MAYBE 1048.65/297.06 MAYBE 1048.65/297.06 1048.65/297.06 We are left with following problem, upon which TcT provides the 1048.65/297.06 certificate MAYBE. 1048.65/297.06 1048.65/297.06 Strict Trs: 1048.65/297.06 { U101(tt(), N, XS) -> fst(splitAt(activate(N), activate(XS))) 1048.65/297.06 , fst(X) -> n__fst(X) 1048.65/297.06 , fst(pair(X, Y)) -> U21(and(isLNat(X), n__isLNat(Y)), X) 1048.65/297.06 , splitAt(X1, X2) -> n__splitAt(X1, X2) 1048.65/297.06 , splitAt(s(N), cons(X, XS)) -> 1048.65/297.06 U81(and(isNatural(N), 1048.65/297.06 n__and(isNatural(X), n__isLNat(activate(XS)))), 1048.65/297.06 N, 1048.65/297.06 X, 1048.65/297.06 activate(XS)) 1048.65/297.06 , splitAt(0(), XS) -> U71(isLNat(XS), XS) 1048.65/297.06 , activate(X) -> X 1048.65/297.06 , activate(n__natsFrom(X)) -> natsFrom(X) 1048.65/297.06 , activate(n__isLNat(X)) -> isLNat(X) 1048.65/297.06 , activate(n__nil()) -> nil() 1048.65/297.06 , activate(n__afterNth(X1, X2)) -> afterNth(X1, X2) 1048.65/297.06 , activate(n__cons(X1, X2)) -> cons(X1, X2) 1048.65/297.06 , activate(n__fst(X)) -> fst(X) 1048.65/297.06 , activate(n__snd(X)) -> snd(X) 1048.65/297.06 , activate(n__tail(X)) -> tail(X) 1048.65/297.06 , activate(n__take(X1, X2)) -> take(X1, X2) 1048.65/297.06 , activate(n__0()) -> 0() 1048.65/297.06 , activate(n__head(X)) -> head(X) 1048.65/297.06 , activate(n__s(X)) -> s(X) 1048.65/297.06 , activate(n__sel(X1, X2)) -> sel(X1, X2) 1048.65/297.06 , activate(n__pair(X1, X2)) -> pair(X1, X2) 1048.65/297.06 , activate(n__splitAt(X1, X2)) -> splitAt(X1, X2) 1048.65/297.06 , activate(n__and(X1, X2)) -> and(X1, X2) 1048.65/297.06 , U11(tt(), N, XS) -> snd(splitAt(activate(N), activate(XS))) 1048.65/297.06 , snd(X) -> n__snd(X) 1048.65/297.06 , snd(pair(X, Y)) -> U61(and(isLNat(X), n__isLNat(Y)), Y) 1048.65/297.06 , U21(tt(), X) -> activate(X) 1048.65/297.06 , U31(tt(), N) -> activate(N) 1048.65/297.06 , U41(tt(), N) -> cons(activate(N), n__natsFrom(s(activate(N)))) 1048.65/297.06 , cons(X1, X2) -> n__cons(X1, X2) 1048.65/297.06 , s(X) -> n__s(X) 1048.65/297.06 , U51(tt(), N, XS) -> head(afterNth(activate(N), activate(XS))) 1048.65/297.06 , head(X) -> n__head(X) 1048.65/297.06 , head(cons(N, XS)) -> 1048.65/297.06 U31(and(isNatural(N), n__isLNat(activate(XS))), N) 1048.65/297.06 , afterNth(N, XS) -> U11(and(isNatural(N), n__isLNat(XS)), N, XS) 1048.65/297.06 , afterNth(X1, X2) -> n__afterNth(X1, X2) 1048.65/297.06 , U61(tt(), Y) -> activate(Y) 1048.65/297.06 , U71(tt(), XS) -> pair(nil(), activate(XS)) 1048.65/297.06 , pair(X1, X2) -> n__pair(X1, X2) 1048.65/297.06 , nil() -> n__nil() 1048.65/297.06 , U81(tt(), N, X, XS) -> 1048.65/297.06 U82(splitAt(activate(N), activate(XS)), activate(X)) 1048.65/297.06 , U82(pair(YS, ZS), X) -> pair(cons(activate(X), YS), ZS) 1048.65/297.06 , U91(tt(), XS) -> activate(XS) 1048.65/297.06 , and(X1, X2) -> n__and(X1, X2) 1048.65/297.06 , and(tt(), X) -> activate(X) 1048.65/297.06 , isNatural(n__0()) -> tt() 1048.65/297.06 , isNatural(n__head(V1)) -> isLNat(activate(V1)) 1048.65/297.06 , isNatural(n__s(V1)) -> isNatural(activate(V1)) 1048.65/297.06 , isNatural(n__sel(V1, V2)) -> 1048.65/297.06 and(isNatural(activate(V1)), n__isLNat(activate(V2))) 1048.65/297.06 , isLNat(X) -> n__isLNat(X) 1048.65/297.06 , isLNat(n__natsFrom(V1)) -> isNatural(activate(V1)) 1048.65/297.06 , isLNat(n__nil()) -> tt() 1048.65/297.06 , isLNat(n__afterNth(V1, V2)) -> 1048.65/297.06 and(isNatural(activate(V1)), n__isLNat(activate(V2))) 1048.65/297.06 , isLNat(n__cons(V1, V2)) -> 1048.65/297.06 and(isNatural(activate(V1)), n__isLNat(activate(V2))) 1048.65/297.06 , isLNat(n__fst(V1)) -> isPLNat(activate(V1)) 1048.65/297.06 , isLNat(n__snd(V1)) -> isPLNat(activate(V1)) 1048.65/297.06 , isLNat(n__tail(V1)) -> isLNat(activate(V1)) 1048.65/297.06 , isLNat(n__take(V1, V2)) -> 1048.65/297.06 and(isNatural(activate(V1)), n__isLNat(activate(V2))) 1048.65/297.06 , isPLNat(n__pair(V1, V2)) -> 1048.65/297.06 and(isLNat(activate(V1)), n__isLNat(activate(V2))) 1048.65/297.06 , isPLNat(n__splitAt(V1, V2)) -> 1048.65/297.06 and(isNatural(activate(V1)), n__isLNat(activate(V2))) 1048.65/297.06 , natsFrom(N) -> U41(isNatural(N), N) 1048.65/297.06 , natsFrom(X) -> n__natsFrom(X) 1048.65/297.06 , sel(N, XS) -> U51(and(isNatural(N), n__isLNat(XS)), N, XS) 1048.65/297.06 , sel(X1, X2) -> n__sel(X1, X2) 1048.65/297.06 , 0() -> n__0() 1048.65/297.06 , tail(X) -> n__tail(X) 1048.65/297.06 , tail(cons(N, XS)) -> 1048.65/297.06 U91(and(isNatural(N), n__isLNat(activate(XS))), activate(XS)) 1048.65/297.06 , take(N, XS) -> U101(and(isNatural(N), n__isLNat(XS)), N, XS) 1048.65/297.06 , take(X1, X2) -> n__take(X1, X2) } 1048.65/297.06 Obligation: 1048.65/297.06 innermost runtime complexity 1048.65/297.06 Answer: 1048.65/297.06 MAYBE 1048.65/297.06 1048.65/297.06 Arguments of following rules are not normal-forms: 1048.65/297.06 1048.65/297.06 { fst(pair(X, Y)) -> U21(and(isLNat(X), n__isLNat(Y)), X) 1048.65/297.06 , splitAt(s(N), cons(X, XS)) -> 1048.65/297.06 U81(and(isNatural(N), 1048.65/297.06 n__and(isNatural(X), n__isLNat(activate(XS)))), 1048.65/297.06 N, 1048.65/297.06 X, 1048.65/297.06 activate(XS)) 1048.65/297.06 , splitAt(0(), XS) -> U71(isLNat(XS), XS) 1048.65/297.06 , snd(pair(X, Y)) -> U61(and(isLNat(X), n__isLNat(Y)), Y) 1048.65/297.06 , head(cons(N, XS)) -> 1048.65/297.06 U31(and(isNatural(N), n__isLNat(activate(XS))), N) 1048.65/297.06 , U82(pair(YS, ZS), X) -> pair(cons(activate(X), YS), ZS) 1048.65/297.06 , tail(cons(N, XS)) -> 1048.65/297.06 U91(and(isNatural(N), n__isLNat(activate(XS))), activate(XS)) } 1048.65/297.06 1048.65/297.06 All above mentioned rules can be savely removed. 1048.65/297.06 1048.65/297.06 We are left with following problem, upon which TcT provides the 1048.65/297.06 certificate MAYBE. 1048.65/297.06 1048.65/297.06 Strict Trs: 1048.65/297.06 { U101(tt(), N, XS) -> fst(splitAt(activate(N), activate(XS))) 1048.65/297.06 , fst(X) -> n__fst(X) 1048.65/297.06 , splitAt(X1, X2) -> n__splitAt(X1, X2) 1048.65/297.06 , activate(X) -> X 1048.65/297.06 , activate(n__natsFrom(X)) -> natsFrom(X) 1048.65/297.06 , activate(n__isLNat(X)) -> isLNat(X) 1048.65/297.06 , activate(n__nil()) -> nil() 1048.65/297.06 , activate(n__afterNth(X1, X2)) -> afterNth(X1, X2) 1048.65/297.06 , activate(n__cons(X1, X2)) -> cons(X1, X2) 1048.65/297.06 , activate(n__fst(X)) -> fst(X) 1048.65/297.06 , activate(n__snd(X)) -> snd(X) 1048.65/297.06 , activate(n__tail(X)) -> tail(X) 1048.65/297.06 , activate(n__take(X1, X2)) -> take(X1, X2) 1048.65/297.06 , activate(n__0()) -> 0() 1048.65/297.06 , activate(n__head(X)) -> head(X) 1048.65/297.06 , activate(n__s(X)) -> s(X) 1048.65/297.06 , activate(n__sel(X1, X2)) -> sel(X1, X2) 1048.65/297.06 , activate(n__pair(X1, X2)) -> pair(X1, X2) 1048.65/297.06 , activate(n__splitAt(X1, X2)) -> splitAt(X1, X2) 1048.65/297.06 , activate(n__and(X1, X2)) -> and(X1, X2) 1048.65/297.06 , U11(tt(), N, XS) -> snd(splitAt(activate(N), activate(XS))) 1048.65/297.06 , snd(X) -> n__snd(X) 1048.65/297.06 , U21(tt(), X) -> activate(X) 1048.65/297.06 , U31(tt(), N) -> activate(N) 1048.65/297.06 , U41(tt(), N) -> cons(activate(N), n__natsFrom(s(activate(N)))) 1048.65/297.06 , cons(X1, X2) -> n__cons(X1, X2) 1048.65/297.06 , s(X) -> n__s(X) 1048.65/297.06 , U51(tt(), N, XS) -> head(afterNth(activate(N), activate(XS))) 1048.65/297.06 , head(X) -> n__head(X) 1048.65/297.06 , afterNth(N, XS) -> U11(and(isNatural(N), n__isLNat(XS)), N, XS) 1048.65/297.06 , afterNth(X1, X2) -> n__afterNth(X1, X2) 1048.65/297.06 , U61(tt(), Y) -> activate(Y) 1048.65/297.06 , U71(tt(), XS) -> pair(nil(), activate(XS)) 1048.65/297.06 , pair(X1, X2) -> n__pair(X1, X2) 1048.65/297.06 , nil() -> n__nil() 1048.65/297.06 , U81(tt(), N, X, XS) -> 1048.65/297.06 U82(splitAt(activate(N), activate(XS)), activate(X)) 1048.65/297.06 , U91(tt(), XS) -> activate(XS) 1048.65/297.06 , and(X1, X2) -> n__and(X1, X2) 1048.65/297.06 , and(tt(), X) -> activate(X) 1048.65/297.06 , isNatural(n__0()) -> tt() 1048.65/297.06 , isNatural(n__head(V1)) -> isLNat(activate(V1)) 1048.65/297.06 , isNatural(n__s(V1)) -> isNatural(activate(V1)) 1048.65/297.06 , isNatural(n__sel(V1, V2)) -> 1048.65/297.06 and(isNatural(activate(V1)), n__isLNat(activate(V2))) 1048.65/297.06 , isLNat(X) -> n__isLNat(X) 1048.65/297.06 , isLNat(n__natsFrom(V1)) -> isNatural(activate(V1)) 1048.65/297.06 , isLNat(n__nil()) -> tt() 1048.65/297.06 , isLNat(n__afterNth(V1, V2)) -> 1048.65/297.06 and(isNatural(activate(V1)), n__isLNat(activate(V2))) 1048.65/297.06 , isLNat(n__cons(V1, V2)) -> 1048.65/297.06 and(isNatural(activate(V1)), n__isLNat(activate(V2))) 1048.65/297.06 , isLNat(n__fst(V1)) -> isPLNat(activate(V1)) 1048.65/297.06 , isLNat(n__snd(V1)) -> isPLNat(activate(V1)) 1048.65/297.06 , isLNat(n__tail(V1)) -> isLNat(activate(V1)) 1048.65/297.06 , isLNat(n__take(V1, V2)) -> 1048.65/297.06 and(isNatural(activate(V1)), n__isLNat(activate(V2))) 1048.65/297.06 , isPLNat(n__pair(V1, V2)) -> 1048.65/297.06 and(isLNat(activate(V1)), n__isLNat(activate(V2))) 1048.65/297.06 , isPLNat(n__splitAt(V1, V2)) -> 1048.65/297.06 and(isNatural(activate(V1)), n__isLNat(activate(V2))) 1048.65/297.06 , natsFrom(N) -> U41(isNatural(N), N) 1048.65/297.06 , natsFrom(X) -> n__natsFrom(X) 1048.65/297.06 , sel(N, XS) -> U51(and(isNatural(N), n__isLNat(XS)), N, XS) 1048.65/297.06 , sel(X1, X2) -> n__sel(X1, X2) 1048.65/297.06 , 0() -> n__0() 1048.65/297.06 , tail(X) -> n__tail(X) 1048.65/297.06 , take(N, XS) -> U101(and(isNatural(N), n__isLNat(XS)), N, XS) 1048.65/297.06 , take(X1, X2) -> n__take(X1, X2) } 1048.65/297.06 Obligation: 1048.65/297.06 innermost runtime complexity 1048.65/297.06 Answer: 1048.65/297.06 MAYBE 1048.65/297.06 1048.65/297.06 None of the processors succeeded. 1048.65/297.06 1048.65/297.06 Details of failed attempt(s): 1048.65/297.06 ----------------------------- 1048.65/297.06 1) 'empty' failed due to the following reason: 1048.65/297.06 1048.65/297.06 Empty strict component of the problem is NOT empty. 1048.65/297.06 1048.65/297.06 2) 'Best' failed due to the following reason: 1048.65/297.06 1048.65/297.06 None of the processors succeeded. 1048.65/297.06 1048.65/297.06 Details of failed attempt(s): 1048.65/297.06 ----------------------------- 1048.65/297.06 1) 'With Problem ... (timeout of 297 seconds)' failed due to the 1048.65/297.06 following reason: 1048.65/297.06 1048.65/297.06 Computation stopped due to timeout after 297.0 seconds. 1048.65/297.06 1048.65/297.06 2) 'Best' failed due to the following reason: 1048.65/297.06 1048.65/297.06 None of the processors succeeded. 1048.65/297.06 1048.65/297.06 Details of failed attempt(s): 1048.65/297.06 ----------------------------- 1048.65/297.06 1) 'With Problem ... (timeout of 148 seconds) (timeout of 297 1048.65/297.06 seconds)' failed due to the following reason: 1048.65/297.06 1048.65/297.06 Computation stopped due to timeout after 148.0 seconds. 1048.65/297.06 1048.65/297.06 2) 'Best' failed due to the following reason: 1048.65/297.06 1048.65/297.06 None of the processors succeeded. 1048.65/297.06 1048.65/297.06 Details of failed attempt(s): 1048.65/297.06 ----------------------------- 1048.65/297.06 1) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due 1048.65/297.06 to the following reason: 1048.65/297.06 1048.65/297.06 The input cannot be shown compatible 1048.65/297.06 1048.65/297.06 2) 'bsearch-popstar (timeout of 297 seconds)' failed due to the 1048.65/297.06 following reason: 1048.65/297.06 1048.65/297.06 The input cannot be shown compatible 1048.65/297.06 1048.65/297.06 1048.65/297.06 3) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)' 1048.65/297.06 failed due to the following reason: 1048.65/297.06 1048.65/297.06 None of the processors succeeded. 1048.65/297.06 1048.65/297.06 Details of failed attempt(s): 1048.65/297.06 ----------------------------- 1048.65/297.06 1) 'Bounds with minimal-enrichment and initial automaton 'match'' 1048.65/297.06 failed due to the following reason: 1048.65/297.06 1048.65/297.06 match-boundness of the problem could not be verified. 1048.65/297.06 1048.65/297.06 2) 'Bounds with perSymbol-enrichment and initial automaton 'match'' 1048.65/297.06 failed due to the following reason: 1048.65/297.06 1048.65/297.06 match-boundness of the problem could not be verified. 1048.65/297.06 1048.65/297.06 1048.65/297.06 1048.65/297.06 1048.65/297.06 1048.65/297.06 Arrrr.. 1051.76/300.04 EOF