186.21/297.62 , a__quot(X1, X2) -> quot(X1, X2) 1186.21/297.62 , a__quot(s(X), s(Y)) -> 1186.21/297.62 s(a__quot(a__minus(mark(X), mark(Y)), s(mark(Y)))) 1186.21/297.62 , a__quot(0(), s(Y)) -> 0() 1186.21/297.62 , a__zWquot(X1, X2) -> zWquot(X1, X2) 1186.21/297.62 , a__zWquot(XS, nil()) -> nil() 1186.21/297.62 , a__zWquot(cons(X, XS), cons(Y, YS)) -> 1186.21/297.62 cons(a__quot(mark(X), mark(Y)), zWquot(XS, YS)) 1186.21/297.62 , a__zWquot(nil(), XS) -> nil() } 1186.21/297.62 Weak DPs: 1186.21/297.62 { mark^#(0()) -> c_6() 1186.21/297.62 , mark^#(nil()) -> c_7() 1186.21/297.62 , a__zWquot^#(XS, nil()) -> c_22() 1186.21/297.62 , a__zWquot^#(nil(), XS) -> c_24() 1186.21/297.62 , a__minus^#(X, 0()) -> c_16() 1186.21/297.62 , a__quot^#(0(), s(Y)) -> c_20() } 1186.21/297.62 Obligation: 1186.21/297.62 runtime complexity 1186.21/297.62 Answer: 1186.21/297.62 MAYBE 1186.21/297.62 1186.21/297.62 Empty strict component of the problem is NOT empty. 1186.21/297.62 1186.21/297.62 1186.21/297.62 Arrrr.. 1187.28/298.60 EOF