MAYBE 840.91/297.20 MAYBE 840.91/297.20 840.91/297.20 We are left with following problem, upon which TcT provides the 840.91/297.20 certificate MAYBE. 840.91/297.20 840.91/297.20 Strict Trs: 840.91/297.20 { active(U101(X1, X2, X3)) -> U101(active(X1), X2, X3) 840.91/297.20 , active(U101(tt(), V1, V2)) -> mark(U102(isNatural(V1), V2)) 840.91/297.20 , active(U102(X1, X2)) -> U102(active(X1), X2) 840.91/297.20 , active(U102(tt(), V2)) -> mark(U103(isLNat(V2))) 840.91/297.20 , active(isNatural(s(V1))) -> mark(U121(isNaturalKind(V1), V1)) 840.91/297.20 , active(isNatural(head(V1))) -> mark(U111(isLNatKind(V1), V1)) 840.91/297.20 , active(isNatural(0())) -> mark(tt()) 840.91/297.20 , active(isNatural(sel(V1, V2))) -> 840.91/297.20 mark(U131(and(isNaturalKind(V1), isLNatKind(V2)), V1, V2)) 840.91/297.20 , active(U103(X)) -> U103(active(X)) 840.91/297.20 , active(U103(tt())) -> mark(tt()) 840.91/297.20 , active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1), V1)) 840.91/297.20 , active(isLNat(cons(V1, V2))) -> 840.91/297.20 mark(U51(and(isNaturalKind(V1), isLNatKind(V2)), V1, V2)) 840.91/297.20 , active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1), V1)) 840.91/297.20 , active(isLNat(afterNth(V1, V2))) -> 840.91/297.20 mark(U41(and(isNaturalKind(V1), isLNatKind(V2)), V1, V2)) 840.91/297.20 , active(isLNat(nil())) -> mark(tt()) 840.91/297.20 , active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1), V1)) 840.91/297.20 , active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1), V1)) 840.91/297.20 , active(isLNat(take(V1, V2))) -> 840.91/297.20 mark(U101(and(isNaturalKind(V1), isLNatKind(V2)), V1, V2)) 840.91/297.20 , active(U11(X1, X2, X3)) -> U11(active(X1), X2, X3) 840.91/297.20 , active(U11(tt(), N, XS)) -> mark(snd(splitAt(N, XS))) 840.91/297.20 , active(snd(X)) -> snd(active(X)) 840.91/297.20 , active(snd(pair(X, Y))) -> 840.91/297.20 mark(U181(and(and(isLNat(X), isLNatKind(X)), 840.91/297.20 and(isLNat(Y), isLNatKind(Y))), 840.91/297.20 Y)) 840.91/297.20 , active(splitAt(X1, X2)) -> splitAt(X1, active(X2)) 840.91/297.20 , active(splitAt(X1, X2)) -> splitAt(active(X1), X2) 840.91/297.20 , active(splitAt(s(N), cons(X, XS))) -> 840.91/297.20 mark(U201(and(and(isNatural(N), isNaturalKind(N)), 840.91/297.20 and(and(isNatural(X), isNaturalKind(X)), 840.91/297.20 and(isLNat(XS), isLNatKind(XS)))), 840.91/297.20 N, 840.91/297.20 X, 840.91/297.20 XS)) 840.91/297.20 , active(splitAt(0(), XS)) -> 840.91/297.20 mark(U191(and(isLNat(XS), isLNatKind(XS)), XS)) 840.91/297.20 , active(U111(X1, X2)) -> U111(active(X1), X2) 840.91/297.20 , active(U111(tt(), V1)) -> mark(U112(isLNat(V1))) 840.91/297.20 , active(U112(X)) -> U112(active(X)) 840.91/297.20 , active(U112(tt())) -> mark(tt()) 840.91/297.20 , active(U121(X1, X2)) -> U121(active(X1), X2) 840.91/297.20 , active(U121(tt(), V1)) -> mark(U122(isNatural(V1))) 840.91/297.20 , active(U122(X)) -> U122(active(X)) 840.91/297.20 , active(U122(tt())) -> mark(tt()) 840.91/297.20 , active(U131(X1, X2, X3)) -> U131(active(X1), X2, X3) 840.91/297.20 , active(U131(tt(), V1, V2)) -> mark(U132(isNatural(V1), V2)) 840.91/297.20 , active(U132(X1, X2)) -> U132(active(X1), X2) 840.91/297.20 , active(U132(tt(), V2)) -> mark(U133(isLNat(V2))) 840.91/297.20 , active(U133(X)) -> U133(active(X)) 840.91/297.20 , active(U133(tt())) -> mark(tt()) 840.91/297.20 , active(U141(X1, X2, X3)) -> U141(active(X1), X2, X3) 840.91/297.20 , active(U141(tt(), V1, V2)) -> mark(U142(isLNat(V1), V2)) 840.91/297.20 , active(U142(X1, X2)) -> U142(active(X1), X2) 840.91/297.20 , active(U142(tt(), V2)) -> mark(U143(isLNat(V2))) 840.91/297.20 , active(U143(X)) -> U143(active(X)) 840.91/297.20 , active(U143(tt())) -> mark(tt()) 840.91/297.20 , active(U151(X1, X2, X3)) -> U151(active(X1), X2, X3) 840.91/297.20 , active(U151(tt(), V1, V2)) -> mark(U152(isNatural(V1), V2)) 840.91/297.20 , active(U152(X1, X2)) -> U152(active(X1), X2) 840.91/297.20 , active(U152(tt(), V2)) -> mark(U153(isLNat(V2))) 840.91/297.20 , active(U153(X)) -> U153(active(X)) 840.91/297.20 , active(U153(tt())) -> mark(tt()) 840.91/297.20 , active(U161(X1, X2)) -> U161(active(X1), X2) 840.91/297.20 , active(U161(tt(), N)) -> mark(cons(N, natsFrom(s(N)))) 840.91/297.20 , active(cons(X1, X2)) -> cons(active(X1), X2) 840.91/297.20 , active(natsFrom(N)) -> 840.91/297.20 mark(U161(and(isNatural(N), isNaturalKind(N)), N)) 840.91/297.20 , active(natsFrom(X)) -> natsFrom(active(X)) 840.91/297.20 , active(s(X)) -> s(active(X)) 840.91/297.20 , active(U171(X1, X2, X3)) -> U171(active(X1), X2, X3) 840.91/297.20 , active(U171(tt(), N, XS)) -> mark(head(afterNth(N, XS))) 840.91/297.20 , active(head(X)) -> head(active(X)) 840.91/297.20 , active(head(cons(N, XS))) -> 840.91/297.20 mark(U31(and(and(isNatural(N), isNaturalKind(N)), 840.91/297.20 and(isLNat(XS), isLNatKind(XS))), 840.91/297.20 N)) 840.91/297.20 , active(afterNth(N, XS)) -> 840.91/297.20 mark(U11(and(and(isNatural(N), isNaturalKind(N)), 840.91/297.20 and(isLNat(XS), isLNatKind(XS))), 840.91/297.20 N, 840.91/297.20 XS)) 840.91/297.20 , active(afterNth(X1, X2)) -> afterNth(X1, active(X2)) 840.91/297.20 , active(afterNth(X1, X2)) -> afterNth(active(X1), X2) 840.91/297.20 , active(U181(X1, X2)) -> U181(active(X1), X2) 840.91/297.20 , active(U181(tt(), Y)) -> mark(Y) 840.91/297.20 , active(U191(X1, X2)) -> U191(active(X1), X2) 840.91/297.20 , active(U191(tt(), XS)) -> mark(pair(nil(), XS)) 840.91/297.20 , active(pair(X1, X2)) -> pair(X1, active(X2)) 840.91/297.20 , active(pair(X1, X2)) -> pair(active(X1), X2) 840.91/297.20 , active(U201(X1, X2, X3, X4)) -> U201(active(X1), X2, X3, X4) 840.91/297.20 , active(U201(tt(), N, X, XS)) -> mark(U202(splitAt(N, XS), X)) 840.91/297.20 , active(U202(X1, X2)) -> U202(active(X1), X2) 840.91/297.20 , active(U202(pair(YS, ZS), X)) -> mark(pair(cons(X, YS), ZS)) 840.91/297.20 , active(U21(X1, X2)) -> U21(active(X1), X2) 840.91/297.20 , active(U21(tt(), X)) -> mark(X) 840.91/297.20 , active(U211(X1, X2)) -> U211(active(X1), X2) 840.91/297.20 , active(U211(tt(), XS)) -> mark(XS) 840.91/297.20 , active(U221(X1, X2, X3)) -> U221(active(X1), X2, X3) 840.91/297.20 , active(U221(tt(), N, XS)) -> mark(fst(splitAt(N, XS))) 840.91/297.20 , active(fst(X)) -> fst(active(X)) 840.91/297.20 , active(fst(pair(X, Y))) -> 840.91/297.20 mark(U21(and(and(isLNat(X), isLNatKind(X)), 840.91/297.20 and(isLNat(Y), isLNatKind(Y))), 840.91/297.20 X)) 840.91/297.20 , active(U31(X1, X2)) -> U31(active(X1), X2) 840.91/297.20 , active(U31(tt(), N)) -> mark(N) 840.91/297.20 , active(U41(X1, X2, X3)) -> U41(active(X1), X2, X3) 840.91/297.20 , active(U41(tt(), V1, V2)) -> mark(U42(isNatural(V1), V2)) 840.91/297.20 , active(U42(X1, X2)) -> U42(active(X1), X2) 840.91/297.20 , active(U42(tt(), V2)) -> mark(U43(isLNat(V2))) 840.91/297.20 , active(U43(X)) -> U43(active(X)) 840.91/297.20 , active(U43(tt())) -> mark(tt()) 840.91/297.20 , active(U51(X1, X2, X3)) -> U51(active(X1), X2, X3) 840.91/297.20 , active(U51(tt(), V1, V2)) -> mark(U52(isNatural(V1), V2)) 840.91/297.20 , active(U52(X1, X2)) -> U52(active(X1), X2) 840.91/297.20 , active(U52(tt(), V2)) -> mark(U53(isLNat(V2))) 840.91/297.20 , active(U53(X)) -> U53(active(X)) 840.91/297.20 , active(U53(tt())) -> mark(tt()) 840.91/297.20 , active(U61(X1, X2)) -> U61(active(X1), X2) 840.91/297.20 , active(U61(tt(), V1)) -> mark(U62(isPLNat(V1))) 840.91/297.20 , active(U62(X)) -> U62(active(X)) 840.91/297.20 , active(U62(tt())) -> mark(tt()) 840.91/297.20 , active(isPLNat(splitAt(V1, V2))) -> 840.91/297.20 mark(U151(and(isNaturalKind(V1), isLNatKind(V2)), V1, V2)) 840.91/297.20 , active(isPLNat(pair(V1, V2))) -> 840.91/297.20 mark(U141(and(isLNatKind(V1), isLNatKind(V2)), V1, V2)) 840.91/297.20 , active(U71(X1, X2)) -> U71(active(X1), X2) 840.91/297.20 , active(U71(tt(), V1)) -> mark(U72(isNatural(V1))) 840.91/297.20 , active(U72(X)) -> U72(active(X)) 840.91/297.20 , active(U72(tt())) -> mark(tt()) 840.91/297.20 , active(U81(X1, X2)) -> U81(active(X1), X2) 840.91/297.20 , active(U81(tt(), V1)) -> mark(U82(isPLNat(V1))) 840.91/297.20 , active(U82(X)) -> U82(active(X)) 840.91/297.20 , active(U82(tt())) -> mark(tt()) 840.91/297.20 , active(U91(X1, X2)) -> U91(active(X1), X2) 840.91/297.20 , active(U91(tt(), V1)) -> mark(U92(isLNat(V1))) 840.91/297.20 , active(U92(X)) -> U92(active(X)) 840.91/297.20 , active(U92(tt())) -> mark(tt()) 840.91/297.20 , active(and(X1, X2)) -> and(active(X1), X2) 840.91/297.20 , active(and(tt(), X)) -> mark(X) 840.91/297.20 , active(isNaturalKind(s(V1))) -> mark(isNaturalKind(V1)) 840.91/297.20 , active(isNaturalKind(head(V1))) -> mark(isLNatKind(V1)) 840.91/297.20 , active(isNaturalKind(0())) -> mark(tt()) 840.91/297.20 , active(isNaturalKind(sel(V1, V2))) -> 840.91/297.20 mark(and(isNaturalKind(V1), isLNatKind(V2))) 840.91/297.20 , active(isLNatKind(snd(V1))) -> mark(isPLNatKind(V1)) 840.91/297.20 , active(isLNatKind(cons(V1, V2))) -> 840.91/297.20 mark(and(isNaturalKind(V1), isLNatKind(V2))) 840.91/297.20 , active(isLNatKind(natsFrom(V1))) -> mark(isNaturalKind(V1)) 840.91/297.20 , active(isLNatKind(afterNth(V1, V2))) -> 840.91/297.20 mark(and(isNaturalKind(V1), isLNatKind(V2))) 840.91/297.20 , active(isLNatKind(nil())) -> mark(tt()) 840.91/297.20 , active(isLNatKind(fst(V1))) -> mark(isPLNatKind(V1)) 840.91/297.20 , active(isLNatKind(tail(V1))) -> mark(isLNatKind(V1)) 840.91/297.20 , active(isLNatKind(take(V1, V2))) -> 840.91/297.20 mark(and(isNaturalKind(V1), isLNatKind(V2))) 840.91/297.20 , active(isPLNatKind(splitAt(V1, V2))) -> 840.91/297.20 mark(and(isNaturalKind(V1), isLNatKind(V2))) 840.91/297.20 , active(isPLNatKind(pair(V1, V2))) -> 840.91/297.20 mark(and(isLNatKind(V1), isLNatKind(V2))) 840.91/297.20 , active(tail(X)) -> tail(active(X)) 840.91/297.20 , active(tail(cons(N, XS))) -> 840.91/297.20 mark(U211(and(and(isNatural(N), isNaturalKind(N)), 840.91/297.20 and(isLNat(XS), isLNatKind(XS))), 840.91/297.20 XS)) 840.91/297.20 , active(take(N, XS)) -> 840.91/297.20 mark(U221(and(and(isNatural(N), isNaturalKind(N)), 840.91/297.20 and(isLNat(XS), isLNatKind(XS))), 840.91/297.21 N, 840.91/297.21 XS)) 840.91/297.21 , active(take(X1, X2)) -> take(X1, active(X2)) 840.91/297.21 , active(take(X1, X2)) -> take(active(X1), X2) 840.91/297.21 , active(sel(N, XS)) -> 840.91/297.21 mark(U171(and(and(isNatural(N), isNaturalKind(N)), 840.91/297.21 and(isLNat(XS), isLNatKind(XS))), 840.91/297.21 N, 840.91/297.21 XS)) 840.91/297.21 , active(sel(X1, X2)) -> sel(X1, active(X2)) 840.91/297.21 , active(sel(X1, X2)) -> sel(active(X1), X2) 840.91/297.21 , U101(mark(X1), X2, X3) -> mark(U101(X1, X2, X3)) 840.91/297.21 , U101(ok(X1), ok(X2), ok(X3)) -> ok(U101(X1, X2, X3)) 840.91/297.21 , U102(mark(X1), X2) -> mark(U102(X1, X2)) 840.91/297.21 , U102(ok(X1), ok(X2)) -> ok(U102(X1, X2)) 840.91/297.21 , isNatural(ok(X)) -> ok(isNatural(X)) 840.91/297.21 , U103(mark(X)) -> mark(U103(X)) 840.91/297.21 , U103(ok(X)) -> ok(U103(X)) 840.91/297.21 , isLNat(ok(X)) -> ok(isLNat(X)) 840.91/297.21 , U11(mark(X1), X2, X3) -> mark(U11(X1, X2, X3)) 840.91/297.21 , U11(ok(X1), ok(X2), ok(X3)) -> ok(U11(X1, X2, X3)) 840.91/297.21 , snd(mark(X)) -> mark(snd(X)) 840.91/297.21 , snd(ok(X)) -> ok(snd(X)) 840.91/297.21 , splitAt(X1, mark(X2)) -> mark(splitAt(X1, X2)) 840.91/297.21 , splitAt(mark(X1), X2) -> mark(splitAt(X1, X2)) 840.91/297.21 , splitAt(ok(X1), ok(X2)) -> ok(splitAt(X1, X2)) 840.91/297.21 , U111(mark(X1), X2) -> mark(U111(X1, X2)) 840.91/297.21 , U111(ok(X1), ok(X2)) -> ok(U111(X1, X2)) 840.91/297.21 , U112(mark(X)) -> mark(U112(X)) 840.91/297.21 , U112(ok(X)) -> ok(U112(X)) 840.91/297.21 , U121(mark(X1), X2) -> mark(U121(X1, X2)) 840.91/297.21 , U121(ok(X1), ok(X2)) -> ok(U121(X1, X2)) 840.91/297.21 , U122(mark(X)) -> mark(U122(X)) 840.91/297.21 , U122(ok(X)) -> ok(U122(X)) 840.91/297.21 , U131(mark(X1), X2, X3) -> mark(U131(X1, X2, X3)) 840.91/297.21 , U131(ok(X1), ok(X2), ok(X3)) -> ok(U131(X1, X2, X3)) 840.91/297.21 , U132(mark(X1), X2) -> mark(U132(X1, X2)) 840.91/297.21 , U132(ok(X1), ok(X2)) -> ok(U132(X1, X2)) 840.91/297.21 , U133(mark(X)) -> mark(U133(X)) 840.91/297.21 , U133(ok(X)) -> ok(U133(X)) 840.91/297.21 , U141(mark(X1), X2, X3) -> mark(U141(X1, X2, X3)) 840.91/297.21 , U141(ok(X1), ok(X2), ok(X3)) -> ok(U141(X1, X2, X3)) 840.91/297.21 , U142(mark(X1), X2) -> mark(U142(X1, X2)) 840.91/297.21 , U142(ok(X1), ok(X2)) -> ok(U142(X1, X2)) 840.91/297.21 , U143(mark(X)) -> mark(U143(X)) 840.91/297.21 , U143(ok(X)) -> ok(U143(X)) 840.91/297.21 , U151(mark(X1), X2, X3) -> mark(U151(X1, X2, X3)) 840.91/297.21 , U151(ok(X1), ok(X2), ok(X3)) -> ok(U151(X1, X2, X3)) 840.91/297.21 , U152(mark(X1), X2) -> mark(U152(X1, X2)) 840.91/297.21 , U152(ok(X1), ok(X2)) -> ok(U152(X1, X2)) 840.91/297.21 , U153(mark(X)) -> mark(U153(X)) 840.91/297.21 , U153(ok(X)) -> ok(U153(X)) 840.91/297.21 , U161(mark(X1), X2) -> mark(U161(X1, X2)) 840.91/297.21 , U161(ok(X1), ok(X2)) -> ok(U161(X1, X2)) 840.91/297.21 , cons(mark(X1), X2) -> mark(cons(X1, X2)) 840.91/297.21 , cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)) 840.91/297.21 , natsFrom(mark(X)) -> mark(natsFrom(X)) 840.91/297.21 , natsFrom(ok(X)) -> ok(natsFrom(X)) 840.91/297.21 , s(mark(X)) -> mark(s(X)) 840.91/297.21 , s(ok(X)) -> ok(s(X)) 840.91/297.21 , U171(mark(X1), X2, X3) -> mark(U171(X1, X2, X3)) 840.91/297.21 , U171(ok(X1), ok(X2), ok(X3)) -> ok(U171(X1, X2, X3)) 840.91/297.21 , head(mark(X)) -> mark(head(X)) 840.91/297.21 , head(ok(X)) -> ok(head(X)) 840.91/297.21 , afterNth(X1, mark(X2)) -> mark(afterNth(X1, X2)) 840.91/297.21 , afterNth(mark(X1), X2) -> mark(afterNth(X1, X2)) 840.91/297.21 , afterNth(ok(X1), ok(X2)) -> ok(afterNth(X1, X2)) 840.91/297.21 , U181(mark(X1), X2) -> mark(U181(X1, X2)) 840.91/297.21 , U181(ok(X1), ok(X2)) -> ok(U181(X1, X2)) 840.91/297.21 , U191(mark(X1), X2) -> mark(U191(X1, X2)) 840.91/297.21 , U191(ok(X1), ok(X2)) -> ok(U191(X1, X2)) 840.91/297.21 , pair(X1, mark(X2)) -> mark(pair(X1, X2)) 840.91/297.21 , pair(mark(X1), X2) -> mark(pair(X1, X2)) 840.91/297.21 , pair(ok(X1), ok(X2)) -> ok(pair(X1, X2)) 840.91/297.21 , U201(mark(X1), X2, X3, X4) -> mark(U201(X1, X2, X3, X4)) 840.91/297.21 , U201(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U201(X1, X2, X3, X4)) 840.91/297.21 , U202(mark(X1), X2) -> mark(U202(X1, X2)) 840.91/297.21 , U202(ok(X1), ok(X2)) -> ok(U202(X1, X2)) 840.91/297.21 , U21(mark(X1), X2) -> mark(U21(X1, X2)) 840.91/297.21 , U21(ok(X1), ok(X2)) -> ok(U21(X1, X2)) 840.91/297.21 , U211(mark(X1), X2) -> mark(U211(X1, X2)) 840.91/297.21 , U211(ok(X1), ok(X2)) -> ok(U211(X1, X2)) 840.91/297.21 , U221(mark(X1), X2, X3) -> mark(U221(X1, X2, X3)) 840.91/297.21 , U221(ok(X1), ok(X2), ok(X3)) -> ok(U221(X1, X2, X3)) 840.91/297.21 , fst(mark(X)) -> mark(fst(X)) 840.91/297.21 , fst(ok(X)) -> ok(fst(X)) 840.91/297.21 , U31(mark(X1), X2) -> mark(U31(X1, X2)) 840.91/297.21 , U31(ok(X1), ok(X2)) -> ok(U31(X1, X2)) 840.91/297.21 , U41(mark(X1), X2, X3) -> mark(U41(X1, X2, X3)) 840.91/297.21 , U41(ok(X1), ok(X2), ok(X3)) -> ok(U41(X1, X2, X3)) 840.91/297.21 , U42(mark(X1), X2) -> mark(U42(X1, X2)) 840.91/297.21 , U42(ok(X1), ok(X2)) -> ok(U42(X1, X2)) 840.91/297.21 , U43(mark(X)) -> mark(U43(X)) 840.91/297.21 , U43(ok(X)) -> ok(U43(X)) 840.91/297.21 , U51(mark(X1), X2, X3) -> mark(U51(X1, X2, X3)) 840.91/297.21 , U51(ok(X1), ok(X2), ok(X3)) -> ok(U51(X1, X2, X3)) 840.91/297.21 , U52(mark(X1), X2) -> mark(U52(X1, X2)) 840.91/297.21 , U52(ok(X1), ok(X2)) -> ok(U52(X1, X2)) 840.91/297.21 , U53(mark(X)) -> mark(U53(X)) 840.91/297.21 , U53(ok(X)) -> ok(U53(X)) 840.91/297.21 , U61(mark(X1), X2) -> mark(U61(X1, X2)) 840.91/297.21 , U61(ok(X1), ok(X2)) -> ok(U61(X1, X2)) 840.91/297.21 , U62(mark(X)) -> mark(U62(X)) 840.91/297.21 , U62(ok(X)) -> ok(U62(X)) 840.91/297.21 , isPLNat(ok(X)) -> ok(isPLNat(X)) 840.91/297.21 , U71(mark(X1), X2) -> mark(U71(X1, X2)) 840.91/297.21 , U71(ok(X1), ok(X2)) -> ok(U71(X1, X2)) 840.91/297.21 , U72(mark(X)) -> mark(U72(X)) 840.91/297.21 , U72(ok(X)) -> ok(U72(X)) 840.91/297.21 , U81(mark(X1), X2) -> mark(U81(X1, X2)) 840.91/297.21 , U81(ok(X1), ok(X2)) -> ok(U81(X1, X2)) 840.91/297.21 , U82(mark(X)) -> mark(U82(X)) 840.91/297.21 , U82(ok(X)) -> ok(U82(X)) 840.91/297.21 , U91(mark(X1), X2) -> mark(U91(X1, X2)) 840.91/297.21 , U91(ok(X1), ok(X2)) -> ok(U91(X1, X2)) 840.91/297.21 , U92(mark(X)) -> mark(U92(X)) 840.91/297.21 , U92(ok(X)) -> ok(U92(X)) 840.91/297.21 , and(mark(X1), X2) -> mark(and(X1, X2)) 840.91/297.21 , and(ok(X1), ok(X2)) -> ok(and(X1, X2)) 840.91/297.21 , isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) 840.91/297.21 , isLNatKind(ok(X)) -> ok(isLNatKind(X)) 840.91/297.21 , isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) 840.91/297.21 , tail(mark(X)) -> mark(tail(X)) 840.91/297.21 , tail(ok(X)) -> ok(tail(X)) 840.91/297.21 , take(X1, mark(X2)) -> mark(take(X1, X2)) 840.91/297.21 , take(mark(X1), X2) -> mark(take(X1, X2)) 840.91/297.21 , take(ok(X1), ok(X2)) -> ok(take(X1, X2)) 840.91/297.21 , sel(X1, mark(X2)) -> mark(sel(X1, X2)) 840.91/297.21 , sel(mark(X1), X2) -> mark(sel(X1, X2)) 840.91/297.21 , sel(ok(X1), ok(X2)) -> ok(sel(X1, X2)) 840.91/297.21 , proper(U101(X1, X2, X3)) -> 840.91/297.21 U101(proper(X1), proper(X2), proper(X3)) 840.91/297.21 , proper(tt()) -> ok(tt()) 840.91/297.21 , proper(U102(X1, X2)) -> U102(proper(X1), proper(X2)) 840.91/297.21 , proper(isNatural(X)) -> isNatural(proper(X)) 840.91/297.21 , proper(U103(X)) -> U103(proper(X)) 840.91/297.21 , proper(isLNat(X)) -> isLNat(proper(X)) 840.91/297.21 , proper(U11(X1, X2, X3)) -> 840.91/297.21 U11(proper(X1), proper(X2), proper(X3)) 840.91/297.21 , proper(snd(X)) -> snd(proper(X)) 840.91/297.21 , proper(splitAt(X1, X2)) -> splitAt(proper(X1), proper(X2)) 840.91/297.21 , proper(U111(X1, X2)) -> U111(proper(X1), proper(X2)) 840.91/297.21 , proper(U112(X)) -> U112(proper(X)) 840.91/297.21 , proper(U121(X1, X2)) -> U121(proper(X1), proper(X2)) 840.91/297.21 , proper(U122(X)) -> U122(proper(X)) 840.91/297.21 , proper(U131(X1, X2, X3)) -> 840.91/297.21 U131(proper(X1), proper(X2), proper(X3)) 840.91/297.21 , proper(U132(X1, X2)) -> U132(proper(X1), proper(X2)) 840.91/297.21 , proper(U133(X)) -> U133(proper(X)) 840.91/297.21 , proper(U141(X1, X2, X3)) -> 840.91/297.21 U141(proper(X1), proper(X2), proper(X3)) 840.91/297.21 , proper(U142(X1, X2)) -> U142(proper(X1), proper(X2)) 840.91/297.21 , proper(U143(X)) -> U143(proper(X)) 840.91/297.21 , proper(U151(X1, X2, X3)) -> 840.91/297.21 U151(proper(X1), proper(X2), proper(X3)) 840.91/297.21 , proper(U152(X1, X2)) -> U152(proper(X1), proper(X2)) 840.91/297.21 , proper(U153(X)) -> U153(proper(X)) 840.91/297.21 , proper(U161(X1, X2)) -> U161(proper(X1), proper(X2)) 840.91/297.21 , proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)) 840.91/297.21 , proper(natsFrom(X)) -> natsFrom(proper(X)) 840.91/297.21 , proper(s(X)) -> s(proper(X)) 840.91/297.21 , proper(U171(X1, X2, X3)) -> 840.91/297.21 U171(proper(X1), proper(X2), proper(X3)) 840.91/297.21 , proper(head(X)) -> head(proper(X)) 840.91/297.21 , proper(afterNth(X1, X2)) -> afterNth(proper(X1), proper(X2)) 840.91/297.21 , proper(U181(X1, X2)) -> U181(proper(X1), proper(X2)) 840.91/297.21 , proper(U191(X1, X2)) -> U191(proper(X1), proper(X2)) 840.91/297.21 , proper(pair(X1, X2)) -> pair(proper(X1), proper(X2)) 840.91/297.21 , proper(nil()) -> ok(nil()) 840.91/297.21 , proper(U201(X1, X2, X3, X4)) -> 840.91/297.21 U201(proper(X1), proper(X2), proper(X3), proper(X4)) 840.91/297.21 , proper(U202(X1, X2)) -> U202(proper(X1), proper(X2)) 840.91/297.21 , proper(U21(X1, X2)) -> U21(proper(X1), proper(X2)) 840.91/297.21 , proper(U211(X1, X2)) -> U211(proper(X1), proper(X2)) 840.91/297.21 , proper(U221(X1, X2, X3)) -> 840.91/297.21 U221(proper(X1), proper(X2), proper(X3)) 840.91/297.21 , proper(fst(X)) -> fst(proper(X)) 840.91/297.21 , proper(U31(X1, X2)) -> U31(proper(X1), proper(X2)) 840.91/297.21 , proper(U41(X1, X2, X3)) -> 840.91/297.21 U41(proper(X1), proper(X2), proper(X3)) 840.91/297.21 , proper(U42(X1, X2)) -> U42(proper(X1), proper(X2)) 840.91/297.21 , proper(U43(X)) -> U43(proper(X)) 840.91/297.21 , proper(U51(X1, X2, X3)) -> 840.91/297.21 U51(proper(X1), proper(X2), proper(X3)) 840.91/297.21 , proper(U52(X1, X2)) -> U52(proper(X1), proper(X2)) 840.91/297.21 , proper(U53(X)) -> U53(proper(X)) 840.91/297.21 , proper(U61(X1, X2)) -> U61(proper(X1), proper(X2)) 840.91/297.21 , proper(U62(X)) -> U62(proper(X)) 840.91/297.21 , proper(isPLNat(X)) -> isPLNat(proper(X)) 840.91/297.21 , proper(U71(X1, X2)) -> U71(proper(X1), proper(X2)) 840.91/297.21 , proper(U72(X)) -> U72(proper(X)) 840.91/297.21 , proper(U81(X1, X2)) -> U81(proper(X1), proper(X2)) 840.91/297.21 , proper(U82(X)) -> U82(proper(X)) 840.91/297.21 , proper(U91(X1, X2)) -> U91(proper(X1), proper(X2)) 840.91/297.21 , proper(U92(X)) -> U92(proper(X)) 840.91/297.21 , proper(and(X1, X2)) -> and(proper(X1), proper(X2)) 840.91/297.21 , proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) 840.91/297.21 , proper(isLNatKind(X)) -> isLNatKind(proper(X)) 840.91/297.21 , proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) 840.91/297.21 , proper(tail(X)) -> tail(proper(X)) 840.91/297.21 , proper(take(X1, X2)) -> take(proper(X1), proper(X2)) 840.91/297.21 , proper(0()) -> ok(0()) 840.91/297.21 , proper(sel(X1, X2)) -> sel(proper(X1), proper(X2)) 840.91/297.21 , top(mark(X)) -> top(proper(X)) 840.91/297.21 , top(ok(X)) -> top(active(X)) } 840.91/297.21 Obligation: 840.91/297.21 innermost runtime complexity 840.91/297.21 Answer: 840.91/297.21 MAYBE 840.91/297.21 840.91/297.21 None of the processors succeeded. 840.91/297.21 840.91/297.21 Details of failed attempt(s): 840.91/297.21 ----------------------------- 840.91/297.21 1) 'empty' failed due to the following reason: 840.91/297.21 840.91/297.21 Empty strict component of the problem is NOT empty. 840.91/297.21 840.91/297.21 2) 'Best' failed due to the following reason: 840.91/297.21 840.91/297.21 None of the processors succeeded. 840.91/297.21 840.91/297.21 Details of failed attempt(s): 840.91/297.21 ----------------------------- 840.91/297.21 1) 'With Problem ... (timeout of 297 seconds)' failed due to the 840.91/297.21 following reason: 840.91/297.21 840.91/297.21 Computation stopped due to timeout after 297.0 seconds. 840.91/297.21 840.91/297.21 2) 'Best' failed due to the following reason: 840.91/297.21 840.91/297.21 None of the processors succeeded. 840.91/297.21 840.91/297.21 Details of failed attempt(s): 840.91/297.21 ----------------------------- 840.91/297.21 1) 'With Problem ... (timeout of 148 seconds) (timeout of 297 840.91/297.21 seconds)' failed due to the following reason: 840.91/297.21 840.91/297.21 Computation stopped due to timeout after 148.0 seconds. 840.91/297.21 840.91/297.21 2) 'Best' failed due to the following reason: 840.91/297.21 840.91/297.21 None of the processors succeeded. 840.91/297.21 840.91/297.21 Details of failed attempt(s): 840.91/297.21 ----------------------------- 840.91/297.21 1) 'bsearch-popstar (timeout of 297 seconds)' failed due to the 840.91/297.21 following reason: 840.91/297.21 840.91/297.21 The input cannot be shown compatible 840.91/297.21 840.91/297.21 2) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due 840.91/297.21 to the following reason: 840.91/297.21 840.91/297.21 The input cannot be shown compatible 840.91/297.21 840.91/297.21 840.91/297.21 3) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)' 840.91/297.21 failed due to the following reason: 840.91/297.21 840.91/297.21 None of the processors succeeded. 840.91/297.21 840.91/297.21 Details of failed attempt(s): 840.91/297.21 ----------------------------- 840.91/297.21 1) 'Bounds with minimal-enrichment and initial automaton 'match'' 840.91/297.21 failed due to the following reason: 840.91/297.21 840.91/297.21 match-boundness of the problem could not be verified. 840.91/297.21 840.91/297.21 2) 'Bounds with perSymbol-enrichment and initial automaton 'match'' 840.91/297.21 failed due to the following reason: 840.91/297.21 840.91/297.21 match-boundness of the problem could not be verified. 840.91/297.21 840.91/297.21 840.91/297.21 840.91/297.21 840.91/297.21 840.91/297.21 Arrrr.. 840.91/297.24 EOF