MAYBE
TRS:
{ cons(X1, X2) -> n__cons(X1, X2),
0() -> n__0(),
zeros() -> cons(0(), n__zeros()),
zeros() -> n__zeros(),
U102(tt(), V1, V2) -> U103(isNatIListKind(activate(V2)), activate(V1), activate(V2)),
isNatKind(n__0()) -> tt(),
isNatKind(n__length(V1)) -> U71(isNatIListKind(activate(V1))),
isNatKind(n__s(V1)) -> U81(isNatKind(activate(V1))),
activate(X) -> X,
activate(n__zeros()) -> zeros(),
activate(n__take(X1, X2)) -> take(activate(X1), activate(X2)),
activate(n__0()) -> 0(),
activate(n__length(X)) -> length(activate(X)),
activate(n__s(X)) -> s(activate(X)),
activate(n__cons(X1, X2)) -> cons(activate(X1), X2),
activate(n__nil()) -> nil(),
U101(tt(), V1, V2) -> U102(isNatKind(activate(V1)), activate(V1), activate(V2)),
U103(tt(), V1, V2) -> U104(isNatIListKind(activate(V2)), activate(V1), activate(V2)),
isNatIListKind(n__zeros()) -> tt(),
isNatIListKind(n__take(V1, V2)) -> U61(isNatKind(activate(V1)), activate(V2)),
isNatIListKind(n__cons(V1, V2)) -> U51(isNatKind(activate(V1)), activate(V2)),
isNatIListKind(n__nil()) -> tt(),
U104(tt(), V1, V2) -> U105(isNat(activate(V1)), activate(V2)),
U105(tt(), V2) -> U106(isNatIList(activate(V2))),
isNat(n__0()) -> tt(),
isNat(n__length(V1)) -> U11(isNatIListKind(activate(V1)), activate(V1)),
isNat(n__s(V1)) -> U21(isNatKind(activate(V1)), activate(V1)),
U106(tt()) -> tt(),
isNatIList(V) -> U31(isNatIListKind(activate(V)), activate(V)),
isNatIList(n__zeros()) -> tt(),
isNatIList(n__cons(V1, V2)) -> U41(isNatKind(activate(V1)), activate(V1), activate(V2)),
U12(tt(), V1) -> U13(isNatList(activate(V1))),
U11(tt(), V1) -> U12(isNatIListKind(activate(V1)), activate(V1)),
U112(tt(), L, N) -> U113(isNat(activate(N)), activate(L), activate(N)),
U111(tt(), L, N) -> U112(isNatIListKind(activate(L)), activate(L), activate(N)),
U113(tt(), L, N) -> U114(isNatKind(activate(N)), activate(L)),
U114(tt(), L) -> s(length(activate(L))),
s(X) -> n__s(X),
length(X) -> n__length(X),
length(cons(N, L)) -> U111(isNatList(activate(L)), activate(L), N),
length(nil()) -> 0(),
U13(tt()) -> tt(),
isNatList(n__take(V1, V2)) -> U101(isNatKind(activate(V1)), activate(V1), activate(V2)),
isNatList(n__cons(V1, V2)) -> U91(isNatKind(activate(V1)), activate(V1), activate(V2)),
isNatList(n__nil()) -> tt(),
U122(tt()) -> nil(),
U121(tt(), IL) -> U122(isNatIListKind(activate(IL))),
nil() -> n__nil(),
U132(tt(), IL, M, N) -> U133(isNat(activate(M)), activate(IL), activate(M), activate(N)),
U131(tt(), IL, M, N) -> U132(isNatIListKind(activate(IL)), activate(IL), activate(M), activate(N)),
U133(tt(), IL, M, N) -> U134(isNatKind(activate(M)), activate(IL), activate(M), activate(N)),
U134(tt(), IL, M, N) -> U135(isNat(activate(N)), activate(IL), activate(M), activate(N)),
U135(tt(), IL, M, N) -> U136(isNatKind(activate(N)), activate(IL), activate(M), activate(N)),
U136(tt(), IL, M, N) -> cons(activate(N), n__take(activate(M), activate(IL))),
U22(tt(), V1) -> U23(isNat(activate(V1))),
U21(tt(), V1) -> U22(isNatKind(activate(V1)), activate(V1)),
U23(tt()) -> tt(),
U32(tt(), V) -> U33(isNatList(activate(V))),
U31(tt(), V) -> U32(isNatIListKind(activate(V)), activate(V)),
U33(tt()) -> tt(),
U42(tt(), V1, V2) -> U43(isNatIListKind(activate(V2)), activate(V1), activate(V2)),
U41(tt(), V1, V2) -> U42(isNatKind(activate(V1)), activate(V1), activate(V2)),
U43(tt(), V1, V2) -> U44(isNatIListKind(activate(V2)), activate(V1), activate(V2)),
U44(tt(), V1, V2) -> U45(isNat(activate(V1)), activate(V2)),
U45(tt(), V2) -> U46(isNatIList(activate(V2))),
U46(tt()) -> tt(),
U52(tt()) -> tt(),
U51(tt(), V2) -> U52(isNatIListKind(activate(V2))),
U62(tt()) -> tt(),
U61(tt(), V2) -> U62(isNatIListKind(activate(V2))),
U71(tt()) -> tt(),
U81(tt()) -> tt(),
U92(tt(), V1, V2) -> U93(isNatIListKind(activate(V2)), activate(V1), activate(V2)),
U91(tt(), V1, V2) -> U92(isNatKind(activate(V1)), activate(V1), activate(V2)),
U93(tt(), V1, V2) -> U94(isNatIListKind(activate(V2)), activate(V1), activate(V2)),
U94(tt(), V1, V2) -> U95(isNat(activate(V1)), activate(V2)),
U95(tt(), V2) -> U96(isNatList(activate(V2))),
U96(tt()) -> tt(),
take(X1, X2) -> n__take(X1, X2),
take(0(), IL) -> U121(isNatIList(IL), IL),
take(s(M), cons(N, IL)) -> U131(isNatIList(activate(IL)), activate(IL), M, N)}
DP:
Strict:
{
zeros#() -> cons#(0(), n__zeros()),
zeros#() -> 0#(),
U102#(tt(), V1, V2) -> activate#(V1),
U102#(tt(), V1, V2) -> activate#(V2),
U102#(tt(), V1, V2) -> U103#(isNatIListKind(activate(V2)), activate(V1), activate(V2)),
U102#(tt(), V1, V2) -> isNatIListKind#(activate(V2)),
isNatKind#(n__length(V1)) -> activate#(V1),
isNatKind#(n__length(V1)) -> isNatIListKind#(activate(V1)),
isNatKind#(n__length(V1)) -> U71#(isNatIListKind(activate(V1))),
isNatKind#(n__s(V1)) -> isNatKind#(activate(V1)),
isNatKind#(n__s(V1)) -> activate#(V1),
isNatKind#(n__s(V1)) -> U81#(isNatKind(activate(V1))),
activate#(n__zeros()) -> zeros#(),
activate#(n__take(X1, X2)) -> activate#(X1),
activate#(n__take(X1, X2)) -> activate#(X2),
activate#(n__take(X1, X2)) -> take#(activate(X1), activate(X2)),
activate#(n__0()) -> 0#(),
activate#(n__length(X)) -> activate#(X),
activate#(n__length(X)) -> length#(activate(X)),
activate#(n__s(X)) -> activate#(X),
activate#(n__s(X)) -> s#(activate(X)),
activate#(n__cons(X1, X2)) -> cons#(activate(X1), X2),
activate#(n__cons(X1, X2)) -> activate#(X1),
activate#(n__nil()) -> nil#(),
U101#(tt(), V1, V2) -> U102#(isNatKind(activate(V1)), activate(V1), activate(V2)),
U101#(tt(), V1, V2) -> isNatKind#(activate(V1)),
U101#(tt(), V1, V2) -> activate#(V1),
U101#(tt(), V1, V2) -> activate#(V2),
U103#(tt(), V1, V2) -> activate#(V1),
U103#(tt(), V1, V2) -> activate#(V2),
U103#(tt(), V1, V2) -> isNatIListKind#(activate(V2)),
U103#(tt(), V1, V2) -> U104#(isNatIListKind(activate(V2)), activate(V1), activate(V2)),
isNatIListKind#(n__take(V1, V2)) -> isNatKind#(activate(V1)),
isNatIListKind#(n__take(V1, V2)) -> activate#(V1),
isNatIListKind#(n__take(V1, V2)) -> activate#(V2),
isNatIListKind#(n__take(V1, V2)) -> U61#(isNatKind(activate(V1)), activate(V2)),
isNatIListKind#(n__cons(V1, V2)) -> isNatKind#(activate(V1)),
isNatIListKind#(n__cons(V1, V2)) -> activate#(V1),
isNatIListKind#(n__cons(V1, V2)) -> activate#(V2),
isNatIListKind#(n__cons(V1, V2)) -> U51#(isNatKind(activate(V1)), activate(V2)),
U104#(tt(), V1, V2) -> activate#(V1),
U104#(tt(), V1, V2) -> activate#(V2),
U104#(tt(), V1, V2) -> U105#(isNat(activate(V1)), activate(V2)),
U104#(tt(), V1, V2) -> isNat#(activate(V1)),
U105#(tt(), V2) -> activate#(V2),
U105#(tt(), V2) -> U106#(isNatIList(activate(V2))),
U105#(tt(), V2) -> isNatIList#(activate(V2)),
isNat#(n__length(V1)) -> activate#(V1),
isNat#(n__length(V1)) -> isNatIListKind#(activate(V1)),
isNat#(n__length(V1)) -> U11#(isNatIListKind(activate(V1)), activate(V1)),
isNat#(n__s(V1)) -> isNatKind#(activate(V1)),
isNat#(n__s(V1)) -> activate#(V1),
isNat#(n__s(V1)) -> U21#(isNatKind(activate(V1)), activate(V1)),
isNatIList#(V) -> activate#(V),
isNatIList#(V) -> isNatIListKind#(activate(V)),
isNatIList#(V) -> U31#(isNatIListKind(activate(V)), activate(V)),
isNatIList#(n__cons(V1, V2)) -> isNatKind#(activate(V1)),
isNatIList#(n__cons(V1, V2)) -> activate#(V1),
isNatIList#(n__cons(V1, V2)) -> activate#(V2),
isNatIList#(n__cons(V1, V2)) -> U41#(isNatKind(activate(V1)), activate(V1), activate(V2)),
U12#(tt(), V1) -> activate#(V1),
U12#(tt(), V1) -> U13#(isNatList(activate(V1))),
U12#(tt(), V1) -> isNatList#(activate(V1)),
U11#(tt(), V1) -> activate#(V1),
U11#(tt(), V1) -> isNatIListKind#(activate(V1)),
U11#(tt(), V1) -> U12#(isNatIListKind(activate(V1)), activate(V1)),
U112#(tt(), L, N) -> activate#(L),
U112#(tt(), L, N) -> activate#(N),
U112#(tt(), L, N) -> isNat#(activate(N)),
U112#(tt(), L, N) -> U113#(isNat(activate(N)), activate(L), activate(N)),
U111#(tt(), L, N) -> activate#(L),
U111#(tt(), L, N) -> activate#(N),
U111#(tt(), L, N) -> isNatIListKind#(activate(L)),
U111#(tt(), L, N) -> U112#(isNatIListKind(activate(L)), activate(L), activate(N)),
U113#(tt(), L, N) -> isNatKind#(activate(N)),
U113#(tt(), L, N) -> activate#(L),
U113#(tt(), L, N) -> activate#(N),
U113#(tt(), L, N) -> U114#(isNatKind(activate(N)), activate(L)),
U114#(tt(), L) -> activate#(L),
U114#(tt(), L) -> s#(length(activate(L))),
U114#(tt(), L) -> length#(activate(L)),
length#(cons(N, L)) -> activate#(L),
length#(cons(N, L)) -> U111#(isNatList(activate(L)), activate(L), N),
length#(cons(N, L)) -> isNatList#(activate(L)),
length#(nil()) -> 0#(),
isNatList#(n__take(V1, V2)) -> isNatKind#(activate(V1)),
isNatList#(n__take(V1, V2)) -> activate#(V1),
isNatList#(n__take(V1, V2)) -> activate#(V2),
isNatList#(n__take(V1, V2)) -> U101#(isNatKind(activate(V1)), activate(V1), activate(V2)),
isNatList#(n__cons(V1, V2)) -> isNatKind#(activate(V1)),
isNatList#(n__cons(V1, V2)) -> activate#(V1),
isNatList#(n__cons(V1, V2)) -> activate#(V2),
isNatList#(n__cons(V1, V2)) -> U91#(isNatKind(activate(V1)), activate(V1), activate(V2)),
U122#(tt()) -> nil#(),
U121#(tt(), IL) -> activate#(IL),
U121#(tt(), IL) -> isNatIListKind#(activate(IL)),
U121#(tt(), IL) -> U122#(isNatIListKind(activate(IL))),
U132#(tt(), IL, M, N) -> activate#(N),
U132#(tt(), IL, M, N) -> activate#(IL),
U132#(tt(), IL, M, N) -> activate#(M),
U132#(tt(), IL, M, N) -> isNat#(activate(M)),
U132#(tt(), IL, M, N) -> U133#(isNat(activate(M)), activate(IL), activate(M), activate(N)),
U131#(tt(), IL, M, N) -> activate#(N),
U131#(tt(), IL, M, N) -> activate#(IL),
U131#(tt(), IL, M, N) -> activate#(M),
U131#(tt(), IL, M, N) -> isNatIListKind#(activate(IL)),
U131#(tt(), IL, M, N) -> U132#(isNatIListKind(activate(IL)), activate(IL), activate(M), activate(N)),
U133#(tt(), IL, M, N) -> isNatKind#(activate(M)),
U133#(tt(), IL, M, N) -> activate#(N),
U133#(tt(), IL, M, N) -> activate#(IL),
U133#(tt(), IL, M, N) -> activate#(M),
U133#(tt(), IL, M, N) -> U134#(isNatKind(activate(M)), activate(IL), activate(M), activate(N)),
U134#(tt(), IL, M, N) -> activate#(N),
U134#(tt(), IL, M, N) -> activate#(IL),
U134#(tt(), IL, M, N) -> activate#(M),
U134#(tt(), IL, M, N) -> isNat#(activate(N)),
U134#(tt(), IL, M, N) -> U135#(isNat(activate(N)), activate(IL), activate(M), activate(N)),
U135#(tt(), IL, M, N) -> isNatKind#(activate(N)),
U135#(tt(), IL, M, N) -> activate#(N),
U135#(tt(), IL, M, N) -> activate#(IL),
U135#(tt(), IL, M, N) -> activate#(M),
U135#(tt(), IL, M, N) -> U136#(isNatKind(activate(N)), activate(IL), activate(M), activate(N)),
U136#(tt(), IL, M, N) -> cons#(activate(N), n__take(activate(M), activate(IL))),
U136#(tt(), IL, M, N) -> activate#(N),
U136#(tt(), IL, M, N) -> activate#(IL),
U136#(tt(), IL, M, N) -> activate#(M),
U22#(tt(), V1) -> activate#(V1),
U22#(tt(), V1) -> isNat#(activate(V1)),
U22#(tt(), V1) -> U23#(isNat(activate(V1))),
U21#(tt(), V1) -> isNatKind#(activate(V1)),
U21#(tt(), V1) -> activate#(V1),
U21#(tt(), V1) -> U22#(isNatKind(activate(V1)), activate(V1)),
U32#(tt(), V) -> activate#(V),
U32#(tt(), V) -> isNatList#(activate(V)),
U32#(tt(), V) -> U33#(isNatList(activate(V))),
U31#(tt(), V) -> activate#(V),
U31#(tt(), V) -> isNatIListKind#(activate(V)),
U31#(tt(), V) -> U32#(isNatIListKind(activate(V)), activate(V)),
U42#(tt(), V1, V2) -> activate#(V1),
U42#(tt(), V1, V2) -> activate#(V2),
U42#(tt(), V1, V2) -> isNatIListKind#(activate(V2)),
U42#(tt(), V1, V2) -> U43#(isNatIListKind(activate(V2)), activate(V1), activate(V2)),
U41#(tt(), V1, V2) -> isNatKind#(activate(V1)),
U41#(tt(), V1, V2) -> activate#(V1),
U41#(tt(), V1, V2) -> activate#(V2),
U41#(tt(), V1, V2) -> U42#(isNatKind(activate(V1)), activate(V1), activate(V2)),
U43#(tt(), V1, V2) -> activate#(V1),
U43#(tt(), V1, V2) -> activate#(V2),
U43#(tt(), V1, V2) -> isNatIListKind#(activate(V2)),
U43#(tt(), V1, V2) -> U44#(isNatIListKind(activate(V2)), activate(V1), activate(V2)),
U44#(tt(), V1, V2) -> activate#(V1),
U44#(tt(), V1, V2) -> activate#(V2),
U44#(tt(), V1, V2) -> isNat#(activate(V1)),
U44#(tt(), V1, V2) -> U45#(isNat(activate(V1)), activate(V2)),
U45#(tt(), V2) -> activate#(V2),
U45#(tt(), V2) -> isNatIList#(activate(V2)),
U45#(tt(), V2) -> U46#(isNatIList(activate(V2))),
U51#(tt(), V2) -> activate#(V2),
U51#(tt(), V2) -> isNatIListKind#(activate(V2)),
U51#(tt(), V2) -> U52#(isNatIListKind(activate(V2))),
U61#(tt(), V2) -> activate#(V2),
U61#(tt(), V2) -> isNatIListKind#(activate(V2)),
U61#(tt(), V2) -> U62#(isNatIListKind(activate(V2))),
U92#(tt(), V1, V2) -> activate#(V1),
U92#(tt(), V1, V2) -> activate#(V2),
U92#(tt(), V1, V2) -> isNatIListKind#(activate(V2)),
U92#(tt(), V1, V2) -> U93#(isNatIListKind(activate(V2)), activate(V1), activate(V2)),
U91#(tt(), V1, V2) -> isNatKind#(activate(V1)),
U91#(tt(), V1, V2) -> activate#(V1),
U91#(tt(), V1, V2) -> activate#(V2),
U91#(tt(), V1, V2) -> U92#(isNatKind(activate(V1)), activate(V1), activate(V2)),
U93#(tt(), V1, V2) -> activate#(V1),
U93#(tt(), V1, V2) -> activate#(V2),
U93#(tt(), V1, V2) -> isNatIListKind#(activate(V2)),
U93#(tt(), V1, V2) -> U94#(isNatIListKind(activate(V2)), activate(V1), activate(V2)),
U94#(tt(), V1, V2) -> activate#(V1),
U94#(tt(), V1, V2) -> activate#(V2),
U94#(tt(), V1, V2) -> isNat#(activate(V1)),
U94#(tt(), V1, V2) -> U95#(isNat(activate(V1)), activate(V2)),
U95#(tt(), V2) -> activate#(V2),
U95#(tt(), V2) -> isNatList#(activate(V2)),
U95#(tt(), V2) -> U96#(isNatList(activate(V2))),
take#(0(), IL) -> isNatIList#(IL),
take#(0(), IL) -> U121#(isNatIList(IL), IL),
take#(s(M), cons(N, IL)) -> activate#(IL),
take#(s(M), cons(N, IL)) -> isNatIList#(activate(IL)),
take#(s(M), cons(N, IL)) -> U131#(isNatIList(activate(IL)), activate(IL), M, N)
}
Weak:
{ cons(X1, X2) -> n__cons(X1, X2),
0() -> n__0(),
zeros() -> cons(0(), n__zeros()),
zeros() -> n__zeros(),
U102(tt(), V1, V2) -> U103(isNatIListKind(activate(V2)), activate(V1), activate(V2)),
isNatKind(n__0()) -> tt(),
isNatKind(n__length(V1)) -> U71(isNatIListKind(activate(V1))),
isNatKind(n__s(V1)) -> U81(isNatKind(activate(V1))),
activate(X) -> X,
activate(n__zeros()) -> zeros(),
activate(n__take(X1, X2)) -> take(activate(X1), activate(X2)),
activate(n__0()) -> 0(),
activate(n__length(X)) -> length(activate(X)),
activate(n__s(X)) -> s(activate(X)),
activate(n__cons(X1, X2)) -> cons(activate(X1), X2),
activate(n__nil()) -> nil(),
U101(tt(), V1, V2) -> U102(isNatKind(activate(V1)), activate(V1), activate(V2)),
U103(tt(), V1, V2) -> U104(isNatIListKind(activate(V2)), activate(V1), activate(V2)),
isNatIListKind(n__zeros()) -> tt(),
isNatIListKind(n__take(V1, V2)) -> U61(isNatKind(activate(V1)), activate(V2)),
isNatIListKind(n__cons(V1, V2)) -> U51(isNatKind(activate(V1)), activate(V2)),
isNatIListKind(n__nil()) -> tt(),
U104(tt(), V1, V2) -> U105(isNat(activate(V1)), activate(V2)),
U105(tt(), V2) -> U106(isNatIList(activate(V2))),
isNat(n__0()) -> tt(),
isNat(n__length(V1)) -> U11(isNatIListKind(activate(V1)), activate(V1)),
isNat(n__s(V1)) -> U21(isNatKind(activate(V1)), activate(V1)),
U106(tt()) -> tt(),
isNatIList(V) -> U31(isNatIListKind(activate(V)), activate(V)),
isNatIList(n__zeros()) -> tt(),
isNatIList(n__cons(V1, V2)) -> U41(isNatKind(activate(V1)), activate(V1), activate(V2)),
U12(tt(), V1) -> U13(isNatList(activate(V1))),
U11(tt(), V1) -> U12(isNatIListKind(activate(V1)), activate(V1)),
U112(tt(), L, N) -> U113(isNat(activate(N)), activate(L), activate(N)),
U111(tt(), L, N) -> U112(isNatIListKind(activate(L)), activate(L), activate(N)),
U113(tt(), L, N) -> U114(isNatKind(activate(N)), activate(L)),
U114(tt(), L) -> s(length(activate(L))),
s(X) -> n__s(X),
length(X) -> n__length(X),
length(cons(N, L)) -> U111(isNatList(activate(L)), activate(L), N),
length(nil()) -> 0(),
U13(tt()) -> tt(),
isNatList(n__take(V1, V2)) -> U101(isNatKind(activate(V1)), activate(V1), activate(V2)),
isNatList(n__cons(V1, V2)) -> U91(isNatKind(activate(V1)), activate(V1), activate(V2)),
isNatList(n__nil()) -> tt(),
U122(tt()) -> nil(),
U121(tt(), IL) -> U122(isNatIListKind(activate(IL))),
nil() -> n__nil(),
U132(tt(), IL, M, N) -> U133(isNat(activate(M)), activate(IL), activate(M), activate(N)),
U131(tt(), IL, M, N) -> U132(isNatIListKind(activate(IL)), activate(IL), activate(M), activate(N)),
U133(tt(), IL, M, N) -> U134(isNatKind(activate(M)), activate(IL), activate(M), activate(N)),
U134(tt(), IL, M, N) -> U135(isNat(activate(N)), activate(IL), activate(M), activate(N)),
U135(tt(), IL, M, N) -> U136(isNatKind(activate(N)), activate(IL), activate(M), activate(N)),
U136(tt(), IL, M, N) -> cons(activate(N), n__take(activate(M), activate(IL))),
U22(tt(), V1) -> U23(isNat(activate(V1))),
U21(tt(), V1) -> U22(isNatKind(activate(V1)), activate(V1)),
U23(tt()) -> tt(),
U32(tt(), V) -> U33(isNatList(activate(V))),
U31(tt(), V) -> U32(isNatIListKind(activate(V)), activate(V)),
U33(tt()) -> tt(),
U42(tt(), V1, V2) -> U43(isNatIListKind(activate(V2)), activate(V1), activate(V2)),
U41(tt(), V1, V2) -> U42(isNatKind(activate(V1)), activate(V1), activate(V2)),
U43(tt(), V1, V2) -> U44(isNatIListKind(activate(V2)), activate(V1), activate(V2)),
U44(tt(), V1, V2) -> U45(isNat(activate(V1)), activate(V2)),
U45(tt(), V2) -> U46(isNatIList(activate(V2))),
U46(tt()) -> tt(),
U52(tt()) -> tt(),
U51(tt(), V2) -> U52(isNatIListKind(activate(V2))),
U62(tt()) -> tt(),
U61(tt(), V2) -> U62(isNatIListKind(activate(V2))),
U71(tt()) -> tt(),
U81(tt()) -> tt(),
U92(tt(), V1, V2) -> U93(isNatIListKind(activate(V2)), activate(V1), activate(V2)),
U91(tt(), V1, V2) -> U92(isNatKind(activate(V1)), activate(V1), activate(V2)),
U93(tt(), V1, V2) -> U94(isNatIListKind(activate(V2)), activate(V1), activate(V2)),
U94(tt(), V1, V2) -> U95(isNat(activate(V1)), activate(V2)),
U95(tt(), V2) -> U96(isNatList(activate(V2))),
U96(tt()) -> tt(),
take(X1, X2) -> n__take(X1, X2),
take(0(), IL) -> U121(isNatIList(IL), IL),
take(s(M), cons(N, IL)) -> U131(isNatIList(activate(IL)), activate(IL), M, N)}
EDG:
{
(activate#(n__s(X)) -> activate#(X), activate#(n__nil()) -> nil#())
(activate#(n__s(X)) -> activate#(X), activate#(n__cons(X1, X2)) -> activate#(X1))
(activate#(n__s(X)) -> activate#(X), activate#(n__cons(X1, X2)) -> cons#(activate(X1), X2))
(activate#(n__s(X)) -> activate#(X), activate#(n__s(X)) -> s#(activate(X)))
(activate#(n__s(X)) -> activate#(X), activate#(n__s(X)) -> activate#(X))
(activate#(n__s(X)) -> activate#(X), activate#(n__length(X)) -> length#(activate(X)))
(activate#(n__s(X)) -> activate#(X), activate#(n__length(X)) -> activate#(X))
(activate#(n__s(X)) -> activate#(X), activate#(n__0()) -> 0#())
(activate#(n__s(X)) -> activate#(X), activate#(n__take(X1, X2)) -> take#(activate(X1), activate(X2)))
(activate#(n__s(X)) -> activate#(X), activate#(n__take(X1, X2)) -> activate#(X2))
(activate#(n__s(X)) -> activate#(X), activate#(n__take(X1, X2)) -> activate#(X1))
(activate#(n__s(X)) -> activate#(X), activate#(n__zeros()) -> zeros#())
(U132#(tt(), IL, M, N) -> activate#(IL), activate#(n__nil()) -> nil#())
(U132#(tt(), IL, M, N) -> activate#(IL), activate#(n__cons(X1, X2)) -> activate#(X1))
(U132#(tt(), IL, M, N) -> activate#(IL), activate#(n__cons(X1, X2)) -> cons#(activate(X1), X2))
(U132#(tt(), IL, M, N) -> activate#(IL), activate#(n__s(X)) -> s#(activate(X)))
(U132#(tt(), IL, M, N) -> activate#(IL), activate#(n__s(X)) -> activate#(X))
(U132#(tt(), IL, M, N) -> activate#(IL), activate#(n__length(X)) -> length#(activate(X)))
(U132#(tt(), IL, M, N) -> activate#(IL), activate#(n__length(X)) -> activate#(X))
(U132#(tt(), IL, M, N) -> activate#(IL), activate#(n__0()) -> 0#())
(U132#(tt(), IL, M, N) -> activate#(IL), activate#(n__take(X1, X2)) -> take#(activate(X1), activate(X2)))
(U132#(tt(), IL, M, N) -> activate#(IL), activate#(n__take(X1, X2)) -> activate#(X2))
(U132#(tt(), IL, M, N) -> activate#(IL), activate#(n__take(X1, X2)) -> activate#(X1))
(U132#(tt(), IL, M, N) -> activate#(IL), activate#(n__zeros()) -> zeros#())
(U133#(tt(), IL, M, N) -> activate#(IL), activate#(n__nil()) -> nil#())
(U133#(tt(), IL, M, N) -> activate#(IL), activate#(n__cons(X1, X2)) -> activate#(X1))
(U133#(tt(), IL, M, N) -> activate#(IL), activate#(n__cons(X1, X2)) -> cons#(activate(X1), X2))
(U133#(tt(), IL, M, N) -> activate#(IL), activate#(n__s(X)) -> s#(activate(X)))
(U133#(tt(), IL, M, N) -> activate#(IL), activate#(n__s(X)) -> activate#(X))
(U133#(tt(), IL, M, N) -> activate#(IL), activate#(n__length(X)) -> length#(activate(X)))
(U133#(tt(), IL, M, N) -> activate#(IL), activate#(n__length(X)) -> activate#(X))
(U133#(tt(), IL, M, N) -> activate#(IL), activate#(n__0()) -> 0#())
(U133#(tt(), IL, M, N) -> activate#(IL), activate#(n__take(X1, X2)) -> take#(activate(X1), activate(X2)))
(U133#(tt(), IL, M, N) -> activate#(IL), activate#(n__take(X1, X2)) -> activate#(X2))
(U133#(tt(), IL, M, N) -> activate#(IL), activate#(n__take(X1, X2)) -> activate#(X1))
(U133#(tt(), IL, M, N) -> activate#(IL), activate#(n__zeros()) -> zeros#())
(U135#(tt(), IL, M, N) -> activate#(IL), activate#(n__nil()) -> nil#())
(U135#(tt(), IL, M, N) -> activate#(IL), activate#(n__cons(X1, X2)) -> activate#(X1))
(U135#(tt(), IL, M, N) -> activate#(IL), activate#(n__cons(X1, X2)) -> cons#(activate(X1), X2))
(U135#(tt(), IL, M, N) -> activate#(IL), activate#(n__s(X)) -> s#(activate(X)))
(U135#(tt(), IL, M, N) -> activate#(IL), activate#(n__s(X)) -> activate#(X))
(U135#(tt(), IL, M, N) -> activate#(IL), activate#(n__length(X)) -> length#(activate(X)))
(U135#(tt(), IL, M, N) -> activate#(IL), activate#(n__length(X)) -> activate#(X))
(U135#(tt(), IL, M, N) -> activate#(IL), activate#(n__0()) -> 0#())
(U135#(tt(), IL, M, N) -> activate#(IL), activate#(n__take(X1, X2)) -> take#(activate(X1), activate(X2)))
(U135#(tt(), IL, M, N) -> activate#(IL), activate#(n__take(X1, X2)) -> activate#(X2))
(U135#(tt(), IL, M, N) -> activate#(IL), activate#(n__take(X1, X2)) -> activate#(X1))
(U135#(tt(), IL, M, N) -> activate#(IL), activate#(n__zeros()) -> zeros#())
(take#(0(), IL) -> isNatIList#(IL), isNatIList#(n__cons(V1, V2)) -> U41#(isNatKind(activate(V1)), activate(V1), activate(V2)))
(take#(0(), IL) -> isNatIList#(IL), isNatIList#(n__cons(V1, V2)) -> activate#(V2))
(take#(0(), IL) -> isNatIList#(IL), isNatIList#(n__cons(V1, V2)) -> activate#(V1))
(take#(0(), IL) -> isNatIList#(IL), isNatIList#(n__cons(V1, V2)) -> isNatKind#(activate(V1)))
(take#(0(), IL) -> isNatIList#(IL), isNatIList#(V) -> U31#(isNatIListKind(activate(V)), activate(V)))
(take#(0(), IL) -> isNatIList#(IL), isNatIList#(V) -> isNatIListKind#(activate(V)))
(take#(0(), IL) -> isNatIList#(IL), isNatIList#(V) -> activate#(V))
(activate#(n__take(X1, X2)) -> take#(activate(X1), activate(X2)), take#(s(M), cons(N, IL)) -> U131#(isNatIList(activate(IL)), activate(IL), M, N))
(activate#(n__take(X1, X2)) -> take#(activate(X1), activate(X2)), take#(s(M), cons(N, IL)) -> isNatIList#(activate(IL)))
(activate#(n__take(X1, X2)) -> take#(activate(X1), activate(X2)), take#(s(M), cons(N, IL)) -> activate#(IL))
(activate#(n__take(X1, X2)) -> take#(activate(X1), activate(X2)), take#(0(), IL) -> U121#(isNatIList(IL), IL))
(activate#(n__take(X1, X2)) -> take#(activate(X1), activate(X2)), take#(0(), IL) -> isNatIList#(IL))
(isNatIListKind#(n__cons(V1, V2)) -> U51#(isNatKind(activate(V1)), activate(V2)), U51#(tt(), V2) -> U52#(isNatIListKind(activate(V2))))
(isNatIListKind#(n__cons(V1, V2)) -> U51#(isNatKind(activate(V1)), activate(V2)), U51#(tt(), V2) -> isNatIListKind#(activate(V2)))
(isNatIListKind#(n__cons(V1, V2)) -> U51#(isNatKind(activate(V1)), activate(V2)), U51#(tt(), V2) -> activate#(V2))
(isNat#(n__length(V1)) -> U11#(isNatIListKind(activate(V1)), activate(V1)), U11#(tt(), V1) -> U12#(isNatIListKind(activate(V1)), activate(V1)))
(isNat#(n__length(V1)) -> U11#(isNatIListKind(activate(V1)), activate(V1)), U11#(tt(), V1) -> isNatIListKind#(activate(V1)))
(isNat#(n__length(V1)) -> U11#(isNatIListKind(activate(V1)), activate(V1)), U11#(tt(), V1) -> activate#(V1))
(isNatIList#(V) -> U31#(isNatIListKind(activate(V)), activate(V)), U31#(tt(), V) -> U32#(isNatIListKind(activate(V)), activate(V)))
(isNatIList#(V) -> U31#(isNatIListKind(activate(V)), activate(V)), U31#(tt(), V) -> isNatIListKind#(activate(V)))
(isNatIList#(V) -> U31#(isNatIListKind(activate(V)), activate(V)), U31#(tt(), V) -> activate#(V))
(U113#(tt(), L, N) -> U114#(isNatKind(activate(N)), activate(L)), U114#(tt(), L) -> length#(activate(L)))
(U113#(tt(), L, N) -> U114#(isNatKind(activate(N)), activate(L)), U114#(tt(), L) -> s#(length(activate(L))))
(U113#(tt(), L, N) -> U114#(isNatKind(activate(N)), activate(L)), U114#(tt(), L) -> activate#(L))
(U31#(tt(), V) -> U32#(isNatIListKind(activate(V)), activate(V)), U32#(tt(), V) -> U33#(isNatList(activate(V))))
(U31#(tt(), V) -> U32#(isNatIListKind(activate(V)), activate(V)), U32#(tt(), V) -> isNatList#(activate(V)))
(U31#(tt(), V) -> U32#(isNatIListKind(activate(V)), activate(V)), U32#(tt(), V) -> activate#(V))
(U94#(tt(), V1, V2) -> U95#(isNat(activate(V1)), activate(V2)), U95#(tt(), V2) -> U96#(isNatList(activate(V2))))
(U94#(tt(), V1, V2) -> U95#(isNat(activate(V1)), activate(V2)), U95#(tt(), V2) -> isNatList#(activate(V2)))
(U94#(tt(), V1, V2) -> U95#(isNat(activate(V1)), activate(V2)), U95#(tt(), V2) -> activate#(V2))
(U101#(tt(), V1, V2) -> U102#(isNatKind(activate(V1)), activate(V1), activate(V2)), U102#(tt(), V1, V2) -> isNatIListKind#(activate(V2)))
(U101#(tt(), V1, V2) -> U102#(isNatKind(activate(V1)), activate(V1), activate(V2)), U102#(tt(), V1, V2) -> U103#(isNatIListKind(activate(V2)), activate(V1), activate(V2)))
(U101#(tt(), V1, V2) -> U102#(isNatKind(activate(V1)), activate(V1), activate(V2)), U102#(tt(), V1, V2) -> activate#(V2))
(U101#(tt(), V1, V2) -> U102#(isNatKind(activate(V1)), activate(V1), activate(V2)), U102#(tt(), V1, V2) -> activate#(V1))
(isNatIList#(n__cons(V1, V2)) -> U41#(isNatKind(activate(V1)), activate(V1), activate(V2)), U41#(tt(), V1, V2) -> U42#(isNatKind(activate(V1)), activate(V1), activate(V2)))
(isNatIList#(n__cons(V1, V2)) -> U41#(isNatKind(activate(V1)), activate(V1), activate(V2)), U41#(tt(), V1, V2) -> activate#(V2))
(isNatIList#(n__cons(V1, V2)) -> U41#(isNatKind(activate(V1)), activate(V1), activate(V2)), U41#(tt(), V1, V2) -> activate#(V1))
(isNatIList#(n__cons(V1, V2)) -> U41#(isNatKind(activate(V1)), activate(V1), activate(V2)), U41#(tt(), V1, V2) -> isNatKind#(activate(V1)))
(U111#(tt(), L, N) -> U112#(isNatIListKind(activate(L)), activate(L), activate(N)), U112#(tt(), L, N) -> U113#(isNat(activate(N)), activate(L), activate(N)))
(U111#(tt(), L, N) -> U112#(isNatIListKind(activate(L)), activate(L), activate(N)), U112#(tt(), L, N) -> isNat#(activate(N)))
(U111#(tt(), L, N) -> U112#(isNatIListKind(activate(L)), activate(L), activate(N)), U112#(tt(), L, N) -> activate#(N))
(U111#(tt(), L, N) -> U112#(isNatIListKind(activate(L)), activate(L), activate(N)), U112#(tt(), L, N) -> activate#(L))
(isNatList#(n__cons(V1, V2)) -> U91#(isNatKind(activate(V1)), activate(V1), activate(V2)), U91#(tt(), V1, V2) -> U92#(isNatKind(activate(V1)), activate(V1), activate(V2)))
(isNatList#(n__cons(V1, V2)) -> U91#(isNatKind(activate(V1)), activate(V1), activate(V2)), U91#(tt(), V1, V2) -> activate#(V2))
(isNatList#(n__cons(V1, V2)) -> U91#(isNatKind(activate(V1)), activate(V1), activate(V2)), U91#(tt(), V1, V2) -> activate#(V1))
(isNatList#(n__cons(V1, V2)) -> U91#(isNatKind(activate(V1)), activate(V1), activate(V2)), U91#(tt(), V1, V2) -> isNatKind#(activate(V1)))
(U41#(tt(), V1, V2) -> U42#(isNatKind(activate(V1)), activate(V1), activate(V2)), U42#(tt(), V1, V2) -> U43#(isNatIListKind(activate(V2)), activate(V1), activate(V2)))
(U41#(tt(), V1, V2) -> U42#(isNatKind(activate(V1)), activate(V1), activate(V2)), U42#(tt(), V1, V2) -> isNatIListKind#(activate(V2)))
(U41#(tt(), V1, V2) -> U42#(isNatKind(activate(V1)), activate(V1), activate(V2)), U42#(tt(), V1, V2) -> activate#(V2))
(U41#(tt(), V1, V2) -> U42#(isNatKind(activate(V1)), activate(V1), activate(V2)), U42#(tt(), V1, V2) -> activate#(V1))
(U92#(tt(), V1, V2) -> U93#(isNatIListKind(activate(V2)), activate(V1), activate(V2)), U93#(tt(), V1, V2) -> U94#(isNatIListKind(activate(V2)), activate(V1), activate(V2)))
(U92#(tt(), V1, V2) -> U93#(isNatIListKind(activate(V2)), activate(V1), activate(V2)), U93#(tt(), V1, V2) -> isNatIListKind#(activate(V2)))
(U92#(tt(), V1, V2) -> U93#(isNatIListKind(activate(V2)), activate(V1), activate(V2)), U93#(tt(), V1, V2) -> activate#(V2))
(U92#(tt(), V1, V2) -> U93#(isNatIListKind(activate(V2)), activate(V1), activate(V2)), U93#(tt(), V1, V2) -> activate#(V1))
(U93#(tt(), V1, V2) -> U94#(isNatIListKind(activate(V2)), activate(V1), activate(V2)), U94#(tt(), V1, V2) -> U95#(isNat(activate(V1)), activate(V2)))
(U93#(tt(), V1, V2) -> U94#(isNatIListKind(activate(V2)), activate(V1), activate(V2)), U94#(tt(), V1, V2) -> isNat#(activate(V1)))
(U93#(tt(), V1, V2) -> U94#(isNatIListKind(activate(V2)), activate(V1), activate(V2)), U94#(tt(), V1, V2) -> activate#(V2))
(U93#(tt(), V1, V2) -> U94#(isNatIListKind(activate(V2)), activate(V1), activate(V2)), U94#(tt(), V1, V2) -> activate#(V1))
(isNatIList#(V) -> isNatIListKind#(activate(V)), isNatIListKind#(n__cons(V1, V2)) -> U51#(isNatKind(activate(V1)), activate(V2)))
(isNatIList#(V) -> isNatIListKind#(activate(V)), isNatIListKind#(n__cons(V1, V2)) -> activate#(V2))
(isNatIList#(V) -> isNatIListKind#(activate(V)), isNatIListKind#(n__cons(V1, V2)) -> activate#(V1))
(isNatIList#(V) -> isNatIListKind#(activate(V)), isNatIListKind#(n__cons(V1, V2)) -> isNatKind#(activate(V1)))
(isNatIList#(V) -> isNatIListKind#(activate(V)), isNatIListKind#(n__take(V1, V2)) -> U61#(isNatKind(activate(V1)), activate(V2)))
(isNatIList#(V) -> isNatIListKind#(activate(V)), isNatIListKind#(n__take(V1, V2)) -> activate#(V2))
(isNatIList#(V) -> isNatIListKind#(activate(V)), isNatIListKind#(n__take(V1, V2)) -> activate#(V1))
(isNatIList#(V) -> isNatIListKind#(activate(V)), isNatIListKind#(n__take(V1, V2)) -> isNatKind#(activate(V1)))
(U31#(tt(), V) -> isNatIListKind#(activate(V)), isNatIListKind#(n__cons(V1, V2)) -> U51#(isNatKind(activate(V1)), activate(V2)))
(U31#(tt(), V) -> isNatIListKind#(activate(V)), isNatIListKind#(n__cons(V1, V2)) -> activate#(V2))
(U31#(tt(), V) -> isNatIListKind#(activate(V)), isNatIListKind#(n__cons(V1, V2)) -> activate#(V1))
(U31#(tt(), V) -> isNatIListKind#(activate(V)), isNatIListKind#(n__cons(V1, V2)) -> isNatKind#(activate(V1)))
(U31#(tt(), V) -> isNatIListKind#(activate(V)), isNatIListKind#(n__take(V1, V2)) -> U61#(isNatKind(activate(V1)), activate(V2)))
(U31#(tt(), V) -> isNatIListKind#(activate(V)), isNatIListKind#(n__take(V1, V2)) -> activate#(V2))
(U31#(tt(), V) -> isNatIListKind#(activate(V)), isNatIListKind#(n__take(V1, V2)) -> activate#(V1))
(U31#(tt(), V) -> isNatIListKind#(activate(V)), isNatIListKind#(n__take(V1, V2)) -> isNatKind#(activate(V1)))
(U133#(tt(), IL, M, N) -> isNatKind#(activate(M)), isNatKind#(n__s(V1)) -> U81#(isNatKind(activate(V1))))
(U133#(tt(), IL, M, N) -> isNatKind#(activate(M)), isNatKind#(n__s(V1)) -> activate#(V1))
(U133#(tt(), IL, M, N) -> isNatKind#(activate(M)), isNatKind#(n__s(V1)) -> isNatKind#(activate(V1)))
(U133#(tt(), IL, M, N) -> isNatKind#(activate(M)), isNatKind#(n__length(V1)) -> U71#(isNatIListKind(activate(V1))))
(U133#(tt(), IL, M, N) -> isNatKind#(activate(M)), isNatKind#(n__length(V1)) -> isNatIListKind#(activate(V1)))
(U133#(tt(), IL, M, N) -> isNatKind#(activate(M)), isNatKind#(n__length(V1)) -> activate#(V1))
(U131#(tt(), IL, M, N) -> isNatIListKind#(activate(IL)), isNatIListKind#(n__cons(V1, V2)) -> U51#(isNatKind(activate(V1)), activate(V2)))
(U131#(tt(), IL, M, N) -> isNatIListKind#(activate(IL)), isNatIListKind#(n__cons(V1, V2)) -> activate#(V2))
(U131#(tt(), IL, M, N) -> isNatIListKind#(activate(IL)), isNatIListKind#(n__cons(V1, V2)) -> activate#(V1))
(U131#(tt(), IL, M, N) -> isNatIListKind#(activate(IL)), isNatIListKind#(n__cons(V1, V2)) -> isNatKind#(activate(V1)))
(U131#(tt(), IL, M, N) -> isNatIListKind#(activate(IL)), isNatIListKind#(n__take(V1, V2)) -> U61#(isNatKind(activate(V1)), activate(V2)))
(U131#(tt(), IL, M, N) -> isNatIListKind#(activate(IL)), isNatIListKind#(n__take(V1, V2)) -> activate#(V2))
(U131#(tt(), IL, M, N) -> isNatIListKind#(activate(IL)), isNatIListKind#(n__take(V1, V2)) -> activate#(V1))
(U131#(tt(), IL, M, N) -> isNatIListKind#(activate(IL)), isNatIListKind#(n__take(V1, V2)) -> isNatKind#(activate(V1)))
(U112#(tt(), L, N) -> isNat#(activate(N)), isNat#(n__s(V1)) -> U21#(isNatKind(activate(V1)), activate(V1)))
(U112#(tt(), L, N) -> isNat#(activate(N)), isNat#(n__s(V1)) -> activate#(V1))
(U112#(tt(), L, N) -> isNat#(activate(N)), isNat#(n__s(V1)) -> isNatKind#(activate(V1)))
(U112#(tt(), L, N) -> isNat#(activate(N)), isNat#(n__length(V1)) -> U11#(isNatIListKind(activate(V1)), activate(V1)))
(U112#(tt(), L, N) -> isNat#(activate(N)), isNat#(n__length(V1)) -> isNatIListKind#(activate(V1)))
(U112#(tt(), L, N) -> isNat#(activate(N)), isNat#(n__length(V1)) -> activate#(V1))
(U134#(tt(), IL, M, N) -> isNat#(activate(N)), isNat#(n__s(V1)) -> U21#(isNatKind(activate(V1)), activate(V1)))
(U134#(tt(), IL, M, N) -> isNat#(activate(N)), isNat#(n__s(V1)) -> activate#(V1))
(U134#(tt(), IL, M, N) -> isNat#(activate(N)), isNat#(n__s(V1)) -> isNatKind#(activate(V1)))
(U134#(tt(), IL, M, N) -> isNat#(activate(N)), isNat#(n__length(V1)) -> U11#(isNatIListKind(activate(V1)), activate(V1)))
(U134#(tt(), IL, M, N) -> isNat#(activate(N)), isNat#(n__length(V1)) -> isNatIListKind#(activate(V1)))
(U134#(tt(), IL, M, N) -> isNat#(activate(N)), isNat#(n__length(V1)) -> activate#(V1))
(U111#(tt(), L, N) -> isNatIListKind#(activate(L)), isNatIListKind#(n__cons(V1, V2)) -> U51#(isNatKind(activate(V1)), activate(V2)))
(U111#(tt(), L, N) -> isNatIListKind#(activate(L)), isNatIListKind#(n__cons(V1, V2)) -> activate#(V2))
(U111#(tt(), L, N) -> isNatIListKind#(activate(L)), isNatIListKind#(n__cons(V1, V2)) -> activate#(V1))
(U111#(tt(), L, N) -> isNatIListKind#(activate(L)), isNatIListKind#(n__cons(V1, V2)) -> isNatKind#(activate(V1)))
(U111#(tt(), L, N) -> isNatIListKind#(activate(L)), isNatIListKind#(n__take(V1, V2)) -> U61#(isNatKind(activate(V1)), activate(V2)))
(U111#(tt(), L, N) -> isNatIListKind#(activate(L)), isNatIListKind#(n__take(V1, V2)) -> activate#(V2))
(U111#(tt(), L, N) -> isNatIListKind#(activate(L)), isNatIListKind#(n__take(V1, V2)) -> activate#(V1))
(U111#(tt(), L, N) -> isNatIListKind#(activate(L)), isNatIListKind#(n__take(V1, V2)) -> isNatKind#(activate(V1)))
(length#(cons(N, L)) -> isNatList#(activate(L)), isNatList#(n__cons(V1, V2)) -> U91#(isNatKind(activate(V1)), activate(V1), activate(V2)))
(length#(cons(N, L)) -> isNatList#(activate(L)), isNatList#(n__cons(V1, V2)) -> activate#(V2))
(length#(cons(N, L)) -> isNatList#(activate(L)), isNatList#(n__cons(V1, V2)) -> activate#(V1))
(length#(cons(N, L)) -> isNatList#(activate(L)), isNatList#(n__cons(V1, V2)) -> isNatKind#(activate(V1)))
(length#(cons(N, L)) -> isNatList#(activate(L)), isNatList#(n__take(V1, V2)) -> U101#(isNatKind(activate(V1)), activate(V1), activate(V2)))
(length#(cons(N, L)) -> isNatList#(activate(L)), isNatList#(n__take(V1, V2)) -> activate#(V2))
(length#(cons(N, L)) -> isNatList#(activate(L)), isNatList#(n__take(V1, V2)) -> activate#(V1))
(length#(cons(N, L)) -> isNatList#(activate(L)), isNatList#(n__take(V1, V2)) -> isNatKind#(activate(V1)))
(U103#(tt(), V1, V2) -> isNatIListKind#(activate(V2)), isNatIListKind#(n__cons(V1, V2)) -> U51#(isNatKind(activate(V1)), activate(V2)))
(U103#(tt(), V1, V2) -> isNatIListKind#(activate(V2)), isNatIListKind#(n__cons(V1, V2)) -> activate#(V2))
(U103#(tt(), V1, V2) -> isNatIListKind#(activate(V2)), isNatIListKind#(n__cons(V1, V2)) -> activate#(V1))
(U103#(tt(), V1, V2) -> isNatIListKind#(activate(V2)), isNatIListKind#(n__cons(V1, V2)) -> isNatKind#(activate(V1)))
(U103#(tt(), V1, V2) -> isNatIListKind#(activate(V2)), isNatIListKind#(n__take(V1, V2)) -> U61#(isNatKind(activate(V1)), activate(V2)))
(U103#(tt(), V1, V2) -> isNatIListKind#(activate(V2)), isNatIListKind#(n__take(V1, V2)) -> activate#(V2))
(U103#(tt(), V1, V2) -> isNatIListKind#(activate(V2)), isNatIListKind#(n__take(V1, V2)) -> activate#(V1))
(U103#(tt(), V1, V2) -> isNatIListKind#(activate(V2)), isNatIListKind#(n__take(V1, V2)) -> isNatKind#(activate(V1)))
(U42#(tt(), V1, V2) -> isNatIListKind#(activate(V2)), isNatIListKind#(n__cons(V1, V2)) -> U51#(isNatKind(activate(V1)), activate(V2)))
(U42#(tt(), V1, V2) -> isNatIListKind#(activate(V2)), isNatIListKind#(n__cons(V1, V2)) -> activate#(V2))
(U42#(tt(), V1, V2) -> isNatIListKind#(activate(V2)), isNatIListKind#(n__cons(V1, V2)) -> activate#(V1))
(U42#(tt(), V1, V2) -> isNatIListKind#(activate(V2)), isNatIListKind#(n__cons(V1, V2)) -> isNatKind#(activate(V1)))
(U42#(tt(), V1, V2) -> isNatIListKind#(activate(V2)), isNatIListKind#(n__take(V1, V2)) -> U61#(isNatKind(activate(V1)), activate(V2)))
(U42#(tt(), V1, V2) -> isNatIListKind#(activate(V2)), isNatIListKind#(n__take(V1, V2)) -> activate#(V2))
(U42#(tt(), V1, V2) -> isNatIListKind#(activate(V2)), isNatIListKind#(n__take(V1, V2)) -> activate#(V1))
(U42#(tt(), V1, V2) -> isNatIListKind#(activate(V2)), isNatIListKind#(n__take(V1, V2)) -> isNatKind#(activate(V1)))
(U45#(tt(), V2) -> isNatIList#(activate(V2)), isNatIList#(n__cons(V1, V2)) -> U41#(isNatKind(activate(V1)), activate(V1), activate(V2)))
(U45#(tt(), V2) -> isNatIList#(activate(V2)), isNatIList#(n__cons(V1, V2)) -> activate#(V2))
(U45#(tt(), V2) -> isNatIList#(activate(V2)), isNatIList#(n__cons(V1, V2)) -> activate#(V1))
(U45#(tt(), V2) -> isNatIList#(activate(V2)), isNatIList#(n__cons(V1, V2)) -> isNatKind#(activate(V1)))
(U45#(tt(), V2) -> isNatIList#(activate(V2)), isNatIList#(V) -> U31#(isNatIListKind(activate(V)), activate(V)))
(U45#(tt(), V2) -> isNatIList#(activate(V2)), isNatIList#(V) -> isNatIListKind#(activate(V)))
(U45#(tt(), V2) -> isNatIList#(activate(V2)), isNatIList#(V) -> activate#(V))
(U61#(tt(), V2) -> isNatIListKind#(activate(V2)), isNatIListKind#(n__cons(V1, V2)) -> U51#(isNatKind(activate(V1)), activate(V2)))
(U61#(tt(), V2) -> isNatIListKind#(activate(V2)), isNatIListKind#(n__cons(V1, V2)) -> activate#(V2))
(U61#(tt(), V2) -> isNatIListKind#(activate(V2)), isNatIListKind#(n__cons(V1, V2)) -> activate#(V1))
(U61#(tt(), V2) -> isNatIListKind#(activate(V2)), isNatIListKind#(n__cons(V1, V2)) -> isNatKind#(activate(V1)))
(U61#(tt(), V2) -> isNatIListKind#(activate(V2)), isNatIListKind#(n__take(V1, V2)) -> U61#(isNatKind(activate(V1)), activate(V2)))
(U61#(tt(), V2) -> isNatIListKind#(activate(V2)), isNatIListKind#(n__take(V1, V2)) -> activate#(V2))
(U61#(tt(), V2) -> isNatIListKind#(activate(V2)), isNatIListKind#(n__take(V1, V2)) -> activate#(V1))
(U61#(tt(), V2) -> isNatIListKind#(activate(V2)), isNatIListKind#(n__take(V1, V2)) -> isNatKind#(activate(V1)))
(U93#(tt(), V1, V2) -> isNatIListKind#(activate(V2)), isNatIListKind#(n__cons(V1, V2)) -> U51#(isNatKind(activate(V1)), activate(V2)))
(U93#(tt(), V1, V2) -> isNatIListKind#(activate(V2)), isNatIListKind#(n__cons(V1, V2)) -> activate#(V2))
(U93#(tt(), V1, V2) -> isNatIListKind#(activate(V2)), isNatIListKind#(n__cons(V1, V2)) -> activate#(V1))
(U93#(tt(), V1, V2) -> isNatIListKind#(activate(V2)), isNatIListKind#(n__cons(V1, V2)) -> isNatKind#(activate(V1)))
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(U93#(tt(), V1, V2) -> isNatIListKind#(activate(V2)), isNatIListKind#(n__take(V1, V2)) -> activate#(V2))
(U93#(tt(), V1, V2) -> isNatIListKind#(activate(V2)), isNatIListKind#(n__take(V1, V2)) -> activate#(V1))
(U93#(tt(), V1, V2) -> isNatIListKind#(activate(V2)), isNatIListKind#(n__take(V1, V2)) -> isNatKind#(activate(V1)))
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(isNatKind#(n__length(V1)) -> isNatIListKind#(activate(V1)), isNatIListKind#(n__take(V1, V2)) -> isNatKind#(activate(V1)))
(U101#(tt(), V1, V2) -> isNatKind#(activate(V1)), isNatKind#(n__s(V1)) -> U81#(isNatKind(activate(V1))))
(U101#(tt(), V1, V2) -> isNatKind#(activate(V1)), isNatKind#(n__s(V1)) -> activate#(V1))
(U101#(tt(), V1, V2) -> isNatKind#(activate(V1)), isNatKind#(n__s(V1)) -> isNatKind#(activate(V1)))
(U101#(tt(), V1, V2) -> isNatKind#(activate(V1)), isNatKind#(n__length(V1)) -> U71#(isNatIListKind(activate(V1))))
(U101#(tt(), V1, V2) -> isNatKind#(activate(V1)), isNatKind#(n__length(V1)) -> isNatIListKind#(activate(V1)))
(U101#(tt(), V1, V2) -> isNatKind#(activate(V1)), isNatKind#(n__length(V1)) -> activate#(V1))
(isNatIListKind#(n__cons(V1, V2)) -> isNatKind#(activate(V1)), isNatKind#(n__s(V1)) -> U81#(isNatKind(activate(V1))))
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(isNatIListKind#(n__cons(V1, V2)) -> isNatKind#(activate(V1)), isNatKind#(n__s(V1)) -> isNatKind#(activate(V1)))
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(isNat#(n__length(V1)) -> isNatIListKind#(activate(V1)), isNatIListKind#(n__cons(V1, V2)) -> U51#(isNatKind(activate(V1)), activate(V2)))
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(isNat#(n__length(V1)) -> isNatIListKind#(activate(V1)), isNatIListKind#(n__take(V1, V2)) -> U61#(isNatKind(activate(V1)), activate(V2)))
(isNat#(n__length(V1)) -> isNatIListKind#(activate(V1)), isNatIListKind#(n__take(V1, V2)) -> activate#(V2))
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(isNat#(n__length(V1)) -> isNatIListKind#(activate(V1)), isNatIListKind#(n__take(V1, V2)) -> isNatKind#(activate(V1)))
(isNatIList#(n__cons(V1, V2)) -> isNatKind#(activate(V1)), isNatKind#(n__s(V1)) -> U81#(isNatKind(activate(V1))))
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(isNatIList#(n__cons(V1, V2)) -> isNatKind#(activate(V1)), isNatKind#(n__s(V1)) -> isNatKind#(activate(V1)))
(isNatIList#(n__cons(V1, V2)) -> isNatKind#(activate(V1)), isNatKind#(n__length(V1)) -> U71#(isNatIListKind(activate(V1))))
(isNatIList#(n__cons(V1, V2)) -> isNatKind#(activate(V1)), isNatKind#(n__length(V1)) -> isNatIListKind#(activate(V1)))
(isNatIList#(n__cons(V1, V2)) -> isNatKind#(activate(V1)), isNatKind#(n__length(V1)) -> activate#(V1))
(U11#(tt(), V1) -> isNatIListKind#(activate(V1)), isNatIListKind#(n__cons(V1, V2)) -> U51#(isNatKind(activate(V1)), activate(V2)))
(U11#(tt(), V1) -> isNatIListKind#(activate(V1)), isNatIListKind#(n__cons(V1, V2)) -> activate#(V2))
(U11#(tt(), V1) -> isNatIListKind#(activate(V1)), isNatIListKind#(n__cons(V1, V2)) -> activate#(V1))
(U11#(tt(), V1) -> isNatIListKind#(activate(V1)), isNatIListKind#(n__cons(V1, V2)) -> isNatKind#(activate(V1)))
(U11#(tt(), V1) -> isNatIListKind#(activate(V1)), isNatIListKind#(n__take(V1, V2)) -> U61#(isNatKind(activate(V1)), activate(V2)))
(U11#(tt(), V1) -> isNatIListKind#(activate(V1)), isNatIListKind#(n__take(V1, V2)) -> activate#(V2))
(U11#(tt(), V1) -> isNatIListKind#(activate(V1)), isNatIListKind#(n__take(V1, V2)) -> activate#(V1))
(U11#(tt(), V1) -> isNatIListKind#(activate(V1)), isNatIListKind#(n__take(V1, V2)) -> isNatKind#(activate(V1)))
(isNatList#(n__cons(V1, V2)) -> isNatKind#(activate(V1)), isNatKind#(n__s(V1)) -> U81#(isNatKind(activate(V1))))
(isNatList#(n__cons(V1, V2)) -> isNatKind#(activate(V1)), isNatKind#(n__s(V1)) -> activate#(V1))
(isNatList#(n__cons(V1, V2)) -> isNatKind#(activate(V1)), isNatKind#(n__s(V1)) -> isNatKind#(activate(V1)))
(isNatList#(n__cons(V1, V2)) -> isNatKind#(activate(V1)), isNatKind#(n__length(V1)) -> U71#(isNatIListKind(activate(V1))))
(isNatList#(n__cons(V1, V2)) -> isNatKind#(activate(V1)), isNatKind#(n__length(V1)) -> isNatIListKind#(activate(V1)))
(isNatList#(n__cons(V1, V2)) -> isNatKind#(activate(V1)), isNatKind#(n__length(V1)) -> activate#(V1))
(U21#(tt(), V1) -> isNatKind#(activate(V1)), isNatKind#(n__s(V1)) -> U81#(isNatKind(activate(V1))))
(U21#(tt(), V1) -> isNatKind#(activate(V1)), isNatKind#(n__s(V1)) -> activate#(V1))
(U21#(tt(), V1) -> isNatKind#(activate(V1)), isNatKind#(n__s(V1)) -> isNatKind#(activate(V1)))
(U21#(tt(), V1) -> isNatKind#(activate(V1)), isNatKind#(n__length(V1)) -> U71#(isNatIListKind(activate(V1))))
(U21#(tt(), V1) -> isNatKind#(activate(V1)), isNatKind#(n__length(V1)) -> isNatIListKind#(activate(V1)))
(U21#(tt(), V1) -> isNatKind#(activate(V1)), isNatKind#(n__length(V1)) -> activate#(V1))
(U44#(tt(), V1, V2) -> isNat#(activate(V1)), isNat#(n__s(V1)) -> U21#(isNatKind(activate(V1)), activate(V1)))
(U44#(tt(), V1, V2) -> isNat#(activate(V1)), isNat#(n__s(V1)) -> activate#(V1))
(U44#(tt(), V1, V2) -> isNat#(activate(V1)), isNat#(n__s(V1)) -> isNatKind#(activate(V1)))
(U44#(tt(), V1, V2) -> isNat#(activate(V1)), isNat#(n__length(V1)) -> U11#(isNatIListKind(activate(V1)), activate(V1)))
(U44#(tt(), V1, V2) -> isNat#(activate(V1)), isNat#(n__length(V1)) -> isNatIListKind#(activate(V1)))
(U44#(tt(), V1, V2) -> isNat#(activate(V1)), isNat#(n__length(V1)) -> activate#(V1))
(U94#(tt(), V1, V2) -> isNat#(activate(V1)), isNat#(n__s(V1)) -> U21#(isNatKind(activate(V1)), activate(V1)))
(U94#(tt(), V1, V2) -> isNat#(activate(V1)), isNat#(n__s(V1)) -> activate#(V1))
(U94#(tt(), V1, V2) -> isNat#(activate(V1)), isNat#(n__s(V1)) -> isNatKind#(activate(V1)))
(U94#(tt(), V1, V2) -> isNat#(activate(V1)), isNat#(n__length(V1)) -> U11#(isNatIListKind(activate(V1)), activate(V1)))
(U94#(tt(), V1, V2) -> isNat#(activate(V1)), isNat#(n__length(V1)) -> isNatIListKind#(activate(V1)))
(U94#(tt(), V1, V2) -> isNat#(activate(V1)), isNat#(n__length(V1)) -> activate#(V1))
(U132#(tt(), IL, M, N) -> activate#(M), activate#(n__nil()) -> nil#())
(U132#(tt(), IL, M, N) -> activate#(M), activate#(n__cons(X1, X2)) -> activate#(X1))
(U132#(tt(), IL, M, N) -> activate#(M), activate#(n__cons(X1, X2)) -> cons#(activate(X1), X2))
(U132#(tt(), IL, M, N) -> activate#(M), activate#(n__s(X)) -> s#(activate(X)))
(U132#(tt(), IL, M, N) -> activate#(M), activate#(n__s(X)) -> activate#(X))
(U132#(tt(), IL, M, N) -> activate#(M), activate#(n__length(X)) -> length#(activate(X)))
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(U132#(tt(), IL, M, N) -> activate#(M), activate#(n__take(X1, X2)) -> activate#(X2))
(U132#(tt(), IL, M, N) -> activate#(M), activate#(n__take(X1, X2)) -> activate#(X1))
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(U133#(tt(), IL, M, N) -> activate#(M), activate#(n__s(X)) -> activate#(X))
(U133#(tt(), IL, M, N) -> activate#(M), activate#(n__length(X)) -> length#(activate(X)))
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(U133#(tt(), IL, M, N) -> activate#(M), activate#(n__take(X1, X2)) -> activate#(X2))
(U133#(tt(), IL, M, N) -> activate#(M), activate#(n__take(X1, X2)) -> activate#(X1))
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(U135#(tt(), IL, M, N) -> activate#(M), activate#(n__cons(X1, X2)) -> cons#(activate(X1), X2))
(U135#(tt(), IL, M, N) -> activate#(M), activate#(n__s(X)) -> s#(activate(X)))
(U135#(tt(), IL, M, N) -> activate#(M), activate#(n__s(X)) -> activate#(X))
(U135#(tt(), IL, M, N) -> activate#(M), activate#(n__length(X)) -> length#(activate(X)))
(U135#(tt(), IL, M, N) -> activate#(M), activate#(n__length(X)) -> activate#(X))
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(U135#(tt(), IL, M, N) -> activate#(M), activate#(n__take(X1, X2)) -> activate#(X2))
(U135#(tt(), IL, M, N) -> activate#(M), activate#(n__take(X1, X2)) -> activate#(X1))
(U135#(tt(), IL, M, N) -> activate#(M), activate#(n__zeros()) -> zeros#())
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(U102#(tt(), V1, V2) -> activate#(V1), activate#(n__cons(X1, X2)) -> cons#(activate(X1), X2))
(U102#(tt(), V1, V2) -> activate#(V1), activate#(n__s(X)) -> s#(activate(X)))
(U102#(tt(), V1, V2) -> activate#(V1), activate#(n__s(X)) -> activate#(X))
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(U102#(tt(), V1, V2) -> activate#(V1), activate#(n__length(X)) -> activate#(X))
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(U102#(tt(), V1, V2) -> activate#(V1), activate#(n__take(X1, X2)) -> take#(activate(X1), activate(X2)))
(U102#(tt(), V1, V2) -> activate#(V1), activate#(n__take(X1, X2)) -> activate#(X2))
(U102#(tt(), V1, V2) -> activate#(V1), activate#(n__take(X1, X2)) -> activate#(X1))
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(isNatKind#(n__s(V1)) -> activate#(V1), activate#(n__take(X1, X2)) -> activate#(X2))
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(U103#(tt(), V1, V2) -> activate#(V1), activate#(n__cons(X1, X2)) -> activate#(X1))
(U103#(tt(), V1, V2) -> activate#(V1), activate#(n__cons(X1, X2)) -> cons#(activate(X1), X2))
(U103#(tt(), V1, V2) -> activate#(V1), activate#(n__s(X)) -> s#(activate(X)))
(U103#(tt(), V1, V2) -> activate#(V1), activate#(n__s(X)) -> activate#(X))
(U103#(tt(), V1, V2) -> activate#(V1), activate#(n__length(X)) -> length#(activate(X)))
(U103#(tt(), V1, V2) -> activate#(V1), activate#(n__length(X)) -> activate#(X))
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(U103#(tt(), V1, V2) -> activate#(V1), activate#(n__take(X1, X2)) -> take#(activate(X1), activate(X2)))
(U103#(tt(), V1, V2) -> activate#(V1), activate#(n__take(X1, X2)) -> activate#(X2))
(U103#(tt(), V1, V2) -> activate#(V1), activate#(n__take(X1, X2)) -> activate#(X1))
(U103#(tt(), V1, V2) -> activate#(V1), activate#(n__zeros()) -> zeros#())
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(isNatIListKind#(n__cons(V1, V2)) -> activate#(V1), activate#(n__cons(X1, X2)) -> activate#(X1))
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(isNat#(n__length(V1)) -> activate#(V1), activate#(n__cons(X1, X2)) -> activate#(X1))
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(isNatIList#(n__cons(V1, V2)) -> activate#(V1), activate#(n__zeros()) -> zeros#())
(U11#(tt(), V1) -> activate#(V1), activate#(n__nil()) -> nil#())
(U11#(tt(), V1) -> activate#(V1), activate#(n__cons(X1, X2)) -> activate#(X1))
(U11#(tt(), V1) -> activate#(V1), activate#(n__cons(X1, X2)) -> cons#(activate(X1), X2))
(U11#(tt(), V1) -> activate#(V1), activate#(n__s(X)) -> s#(activate(X)))
(U11#(tt(), V1) -> activate#(V1), activate#(n__s(X)) -> activate#(X))
(U11#(tt(), V1) -> activate#(V1), activate#(n__length(X)) -> length#(activate(X)))
(U11#(tt(), V1) -> activate#(V1), activate#(n__length(X)) -> activate#(X))
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(U11#(tt(), V1) -> activate#(V1), activate#(n__take(X1, X2)) -> activate#(X1))
(U11#(tt(), V1) -> activate#(V1), activate#(n__zeros()) -> zeros#())
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(U21#(tt(), V1) -> activate#(V1), activate#(n__nil()) -> nil#())
(U21#(tt(), V1) -> activate#(V1), activate#(n__cons(X1, X2)) -> activate#(X1))
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(U21#(tt(), V1) -> activate#(V1), activate#(n__zeros()) -> zeros#())
(U41#(tt(), V1, V2) -> activate#(V1), activate#(n__nil()) -> nil#())
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(U44#(tt(), V1, V2) -> activate#(V1), activate#(n__zeros()) -> zeros#())
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(U91#(tt(), V1, V2) -> activate#(V1), activate#(n__s(X)) -> activate#(X))
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(U94#(tt(), V1, V2) -> activate#(V1), activate#(n__cons(X1, X2)) -> activate#(X1))
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(U94#(tt(), V1, V2) -> activate#(V1), activate#(n__take(X1, X2)) -> activate#(X2))
(U94#(tt(), V1, V2) -> activate#(V1), activate#(n__take(X1, X2)) -> activate#(X1))
(U94#(tt(), V1, V2) -> activate#(V1), activate#(n__zeros()) -> zeros#())
(U121#(tt(), IL) -> U122#(isNatIListKind(activate(IL))), U122#(tt()) -> nil#())
(isNatIList#(V) -> activate#(V), activate#(n__nil()) -> nil#())
(isNatIList#(V) -> activate#(V), activate#(n__cons(X1, X2)) -> activate#(X1))
(isNatIList#(V) -> activate#(V), activate#(n__cons(X1, X2)) -> cons#(activate(X1), X2))
(isNatIList#(V) -> activate#(V), activate#(n__s(X)) -> s#(activate(X)))
(isNatIList#(V) -> activate#(V), activate#(n__s(X)) -> activate#(X))
(isNatIList#(V) -> activate#(V), activate#(n__length(X)) -> length#(activate(X)))
(isNatIList#(V) -> activate#(V), activate#(n__length(X)) -> activate#(X))
(isNatIList#(V) -> activate#(V), activate#(n__0()) -> 0#())
(isNatIList#(V) -> activate#(V), activate#(n__take(X1, X2)) -> take#(activate(X1), activate(X2)))
(isNatIList#(V) -> activate#(V), activate#(n__take(X1, X2)) -> activate#(X2))
(isNatIList#(V) -> activate#(V), activate#(n__take(X1, X2)) -> activate#(X1))
(isNatIList#(V) -> activate#(V), activate#(n__zeros()) -> zeros#())
(U31#(tt(), V) -> activate#(V), activate#(n__nil()) -> nil#())
(U31#(tt(), V) -> activate#(V), activate#(n__cons(X1, X2)) -> activate#(X1))
(U31#(tt(), V) -> activate#(V), activate#(n__cons(X1, X2)) -> cons#(activate(X1), X2))
(U31#(tt(), V) -> activate#(V), activate#(n__s(X)) -> s#(activate(X)))
(U31#(tt(), V) -> activate#(V), activate#(n__s(X)) -> activate#(X))
(U31#(tt(), V) -> activate#(V), activate#(n__length(X)) -> length#(activate(X)))
(U31#(tt(), V) -> activate#(V), activate#(n__length(X)) -> activate#(X))
(U31#(tt(), V) -> activate#(V), activate#(n__0()) -> 0#())
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(U31#(tt(), V) -> activate#(V), activate#(n__take(X1, X2)) -> activate#(X2))
(U31#(tt(), V) -> activate#(V), activate#(n__take(X1, X2)) -> activate#(X1))
(U31#(tt(), V) -> activate#(V), activate#(n__zeros()) -> zeros#())
(U132#(tt(), IL, M, N) -> U133#(isNat(activate(M)), activate(IL), activate(M), activate(N)), U133#(tt(), IL, M, N) -> U134#(isNatKind(activate(M)), activate(IL), activate(M), activate(N)))
(U132#(tt(), IL, M, N) -> U133#(isNat(activate(M)), activate(IL), activate(M), activate(N)), U133#(tt(), IL, M, N) -> activate#(M))
(U132#(tt(), IL, M, N) -> U133#(isNat(activate(M)), activate(IL), activate(M), activate(N)), U133#(tt(), IL, M, N) -> activate#(IL))
(U132#(tt(), IL, M, N) -> U133#(isNat(activate(M)), activate(IL), activate(M), activate(N)), U133#(tt(), IL, M, N) -> activate#(N))
(U132#(tt(), IL, M, N) -> U133#(isNat(activate(M)), activate(IL), activate(M), activate(N)), U133#(tt(), IL, M, N) -> isNatKind#(activate(M)))
(U133#(tt(), IL, M, N) -> U134#(isNatKind(activate(M)), activate(IL), activate(M), activate(N)), U134#(tt(), IL, M, N) -> U135#(isNat(activate(N)), activate(IL), activate(M), activate(N)))
(U133#(tt(), IL, M, N) -> U134#(isNatKind(activate(M)), activate(IL), activate(M), activate(N)), U134#(tt(), IL, M, N) -> isNat#(activate(N)))
(U133#(tt(), IL, M, N) -> U134#(isNatKind(activate(M)), activate(IL), activate(M), activate(N)), U134#(tt(), IL, M, N) -> activate#(M))
(U133#(tt(), IL, M, N) -> U134#(isNatKind(activate(M)), activate(IL), activate(M), activate(N)), U134#(tt(), IL, M, N) -> activate#(IL))
(U133#(tt(), IL, M, N) -> U134#(isNatKind(activate(M)), activate(IL), activate(M), activate(N)), U134#(tt(), IL, M, N) -> activate#(N))
(U135#(tt(), IL, M, N) -> U136#(isNatKind(activate(N)), activate(IL), activate(M), activate(N)), U136#(tt(), IL, M, N) -> activate#(M))
(U135#(tt(), IL, M, N) -> U136#(isNatKind(activate(N)), activate(IL), activate(M), activate(N)), U136#(tt(), IL, M, N) -> activate#(IL))
(U135#(tt(), IL, M, N) -> U136#(isNatKind(activate(N)), activate(IL), activate(M), activate(N)), U136#(tt(), IL, M, N) -> activate#(N))
(U135#(tt(), IL, M, N) -> U136#(isNatKind(activate(N)), activate(IL), activate(M), activate(N)), U136#(tt(), IL, M, N) -> cons#(activate(N), n__take(activate(M), activate(IL))))
(U102#(tt(), V1, V2) -> activate#(V2), activate#(n__nil()) -> nil#())
(U102#(tt(), V1, V2) -> activate#(V2), activate#(n__cons(X1, X2)) -> activate#(X1))
(U102#(tt(), V1, V2) -> activate#(V2), activate#(n__cons(X1, X2)) -> cons#(activate(X1), X2))
(U102#(tt(), V1, V2) -> activate#(V2), activate#(n__s(X)) -> s#(activate(X)))
(U102#(tt(), V1, V2) -> activate#(V2), activate#(n__s(X)) -> activate#(X))
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(U102#(tt(), V1, V2) -> activate#(V2), activate#(n__length(X)) -> activate#(X))
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(U102#(tt(), V1, V2) -> activate#(V2), activate#(n__take(X1, X2)) -> activate#(X2))
(U102#(tt(), V1, V2) -> activate#(V2), activate#(n__take(X1, X2)) -> activate#(X1))
(U102#(tt(), V1, V2) -> activate#(V2), activate#(n__zeros()) -> zeros#())
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(U103#(tt(), V1, V2) -> activate#(V2), activate#(n__cons(X1, X2)) -> cons#(activate(X1), X2))
(U103#(tt(), V1, V2) -> activate#(V2), activate#(n__s(X)) -> s#(activate(X)))
(U103#(tt(), V1, V2) -> activate#(V2), activate#(n__s(X)) -> activate#(X))
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(U103#(tt(), V1, V2) -> activate#(V2), activate#(n__length(X)) -> activate#(X))
(U103#(tt(), V1, V2) -> activate#(V2), activate#(n__0()) -> 0#())
(U103#(tt(), V1, V2) -> activate#(V2), activate#(n__take(X1, X2)) -> take#(activate(X1), activate(X2)))
(U103#(tt(), V1, V2) -> activate#(V2), activate#(n__take(X1, X2)) -> activate#(X2))
(U103#(tt(), V1, V2) -> activate#(V2), activate#(n__take(X1, X2)) -> activate#(X1))
(U103#(tt(), V1, V2) -> activate#(V2), activate#(n__zeros()) -> zeros#())
(isNatIListKind#(n__cons(V1, V2)) -> activate#(V2), activate#(n__nil()) -> nil#())
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(isNatIListKind#(n__take(V1, V2)) -> activate#(V2), activate#(n__take(X1, X2)) -> activate#(X1))
(isNatIListKind#(n__take(V1, V2)) -> activate#(V2), activate#(n__take(X1, X2)) -> activate#(X2))
(isNatIListKind#(n__take(V1, V2)) -> activate#(V2), activate#(n__take(X1, X2)) -> take#(activate(X1), activate(X2)))
(isNatIListKind#(n__take(V1, V2)) -> activate#(V2), activate#(n__0()) -> 0#())
(isNatIListKind#(n__take(V1, V2)) -> activate#(V2), activate#(n__length(X)) -> activate#(X))
(isNatIListKind#(n__take(V1, V2)) -> activate#(V2), activate#(n__length(X)) -> length#(activate(X)))
(isNatIListKind#(n__take(V1, V2)) -> activate#(V2), activate#(n__s(X)) -> activate#(X))
(isNatIListKind#(n__take(V1, V2)) -> activate#(V2), activate#(n__s(X)) -> s#(activate(X)))
(isNatIListKind#(n__take(V1, V2)) -> activate#(V2), activate#(n__cons(X1, X2)) -> cons#(activate(X1), X2))
(isNatIListKind#(n__take(V1, V2)) -> activate#(V2), activate#(n__cons(X1, X2)) -> activate#(X1))
(isNatIListKind#(n__take(V1, V2)) -> activate#(V2), activate#(n__nil()) -> nil#())
(U101#(tt(), V1, V2) -> activate#(V2), activate#(n__zeros()) -> zeros#())
(U101#(tt(), V1, V2) -> activate#(V2), activate#(n__take(X1, X2)) -> activate#(X1))
(U101#(tt(), V1, V2) -> activate#(V2), activate#(n__take(X1, X2)) -> activate#(X2))
(U101#(tt(), V1, V2) -> activate#(V2), activate#(n__take(X1, X2)) -> take#(activate(X1), activate(X2)))
(U101#(tt(), V1, V2) -> activate#(V2), activate#(n__0()) -> 0#())
(U101#(tt(), V1, V2) -> activate#(V2), activate#(n__length(X)) -> activate#(X))
(U101#(tt(), V1, V2) -> activate#(V2), activate#(n__length(X)) -> length#(activate(X)))
(U101#(tt(), V1, V2) -> activate#(V2), activate#(n__s(X)) -> activate#(X))
(U101#(tt(), V1, V2) -> activate#(V2), activate#(n__s(X)) -> s#(activate(X)))
(U101#(tt(), V1, V2) -> activate#(V2), activate#(n__cons(X1, X2)) -> cons#(activate(X1), X2))
(U101#(tt(), V1, V2) -> activate#(V2), activate#(n__cons(X1, X2)) -> activate#(X1))
(U101#(tt(), V1, V2) -> activate#(V2), activate#(n__nil()) -> nil#())
(take#(0(), IL) -> U121#(isNatIList(IL), IL), U121#(tt(), IL) -> activate#(IL))
(take#(0(), IL) -> U121#(isNatIList(IL), IL), U121#(tt(), IL) -> isNatIListKind#(activate(IL)))
(take#(0(), IL) -> U121#(isNatIList(IL), IL), U121#(tt(), IL) -> U122#(isNatIListKind(activate(IL))))
(U134#(tt(), IL, M, N) -> U135#(isNat(activate(N)), activate(IL), activate(M), activate(N)), U135#(tt(), IL, M, N) -> isNatKind#(activate(N)))
(U134#(tt(), IL, M, N) -> U135#(isNat(activate(N)), activate(IL), activate(M), activate(N)), U135#(tt(), IL, M, N) -> activate#(N))
(U134#(tt(), IL, M, N) -> U135#(isNat(activate(N)), activate(IL), activate(M), activate(N)), U135#(tt(), IL, M, N) -> activate#(IL))
(U134#(tt(), IL, M, N) -> U135#(isNat(activate(N)), activate(IL), activate(M), activate(N)), U135#(tt(), IL, M, N) -> activate#(M))
(U134#(tt(), IL, M, N) -> U135#(isNat(activate(N)), activate(IL), activate(M), activate(N)), U135#(tt(), IL, M, N) -> U136#(isNatKind(activate(N)), activate(IL), activate(M), activate(N)))
(U131#(tt(), IL, M, N) -> U132#(isNatIListKind(activate(IL)), activate(IL), activate(M), activate(N)), U132#(tt(), IL, M, N) -> activate#(N))
(U131#(tt(), IL, M, N) -> U132#(isNatIListKind(activate(IL)), activate(IL), activate(M), activate(N)), U132#(tt(), IL, M, N) -> activate#(IL))
(U131#(tt(), IL, M, N) -> U132#(isNatIListKind(activate(IL)), activate(IL), activate(M), activate(N)), U132#(tt(), IL, M, N) -> activate#(M))
(U131#(tt(), IL, M, N) -> U132#(isNatIListKind(activate(IL)), activate(IL), activate(M), activate(N)), U132#(tt(), IL, M, N) -> isNat#(activate(M)))
(U131#(tt(), IL, M, N) -> U132#(isNatIListKind(activate(IL)), activate(IL), activate(M), activate(N)), U132#(tt(), IL, M, N) -> U133#(isNat(activate(M)), activate(IL), activate(M), activate(N)))
(U32#(tt(), V) -> activate#(V), activate#(n__zeros()) -> zeros#())
(U32#(tt(), V) -> activate#(V), activate#(n__take(X1, X2)) -> activate#(X1))
(U32#(tt(), V) -> activate#(V), activate#(n__take(X1, X2)) -> activate#(X2))
(U32#(tt(), V) -> activate#(V), activate#(n__take(X1, X2)) -> take#(activate(X1), activate(X2)))
(U32#(tt(), V) -> activate#(V), activate#(n__0()) -> 0#())
(U32#(tt(), V) -> activate#(V), activate#(n__length(X)) -> activate#(X))
(U32#(tt(), V) -> activate#(V), activate#(n__length(X)) -> length#(activate(X)))
(U32#(tt(), V) -> activate#(V), activate#(n__s(X)) -> activate#(X))
(U32#(tt(), V) -> activate#(V), activate#(n__s(X)) -> s#(activate(X)))
(U32#(tt(), V) -> activate#(V), activate#(n__cons(X1, X2)) -> cons#(activate(X1), X2))
(U32#(tt(), V) -> activate#(V), activate#(n__cons(X1, X2)) -> activate#(X1))
(U32#(tt(), V) -> activate#(V), activate#(n__nil()) -> nil#())
(take#(s(M), cons(N, IL)) -> U131#(isNatIList(activate(IL)), activate(IL), M, N), U131#(tt(), IL, M, N) -> activate#(N))
(take#(s(M), cons(N, IL)) -> U131#(isNatIList(activate(IL)), activate(IL), M, N), U131#(tt(), IL, M, N) -> activate#(IL))
(take#(s(M), cons(N, IL)) -> U131#(isNatIList(activate(IL)), activate(IL), M, N), U131#(tt(), IL, M, N) -> activate#(M))
(take#(s(M), cons(N, IL)) -> U131#(isNatIList(activate(IL)), activate(IL), M, N), U131#(tt(), IL, M, N) -> isNatIListKind#(activate(IL)))
(take#(s(M), cons(N, IL)) -> U131#(isNatIList(activate(IL)), activate(IL), M, N), U131#(tt(), IL, M, N) -> U132#(isNatIListKind(activate(IL)), activate(IL), activate(M), activate(N)))
(U93#(tt(), V1, V2) -> activate#(V1), activate#(n__zeros()) -> zeros#())
(U93#(tt(), V1, V2) -> activate#(V1), activate#(n__take(X1, X2)) -> activate#(X1))
(U93#(tt(), V1, V2) -> activate#(V1), activate#(n__take(X1, X2)) -> activate#(X2))
(U93#(tt(), V1, V2) -> activate#(V1), activate#(n__take(X1, X2)) -> take#(activate(X1), activate(X2)))
(U93#(tt(), V1, V2) -> activate#(V1), activate#(n__0()) -> 0#())
(U93#(tt(), V1, V2) -> activate#(V1), activate#(n__length(X)) -> activate#(X))
(U93#(tt(), V1, V2) -> activate#(V1), activate#(n__length(X)) -> length#(activate(X)))
(U93#(tt(), V1, V2) -> activate#(V1), activate#(n__s(X)) -> activate#(X))
(U93#(tt(), V1, V2) -> activate#(V1), activate#(n__s(X)) -> s#(activate(X)))
(U93#(tt(), V1, V2) -> activate#(V1), activate#(n__cons(X1, X2)) -> cons#(activate(X1), X2))
(U93#(tt(), V1, V2) -> activate#(V1), activate#(n__cons(X1, X2)) -> activate#(X1))
(U93#(tt(), V1, V2) -> activate#(V1), activate#(n__nil()) -> nil#())
(U92#(tt(), V1, V2) -> activate#(V1), activate#(n__zeros()) -> zeros#())
(U92#(tt(), V1, V2) -> activate#(V1), activate#(n__take(X1, X2)) -> activate#(X1))
(U92#(tt(), V1, V2) -> activate#(V1), activate#(n__take(X1, X2)) -> activate#(X2))
(U92#(tt(), V1, V2) -> activate#(V1), activate#(n__take(X1, X2)) -> take#(activate(X1), activate(X2)))
(U92#(tt(), V1, V2) -> activate#(V1), activate#(n__0()) -> 0#())
(U92#(tt(), V1, V2) -> activate#(V1), activate#(n__length(X)) -> activate#(X))
(U92#(tt(), V1, V2) -> activate#(V1), activate#(n__length(X)) -> length#(activate(X)))
(U92#(tt(), V1, V2) -> activate#(V1), activate#(n__s(X)) -> activate#(X))
(U92#(tt(), V1, V2) -> activate#(V1), activate#(n__s(X)) -> s#(activate(X)))
(U92#(tt(), V1, V2) -> activate#(V1), activate#(n__cons(X1, X2)) -> cons#(activate(X1), X2))
(U92#(tt(), V1, V2) -> activate#(V1), activate#(n__cons(X1, X2)) -> activate#(X1))
(U92#(tt(), V1, V2) -> activate#(V1), activate#(n__nil()) -> nil#())
(U43#(tt(), V1, V2) -> activate#(V1), activate#(n__zeros()) -> zeros#())
(U43#(tt(), V1, V2) -> activate#(V1), activate#(n__take(X1, X2)) -> activate#(X1))
(U43#(tt(), V1, V2) -> activate#(V1), activate#(n__take(X1, X2)) -> activate#(X2))
(U43#(tt(), V1, V2) -> activate#(V1), activate#(n__take(X1, X2)) -> take#(activate(X1), activate(X2)))
(U43#(tt(), V1, V2) -> activate#(V1), activate#(n__0()) -> 0#())
(U43#(tt(), V1, V2) -> activate#(V1), activate#(n__length(X)) -> activate#(X))
(U43#(tt(), V1, V2) -> activate#(V1), activate#(n__length(X)) -> length#(activate(X)))
(U43#(tt(), V1, V2) -> activate#(V1), activate#(n__s(X)) -> activate#(X))
(U43#(tt(), V1, V2) -> activate#(V1), activate#(n__s(X)) -> s#(activate(X)))
(U43#(tt(), V1, V2) -> activate#(V1), activate#(n__cons(X1, X2)) -> cons#(activate(X1), X2))
(U43#(tt(), V1, V2) -> activate#(V1), activate#(n__cons(X1, X2)) -> activate#(X1))
(U43#(tt(), V1, V2) -> activate#(V1), activate#(n__nil()) -> nil#())
(U42#(tt(), V1, V2) -> activate#(V1), activate#(n__zeros()) -> zeros#())
(U42#(tt(), V1, V2) -> activate#(V1), activate#(n__take(X1, X2)) -> activate#(X1))
(U42#(tt(), V1, V2) -> activate#(V1), activate#(n__take(X1, X2)) -> activate#(X2))
(U42#(tt(), V1, V2) -> activate#(V1), activate#(n__take(X1, X2)) -> take#(activate(X1), activate(X2)))
(U42#(tt(), V1, V2) -> activate#(V1), activate#(n__0()) -> 0#())
(U42#(tt(), V1, V2) -> activate#(V1), activate#(n__length(X)) -> activate#(X))
(U42#(tt(), V1, V2) -> activate#(V1), activate#(n__length(X)) -> length#(activate(X)))
(U42#(tt(), V1, V2) -> activate#(V1), activate#(n__s(X)) -> activate#(X))
(U42#(tt(), V1, V2) -> activate#(V1), activate#(n__s(X)) -> s#(activate(X)))
(U42#(tt(), V1, V2) -> activate#(V1), activate#(n__cons(X1, X2)) -> cons#(activate(X1), X2))
(U42#(tt(), V1, V2) -> activate#(V1), activate#(n__cons(X1, X2)) -> activate#(X1))
(U42#(tt(), V1, V2) -> activate#(V1), activate#(n__nil()) -> nil#())
(U22#(tt(), V1) -> activate#(V1), activate#(n__zeros()) -> zeros#())
(U22#(tt(), V1) -> activate#(V1), activate#(n__take(X1, X2)) -> activate#(X1))
(U22#(tt(), V1) -> activate#(V1), activate#(n__take(X1, X2)) -> activate#(X2))
(U22#(tt(), V1) -> activate#(V1), activate#(n__take(X1, X2)) -> take#(activate(X1), activate(X2)))
(U22#(tt(), V1) -> activate#(V1), activate#(n__0()) -> 0#())
(U22#(tt(), V1) -> activate#(V1), activate#(n__length(X)) -> activate#(X))
(U22#(tt(), V1) -> activate#(V1), activate#(n__length(X)) -> length#(activate(X)))
(U22#(tt(), V1) -> activate#(V1), activate#(n__s(X)) -> activate#(X))
(U22#(tt(), V1) -> activate#(V1), activate#(n__s(X)) -> s#(activate(X)))
(U22#(tt(), V1) -> activate#(V1), activate#(n__cons(X1, X2)) -> cons#(activate(X1), X2))
(U22#(tt(), V1) -> activate#(V1), activate#(n__cons(X1, X2)) -> activate#(X1))
(U22#(tt(), V1) -> activate#(V1), activate#(n__nil()) -> nil#())
(isNatList#(n__take(V1, V2)) -> activate#(V1), activate#(n__zeros()) -> zeros#())
(isNatList#(n__take(V1, V2)) -> activate#(V1), activate#(n__take(X1, X2)) -> activate#(X1))
(isNatList#(n__take(V1, V2)) -> activate#(V1), activate#(n__take(X1, X2)) -> activate#(X2))
(isNatList#(n__take(V1, V2)) -> activate#(V1), activate#(n__take(X1, X2)) -> take#(activate(X1), activate(X2)))
(isNatList#(n__take(V1, V2)) -> activate#(V1), activate#(n__0()) -> 0#())
(isNatList#(n__take(V1, V2)) -> activate#(V1), activate#(n__length(X)) -> activate#(X))
(isNatList#(n__take(V1, V2)) -> activate#(V1), activate#(n__length(X)) -> length#(activate(X)))
(isNatList#(n__take(V1, V2)) -> activate#(V1), activate#(n__s(X)) -> activate#(X))
(isNatList#(n__take(V1, V2)) -> activate#(V1), activate#(n__s(X)) -> s#(activate(X)))
(isNatList#(n__take(V1, V2)) -> activate#(V1), activate#(n__cons(X1, X2)) -> cons#(activate(X1), X2))
(isNatList#(n__take(V1, V2)) -> activate#(V1), activate#(n__cons(X1, X2)) -> activate#(X1))
(isNatList#(n__take(V1, V2)) -> activate#(V1), activate#(n__nil()) -> nil#())
(U12#(tt(), V1) -> activate#(V1), activate#(n__zeros()) -> zeros#())
(U12#(tt(), V1) -> activate#(V1), activate#(n__take(X1, X2)) -> activate#(X1))
(U12#(tt(), V1) -> activate#(V1), activate#(n__take(X1, X2)) -> activate#(X2))
(U12#(tt(), V1) -> activate#(V1), activate#(n__take(X1, X2)) -> take#(activate(X1), activate(X2)))
(U12#(tt(), V1) -> activate#(V1), activate#(n__0()) -> 0#())
(U12#(tt(), V1) -> activate#(V1), activate#(n__length(X)) -> activate#(X))
(U12#(tt(), V1) -> activate#(V1), activate#(n__length(X)) -> length#(activate(X)))
(U12#(tt(), V1) -> activate#(V1), activate#(n__s(X)) -> activate#(X))
(U12#(tt(), V1) -> activate#(V1), activate#(n__s(X)) -> s#(activate(X)))
(U12#(tt(), V1) -> activate#(V1), activate#(n__cons(X1, X2)) -> cons#(activate(X1), X2))
(U12#(tt(), V1) -> activate#(V1), activate#(n__cons(X1, X2)) -> activate#(X1))
(U12#(tt(), V1) -> activate#(V1), activate#(n__nil()) -> nil#())
(isNat#(n__s(V1)) -> activate#(V1), activate#(n__zeros()) -> zeros#())
(isNat#(n__s(V1)) -> activate#(V1), activate#(n__take(X1, X2)) -> activate#(X1))
(isNat#(n__s(V1)) -> activate#(V1), activate#(n__take(X1, X2)) -> activate#(X2))
(isNat#(n__s(V1)) -> activate#(V1), activate#(n__take(X1, X2)) -> take#(activate(X1), activate(X2)))
(isNat#(n__s(V1)) -> activate#(V1), activate#(n__0()) -> 0#())
(isNat#(n__s(V1)) -> activate#(V1), activate#(n__length(X)) -> activate#(X))
(isNat#(n__s(V1)) -> activate#(V1), activate#(n__length(X)) -> length#(activate(X)))
(isNat#(n__s(V1)) -> activate#(V1), activate#(n__s(X)) -> activate#(X))
(isNat#(n__s(V1)) -> activate#(V1), activate#(n__s(X)) -> s#(activate(X)))
(isNat#(n__s(V1)) -> activate#(V1), activate#(n__cons(X1, X2)) -> cons#(activate(X1), X2))
(isNat#(n__s(V1)) -> activate#(V1), activate#(n__cons(X1, X2)) -> activate#(X1))
(isNat#(n__s(V1)) -> activate#(V1), activate#(n__nil()) -> nil#())
(U104#(tt(), V1, V2) -> activate#(V1), activate#(n__zeros()) -> zeros#())
(U104#(tt(), V1, V2) -> activate#(V1), activate#(n__take(X1, X2)) -> activate#(X1))
(U104#(tt(), V1, V2) -> activate#(V1), activate#(n__take(X1, X2)) -> activate#(X2))
(U104#(tt(), V1, V2) -> activate#(V1), activate#(n__take(X1, X2)) -> take#(activate(X1), activate(X2)))
(U104#(tt(), V1, V2) -> activate#(V1), activate#(n__0()) -> 0#())
(U104#(tt(), V1, V2) -> activate#(V1), activate#(n__length(X)) -> activate#(X))
(U104#(tt(), V1, V2) -> activate#(V1), activate#(n__length(X)) -> length#(activate(X)))
(U104#(tt(), V1, V2) -> activate#(V1), activate#(n__s(X)) -> activate#(X))
(U104#(tt(), V1, V2) -> activate#(V1), activate#(n__s(X)) -> s#(activate(X)))
(U104#(tt(), V1, V2) -> activate#(V1), activate#(n__cons(X1, X2)) -> cons#(activate(X1), X2))
(U104#(tt(), V1, V2) -> activate#(V1), activate#(n__cons(X1, X2)) -> activate#(X1))
(U104#(tt(), V1, V2) -> activate#(V1), activate#(n__nil()) -> nil#())
(isNatIListKind#(n__take(V1, V2)) -> activate#(V1), activate#(n__zeros()) -> zeros#())
(isNatIListKind#(n__take(V1, V2)) -> activate#(V1), activate#(n__take(X1, X2)) -> activate#(X1))
(isNatIListKind#(n__take(V1, V2)) -> activate#(V1), activate#(n__take(X1, X2)) -> activate#(X2))
(isNatIListKind#(n__take(V1, V2)) -> activate#(V1), activate#(n__take(X1, X2)) -> take#(activate(X1), activate(X2)))
(isNatIListKind#(n__take(V1, V2)) -> activate#(V1), activate#(n__0()) -> 0#())
(isNatIListKind#(n__take(V1, V2)) -> activate#(V1), activate#(n__length(X)) -> activate#(X))
(isNatIListKind#(n__take(V1, V2)) -> activate#(V1), activate#(n__length(X)) -> length#(activate(X)))
(isNatIListKind#(n__take(V1, V2)) -> activate#(V1), activate#(n__s(X)) -> activate#(X))
(isNatIListKind#(n__take(V1, V2)) -> activate#(V1), activate#(n__s(X)) -> s#(activate(X)))
(isNatIListKind#(n__take(V1, V2)) -> activate#(V1), activate#(n__cons(X1, X2)) -> cons#(activate(X1), X2))
(isNatIListKind#(n__take(V1, V2)) -> activate#(V1), activate#(n__cons(X1, X2)) -> activate#(X1))
(isNatIListKind#(n__take(V1, V2)) -> activate#(V1), activate#(n__nil()) -> nil#())
(U101#(tt(), V1, V2) -> activate#(V1), activate#(n__zeros()) -> zeros#())
(U101#(tt(), V1, V2) -> activate#(V1), activate#(n__take(X1, X2)) -> activate#(X1))
(U101#(tt(), V1, V2) -> activate#(V1), activate#(n__take(X1, X2)) -> activate#(X2))
(U101#(tt(), V1, V2) -> activate#(V1), activate#(n__take(X1, X2)) -> take#(activate(X1), activate(X2)))
(U101#(tt(), V1, V2) -> activate#(V1), activate#(n__0()) -> 0#())
(U101#(tt(), V1, V2) -> activate#(V1), activate#(n__length(X)) -> activate#(X))
(U101#(tt(), V1, V2) -> activate#(V1), activate#(n__length(X)) -> length#(activate(X)))
(U101#(tt(), V1, V2) -> activate#(V1), activate#(n__s(X)) -> activate#(X))
(U101#(tt(), V1, V2) -> activate#(V1), activate#(n__s(X)) -> s#(activate(X)))
(U101#(tt(), V1, V2) -> activate#(V1), activate#(n__cons(X1, X2)) -> cons#(activate(X1), X2))
(U101#(tt(), V1, V2) -> activate#(V1), activate#(n__cons(X1, X2)) -> activate#(X1))
(U101#(tt(), V1, V2) -> activate#(V1), activate#(n__nil()) -> nil#())
(isNatKind#(n__length(V1)) -> activate#(V1), activate#(n__zeros()) -> zeros#())
(isNatKind#(n__length(V1)) -> activate#(V1), activate#(n__take(X1, X2)) -> activate#(X1))
(isNatKind#(n__length(V1)) -> activate#(V1), activate#(n__take(X1, X2)) -> activate#(X2))
(isNatKind#(n__length(V1)) -> activate#(V1), activate#(n__take(X1, X2)) -> take#(activate(X1), activate(X2)))
(isNatKind#(n__length(V1)) -> activate#(V1), activate#(n__0()) -> 0#())
(isNatKind#(n__length(V1)) -> activate#(V1), activate#(n__length(X)) -> activate#(X))
(isNatKind#(n__length(V1)) -> activate#(V1), activate#(n__length(X)) -> length#(activate(X)))
(isNatKind#(n__length(V1)) -> activate#(V1), activate#(n__s(X)) -> activate#(X))
(isNatKind#(n__length(V1)) -> activate#(V1), activate#(n__s(X)) -> s#(activate(X)))
(isNatKind#(n__length(V1)) -> activate#(V1), activate#(n__cons(X1, X2)) -> cons#(activate(X1), X2))
(isNatKind#(n__length(V1)) -> activate#(V1), activate#(n__cons(X1, X2)) -> activate#(X1))
(isNatKind#(n__length(V1)) -> activate#(V1), activate#(n__nil()) -> nil#())
(U136#(tt(), IL, M, N) -> activate#(M), activate#(n__zeros()) -> zeros#())
(U136#(tt(), IL, M, N) -> activate#(M), activate#(n__take(X1, X2)) -> activate#(X1))
(U136#(tt(), IL, M, N) -> activate#(M), activate#(n__take(X1, X2)) -> activate#(X2))
(U136#(tt(), IL, M, N) -> activate#(M), activate#(n__take(X1, X2)) -> take#(activate(X1), activate(X2)))
(U136#(tt(), IL, M, N) -> activate#(M), activate#(n__0()) -> 0#())
(U136#(tt(), IL, M, N) -> activate#(M), activate#(n__length(X)) -> activate#(X))
(U136#(tt(), IL, M, N) -> activate#(M), activate#(n__length(X)) -> length#(activate(X)))
(U136#(tt(), IL, M, N) -> activate#(M), activate#(n__s(X)) -> activate#(X))
(U136#(tt(), IL, M, N) -> activate#(M), activate#(n__s(X)) -> s#(activate(X)))
(U136#(tt(), IL, M, N) -> activate#(M), activate#(n__cons(X1, X2)) -> cons#(activate(X1), X2))
(U136#(tt(), IL, M, N) -> activate#(M), activate#(n__cons(X1, X2)) -> activate#(X1))
(U136#(tt(), IL, M, N) -> activate#(M), activate#(n__nil()) -> nil#())
(U134#(tt(), IL, M, N) -> activate#(M), activate#(n__zeros()) -> zeros#())
(U134#(tt(), IL, M, N) -> activate#(M), activate#(n__take(X1, X2)) -> activate#(X1))
(U134#(tt(), IL, M, N) -> activate#(M), activate#(n__take(X1, X2)) -> activate#(X2))
(U134#(tt(), IL, M, N) -> activate#(M), activate#(n__take(X1, X2)) -> take#(activate(X1), activate(X2)))
(U134#(tt(), IL, M, N) -> activate#(M), activate#(n__0()) -> 0#())
(U134#(tt(), IL, M, N) -> activate#(M), activate#(n__length(X)) -> activate#(X))
(U134#(tt(), IL, M, N) -> activate#(M), activate#(n__length(X)) -> length#(activate(X)))
(U134#(tt(), IL, M, N) -> activate#(M), activate#(n__s(X)) -> activate#(X))
(U134#(tt(), IL, M, N) -> activate#(M), activate#(n__s(X)) -> s#(activate(X)))
(U134#(tt(), IL, M, N) -> activate#(M), activate#(n__cons(X1, X2)) -> cons#(activate(X1), X2))
(U134#(tt(), IL, M, N) -> activate#(M), activate#(n__cons(X1, X2)) -> activate#(X1))
(U134#(tt(), IL, M, N) -> activate#(M), activate#(n__nil()) -> nil#())
(U131#(tt(), IL, M, N) -> activate#(M), activate#(n__zeros()) -> zeros#())
(U131#(tt(), IL, M, N) -> activate#(M), activate#(n__take(X1, X2)) -> activate#(X1))
(U131#(tt(), IL, M, N) -> activate#(M), activate#(n__take(X1, X2)) -> activate#(X2))
(U131#(tt(), IL, M, N) -> activate#(M), activate#(n__take(X1, X2)) -> take#(activate(X1), activate(X2)))
(U131#(tt(), IL, M, N) -> activate#(M), activate#(n__0()) -> 0#())
(U131#(tt(), IL, M, N) -> activate#(M), activate#(n__length(X)) -> activate#(X))
(U131#(tt(), IL, M, N) -> activate#(M), activate#(n__length(X)) -> length#(activate(X)))
(U131#(tt(), IL, M, N) -> activate#(M), activate#(n__s(X)) -> activate#(X))
(U131#(tt(), IL, M, N) -> activate#(M), activate#(n__s(X)) -> s#(activate(X)))
(U131#(tt(), IL, M, N) -> activate#(M), activate#(n__cons(X1, X2)) -> cons#(activate(X1), X2))
(U131#(tt(), IL, M, N) -> activate#(M), activate#(n__cons(X1, X2)) -> activate#(X1))
(U131#(tt(), IL, M, N) -> activate#(M), activate#(n__nil()) -> nil#())
(length#(cons(N, L)) -> U111#(isNatList(activate(L)), activate(L), N), U111#(tt(), L, N) -> activate#(L))
(length#(cons(N, L)) -> U111#(isNatList(activate(L)), activate(L), N), U111#(tt(), L, N) -> activate#(N))
(length#(cons(N, L)) -> U111#(isNatList(activate(L)), activate(L), N), U111#(tt(), L, N) -> isNatIListKind#(activate(L)))
(length#(cons(N, L)) -> U111#(isNatList(activate(L)), activate(L), N), U111#(tt(), L, N) -> U112#(isNatIListKind(activate(L)), activate(L), activate(N)))
(U91#(tt(), V1, V2) -> isNatKind#(activate(V1)), isNatKind#(n__length(V1)) -> activate#(V1))
(U91#(tt(), V1, V2) -> isNatKind#(activate(V1)), isNatKind#(n__length(V1)) -> isNatIListKind#(activate(V1)))
(U91#(tt(), V1, V2) -> isNatKind#(activate(V1)), isNatKind#(n__length(V1)) -> U71#(isNatIListKind(activate(V1))))
(U91#(tt(), V1, V2) -> isNatKind#(activate(V1)), isNatKind#(n__s(V1)) -> isNatKind#(activate(V1)))
(U91#(tt(), V1, V2) -> isNatKind#(activate(V1)), isNatKind#(n__s(V1)) -> activate#(V1))
(U91#(tt(), V1, V2) -> isNatKind#(activate(V1)), isNatKind#(n__s(V1)) -> U81#(isNatKind(activate(V1))))
(U41#(tt(), V1, V2) -> isNatKind#(activate(V1)), isNatKind#(n__length(V1)) -> activate#(V1))
(U41#(tt(), V1, V2) -> isNatKind#(activate(V1)), isNatKind#(n__length(V1)) -> isNatIListKind#(activate(V1)))
(U41#(tt(), V1, V2) -> isNatKind#(activate(V1)), isNatKind#(n__length(V1)) -> U71#(isNatIListKind(activate(V1))))
(U41#(tt(), V1, V2) -> isNatKind#(activate(V1)), isNatKind#(n__s(V1)) -> isNatKind#(activate(V1)))
(U41#(tt(), V1, V2) -> isNatKind#(activate(V1)), isNatKind#(n__s(V1)) -> activate#(V1))
(U41#(tt(), V1, V2) -> isNatKind#(activate(V1)), isNatKind#(n__s(V1)) -> U81#(isNatKind(activate(V1))))
(U22#(tt(), V1) -> isNat#(activate(V1)), isNat#(n__length(V1)) -> activate#(V1))
(U22#(tt(), V1) -> isNat#(activate(V1)), isNat#(n__length(V1)) -> isNatIListKind#(activate(V1)))
(U22#(tt(), V1) -> isNat#(activate(V1)), isNat#(n__length(V1)) -> U11#(isNatIListKind(activate(V1)), activate(V1)))
(U22#(tt(), V1) -> isNat#(activate(V1)), isNat#(n__s(V1)) -> isNatKind#(activate(V1)))
(U22#(tt(), V1) -> isNat#(activate(V1)), isNat#(n__s(V1)) -> activate#(V1))
(U22#(tt(), V1) -> isNat#(activate(V1)), isNat#(n__s(V1)) -> U21#(isNatKind(activate(V1)), activate(V1)))
(isNatList#(n__take(V1, V2)) -> isNatKind#(activate(V1)), isNatKind#(n__length(V1)) -> activate#(V1))
(isNatList#(n__take(V1, V2)) -> isNatKind#(activate(V1)), isNatKind#(n__length(V1)) -> isNatIListKind#(activate(V1)))
(isNatList#(n__take(V1, V2)) -> isNatKind#(activate(V1)), isNatKind#(n__length(V1)) -> U71#(isNatIListKind(activate(V1))))
(isNatList#(n__take(V1, V2)) -> isNatKind#(activate(V1)), isNatKind#(n__s(V1)) -> isNatKind#(activate(V1)))
(isNatList#(n__take(V1, V2)) -> isNatKind#(activate(V1)), isNatKind#(n__s(V1)) -> activate#(V1))
(isNatList#(n__take(V1, V2)) -> isNatKind#(activate(V1)), isNatKind#(n__s(V1)) -> U81#(isNatKind(activate(V1))))
(U12#(tt(), V1) -> isNatList#(activate(V1)), isNatList#(n__take(V1, V2)) -> isNatKind#(activate(V1)))
(U12#(tt(), V1) -> isNatList#(activate(V1)), isNatList#(n__take(V1, V2)) -> activate#(V1))
(U12#(tt(), V1) -> isNatList#(activate(V1)), isNatList#(n__take(V1, V2)) -> activate#(V2))
(U12#(tt(), V1) -> isNatList#(activate(V1)), isNatList#(n__take(V1, V2)) -> U101#(isNatKind(activate(V1)), activate(V1), activate(V2)))
(U12#(tt(), V1) -> isNatList#(activate(V1)), isNatList#(n__cons(V1, V2)) -> isNatKind#(activate(V1)))
(U12#(tt(), V1) -> isNatList#(activate(V1)), isNatList#(n__cons(V1, V2)) -> activate#(V1))
(U12#(tt(), V1) -> isNatList#(activate(V1)), isNatList#(n__cons(V1, V2)) -> activate#(V2))
(U12#(tt(), V1) -> isNatList#(activate(V1)), isNatList#(n__cons(V1, V2)) -> U91#(isNatKind(activate(V1)), activate(V1), activate(V2)))
(isNat#(n__s(V1)) -> isNatKind#(activate(V1)), isNatKind#(n__length(V1)) -> activate#(V1))
(isNat#(n__s(V1)) -> isNatKind#(activate(V1)), isNatKind#(n__length(V1)) -> isNatIListKind#(activate(V1)))
(isNat#(n__s(V1)) -> isNatKind#(activate(V1)), isNatKind#(n__length(V1)) -> U71#(isNatIListKind(activate(V1))))
(isNat#(n__s(V1)) -> isNatKind#(activate(V1)), isNatKind#(n__s(V1)) -> isNatKind#(activate(V1)))
(isNat#(n__s(V1)) -> isNatKind#(activate(V1)), isNatKind#(n__s(V1)) -> activate#(V1))
(isNat#(n__s(V1)) -> isNatKind#(activate(V1)), isNatKind#(n__s(V1)) -> U81#(isNatKind(activate(V1))))
(U104#(tt(), V1, V2) -> isNat#(activate(V1)), isNat#(n__length(V1)) -> activate#(V1))
(U104#(tt(), V1, V2) -> isNat#(activate(V1)), isNat#(n__length(V1)) -> isNatIListKind#(activate(V1)))
(U104#(tt(), V1, V2) -> isNat#(activate(V1)), isNat#(n__length(V1)) -> U11#(isNatIListKind(activate(V1)), activate(V1)))
(U104#(tt(), V1, V2) -> isNat#(activate(V1)), isNat#(n__s(V1)) -> isNatKind#(activate(V1)))
(U104#(tt(), V1, V2) -> isNat#(activate(V1)), isNat#(n__s(V1)) -> activate#(V1))
(U104#(tt(), V1, V2) -> isNat#(activate(V1)), isNat#(n__s(V1)) -> U21#(isNatKind(activate(V1)), activate(V1)))
(isNatIListKind#(n__take(V1, V2)) -> isNatKind#(activate(V1)), isNatKind#(n__length(V1)) -> activate#(V1))
(isNatIListKind#(n__take(V1, V2)) -> isNatKind#(activate(V1)), isNatKind#(n__length(V1)) -> isNatIListKind#(activate(V1)))
(isNatIListKind#(n__take(V1, V2)) -> isNatKind#(activate(V1)), isNatKind#(n__length(V1)) -> U71#(isNatIListKind(activate(V1))))
(isNatIListKind#(n__take(V1, V2)) -> isNatKind#(activate(V1)), isNatKind#(n__s(V1)) -> isNatKind#(activate(V1)))
(isNatIListKind#(n__take(V1, V2)) -> isNatKind#(activate(V1)), isNatKind#(n__s(V1)) -> activate#(V1))
(isNatIListKind#(n__take(V1, V2)) -> isNatKind#(activate(V1)), isNatKind#(n__s(V1)) -> U81#(isNatKind(activate(V1))))
(isNatKind#(n__s(V1)) -> isNatKind#(activate(V1)), isNatKind#(n__length(V1)) -> activate#(V1))
(isNatKind#(n__s(V1)) -> isNatKind#(activate(V1)), isNatKind#(n__length(V1)) -> isNatIListKind#(activate(V1)))
(isNatKind#(n__s(V1)) -> isNatKind#(activate(V1)), isNatKind#(n__length(V1)) -> U71#(isNatIListKind(activate(V1))))
(isNatKind#(n__s(V1)) -> isNatKind#(activate(V1)), isNatKind#(n__s(V1)) -> isNatKind#(activate(V1)))
(isNatKind#(n__s(V1)) -> isNatKind#(activate(V1)), isNatKind#(n__s(V1)) -> activate#(V1))
(isNatKind#(n__s(V1)) -> isNatKind#(activate(V1)), isNatKind#(n__s(V1)) -> U81#(isNatKind(activate(V1))))
(U95#(tt(), V2) -> isNatList#(activate(V2)), isNatList#(n__take(V1, V2)) -> isNatKind#(activate(V1)))
(U95#(tt(), V2) -> isNatList#(activate(V2)), isNatList#(n__take(V1, V2)) -> activate#(V1))
(U95#(tt(), V2) -> isNatList#(activate(V2)), isNatList#(n__take(V1, V2)) -> activate#(V2))
(U95#(tt(), V2) -> isNatList#(activate(V2)), isNatList#(n__take(V1, V2)) -> U101#(isNatKind(activate(V1)), activate(V1), activate(V2)))
(U95#(tt(), V2) -> isNatList#(activate(V2)), isNatList#(n__cons(V1, V2)) -> isNatKind#(activate(V1)))
(U95#(tt(), V2) -> isNatList#(activate(V2)), isNatList#(n__cons(V1, V2)) -> activate#(V1))
(U95#(tt(), V2) -> isNatList#(activate(V2)), isNatList#(n__cons(V1, V2)) -> activate#(V2))
(U95#(tt(), V2) -> isNatList#(activate(V2)), isNatList#(n__cons(V1, V2)) -> U91#(isNatKind(activate(V1)), activate(V1), activate(V2)))
(U92#(tt(), V1, V2) -> isNatIListKind#(activate(V2)), isNatIListKind#(n__take(V1, V2)) -> isNatKind#(activate(V1)))
(U92#(tt(), V1, V2) -> isNatIListKind#(activate(V2)), isNatIListKind#(n__take(V1, V2)) -> activate#(V1))
(U92#(tt(), V1, V2) -> isNatIListKind#(activate(V2)), isNatIListKind#(n__take(V1, V2)) -> activate#(V2))
(U92#(tt(), V1, V2) -> isNatIListKind#(activate(V2)), isNatIListKind#(n__take(V1, V2)) -> U61#(isNatKind(activate(V1)), activate(V2)))
(U92#(tt(), V1, V2) -> isNatIListKind#(activate(V2)), isNatIListKind#(n__cons(V1, V2)) -> isNatKind#(activate(V1)))
(U92#(tt(), V1, V2) -> isNatIListKind#(activate(V2)), isNatIListKind#(n__cons(V1, V2)) -> activate#(V1))
(U92#(tt(), V1, V2) -> isNatIListKind#(activate(V2)), isNatIListKind#(n__cons(V1, V2)) -> activate#(V2))
(U92#(tt(), V1, V2) -> isNatIListKind#(activate(V2)), isNatIListKind#(n__cons(V1, V2)) -> U51#(isNatKind(activate(V1)), activate(V2)))
(U51#(tt(), V2) -> isNatIListKind#(activate(V2)), isNatIListKind#(n__take(V1, V2)) -> isNatKind#(activate(V1)))
(U51#(tt(), V2) -> isNatIListKind#(activate(V2)), isNatIListKind#(n__take(V1, V2)) -> activate#(V1))
(U51#(tt(), V2) -> isNatIListKind#(activate(V2)), isNatIListKind#(n__take(V1, V2)) -> activate#(V2))
(U51#(tt(), V2) -> isNatIListKind#(activate(V2)), isNatIListKind#(n__take(V1, V2)) -> U61#(isNatKind(activate(V1)), activate(V2)))
(U51#(tt(), V2) -> isNatIListKind#(activate(V2)), isNatIListKind#(n__cons(V1, V2)) -> isNatKind#(activate(V1)))
(U51#(tt(), V2) -> isNatIListKind#(activate(V2)), isNatIListKind#(n__cons(V1, V2)) -> activate#(V1))
(U51#(tt(), V2) -> isNatIListKind#(activate(V2)), isNatIListKind#(n__cons(V1, V2)) -> activate#(V2))
(U51#(tt(), V2) -> isNatIListKind#(activate(V2)), isNatIListKind#(n__cons(V1, V2)) -> U51#(isNatKind(activate(V1)), activate(V2)))
(U43#(tt(), V1, V2) -> isNatIListKind#(activate(V2)), isNatIListKind#(n__take(V1, V2)) -> isNatKind#(activate(V1)))
(U43#(tt(), V1, V2) -> isNatIListKind#(activate(V2)), isNatIListKind#(n__take(V1, V2)) -> activate#(V1))
(U43#(tt(), V1, V2) -> isNatIListKind#(activate(V2)), isNatIListKind#(n__take(V1, V2)) -> activate#(V2))
(U43#(tt(), V1, V2) -> isNatIListKind#(activate(V2)), isNatIListKind#(n__take(V1, V2)) -> U61#(isNatKind(activate(V1)), activate(V2)))
(U43#(tt(), V1, V2) -> isNatIListKind#(activate(V2)), isNatIListKind#(n__cons(V1, V2)) -> isNatKind#(activate(V1)))
(U43#(tt(), V1, V2) -> isNatIListKind#(activate(V2)), isNatIListKind#(n__cons(V1, V2)) -> activate#(V1))
(U43#(tt(), V1, V2) -> isNatIListKind#(activate(V2)), isNatIListKind#(n__cons(V1, V2)) -> activate#(V2))
(U43#(tt(), V1, V2) -> isNatIListKind#(activate(V2)), isNatIListKind#(n__cons(V1, V2)) -> U51#(isNatKind(activate(V1)), activate(V2)))
(U105#(tt(), V2) -> isNatIList#(activate(V2)), isNatIList#(V) -> activate#(V))
(U105#(tt(), V2) -> isNatIList#(activate(V2)), isNatIList#(V) -> isNatIListKind#(activate(V)))
(U105#(tt(), V2) -> isNatIList#(activate(V2)), isNatIList#(V) -> U31#(isNatIListKind(activate(V)), activate(V)))
(U105#(tt(), V2) -> isNatIList#(activate(V2)), isNatIList#(n__cons(V1, V2)) -> isNatKind#(activate(V1)))
(U105#(tt(), V2) -> isNatIList#(activate(V2)), isNatIList#(n__cons(V1, V2)) -> activate#(V1))
(U105#(tt(), V2) -> isNatIList#(activate(V2)), isNatIList#(n__cons(V1, V2)) -> activate#(V2))
(U105#(tt(), V2) -> isNatIList#(activate(V2)), isNatIList#(n__cons(V1, V2)) -> U41#(isNatKind(activate(V1)), activate(V1), activate(V2)))
(U102#(tt(), V1, V2) -> isNatIListKind#(activate(V2)), isNatIListKind#(n__take(V1, V2)) -> isNatKind#(activate(V1)))
(U102#(tt(), V1, V2) -> isNatIListKind#(activate(V2)), isNatIListKind#(n__take(V1, V2)) -> activate#(V1))
(U102#(tt(), V1, V2) -> isNatIListKind#(activate(V2)), isNatIListKind#(n__take(V1, V2)) -> activate#(V2))
(U102#(tt(), V1, V2) -> isNatIListKind#(activate(V2)), isNatIListKind#(n__take(V1, V2)) -> U61#(isNatKind(activate(V1)), activate(V2)))
(U102#(tt(), V1, V2) -> isNatIListKind#(activate(V2)), isNatIListKind#(n__cons(V1, V2)) -> isNatKind#(activate(V1)))
(U102#(tt(), V1, V2) -> isNatIListKind#(activate(V2)), isNatIListKind#(n__cons(V1, V2)) -> activate#(V1))
(U102#(tt(), V1, V2) -> isNatIListKind#(activate(V2)), isNatIListKind#(n__cons(V1, V2)) -> activate#(V2))
(U102#(tt(), V1, V2) -> isNatIListKind#(activate(V2)), isNatIListKind#(n__cons(V1, V2)) -> U51#(isNatKind(activate(V1)), activate(V2)))
(U114#(tt(), L) -> length#(activate(L)), length#(cons(N, L)) -> activate#(L))
(U114#(tt(), L) -> length#(activate(L)), length#(cons(N, L)) -> U111#(isNatList(activate(L)), activate(L), N))
(U114#(tt(), L) -> length#(activate(L)), length#(cons(N, L)) -> isNatList#(activate(L)))
(U114#(tt(), L) -> length#(activate(L)), length#(nil()) -> 0#())
(U135#(tt(), IL, M, N) -> isNatKind#(activate(N)), isNatKind#(n__length(V1)) -> activate#(V1))
(U135#(tt(), IL, M, N) -> isNatKind#(activate(N)), isNatKind#(n__length(V1)) -> isNatIListKind#(activate(V1)))
(U135#(tt(), IL, M, N) -> isNatKind#(activate(N)), isNatKind#(n__length(V1)) -> U71#(isNatIListKind(activate(V1))))
(U135#(tt(), IL, M, N) -> isNatKind#(activate(N)), isNatKind#(n__s(V1)) -> isNatKind#(activate(V1)))
(U135#(tt(), IL, M, N) -> isNatKind#(activate(N)), isNatKind#(n__s(V1)) -> activate#(V1))
(U135#(tt(), IL, M, N) -> isNatKind#(activate(N)), isNatKind#(n__s(V1)) -> U81#(isNatKind(activate(V1))))
(U113#(tt(), L, N) -> isNatKind#(activate(N)), isNatKind#(n__length(V1)) -> activate#(V1))
(U113#(tt(), L, N) -> isNatKind#(activate(N)), isNatKind#(n__length(V1)) -> isNatIListKind#(activate(V1)))
(U113#(tt(), L, N) -> isNatKind#(activate(N)), isNatKind#(n__length(V1)) -> U71#(isNatIListKind(activate(V1))))
(U113#(tt(), L, N) -> isNatKind#(activate(N)), isNatKind#(n__s(V1)) -> isNatKind#(activate(V1)))
(U113#(tt(), L, N) -> isNatKind#(activate(N)), isNatKind#(n__s(V1)) -> activate#(V1))
(U113#(tt(), L, N) -> isNatKind#(activate(N)), isNatKind#(n__s(V1)) -> U81#(isNatKind(activate(V1))))
(take#(s(M), cons(N, IL)) -> isNatIList#(activate(IL)), isNatIList#(V) -> activate#(V))
(take#(s(M), cons(N, IL)) -> isNatIList#(activate(IL)), isNatIList#(V) -> isNatIListKind#(activate(V)))
(take#(s(M), cons(N, IL)) -> isNatIList#(activate(IL)), isNatIList#(V) -> U31#(isNatIListKind(activate(V)), activate(V)))
(take#(s(M), cons(N, IL)) -> isNatIList#(activate(IL)), isNatIList#(n__cons(V1, V2)) -> isNatKind#(activate(V1)))
(take#(s(M), cons(N, IL)) -> isNatIList#(activate(IL)), isNatIList#(n__cons(V1, V2)) -> activate#(V1))
(take#(s(M), cons(N, IL)) -> isNatIList#(activate(IL)), isNatIList#(n__cons(V1, V2)) -> activate#(V2))
(take#(s(M), cons(N, IL)) -> isNatIList#(activate(IL)), isNatIList#(n__cons(V1, V2)) -> U41#(isNatKind(activate(V1)), activate(V1), activate(V2)))
(U121#(tt(), IL) -> isNatIListKind#(activate(IL)), isNatIListKind#(n__take(V1, V2)) -> isNatKind#(activate(V1)))
(U121#(tt(), IL) -> isNatIListKind#(activate(IL)), isNatIListKind#(n__take(V1, V2)) -> activate#(V1))
(U121#(tt(), IL) -> isNatIListKind#(activate(IL)), isNatIListKind#(n__take(V1, V2)) -> activate#(V2))
(U121#(tt(), IL) -> isNatIListKind#(activate(IL)), isNatIListKind#(n__take(V1, V2)) -> U61#(isNatKind(activate(V1)), activate(V2)))
(U121#(tt(), IL) -> isNatIListKind#(activate(IL)), isNatIListKind#(n__cons(V1, V2)) -> isNatKind#(activate(V1)))
(U121#(tt(), IL) -> isNatIListKind#(activate(IL)), isNatIListKind#(n__cons(V1, V2)) -> activate#(V1))
(U121#(tt(), IL) -> isNatIListKind#(activate(IL)), isNatIListKind#(n__cons(V1, V2)) -> activate#(V2))
(U121#(tt(), IL) -> isNatIListKind#(activate(IL)), isNatIListKind#(n__cons(V1, V2)) -> U51#(isNatKind(activate(V1)), activate(V2)))
(U132#(tt(), IL, M, N) -> isNat#(activate(M)), isNat#(n__length(V1)) -> activate#(V1))
(U132#(tt(), IL, M, N) -> isNat#(activate(M)), isNat#(n__length(V1)) -> isNatIListKind#(activate(V1)))
(U132#(tt(), IL, M, N) -> isNat#(activate(M)), isNat#(n__length(V1)) -> U11#(isNatIListKind(activate(V1)), activate(V1)))
(U132#(tt(), IL, M, N) -> isNat#(activate(M)), isNat#(n__s(V1)) -> isNatKind#(activate(V1)))
(U132#(tt(), IL, M, N) -> isNat#(activate(M)), isNat#(n__s(V1)) -> activate#(V1))
(U132#(tt(), IL, M, N) -> isNat#(activate(M)), isNat#(n__s(V1)) -> U21#(isNatKind(activate(V1)), activate(V1)))
(U32#(tt(), V) -> isNatList#(activate(V)), isNatList#(n__take(V1, V2)) -> isNatKind#(activate(V1)))
(U32#(tt(), V) -> isNatList#(activate(V)), isNatList#(n__take(V1, V2)) -> activate#(V1))
(U32#(tt(), V) -> isNatList#(activate(V)), isNatList#(n__take(V1, V2)) -> activate#(V2))
(U32#(tt(), V) -> isNatList#(activate(V)), isNatList#(n__take(V1, V2)) -> U101#(isNatKind(activate(V1)), activate(V1), activate(V2)))
(U32#(tt(), V) -> isNatList#(activate(V)), isNatList#(n__cons(V1, V2)) -> isNatKind#(activate(V1)))
(U32#(tt(), V) -> isNatList#(activate(V)), isNatList#(n__cons(V1, V2)) -> activate#(V1))
(U32#(tt(), V) -> isNatList#(activate(V)), isNatList#(n__cons(V1, V2)) -> activate#(V2))
(U32#(tt(), V) -> isNatList#(activate(V)), isNatList#(n__cons(V1, V2)) -> U91#(isNatKind(activate(V1)), activate(V1), activate(V2)))
(activate#(n__length(X)) -> length#(activate(X)), length#(cons(N, L)) -> activate#(L))
(activate#(n__length(X)) -> length#(activate(X)), length#(cons(N, L)) -> U111#(isNatList(activate(L)), activate(L), N))
(activate#(n__length(X)) -> length#(activate(X)), length#(cons(N, L)) -> isNatList#(activate(L)))
(activate#(n__length(X)) -> length#(activate(X)), length#(nil()) -> 0#())
(U91#(tt(), V1, V2) -> U92#(isNatKind(activate(V1)), activate(V1), activate(V2)), U92#(tt(), V1, V2) -> activate#(V1))
(U91#(tt(), V1, V2) -> U92#(isNatKind(activate(V1)), activate(V1), activate(V2)), U92#(tt(), V1, V2) -> activate#(V2))
(U91#(tt(), V1, V2) -> U92#(isNatKind(activate(V1)), activate(V1), activate(V2)), U92#(tt(), V1, V2) -> isNatIListKind#(activate(V2)))
(U91#(tt(), V1, V2) -> U92#(isNatKind(activate(V1)), activate(V1), activate(V2)), U92#(tt(), V1, V2) -> U93#(isNatIListKind(activate(V2)), activate(V1), activate(V2)))
(U43#(tt(), V1, V2) -> U44#(isNatIListKind(activate(V2)), activate(V1), activate(V2)), U44#(tt(), V1, V2) -> activate#(V1))
(U43#(tt(), V1, V2) -> U44#(isNatIListKind(activate(V2)), activate(V1), activate(V2)), U44#(tt(), V1, V2) -> activate#(V2))
(U43#(tt(), V1, V2) -> U44#(isNatIListKind(activate(V2)), activate(V1), activate(V2)), U44#(tt(), V1, V2) -> isNat#(activate(V1)))
(U43#(tt(), V1, V2) -> U44#(isNatIListKind(activate(V2)), activate(V1), activate(V2)), U44#(tt(), V1, V2) -> U45#(isNat(activate(V1)), activate(V2)))
(U42#(tt(), V1, V2) -> U43#(isNatIListKind(activate(V2)), activate(V1), activate(V2)), U43#(tt(), V1, V2) -> activate#(V1))
(U42#(tt(), V1, V2) -> U43#(isNatIListKind(activate(V2)), activate(V1), activate(V2)), U43#(tt(), V1, V2) -> activate#(V2))
(U42#(tt(), V1, V2) -> U43#(isNatIListKind(activate(V2)), activate(V1), activate(V2)), U43#(tt(), V1, V2) -> isNatIListKind#(activate(V2)))
(U42#(tt(), V1, V2) -> U43#(isNatIListKind(activate(V2)), activate(V1), activate(V2)), U43#(tt(), V1, V2) -> U44#(isNatIListKind(activate(V2)), activate(V1), activate(V2)))
(isNatList#(n__take(V1, V2)) -> U101#(isNatKind(activate(V1)), activate(V1), activate(V2)), U101#(tt(), V1, V2) -> U102#(isNatKind(activate(V1)), activate(V1), activate(V2)))
(isNatList#(n__take(V1, V2)) -> U101#(isNatKind(activate(V1)), activate(V1), activate(V2)), U101#(tt(), V1, V2) -> isNatKind#(activate(V1)))
(isNatList#(n__take(V1, V2)) -> U101#(isNatKind(activate(V1)), activate(V1), activate(V2)), U101#(tt(), V1, V2) -> activate#(V1))
(isNatList#(n__take(V1, V2)) -> U101#(isNatKind(activate(V1)), activate(V1), activate(V2)), U101#(tt(), V1, V2) -> activate#(V2))
(U112#(tt(), L, N) -> U113#(isNat(activate(N)), activate(L), activate(N)), U113#(tt(), L, N) -> isNatKind#(activate(N)))
(U112#(tt(), L, N) -> U113#(isNat(activate(N)), activate(L), activate(N)), U113#(tt(), L, N) -> activate#(L))
(U112#(tt(), L, N) -> U113#(isNat(activate(N)), activate(L), activate(N)), U113#(tt(), L, N) -> activate#(N))
(U112#(tt(), L, N) -> U113#(isNat(activate(N)), activate(L), activate(N)), U113#(tt(), L, N) -> U114#(isNatKind(activate(N)), activate(L)))
(U103#(tt(), V1, V2) -> U104#(isNatIListKind(activate(V2)), activate(V1), activate(V2)), U104#(tt(), V1, V2) -> activate#(V1))
(U103#(tt(), V1, V2) -> U104#(isNatIListKind(activate(V2)), activate(V1), activate(V2)), U104#(tt(), V1, V2) -> activate#(V2))
(U103#(tt(), V1, V2) -> U104#(isNatIListKind(activate(V2)), activate(V1), activate(V2)), U104#(tt(), V1, V2) -> U105#(isNat(activate(V1)), activate(V2)))
(U103#(tt(), V1, V2) -> U104#(isNatIListKind(activate(V2)), activate(V1), activate(V2)), U104#(tt(), V1, V2) -> isNat#(activate(V1)))
(U102#(tt(), V1, V2) -> U103#(isNatIListKind(activate(V2)), activate(V1), activate(V2)), U103#(tt(), V1, V2) -> activate#(V1))
(U102#(tt(), V1, V2) -> U103#(isNatIListKind(activate(V2)), activate(V1), activate(V2)), U103#(tt(), V1, V2) -> activate#(V2))
(U102#(tt(), V1, V2) -> U103#(isNatIListKind(activate(V2)), activate(V1), activate(V2)), U103#(tt(), V1, V2) -> isNatIListKind#(activate(V2)))
(U102#(tt(), V1, V2) -> U103#(isNatIListKind(activate(V2)), activate(V1), activate(V2)), U103#(tt(), V1, V2) -> U104#(isNatIListKind(activate(V2)), activate(V1), activate(V2)))
(U44#(tt(), V1, V2) -> U45#(isNat(activate(V1)), activate(V2)), U45#(tt(), V2) -> activate#(V2))
(U44#(tt(), V1, V2) -> U45#(isNat(activate(V1)), activate(V2)), U45#(tt(), V2) -> isNatIList#(activate(V2)))
(U44#(tt(), V1, V2) -> U45#(isNat(activate(V1)), activate(V2)), U45#(tt(), V2) -> U46#(isNatIList(activate(V2))))
(U21#(tt(), V1) -> U22#(isNatKind(activate(V1)), activate(V1)), U22#(tt(), V1) -> activate#(V1))
(U21#(tt(), V1) -> U22#(isNatKind(activate(V1)), activate(V1)), U22#(tt(), V1) -> isNat#(activate(V1)))
(U21#(tt(), V1) -> U22#(isNatKind(activate(V1)), activate(V1)), U22#(tt(), V1) -> U23#(isNat(activate(V1))))
(U11#(tt(), V1) -> U12#(isNatIListKind(activate(V1)), activate(V1)), U12#(tt(), V1) -> activate#(V1))
(U11#(tt(), V1) -> U12#(isNatIListKind(activate(V1)), activate(V1)), U12#(tt(), V1) -> U13#(isNatList(activate(V1))))
(U11#(tt(), V1) -> U12#(isNatIListKind(activate(V1)), activate(V1)), U12#(tt(), V1) -> isNatList#(activate(V1)))
(isNat#(n__s(V1)) -> U21#(isNatKind(activate(V1)), activate(V1)), U21#(tt(), V1) -> isNatKind#(activate(V1)))
(isNat#(n__s(V1)) -> U21#(isNatKind(activate(V1)), activate(V1)), U21#(tt(), V1) -> activate#(V1))
(isNat#(n__s(V1)) -> U21#(isNatKind(activate(V1)), activate(V1)), U21#(tt(), V1) -> U22#(isNatKind(activate(V1)), activate(V1)))
(U104#(tt(), V1, V2) -> U105#(isNat(activate(V1)), activate(V2)), U105#(tt(), V2) -> activate#(V2))
(U104#(tt(), V1, V2) -> U105#(isNat(activate(V1)), activate(V2)), U105#(tt(), V2) -> U106#(isNatIList(activate(V2))))
(U104#(tt(), V1, V2) -> U105#(isNat(activate(V1)), activate(V2)), U105#(tt(), V2) -> isNatIList#(activate(V2)))
(isNatIListKind#(n__take(V1, V2)) -> U61#(isNatKind(activate(V1)), activate(V2)), U61#(tt(), V2) -> activate#(V2))
(isNatIListKind#(n__take(V1, V2)) -> U61#(isNatKind(activate(V1)), activate(V2)), U61#(tt(), V2) -> isNatIListKind#(activate(V2)))
(isNatIListKind#(n__take(V1, V2)) -> U61#(isNatKind(activate(V1)), activate(V2)), U61#(tt(), V2) -> U62#(isNatIListKind(activate(V2))))
(take#(s(M), cons(N, IL)) -> activate#(IL), activate#(n__zeros()) -> zeros#())
(take#(s(M), cons(N, IL)) -> activate#(IL), activate#(n__take(X1, X2)) -> activate#(X1))
(take#(s(M), cons(N, IL)) -> activate#(IL), activate#(n__take(X1, X2)) -> activate#(X2))
(take#(s(M), cons(N, IL)) -> activate#(IL), activate#(n__take(X1, X2)) -> take#(activate(X1), activate(X2)))
(take#(s(M), cons(N, IL)) -> activate#(IL), activate#(n__0()) -> 0#())
(take#(s(M), cons(N, IL)) -> activate#(IL), activate#(n__length(X)) -> activate#(X))
(take#(s(M), cons(N, IL)) -> activate#(IL), activate#(n__length(X)) -> length#(activate(X)))
(take#(s(M), cons(N, IL)) -> activate#(IL), activate#(n__s(X)) -> activate#(X))
(take#(s(M), cons(N, IL)) -> activate#(IL), activate#(n__s(X)) -> s#(activate(X)))
(take#(s(M), cons(N, IL)) -> activate#(IL), activate#(n__cons(X1, X2)) -> cons#(activate(X1), X2))
(take#(s(M), cons(N, IL)) -> activate#(IL), activate#(n__cons(X1, X2)) -> activate#(X1))
(take#(s(M), cons(N, IL)) -> activate#(IL), activate#(n__nil()) -> nil#())
(U136#(tt(), IL, M, N) -> activate#(IL), activate#(n__zeros()) -> zeros#())
(U136#(tt(), IL, M, N) -> activate#(IL), activate#(n__take(X1, X2)) -> activate#(X1))
(U136#(tt(), IL, M, N) -> activate#(IL), activate#(n__take(X1, X2)) -> activate#(X2))
(U136#(tt(), IL, M, N) -> activate#(IL), activate#(n__take(X1, X2)) -> take#(activate(X1), activate(X2)))
(U136#(tt(), IL, M, N) -> activate#(IL), activate#(n__0()) -> 0#())
(U136#(tt(), IL, M, N) -> activate#(IL), activate#(n__length(X)) -> activate#(X))
(U136#(tt(), IL, M, N) -> activate#(IL), activate#(n__length(X)) -> length#(activate(X)))
(U136#(tt(), IL, M, N) -> activate#(IL), activate#(n__s(X)) -> activate#(X))
(U136#(tt(), IL, M, N) -> activate#(IL), activate#(n__s(X)) -> s#(activate(X)))
(U136#(tt(), IL, M, N) -> activate#(IL), activate#(n__cons(X1, X2)) -> cons#(activate(X1), X2))
(U136#(tt(), IL, M, N) -> activate#(IL), activate#(n__cons(X1, X2)) -> activate#(X1))
(U136#(tt(), IL, M, N) -> activate#(IL), activate#(n__nil()) -> nil#())
(U134#(tt(), IL, M, N) -> activate#(IL), activate#(n__zeros()) -> zeros#())
(U134#(tt(), IL, M, N) -> activate#(IL), activate#(n__take(X1, X2)) -> activate#(X1))
(U134#(tt(), IL, M, N) -> activate#(IL), activate#(n__take(X1, X2)) -> activate#(X2))
(U134#(tt(), IL, M, N) -> activate#(IL), activate#(n__take(X1, X2)) -> take#(activate(X1), activate(X2)))
(U134#(tt(), IL, M, N) -> activate#(IL), activate#(n__0()) -> 0#())
(U134#(tt(), IL, M, N) -> activate#(IL), activate#(n__length(X)) -> activate#(X))
(U134#(tt(), IL, M, N) -> activate#(IL), activate#(n__length(X)) -> length#(activate(X)))
(U134#(tt(), IL, M, N) -> activate#(IL), activate#(n__s(X)) -> activate#(X))
(U134#(tt(), IL, M, N) -> activate#(IL), activate#(n__s(X)) -> s#(activate(X)))
(U134#(tt(), IL, M, N) -> activate#(IL), activate#(n__cons(X1, X2)) -> cons#(activate(X1), X2))
(U134#(tt(), IL, M, N) -> activate#(IL), activate#(n__cons(X1, X2)) -> activate#(X1))
(U134#(tt(), IL, M, N) -> activate#(IL), activate#(n__nil()) -> nil#())
(U131#(tt(), IL, M, N) -> activate#(IL), activate#(n__zeros()) -> zeros#())
(U131#(tt(), IL, M, N) -> activate#(IL), activate#(n__take(X1, X2)) -> activate#(X1))
(U131#(tt(), IL, M, N) -> activate#(IL), activate#(n__take(X1, X2)) -> activate#(X2))
(U131#(tt(), IL, M, N) -> activate#(IL), activate#(n__take(X1, X2)) -> take#(activate(X1), activate(X2)))
(U131#(tt(), IL, M, N) -> activate#(IL), activate#(n__0()) -> 0#())
(U131#(tt(), IL, M, N) -> activate#(IL), activate#(n__length(X)) -> activate#(X))
(U131#(tt(), IL, M, N) -> activate#(IL), activate#(n__length(X)) -> length#(activate(X)))
(U131#(tt(), IL, M, N) -> activate#(IL), activate#(n__s(X)) -> activate#(X))
(U131#(tt(), IL, M, N) -> activate#(IL), activate#(n__s(X)) -> s#(activate(X)))
(U131#(tt(), IL, M, N) -> activate#(IL), activate#(n__cons(X1, X2)) -> cons#(activate(X1), X2))
(U131#(tt(), IL, M, N) -> activate#(IL), activate#(n__cons(X1, X2)) -> activate#(X1))
(U131#(tt(), IL, M, N) -> activate#(IL), activate#(n__nil()) -> nil#())
(U121#(tt(), IL) -> activate#(IL), activate#(n__zeros()) -> zeros#())
(U121#(tt(), IL) -> activate#(IL), activate#(n__take(X1, X2)) -> activate#(X1))
(U121#(tt(), IL) -> activate#(IL), activate#(n__take(X1, X2)) -> activate#(X2))
(U121#(tt(), IL) -> activate#(IL), activate#(n__take(X1, X2)) -> take#(activate(X1), activate(X2)))
(U121#(tt(), IL) -> activate#(IL), activate#(n__0()) -> 0#())
(U121#(tt(), IL) -> activate#(IL), activate#(n__length(X)) -> activate#(X))
(U121#(tt(), IL) -> activate#(IL), activate#(n__length(X)) -> length#(activate(X)))
(U121#(tt(), IL) -> activate#(IL), activate#(n__s(X)) -> activate#(X))
(U121#(tt(), IL) -> activate#(IL), activate#(n__s(X)) -> s#(activate(X)))
(U121#(tt(), IL) -> activate#(IL), activate#(n__cons(X1, X2)) -> cons#(activate(X1), X2))
(U121#(tt(), IL) -> activate#(IL), activate#(n__cons(X1, X2)) -> activate#(X1))
(U121#(tt(), IL) -> activate#(IL), activate#(n__nil()) -> nil#())
(activate#(n__length(X)) -> activate#(X), activate#(n__zeros()) -> zeros#())
(activate#(n__length(X)) -> activate#(X), activate#(n__take(X1, X2)) -> activate#(X1))
(activate#(n__length(X)) -> activate#(X), activate#(n__take(X1, X2)) -> activate#(X2))
(activate#(n__length(X)) -> activate#(X), activate#(n__take(X1, X2)) -> take#(activate(X1), activate(X2)))
(activate#(n__length(X)) -> activate#(X), activate#(n__0()) -> 0#())
(activate#(n__length(X)) -> activate#(X), activate#(n__length(X)) -> activate#(X))
(activate#(n__length(X)) -> activate#(X), activate#(n__length(X)) -> length#(activate(X)))
(activate#(n__length(X)) -> activate#(X), activate#(n__s(X)) -> activate#(X))
(activate#(n__length(X)) -> activate#(X), activate#(n__s(X)) -> s#(activate(X)))
(activate#(n__length(X)) -> activate#(X), activate#(n__cons(X1, X2)) -> cons#(activate(X1), X2))
(activate#(n__length(X)) -> activate#(X), activate#(n__cons(X1, X2)) -> activate#(X1))
(activate#(n__length(X)) -> activate#(X), activate#(n__nil()) -> nil#())
}
SCCS:
Scc:
{
U102#(tt(), V1, V2) -> activate#(V1),
U102#(tt(), V1, V2) -> activate#(V2),
U102#(tt(), V1, V2) -> U103#(isNatIListKind(activate(V2)), activate(V1), activate(V2)),
U102#(tt(), V1, V2) -> isNatIListKind#(activate(V2)),
isNatKind#(n__length(V1)) -> activate#(V1),
isNatKind#(n__length(V1)) -> isNatIListKind#(activate(V1)),
isNatKind#(n__s(V1)) -> isNatKind#(activate(V1)),
isNatKind#(n__s(V1)) -> activate#(V1),
activate#(n__take(X1, X2)) -> activate#(X1),
activate#(n__take(X1, X2)) -> activate#(X2),
activate#(n__take(X1, X2)) -> take#(activate(X1), activate(X2)),
activate#(n__length(X)) -> activate#(X),
activate#(n__length(X)) -> length#(activate(X)),
activate#(n__s(X)) -> activate#(X),
activate#(n__cons(X1, X2)) -> activate#(X1),
U101#(tt(), V1, V2) -> U102#(isNatKind(activate(V1)), activate(V1), activate(V2)),
U101#(tt(), V1, V2) -> isNatKind#(activate(V1)),
U101#(tt(), V1, V2) -> activate#(V1),
U101#(tt(), V1, V2) -> activate#(V2),
U103#(tt(), V1, V2) -> activate#(V1),
U103#(tt(), V1, V2) -> activate#(V2),
U103#(tt(), V1, V2) -> isNatIListKind#(activate(V2)),
U103#(tt(), V1, V2) -> U104#(isNatIListKind(activate(V2)), activate(V1), activate(V2)),
isNatIListKind#(n__take(V1, V2)) -> isNatKind#(activate(V1)),
isNatIListKind#(n__take(V1, V2)) -> activate#(V1),
isNatIListKind#(n__take(V1, V2)) -> activate#(V2),
isNatIListKind#(n__take(V1, V2)) -> U61#(isNatKind(activate(V1)), activate(V2)),
isNatIListKind#(n__cons(V1, V2)) -> isNatKind#(activate(V1)),
isNatIListKind#(n__cons(V1, V2)) -> activate#(V1),
isNatIListKind#(n__cons(V1, V2)) -> activate#(V2),
isNatIListKind#(n__cons(V1, V2)) -> U51#(isNatKind(activate(V1)), activate(V2)),
U104#(tt(), V1, V2) -> activate#(V1),
U104#(tt(), V1, V2) -> activate#(V2),
U104#(tt(), V1, V2) -> U105#(isNat(activate(V1)), activate(V2)),
U104#(tt(), V1, V2) -> isNat#(activate(V1)),
U105#(tt(), V2) -> activate#(V2),
U105#(tt(), V2) -> isNatIList#(activate(V2)),
isNat#(n__length(V1)) -> activate#(V1),
isNat#(n__length(V1)) -> isNatIListKind#(activate(V1)),
isNat#(n__length(V1)) -> U11#(isNatIListKind(activate(V1)), activate(V1)),
isNat#(n__s(V1)) -> isNatKind#(activate(V1)),
isNat#(n__s(V1)) -> activate#(V1),
isNat#(n__s(V1)) -> U21#(isNatKind(activate(V1)), activate(V1)),
isNatIList#(V) -> activate#(V),
isNatIList#(V) -> isNatIListKind#(activate(V)),
isNatIList#(V) -> U31#(isNatIListKind(activate(V)), activate(V)),
isNatIList#(n__cons(V1, V2)) -> isNatKind#(activate(V1)),
isNatIList#(n__cons(V1, V2)) -> activate#(V1),
isNatIList#(n__cons(V1, V2)) -> activate#(V2),
isNatIList#(n__cons(V1, V2)) -> U41#(isNatKind(activate(V1)), activate(V1), activate(V2)),
U12#(tt(), V1) -> activate#(V1),
U12#(tt(), V1) -> isNatList#(activate(V1)),
U11#(tt(), V1) -> activate#(V1),
U11#(tt(), V1) -> isNatIListKind#(activate(V1)),
U11#(tt(), V1) -> U12#(isNatIListKind(activate(V1)), activate(V1)),
U112#(tt(), L, N) -> activate#(L),
U112#(tt(), L, N) -> activate#(N),
U112#(tt(), L, N) -> isNat#(activate(N)),
U112#(tt(), L, N) -> U113#(isNat(activate(N)), activate(L), activate(N)),
U111#(tt(), L, N) -> activate#(L),
U111#(tt(), L, N) -> activate#(N),
U111#(tt(), L, N) -> isNatIListKind#(activate(L)),
U111#(tt(), L, N) -> U112#(isNatIListKind(activate(L)), activate(L), activate(N)),
U113#(tt(), L, N) -> isNatKind#(activate(N)),
U113#(tt(), L, N) -> activate#(L),
U113#(tt(), L, N) -> activate#(N),
U113#(tt(), L, N) -> U114#(isNatKind(activate(N)), activate(L)),
U114#(tt(), L) -> activate#(L),
U114#(tt(), L) -> length#(activate(L)),
length#(cons(N, L)) -> activate#(L),
length#(cons(N, L)) -> U111#(isNatList(activate(L)), activate(L), N),
length#(cons(N, L)) -> isNatList#(activate(L)),
isNatList#(n__take(V1, V2)) -> isNatKind#(activate(V1)),
isNatList#(n__take(V1, V2)) -> activate#(V1),
isNatList#(n__take(V1, V2)) -> activate#(V2),
isNatList#(n__take(V1, V2)) -> U101#(isNatKind(activate(V1)), activate(V1), activate(V2)),
isNatList#(n__cons(V1, V2)) -> isNatKind#(activate(V1)),
isNatList#(n__cons(V1, V2)) -> activate#(V1),
isNatList#(n__cons(V1, V2)) -> activate#(V2),
isNatList#(n__cons(V1, V2)) -> U91#(isNatKind(activate(V1)), activate(V1), activate(V2)),
U121#(tt(), IL) -> activate#(IL),
U121#(tt(), IL) -> isNatIListKind#(activate(IL)),
U132#(tt(), IL, M, N) -> activate#(N),
U132#(tt(), IL, M, N) -> activate#(IL),
U132#(tt(), IL, M, N) -> activate#(M),
U132#(tt(), IL, M, N) -> isNat#(activate(M)),
U132#(tt(), IL, M, N) -> U133#(isNat(activate(M)), activate(IL), activate(M), activate(N)),
U131#(tt(), IL, M, N) -> activate#(N),
U131#(tt(), IL, M, N) -> activate#(IL),
U131#(tt(), IL, M, N) -> activate#(M),
U131#(tt(), IL, M, N) -> isNatIListKind#(activate(IL)),
U131#(tt(), IL, M, N) -> U132#(isNatIListKind(activate(IL)), activate(IL), activate(M), activate(N)),
U133#(tt(), IL, M, N) -> isNatKind#(activate(M)),
U133#(tt(), IL, M, N) -> activate#(N),
U133#(tt(), IL, M, N) -> activate#(IL),
U133#(tt(), IL, M, N) -> activate#(M),
U133#(tt(), IL, M, N) -> U134#(isNatKind(activate(M)), activate(IL), activate(M), activate(N)),
U134#(tt(), IL, M, N) -> activate#(N),
U134#(tt(), IL, M, N) -> activate#(IL),
U134#(tt(), IL, M, N) -> activate#(M),
U134#(tt(), IL, M, N) -> isNat#(activate(N)),
U134#(tt(), IL, M, N) -> U135#(isNat(activate(N)), activate(IL), activate(M), activate(N)),
U135#(tt(), IL, M, N) -> isNatKind#(activate(N)),
U135#(tt(), IL, M, N) -> activate#(N),
U135#(tt(), IL, M, N) -> activate#(IL),
U135#(tt(), IL, M, N) -> activate#(M),
U135#(tt(), IL, M, N) -> U136#(isNatKind(activate(N)), activate(IL), activate(M), activate(N)),
U136#(tt(), IL, M, N) -> activate#(N),
U136#(tt(), IL, M, N) -> activate#(IL),
U136#(tt(), IL, M, N) -> activate#(M),
U22#(tt(), V1) -> activate#(V1),
U22#(tt(), V1) -> isNat#(activate(V1)),
U21#(tt(), V1) -> isNatKind#(activate(V1)),
U21#(tt(), V1) -> activate#(V1),
U21#(tt(), V1) -> U22#(isNatKind(activate(V1)), activate(V1)),
U32#(tt(), V) -> activate#(V),
U32#(tt(), V) -> isNatList#(activate(V)),
U31#(tt(), V) -> activate#(V),
U31#(tt(), V) -> isNatIListKind#(activate(V)),
U31#(tt(), V) -> U32#(isNatIListKind(activate(V)), activate(V)),
U42#(tt(), V1, V2) -> activate#(V1),
U42#(tt(), V1, V2) -> activate#(V2),
U42#(tt(), V1, V2) -> isNatIListKind#(activate(V2)),
U42#(tt(), V1, V2) -> U43#(isNatIListKind(activate(V2)), activate(V1), activate(V2)),
U41#(tt(), V1, V2) -> isNatKind#(activate(V1)),
U41#(tt(), V1, V2) -> activate#(V1),
U41#(tt(), V1, V2) -> activate#(V2),
U41#(tt(), V1, V2) -> U42#(isNatKind(activate(V1)), activate(V1), activate(V2)),
U43#(tt(), V1, V2) -> activate#(V1),
U43#(tt(), V1, V2) -> activate#(V2),
U43#(tt(), V1, V2) -> isNatIListKind#(activate(V2)),
U43#(tt(), V1, V2) -> U44#(isNatIListKind(activate(V2)), activate(V1), activate(V2)),
U44#(tt(), V1, V2) -> activate#(V1),
U44#(tt(), V1, V2) -> activate#(V2),
U44#(tt(), V1, V2) -> isNat#(activate(V1)),
U44#(tt(), V1, V2) -> U45#(isNat(activate(V1)), activate(V2)),
U45#(tt(), V2) -> activate#(V2),
U45#(tt(), V2) -> isNatIList#(activate(V2)),
U51#(tt(), V2) -> activate#(V2),
U51#(tt(), V2) -> isNatIListKind#(activate(V2)),
U61#(tt(), V2) -> activate#(V2),
U61#(tt(), V2) -> isNatIListKind#(activate(V2)),
U92#(tt(), V1, V2) -> activate#(V1),
U92#(tt(), V1, V2) -> activate#(V2),
U92#(tt(), V1, V2) -> isNatIListKind#(activate(V2)),
U92#(tt(), V1, V2) -> U93#(isNatIListKind(activate(V2)), activate(V1), activate(V2)),
U91#(tt(), V1, V2) -> isNatKind#(activate(V1)),
U91#(tt(), V1, V2) -> activate#(V1),
U91#(tt(), V1, V2) -> activate#(V2),
U91#(tt(), V1, V2) -> U92#(isNatKind(activate(V1)), activate(V1), activate(V2)),
U93#(tt(), V1, V2) -> activate#(V1),
U93#(tt(), V1, V2) -> activate#(V2),
U93#(tt(), V1, V2) -> isNatIListKind#(activate(V2)),
U93#(tt(), V1, V2) -> U94#(isNatIListKind(activate(V2)), activate(V1), activate(V2)),
U94#(tt(), V1, V2) -> activate#(V1),
U94#(tt(), V1, V2) -> activate#(V2),
U94#(tt(), V1, V2) -> isNat#(activate(V1)),
U94#(tt(), V1, V2) -> U95#(isNat(activate(V1)), activate(V2)),
U95#(tt(), V2) -> activate#(V2),
U95#(tt(), V2) -> isNatList#(activate(V2)),
take#(0(), IL) -> isNatIList#(IL),
take#(0(), IL) -> U121#(isNatIList(IL), IL),
take#(s(M), cons(N, IL)) -> activate#(IL),
take#(s(M), cons(N, IL)) -> isNatIList#(activate(IL)),
take#(s(M), cons(N, IL)) -> U131#(isNatIList(activate(IL)), activate(IL), M, N)
}
SCC:
Strict:
{
U102#(tt(), V1, V2) -> activate#(V1),
U102#(tt(), V1, V2) -> activate#(V2),
U102#(tt(), V1, V2) -> U103#(isNatIListKind(activate(V2)), activate(V1), activate(V2)),
U102#(tt(), V1, V2) -> isNatIListKind#(activate(V2)),
isNatKind#(n__length(V1)) -> activate#(V1),
isNatKind#(n__length(V1)) -> isNatIListKind#(activate(V1)),
isNatKind#(n__s(V1)) -> isNatKind#(activate(V1)),
isNatKind#(n__s(V1)) -> activate#(V1),
activate#(n__take(X1, X2)) -> activate#(X1),
activate#(n__take(X1, X2)) -> activate#(X2),
activate#(n__take(X1, X2)) -> take#(activate(X1), activate(X2)),
activate#(n__length(X)) -> activate#(X),
activate#(n__length(X)) -> length#(activate(X)),
activate#(n__s(X)) -> activate#(X),
activate#(n__cons(X1, X2)) -> activate#(X1),
U101#(tt(), V1, V2) -> U102#(isNatKind(activate(V1)), activate(V1), activate(V2)),
U101#(tt(), V1, V2) -> isNatKind#(activate(V1)),
U101#(tt(), V1, V2) -> activate#(V1),
U101#(tt(), V1, V2) -> activate#(V2),
U103#(tt(), V1, V2) -> activate#(V1),
U103#(tt(), V1, V2) -> activate#(V2),
U103#(tt(), V1, V2) -> isNatIListKind#(activate(V2)),
U103#(tt(), V1, V2) -> U104#(isNatIListKind(activate(V2)), activate(V1), activate(V2)),
isNatIListKind#(n__take(V1, V2)) -> isNatKind#(activate(V1)),
isNatIListKind#(n__take(V1, V2)) -> activate#(V1),
isNatIListKind#(n__take(V1, V2)) -> activate#(V2),
isNatIListKind#(n__take(V1, V2)) -> U61#(isNatKind(activate(V1)), activate(V2)),
isNatIListKind#(n__cons(V1, V2)) -> isNatKind#(activate(V1)),
isNatIListKind#(n__cons(V1, V2)) -> activate#(V1),
isNatIListKind#(n__cons(V1, V2)) -> activate#(V2),
isNatIListKind#(n__cons(V1, V2)) -> U51#(isNatKind(activate(V1)), activate(V2)),
U104#(tt(), V1, V2) -> activate#(V1),
U104#(tt(), V1, V2) -> activate#(V2),
U104#(tt(), V1, V2) -> U105#(isNat(activate(V1)), activate(V2)),
U104#(tt(), V1, V2) -> isNat#(activate(V1)),
U105#(tt(), V2) -> activate#(V2),
U105#(tt(), V2) -> isNatIList#(activate(V2)),
isNat#(n__length(V1)) -> activate#(V1),
isNat#(n__length(V1)) -> isNatIListKind#(activate(V1)),
isNat#(n__length(V1)) -> U11#(isNatIListKind(activate(V1)), activate(V1)),
isNat#(n__s(V1)) -> isNatKind#(activate(V1)),
isNat#(n__s(V1)) -> activate#(V1),
isNat#(n__s(V1)) -> U21#(isNatKind(activate(V1)), activate(V1)),
isNatIList#(V) -> activate#(V),
isNatIList#(V) -> isNatIListKind#(activate(V)),
isNatIList#(V) -> U31#(isNatIListKind(activate(V)), activate(V)),
isNatIList#(n__cons(V1, V2)) -> isNatKind#(activate(V1)),
isNatIList#(n__cons(V1, V2)) -> activate#(V1),
isNatIList#(n__cons(V1, V2)) -> activate#(V2),
isNatIList#(n__cons(V1, V2)) -> U41#(isNatKind(activate(V1)), activate(V1), activate(V2)),
U12#(tt(), V1) -> activate#(V1),
U12#(tt(), V1) -> isNatList#(activate(V1)),
U11#(tt(), V1) -> activate#(V1),
U11#(tt(), V1) -> isNatIListKind#(activate(V1)),
U11#(tt(), V1) -> U12#(isNatIListKind(activate(V1)), activate(V1)),
U112#(tt(), L, N) -> activate#(L),
U112#(tt(), L, N) -> activate#(N),
U112#(tt(), L, N) -> isNat#(activate(N)),
U112#(tt(), L, N) -> U113#(isNat(activate(N)), activate(L), activate(N)),
U111#(tt(), L, N) -> activate#(L),
U111#(tt(), L, N) -> activate#(N),
U111#(tt(), L, N) -> isNatIListKind#(activate(L)),
U111#(tt(), L, N) -> U112#(isNatIListKind(activate(L)), activate(L), activate(N)),
U113#(tt(), L, N) -> isNatKind#(activate(N)),
U113#(tt(), L, N) -> activate#(L),
U113#(tt(), L, N) -> activate#(N),
U113#(tt(), L, N) -> U114#(isNatKind(activate(N)), activate(L)),
U114#(tt(), L) -> activate#(L),
U114#(tt(), L) -> length#(activate(L)),
length#(cons(N, L)) -> activate#(L),
length#(cons(N, L)) -> U111#(isNatList(activate(L)), activate(L), N),
length#(cons(N, L)) -> isNatList#(activate(L)),
isNatList#(n__take(V1, V2)) -> isNatKind#(activate(V1)),
isNatList#(n__take(V1, V2)) -> activate#(V1),
isNatList#(n__take(V1, V2)) -> activate#(V2),
isNatList#(n__take(V1, V2)) -> U101#(isNatKind(activate(V1)), activate(V1), activate(V2)),
isNatList#(n__cons(V1, V2)) -> isNatKind#(activate(V1)),
isNatList#(n__cons(V1, V2)) -> activate#(V1),
isNatList#(n__cons(V1, V2)) -> activate#(V2),
isNatList#(n__cons(V1, V2)) -> U91#(isNatKind(activate(V1)), activate(V1), activate(V2)),
U121#(tt(), IL) -> activate#(IL),
U121#(tt(), IL) -> isNatIListKind#(activate(IL)),
U132#(tt(), IL, M, N) -> activate#(N),
U132#(tt(), IL, M, N) -> activate#(IL),
U132#(tt(), IL, M, N) -> activate#(M),
U132#(tt(), IL, M, N) -> isNat#(activate(M)),
U132#(tt(), IL, M, N) -> U133#(isNat(activate(M)), activate(IL), activate(M), activate(N)),
U131#(tt(), IL, M, N) -> activate#(N),
U131#(tt(), IL, M, N) -> activate#(IL),
U131#(tt(), IL, M, N) -> activate#(M),
U131#(tt(), IL, M, N) -> isNatIListKind#(activate(IL)),
U131#(tt(), IL, M, N) -> U132#(isNatIListKind(activate(IL)), activate(IL), activate(M), activate(N)),
U133#(tt(), IL, M, N) -> isNatKind#(activate(M)),
U133#(tt(), IL, M, N) -> activate#(N),
U133#(tt(), IL, M, N) -> activate#(IL),
U133#(tt(), IL, M, N) -> activate#(M),
U133#(tt(), IL, M, N) -> U134#(isNatKind(activate(M)), activate(IL), activate(M), activate(N)),
U134#(tt(), IL, M, N) -> activate#(N),
U134#(tt(), IL, M, N) -> activate#(IL),
U134#(tt(), IL, M, N) -> activate#(M),
U134#(tt(), IL, M, N) -> isNat#(activate(N)),
U134#(tt(), IL, M, N) -> U135#(isNat(activate(N)), activate(IL), activate(M), activate(N)),
U135#(tt(), IL, M, N) -> isNatKind#(activate(N)),
U135#(tt(), IL, M, N) -> activate#(N),
U135#(tt(), IL, M, N) -> activate#(IL),
U135#(tt(), IL, M, N) -> activate#(M),
U135#(tt(), IL, M, N) -> U136#(isNatKind(activate(N)), activate(IL), activate(M), activate(N)),
U136#(tt(), IL, M, N) -> activate#(N),
U136#(tt(), IL, M, N) -> activate#(IL),
U136#(tt(), IL, M, N) -> activate#(M),
U22#(tt(), V1) -> activate#(V1),
U22#(tt(), V1) -> isNat#(activate(V1)),
U21#(tt(), V1) -> isNatKind#(activate(V1)),
U21#(tt(), V1) -> activate#(V1),
U21#(tt(), V1) -> U22#(isNatKind(activate(V1)), activate(V1)),
U32#(tt(), V) -> activate#(V),
U32#(tt(), V) -> isNatList#(activate(V)),
U31#(tt(), V) -> activate#(V),
U31#(tt(), V) -> isNatIListKind#(activate(V)),
U31#(tt(), V) -> U32#(isNatIListKind(activate(V)), activate(V)),
U42#(tt(), V1, V2) -> activate#(V1),
U42#(tt(), V1, V2) -> activate#(V2),
U42#(tt(), V1, V2) -> isNatIListKind#(activate(V2)),
U42#(tt(), V1, V2) -> U43#(isNatIListKind(activate(V2)), activate(V1), activate(V2)),
U41#(tt(), V1, V2) -> isNatKind#(activate(V1)),
U41#(tt(), V1, V2) -> activate#(V1),
U41#(tt(), V1, V2) -> activate#(V2),
U41#(tt(), V1, V2) -> U42#(isNatKind(activate(V1)), activate(V1), activate(V2)),
U43#(tt(), V1, V2) -> activate#(V1),
U43#(tt(), V1, V2) -> activate#(V2),
U43#(tt(), V1, V2) -> isNatIListKind#(activate(V2)),
U43#(tt(), V1, V2) -> U44#(isNatIListKind(activate(V2)), activate(V1), activate(V2)),
U44#(tt(), V1, V2) -> activate#(V1),
U44#(tt(), V1, V2) -> activate#(V2),
U44#(tt(), V1, V2) -> isNat#(activate(V1)),
U44#(tt(), V1, V2) -> U45#(isNat(activate(V1)), activate(V2)),
U45#(tt(), V2) -> activate#(V2),
U45#(tt(), V2) -> isNatIList#(activate(V2)),
U51#(tt(), V2) -> activate#(V2),
U51#(tt(), V2) -> isNatIListKind#(activate(V2)),
U61#(tt(), V2) -> activate#(V2),
U61#(tt(), V2) -> isNatIListKind#(activate(V2)),
U92#(tt(), V1, V2) -> activate#(V1),
U92#(tt(), V1, V2) -> activate#(V2),
U92#(tt(), V1, V2) -> isNatIListKind#(activate(V2)),
U92#(tt(), V1, V2) -> U93#(isNatIListKind(activate(V2)), activate(V1), activate(V2)),
U91#(tt(), V1, V2) -> isNatKind#(activate(V1)),
U91#(tt(), V1, V2) -> activate#(V1),
U91#(tt(), V1, V2) -> activate#(V2),
U91#(tt(), V1, V2) -> U92#(isNatKind(activate(V1)), activate(V1), activate(V2)),
U93#(tt(), V1, V2) -> activate#(V1),
U93#(tt(), V1, V2) -> activate#(V2),
U93#(tt(), V1, V2) -> isNatIListKind#(activate(V2)),
U93#(tt(), V1, V2) -> U94#(isNatIListKind(activate(V2)), activate(V1), activate(V2)),
U94#(tt(), V1, V2) -> activate#(V1),
U94#(tt(), V1, V2) -> activate#(V2),
U94#(tt(), V1, V2) -> isNat#(activate(V1)),
U94#(tt(), V1, V2) -> U95#(isNat(activate(V1)), activate(V2)),
U95#(tt(), V2) -> activate#(V2),
U95#(tt(), V2) -> isNatList#(activate(V2)),
take#(0(), IL) -> isNatIList#(IL),
take#(0(), IL) -> U121#(isNatIList(IL), IL),
take#(s(M), cons(N, IL)) -> activate#(IL),
take#(s(M), cons(N, IL)) -> isNatIList#(activate(IL)),
take#(s(M), cons(N, IL)) -> U131#(isNatIList(activate(IL)), activate(IL), M, N)
}
Weak:
{ cons(X1, X2) -> n__cons(X1, X2),
0() -> n__0(),
zeros() -> cons(0(), n__zeros()),
zeros() -> n__zeros(),
U102(tt(), V1, V2) -> U103(isNatIListKind(activate(V2)), activate(V1), activate(V2)),
isNatKind(n__0()) -> tt(),
isNatKind(n__length(V1)) -> U71(isNatIListKind(activate(V1))),
isNatKind(n__s(V1)) -> U81(isNatKind(activate(V1))),
activate(X) -> X,
activate(n__zeros()) -> zeros(),
activate(n__take(X1, X2)) -> take(activate(X1), activate(X2)),
activate(n__0()) -> 0(),
activate(n__length(X)) -> length(activate(X)),
activate(n__s(X)) -> s(activate(X)),
activate(n__cons(X1, X2)) -> cons(activate(X1), X2),
activate(n__nil()) -> nil(),
U101(tt(), V1, V2) -> U102(isNatKind(activate(V1)), activate(V1), activate(V2)),
U103(tt(), V1, V2) -> U104(isNatIListKind(activate(V2)), activate(V1), activate(V2)),
isNatIListKind(n__zeros()) -> tt(),
isNatIListKind(n__take(V1, V2)) -> U61(isNatKind(activate(V1)), activate(V2)),
isNatIListKind(n__cons(V1, V2)) -> U51(isNatKind(activate(V1)), activate(V2)),
isNatIListKind(n__nil()) -> tt(),
U104(tt(), V1, V2) -> U105(isNat(activate(V1)), activate(V2)),
U105(tt(), V2) -> U106(isNatIList(activate(V2))),
isNat(n__0()) -> tt(),
isNat(n__length(V1)) -> U11(isNatIListKind(activate(V1)), activate(V1)),
isNat(n__s(V1)) -> U21(isNatKind(activate(V1)), activate(V1)),
U106(tt()) -> tt(),
isNatIList(V) -> U31(isNatIListKind(activate(V)), activate(V)),
isNatIList(n__zeros()) -> tt(),
isNatIList(n__cons(V1, V2)) -> U41(isNatKind(activate(V1)), activate(V1), activate(V2)),
U12(tt(), V1) -> U13(isNatList(activate(V1))),
U11(tt(), V1) -> U12(isNatIListKind(activate(V1)), activate(V1)),
U112(tt(), L, N) -> U113(isNat(activate(N)), activate(L), activate(N)),
U111(tt(), L, N) -> U112(isNatIListKind(activate(L)), activate(L), activate(N)),
U113(tt(), L, N) -> U114(isNatKind(activate(N)), activate(L)),
U114(tt(), L) -> s(length(activate(L))),
s(X) -> n__s(X),
length(X) -> n__length(X),
length(cons(N, L)) -> U111(isNatList(activate(L)), activate(L), N),
length(nil()) -> 0(),
U13(tt()) -> tt(),
isNatList(n__take(V1, V2)) -> U101(isNatKind(activate(V1)), activate(V1), activate(V2)),
isNatList(n__cons(V1, V2)) -> U91(isNatKind(activate(V1)), activate(V1), activate(V2)),
isNatList(n__nil()) -> tt(),
U122(tt()) -> nil(),
U121(tt(), IL) -> U122(isNatIListKind(activate(IL))),
nil() -> n__nil(),
U132(tt(), IL, M, N) -> U133(isNat(activate(M)), activate(IL), activate(M), activate(N)),
U131(tt(), IL, M, N) -> U132(isNatIListKind(activate(IL)), activate(IL), activate(M), activate(N)),
U133(tt(), IL, M, N) -> U134(isNatKind(activate(M)), activate(IL), activate(M), activate(N)),
U134(tt(), IL, M, N) -> U135(isNat(activate(N)), activate(IL), activate(M), activate(N)),
U135(tt(), IL, M, N) -> U136(isNatKind(activate(N)), activate(IL), activate(M), activate(N)),
U136(tt(), IL, M, N) -> cons(activate(N), n__take(activate(M), activate(IL))),
U22(tt(), V1) -> U23(isNat(activate(V1))),
U21(tt(), V1) -> U22(isNatKind(activate(V1)), activate(V1)),
U23(tt()) -> tt(),
U32(tt(), V) -> U33(isNatList(activate(V))),
U31(tt(), V) -> U32(isNatIListKind(activate(V)), activate(V)),
U33(tt()) -> tt(),
U42(tt(), V1, V2) -> U43(isNatIListKind(activate(V2)), activate(V1), activate(V2)),
U41(tt(), V1, V2) -> U42(isNatKind(activate(V1)), activate(V1), activate(V2)),
U43(tt(), V1, V2) -> U44(isNatIListKind(activate(V2)), activate(V1), activate(V2)),
U44(tt(), V1, V2) -> U45(isNat(activate(V1)), activate(V2)),
U45(tt(), V2) -> U46(isNatIList(activate(V2))),
U46(tt()) -> tt(),
U52(tt()) -> tt(),
U51(tt(), V2) -> U52(isNatIListKind(activate(V2))),
U62(tt()) -> tt(),
U61(tt(), V2) -> U62(isNatIListKind(activate(V2))),
U71(tt()) -> tt(),
U81(tt()) -> tt(),
U92(tt(), V1, V2) -> U93(isNatIListKind(activate(V2)), activate(V1), activate(V2)),
U91(tt(), V1, V2) -> U92(isNatKind(activate(V1)), activate(V1), activate(V2)),
U93(tt(), V1, V2) -> U94(isNatIListKind(activate(V2)), activate(V1), activate(V2)),
U94(tt(), V1, V2) -> U95(isNat(activate(V1)), activate(V2)),
U95(tt(), V2) -> U96(isNatList(activate(V2))),
U96(tt()) -> tt(),
take(X1, X2) -> n__take(X1, X2),
take(0(), IL) -> U121(isNatIList(IL), IL),
take(s(M), cons(N, IL)) -> U131(isNatIList(activate(IL)), activate(IL), M, N)}
POLY:
Argument Filtering:
pi(take#) = [0,1], pi(take) = [0,1], pi(n__nil) = [], pi(n__cons) = [0,1], pi(n__s) = 0, pi(n__length) = 0, pi(n__0) = [], pi(U96) = [], pi(U95#) = 1, pi(U95) = [], pi(U94#) = [1,2], pi(U94) = [], pi(U93#) = [1,2], pi(U93) = [], pi(U91#) = [1,2], pi(U91) = [], pi(U92#) = [1,2], pi(U92) = [], pi(U81) = [], pi(U71) = [], pi(U61#) = 1, pi(U61) = [], pi(U62) = [], pi(U51#) = 1, pi(U51) = [], pi(U52) = [], pi(U46) = [], pi(U45#) = 1, pi(U45) = [], pi(U44#) = [1,2], pi(U44) = [], pi(U43#) = [1,2], pi(U43) = [], pi(U41#) = [1,2], pi(U41) = [], pi(U42#) = [1,2], pi(U42) = [], pi(U33) = [], pi(U31#) = 1, pi(U31) = [], pi(U32#) = 1, pi(U32) = [], pi(U23) = [], pi(U21#) = 1, pi(U21) = [], pi(U22#) = 1, pi(U22) = [], pi(n__take) = [0,1], pi(U136#) = [1,2,3], pi(U136) = [1,2,3], pi(U135#) = [1,2,3], pi(U135) = [1,2,3], pi(U134#) = [1,2,3], pi(U134) = [1,2,3], pi(U133#) = [1,2,3], pi(U133) = [1,2,3], pi(U131#) = [1,2,3], pi(U131) = [1,2,3], pi(U132#) = [1,2,3], pi(U132) = [1,2,3], pi(nil) = [], pi(U121#) = 1, pi(U121) = 1, pi(U122) = [], pi(isNatList#) = 0, pi(isNatList) = [], pi(U13) = [], pi(length#) = 0, pi(length) = 0, pi(s) = 0, pi(U114#) = 1, pi(U114) = 1, pi(U113#) = [1,2], pi(U113) = 1, pi(U111#) = [1,2], pi(U111) = [1,2], pi(U112#) = [1,2], pi(U112) = [1,2], pi(U11#) = 1, pi(U11) = [], pi(U12#) = 1, pi(U12) = [], pi(isNatIList#) = 0, pi(isNatIList) = [], pi(U106) = [], pi(isNat#) = 0, pi(isNat) = [], pi(U105#) = 1, pi(U105) = [], pi(U104#) = [1,2], pi(U104) = [], pi(isNatIListKind#) = 0, pi(isNatIListKind) = [], pi(U103#) = [1,2], pi(U103) = [], pi(tt) = [], pi(U101#) = [1,2], pi(U101) = [], pi(activate#) = 0, pi(activate) = 0, pi(isNatKind#) = 0, pi(isNatKind) = [], pi(U102#) = [1,2], pi(U102) = [], pi(zeros) = [], pi(n__zeros) = [], pi(0) = [], pi(cons) = [0,1]
Usable Rules:
{}
Interpretation:
[U136#](x0, x1, x2) = x0 + x1 + x2,
[U135#](x0, x1, x2) = x0 + x1 + x2,
[U134#](x0, x1, x2) = x0 + x1 + x2,
[U133#](x0, x1, x2) = x0 + x1 + x2,
[U131#](x0, x1, x2) = x0 + x1 + x2,
[U132#](x0, x1, x2) = x0 + x1 + x2,
[U94#](x0, x1) = x0 + x1,
[U93#](x0, x1) = x0 + x1,
[U91#](x0, x1) = x0 + x1,
[U92#](x0, x1) = x0 + x1,
[U44#](x0, x1) = x0 + x1,
[U43#](x0, x1) = x0 + x1,
[U41#](x0, x1) = x0 + x1,
[U42#](x0, x1) = x0 + x1,
[U113#](x0, x1) = x0 + x1,
[U111#](x0, x1) = x0 + x1,
[U112#](x0, x1) = x0 + x1,
[U104#](x0, x1) = x0 + x1,
[U103#](x0, x1) = x0 + x1,
[U101#](x0, x1) = x0 + x1,
[U102#](x0, x1) = x0 + x1,
[take#](x0, x1) = x0 + x1 + 1,
[n__cons](x0, x1) = x0 + x1,
[n__take](x0, x1) = x0 + x1 + 1,
[cons](x0, x1) = x0 + x1,
[0] = 0
Strict:
{ U102#(tt(), V1, V2) -> activate#(V1),
U102#(tt(), V1, V2) -> activate#(V2),
U102#(tt(), V1, V2) -> U103#(isNatIListKind(activate(V2)), activate(V1), activate(V2)),
U102#(tt(), V1, V2) -> isNatIListKind#(activate(V2)),
isNatKind#(n__length(V1)) -> activate#(V1),
isNatKind#(n__length(V1)) -> isNatIListKind#(activate(V1)),
isNatKind#(n__s(V1)) -> isNatKind#(activate(V1)),
isNatKind#(n__s(V1)) -> activate#(V1),
activate#(n__take(X1, X2)) -> take#(activate(X1), activate(X2)),
activate#(n__length(X)) -> activate#(X),
activate#(n__length(X)) -> length#(activate(X)),
activate#(n__s(X)) -> activate#(X),
activate#(n__cons(X1, X2)) -> activate#(X1),
U101#(tt(), V1, V2) -> U102#(isNatKind(activate(V1)), activate(V1), activate(V2)),
U101#(tt(), V1, V2) -> isNatKind#(activate(V1)),
U101#(tt(), V1, V2) -> activate#(V1),
U101#(tt(), V1, V2) -> activate#(V2),
U103#(tt(), V1, V2) -> activate#(V1),
U103#(tt(), V1, V2) -> activate#(V2),
U103#(tt(), V1, V2) -> isNatIListKind#(activate(V2)),
U103#(tt(), V1, V2) -> U104#(isNatIListKind(activate(V2)), activate(V1), activate(V2)),
isNatIListKind#(n__cons(V1, V2)) -> isNatKind#(activate(V1)),
isNatIListKind#(n__cons(V1, V2)) -> activate#(V1),
isNatIListKind#(n__cons(V1, V2)) -> activate#(V2),
isNatIListKind#(n__cons(V1, V2)) -> U51#(isNatKind(activate(V1)), activate(V2)),
U104#(tt(), V1, V2) -> activate#(V1),
U104#(tt(), V1, V2) -> activate#(V2),
U104#(tt(), V1, V2) -> U105#(isNat(activate(V1)), activate(V2)),
U104#(tt(), V1, V2) -> isNat#(activate(V1)),
U105#(tt(), V2) -> activate#(V2),
U105#(tt(), V2) -> isNatIList#(activate(V2)),
isNat#(n__length(V1)) -> activate#(V1),
isNat#(n__length(V1)) -> isNatIListKind#(activate(V1)),
isNat#(n__length(V1)) -> U11#(isNatIListKind(activate(V1)), activate(V1)),
isNat#(n__s(V1)) -> isNatKind#(activate(V1)),
isNat#(n__s(V1)) -> activate#(V1),
isNat#(n__s(V1)) -> U21#(isNatKind(activate(V1)), activate(V1)),
isNatIList#(V) -> activate#(V),
isNatIList#(V) -> isNatIListKind#(activate(V)),
isNatIList#(V) -> U31#(isNatIListKind(activate(V)), activate(V)),
isNatIList#(n__cons(V1, V2)) -> isNatKind#(activate(V1)),
isNatIList#(n__cons(V1, V2)) -> activate#(V1),
isNatIList#(n__cons(V1, V2)) -> activate#(V2),
isNatIList#(n__cons(V1, V2)) -> U41#(isNatKind(activate(V1)), activate(V1), activate(V2)),
U12#(tt(), V1) -> activate#(V1),
U12#(tt(), V1) -> isNatList#(activate(V1)),
U11#(tt(), V1) -> activate#(V1),
U11#(tt(), V1) -> isNatIListKind#(activate(V1)),
U11#(tt(), V1) -> U12#(isNatIListKind(activate(V1)), activate(V1)),
U112#(tt(), L, N) -> activate#(L),
U112#(tt(), L, N) -> activate#(N),
U112#(tt(), L, N) -> isNat#(activate(N)),
U112#(tt(), L, N) -> U113#(isNat(activate(N)), activate(L), activate(N)),
U111#(tt(), L, N) -> activate#(L),
U111#(tt(), L, N) -> activate#(N),
U111#(tt(), L, N) -> isNatIListKind#(activate(L)),
U111#(tt(), L, N) -> U112#(isNatIListKind(activate(L)), activate(L), activate(N)),
U113#(tt(), L, N) -> isNatKind#(activate(N)),
U113#(tt(), L, N) -> activate#(L),
U113#(tt(), L, N) -> activate#(N),
U113#(tt(), L, N) -> U114#(isNatKind(activate(N)), activate(L)),
U114#(tt(), L) -> activate#(L),
U114#(tt(), L) -> length#(activate(L)),
length#(cons(N, L)) -> activate#(L),
length#(cons(N, L)) -> U111#(isNatList(activate(L)), activate(L), N),
length#(cons(N, L)) -> isNatList#(activate(L)),
isNatList#(n__cons(V1, V2)) -> isNatKind#(activate(V1)),
isNatList#(n__cons(V1, V2)) -> activate#(V1),
isNatList#(n__cons(V1, V2)) -> activate#(V2),
isNatList#(n__cons(V1, V2)) -> U91#(isNatKind(activate(V1)), activate(V1), activate(V2)),
U121#(tt(), IL) -> activate#(IL),
U121#(tt(), IL) -> isNatIListKind#(activate(IL)),
U132#(tt(), IL, M, N) -> activate#(N),
U132#(tt(), IL, M, N) -> activate#(IL),
U132#(tt(), IL, M, N) -> activate#(M),
U132#(tt(), IL, M, N) -> isNat#(activate(M)),
U132#(tt(), IL, M, N) -> U133#(isNat(activate(M)), activate(IL), activate(M), activate(N)),
U131#(tt(), IL, M, N) -> activate#(N),
U131#(tt(), IL, M, N) -> activate#(IL),
U131#(tt(), IL, M, N) -> activate#(M),
U131#(tt(), IL, M, N) -> isNatIListKind#(activate(IL)),
U131#(tt(), IL, M, N) -> U132#(isNatIListKind(activate(IL)), activate(IL), activate(M), activate(N)),
U133#(tt(), IL, M, N) -> isNatKind#(activate(M)),
U133#(tt(), IL, M, N) -> activate#(N),
U133#(tt(), IL, M, N) -> activate#(IL),
U133#(tt(), IL, M, N) -> activate#(M),
U133#(tt(), IL, M, N) -> U134#(isNatKind(activate(M)), activate(IL), activate(M), activate(N)),
U134#(tt(), IL, M, N) -> activate#(N),
U134#(tt(), IL, M, N) -> activate#(IL),
U134#(tt(), IL, M, N) -> activate#(M),
U134#(tt(), IL, M, N) -> isNat#(activate(N)),
U134#(tt(), IL, M, N) -> U135#(isNat(activate(N)), activate(IL), activate(M), activate(N)),
U135#(tt(), IL, M, N) -> isNatKind#(activate(N)),
U135#(tt(), IL, M, N) -> activate#(N),
U135#(tt(), IL, M, N) -> activate#(IL),
U135#(tt(), IL, M, N) -> activate#(M),
U135#(tt(), IL, M, N) -> U136#(isNatKind(activate(N)), activate(IL), activate(M), activate(N)),
U136#(tt(), IL, M, N) -> activate#(N),
U136#(tt(), IL, M, N) -> activate#(IL),
U136#(tt(), IL, M, N) -> activate#(M),
U22#(tt(), V1) -> activate#(V1),
U22#(tt(), V1) -> isNat#(activate(V1)),
U21#(tt(), V1) -> isNatKind#(activate(V1)),
U21#(tt(), V1) -> activate#(V1),
U21#(tt(), V1) -> U22#(isNatKind(activate(V1)), activate(V1)),
U32#(tt(), V) -> activate#(V),
U32#(tt(), V) -> isNatList#(activate(V)),
U31#(tt(), V) -> activate#(V),
U31#(tt(), V) -> isNatIListKind#(activate(V)),
U31#(tt(), V) -> U32#(isNatIListKind(activate(V)), activate(V)),
U42#(tt(), V1, V2) -> activate#(V1),
U42#(tt(), V1, V2) -> activate#(V2),
U42#(tt(), V1, V2) -> isNatIListKind#(activate(V2)),
U42#(tt(), V1, V2) -> U43#(isNatIListKind(activate(V2)), activate(V1), activate(V2)),
U41#(tt(), V1, V2) -> isNatKind#(activate(V1)),
U41#(tt(), V1, V2) -> activate#(V1),
U41#(tt(), V1, V2) -> activate#(V2),
U41#(tt(), V1, V2) -> U42#(isNatKind(activate(V1)), activate(V1), activate(V2)),
U43#(tt(), V1, V2) -> activate#(V1),
U43#(tt(), V1, V2) -> activate#(V2),
U43#(tt(), V1, V2) -> isNatIListKind#(activate(V2)),
U43#(tt(), V1, V2) -> U44#(isNatIListKind(activate(V2)), activate(V1), activate(V2)),
U44#(tt(), V1, V2) -> activate#(V1),
U44#(tt(), V1, V2) -> activate#(V2),
U44#(tt(), V1, V2) -> isNat#(activate(V1)),
U44#(tt(), V1, V2) -> U45#(isNat(activate(V1)), activate(V2)),
U45#(tt(), V2) -> activate#(V2),
U45#(tt(), V2) -> isNatIList#(activate(V2)),
U51#(tt(), V2) -> activate#(V2),
U51#(tt(), V2) -> isNatIListKind#(activate(V2)),
U61#(tt(), V2) -> activate#(V2),
U61#(tt(), V2) -> isNatIListKind#(activate(V2)),
U92#(tt(), V1, V2) -> activate#(V1),
U92#(tt(), V1, V2) -> activate#(V2),
U92#(tt(), V1, V2) -> isNatIListKind#(activate(V2)),
U92#(tt(), V1, V2) -> U93#(isNatIListKind(activate(V2)), activate(V1), activate(V2)),
U91#(tt(), V1, V2) -> isNatKind#(activate(V1)),
U91#(tt(), V1, V2) -> activate#(V1),
U91#(tt(), V1, V2) -> activate#(V2),
U91#(tt(), V1, V2) -> U92#(isNatKind(activate(V1)), activate(V1), activate(V2)),
U93#(tt(), V1, V2) -> activate#(V1),
U93#(tt(), V1, V2) -> activate#(V2),
U93#(tt(), V1, V2) -> isNatIListKind#(activate(V2)),
U93#(tt(), V1, V2) -> U94#(isNatIListKind(activate(V2)), activate(V1), activate(V2)),
U94#(tt(), V1, V2) -> activate#(V1),
U94#(tt(), V1, V2) -> activate#(V2),
U94#(tt(), V1, V2) -> isNat#(activate(V1)),
U94#(tt(), V1, V2) -> U95#(isNat(activate(V1)), activate(V2)),
U95#(tt(), V2) -> activate#(V2),
U95#(tt(), V2) -> isNatList#(activate(V2))}
Weak:
{ cons(X1, X2) -> n__cons(X1, X2),
0() -> n__0(),
zeros() -> cons(0(), n__zeros()),
zeros() -> n__zeros(),
U102(tt(), V1, V2) -> U103(isNatIListKind(activate(V2)), activate(V1), activate(V2)),
isNatKind(n__0()) -> tt(),
isNatKind(n__length(V1)) -> U71(isNatIListKind(activate(V1))),
isNatKind(n__s(V1)) -> U81(isNatKind(activate(V1))),
activate(X) -> X,
activate(n__zeros()) -> zeros(),
activate(n__take(X1, X2)) -> take(activate(X1), activate(X2)),
activate(n__0()) -> 0(),
activate(n__length(X)) -> length(activate(X)),
activate(n__s(X)) -> s(activate(X)),
activate(n__cons(X1, X2)) -> cons(activate(X1), X2),
activate(n__nil()) -> nil(),
U101(tt(), V1, V2) -> U102(isNatKind(activate(V1)), activate(V1), activate(V2)),
U103(tt(), V1, V2) -> U104(isNatIListKind(activate(V2)), activate(V1), activate(V2)),
isNatIListKind(n__zeros()) -> tt(),
isNatIListKind(n__take(V1, V2)) -> U61(isNatKind(activate(V1)), activate(V2)),
isNatIListKind(n__cons(V1, V2)) -> U51(isNatKind(activate(V1)), activate(V2)),
isNatIListKind(n__nil()) -> tt(),
U104(tt(), V1, V2) -> U105(isNat(activate(V1)), activate(V2)),
U105(tt(), V2) -> U106(isNatIList(activate(V2))),
isNat(n__0()) -> tt(),
isNat(n__length(V1)) -> U11(isNatIListKind(activate(V1)), activate(V1)),
isNat(n__s(V1)) -> U21(isNatKind(activate(V1)), activate(V1)),
U106(tt()) -> tt(),
isNatIList(V) -> U31(isNatIListKind(activate(V)), activate(V)),
isNatIList(n__zeros()) -> tt(),
isNatIList(n__cons(V1, V2)) -> U41(isNatKind(activate(V1)), activate(V1), activate(V2)),
U12(tt(), V1) -> U13(isNatList(activate(V1))),
U11(tt(), V1) -> U12(isNatIListKind(activate(V1)), activate(V1)),
U112(tt(), L, N) -> U113(isNat(activate(N)), activate(L), activate(N)),
U111(tt(), L, N) -> U112(isNatIListKind(activate(L)), activate(L), activate(N)),
U113(tt(), L, N) -> U114(isNatKind(activate(N)), activate(L)),
U114(tt(), L) -> s(length(activate(L))),
s(X) -> n__s(X),
length(X) -> n__length(X),
length(cons(N, L)) -> U111(isNatList(activate(L)), activate(L), N),
length(nil()) -> 0(),
U13(tt()) -> tt(),
isNatList(n__take(V1, V2)) -> U101(isNatKind(activate(V1)), activate(V1), activate(V2)),
isNatList(n__cons(V1, V2)) -> U91(isNatKind(activate(V1)), activate(V1), activate(V2)),
isNatList(n__nil()) -> tt(),
U122(tt()) -> nil(),
U121(tt(), IL) -> U122(isNatIListKind(activate(IL))),
nil() -> n__nil(),
U132(tt(), IL, M, N) -> U133(isNat(activate(M)), activate(IL), activate(M), activate(N)),
U131(tt(), IL, M, N) -> U132(isNatIListKind(activate(IL)), activate(IL), activate(M), activate(N)),
U133(tt(), IL, M, N) -> U134(isNatKind(activate(M)), activate(IL), activate(M), activate(N)),
U134(tt(), IL, M, N) -> U135(isNat(activate(N)), activate(IL), activate(M), activate(N)),
U135(tt(), IL, M, N) -> U136(isNatKind(activate(N)), activate(IL), activate(M), activate(N)),
U136(tt(), IL, M, N) -> cons(activate(N), n__take(activate(M), activate(IL))),
U22(tt(), V1) -> U23(isNat(activate(V1))),
U21(tt(), V1) -> U22(isNatKind(activate(V1)), activate(V1)),
U23(tt()) -> tt(),
U32(tt(), V) -> U33(isNatList(activate(V))),
U31(tt(), V) -> U32(isNatIListKind(activate(V)), activate(V)),
U33(tt()) -> tt(),
U42(tt(), V1, V2) -> U43(isNatIListKind(activate(V2)), activate(V1), activate(V2)),
U41(tt(), V1, V2) -> U42(isNatKind(activate(V1)), activate(V1), activate(V2)),
U43(tt(), V1, V2) -> U44(isNatIListKind(activate(V2)), activate(V1), activate(V2)),
U44(tt(), V1, V2) -> U45(isNat(activate(V1)), activate(V2)),
U45(tt(), V2) -> U46(isNatIList(activate(V2))),
U46(tt()) -> tt(),
U52(tt()) -> tt(),
U51(tt(), V2) -> U52(isNatIListKind(activate(V2))),
U62(tt()) -> tt(),
U61(tt(), V2) -> U62(isNatIListKind(activate(V2))),
U71(tt()) -> tt(),
U81(tt()) -> tt(),
U92(tt(), V1, V2) -> U93(isNatIListKind(activate(V2)), activate(V1), activate(V2)),
U91(tt(), V1, V2) -> U92(isNatKind(activate(V1)), activate(V1), activate(V2)),
U93(tt(), V1, V2) -> U94(isNatIListKind(activate(V2)), activate(V1), activate(V2)),
U94(tt(), V1, V2) -> U95(isNat(activate(V1)), activate(V2)),
U95(tt(), V2) -> U96(isNatList(activate(V2))),
U96(tt()) -> tt(),
take(X1, X2) -> n__take(X1, X2),
take(0(), IL) -> U121(isNatIList(IL), IL),
take(s(M), cons(N, IL)) -> U131(isNatIList(activate(IL)), activate(IL), M, N)}
EDG:
{
(U131#(tt(), IL, M, N) -> activate#(M), activate#(n__cons(X1, X2)) -> activate#(X1))
(U131#(tt(), IL, M, N) -> activate#(M), activate#(n__s(X)) -> activate#(X))
(U131#(tt(), IL, M, N) -> activate#(M), activate#(n__length(X)) -> length#(activate(X)))
(U131#(tt(), IL, M, N) -> activate#(M), activate#(n__length(X)) -> activate#(X))
(U131#(tt(), IL, M, N) -> activate#(M), activate#(n__take(X1, X2)) -> take#(activate(X1), activate(X2)))
(U134#(tt(), IL, M, N) -> activate#(M), activate#(n__cons(X1, X2)) -> activate#(X1))
(U134#(tt(), IL, M, N) -> activate#(M), activate#(n__s(X)) -> activate#(X))
(U134#(tt(), IL, M, N) -> activate#(M), activate#(n__length(X)) -> length#(activate(X)))
(U134#(tt(), IL, M, N) -> activate#(M), activate#(n__length(X)) -> activate#(X))
(U134#(tt(), IL, M, N) -> activate#(M), activate#(n__take(X1, X2)) -> take#(activate(X1), activate(X2)))
(U136#(tt(), IL, M, N) -> activate#(M), activate#(n__cons(X1, X2)) -> activate#(X1))
(U136#(tt(), IL, M, N) -> activate#(M), activate#(n__s(X)) -> activate#(X))
(U136#(tt(), IL, M, N) -> activate#(M), activate#(n__length(X)) -> length#(activate(X)))
(U136#(tt(), IL, M, N) -> activate#(M), activate#(n__length(X)) -> activate#(X))
(U136#(tt(), IL, M, N) -> activate#(M), activate#(n__take(X1, X2)) -> take#(activate(X1), activate(X2)))
(U132#(tt(), IL, M, N) -> U133#(isNat(activate(M)), activate(IL), activate(M), activate(N)), U133#(tt(), IL, M, N) -> U134#(isNatKind(activate(M)), activate(IL), activate(M), activate(N)))
(U132#(tt(), IL, M, N) -> U133#(isNat(activate(M)), activate(IL), activate(M), activate(N)), U133#(tt(), IL, M, N) -> activate#(M))
(U132#(tt(), IL, M, N) -> U133#(isNat(activate(M)), activate(IL), activate(M), activate(N)), U133#(tt(), IL, M, N) -> activate#(IL))
(U132#(tt(), IL, M, N) -> U133#(isNat(activate(M)), activate(IL), activate(M), activate(N)), U133#(tt(), IL, M, N) -> activate#(N))
(U132#(tt(), IL, M, N) -> U133#(isNat(activate(M)), activate(IL), activate(M), activate(N)), U133#(tt(), IL, M, N) -> isNatKind#(activate(M)))
(U133#(tt(), IL, M, N) -> U134#(isNatKind(activate(M)), activate(IL), activate(M), activate(N)), U134#(tt(), IL, M, N) -> U135#(isNat(activate(N)), activate(IL), activate(M), activate(N)))
(U133#(tt(), IL, M, N) -> U134#(isNatKind(activate(M)), activate(IL), activate(M), activate(N)), U134#(tt(), IL, M, N) -> isNat#(activate(N)))
(U133#(tt(), IL, M, N) -> U134#(isNatKind(activate(M)), activate(IL), activate(M), activate(N)), U134#(tt(), IL, M, N) -> activate#(M))
(U133#(tt(), IL, M, N) -> U134#(isNatKind(activate(M)), activate(IL), activate(M), activate(N)), U134#(tt(), IL, M, N) -> activate#(IL))
(U133#(tt(), IL, M, N) -> U134#(isNatKind(activate(M)), activate(IL), activate(M), activate(N)), U134#(tt(), IL, M, N) -> activate#(N))
(U135#(tt(), IL, M, N) -> U136#(isNatKind(activate(N)), activate(IL), activate(M), activate(N)), U136#(tt(), IL, M, N) -> activate#(M))
(U135#(tt(), IL, M, N) -> U136#(isNatKind(activate(N)), activate(IL), activate(M), activate(N)), U136#(tt(), IL, M, N) -> activate#(IL))
(U135#(tt(), IL, M, N) -> U136#(isNatKind(activate(N)), activate(IL), activate(M), activate(N)), U136#(tt(), IL, M, N) -> activate#(N))
(isNatIList#(V) -> isNatIListKind#(activate(V)), isNatIListKind#(n__cons(V1, V2)) -> U51#(isNatKind(activate(V1)), activate(V2)))
(isNatIList#(V) -> isNatIListKind#(activate(V)), isNatIListKind#(n__cons(V1, V2)) -> activate#(V2))
(isNatIList#(V) -> isNatIListKind#(activate(V)), isNatIListKind#(n__cons(V1, V2)) -> activate#(V1))
(isNatIList#(V) -> isNatIListKind#(activate(V)), isNatIListKind#(n__cons(V1, V2)) -> isNatKind#(activate(V1)))
(U31#(tt(), V) -> isNatIListKind#(activate(V)), isNatIListKind#(n__cons(V1, V2)) -> U51#(isNatKind(activate(V1)), activate(V2)))
(U31#(tt(), V) -> isNatIListKind#(activate(V)), isNatIListKind#(n__cons(V1, V2)) -> activate#(V2))
(U31#(tt(), V) -> isNatIListKind#(activate(V)), isNatIListKind#(n__cons(V1, V2)) -> activate#(V1))
(U31#(tt(), V) -> isNatIListKind#(activate(V)), isNatIListKind#(n__cons(V1, V2)) -> isNatKind#(activate(V1)))
(U133#(tt(), IL, M, N) -> isNatKind#(activate(M)), isNatKind#(n__s(V1)) -> activate#(V1))
(U133#(tt(), IL, M, N) -> isNatKind#(activate(M)), isNatKind#(n__s(V1)) -> isNatKind#(activate(V1)))
(U133#(tt(), IL, M, N) -> isNatKind#(activate(M)), isNatKind#(n__length(V1)) -> isNatIListKind#(activate(V1)))
(U133#(tt(), IL, M, N) -> isNatKind#(activate(M)), isNatKind#(n__length(V1)) -> activate#(V1))
(U131#(tt(), IL, M, N) -> isNatIListKind#(activate(IL)), isNatIListKind#(n__cons(V1, V2)) -> U51#(isNatKind(activate(V1)), activate(V2)))
(U131#(tt(), IL, M, N) -> isNatIListKind#(activate(IL)), isNatIListKind#(n__cons(V1, V2)) -> activate#(V2))
(U131#(tt(), IL, M, N) -> isNatIListKind#(activate(IL)), isNatIListKind#(n__cons(V1, V2)) -> activate#(V1))
(U131#(tt(), IL, M, N) -> isNatIListKind#(activate(IL)), isNatIListKind#(n__cons(V1, V2)) -> isNatKind#(activate(V1)))
(U113#(tt(), L, N) -> isNatKind#(activate(N)), isNatKind#(n__s(V1)) -> activate#(V1))
(U113#(tt(), L, N) -> isNatKind#(activate(N)), isNatKind#(n__s(V1)) -> isNatKind#(activate(V1)))
(U113#(tt(), L, N) -> isNatKind#(activate(N)), isNatKind#(n__length(V1)) -> isNatIListKind#(activate(V1)))
(U113#(tt(), L, N) -> isNatKind#(activate(N)), isNatKind#(n__length(V1)) -> activate#(V1))
(U135#(tt(), IL, M, N) -> isNatKind#(activate(N)), isNatKind#(n__s(V1)) -> activate#(V1))
(U135#(tt(), IL, M, N) -> isNatKind#(activate(N)), isNatKind#(n__s(V1)) -> isNatKind#(activate(V1)))
(U135#(tt(), IL, M, N) -> isNatKind#(activate(N)), isNatKind#(n__length(V1)) -> isNatIListKind#(activate(V1)))
(U135#(tt(), IL, M, N) -> isNatKind#(activate(N)), isNatKind#(n__length(V1)) -> activate#(V1))
(U114#(tt(), L) -> length#(activate(L)), length#(cons(N, L)) -> isNatList#(activate(L)))
(U114#(tt(), L) -> length#(activate(L)), length#(cons(N, L)) -> U111#(isNatList(activate(L)), activate(L), N))
(U114#(tt(), L) -> length#(activate(L)), length#(cons(N, L)) -> activate#(L))
(U102#(tt(), V1, V2) -> isNatIListKind#(activate(V2)), isNatIListKind#(n__cons(V1, V2)) -> U51#(isNatKind(activate(V1)), activate(V2)))
(U102#(tt(), V1, V2) -> isNatIListKind#(activate(V2)), isNatIListKind#(n__cons(V1, V2)) -> activate#(V2))
(U102#(tt(), V1, V2) -> isNatIListKind#(activate(V2)), isNatIListKind#(n__cons(V1, V2)) -> activate#(V1))
(U102#(tt(), V1, V2) -> isNatIListKind#(activate(V2)), isNatIListKind#(n__cons(V1, V2)) -> isNatKind#(activate(V1)))
(U105#(tt(), V2) -> isNatIList#(activate(V2)), isNatIList#(n__cons(V1, V2)) -> U41#(isNatKind(activate(V1)), activate(V1), activate(V2)))
(U105#(tt(), V2) -> isNatIList#(activate(V2)), isNatIList#(n__cons(V1, V2)) -> activate#(V2))
(U105#(tt(), V2) -> isNatIList#(activate(V2)), isNatIList#(n__cons(V1, V2)) -> activate#(V1))
(U105#(tt(), V2) -> isNatIList#(activate(V2)), isNatIList#(n__cons(V1, V2)) -> isNatKind#(activate(V1)))
(U105#(tt(), V2) -> isNatIList#(activate(V2)), isNatIList#(V) -> U31#(isNatIListKind(activate(V)), activate(V)))
(U105#(tt(), V2) -> isNatIList#(activate(V2)), isNatIList#(V) -> isNatIListKind#(activate(V)))
(U105#(tt(), V2) -> isNatIList#(activate(V2)), isNatIList#(V) -> activate#(V))
(U43#(tt(), V1, V2) -> isNatIListKind#(activate(V2)), isNatIListKind#(n__cons(V1, V2)) -> U51#(isNatKind(activate(V1)), activate(V2)))
(U43#(tt(), V1, V2) -> isNatIListKind#(activate(V2)), isNatIListKind#(n__cons(V1, V2)) -> activate#(V2))
(U43#(tt(), V1, V2) -> isNatIListKind#(activate(V2)), isNatIListKind#(n__cons(V1, V2)) -> activate#(V1))
(U43#(tt(), V1, V2) -> isNatIListKind#(activate(V2)), isNatIListKind#(n__cons(V1, V2)) -> isNatKind#(activate(V1)))
(U51#(tt(), V2) -> isNatIListKind#(activate(V2)), isNatIListKind#(n__cons(V1, V2)) -> U51#(isNatKind(activate(V1)), activate(V2)))
(U51#(tt(), V2) -> isNatIListKind#(activate(V2)), isNatIListKind#(n__cons(V1, V2)) -> activate#(V2))
(U51#(tt(), V2) -> isNatIListKind#(activate(V2)), isNatIListKind#(n__cons(V1, V2)) -> activate#(V1))
(U51#(tt(), V2) -> isNatIListKind#(activate(V2)), isNatIListKind#(n__cons(V1, V2)) -> isNatKind#(activate(V1)))
(U92#(tt(), V1, V2) -> isNatIListKind#(activate(V2)), isNatIListKind#(n__cons(V1, V2)) -> U51#(isNatKind(activate(V1)), activate(V2)))
(U92#(tt(), V1, V2) -> isNatIListKind#(activate(V2)), isNatIListKind#(n__cons(V1, V2)) -> activate#(V2))
(U92#(tt(), V1, V2) -> isNatIListKind#(activate(V2)), isNatIListKind#(n__cons(V1, V2)) -> activate#(V1))
(U92#(tt(), V1, V2) -> isNatIListKind#(activate(V2)), isNatIListKind#(n__cons(V1, V2)) -> isNatKind#(activate(V1)))
(U95#(tt(), V2) -> isNatList#(activate(V2)), isNatList#(n__cons(V1, V2)) -> U91#(isNatKind(activate(V1)), activate(V1), activate(V2)))
(U95#(tt(), V2) -> isNatList#(activate(V2)), isNatList#(n__cons(V1, V2)) -> activate#(V2))
(U95#(tt(), V2) -> isNatList#(activate(V2)), isNatList#(n__cons(V1, V2)) -> activate#(V1))
(U95#(tt(), V2) -> isNatList#(activate(V2)), isNatList#(n__cons(V1, V2)) -> isNatKind#(activate(V1)))
(isNatKind#(n__s(V1)) -> isNatKind#(activate(V1)), isNatKind#(n__s(V1)) -> activate#(V1))
(isNatKind#(n__s(V1)) -> isNatKind#(activate(V1)), isNatKind#(n__s(V1)) -> isNatKind#(activate(V1)))
(isNatKind#(n__s(V1)) -> isNatKind#(activate(V1)), isNatKind#(n__length(V1)) -> isNatIListKind#(activate(V1)))
(isNatKind#(n__s(V1)) -> isNatKind#(activate(V1)), isNatKind#(n__length(V1)) -> activate#(V1))
(isNatIListKind#(n__cons(V1, V2)) -> isNatKind#(activate(V1)), isNatKind#(n__s(V1)) -> activate#(V1))
(isNatIListKind#(n__cons(V1, V2)) -> isNatKind#(activate(V1)), isNatKind#(n__s(V1)) -> isNatKind#(activate(V1)))
(isNatIListKind#(n__cons(V1, V2)) -> isNatKind#(activate(V1)), isNatKind#(n__length(V1)) -> isNatIListKind#(activate(V1)))
(isNatIListKind#(n__cons(V1, V2)) -> isNatKind#(activate(V1)), isNatKind#(n__length(V1)) -> activate#(V1))
(isNat#(n__length(V1)) -> isNatIListKind#(activate(V1)), isNatIListKind#(n__cons(V1, V2)) -> U51#(isNatKind(activate(V1)), activate(V2)))
(isNat#(n__length(V1)) -> isNatIListKind#(activate(V1)), isNatIListKind#(n__cons(V1, V2)) -> activate#(V2))
(isNat#(n__length(V1)) -> isNatIListKind#(activate(V1)), isNatIListKind#(n__cons(V1, V2)) -> activate#(V1))
(isNat#(n__length(V1)) -> isNatIListKind#(activate(V1)), isNatIListKind#(n__cons(V1, V2)) -> isNatKind#(activate(V1)))
(isNatIList#(n__cons(V1, V2)) -> isNatKind#(activate(V1)), isNatKind#(n__s(V1)) -> activate#(V1))
(isNatIList#(n__cons(V1, V2)) -> isNatKind#(activate(V1)), isNatKind#(n__s(V1)) -> isNatKind#(activate(V1)))
(isNatIList#(n__cons(V1, V2)) -> isNatKind#(activate(V1)), isNatKind#(n__length(V1)) -> isNatIListKind#(activate(V1)))
(isNatIList#(n__cons(V1, V2)) -> isNatKind#(activate(V1)), isNatKind#(n__length(V1)) -> activate#(V1))
(U11#(tt(), V1) -> isNatIListKind#(activate(V1)), isNatIListKind#(n__cons(V1, V2)) -> U51#(isNatKind(activate(V1)), activate(V2)))
(U11#(tt(), V1) -> isNatIListKind#(activate(V1)), isNatIListKind#(n__cons(V1, V2)) -> activate#(V2))
(U11#(tt(), V1) -> isNatIListKind#(activate(V1)), isNatIListKind#(n__cons(V1, V2)) -> activate#(V1))
(U11#(tt(), V1) -> isNatIListKind#(activate(V1)), isNatIListKind#(n__cons(V1, V2)) -> isNatKind#(activate(V1)))
(U22#(tt(), V1) -> isNat#(activate(V1)), isNat#(n__s(V1)) -> U21#(isNatKind(activate(V1)), activate(V1)))
(U22#(tt(), V1) -> isNat#(activate(V1)), isNat#(n__s(V1)) -> activate#(V1))
(U22#(tt(), V1) -> isNat#(activate(V1)), isNat#(n__s(V1)) -> isNatKind#(activate(V1)))
(U22#(tt(), V1) -> isNat#(activate(V1)), isNat#(n__length(V1)) -> U11#(isNatIListKind(activate(V1)), activate(V1)))
(U22#(tt(), V1) -> isNat#(activate(V1)), isNat#(n__length(V1)) -> isNatIListKind#(activate(V1)))
(U22#(tt(), V1) -> isNat#(activate(V1)), isNat#(n__length(V1)) -> activate#(V1))
(U41#(tt(), V1, V2) -> isNatKind#(activate(V1)), isNatKind#(n__s(V1)) -> activate#(V1))
(U41#(tt(), V1, V2) -> isNatKind#(activate(V1)), isNatKind#(n__s(V1)) -> isNatKind#(activate(V1)))
(U41#(tt(), V1, V2) -> isNatKind#(activate(V1)), isNatKind#(n__length(V1)) -> isNatIListKind#(activate(V1)))
(U41#(tt(), V1, V2) -> isNatKind#(activate(V1)), isNatKind#(n__length(V1)) -> activate#(V1))
(U91#(tt(), V1, V2) -> isNatKind#(activate(V1)), isNatKind#(n__s(V1)) -> activate#(V1))
(U91#(tt(), V1, V2) -> isNatKind#(activate(V1)), isNatKind#(n__s(V1)) -> isNatKind#(activate(V1)))
(U91#(tt(), V1, V2) -> isNatKind#(activate(V1)), isNatKind#(n__length(V1)) -> isNatIListKind#(activate(V1)))
(U91#(tt(), V1, V2) -> isNatKind#(activate(V1)), isNatKind#(n__length(V1)) -> activate#(V1))
(activate#(n__length(X)) -> activate#(X), activate#(n__cons(X1, X2)) -> activate#(X1))
(activate#(n__length(X)) -> activate#(X), activate#(n__s(X)) -> activate#(X))
(activate#(n__length(X)) -> activate#(X), activate#(n__length(X)) -> length#(activate(X)))
(activate#(n__length(X)) -> activate#(X), activate#(n__length(X)) -> activate#(X))
(activate#(n__length(X)) -> activate#(X), activate#(n__take(X1, X2)) -> take#(activate(X1), activate(X2)))
(U102#(tt(), V1, V2) -> U103#(isNatIListKind(activate(V2)), activate(V1), activate(V2)), U103#(tt(), V1, V2) -> U104#(isNatIListKind(activate(V2)), activate(V1), activate(V2)))
(U102#(tt(), V1, V2) -> U103#(isNatIListKind(activate(V2)), activate(V1), activate(V2)), U103#(tt(), V1, V2) -> isNatIListKind#(activate(V2)))
(U102#(tt(), V1, V2) -> U103#(isNatIListKind(activate(V2)), activate(V1), activate(V2)), U103#(tt(), V1, V2) -> activate#(V2))
(U102#(tt(), V1, V2) -> U103#(isNatIListKind(activate(V2)), activate(V1), activate(V2)), U103#(tt(), V1, V2) -> activate#(V1))
(U103#(tt(), V1, V2) -> U104#(isNatIListKind(activate(V2)), activate(V1), activate(V2)), U104#(tt(), V1, V2) -> isNat#(activate(V1)))
(U103#(tt(), V1, V2) -> U104#(isNatIListKind(activate(V2)), activate(V1), activate(V2)), U104#(tt(), V1, V2) -> U105#(isNat(activate(V1)), activate(V2)))
(U103#(tt(), V1, V2) -> U104#(isNatIListKind(activate(V2)), activate(V1), activate(V2)), U104#(tt(), V1, V2) -> activate#(V2))
(U103#(tt(), V1, V2) -> U104#(isNatIListKind(activate(V2)), activate(V1), activate(V2)), U104#(tt(), V1, V2) -> activate#(V1))
(U112#(tt(), L, N) -> U113#(isNat(activate(N)), activate(L), activate(N)), U113#(tt(), L, N) -> U114#(isNatKind(activate(N)), activate(L)))
(U112#(tt(), L, N) -> U113#(isNat(activate(N)), activate(L), activate(N)), U113#(tt(), L, N) -> activate#(N))
(U112#(tt(), L, N) -> U113#(isNat(activate(N)), activate(L), activate(N)), U113#(tt(), L, N) -> activate#(L))
(U112#(tt(), L, N) -> U113#(isNat(activate(N)), activate(L), activate(N)), U113#(tt(), L, N) -> isNatKind#(activate(N)))
(isNatList#(n__cons(V1, V2)) -> U91#(isNatKind(activate(V1)), activate(V1), activate(V2)), U91#(tt(), V1, V2) -> U92#(isNatKind(activate(V1)), activate(V1), activate(V2)))
(isNatList#(n__cons(V1, V2)) -> U91#(isNatKind(activate(V1)), activate(V1), activate(V2)), U91#(tt(), V1, V2) -> activate#(V2))
(isNatList#(n__cons(V1, V2)) -> U91#(isNatKind(activate(V1)), activate(V1), activate(V2)), U91#(tt(), V1, V2) -> activate#(V1))
(isNatList#(n__cons(V1, V2)) -> U91#(isNatKind(activate(V1)), activate(V1), activate(V2)), U91#(tt(), V1, V2) -> isNatKind#(activate(V1)))
(U41#(tt(), V1, V2) -> U42#(isNatKind(activate(V1)), activate(V1), activate(V2)), U42#(tt(), V1, V2) -> U43#(isNatIListKind(activate(V2)), activate(V1), activate(V2)))
(U41#(tt(), V1, V2) -> U42#(isNatKind(activate(V1)), activate(V1), activate(V2)), U42#(tt(), V1, V2) -> isNatIListKind#(activate(V2)))
(U41#(tt(), V1, V2) -> U42#(isNatKind(activate(V1)), activate(V1), activate(V2)), U42#(tt(), V1, V2) -> activate#(V2))
(U41#(tt(), V1, V2) -> U42#(isNatKind(activate(V1)), activate(V1), activate(V2)), U42#(tt(), V1, V2) -> activate#(V1))
(U92#(tt(), V1, V2) -> U93#(isNatIListKind(activate(V2)), activate(V1), activate(V2)), U93#(tt(), V1, V2) -> U94#(isNatIListKind(activate(V2)), activate(V1), activate(V2)))
(U92#(tt(), V1, V2) -> U93#(isNatIListKind(activate(V2)), activate(V1), activate(V2)), U93#(tt(), V1, V2) -> isNatIListKind#(activate(V2)))
(U92#(tt(), V1, V2) -> U93#(isNatIListKind(activate(V2)), activate(V1), activate(V2)), U93#(tt(), V1, V2) -> activate#(V2))
(U92#(tt(), V1, V2) -> U93#(isNatIListKind(activate(V2)), activate(V1), activate(V2)), U93#(tt(), V1, V2) -> activate#(V1))
(U93#(tt(), V1, V2) -> U94#(isNatIListKind(activate(V2)), activate(V1), activate(V2)), U94#(tt(), V1, V2) -> U95#(isNat(activate(V1)), activate(V2)))
(U93#(tt(), V1, V2) -> U94#(isNatIListKind(activate(V2)), activate(V1), activate(V2)), U94#(tt(), V1, V2) -> isNat#(activate(V1)))
(U93#(tt(), V1, V2) -> U94#(isNatIListKind(activate(V2)), activate(V1), activate(V2)), U94#(tt(), V1, V2) -> activate#(V2))
(U93#(tt(), V1, V2) -> U94#(isNatIListKind(activate(V2)), activate(V1), activate(V2)), U94#(tt(), V1, V2) -> activate#(V1))
(U104#(tt(), V1, V2) -> U105#(isNat(activate(V1)), activate(V2)), U105#(tt(), V2) -> isNatIList#(activate(V2)))
(U104#(tt(), V1, V2) -> U105#(isNat(activate(V1)), activate(V2)), U105#(tt(), V2) -> activate#(V2))
(isNat#(n__s(V1)) -> U21#(isNatKind(activate(V1)), activate(V1)), U21#(tt(), V1) -> U22#(isNatKind(activate(V1)), activate(V1)))
(isNat#(n__s(V1)) -> U21#(isNatKind(activate(V1)), activate(V1)), U21#(tt(), V1) -> activate#(V1))
(isNat#(n__s(V1)) -> U21#(isNatKind(activate(V1)), activate(V1)), U21#(tt(), V1) -> isNatKind#(activate(V1)))
(U11#(tt(), V1) -> U12#(isNatIListKind(activate(V1)), activate(V1)), U12#(tt(), V1) -> isNatList#(activate(V1)))
(U11#(tt(), V1) -> U12#(isNatIListKind(activate(V1)), activate(V1)), U12#(tt(), V1) -> activate#(V1))
(U21#(tt(), V1) -> U22#(isNatKind(activate(V1)), activate(V1)), U22#(tt(), V1) -> isNat#(activate(V1)))
(U21#(tt(), V1) -> U22#(isNatKind(activate(V1)), activate(V1)), U22#(tt(), V1) -> activate#(V1))
(U44#(tt(), V1, V2) -> U45#(isNat(activate(V1)), activate(V2)), U45#(tt(), V2) -> isNatIList#(activate(V2)))
(U44#(tt(), V1, V2) -> U45#(isNat(activate(V1)), activate(V2)), U45#(tt(), V2) -> activate#(V2))
(U102#(tt(), V1, V2) -> activate#(V1), activate#(n__cons(X1, X2)) -> activate#(X1))
(U102#(tt(), V1, V2) -> activate#(V1), activate#(n__s(X)) -> activate#(X))
(U102#(tt(), V1, V2) -> activate#(V1), activate#(n__length(X)) -> length#(activate(X)))
(U102#(tt(), V1, V2) -> activate#(V1), activate#(n__length(X)) -> activate#(X))
(U102#(tt(), V1, V2) -> activate#(V1), activate#(n__take(X1, X2)) -> take#(activate(X1), activate(X2)))
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(U51#(tt(), V2) -> activate#(V2), activate#(n__cons(X1, X2)) -> activate#(X1))
(U44#(tt(), V1, V2) -> activate#(V2), activate#(n__take(X1, X2)) -> take#(activate(X1), activate(X2)))
(U44#(tt(), V1, V2) -> activate#(V2), activate#(n__length(X)) -> activate#(X))
(U44#(tt(), V1, V2) -> activate#(V2), activate#(n__length(X)) -> length#(activate(X)))
(U44#(tt(), V1, V2) -> activate#(V2), activate#(n__s(X)) -> activate#(X))
(U44#(tt(), V1, V2) -> activate#(V2), activate#(n__cons(X1, X2)) -> activate#(X1))
(U41#(tt(), V1, V2) -> activate#(V2), activate#(n__take(X1, X2)) -> take#(activate(X1), activate(X2)))
(U41#(tt(), V1, V2) -> activate#(V2), activate#(n__length(X)) -> activate#(X))
(U41#(tt(), V1, V2) -> activate#(V2), activate#(n__length(X)) -> length#(activate(X)))
(U41#(tt(), V1, V2) -> activate#(V2), activate#(n__s(X)) -> activate#(X))
(U41#(tt(), V1, V2) -> activate#(V2), activate#(n__cons(X1, X2)) -> activate#(X1))
(isNatList#(n__cons(V1, V2)) -> activate#(V2), activate#(n__take(X1, X2)) -> take#(activate(X1), activate(X2)))
(isNatList#(n__cons(V1, V2)) -> activate#(V2), activate#(n__length(X)) -> activate#(X))
(isNatList#(n__cons(V1, V2)) -> activate#(V2), activate#(n__length(X)) -> length#(activate(X)))
(isNatList#(n__cons(V1, V2)) -> activate#(V2), activate#(n__s(X)) -> activate#(X))
(isNatList#(n__cons(V1, V2)) -> activate#(V2), activate#(n__cons(X1, X2)) -> activate#(X1))
(U105#(tt(), V2) -> activate#(V2), activate#(n__take(X1, X2)) -> take#(activate(X1), activate(X2)))
(U105#(tt(), V2) -> activate#(V2), activate#(n__length(X)) -> activate#(X))
(U105#(tt(), V2) -> activate#(V2), activate#(n__length(X)) -> length#(activate(X)))
(U105#(tt(), V2) -> activate#(V2), activate#(n__s(X)) -> activate#(X))
(U105#(tt(), V2) -> activate#(V2), activate#(n__cons(X1, X2)) -> activate#(X1))
(isNatIListKind#(n__cons(V1, V2)) -> activate#(V2), activate#(n__take(X1, X2)) -> take#(activate(X1), activate(X2)))
(isNatIListKind#(n__cons(V1, V2)) -> activate#(V2), activate#(n__length(X)) -> activate#(X))
(isNatIListKind#(n__cons(V1, V2)) -> activate#(V2), activate#(n__length(X)) -> length#(activate(X)))
(isNatIListKind#(n__cons(V1, V2)) -> activate#(V2), activate#(n__s(X)) -> activate#(X))
(isNatIListKind#(n__cons(V1, V2)) -> activate#(V2), activate#(n__cons(X1, X2)) -> activate#(X1))
(U101#(tt(), V1, V2) -> activate#(V2), activate#(n__take(X1, X2)) -> take#(activate(X1), activate(X2)))
(U101#(tt(), V1, V2) -> activate#(V2), activate#(n__length(X)) -> activate#(X))
(U101#(tt(), V1, V2) -> activate#(V2), activate#(n__length(X)) -> length#(activate(X)))
(U101#(tt(), V1, V2) -> activate#(V2), activate#(n__s(X)) -> activate#(X))
(U101#(tt(), V1, V2) -> activate#(V2), activate#(n__cons(X1, X2)) -> activate#(X1))
(U31#(tt(), V) -> activate#(V), activate#(n__take(X1, X2)) -> take#(activate(X1), activate(X2)))
(U31#(tt(), V) -> activate#(V), activate#(n__length(X)) -> activate#(X))
(U31#(tt(), V) -> activate#(V), activate#(n__length(X)) -> length#(activate(X)))
(U31#(tt(), V) -> activate#(V), activate#(n__s(X)) -> activate#(X))
(U31#(tt(), V) -> activate#(V), activate#(n__cons(X1, X2)) -> activate#(X1))
(isNatIList#(V) -> activate#(V), activate#(n__take(X1, X2)) -> take#(activate(X1), activate(X2)))
(isNatIList#(V) -> activate#(V), activate#(n__length(X)) -> activate#(X))
(isNatIList#(V) -> activate#(V), activate#(n__length(X)) -> length#(activate(X)))
(isNatIList#(V) -> activate#(V), activate#(n__s(X)) -> activate#(X))
(isNatIList#(V) -> activate#(V), activate#(n__cons(X1, X2)) -> activate#(X1))
(U135#(tt(), IL, M, N) -> activate#(IL), activate#(n__take(X1, X2)) -> take#(activate(X1), activate(X2)))
(U135#(tt(), IL, M, N) -> activate#(IL), activate#(n__length(X)) -> activate#(X))
(U135#(tt(), IL, M, N) -> activate#(IL), activate#(n__length(X)) -> length#(activate(X)))
(U135#(tt(), IL, M, N) -> activate#(IL), activate#(n__s(X)) -> activate#(X))
(U135#(tt(), IL, M, N) -> activate#(IL), activate#(n__cons(X1, X2)) -> activate#(X1))
(U133#(tt(), IL, M, N) -> activate#(IL), activate#(n__take(X1, X2)) -> take#(activate(X1), activate(X2)))
(U133#(tt(), IL, M, N) -> activate#(IL), activate#(n__length(X)) -> activate#(X))
(U133#(tt(), IL, M, N) -> activate#(IL), activate#(n__length(X)) -> length#(activate(X)))
(U133#(tt(), IL, M, N) -> activate#(IL), activate#(n__s(X)) -> activate#(X))
(U133#(tt(), IL, M, N) -> activate#(IL), activate#(n__cons(X1, X2)) -> activate#(X1))
(U132#(tt(), IL, M, N) -> activate#(IL), activate#(n__take(X1, X2)) -> take#(activate(X1), activate(X2)))
(U132#(tt(), IL, M, N) -> activate#(IL), activate#(n__length(X)) -> activate#(X))
(U132#(tt(), IL, M, N) -> activate#(IL), activate#(n__length(X)) -> length#(activate(X)))
(U132#(tt(), IL, M, N) -> activate#(IL), activate#(n__s(X)) -> activate#(X))
(U132#(tt(), IL, M, N) -> activate#(IL), activate#(n__cons(X1, X2)) -> activate#(X1))
(length#(cons(N, L)) -> activate#(L), activate#(n__take(X1, X2)) -> take#(activate(X1), activate(X2)))
(length#(cons(N, L)) -> activate#(L), activate#(n__length(X)) -> activate#(X))
(length#(cons(N, L)) -> activate#(L), activate#(n__length(X)) -> length#(activate(X)))
(length#(cons(N, L)) -> activate#(L), activate#(n__s(X)) -> activate#(X))
(length#(cons(N, L)) -> activate#(L), activate#(n__cons(X1, X2)) -> activate#(X1))
(U113#(tt(), L, N) -> activate#(L), activate#(n__take(X1, X2)) -> take#(activate(X1), activate(X2)))
(U113#(tt(), L, N) -> activate#(L), activate#(n__length(X)) -> activate#(X))
(U113#(tt(), L, N) -> activate#(L), activate#(n__length(X)) -> length#(activate(X)))
(U113#(tt(), L, N) -> activate#(L), activate#(n__s(X)) -> activate#(X))
(U113#(tt(), L, N) -> activate#(L), activate#(n__cons(X1, X2)) -> activate#(X1))
(U112#(tt(), L, N) -> activate#(L), activate#(n__take(X1, X2)) -> take#(activate(X1), activate(X2)))
(U112#(tt(), L, N) -> activate#(L), activate#(n__length(X)) -> activate#(X))
(U112#(tt(), L, N) -> activate#(L), activate#(n__length(X)) -> length#(activate(X)))
(U112#(tt(), L, N) -> activate#(L), activate#(n__s(X)) -> activate#(X))
(U112#(tt(), L, N) -> activate#(L), activate#(n__cons(X1, X2)) -> activate#(X1))
(U93#(tt(), V1, V2) -> activate#(V1), activate#(n__take(X1, X2)) -> take#(activate(X1), activate(X2)))
(U93#(tt(), V1, V2) -> activate#(V1), activate#(n__length(X)) -> activate#(X))
(U93#(tt(), V1, V2) -> activate#(V1), activate#(n__length(X)) -> length#(activate(X)))
(U93#(tt(), V1, V2) -> activate#(V1), activate#(n__s(X)) -> activate#(X))
(U93#(tt(), V1, V2) -> activate#(V1), activate#(n__cons(X1, X2)) -> activate#(X1))
(U92#(tt(), V1, V2) -> activate#(V1), activate#(n__take(X1, X2)) -> take#(activate(X1), activate(X2)))
(U92#(tt(), V1, V2) -> activate#(V1), activate#(n__length(X)) -> activate#(X))
(U92#(tt(), V1, V2) -> activate#(V1), activate#(n__length(X)) -> length#(activate(X)))
(U92#(tt(), V1, V2) -> activate#(V1), activate#(n__s(X)) -> activate#(X))
(U92#(tt(), V1, V2) -> activate#(V1), activate#(n__cons(X1, X2)) -> activate#(X1))
(U43#(tt(), V1, V2) -> activate#(V1), activate#(n__take(X1, X2)) -> take#(activate(X1), activate(X2)))
(U43#(tt(), V1, V2) -> activate#(V1), activate#(n__length(X)) -> activate#(X))
(U43#(tt(), V1, V2) -> activate#(V1), activate#(n__length(X)) -> length#(activate(X)))
(U43#(tt(), V1, V2) -> activate#(V1), activate#(n__s(X)) -> activate#(X))
(U43#(tt(), V1, V2) -> activate#(V1), activate#(n__cons(X1, X2)) -> activate#(X1))
(U42#(tt(), V1, V2) -> activate#(V1), activate#(n__take(X1, X2)) -> take#(activate(X1), activate(X2)))
(U42#(tt(), V1, V2) -> activate#(V1), activate#(n__length(X)) -> activate#(X))
(U42#(tt(), V1, V2) -> activate#(V1), activate#(n__length(X)) -> length#(activate(X)))
(U42#(tt(), V1, V2) -> activate#(V1), activate#(n__s(X)) -> activate#(X))
(U42#(tt(), V1, V2) -> activate#(V1), activate#(n__cons(X1, X2)) -> activate#(X1))
(U22#(tt(), V1) -> activate#(V1), activate#(n__take(X1, X2)) -> take#(activate(X1), activate(X2)))
(U22#(tt(), V1) -> activate#(V1), activate#(n__length(X)) -> activate#(X))
(U22#(tt(), V1) -> activate#(V1), activate#(n__length(X)) -> length#(activate(X)))
(U22#(tt(), V1) -> activate#(V1), activate#(n__s(X)) -> activate#(X))
(U22#(tt(), V1) -> activate#(V1), activate#(n__cons(X1, X2)) -> activate#(X1))
(U11#(tt(), V1) -> activate#(V1), activate#(n__take(X1, X2)) -> take#(activate(X1), activate(X2)))
(U11#(tt(), V1) -> activate#(V1), activate#(n__length(X)) -> activate#(X))
(U11#(tt(), V1) -> activate#(V1), activate#(n__length(X)) -> length#(activate(X)))
(U11#(tt(), V1) -> activate#(V1), activate#(n__s(X)) -> activate#(X))
(U11#(tt(), V1) -> activate#(V1), activate#(n__cons(X1, X2)) -> activate#(X1))
(isNatIList#(n__cons(V1, V2)) -> activate#(V1), activate#(n__take(X1, X2)) -> take#(activate(X1), activate(X2)))
(isNatIList#(n__cons(V1, V2)) -> activate#(V1), activate#(n__length(X)) -> activate#(X))
(isNatIList#(n__cons(V1, V2)) -> activate#(V1), activate#(n__length(X)) -> length#(activate(X)))
(isNatIList#(n__cons(V1, V2)) -> activate#(V1), activate#(n__s(X)) -> activate#(X))
(isNatIList#(n__cons(V1, V2)) -> activate#(V1), activate#(n__cons(X1, X2)) -> activate#(X1))
(isNat#(n__length(V1)) -> activate#(V1), activate#(n__take(X1, X2)) -> take#(activate(X1), activate(X2)))
(isNat#(n__length(V1)) -> activate#(V1), activate#(n__length(X)) -> activate#(X))
(isNat#(n__length(V1)) -> activate#(V1), activate#(n__length(X)) -> length#(activate(X)))
(isNat#(n__length(V1)) -> activate#(V1), activate#(n__s(X)) -> activate#(X))
(isNat#(n__length(V1)) -> activate#(V1), activate#(n__cons(X1, X2)) -> activate#(X1))
(isNatIListKind#(n__cons(V1, V2)) -> activate#(V1), activate#(n__take(X1, X2)) -> take#(activate(X1), activate(X2)))
(isNatIListKind#(n__cons(V1, V2)) -> activate#(V1), activate#(n__length(X)) -> activate#(X))
(isNatIListKind#(n__cons(V1, V2)) -> activate#(V1), activate#(n__length(X)) -> length#(activate(X)))
(isNatIListKind#(n__cons(V1, V2)) -> activate#(V1), activate#(n__s(X)) -> activate#(X))
(isNatIListKind#(n__cons(V1, V2)) -> activate#(V1), activate#(n__cons(X1, X2)) -> activate#(X1))
(U101#(tt(), V1, V2) -> activate#(V1), activate#(n__take(X1, X2)) -> take#(activate(X1), activate(X2)))
(U101#(tt(), V1, V2) -> activate#(V1), activate#(n__length(X)) -> activate#(X))
(U101#(tt(), V1, V2) -> activate#(V1), activate#(n__length(X)) -> length#(activate(X)))
(U101#(tt(), V1, V2) -> activate#(V1), activate#(n__s(X)) -> activate#(X))
(U101#(tt(), V1, V2) -> activate#(V1), activate#(n__cons(X1, X2)) -> activate#(X1))
(isNatKind#(n__length(V1)) -> activate#(V1), activate#(n__take(X1, X2)) -> take#(activate(X1), activate(X2)))
(isNatKind#(n__length(V1)) -> activate#(V1), activate#(n__length(X)) -> activate#(X))
(isNatKind#(n__length(V1)) -> activate#(V1), activate#(n__length(X)) -> length#(activate(X)))
(isNatKind#(n__length(V1)) -> activate#(V1), activate#(n__s(X)) -> activate#(X))
(isNatKind#(n__length(V1)) -> activate#(V1), activate#(n__cons(X1, X2)) -> activate#(X1))
(U94#(tt(), V1, V2) -> U95#(isNat(activate(V1)), activate(V2)), U95#(tt(), V2) -> activate#(V2))
(U94#(tt(), V1, V2) -> U95#(isNat(activate(V1)), activate(V2)), U95#(tt(), V2) -> isNatList#(activate(V2)))
(U31#(tt(), V) -> U32#(isNatIListKind(activate(V)), activate(V)), U32#(tt(), V) -> activate#(V))
(U31#(tt(), V) -> U32#(isNatIListKind(activate(V)), activate(V)), U32#(tt(), V) -> isNatList#(activate(V)))
(U113#(tt(), L, N) -> U114#(isNatKind(activate(N)), activate(L)), U114#(tt(), L) -> activate#(L))
(U113#(tt(), L, N) -> U114#(isNatKind(activate(N)), activate(L)), U114#(tt(), L) -> length#(activate(L)))
(isNatIList#(V) -> U31#(isNatIListKind(activate(V)), activate(V)), U31#(tt(), V) -> activate#(V))
(isNatIList#(V) -> U31#(isNatIListKind(activate(V)), activate(V)), U31#(tt(), V) -> isNatIListKind#(activate(V)))
(isNatIList#(V) -> U31#(isNatIListKind(activate(V)), activate(V)), U31#(tt(), V) -> U32#(isNatIListKind(activate(V)), activate(V)))
(isNat#(n__length(V1)) -> U11#(isNatIListKind(activate(V1)), activate(V1)), U11#(tt(), V1) -> activate#(V1))
(isNat#(n__length(V1)) -> U11#(isNatIListKind(activate(V1)), activate(V1)), U11#(tt(), V1) -> isNatIListKind#(activate(V1)))
(isNat#(n__length(V1)) -> U11#(isNatIListKind(activate(V1)), activate(V1)), U11#(tt(), V1) -> U12#(isNatIListKind(activate(V1)), activate(V1)))
(isNatIListKind#(n__cons(V1, V2)) -> U51#(isNatKind(activate(V1)), activate(V2)), U51#(tt(), V2) -> activate#(V2))
(isNatIListKind#(n__cons(V1, V2)) -> U51#(isNatKind(activate(V1)), activate(V2)), U51#(tt(), V2) -> isNatIListKind#(activate(V2)))
(length#(cons(N, L)) -> U111#(isNatList(activate(L)), activate(L), N), U111#(tt(), L, N) -> activate#(L))
(length#(cons(N, L)) -> U111#(isNatList(activate(L)), activate(L), N), U111#(tt(), L, N) -> activate#(N))
(length#(cons(N, L)) -> U111#(isNatList(activate(L)), activate(L), N), U111#(tt(), L, N) -> isNatIListKind#(activate(L)))
(length#(cons(N, L)) -> U111#(isNatList(activate(L)), activate(L), N), U111#(tt(), L, N) -> U112#(isNatIListKind(activate(L)), activate(L), activate(N)))
(U91#(tt(), V1, V2) -> U92#(isNatKind(activate(V1)), activate(V1), activate(V2)), U92#(tt(), V1, V2) -> activate#(V1))
(U91#(tt(), V1, V2) -> U92#(isNatKind(activate(V1)), activate(V1), activate(V2)), U92#(tt(), V1, V2) -> activate#(V2))
(U91#(tt(), V1, V2) -> U92#(isNatKind(activate(V1)), activate(V1), activate(V2)), U92#(tt(), V1, V2) -> isNatIListKind#(activate(V2)))
(U91#(tt(), V1, V2) -> U92#(isNatKind(activate(V1)), activate(V1), activate(V2)), U92#(tt(), V1, V2) -> U93#(isNatIListKind(activate(V2)), activate(V1), activate(V2)))
(U43#(tt(), V1, V2) -> U44#(isNatIListKind(activate(V2)), activate(V1), activate(V2)), U44#(tt(), V1, V2) -> activate#(V1))
(U43#(tt(), V1, V2) -> U44#(isNatIListKind(activate(V2)), activate(V1), activate(V2)), U44#(tt(), V1, V2) -> activate#(V2))
(U43#(tt(), V1, V2) -> U44#(isNatIListKind(activate(V2)), activate(V1), activate(V2)), U44#(tt(), V1, V2) -> isNat#(activate(V1)))
(U43#(tt(), V1, V2) -> U44#(isNatIListKind(activate(V2)), activate(V1), activate(V2)), U44#(tt(), V1, V2) -> U45#(isNat(activate(V1)), activate(V2)))
(U42#(tt(), V1, V2) -> U43#(isNatIListKind(activate(V2)), activate(V1), activate(V2)), U43#(tt(), V1, V2) -> activate#(V1))
(U42#(tt(), V1, V2) -> U43#(isNatIListKind(activate(V2)), activate(V1), activate(V2)), U43#(tt(), V1, V2) -> activate#(V2))
(U42#(tt(), V1, V2) -> U43#(isNatIListKind(activate(V2)), activate(V1), activate(V2)), U43#(tt(), V1, V2) -> isNatIListKind#(activate(V2)))
(U42#(tt(), V1, V2) -> U43#(isNatIListKind(activate(V2)), activate(V1), activate(V2)), U43#(tt(), V1, V2) -> U44#(isNatIListKind(activate(V2)), activate(V1), activate(V2)))
(U111#(tt(), L, N) -> U112#(isNatIListKind(activate(L)), activate(L), activate(N)), U112#(tt(), L, N) -> activate#(L))
(U111#(tt(), L, N) -> U112#(isNatIListKind(activate(L)), activate(L), activate(N)), U112#(tt(), L, N) -> activate#(N))
(U111#(tt(), L, N) -> U112#(isNatIListKind(activate(L)), activate(L), activate(N)), U112#(tt(), L, N) -> isNat#(activate(N)))
(U111#(tt(), L, N) -> U112#(isNatIListKind(activate(L)), activate(L), activate(N)), U112#(tt(), L, N) -> U113#(isNat(activate(N)), activate(L), activate(N)))
(isNatIList#(n__cons(V1, V2)) -> U41#(isNatKind(activate(V1)), activate(V1), activate(V2)), U41#(tt(), V1, V2) -> isNatKind#(activate(V1)))
(isNatIList#(n__cons(V1, V2)) -> U41#(isNatKind(activate(V1)), activate(V1), activate(V2)), U41#(tt(), V1, V2) -> activate#(V1))
(isNatIList#(n__cons(V1, V2)) -> U41#(isNatKind(activate(V1)), activate(V1), activate(V2)), U41#(tt(), V1, V2) -> activate#(V2))
(isNatIList#(n__cons(V1, V2)) -> U41#(isNatKind(activate(V1)), activate(V1), activate(V2)), U41#(tt(), V1, V2) -> U42#(isNatKind(activate(V1)), activate(V1), activate(V2)))
(U101#(tt(), V1, V2) -> U102#(isNatKind(activate(V1)), activate(V1), activate(V2)), U102#(tt(), V1, V2) -> activate#(V1))
(U101#(tt(), V1, V2) -> U102#(isNatKind(activate(V1)), activate(V1), activate(V2)), U102#(tt(), V1, V2) -> activate#(V2))
(U101#(tt(), V1, V2) -> U102#(isNatKind(activate(V1)), activate(V1), activate(V2)), U102#(tt(), V1, V2) -> U103#(isNatIListKind(activate(V2)), activate(V1), activate(V2)))
(U101#(tt(), V1, V2) -> U102#(isNatKind(activate(V1)), activate(V1), activate(V2)), U102#(tt(), V1, V2) -> isNatIListKind#(activate(V2)))
(activate#(n__s(X)) -> activate#(X), activate#(n__take(X1, X2)) -> take#(activate(X1), activate(X2)))
(activate#(n__s(X)) -> activate#(X), activate#(n__length(X)) -> activate#(X))
(activate#(n__s(X)) -> activate#(X), activate#(n__length(X)) -> length#(activate(X)))
(activate#(n__s(X)) -> activate#(X), activate#(n__s(X)) -> activate#(X))
(activate#(n__s(X)) -> activate#(X), activate#(n__cons(X1, X2)) -> activate#(X1))
(U94#(tt(), V1, V2) -> isNat#(activate(V1)), isNat#(n__length(V1)) -> activate#(V1))
(U94#(tt(), V1, V2) -> isNat#(activate(V1)), isNat#(n__length(V1)) -> isNatIListKind#(activate(V1)))
(U94#(tt(), V1, V2) -> isNat#(activate(V1)), isNat#(n__length(V1)) -> U11#(isNatIListKind(activate(V1)), activate(V1)))
(U94#(tt(), V1, V2) -> isNat#(activate(V1)), isNat#(n__s(V1)) -> isNatKind#(activate(V1)))
(U94#(tt(), V1, V2) -> isNat#(activate(V1)), isNat#(n__s(V1)) -> activate#(V1))
(U94#(tt(), V1, V2) -> isNat#(activate(V1)), isNat#(n__s(V1)) -> U21#(isNatKind(activate(V1)), activate(V1)))
(U44#(tt(), V1, V2) -> isNat#(activate(V1)), isNat#(n__length(V1)) -> activate#(V1))
(U44#(tt(), V1, V2) -> isNat#(activate(V1)), isNat#(n__length(V1)) -> isNatIListKind#(activate(V1)))
(U44#(tt(), V1, V2) -> isNat#(activate(V1)), isNat#(n__length(V1)) -> U11#(isNatIListKind(activate(V1)), activate(V1)))
(U44#(tt(), V1, V2) -> isNat#(activate(V1)), isNat#(n__s(V1)) -> isNatKind#(activate(V1)))
(U44#(tt(), V1, V2) -> isNat#(activate(V1)), isNat#(n__s(V1)) -> activate#(V1))
(U44#(tt(), V1, V2) -> isNat#(activate(V1)), isNat#(n__s(V1)) -> U21#(isNatKind(activate(V1)), activate(V1)))
(U21#(tt(), V1) -> isNatKind#(activate(V1)), isNatKind#(n__length(V1)) -> activate#(V1))
(U21#(tt(), V1) -> isNatKind#(activate(V1)), isNatKind#(n__length(V1)) -> isNatIListKind#(activate(V1)))
(U21#(tt(), V1) -> isNatKind#(activate(V1)), isNatKind#(n__s(V1)) -> isNatKind#(activate(V1)))
(U21#(tt(), V1) -> isNatKind#(activate(V1)), isNatKind#(n__s(V1)) -> activate#(V1))
(isNatList#(n__cons(V1, V2)) -> isNatKind#(activate(V1)), isNatKind#(n__length(V1)) -> activate#(V1))
(isNatList#(n__cons(V1, V2)) -> isNatKind#(activate(V1)), isNatKind#(n__length(V1)) -> isNatIListKind#(activate(V1)))
(isNatList#(n__cons(V1, V2)) -> isNatKind#(activate(V1)), isNatKind#(n__s(V1)) -> isNatKind#(activate(V1)))
(isNatList#(n__cons(V1, V2)) -> isNatKind#(activate(V1)), isNatKind#(n__s(V1)) -> activate#(V1))
(U12#(tt(), V1) -> isNatList#(activate(V1)), isNatList#(n__cons(V1, V2)) -> isNatKind#(activate(V1)))
(U12#(tt(), V1) -> isNatList#(activate(V1)), isNatList#(n__cons(V1, V2)) -> activate#(V1))
(U12#(tt(), V1) -> isNatList#(activate(V1)), isNatList#(n__cons(V1, V2)) -> activate#(V2))
(U12#(tt(), V1) -> isNatList#(activate(V1)), isNatList#(n__cons(V1, V2)) -> U91#(isNatKind(activate(V1)), activate(V1), activate(V2)))
(isNat#(n__s(V1)) -> isNatKind#(activate(V1)), isNatKind#(n__length(V1)) -> activate#(V1))
(isNat#(n__s(V1)) -> isNatKind#(activate(V1)), isNatKind#(n__length(V1)) -> isNatIListKind#(activate(V1)))
(isNat#(n__s(V1)) -> isNatKind#(activate(V1)), isNatKind#(n__s(V1)) -> isNatKind#(activate(V1)))
(isNat#(n__s(V1)) -> isNatKind#(activate(V1)), isNatKind#(n__s(V1)) -> activate#(V1))
(U104#(tt(), V1, V2) -> isNat#(activate(V1)), isNat#(n__length(V1)) -> activate#(V1))
(U104#(tt(), V1, V2) -> isNat#(activate(V1)), isNat#(n__length(V1)) -> isNatIListKind#(activate(V1)))
(U104#(tt(), V1, V2) -> isNat#(activate(V1)), isNat#(n__length(V1)) -> U11#(isNatIListKind(activate(V1)), activate(V1)))
(U104#(tt(), V1, V2) -> isNat#(activate(V1)), isNat#(n__s(V1)) -> isNatKind#(activate(V1)))
(U104#(tt(), V1, V2) -> isNat#(activate(V1)), isNat#(n__s(V1)) -> activate#(V1))
(U104#(tt(), V1, V2) -> isNat#(activate(V1)), isNat#(n__s(V1)) -> U21#(isNatKind(activate(V1)), activate(V1)))
(U101#(tt(), V1, V2) -> isNatKind#(activate(V1)), isNatKind#(n__length(V1)) -> activate#(V1))
(U101#(tt(), V1, V2) -> isNatKind#(activate(V1)), isNatKind#(n__length(V1)) -> isNatIListKind#(activate(V1)))
(U101#(tt(), V1, V2) -> isNatKind#(activate(V1)), isNatKind#(n__s(V1)) -> isNatKind#(activate(V1)))
(U101#(tt(), V1, V2) -> isNatKind#(activate(V1)), isNatKind#(n__s(V1)) -> activate#(V1))
(isNatKind#(n__length(V1)) -> isNatIListKind#(activate(V1)), isNatIListKind#(n__cons(V1, V2)) -> isNatKind#(activate(V1)))
(isNatKind#(n__length(V1)) -> isNatIListKind#(activate(V1)), isNatIListKind#(n__cons(V1, V2)) -> activate#(V1))
(isNatKind#(n__length(V1)) -> isNatIListKind#(activate(V1)), isNatIListKind#(n__cons(V1, V2)) -> activate#(V2))
(isNatKind#(n__length(V1)) -> isNatIListKind#(activate(V1)), isNatIListKind#(n__cons(V1, V2)) -> U51#(isNatKind(activate(V1)), activate(V2)))
(U93#(tt(), V1, V2) -> isNatIListKind#(activate(V2)), isNatIListKind#(n__cons(V1, V2)) -> isNatKind#(activate(V1)))
(U93#(tt(), V1, V2) -> isNatIListKind#(activate(V2)), isNatIListKind#(n__cons(V1, V2)) -> activate#(V1))
(U93#(tt(), V1, V2) -> isNatIListKind#(activate(V2)), isNatIListKind#(n__cons(V1, V2)) -> activate#(V2))
(U93#(tt(), V1, V2) -> isNatIListKind#(activate(V2)), isNatIListKind#(n__cons(V1, V2)) -> U51#(isNatKind(activate(V1)), activate(V2)))
(U61#(tt(), V2) -> isNatIListKind#(activate(V2)), isNatIListKind#(n__cons(V1, V2)) -> isNatKind#(activate(V1)))
(U61#(tt(), V2) -> isNatIListKind#(activate(V2)), isNatIListKind#(n__cons(V1, V2)) -> activate#(V1))
(U61#(tt(), V2) -> isNatIListKind#(activate(V2)), isNatIListKind#(n__cons(V1, V2)) -> activate#(V2))
(U61#(tt(), V2) -> isNatIListKind#(activate(V2)), isNatIListKind#(n__cons(V1, V2)) -> U51#(isNatKind(activate(V1)), activate(V2)))
(U45#(tt(), V2) -> isNatIList#(activate(V2)), isNatIList#(V) -> activate#(V))
(U45#(tt(), V2) -> isNatIList#(activate(V2)), isNatIList#(V) -> isNatIListKind#(activate(V)))
(U45#(tt(), V2) -> isNatIList#(activate(V2)), isNatIList#(V) -> U31#(isNatIListKind(activate(V)), activate(V)))
(U45#(tt(), V2) -> isNatIList#(activate(V2)), isNatIList#(n__cons(V1, V2)) -> isNatKind#(activate(V1)))
(U45#(tt(), V2) -> isNatIList#(activate(V2)), isNatIList#(n__cons(V1, V2)) -> activate#(V1))
(U45#(tt(), V2) -> isNatIList#(activate(V2)), isNatIList#(n__cons(V1, V2)) -> activate#(V2))
(U45#(tt(), V2) -> isNatIList#(activate(V2)), isNatIList#(n__cons(V1, V2)) -> U41#(isNatKind(activate(V1)), activate(V1), activate(V2)))
(U42#(tt(), V1, V2) -> isNatIListKind#(activate(V2)), isNatIListKind#(n__cons(V1, V2)) -> isNatKind#(activate(V1)))
(U42#(tt(), V1, V2) -> isNatIListKind#(activate(V2)), isNatIListKind#(n__cons(V1, V2)) -> activate#(V1))
(U42#(tt(), V1, V2) -> isNatIListKind#(activate(V2)), isNatIListKind#(n__cons(V1, V2)) -> activate#(V2))
(U42#(tt(), V1, V2) -> isNatIListKind#(activate(V2)), isNatIListKind#(n__cons(V1, V2)) -> U51#(isNatKind(activate(V1)), activate(V2)))
(U103#(tt(), V1, V2) -> isNatIListKind#(activate(V2)), isNatIListKind#(n__cons(V1, V2)) -> isNatKind#(activate(V1)))
(U103#(tt(), V1, V2) -> isNatIListKind#(activate(V2)), isNatIListKind#(n__cons(V1, V2)) -> activate#(V1))
(U103#(tt(), V1, V2) -> isNatIListKind#(activate(V2)), isNatIListKind#(n__cons(V1, V2)) -> activate#(V2))
(U103#(tt(), V1, V2) -> isNatIListKind#(activate(V2)), isNatIListKind#(n__cons(V1, V2)) -> U51#(isNatKind(activate(V1)), activate(V2)))
(length#(cons(N, L)) -> isNatList#(activate(L)), isNatList#(n__cons(V1, V2)) -> isNatKind#(activate(V1)))
(length#(cons(N, L)) -> isNatList#(activate(L)), isNatList#(n__cons(V1, V2)) -> activate#(V1))
(length#(cons(N, L)) -> isNatList#(activate(L)), isNatList#(n__cons(V1, V2)) -> activate#(V2))
(length#(cons(N, L)) -> isNatList#(activate(L)), isNatList#(n__cons(V1, V2)) -> U91#(isNatKind(activate(V1)), activate(V1), activate(V2)))
(U111#(tt(), L, N) -> isNatIListKind#(activate(L)), isNatIListKind#(n__cons(V1, V2)) -> isNatKind#(activate(V1)))
(U111#(tt(), L, N) -> isNatIListKind#(activate(L)), isNatIListKind#(n__cons(V1, V2)) -> activate#(V1))
(U111#(tt(), L, N) -> isNatIListKind#(activate(L)), isNatIListKind#(n__cons(V1, V2)) -> activate#(V2))
(U111#(tt(), L, N) -> isNatIListKind#(activate(L)), isNatIListKind#(n__cons(V1, V2)) -> U51#(isNatKind(activate(V1)), activate(V2)))
(U134#(tt(), IL, M, N) -> isNat#(activate(N)), isNat#(n__length(V1)) -> activate#(V1))
(U134#(tt(), IL, M, N) -> isNat#(activate(N)), isNat#(n__length(V1)) -> isNatIListKind#(activate(V1)))
(U134#(tt(), IL, M, N) -> isNat#(activate(N)), isNat#(n__length(V1)) -> U11#(isNatIListKind(activate(V1)), activate(V1)))
(U134#(tt(), IL, M, N) -> isNat#(activate(N)), isNat#(n__s(V1)) -> isNatKind#(activate(V1)))
(U134#(tt(), IL, M, N) -> isNat#(activate(N)), isNat#(n__s(V1)) -> activate#(V1))
(U134#(tt(), IL, M, N) -> isNat#(activate(N)), isNat#(n__s(V1)) -> U21#(isNatKind(activate(V1)), activate(V1)))
(U112#(tt(), L, N) -> isNat#(activate(N)), isNat#(n__length(V1)) -> activate#(V1))
(U112#(tt(), L, N) -> isNat#(activate(N)), isNat#(n__length(V1)) -> isNatIListKind#(activate(V1)))
(U112#(tt(), L, N) -> isNat#(activate(N)), isNat#(n__length(V1)) -> U11#(isNatIListKind(activate(V1)), activate(V1)))
(U112#(tt(), L, N) -> isNat#(activate(N)), isNat#(n__s(V1)) -> isNatKind#(activate(V1)))
(U112#(tt(), L, N) -> isNat#(activate(N)), isNat#(n__s(V1)) -> activate#(V1))
(U112#(tt(), L, N) -> isNat#(activate(N)), isNat#(n__s(V1)) -> U21#(isNatKind(activate(V1)), activate(V1)))
(U121#(tt(), IL) -> isNatIListKind#(activate(IL)), isNatIListKind#(n__cons(V1, V2)) -> isNatKind#(activate(V1)))
(U121#(tt(), IL) -> isNatIListKind#(activate(IL)), isNatIListKind#(n__cons(V1, V2)) -> activate#(V1))
(U121#(tt(), IL) -> isNatIListKind#(activate(IL)), isNatIListKind#(n__cons(V1, V2)) -> activate#(V2))
(U121#(tt(), IL) -> isNatIListKind#(activate(IL)), isNatIListKind#(n__cons(V1, V2)) -> U51#(isNatKind(activate(V1)), activate(V2)))
(U132#(tt(), IL, M, N) -> isNat#(activate(M)), isNat#(n__length(V1)) -> activate#(V1))
(U132#(tt(), IL, M, N) -> isNat#(activate(M)), isNat#(n__length(V1)) -> isNatIListKind#(activate(V1)))
(U132#(tt(), IL, M, N) -> isNat#(activate(M)), isNat#(n__length(V1)) -> U11#(isNatIListKind(activate(V1)), activate(V1)))
(U132#(tt(), IL, M, N) -> isNat#(activate(M)), isNat#(n__s(V1)) -> isNatKind#(activate(V1)))
(U132#(tt(), IL, M, N) -> isNat#(activate(M)), isNat#(n__s(V1)) -> activate#(V1))
(U132#(tt(), IL, M, N) -> isNat#(activate(M)), isNat#(n__s(V1)) -> U21#(isNatKind(activate(V1)), activate(V1)))
(U32#(tt(), V) -> isNatList#(activate(V)), isNatList#(n__cons(V1, V2)) -> isNatKind#(activate(V1)))
(U32#(tt(), V) -> isNatList#(activate(V)), isNatList#(n__cons(V1, V2)) -> activate#(V1))
(U32#(tt(), V) -> isNatList#(activate(V)), isNatList#(n__cons(V1, V2)) -> activate#(V2))
(U32#(tt(), V) -> isNatList#(activate(V)), isNatList#(n__cons(V1, V2)) -> U91#(isNatKind(activate(V1)), activate(V1), activate(V2)))
(activate#(n__length(X)) -> length#(activate(X)), length#(cons(N, L)) -> activate#(L))
(activate#(n__length(X)) -> length#(activate(X)), length#(cons(N, L)) -> U111#(isNatList(activate(L)), activate(L), N))
(activate#(n__length(X)) -> length#(activate(X)), length#(cons(N, L)) -> isNatList#(activate(L)))
(U134#(tt(), IL, M, N) -> U135#(isNat(activate(N)), activate(IL), activate(M), activate(N)), U135#(tt(), IL, M, N) -> isNatKind#(activate(N)))
(U134#(tt(), IL, M, N) -> U135#(isNat(activate(N)), activate(IL), activate(M), activate(N)), U135#(tt(), IL, M, N) -> activate#(N))
(U134#(tt(), IL, M, N) -> U135#(isNat(activate(N)), activate(IL), activate(M), activate(N)), U135#(tt(), IL, M, N) -> activate#(IL))
(U134#(tt(), IL, M, N) -> U135#(isNat(activate(N)), activate(IL), activate(M), activate(N)), U135#(tt(), IL, M, N) -> activate#(M))
(U134#(tt(), IL, M, N) -> U135#(isNat(activate(N)), activate(IL), activate(M), activate(N)), U135#(tt(), IL, M, N) -> U136#(isNatKind(activate(N)), activate(IL), activate(M), activate(N)))
(U131#(tt(), IL, M, N) -> U132#(isNatIListKind(activate(IL)), activate(IL), activate(M), activate(N)), U132#(tt(), IL, M, N) -> activate#(N))
(U131#(tt(), IL, M, N) -> U132#(isNatIListKind(activate(IL)), activate(IL), activate(M), activate(N)), U132#(tt(), IL, M, N) -> activate#(IL))
(U131#(tt(), IL, M, N) -> U132#(isNatIListKind(activate(IL)), activate(IL), activate(M), activate(N)), U132#(tt(), IL, M, N) -> activate#(M))
(U131#(tt(), IL, M, N) -> U132#(isNatIListKind(activate(IL)), activate(IL), activate(M), activate(N)), U132#(tt(), IL, M, N) -> isNat#(activate(M)))
(U131#(tt(), IL, M, N) -> U132#(isNatIListKind(activate(IL)), activate(IL), activate(M), activate(N)), U132#(tt(), IL, M, N) -> U133#(isNat(activate(M)), activate(IL), activate(M), activate(N)))
(activate#(n__cons(X1, X2)) -> activate#(X1), activate#(n__take(X1, X2)) -> take#(activate(X1), activate(X2)))
(activate#(n__cons(X1, X2)) -> activate#(X1), activate#(n__length(X)) -> activate#(X))
(activate#(n__cons(X1, X2)) -> activate#(X1), activate#(n__length(X)) -> length#(activate(X)))
(activate#(n__cons(X1, X2)) -> activate#(X1), activate#(n__s(X)) -> activate#(X))
(activate#(n__cons(X1, X2)) -> activate#(X1), activate#(n__cons(X1, X2)) -> activate#(X1))
(U135#(tt(), IL, M, N) -> activate#(M), activate#(n__take(X1, X2)) -> take#(activate(X1), activate(X2)))
(U135#(tt(), IL, M, N) -> activate#(M), activate#(n__length(X)) -> activate#(X))
(U135#(tt(), IL, M, N) -> activate#(M), activate#(n__length(X)) -> length#(activate(X)))
(U135#(tt(), IL, M, N) -> activate#(M), activate#(n__s(X)) -> activate#(X))
(U135#(tt(), IL, M, N) -> activate#(M), activate#(n__cons(X1, X2)) -> activate#(X1))
(U133#(tt(), IL, M, N) -> activate#(M), activate#(n__take(X1, X2)) -> take#(activate(X1), activate(X2)))
(U133#(tt(), IL, M, N) -> activate#(M), activate#(n__length(X)) -> activate#(X))
(U133#(tt(), IL, M, N) -> activate#(M), activate#(n__length(X)) -> length#(activate(X)))
(U133#(tt(), IL, M, N) -> activate#(M), activate#(n__s(X)) -> activate#(X))
(U133#(tt(), IL, M, N) -> activate#(M), activate#(n__cons(X1, X2)) -> activate#(X1))
(U132#(tt(), IL, M, N) -> activate#(M), activate#(n__take(X1, X2)) -> take#(activate(X1), activate(X2)))
(U132#(tt(), IL, M, N) -> activate#(M), activate#(n__length(X)) -> activate#(X))
(U132#(tt(), IL, M, N) -> activate#(M), activate#(n__length(X)) -> length#(activate(X)))
(U132#(tt(), IL, M, N) -> activate#(M), activate#(n__s(X)) -> activate#(X))
(U132#(tt(), IL, M, N) -> activate#(M), activate#(n__cons(X1, X2)) -> activate#(X1))
}
SCCS:
Scc:
{isNatIList#(n__cons(V1, V2)) -> U41#(isNatKind(activate(V1)), activate(V1), activate(V2)),
U42#(tt(), V1, V2) -> U43#(isNatIListKind(activate(V2)), activate(V1), activate(V2)),
U41#(tt(), V1, V2) -> U42#(isNatKind(activate(V1)), activate(V1), activate(V2)),
U43#(tt(), V1, V2) -> U44#(isNatIListKind(activate(V2)), activate(V1), activate(V2)),
U44#(tt(), V1, V2) -> U45#(isNat(activate(V1)), activate(V2)),
U45#(tt(), V2) -> isNatIList#(activate(V2))}
Scc:
{ isNatKind#(n__length(V1)) -> activate#(V1),
isNatKind#(n__length(V1)) -> isNatIListKind#(activate(V1)),
isNatKind#(n__s(V1)) -> isNatKind#(activate(V1)),
isNatKind#(n__s(V1)) -> activate#(V1),
activate#(n__length(X)) -> activate#(X),
activate#(n__length(X)) -> length#(activate(X)),
activate#(n__s(X)) -> activate#(X),
activate#(n__cons(X1, X2)) -> activate#(X1),
isNatIListKind#(n__cons(V1, V2)) -> isNatKind#(activate(V1)),
isNatIListKind#(n__cons(V1, V2)) -> activate#(V1),
isNatIListKind#(n__cons(V1, V2)) -> activate#(V2),
isNatIListKind#(n__cons(V1, V2)) -> U51#(isNatKind(activate(V1)), activate(V2)),
isNat#(n__length(V1)) -> activate#(V1),
isNat#(n__length(V1)) -> isNatIListKind#(activate(V1)),
isNat#(n__length(V1)) -> U11#(isNatIListKind(activate(V1)), activate(V1)),
isNat#(n__s(V1)) -> isNatKind#(activate(V1)),
isNat#(n__s(V1)) -> activate#(V1),
isNat#(n__s(V1)) -> U21#(isNatKind(activate(V1)), activate(V1)),
U12#(tt(), V1) -> activate#(V1),
U12#(tt(), V1) -> isNatList#(activate(V1)),
U11#(tt(), V1) -> activate#(V1),
U11#(tt(), V1) -> isNatIListKind#(activate(V1)),
U11#(tt(), V1) -> U12#(isNatIListKind(activate(V1)), activate(V1)),
U112#(tt(), L, N) -> activate#(L),
U112#(tt(), L, N) -> activate#(N),
U112#(tt(), L, N) -> isNat#(activate(N)),
U112#(tt(), L, N) -> U113#(isNat(activate(N)), activate(L), activate(N)),
U111#(tt(), L, N) -> activate#(L),
U111#(tt(), L, N) -> activate#(N),
U111#(tt(), L, N) -> isNatIListKind#(activate(L)),
U111#(tt(), L, N) -> U112#(isNatIListKind(activate(L)), activate(L), activate(N)),
U113#(tt(), L, N) -> isNatKind#(activate(N)),
U113#(tt(), L, N) -> activate#(L),
U113#(tt(), L, N) -> activate#(N),
U113#(tt(), L, N) -> U114#(isNatKind(activate(N)), activate(L)),
U114#(tt(), L) -> activate#(L),
U114#(tt(), L) -> length#(activate(L)),
length#(cons(N, L)) -> activate#(L),
length#(cons(N, L)) -> U111#(isNatList(activate(L)), activate(L), N),
length#(cons(N, L)) -> isNatList#(activate(L)),
isNatList#(n__cons(V1, V2)) -> isNatKind#(activate(V1)),
isNatList#(n__cons(V1, V2)) -> activate#(V1),
isNatList#(n__cons(V1, V2)) -> activate#(V2),
isNatList#(n__cons(V1, V2)) -> U91#(isNatKind(activate(V1)), activate(V1), activate(V2)),
U22#(tt(), V1) -> activate#(V1),
U22#(tt(), V1) -> isNat#(activate(V1)),
U21#(tt(), V1) -> isNatKind#(activate(V1)),
U21#(tt(), V1) -> activate#(V1),
U21#(tt(), V1) -> U22#(isNatKind(activate(V1)), activate(V1)),
U51#(tt(), V2) -> activate#(V2),
U51#(tt(), V2) -> isNatIListKind#(activate(V2)),
U92#(tt(), V1, V2) -> activate#(V1),
U92#(tt(), V1, V2) -> activate#(V2),
U92#(tt(), V1, V2) -> isNatIListKind#(activate(V2)),
U92#(tt(), V1, V2) -> U93#(isNatIListKind(activate(V2)), activate(V1), activate(V2)),
U91#(tt(), V1, V2) -> isNatKind#(activate(V1)),
U91#(tt(), V1, V2) -> activate#(V1),
U91#(tt(), V1, V2) -> activate#(V2),
U91#(tt(), V1, V2) -> U92#(isNatKind(activate(V1)), activate(V1), activate(V2)),
U93#(tt(), V1, V2) -> activate#(V1),
U93#(tt(), V1, V2) -> activate#(V2),
U93#(tt(), V1, V2) -> isNatIListKind#(activate(V2)),
U93#(tt(), V1, V2) -> U94#(isNatIListKind(activate(V2)), activate(V1), activate(V2)),
U94#(tt(), V1, V2) -> activate#(V1),
U94#(tt(), V1, V2) -> activate#(V2),
U94#(tt(), V1, V2) -> isNat#(activate(V1)),
U94#(tt(), V1, V2) -> U95#(isNat(activate(V1)), activate(V2)),
U95#(tt(), V2) -> activate#(V2),
U95#(tt(), V2) -> isNatList#(activate(V2))}
SCC:
Strict:
{isNatIList#(n__cons(V1, V2)) -> U41#(isNatKind(activate(V1)), activate(V1), activate(V2)),
U42#(tt(), V1, V2) -> U43#(isNatIListKind(activate(V2)), activate(V1), activate(V2)),
U41#(tt(), V1, V2) -> U42#(isNatKind(activate(V1)), activate(V1), activate(V2)),
U43#(tt(), V1, V2) -> U44#(isNatIListKind(activate(V2)), activate(V1), activate(V2)),
U44#(tt(), V1, V2) -> U45#(isNat(activate(V1)), activate(V2)),
U45#(tt(), V2) -> isNatIList#(activate(V2))}
Weak:
{ cons(X1, X2) -> n__cons(X1, X2),
0() -> n__0(),
zeros() -> cons(0(), n__zeros()),
zeros() -> n__zeros(),
U102(tt(), V1, V2) -> U103(isNatIListKind(activate(V2)), activate(V1), activate(V2)),
isNatKind(n__0()) -> tt(),
isNatKind(n__length(V1)) -> U71(isNatIListKind(activate(V1))),
isNatKind(n__s(V1)) -> U81(isNatKind(activate(V1))),
activate(X) -> X,
activate(n__zeros()) -> zeros(),
activate(n__take(X1, X2)) -> take(activate(X1), activate(X2)),
activate(n__0()) -> 0(),
activate(n__length(X)) -> length(activate(X)),
activate(n__s(X)) -> s(activate(X)),
activate(n__cons(X1, X2)) -> cons(activate(X1), X2),
activate(n__nil()) -> nil(),
U101(tt(), V1, V2) -> U102(isNatKind(activate(V1)), activate(V1), activate(V2)),
U103(tt(), V1, V2) -> U104(isNatIListKind(activate(V2)), activate(V1), activate(V2)),
isNatIListKind(n__zeros()) -> tt(),
isNatIListKind(n__take(V1, V2)) -> U61(isNatKind(activate(V1)), activate(V2)),
isNatIListKind(n__cons(V1, V2)) -> U51(isNatKind(activate(V1)), activate(V2)),
isNatIListKind(n__nil()) -> tt(),
U104(tt(), V1, V2) -> U105(isNat(activate(V1)), activate(V2)),
U105(tt(), V2) -> U106(isNatIList(activate(V2))),
isNat(n__0()) -> tt(),
isNat(n__length(V1)) -> U11(isNatIListKind(activate(V1)), activate(V1)),
isNat(n__s(V1)) -> U21(isNatKind(activate(V1)), activate(V1)),
U106(tt()) -> tt(),
isNatIList(V) -> U31(isNatIListKind(activate(V)), activate(V)),
isNatIList(n__zeros()) -> tt(),
isNatIList(n__cons(V1, V2)) -> U41(isNatKind(activate(V1)), activate(V1), activate(V2)),
U12(tt(), V1) -> U13(isNatList(activate(V1))),
U11(tt(), V1) -> U12(isNatIListKind(activate(V1)), activate(V1)),
U112(tt(), L, N) -> U113(isNat(activate(N)), activate(L), activate(N)),
U111(tt(), L, N) -> U112(isNatIListKind(activate(L)), activate(L), activate(N)),
U113(tt(), L, N) -> U114(isNatKind(activate(N)), activate(L)),
U114(tt(), L) -> s(length(activate(L))),
s(X) -> n__s(X),
length(X) -> n__length(X),
length(cons(N, L)) -> U111(isNatList(activate(L)), activate(L), N),
length(nil()) -> 0(),
U13(tt()) -> tt(),
isNatList(n__take(V1, V2)) -> U101(isNatKind(activate(V1)), activate(V1), activate(V2)),
isNatList(n__cons(V1, V2)) -> U91(isNatKind(activate(V1)), activate(V1), activate(V2)),
isNatList(n__nil()) -> tt(),
U122(tt()) -> nil(),
U121(tt(), IL) -> U122(isNatIListKind(activate(IL))),
nil() -> n__nil(),
U132(tt(), IL, M, N) -> U133(isNat(activate(M)), activate(IL), activate(M), activate(N)),
U131(tt(), IL, M, N) -> U132(isNatIListKind(activate(IL)), activate(IL), activate(M), activate(N)),
U133(tt(), IL, M, N) -> U134(isNatKind(activate(M)), activate(IL), activate(M), activate(N)),
U134(tt(), IL, M, N) -> U135(isNat(activate(N)), activate(IL), activate(M), activate(N)),
U135(tt(), IL, M, N) -> U136(isNatKind(activate(N)), activate(IL), activate(M), activate(N)),
U136(tt(), IL, M, N) -> cons(activate(N), n__take(activate(M), activate(IL))),
U22(tt(), V1) -> U23(isNat(activate(V1))),
U21(tt(), V1) -> U22(isNatKind(activate(V1)), activate(V1)),
U23(tt()) -> tt(),
U32(tt(), V) -> U33(isNatList(activate(V))),
U31(tt(), V) -> U32(isNatIListKind(activate(V)), activate(V)),
U33(tt()) -> tt(),
U42(tt(), V1, V2) -> U43(isNatIListKind(activate(V2)), activate(V1), activate(V2)),
U41(tt(), V1, V2) -> U42(isNatKind(activate(V1)), activate(V1), activate(V2)),
U43(tt(), V1, V2) -> U44(isNatIListKind(activate(V2)), activate(V1), activate(V2)),
U44(tt(), V1, V2) -> U45(isNat(activate(V1)), activate(V2)),
U45(tt(), V2) -> U46(isNatIList(activate(V2))),
U46(tt()) -> tt(),
U52(tt()) -> tt(),
U51(tt(), V2) -> U52(isNatIListKind(activate(V2))),
U62(tt()) -> tt(),
U61(tt(), V2) -> U62(isNatIListKind(activate(V2))),
U71(tt()) -> tt(),
U81(tt()) -> tt(),
U92(tt(), V1, V2) -> U93(isNatIListKind(activate(V2)), activate(V1), activate(V2)),
U91(tt(), V1, V2) -> U92(isNatKind(activate(V1)), activate(V1), activate(V2)),
U93(tt(), V1, V2) -> U94(isNatIListKind(activate(V2)), activate(V1), activate(V2)),
U94(tt(), V1, V2) -> U95(isNat(activate(V1)), activate(V2)),
U95(tt(), V2) -> U96(isNatList(activate(V2))),
U96(tt()) -> tt(),
take(X1, X2) -> n__take(X1, X2),
take(0(), IL) -> U121(isNatIList(IL), IL),
take(s(M), cons(N, IL)) -> U131(isNatIList(activate(IL)), activate(IL), M, N)}
Fail
SCC:
Strict:
{ isNatKind#(n__length(V1)) -> activate#(V1),
isNatKind#(n__length(V1)) -> isNatIListKind#(activate(V1)),
isNatKind#(n__s(V1)) -> isNatKind#(activate(V1)),
isNatKind#(n__s(V1)) -> activate#(V1),
activate#(n__length(X)) -> activate#(X),
activate#(n__length(X)) -> length#(activate(X)),
activate#(n__s(X)) -> activate#(X),
activate#(n__cons(X1, X2)) -> activate#(X1),
isNatIListKind#(n__cons(V1, V2)) -> isNatKind#(activate(V1)),
isNatIListKind#(n__cons(V1, V2)) -> activate#(V1),
isNatIListKind#(n__cons(V1, V2)) -> activate#(V2),
isNatIListKind#(n__cons(V1, V2)) -> U51#(isNatKind(activate(V1)), activate(V2)),
isNat#(n__length(V1)) -> activate#(V1),
isNat#(n__length(V1)) -> isNatIListKind#(activate(V1)),
isNat#(n__length(V1)) -> U11#(isNatIListKind(activate(V1)), activate(V1)),
isNat#(n__s(V1)) -> isNatKind#(activate(V1)),
isNat#(n__s(V1)) -> activate#(V1),
isNat#(n__s(V1)) -> U21#(isNatKind(activate(V1)), activate(V1)),
U12#(tt(), V1) -> activate#(V1),
U12#(tt(), V1) -> isNatList#(activate(V1)),
U11#(tt(), V1) -> activate#(V1),
U11#(tt(), V1) -> isNatIListKind#(activate(V1)),
U11#(tt(), V1) -> U12#(isNatIListKind(activate(V1)), activate(V1)),
U112#(tt(), L, N) -> activate#(L),
U112#(tt(), L, N) -> activate#(N),
U112#(tt(), L, N) -> isNat#(activate(N)),
U112#(tt(), L, N) -> U113#(isNat(activate(N)), activate(L), activate(N)),
U111#(tt(), L, N) -> activate#(L),
U111#(tt(), L, N) -> activate#(N),
U111#(tt(), L, N) -> isNatIListKind#(activate(L)),
U111#(tt(), L, N) -> U112#(isNatIListKind(activate(L)), activate(L), activate(N)),
U113#(tt(), L, N) -> isNatKind#(activate(N)),
U113#(tt(), L, N) -> activate#(L),
U113#(tt(), L, N) -> activate#(N),
U113#(tt(), L, N) -> U114#(isNatKind(activate(N)), activate(L)),
U114#(tt(), L) -> activate#(L),
U114#(tt(), L) -> length#(activate(L)),
length#(cons(N, L)) -> activate#(L),
length#(cons(N, L)) -> U111#(isNatList(activate(L)), activate(L), N),
length#(cons(N, L)) -> isNatList#(activate(L)),
isNatList#(n__cons(V1, V2)) -> isNatKind#(activate(V1)),
isNatList#(n__cons(V1, V2)) -> activate#(V1),
isNatList#(n__cons(V1, V2)) -> activate#(V2),
isNatList#(n__cons(V1, V2)) -> U91#(isNatKind(activate(V1)), activate(V1), activate(V2)),
U22#(tt(), V1) -> activate#(V1),
U22#(tt(), V1) -> isNat#(activate(V1)),
U21#(tt(), V1) -> isNatKind#(activate(V1)),
U21#(tt(), V1) -> activate#(V1),
U21#(tt(), V1) -> U22#(isNatKind(activate(V1)), activate(V1)),
U51#(tt(), V2) -> activate#(V2),
U51#(tt(), V2) -> isNatIListKind#(activate(V2)),
U92#(tt(), V1, V2) -> activate#(V1),
U92#(tt(), V1, V2) -> activate#(V2),
U92#(tt(), V1, V2) -> isNatIListKind#(activate(V2)),
U92#(tt(), V1, V2) -> U93#(isNatIListKind(activate(V2)), activate(V1), activate(V2)),
U91#(tt(), V1, V2) -> isNatKind#(activate(V1)),
U91#(tt(), V1, V2) -> activate#(V1),
U91#(tt(), V1, V2) -> activate#(V2),
U91#(tt(), V1, V2) -> U92#(isNatKind(activate(V1)), activate(V1), activate(V2)),
U93#(tt(), V1, V2) -> activate#(V1),
U93#(tt(), V1, V2) -> activate#(V2),
U93#(tt(), V1, V2) -> isNatIListKind#(activate(V2)),
U93#(tt(), V1, V2) -> U94#(isNatIListKind(activate(V2)), activate(V1), activate(V2)),
U94#(tt(), V1, V2) -> activate#(V1),
U94#(tt(), V1, V2) -> activate#(V2),
U94#(tt(), V1, V2) -> isNat#(activate(V1)),
U94#(tt(), V1, V2) -> U95#(isNat(activate(V1)), activate(V2)),
U95#(tt(), V2) -> activate#(V2),
U95#(tt(), V2) -> isNatList#(activate(V2))}
Weak:
{ cons(X1, X2) -> n__cons(X1, X2),
0() -> n__0(),
zeros() -> cons(0(), n__zeros()),
zeros() -> n__zeros(),
U102(tt(), V1, V2) -> U103(isNatIListKind(activate(V2)), activate(V1), activate(V2)),
isNatKind(n__0()) -> tt(),
isNatKind(n__length(V1)) -> U71(isNatIListKind(activate(V1))),
isNatKind(n__s(V1)) -> U81(isNatKind(activate(V1))),
activate(X) -> X,
activate(n__zeros()) -> zeros(),
activate(n__take(X1, X2)) -> take(activate(X1), activate(X2)),
activate(n__0()) -> 0(),
activate(n__length(X)) -> length(activate(X)),
activate(n__s(X)) -> s(activate(X)),
activate(n__cons(X1, X2)) -> cons(activate(X1), X2),
activate(n__nil()) -> nil(),
U101(tt(), V1, V2) -> U102(isNatKind(activate(V1)), activate(V1), activate(V2)),
U103(tt(), V1, V2) -> U104(isNatIListKind(activate(V2)), activate(V1), activate(V2)),
isNatIListKind(n__zeros()) -> tt(),
isNatIListKind(n__take(V1, V2)) -> U61(isNatKind(activate(V1)), activate(V2)),
isNatIListKind(n__cons(V1, V2)) -> U51(isNatKind(activate(V1)), activate(V2)),
isNatIListKind(n__nil()) -> tt(),
U104(tt(), V1, V2) -> U105(isNat(activate(V1)), activate(V2)),
U105(tt(), V2) -> U106(isNatIList(activate(V2))),
isNat(n__0()) -> tt(),
isNat(n__length(V1)) -> U11(isNatIListKind(activate(V1)), activate(V1)),
isNat(n__s(V1)) -> U21(isNatKind(activate(V1)), activate(V1)),
U106(tt()) -> tt(),
isNatIList(V) -> U31(isNatIListKind(activate(V)), activate(V)),
isNatIList(n__zeros()) -> tt(),
isNatIList(n__cons(V1, V2)) -> U41(isNatKind(activate(V1)), activate(V1), activate(V2)),
U12(tt(), V1) -> U13(isNatList(activate(V1))),
U11(tt(), V1) -> U12(isNatIListKind(activate(V1)), activate(V1)),
U112(tt(), L, N) -> U113(isNat(activate(N)), activate(L), activate(N)),
U111(tt(), L, N) -> U112(isNatIListKind(activate(L)), activate(L), activate(N)),
U113(tt(), L, N) -> U114(isNatKind(activate(N)), activate(L)),
U114(tt(), L) -> s(length(activate(L))),
s(X) -> n__s(X),
length(X) -> n__length(X),
length(cons(N, L)) -> U111(isNatList(activate(L)), activate(L), N),
length(nil()) -> 0(),
U13(tt()) -> tt(),
isNatList(n__take(V1, V2)) -> U101(isNatKind(activate(V1)), activate(V1), activate(V2)),
isNatList(n__cons(V1, V2)) -> U91(isNatKind(activate(V1)), activate(V1), activate(V2)),
isNatList(n__nil()) -> tt(),
U122(tt()) -> nil(),
U121(tt(), IL) -> U122(isNatIListKind(activate(IL))),
nil() -> n__nil(),
U132(tt(), IL, M, N) -> U133(isNat(activate(M)), activate(IL), activate(M), activate(N)),
U131(tt(), IL, M, N) -> U132(isNatIListKind(activate(IL)), activate(IL), activate(M), activate(N)),
U133(tt(), IL, M, N) -> U134(isNatKind(activate(M)), activate(IL), activate(M), activate(N)),
U134(tt(), IL, M, N) -> U135(isNat(activate(N)), activate(IL), activate(M), activate(N)),
U135(tt(), IL, M, N) -> U136(isNatKind(activate(N)), activate(IL), activate(M), activate(N)),
U136(tt(), IL, M, N) -> cons(activate(N), n__take(activate(M), activate(IL))),
U22(tt(), V1) -> U23(isNat(activate(V1))),
U21(tt(), V1) -> U22(isNatKind(activate(V1)), activate(V1)),
U23(tt()) -> tt(),
U32(tt(), V) -> U33(isNatList(activate(V))),
U31(tt(), V) -> U32(isNatIListKind(activate(V)), activate(V)),
U33(tt()) -> tt(),
U42(tt(), V1, V2) -> U43(isNatIListKind(activate(V2)), activate(V1), activate(V2)),
U41(tt(), V1, V2) -> U42(isNatKind(activate(V1)), activate(V1), activate(V2)),
U43(tt(), V1, V2) -> U44(isNatIListKind(activate(V2)), activate(V1), activate(V2)),
U44(tt(), V1, V2) -> U45(isNat(activate(V1)), activate(V2)),
U45(tt(), V2) -> U46(isNatIList(activate(V2))),
U46(tt()) -> tt(),
U52(tt()) -> tt(),
U51(tt(), V2) -> U52(isNatIListKind(activate(V2))),
U62(tt()) -> tt(),
U61(tt(), V2) -> U62(isNatIListKind(activate(V2))),
U71(tt()) -> tt(),
U81(tt()) -> tt(),
U92(tt(), V1, V2) -> U93(isNatIListKind(activate(V2)), activate(V1), activate(V2)),
U91(tt(), V1, V2) -> U92(isNatKind(activate(V1)), activate(V1), activate(V2)),
U93(tt(), V1, V2) -> U94(isNatIListKind(activate(V2)), activate(V1), activate(V2)),
U94(tt(), V1, V2) -> U95(isNat(activate(V1)), activate(V2)),
U95(tt(), V2) -> U96(isNatList(activate(V2))),
U96(tt()) -> tt(),
take(X1, X2) -> n__take(X1, X2),
take(0(), IL) -> U121(isNatIList(IL), IL),
take(s(M), cons(N, IL)) -> U131(isNatIList(activate(IL)), activate(IL), M, N)}
POLY:
Argument Filtering:
pi(take) = 1, pi(n__nil) = [], pi(n__cons) = [0,1], pi(n__s) = 0, pi(n__length) = [0], pi(n__0) = [], pi(U96) = [], pi(U95#) = 1, pi(U95) = [], pi(U94#) = [1,2], pi(U94) = [], pi(U93#) = [1,2], pi(U93) = [], pi(U91#) = [1,2], pi(U91) = [], pi(U92#) = [1,2], pi(U92) = [], pi(U81) = [], pi(U71) = [], pi(U61) = [], pi(U62) = [], pi(U51#) = 1, pi(U51) = [], pi(U52) = [], pi(U46) = [], pi(U45) = [], pi(U44) = [], pi(U43) = [], pi(U41) = [], pi(U42) = [], pi(U33) = [], pi(U31) = [], pi(U32) = [], pi(U23) = [], pi(U21#) = 1, pi(U21) = [], pi(U22#) = 1, pi(U22) = [], pi(n__take) = 1, pi(U136) = [1,3], pi(U135) = [1,3], pi(U134) = [1,3], pi(U133) = [1,3], pi(U131) = [1,3], pi(U132) = [1,3], pi(nil) = [], pi(U121) = 1, pi(U122) = [], pi(isNatList#) = 0, pi(isNatList) = [], pi(U13) = [], pi(length#) = 0, pi(length) = [0], pi(s) = 0, pi(U114#) = 1, pi(U114) = [1], pi(U113#) = [1,2], pi(U113) = [1], pi(U111#) = [1,2], pi(U111) = [1], pi(U112#) = [1,2], pi(U112) = [1], pi(U11#) = [1], pi(U11) = [], pi(U12#) = 1, pi(U12) = [], pi(isNatIList) = [], pi(U106) = [], pi(isNat#) = 0, pi(isNat) = [], pi(U105) = [], pi(U104) = [], pi(isNatIListKind#) = 0, pi(isNatIListKind) = [], pi(U103) = [], pi(tt) = [], pi(U101) = [], pi(activate#) = 0, pi(activate) = 0, pi(isNatKind#) = 0, pi(isNatKind) = [], pi(U102) = [], pi(zeros) = [], pi(n__zeros) = [], pi(0) = [], pi(cons) = [0,1]
Usable Rules:
{}
Interpretation:
[U94#](x0, x1) = x0 + x1,
[U93#](x0, x1) = x0 + x1,
[U91#](x0, x1) = x0 + x1,
[U92#](x0, x1) = x0 + x1,
[U113#](x0, x1) = x0 + x1,
[U111#](x0, x1) = x0 + x1,
[U112#](x0, x1) = x0 + x1,
[U11#](x0) = x0 + 1,
[n__cons](x0, x1) = x0 + x1,
[cons](x0, x1) = x0 + x1,
[n__length](x0) = x0 + 1
Strict:
{ isNatKind#(n__s(V1)) -> isNatKind#(activate(V1)),
isNatKind#(n__s(V1)) -> activate#(V1),
activate#(n__s(X)) -> activate#(X),
activate#(n__cons(X1, X2)) -> activate#(X1),
isNatIListKind#(n__cons(V1, V2)) -> isNatKind#(activate(V1)),
isNatIListKind#(n__cons(V1, V2)) -> activate#(V1),
isNatIListKind#(n__cons(V1, V2)) -> activate#(V2),
isNatIListKind#(n__cons(V1, V2)) -> U51#(isNatKind(activate(V1)), activate(V2)),
isNat#(n__length(V1)) -> U11#(isNatIListKind(activate(V1)), activate(V1)),
isNat#(n__s(V1)) -> isNatKind#(activate(V1)),
isNat#(n__s(V1)) -> activate#(V1),
isNat#(n__s(V1)) -> U21#(isNatKind(activate(V1)), activate(V1)),
U12#(tt(), V1) -> activate#(V1),
U12#(tt(), V1) -> isNatList#(activate(V1)),
U112#(tt(), L, N) -> activate#(L),
U112#(tt(), L, N) -> activate#(N),
U112#(tt(), L, N) -> isNat#(activate(N)),
U112#(tt(), L, N) -> U113#(isNat(activate(N)), activate(L), activate(N)),
U111#(tt(), L, N) -> activate#(L),
U111#(tt(), L, N) -> activate#(N),
U111#(tt(), L, N) -> isNatIListKind#(activate(L)),
U111#(tt(), L, N) -> U112#(isNatIListKind(activate(L)), activate(L), activate(N)),
U113#(tt(), L, N) -> isNatKind#(activate(N)),
U113#(tt(), L, N) -> activate#(L),
U113#(tt(), L, N) -> activate#(N),
U113#(tt(), L, N) -> U114#(isNatKind(activate(N)), activate(L)),
U114#(tt(), L) -> activate#(L),
U114#(tt(), L) -> length#(activate(L)),
length#(cons(N, L)) -> activate#(L),
length#(cons(N, L)) -> U111#(isNatList(activate(L)), activate(L), N),
length#(cons(N, L)) -> isNatList#(activate(L)),
isNatList#(n__cons(V1, V2)) -> isNatKind#(activate(V1)),
isNatList#(n__cons(V1, V2)) -> activate#(V1),
isNatList#(n__cons(V1, V2)) -> activate#(V2),
isNatList#(n__cons(V1, V2)) -> U91#(isNatKind(activate(V1)), activate(V1), activate(V2)),
U22#(tt(), V1) -> activate#(V1),
U22#(tt(), V1) -> isNat#(activate(V1)),
U21#(tt(), V1) -> isNatKind#(activate(V1)),
U21#(tt(), V1) -> activate#(V1),
U21#(tt(), V1) -> U22#(isNatKind(activate(V1)), activate(V1)),
U51#(tt(), V2) -> activate#(V2),
U51#(tt(), V2) -> isNatIListKind#(activate(V2)),
U92#(tt(), V1, V2) -> activate#(V1),
U92#(tt(), V1, V2) -> activate#(V2),
U92#(tt(), V1, V2) -> isNatIListKind#(activate(V2)),
U92#(tt(), V1, V2) -> U93#(isNatIListKind(activate(V2)), activate(V1), activate(V2)),
U91#(tt(), V1, V2) -> isNatKind#(activate(V1)),
U91#(tt(), V1, V2) -> activate#(V1),
U91#(tt(), V1, V2) -> activate#(V2),
U91#(tt(), V1, V2) -> U92#(isNatKind(activate(V1)), activate(V1), activate(V2)),
U93#(tt(), V1, V2) -> activate#(V1),
U93#(tt(), V1, V2) -> activate#(V2),
U93#(tt(), V1, V2) -> isNatIListKind#(activate(V2)),
U93#(tt(), V1, V2) -> U94#(isNatIListKind(activate(V2)), activate(V1), activate(V2)),
U94#(tt(), V1, V2) -> activate#(V1),
U94#(tt(), V1, V2) -> activate#(V2),
U94#(tt(), V1, V2) -> isNat#(activate(V1)),
U94#(tt(), V1, V2) -> U95#(isNat(activate(V1)), activate(V2)),
U95#(tt(), V2) -> activate#(V2),
U95#(tt(), V2) -> isNatList#(activate(V2))}
Weak:
{ cons(X1, X2) -> n__cons(X1, X2),
0() -> n__0(),
zeros() -> cons(0(), n__zeros()),
zeros() -> n__zeros(),
U102(tt(), V1, V2) -> U103(isNatIListKind(activate(V2)), activate(V1), activate(V2)),
isNatKind(n__0()) -> tt(),
isNatKind(n__length(V1)) -> U71(isNatIListKind(activate(V1))),
isNatKind(n__s(V1)) -> U81(isNatKind(activate(V1))),
activate(X) -> X,
activate(n__zeros()) -> zeros(),
activate(n__take(X1, X2)) -> take(activate(X1), activate(X2)),
activate(n__0()) -> 0(),
activate(n__length(X)) -> length(activate(X)),
activate(n__s(X)) -> s(activate(X)),
activate(n__cons(X1, X2)) -> cons(activate(X1), X2),
activate(n__nil()) -> nil(),
U101(tt(), V1, V2) -> U102(isNatKind(activate(V1)), activate(V1), activate(V2)),
U103(tt(), V1, V2) -> U104(isNatIListKind(activate(V2)), activate(V1), activate(V2)),
isNatIListKind(n__zeros()) -> tt(),
isNatIListKind(n__take(V1, V2)) -> U61(isNatKind(activate(V1)), activate(V2)),
isNatIListKind(n__cons(V1, V2)) -> U51(isNatKind(activate(V1)), activate(V2)),
isNatIListKind(n__nil()) -> tt(),
U104(tt(), V1, V2) -> U105(isNat(activate(V1)), activate(V2)),
U105(tt(), V2) -> U106(isNatIList(activate(V2))),
isNat(n__0()) -> tt(),
isNat(n__length(V1)) -> U11(isNatIListKind(activate(V1)), activate(V1)),
isNat(n__s(V1)) -> U21(isNatKind(activate(V1)), activate(V1)),
U106(tt()) -> tt(),
isNatIList(V) -> U31(isNatIListKind(activate(V)), activate(V)),
isNatIList(n__zeros()) -> tt(),
isNatIList(n__cons(V1, V2)) -> U41(isNatKind(activate(V1)), activate(V1), activate(V2)),
U12(tt(), V1) -> U13(isNatList(activate(V1))),
U11(tt(), V1) -> U12(isNatIListKind(activate(V1)), activate(V1)),
U112(tt(), L, N) -> U113(isNat(activate(N)), activate(L), activate(N)),
U111(tt(), L, N) -> U112(isNatIListKind(activate(L)), activate(L), activate(N)),
U113(tt(), L, N) -> U114(isNatKind(activate(N)), activate(L)),
U114(tt(), L) -> s(length(activate(L))),
s(X) -> n__s(X),
length(X) -> n__length(X),
length(cons(N, L)) -> U111(isNatList(activate(L)), activate(L), N),
length(nil()) -> 0(),
U13(tt()) -> tt(),
isNatList(n__take(V1, V2)) -> U101(isNatKind(activate(V1)), activate(V1), activate(V2)),
isNatList(n__cons(V1, V2)) -> U91(isNatKind(activate(V1)), activate(V1), activate(V2)),
isNatList(n__nil()) -> tt(),
U122(tt()) -> nil(),
U121(tt(), IL) -> U122(isNatIListKind(activate(IL))),
nil() -> n__nil(),
U132(tt(), IL, M, N) -> U133(isNat(activate(M)), activate(IL), activate(M), activate(N)),
U131(tt(), IL, M, N) -> U132(isNatIListKind(activate(IL)), activate(IL), activate(M), activate(N)),
U133(tt(), IL, M, N) -> U134(isNatKind(activate(M)), activate(IL), activate(M), activate(N)),
U134(tt(), IL, M, N) -> U135(isNat(activate(N)), activate(IL), activate(M), activate(N)),
U135(tt(), IL, M, N) -> U136(isNatKind(activate(N)), activate(IL), activate(M), activate(N)),
U136(tt(), IL, M, N) -> cons(activate(N), n__take(activate(M), activate(IL))),
U22(tt(), V1) -> U23(isNat(activate(V1))),
U21(tt(), V1) -> U22(isNatKind(activate(V1)), activate(V1)),
U23(tt()) -> tt(),
U32(tt(), V) -> U33(isNatList(activate(V))),
U31(tt(), V) -> U32(isNatIListKind(activate(V)), activate(V)),
U33(tt()) -> tt(),
U42(tt(), V1, V2) -> U43(isNatIListKind(activate(V2)), activate(V1), activate(V2)),
U41(tt(), V1, V2) -> U42(isNatKind(activate(V1)), activate(V1), activate(V2)),
U43(tt(), V1, V2) -> U44(isNatIListKind(activate(V2)), activate(V1), activate(V2)),
U44(tt(), V1, V2) -> U45(isNat(activate(V1)), activate(V2)),
U45(tt(), V2) -> U46(isNatIList(activate(V2))),
U46(tt()) -> tt(),
U52(tt()) -> tt(),
U51(tt(), V2) -> U52(isNatIListKind(activate(V2))),
U62(tt()) -> tt(),
U61(tt(), V2) -> U62(isNatIListKind(activate(V2))),
U71(tt()) -> tt(),
U81(tt()) -> tt(),
U92(tt(), V1, V2) -> U93(isNatIListKind(activate(V2)), activate(V1), activate(V2)),
U91(tt(), V1, V2) -> U92(isNatKind(activate(V1)), activate(V1), activate(V2)),
U93(tt(), V1, V2) -> U94(isNatIListKind(activate(V2)), activate(V1), activate(V2)),
U94(tt(), V1, V2) -> U95(isNat(activate(V1)), activate(V2)),
U95(tt(), V2) -> U96(isNatList(activate(V2))),
U96(tt()) -> tt(),
take(X1, X2) -> n__take(X1, X2),
take(0(), IL) -> U121(isNatIList(IL), IL),
take(s(M), cons(N, IL)) -> U131(isNatIList(activate(IL)), activate(IL), M, N)}
EDG:
{
(U113#(tt(), L, N) -> U114#(isNatKind(activate(N)), activate(L)), U114#(tt(), L) -> length#(activate(L)))
(U113#(tt(), L, N) -> U114#(isNatKind(activate(N)), activate(L)), U114#(tt(), L) -> activate#(L))
(U94#(tt(), V1, V2) -> U95#(isNat(activate(V1)), activate(V2)), U95#(tt(), V2) -> isNatList#(activate(V2)))
(U94#(tt(), V1, V2) -> U95#(isNat(activate(V1)), activate(V2)), U95#(tt(), V2) -> activate#(V2))
(isNatList#(n__cons(V1, V2)) -> activate#(V2), activate#(n__cons(X1, X2)) -> activate#(X1))
(isNatList#(n__cons(V1, V2)) -> activate#(V2), activate#(n__s(X)) -> activate#(X))
(U92#(tt(), V1, V2) -> activate#(V2), activate#(n__cons(X1, X2)) -> activate#(X1))
(U92#(tt(), V1, V2) -> activate#(V2), activate#(n__s(X)) -> activate#(X))
(U93#(tt(), V1, V2) -> activate#(V2), activate#(n__cons(X1, X2)) -> activate#(X1))
(U93#(tt(), V1, V2) -> activate#(V2), activate#(n__s(X)) -> activate#(X))
(U95#(tt(), V2) -> activate#(V2), activate#(n__cons(X1, X2)) -> activate#(X1))
(U95#(tt(), V2) -> activate#(V2), activate#(n__s(X)) -> activate#(X))
(U112#(tt(), L, N) -> isNat#(activate(N)), isNat#(n__s(V1)) -> U21#(isNatKind(activate(V1)), activate(V1)))
(U112#(tt(), L, N) -> isNat#(activate(N)), isNat#(n__s(V1)) -> activate#(V1))
(U112#(tt(), L, N) -> isNat#(activate(N)), isNat#(n__s(V1)) -> isNatKind#(activate(V1)))
(U112#(tt(), L, N) -> isNat#(activate(N)), isNat#(n__length(V1)) -> U11#(isNatIListKind(activate(V1)), activate(V1)))
(U111#(tt(), L, N) -> isNatIListKind#(activate(L)), isNatIListKind#(n__cons(V1, V2)) -> U51#(isNatKind(activate(V1)), activate(V2)))
(U111#(tt(), L, N) -> isNatIListKind#(activate(L)), isNatIListKind#(n__cons(V1, V2)) -> activate#(V2))
(U111#(tt(), L, N) -> isNatIListKind#(activate(L)), isNatIListKind#(n__cons(V1, V2)) -> activate#(V1))
(U111#(tt(), L, N) -> isNatIListKind#(activate(L)), isNatIListKind#(n__cons(V1, V2)) -> isNatKind#(activate(V1)))
(length#(cons(N, L)) -> isNatList#(activate(L)), isNatList#(n__cons(V1, V2)) -> U91#(isNatKind(activate(V1)), activate(V1), activate(V2)))
(length#(cons(N, L)) -> isNatList#(activate(L)), isNatList#(n__cons(V1, V2)) -> activate#(V2))
(length#(cons(N, L)) -> isNatList#(activate(L)), isNatList#(n__cons(V1, V2)) -> activate#(V1))
(length#(cons(N, L)) -> isNatList#(activate(L)), isNatList#(n__cons(V1, V2)) -> isNatKind#(activate(V1)))
(U92#(tt(), V1, V2) -> isNatIListKind#(activate(V2)), isNatIListKind#(n__cons(V1, V2)) -> U51#(isNatKind(activate(V1)), activate(V2)))
(U92#(tt(), V1, V2) -> isNatIListKind#(activate(V2)), isNatIListKind#(n__cons(V1, V2)) -> activate#(V2))
(U92#(tt(), V1, V2) -> isNatIListKind#(activate(V2)), isNatIListKind#(n__cons(V1, V2)) -> activate#(V1))
(U92#(tt(), V1, V2) -> isNatIListKind#(activate(V2)), isNatIListKind#(n__cons(V1, V2)) -> isNatKind#(activate(V1)))
(U95#(tt(), V2) -> isNatList#(activate(V2)), isNatList#(n__cons(V1, V2)) -> U91#(isNatKind(activate(V1)), activate(V1), activate(V2)))
(U95#(tt(), V2) -> isNatList#(activate(V2)), isNatList#(n__cons(V1, V2)) -> activate#(V2))
(U95#(tt(), V2) -> isNatList#(activate(V2)), isNatList#(n__cons(V1, V2)) -> activate#(V1))
(U95#(tt(), V2) -> isNatList#(activate(V2)), isNatList#(n__cons(V1, V2)) -> isNatKind#(activate(V1)))
(isNatIListKind#(n__cons(V1, V2)) -> isNatKind#(activate(V1)), isNatKind#(n__s(V1)) -> activate#(V1))
(isNatIListKind#(n__cons(V1, V2)) -> isNatKind#(activate(V1)), isNatKind#(n__s(V1)) -> isNatKind#(activate(V1)))
(U12#(tt(), V1) -> isNatList#(activate(V1)), isNatList#(n__cons(V1, V2)) -> U91#(isNatKind(activate(V1)), activate(V1), activate(V2)))
(U12#(tt(), V1) -> isNatList#(activate(V1)), isNatList#(n__cons(V1, V2)) -> activate#(V2))
(U12#(tt(), V1) -> isNatList#(activate(V1)), isNatList#(n__cons(V1, V2)) -> activate#(V1))
(U12#(tt(), V1) -> isNatList#(activate(V1)), isNatList#(n__cons(V1, V2)) -> isNatKind#(activate(V1)))
(U22#(tt(), V1) -> isNat#(activate(V1)), isNat#(n__s(V1)) -> U21#(isNatKind(activate(V1)), activate(V1)))
(U22#(tt(), V1) -> isNat#(activate(V1)), isNat#(n__s(V1)) -> activate#(V1))
(U22#(tt(), V1) -> isNat#(activate(V1)), isNat#(n__s(V1)) -> isNatKind#(activate(V1)))
(U22#(tt(), V1) -> isNat#(activate(V1)), isNat#(n__length(V1)) -> U11#(isNatIListKind(activate(V1)), activate(V1)))
(U91#(tt(), V1, V2) -> isNatKind#(activate(V1)), isNatKind#(n__s(V1)) -> activate#(V1))
(U91#(tt(), V1, V2) -> isNatKind#(activate(V1)), isNatKind#(n__s(V1)) -> isNatKind#(activate(V1)))
(length#(cons(N, L)) -> U111#(isNatList(activate(L)), activate(L), N), U111#(tt(), L, N) -> U112#(isNatIListKind(activate(L)), activate(L), activate(N)))
(length#(cons(N, L)) -> U111#(isNatList(activate(L)), activate(L), N), U111#(tt(), L, N) -> isNatIListKind#(activate(L)))
(length#(cons(N, L)) -> U111#(isNatList(activate(L)), activate(L), N), U111#(tt(), L, N) -> activate#(N))
(length#(cons(N, L)) -> U111#(isNatList(activate(L)), activate(L), N), U111#(tt(), L, N) -> activate#(L))
(U111#(tt(), L, N) -> activate#(L), activate#(n__cons(X1, X2)) -> activate#(X1))
(U111#(tt(), L, N) -> activate#(L), activate#(n__s(X)) -> activate#(X))
(U114#(tt(), L) -> activate#(L), activate#(n__cons(X1, X2)) -> activate#(X1))
(U114#(tt(), L) -> activate#(L), activate#(n__s(X)) -> activate#(X))
(isNatKind#(n__s(V1)) -> activate#(V1), activate#(n__cons(X1, X2)) -> activate#(X1))
(isNatKind#(n__s(V1)) -> activate#(V1), activate#(n__s(X)) -> activate#(X))
(isNat#(n__s(V1)) -> activate#(V1), activate#(n__cons(X1, X2)) -> activate#(X1))
(isNat#(n__s(V1)) -> activate#(V1), activate#(n__s(X)) -> activate#(X))
(isNatList#(n__cons(V1, V2)) -> activate#(V1), activate#(n__cons(X1, X2)) -> activate#(X1))
(isNatList#(n__cons(V1, V2)) -> activate#(V1), activate#(n__s(X)) -> activate#(X))
(U21#(tt(), V1) -> activate#(V1), activate#(n__cons(X1, X2)) -> activate#(X1))
(U21#(tt(), V1) -> activate#(V1), activate#(n__s(X)) -> activate#(X))
(U91#(tt(), V1, V2) -> activate#(V1), activate#(n__cons(X1, X2)) -> activate#(X1))
(U91#(tt(), V1, V2) -> activate#(V1), activate#(n__s(X)) -> activate#(X))
(U94#(tt(), V1, V2) -> activate#(V1), activate#(n__cons(X1, X2)) -> activate#(X1))
(U94#(tt(), V1, V2) -> activate#(V1), activate#(n__s(X)) -> activate#(X))
(U111#(tt(), L, N) -> activate#(N), activate#(n__cons(X1, X2)) -> activate#(X1))
(U111#(tt(), L, N) -> activate#(N), activate#(n__s(X)) -> activate#(X))
(activate#(n__s(X)) -> activate#(X), activate#(n__cons(X1, X2)) -> activate#(X1))
(activate#(n__s(X)) -> activate#(X), activate#(n__s(X)) -> activate#(X))
(U111#(tt(), L, N) -> U112#(isNatIListKind(activate(L)), activate(L), activate(N)), U112#(tt(), L, N) -> U113#(isNat(activate(N)), activate(L), activate(N)))
(U111#(tt(), L, N) -> U112#(isNatIListKind(activate(L)), activate(L), activate(N)), U112#(tt(), L, N) -> isNat#(activate(N)))
(U111#(tt(), L, N) -> U112#(isNatIListKind(activate(L)), activate(L), activate(N)), U112#(tt(), L, N) -> activate#(N))
(U111#(tt(), L, N) -> U112#(isNatIListKind(activate(L)), activate(L), activate(N)), U112#(tt(), L, N) -> activate#(L))
(U92#(tt(), V1, V2) -> U93#(isNatIListKind(activate(V2)), activate(V1), activate(V2)), U93#(tt(), V1, V2) -> U94#(isNatIListKind(activate(V2)), activate(V1), activate(V2)))
(U92#(tt(), V1, V2) -> U93#(isNatIListKind(activate(V2)), activate(V1), activate(V2)), U93#(tt(), V1, V2) -> isNatIListKind#(activate(V2)))
(U92#(tt(), V1, V2) -> U93#(isNatIListKind(activate(V2)), activate(V1), activate(V2)), U93#(tt(), V1, V2) -> activate#(V2))
(U92#(tt(), V1, V2) -> U93#(isNatIListKind(activate(V2)), activate(V1), activate(V2)), U93#(tt(), V1, V2) -> activate#(V1))
(U93#(tt(), V1, V2) -> U94#(isNatIListKind(activate(V2)), activate(V1), activate(V2)), U94#(tt(), V1, V2) -> U95#(isNat(activate(V1)), activate(V2)))
(U93#(tt(), V1, V2) -> U94#(isNatIListKind(activate(V2)), activate(V1), activate(V2)), U94#(tt(), V1, V2) -> isNat#(activate(V1)))
(U93#(tt(), V1, V2) -> U94#(isNatIListKind(activate(V2)), activate(V1), activate(V2)), U94#(tt(), V1, V2) -> activate#(V2))
(U93#(tt(), V1, V2) -> U94#(isNatIListKind(activate(V2)), activate(V1), activate(V2)), U94#(tt(), V1, V2) -> activate#(V1))
(U91#(tt(), V1, V2) -> U92#(isNatKind(activate(V1)), activate(V1), activate(V2)), U92#(tt(), V1, V2) -> activate#(V1))
(U91#(tt(), V1, V2) -> U92#(isNatKind(activate(V1)), activate(V1), activate(V2)), U92#(tt(), V1, V2) -> activate#(V2))
(U91#(tt(), V1, V2) -> U92#(isNatKind(activate(V1)), activate(V1), activate(V2)), U92#(tt(), V1, V2) -> isNatIListKind#(activate(V2)))
(U91#(tt(), V1, V2) -> U92#(isNatKind(activate(V1)), activate(V1), activate(V2)), U92#(tt(), V1, V2) -> U93#(isNatIListKind(activate(V2)), activate(V1), activate(V2)))
(isNatList#(n__cons(V1, V2)) -> U91#(isNatKind(activate(V1)), activate(V1), activate(V2)), U91#(tt(), V1, V2) -> isNatKind#(activate(V1)))
(isNatList#(n__cons(V1, V2)) -> U91#(isNatKind(activate(V1)), activate(V1), activate(V2)), U91#(tt(), V1, V2) -> activate#(V1))
(isNatList#(n__cons(V1, V2)) -> U91#(isNatKind(activate(V1)), activate(V1), activate(V2)), U91#(tt(), V1, V2) -> activate#(V2))
(isNatList#(n__cons(V1, V2)) -> U91#(isNatKind(activate(V1)), activate(V1), activate(V2)), U91#(tt(), V1, V2) -> U92#(isNatKind(activate(V1)), activate(V1), activate(V2)))
(U112#(tt(), L, N) -> U113#(isNat(activate(N)), activate(L), activate(N)), U113#(tt(), L, N) -> isNatKind#(activate(N)))
(U112#(tt(), L, N) -> U113#(isNat(activate(N)), activate(L), activate(N)), U113#(tt(), L, N) -> activate#(L))
(U112#(tt(), L, N) -> U113#(isNat(activate(N)), activate(L), activate(N)), U113#(tt(), L, N) -> activate#(N))
(U112#(tt(), L, N) -> U113#(isNat(activate(N)), activate(L), activate(N)), U113#(tt(), L, N) -> U114#(isNatKind(activate(N)), activate(L)))
(U113#(tt(), L, N) -> activate#(N), activate#(n__s(X)) -> activate#(X))
(U113#(tt(), L, N) -> activate#(N), activate#(n__cons(X1, X2)) -> activate#(X1))
(U112#(tt(), L, N) -> activate#(N), activate#(n__s(X)) -> activate#(X))
(U112#(tt(), L, N) -> activate#(N), activate#(n__cons(X1, X2)) -> activate#(X1))
(U93#(tt(), V1, V2) -> activate#(V1), activate#(n__s(X)) -> activate#(X))
(U93#(tt(), V1, V2) -> activate#(V1), activate#(n__cons(X1, X2)) -> activate#(X1))
(U92#(tt(), V1, V2) -> activate#(V1), activate#(n__s(X)) -> activate#(X))
(U92#(tt(), V1, V2) -> activate#(V1), activate#(n__cons(X1, X2)) -> activate#(X1))
(U22#(tt(), V1) -> activate#(V1), activate#(n__s(X)) -> activate#(X))
(U22#(tt(), V1) -> activate#(V1), activate#(n__cons(X1, X2)) -> activate#(X1))
(U12#(tt(), V1) -> activate#(V1), activate#(n__s(X)) -> activate#(X))
(U12#(tt(), V1) -> activate#(V1), activate#(n__cons(X1, X2)) -> activate#(X1))
(isNatIListKind#(n__cons(V1, V2)) -> activate#(V1), activate#(n__s(X)) -> activate#(X))
(isNatIListKind#(n__cons(V1, V2)) -> activate#(V1), activate#(n__cons(X1, X2)) -> activate#(X1))
(length#(cons(N, L)) -> activate#(L), activate#(n__s(X)) -> activate#(X))
(length#(cons(N, L)) -> activate#(L), activate#(n__cons(X1, X2)) -> activate#(X1))
(U113#(tt(), L, N) -> activate#(L), activate#(n__s(X)) -> activate#(X))
(U113#(tt(), L, N) -> activate#(L), activate#(n__cons(X1, X2)) -> activate#(X1))
(U112#(tt(), L, N) -> activate#(L), activate#(n__s(X)) -> activate#(X))
(U112#(tt(), L, N) -> activate#(L), activate#(n__cons(X1, X2)) -> activate#(X1))
(U94#(tt(), V1, V2) -> isNat#(activate(V1)), isNat#(n__length(V1)) -> U11#(isNatIListKind(activate(V1)), activate(V1)))
(U94#(tt(), V1, V2) -> isNat#(activate(V1)), isNat#(n__s(V1)) -> isNatKind#(activate(V1)))
(U94#(tt(), V1, V2) -> isNat#(activate(V1)), isNat#(n__s(V1)) -> activate#(V1))
(U94#(tt(), V1, V2) -> isNat#(activate(V1)), isNat#(n__s(V1)) -> U21#(isNatKind(activate(V1)), activate(V1)))
(U21#(tt(), V1) -> isNatKind#(activate(V1)), isNatKind#(n__s(V1)) -> isNatKind#(activate(V1)))
(U21#(tt(), V1) -> isNatKind#(activate(V1)), isNatKind#(n__s(V1)) -> activate#(V1))
(isNatList#(n__cons(V1, V2)) -> isNatKind#(activate(V1)), isNatKind#(n__s(V1)) -> isNatKind#(activate(V1)))
(isNatList#(n__cons(V1, V2)) -> isNatKind#(activate(V1)), isNatKind#(n__s(V1)) -> activate#(V1))
(isNat#(n__s(V1)) -> isNatKind#(activate(V1)), isNatKind#(n__s(V1)) -> isNatKind#(activate(V1)))
(isNat#(n__s(V1)) -> isNatKind#(activate(V1)), isNatKind#(n__s(V1)) -> activate#(V1))
(isNatKind#(n__s(V1)) -> isNatKind#(activate(V1)), isNatKind#(n__s(V1)) -> isNatKind#(activate(V1)))
(isNatKind#(n__s(V1)) -> isNatKind#(activate(V1)), isNatKind#(n__s(V1)) -> activate#(V1))
(U93#(tt(), V1, V2) -> isNatIListKind#(activate(V2)), isNatIListKind#(n__cons(V1, V2)) -> isNatKind#(activate(V1)))
(U93#(tt(), V1, V2) -> isNatIListKind#(activate(V2)), isNatIListKind#(n__cons(V1, V2)) -> activate#(V1))
(U93#(tt(), V1, V2) -> isNatIListKind#(activate(V2)), isNatIListKind#(n__cons(V1, V2)) -> activate#(V2))
(U93#(tt(), V1, V2) -> isNatIListKind#(activate(V2)), isNatIListKind#(n__cons(V1, V2)) -> U51#(isNatKind(activate(V1)), activate(V2)))
(U51#(tt(), V2) -> isNatIListKind#(activate(V2)), isNatIListKind#(n__cons(V1, V2)) -> isNatKind#(activate(V1)))
(U51#(tt(), V2) -> isNatIListKind#(activate(V2)), isNatIListKind#(n__cons(V1, V2)) -> activate#(V1))
(U51#(tt(), V2) -> isNatIListKind#(activate(V2)), isNatIListKind#(n__cons(V1, V2)) -> activate#(V2))
(U51#(tt(), V2) -> isNatIListKind#(activate(V2)), isNatIListKind#(n__cons(V1, V2)) -> U51#(isNatKind(activate(V1)), activate(V2)))
(U114#(tt(), L) -> length#(activate(L)), length#(cons(N, L)) -> activate#(L))
(U114#(tt(), L) -> length#(activate(L)), length#(cons(N, L)) -> U111#(isNatList(activate(L)), activate(L), N))
(U114#(tt(), L) -> length#(activate(L)), length#(cons(N, L)) -> isNatList#(activate(L)))
(U113#(tt(), L, N) -> isNatKind#(activate(N)), isNatKind#(n__s(V1)) -> isNatKind#(activate(V1)))
(U113#(tt(), L, N) -> isNatKind#(activate(N)), isNatKind#(n__s(V1)) -> activate#(V1))
(activate#(n__cons(X1, X2)) -> activate#(X1), activate#(n__s(X)) -> activate#(X))
(activate#(n__cons(X1, X2)) -> activate#(X1), activate#(n__cons(X1, X2)) -> activate#(X1))
(U94#(tt(), V1, V2) -> activate#(V2), activate#(n__s(X)) -> activate#(X))
(U94#(tt(), V1, V2) -> activate#(V2), activate#(n__cons(X1, X2)) -> activate#(X1))
(U91#(tt(), V1, V2) -> activate#(V2), activate#(n__s(X)) -> activate#(X))
(U91#(tt(), V1, V2) -> activate#(V2), activate#(n__cons(X1, X2)) -> activate#(X1))
(U51#(tt(), V2) -> activate#(V2), activate#(n__s(X)) -> activate#(X))
(U51#(tt(), V2) -> activate#(V2), activate#(n__cons(X1, X2)) -> activate#(X1))
(isNatIListKind#(n__cons(V1, V2)) -> activate#(V2), activate#(n__s(X)) -> activate#(X))
(isNatIListKind#(n__cons(V1, V2)) -> activate#(V2), activate#(n__cons(X1, X2)) -> activate#(X1))
(U21#(tt(), V1) -> U22#(isNatKind(activate(V1)), activate(V1)), U22#(tt(), V1) -> activate#(V1))
(U21#(tt(), V1) -> U22#(isNatKind(activate(V1)), activate(V1)), U22#(tt(), V1) -> isNat#(activate(V1)))
(isNat#(n__s(V1)) -> U21#(isNatKind(activate(V1)), activate(V1)), U21#(tt(), V1) -> isNatKind#(activate(V1)))
(isNat#(n__s(V1)) -> U21#(isNatKind(activate(V1)), activate(V1)), U21#(tt(), V1) -> activate#(V1))
(isNat#(n__s(V1)) -> U21#(isNatKind(activate(V1)), activate(V1)), U21#(tt(), V1) -> U22#(isNatKind(activate(V1)), activate(V1)))
(isNatIListKind#(n__cons(V1, V2)) -> U51#(isNatKind(activate(V1)), activate(V2)), U51#(tt(), V2) -> activate#(V2))
(isNatIListKind#(n__cons(V1, V2)) -> U51#(isNatKind(activate(V1)), activate(V2)), U51#(tt(), V2) -> isNatIListKind#(activate(V2)))
}
SCCS:
Scc:
{isNatList#(n__cons(V1, V2)) -> U91#(isNatKind(activate(V1)), activate(V1), activate(V2)),
U92#(tt(), V1, V2) -> U93#(isNatIListKind(activate(V2)), activate(V1), activate(V2)),
U91#(tt(), V1, V2) -> U92#(isNatKind(activate(V1)), activate(V1), activate(V2)),
U93#(tt(), V1, V2) -> U94#(isNatIListKind(activate(V2)), activate(V1), activate(V2)),
U94#(tt(), V1, V2) -> U95#(isNat(activate(V1)), activate(V2)),
U95#(tt(), V2) -> isNatList#(activate(V2))}
Scc:
{ U112#(tt(), L, N) -> U113#(isNat(activate(N)), activate(L), activate(N)),
U111#(tt(), L, N) -> U112#(isNatIListKind(activate(L)), activate(L), activate(N)),
U113#(tt(), L, N) -> U114#(isNatKind(activate(N)), activate(L)),
U114#(tt(), L) -> length#(activate(L)),
length#(cons(N, L)) -> U111#(isNatList(activate(L)), activate(L), N)}
Scc:
{isNat#(n__s(V1)) -> U21#(isNatKind(activate(V1)), activate(V1)),
U22#(tt(), V1) -> isNat#(activate(V1)),
U21#(tt(), V1) -> U22#(isNatKind(activate(V1)), activate(V1))}
Scc:
{isNatIListKind#(n__cons(V1, V2)) -> U51#(isNatKind(activate(V1)), activate(V2)),
U51#(tt(), V2) -> isNatIListKind#(activate(V2))}
Scc:
{ activate#(n__s(X)) -> activate#(X),
activate#(n__cons(X1, X2)) -> activate#(X1)}
Scc:
{isNatKind#(n__s(V1)) -> isNatKind#(activate(V1))}
SCC:
Strict:
{isNatList#(n__cons(V1, V2)) -> U91#(isNatKind(activate(V1)), activate(V1), activate(V2)),
U92#(tt(), V1, V2) -> U93#(isNatIListKind(activate(V2)), activate(V1), activate(V2)),
U91#(tt(), V1, V2) -> U92#(isNatKind(activate(V1)), activate(V1), activate(V2)),
U93#(tt(), V1, V2) -> U94#(isNatIListKind(activate(V2)), activate(V1), activate(V2)),
U94#(tt(), V1, V2) -> U95#(isNat(activate(V1)), activate(V2)),
U95#(tt(), V2) -> isNatList#(activate(V2))}
Weak:
{ cons(X1, X2) -> n__cons(X1, X2),
0() -> n__0(),
zeros() -> cons(0(), n__zeros()),
zeros() -> n__zeros(),
U102(tt(), V1, V2) -> U103(isNatIListKind(activate(V2)), activate(V1), activate(V2)),
isNatKind(n__0()) -> tt(),
isNatKind(n__length(V1)) -> U71(isNatIListKind(activate(V1))),
isNatKind(n__s(V1)) -> U81(isNatKind(activate(V1))),
activate(X) -> X,
activate(n__zeros()) -> zeros(),
activate(n__take(X1, X2)) -> take(activate(X1), activate(X2)),
activate(n__0()) -> 0(),
activate(n__length(X)) -> length(activate(X)),
activate(n__s(X)) -> s(activate(X)),
activate(n__cons(X1, X2)) -> cons(activate(X1), X2),
activate(n__nil()) -> nil(),
U101(tt(), V1, V2) -> U102(isNatKind(activate(V1)), activate(V1), activate(V2)),
U103(tt(), V1, V2) -> U104(isNatIListKind(activate(V2)), activate(V1), activate(V2)),
isNatIListKind(n__zeros()) -> tt(),
isNatIListKind(n__take(V1, V2)) -> U61(isNatKind(activate(V1)), activate(V2)),
isNatIListKind(n__cons(V1, V2)) -> U51(isNatKind(activate(V1)), activate(V2)),
isNatIListKind(n__nil()) -> tt(),
U104(tt(), V1, V2) -> U105(isNat(activate(V1)), activate(V2)),
U105(tt(), V2) -> U106(isNatIList(activate(V2))),
isNat(n__0()) -> tt(),
isNat(n__length(V1)) -> U11(isNatIListKind(activate(V1)), activate(V1)),
isNat(n__s(V1)) -> U21(isNatKind(activate(V1)), activate(V1)),
U106(tt()) -> tt(),
isNatIList(V) -> U31(isNatIListKind(activate(V)), activate(V)),
isNatIList(n__zeros()) -> tt(),
isNatIList(n__cons(V1, V2)) -> U41(isNatKind(activate(V1)), activate(V1), activate(V2)),
U12(tt(), V1) -> U13(isNatList(activate(V1))),
U11(tt(), V1) -> U12(isNatIListKind(activate(V1)), activate(V1)),
U112(tt(), L, N) -> U113(isNat(activate(N)), activate(L), activate(N)),
U111(tt(), L, N) -> U112(isNatIListKind(activate(L)), activate(L), activate(N)),
U113(tt(), L, N) -> U114(isNatKind(activate(N)), activate(L)),
U114(tt(), L) -> s(length(activate(L))),
s(X) -> n__s(X),
length(X) -> n__length(X),
length(cons(N, L)) -> U111(isNatList(activate(L)), activate(L), N),
length(nil()) -> 0(),
U13(tt()) -> tt(),
isNatList(n__take(V1, V2)) -> U101(isNatKind(activate(V1)), activate(V1), activate(V2)),
isNatList(n__cons(V1, V2)) -> U91(isNatKind(activate(V1)), activate(V1), activate(V2)),
isNatList(n__nil()) -> tt(),
U122(tt()) -> nil(),
U121(tt(), IL) -> U122(isNatIListKind(activate(IL))),
nil() -> n__nil(),
U132(tt(), IL, M, N) -> U133(isNat(activate(M)), activate(IL), activate(M), activate(N)),
U131(tt(), IL, M, N) -> U132(isNatIListKind(activate(IL)), activate(IL), activate(M), activate(N)),
U133(tt(), IL, M, N) -> U134(isNatKind(activate(M)), activate(IL), activate(M), activate(N)),
U134(tt(), IL, M, N) -> U135(isNat(activate(N)), activate(IL), activate(M), activate(N)),
U135(tt(), IL, M, N) -> U136(isNatKind(activate(N)), activate(IL), activate(M), activate(N)),
U136(tt(), IL, M, N) -> cons(activate(N), n__take(activate(M), activate(IL))),
U22(tt(), V1) -> U23(isNat(activate(V1))),
U21(tt(), V1) -> U22(isNatKind(activate(V1)), activate(V1)),
U23(tt()) -> tt(),
U32(tt(), V) -> U33(isNatList(activate(V))),
U31(tt(), V) -> U32(isNatIListKind(activate(V)), activate(V)),
U33(tt()) -> tt(),
U42(tt(), V1, V2) -> U43(isNatIListKind(activate(V2)), activate(V1), activate(V2)),
U41(tt(), V1, V2) -> U42(isNatKind(activate(V1)), activate(V1), activate(V2)),
U43(tt(), V1, V2) -> U44(isNatIListKind(activate(V2)), activate(V1), activate(V2)),
U44(tt(), V1, V2) -> U45(isNat(activate(V1)), activate(V2)),
U45(tt(), V2) -> U46(isNatIList(activate(V2))),
U46(tt()) -> tt(),
U52(tt()) -> tt(),
U51(tt(), V2) -> U52(isNatIListKind(activate(V2))),
U62(tt()) -> tt(),
U61(tt(), V2) -> U62(isNatIListKind(activate(V2))),
U71(tt()) -> tt(),
U81(tt()) -> tt(),
U92(tt(), V1, V2) -> U93(isNatIListKind(activate(V2)), activate(V1), activate(V2)),
U91(tt(), V1, V2) -> U92(isNatKind(activate(V1)), activate(V1), activate(V2)),
U93(tt(), V1, V2) -> U94(isNatIListKind(activate(V2)), activate(V1), activate(V2)),
U94(tt(), V1, V2) -> U95(isNat(activate(V1)), activate(V2)),
U95(tt(), V2) -> U96(isNatList(activate(V2))),
U96(tt()) -> tt(),
take(X1, X2) -> n__take(X1, X2),
take(0(), IL) -> U121(isNatIList(IL), IL),
take(s(M), cons(N, IL)) -> U131(isNatIList(activate(IL)), activate(IL), M, N)}
Fail
SCC:
Strict:
{ U112#(tt(), L, N) -> U113#(isNat(activate(N)), activate(L), activate(N)),
U111#(tt(), L, N) -> U112#(isNatIListKind(activate(L)), activate(L), activate(N)),
U113#(tt(), L, N) -> U114#(isNatKind(activate(N)), activate(L)),
U114#(tt(), L) -> length#(activate(L)),
length#(cons(N, L)) -> U111#(isNatList(activate(L)), activate(L), N)}
Weak:
{ cons(X1, X2) -> n__cons(X1, X2),
0() -> n__0(),
zeros() -> cons(0(), n__zeros()),
zeros() -> n__zeros(),
U102(tt(), V1, V2) -> U103(isNatIListKind(activate(V2)), activate(V1), activate(V2)),
isNatKind(n__0()) -> tt(),
isNatKind(n__length(V1)) -> U71(isNatIListKind(activate(V1))),
isNatKind(n__s(V1)) -> U81(isNatKind(activate(V1))),
activate(X) -> X,
activate(n__zeros()) -> zeros(),
activate(n__take(X1, X2)) -> take(activate(X1), activate(X2)),
activate(n__0()) -> 0(),
activate(n__length(X)) -> length(activate(X)),
activate(n__s(X)) -> s(activate(X)),
activate(n__cons(X1, X2)) -> cons(activate(X1), X2),
activate(n__nil()) -> nil(),
U101(tt(), V1, V2) -> U102(isNatKind(activate(V1)), activate(V1), activate(V2)),
U103(tt(), V1, V2) -> U104(isNatIListKind(activate(V2)), activate(V1), activate(V2)),
isNatIListKind(n__zeros()) -> tt(),
isNatIListKind(n__take(V1, V2)) -> U61(isNatKind(activate(V1)), activate(V2)),
isNatIListKind(n__cons(V1, V2)) -> U51(isNatKind(activate(V1)), activate(V2)),
isNatIListKind(n__nil()) -> tt(),
U104(tt(), V1, V2) -> U105(isNat(activate(V1)), activate(V2)),
U105(tt(), V2) -> U106(isNatIList(activate(V2))),
isNat(n__0()) -> tt(),
isNat(n__length(V1)) -> U11(isNatIListKind(activate(V1)), activate(V1)),
isNat(n__s(V1)) -> U21(isNatKind(activate(V1)), activate(V1)),
U106(tt()) -> tt(),
isNatIList(V) -> U31(isNatIListKind(activate(V)), activate(V)),
isNatIList(n__zeros()) -> tt(),
isNatIList(n__cons(V1, V2)) -> U41(isNatKind(activate(V1)), activate(V1), activate(V2)),
U12(tt(), V1) -> U13(isNatList(activate(V1))),
U11(tt(), V1) -> U12(isNatIListKind(activate(V1)), activate(V1)),
U112(tt(), L, N) -> U113(isNat(activate(N)), activate(L), activate(N)),
U111(tt(), L, N) -> U112(isNatIListKind(activate(L)), activate(L), activate(N)),
U113(tt(), L, N) -> U114(isNatKind(activate(N)), activate(L)),
U114(tt(), L) -> s(length(activate(L))),
s(X) -> n__s(X),
length(X) -> n__length(X),
length(cons(N, L)) -> U111(isNatList(activate(L)), activate(L), N),
length(nil()) -> 0(),
U13(tt()) -> tt(),
isNatList(n__take(V1, V2)) -> U101(isNatKind(activate(V1)), activate(V1), activate(V2)),
isNatList(n__cons(V1, V2)) -> U91(isNatKind(activate(V1)), activate(V1), activate(V2)),
isNatList(n__nil()) -> tt(),
U122(tt()) -> nil(),
U121(tt(), IL) -> U122(isNatIListKind(activate(IL))),
nil() -> n__nil(),
U132(tt(), IL, M, N) -> U133(isNat(activate(M)), activate(IL), activate(M), activate(N)),
U131(tt(), IL, M, N) -> U132(isNatIListKind(activate(IL)), activate(IL), activate(M), activate(N)),
U133(tt(), IL, M, N) -> U134(isNatKind(activate(M)), activate(IL), activate(M), activate(N)),
U134(tt(), IL, M, N) -> U135(isNat(activate(N)), activate(IL), activate(M), activate(N)),
U135(tt(), IL, M, N) -> U136(isNatKind(activate(N)), activate(IL), activate(M), activate(N)),
U136(tt(), IL, M, N) -> cons(activate(N), n__take(activate(M), activate(IL))),
U22(tt(), V1) -> U23(isNat(activate(V1))),
U21(tt(), V1) -> U22(isNatKind(activate(V1)), activate(V1)),
U23(tt()) -> tt(),
U32(tt(), V) -> U33(isNatList(activate(V))),
U31(tt(), V) -> U32(isNatIListKind(activate(V)), activate(V)),
U33(tt()) -> tt(),
U42(tt(), V1, V2) -> U43(isNatIListKind(activate(V2)), activate(V1), activate(V2)),
U41(tt(), V1, V2) -> U42(isNatKind(activate(V1)), activate(V1), activate(V2)),
U43(tt(), V1, V2) -> U44(isNatIListKind(activate(V2)), activate(V1), activate(V2)),
U44(tt(), V1, V2) -> U45(isNat(activate(V1)), activate(V2)),
U45(tt(), V2) -> U46(isNatIList(activate(V2))),
U46(tt()) -> tt(),
U52(tt()) -> tt(),
U51(tt(), V2) -> U52(isNatIListKind(activate(V2))),
U62(tt()) -> tt(),
U61(tt(), V2) -> U62(isNatIListKind(activate(V2))),
U71(tt()) -> tt(),
U81(tt()) -> tt(),
U92(tt(), V1, V2) -> U93(isNatIListKind(activate(V2)), activate(V1), activate(V2)),
U91(tt(), V1, V2) -> U92(isNatKind(activate(V1)), activate(V1), activate(V2)),
U93(tt(), V1, V2) -> U94(isNatIListKind(activate(V2)), activate(V1), activate(V2)),
U94(tt(), V1, V2) -> U95(isNat(activate(V1)), activate(V2)),
U95(tt(), V2) -> U96(isNatList(activate(V2))),
U96(tt()) -> tt(),
take(X1, X2) -> n__take(X1, X2),
take(0(), IL) -> U121(isNatIList(IL), IL),
take(s(M), cons(N, IL)) -> U131(isNatIList(activate(IL)), activate(IL), M, N)}
Fail
SCC:
Strict:
{isNat#(n__s(V1)) -> U21#(isNatKind(activate(V1)), activate(V1)),
U22#(tt(), V1) -> isNat#(activate(V1)),
U21#(tt(), V1) -> U22#(isNatKind(activate(V1)), activate(V1))}
Weak:
{ cons(X1, X2) -> n__cons(X1, X2),
0() -> n__0(),
zeros() -> cons(0(), n__zeros()),
zeros() -> n__zeros(),
U102(tt(), V1, V2) -> U103(isNatIListKind(activate(V2)), activate(V1), activate(V2)),
isNatKind(n__0()) -> tt(),
isNatKind(n__length(V1)) -> U71(isNatIListKind(activate(V1))),
isNatKind(n__s(V1)) -> U81(isNatKind(activate(V1))),
activate(X) -> X,
activate(n__zeros()) -> zeros(),
activate(n__take(X1, X2)) -> take(activate(X1), activate(X2)),
activate(n__0()) -> 0(),
activate(n__length(X)) -> length(activate(X)),
activate(n__s(X)) -> s(activate(X)),
activate(n__cons(X1, X2)) -> cons(activate(X1), X2),
activate(n__nil()) -> nil(),
U101(tt(), V1, V2) -> U102(isNatKind(activate(V1)), activate(V1), activate(V2)),
U103(tt(), V1, V2) -> U104(isNatIListKind(activate(V2)), activate(V1), activate(V2)),
isNatIListKind(n__zeros()) -> tt(),
isNatIListKind(n__take(V1, V2)) -> U61(isNatKind(activate(V1)), activate(V2)),
isNatIListKind(n__cons(V1, V2)) -> U51(isNatKind(activate(V1)), activate(V2)),
isNatIListKind(n__nil()) -> tt(),
U104(tt(), V1, V2) -> U105(isNat(activate(V1)), activate(V2)),
U105(tt(), V2) -> U106(isNatIList(activate(V2))),
isNat(n__0()) -> tt(),
isNat(n__length(V1)) -> U11(isNatIListKind(activate(V1)), activate(V1)),
isNat(n__s(V1)) -> U21(isNatKind(activate(V1)), activate(V1)),
U106(tt()) -> tt(),
isNatIList(V) -> U31(isNatIListKind(activate(V)), activate(V)),
isNatIList(n__zeros()) -> tt(),
isNatIList(n__cons(V1, V2)) -> U41(isNatKind(activate(V1)), activate(V1), activate(V2)),
U12(tt(), V1) -> U13(isNatList(activate(V1))),
U11(tt(), V1) -> U12(isNatIListKind(activate(V1)), activate(V1)),
U112(tt(), L, N) -> U113(isNat(activate(N)), activate(L), activate(N)),
U111(tt(), L, N) -> U112(isNatIListKind(activate(L)), activate(L), activate(N)),
U113(tt(), L, N) -> U114(isNatKind(activate(N)), activate(L)),
U114(tt(), L) -> s(length(activate(L))),
s(X) -> n__s(X),
length(X) -> n__length(X),
length(cons(N, L)) -> U111(isNatList(activate(L)), activate(L), N),
length(nil()) -> 0(),
U13(tt()) -> tt(),
isNatList(n__take(V1, V2)) -> U101(isNatKind(activate(V1)), activate(V1), activate(V2)),
isNatList(n__cons(V1, V2)) -> U91(isNatKind(activate(V1)), activate(V1), activate(V2)),
isNatList(n__nil()) -> tt(),
U122(tt()) -> nil(),
U121(tt(), IL) -> U122(isNatIListKind(activate(IL))),
nil() -> n__nil(),
U132(tt(), IL, M, N) -> U133(isNat(activate(M)), activate(IL), activate(M), activate(N)),
U131(tt(), IL, M, N) -> U132(isNatIListKind(activate(IL)), activate(IL), activate(M), activate(N)),
U133(tt(), IL, M, N) -> U134(isNatKind(activate(M)), activate(IL), activate(M), activate(N)),
U134(tt(), IL, M, N) -> U135(isNat(activate(N)), activate(IL), activate(M), activate(N)),
U135(tt(), IL, M, N) -> U136(isNatKind(activate(N)), activate(IL), activate(M), activate(N)),
U136(tt(), IL, M, N) -> cons(activate(N), n__take(activate(M), activate(IL))),
U22(tt(), V1) -> U23(isNat(activate(V1))),
U21(tt(), V1) -> U22(isNatKind(activate(V1)), activate(V1)),
U23(tt()) -> tt(),
U32(tt(), V) -> U33(isNatList(activate(V))),
U31(tt(), V) -> U32(isNatIListKind(activate(V)), activate(V)),
U33(tt()) -> tt(),
U42(tt(), V1, V2) -> U43(isNatIListKind(activate(V2)), activate(V1), activate(V2)),
U41(tt(), V1, V2) -> U42(isNatKind(activate(V1)), activate(V1), activate(V2)),
U43(tt(), V1, V2) -> U44(isNatIListKind(activate(V2)), activate(V1), activate(V2)),
U44(tt(), V1, V2) -> U45(isNat(activate(V1)), activate(V2)),
U45(tt(), V2) -> U46(isNatIList(activate(V2))),
U46(tt()) -> tt(),
U52(tt()) -> tt(),
U51(tt(), V2) -> U52(isNatIListKind(activate(V2))),
U62(tt()) -> tt(),
U61(tt(), V2) -> U62(isNatIListKind(activate(V2))),
U71(tt()) -> tt(),
U81(tt()) -> tt(),
U92(tt(), V1, V2) -> U93(isNatIListKind(activate(V2)), activate(V1), activate(V2)),
U91(tt(), V1, V2) -> U92(isNatKind(activate(V1)), activate(V1), activate(V2)),
U93(tt(), V1, V2) -> U94(isNatIListKind(activate(V2)), activate(V1), activate(V2)),
U94(tt(), V1, V2) -> U95(isNat(activate(V1)), activate(V2)),
U95(tt(), V2) -> U96(isNatList(activate(V2))),
U96(tt()) -> tt(),
take(X1, X2) -> n__take(X1, X2),
take(0(), IL) -> U121(isNatIList(IL), IL),
take(s(M), cons(N, IL)) -> U131(isNatIList(activate(IL)), activate(IL), M, N)}
Fail
SCC:
Strict:
{isNatIListKind#(n__cons(V1, V2)) -> U51#(isNatKind(activate(V1)), activate(V2)),
U51#(tt(), V2) -> isNatIListKind#(activate(V2))}
Weak:
{ cons(X1, X2) -> n__cons(X1, X2),
0() -> n__0(),
zeros() -> cons(0(), n__zeros()),
zeros() -> n__zeros(),
U102(tt(), V1, V2) -> U103(isNatIListKind(activate(V2)), activate(V1), activate(V2)),
isNatKind(n__0()) -> tt(),
isNatKind(n__length(V1)) -> U71(isNatIListKind(activate(V1))),
isNatKind(n__s(V1)) -> U81(isNatKind(activate(V1))),
activate(X) -> X,
activate(n__zeros()) -> zeros(),
activate(n__take(X1, X2)) -> take(activate(X1), activate(X2)),
activate(n__0()) -> 0(),
activate(n__length(X)) -> length(activate(X)),
activate(n__s(X)) -> s(activate(X)),
activate(n__cons(X1, X2)) -> cons(activate(X1), X2),
activate(n__nil()) -> nil(),
U101(tt(), V1, V2) -> U102(isNatKind(activate(V1)), activate(V1), activate(V2)),
U103(tt(), V1, V2) -> U104(isNatIListKind(activate(V2)), activate(V1), activate(V2)),
isNatIListKind(n__zeros()) -> tt(),
isNatIListKind(n__take(V1, V2)) -> U61(isNatKind(activate(V1)), activate(V2)),
isNatIListKind(n__cons(V1, V2)) -> U51(isNatKind(activate(V1)), activate(V2)),
isNatIListKind(n__nil()) -> tt(),
U104(tt(), V1, V2) -> U105(isNat(activate(V1)), activate(V2)),
U105(tt(), V2) -> U106(isNatIList(activate(V2))),
isNat(n__0()) -> tt(),
isNat(n__length(V1)) -> U11(isNatIListKind(activate(V1)), activate(V1)),
isNat(n__s(V1)) -> U21(isNatKind(activate(V1)), activate(V1)),
U106(tt()) -> tt(),
isNatIList(V) -> U31(isNatIListKind(activate(V)), activate(V)),
isNatIList(n__zeros()) -> tt(),
isNatIList(n__cons(V1, V2)) -> U41(isNatKind(activate(V1)), activate(V1), activate(V2)),
U12(tt(), V1) -> U13(isNatList(activate(V1))),
U11(tt(), V1) -> U12(isNatIListKind(activate(V1)), activate(V1)),
U112(tt(), L, N) -> U113(isNat(activate(N)), activate(L), activate(N)),
U111(tt(), L, N) -> U112(isNatIListKind(activate(L)), activate(L), activate(N)),
U113(tt(), L, N) -> U114(isNatKind(activate(N)), activate(L)),
U114(tt(), L) -> s(length(activate(L))),
s(X) -> n__s(X),
length(X) -> n__length(X),
length(cons(N, L)) -> U111(isNatList(activate(L)), activate(L), N),
length(nil()) -> 0(),
U13(tt()) -> tt(),
isNatList(n__take(V1, V2)) -> U101(isNatKind(activate(V1)), activate(V1), activate(V2)),
isNatList(n__cons(V1, V2)) -> U91(isNatKind(activate(V1)), activate(V1), activate(V2)),
isNatList(n__nil()) -> tt(),
U122(tt()) -> nil(),
U121(tt(), IL) -> U122(isNatIListKind(activate(IL))),
nil() -> n__nil(),
U132(tt(), IL, M, N) -> U133(isNat(activate(M)), activate(IL), activate(M), activate(N)),
U131(tt(), IL, M, N) -> U132(isNatIListKind(activate(IL)), activate(IL), activate(M), activate(N)),
U133(tt(), IL, M, N) -> U134(isNatKind(activate(M)), activate(IL), activate(M), activate(N)),
U134(tt(), IL, M, N) -> U135(isNat(activate(N)), activate(IL), activate(M), activate(N)),
U135(tt(), IL, M, N) -> U136(isNatKind(activate(N)), activate(IL), activate(M), activate(N)),
U136(tt(), IL, M, N) -> cons(activate(N), n__take(activate(M), activate(IL))),
U22(tt(), V1) -> U23(isNat(activate(V1))),
U21(tt(), V1) -> U22(isNatKind(activate(V1)), activate(V1)),
U23(tt()) -> tt(),
U32(tt(), V) -> U33(isNatList(activate(V))),
U31(tt(), V) -> U32(isNatIListKind(activate(V)), activate(V)),
U33(tt()) -> tt(),
U42(tt(), V1, V2) -> U43(isNatIListKind(activate(V2)), activate(V1), activate(V2)),
U41(tt(), V1, V2) -> U42(isNatKind(activate(V1)), activate(V1), activate(V2)),
U43(tt(), V1, V2) -> U44(isNatIListKind(activate(V2)), activate(V1), activate(V2)),
U44(tt(), V1, V2) -> U45(isNat(activate(V1)), activate(V2)),
U45(tt(), V2) -> U46(isNatIList(activate(V2))),
U46(tt()) -> tt(),
U52(tt()) -> tt(),
U51(tt(), V2) -> U52(isNatIListKind(activate(V2))),
U62(tt()) -> tt(),
U61(tt(), V2) -> U62(isNatIListKind(activate(V2))),
U71(tt()) -> tt(),
U81(tt()) -> tt(),
U92(tt(), V1, V2) -> U93(isNatIListKind(activate(V2)), activate(V1), activate(V2)),
U91(tt(), V1, V2) -> U92(isNatKind(activate(V1)), activate(V1), activate(V2)),
U93(tt(), V1, V2) -> U94(isNatIListKind(activate(V2)), activate(V1), activate(V2)),
U94(tt(), V1, V2) -> U95(isNat(activate(V1)), activate(V2)),
U95(tt(), V2) -> U96(isNatList(activate(V2))),
U96(tt()) -> tt(),
take(X1, X2) -> n__take(X1, X2),
take(0(), IL) -> U121(isNatIList(IL), IL),
take(s(M), cons(N, IL)) -> U131(isNatIList(activate(IL)), activate(IL), M, N)}
Fail
SCC:
Strict:
{ activate#(n__s(X)) -> activate#(X),
activate#(n__cons(X1, X2)) -> activate#(X1)}
Weak:
{ cons(X1, X2) -> n__cons(X1, X2),
0() -> n__0(),
zeros() -> cons(0(), n__zeros()),
zeros() -> n__zeros(),
U102(tt(), V1, V2) -> U103(isNatIListKind(activate(V2)), activate(V1), activate(V2)),
isNatKind(n__0()) -> tt(),
isNatKind(n__length(V1)) -> U71(isNatIListKind(activate(V1))),
isNatKind(n__s(V1)) -> U81(isNatKind(activate(V1))),
activate(X) -> X,
activate(n__zeros()) -> zeros(),
activate(n__take(X1, X2)) -> take(activate(X1), activate(X2)),
activate(n__0()) -> 0(),
activate(n__length(X)) -> length(activate(X)),
activate(n__s(X)) -> s(activate(X)),
activate(n__cons(X1, X2)) -> cons(activate(X1), X2),
activate(n__nil()) -> nil(),
U101(tt(), V1, V2) -> U102(isNatKind(activate(V1)), activate(V1), activate(V2)),
U103(tt(), V1, V2) -> U104(isNatIListKind(activate(V2)), activate(V1), activate(V2)),
isNatIListKind(n__zeros()) -> tt(),
isNatIListKind(n__take(V1, V2)) -> U61(isNatKind(activate(V1)), activate(V2)),
isNatIListKind(n__cons(V1, V2)) -> U51(isNatKind(activate(V1)), activate(V2)),
isNatIListKind(n__nil()) -> tt(),
U104(tt(), V1, V2) -> U105(isNat(activate(V1)), activate(V2)),
U105(tt(), V2) -> U106(isNatIList(activate(V2))),
isNat(n__0()) -> tt(),
isNat(n__length(V1)) -> U11(isNatIListKind(activate(V1)), activate(V1)),
isNat(n__s(V1)) -> U21(isNatKind(activate(V1)), activate(V1)),
U106(tt()) -> tt(),
isNatIList(V) -> U31(isNatIListKind(activate(V)), activate(V)),
isNatIList(n__zeros()) -> tt(),
isNatIList(n__cons(V1, V2)) -> U41(isNatKind(activate(V1)), activate(V1), activate(V2)),
U12(tt(), V1) -> U13(isNatList(activate(V1))),
U11(tt(), V1) -> U12(isNatIListKind(activate(V1)), activate(V1)),
U112(tt(), L, N) -> U113(isNat(activate(N)), activate(L), activate(N)),
U111(tt(), L, N) -> U112(isNatIListKind(activate(L)), activate(L), activate(N)),
U113(tt(), L, N) -> U114(isNatKind(activate(N)), activate(L)),
U114(tt(), L) -> s(length(activate(L))),
s(X) -> n__s(X),
length(X) -> n__length(X),
length(cons(N, L)) -> U111(isNatList(activate(L)), activate(L), N),
length(nil()) -> 0(),
U13(tt()) -> tt(),
isNatList(n__take(V1, V2)) -> U101(isNatKind(activate(V1)), activate(V1), activate(V2)),
isNatList(n__cons(V1, V2)) -> U91(isNatKind(activate(V1)), activate(V1), activate(V2)),
isNatList(n__nil()) -> tt(),
U122(tt()) -> nil(),
U121(tt(), IL) -> U122(isNatIListKind(activate(IL))),
nil() -> n__nil(),
U132(tt(), IL, M, N) -> U133(isNat(activate(M)), activate(IL), activate(M), activate(N)),
U131(tt(), IL, M, N) -> U132(isNatIListKind(activate(IL)), activate(IL), activate(M), activate(N)),
U133(tt(), IL, M, N) -> U134(isNatKind(activate(M)), activate(IL), activate(M), activate(N)),
U134(tt(), IL, M, N) -> U135(isNat(activate(N)), activate(IL), activate(M), activate(N)),
U135(tt(), IL, M, N) -> U136(isNatKind(activate(N)), activate(IL), activate(M), activate(N)),
U136(tt(), IL, M, N) -> cons(activate(N), n__take(activate(M), activate(IL))),
U22(tt(), V1) -> U23(isNat(activate(V1))),
U21(tt(), V1) -> U22(isNatKind(activate(V1)), activate(V1)),
U23(tt()) -> tt(),
U32(tt(), V) -> U33(isNatList(activate(V))),
U31(tt(), V) -> U32(isNatIListKind(activate(V)), activate(V)),
U33(tt()) -> tt(),
U42(tt(), V1, V2) -> U43(isNatIListKind(activate(V2)), activate(V1), activate(V2)),
U41(tt(), V1, V2) -> U42(isNatKind(activate(V1)), activate(V1), activate(V2)),
U43(tt(), V1, V2) -> U44(isNatIListKind(activate(V2)), activate(V1), activate(V2)),
U44(tt(), V1, V2) -> U45(isNat(activate(V1)), activate(V2)),
U45(tt(), V2) -> U46(isNatIList(activate(V2))),
U46(tt()) -> tt(),
U52(tt()) -> tt(),
U51(tt(), V2) -> U52(isNatIListKind(activate(V2))),
U62(tt()) -> tt(),
U61(tt(), V2) -> U62(isNatIListKind(activate(V2))),
U71(tt()) -> tt(),
U81(tt()) -> tt(),
U92(tt(), V1, V2) -> U93(isNatIListKind(activate(V2)), activate(V1), activate(V2)),
U91(tt(), V1, V2) -> U92(isNatKind(activate(V1)), activate(V1), activate(V2)),
U93(tt(), V1, V2) -> U94(isNatIListKind(activate(V2)), activate(V1), activate(V2)),
U94(tt(), V1, V2) -> U95(isNat(activate(V1)), activate(V2)),
U95(tt(), V2) -> U96(isNatList(activate(V2))),
U96(tt()) -> tt(),
take(X1, X2) -> n__take(X1, X2),
take(0(), IL) -> U121(isNatIList(IL), IL),
take(s(M), cons(N, IL)) -> U131(isNatIList(activate(IL)), activate(IL), M, N)}
SPSC:
Simple Projection:
pi(activate#) = 0
Strict:
{activate#(n__cons(X1, X2)) -> activate#(X1)}
EDG:
{(activate#(n__cons(X1, X2)) -> activate#(X1), activate#(n__cons(X1, X2)) -> activate#(X1))}
SCCS:
Scc:
{activate#(n__cons(X1, X2)) -> activate#(X1)}
SCC:
Strict:
{activate#(n__cons(X1, X2)) -> activate#(X1)}
Weak:
{ cons(X1, X2) -> n__cons(X1, X2),
0() -> n__0(),
zeros() -> cons(0(), n__zeros()),
zeros() -> n__zeros(),
U102(tt(), V1, V2) -> U103(isNatIListKind(activate(V2)), activate(V1), activate(V2)),
isNatKind(n__0()) -> tt(),
isNatKind(n__length(V1)) -> U71(isNatIListKind(activate(V1))),
isNatKind(n__s(V1)) -> U81(isNatKind(activate(V1))),
activate(X) -> X,
activate(n__zeros()) -> zeros(),
activate(n__take(X1, X2)) -> take(activate(X1), activate(X2)),
activate(n__0()) -> 0(),
activate(n__length(X)) -> length(activate(X)),
activate(n__s(X)) -> s(activate(X)),
activate(n__cons(X1, X2)) -> cons(activate(X1), X2),
activate(n__nil()) -> nil(),
U101(tt(), V1, V2) -> U102(isNatKind(activate(V1)), activate(V1), activate(V2)),
U103(tt(), V1, V2) -> U104(isNatIListKind(activate(V2)), activate(V1), activate(V2)),
isNatIListKind(n__zeros()) -> tt(),
isNatIListKind(n__take(V1, V2)) -> U61(isNatKind(activate(V1)), activate(V2)),
isNatIListKind(n__cons(V1, V2)) -> U51(isNatKind(activate(V1)), activate(V2)),
isNatIListKind(n__nil()) -> tt(),
U104(tt(), V1, V2) -> U105(isNat(activate(V1)), activate(V2)),
U105(tt(), V2) -> U106(isNatIList(activate(V2))),
isNat(n__0()) -> tt(),
isNat(n__length(V1)) -> U11(isNatIListKind(activate(V1)), activate(V1)),
isNat(n__s(V1)) -> U21(isNatKind(activate(V1)), activate(V1)),
U106(tt()) -> tt(),
isNatIList(V) -> U31(isNatIListKind(activate(V)), activate(V)),
isNatIList(n__zeros()) -> tt(),
isNatIList(n__cons(V1, V2)) -> U41(isNatKind(activate(V1)), activate(V1), activate(V2)),
U12(tt(), V1) -> U13(isNatList(activate(V1))),
U11(tt(), V1) -> U12(isNatIListKind(activate(V1)), activate(V1)),
U112(tt(), L, N) -> U113(isNat(activate(N)), activate(L), activate(N)),
U111(tt(), L, N) -> U112(isNatIListKind(activate(L)), activate(L), activate(N)),
U113(tt(), L, N) -> U114(isNatKind(activate(N)), activate(L)),
U114(tt(), L) -> s(length(activate(L))),
s(X) -> n__s(X),
length(X) -> n__length(X),
length(cons(N, L)) -> U111(isNatList(activate(L)), activate(L), N),
length(nil()) -> 0(),
U13(tt()) -> tt(),
isNatList(n__take(V1, V2)) -> U101(isNatKind(activate(V1)), activate(V1), activate(V2)),
isNatList(n__cons(V1, V2)) -> U91(isNatKind(activate(V1)), activate(V1), activate(V2)),
isNatList(n__nil()) -> tt(),
U122(tt()) -> nil(),
U121(tt(), IL) -> U122(isNatIListKind(activate(IL))),
nil() -> n__nil(),
U132(tt(), IL, M, N) -> U133(isNat(activate(M)), activate(IL), activate(M), activate(N)),
U131(tt(), IL, M, N) -> U132(isNatIListKind(activate(IL)), activate(IL), activate(M), activate(N)),
U133(tt(), IL, M, N) -> U134(isNatKind(activate(M)), activate(IL), activate(M), activate(N)),
U134(tt(), IL, M, N) -> U135(isNat(activate(N)), activate(IL), activate(M), activate(N)),
U135(tt(), IL, M, N) -> U136(isNatKind(activate(N)), activate(IL), activate(M), activate(N)),
U136(tt(), IL, M, N) -> cons(activate(N), n__take(activate(M), activate(IL))),
U22(tt(), V1) -> U23(isNat(activate(V1))),
U21(tt(), V1) -> U22(isNatKind(activate(V1)), activate(V1)),
U23(tt()) -> tt(),
U32(tt(), V) -> U33(isNatList(activate(V))),
U31(tt(), V) -> U32(isNatIListKind(activate(V)), activate(V)),
U33(tt()) -> tt(),
U42(tt(), V1, V2) -> U43(isNatIListKind(activate(V2)), activate(V1), activate(V2)),
U41(tt(), V1, V2) -> U42(isNatKind(activate(V1)), activate(V1), activate(V2)),
U43(tt(), V1, V2) -> U44(isNatIListKind(activate(V2)), activate(V1), activate(V2)),
U44(tt(), V1, V2) -> U45(isNat(activate(V1)), activate(V2)),
U45(tt(), V2) -> U46(isNatIList(activate(V2))),
U46(tt()) -> tt(),
U52(tt()) -> tt(),
U51(tt(), V2) -> U52(isNatIListKind(activate(V2))),
U62(tt()) -> tt(),
U61(tt(), V2) -> U62(isNatIListKind(activate(V2))),
U71(tt()) -> tt(),
U81(tt()) -> tt(),
U92(tt(), V1, V2) -> U93(isNatIListKind(activate(V2)), activate(V1), activate(V2)),
U91(tt(), V1, V2) -> U92(isNatKind(activate(V1)), activate(V1), activate(V2)),
U93(tt(), V1, V2) -> U94(isNatIListKind(activate(V2)), activate(V1), activate(V2)),
U94(tt(), V1, V2) -> U95(isNat(activate(V1)), activate(V2)),
U95(tt(), V2) -> U96(isNatList(activate(V2))),
U96(tt()) -> tt(),
take(X1, X2) -> n__take(X1, X2),
take(0(), IL) -> U121(isNatIList(IL), IL),
take(s(M), cons(N, IL)) -> U131(isNatIList(activate(IL)), activate(IL), M, N)}
SPSC:
Simple Projection:
pi(activate#) = 0
Strict:
{}
Qed
SCC:
Strict:
{isNatKind#(n__s(V1)) -> isNatKind#(activate(V1))}
Weak:
{ cons(X1, X2) -> n__cons(X1, X2),
0() -> n__0(),
zeros() -> cons(0(), n__zeros()),
zeros() -> n__zeros(),
U102(tt(), V1, V2) -> U103(isNatIListKind(activate(V2)), activate(V1), activate(V2)),
isNatKind(n__0()) -> tt(),
isNatKind(n__length(V1)) -> U71(isNatIListKind(activate(V1))),
isNatKind(n__s(V1)) -> U81(isNatKind(activate(V1))),
activate(X) -> X,
activate(n__zeros()) -> zeros(),
activate(n__take(X1, X2)) -> take(activate(X1), activate(X2)),
activate(n__0()) -> 0(),
activate(n__length(X)) -> length(activate(X)),
activate(n__s(X)) -> s(activate(X)),
activate(n__cons(X1, X2)) -> cons(activate(X1), X2),
activate(n__nil()) -> nil(),
U101(tt(), V1, V2) -> U102(isNatKind(activate(V1)), activate(V1), activate(V2)),
U103(tt(), V1, V2) -> U104(isNatIListKind(activate(V2)), activate(V1), activate(V2)),
isNatIListKind(n__zeros()) -> tt(),
isNatIListKind(n__take(V1, V2)) -> U61(isNatKind(activate(V1)), activate(V2)),
isNatIListKind(n__cons(V1, V2)) -> U51(isNatKind(activate(V1)), activate(V2)),
isNatIListKind(n__nil()) -> tt(),
U104(tt(), V1, V2) -> U105(isNat(activate(V1)), activate(V2)),
U105(tt(), V2) -> U106(isNatIList(activate(V2))),
isNat(n__0()) -> tt(),
isNat(n__length(V1)) -> U11(isNatIListKind(activate(V1)), activate(V1)),
isNat(n__s(V1)) -> U21(isNatKind(activate(V1)), activate(V1)),
U106(tt()) -> tt(),
isNatIList(V) -> U31(isNatIListKind(activate(V)), activate(V)),
isNatIList(n__zeros()) -> tt(),
isNatIList(n__cons(V1, V2)) -> U41(isNatKind(activate(V1)), activate(V1), activate(V2)),
U12(tt(), V1) -> U13(isNatList(activate(V1))),
U11(tt(), V1) -> U12(isNatIListKind(activate(V1)), activate(V1)),
U112(tt(), L, N) -> U113(isNat(activate(N)), activate(L), activate(N)),
U111(tt(), L, N) -> U112(isNatIListKind(activate(L)), activate(L), activate(N)),
U113(tt(), L, N) -> U114(isNatKind(activate(N)), activate(L)),
U114(tt(), L) -> s(length(activate(L))),
s(X) -> n__s(X),
length(X) -> n__length(X),
length(cons(N, L)) -> U111(isNatList(activate(L)), activate(L), N),
length(nil()) -> 0(),
U13(tt()) -> tt(),
isNatList(n__take(V1, V2)) -> U101(isNatKind(activate(V1)), activate(V1), activate(V2)),
isNatList(n__cons(V1, V2)) -> U91(isNatKind(activate(V1)), activate(V1), activate(V2)),
isNatList(n__nil()) -> tt(),
U122(tt()) -> nil(),
U121(tt(), IL) -> U122(isNatIListKind(activate(IL))),
nil() -> n__nil(),
U132(tt(), IL, M, N) -> U133(isNat(activate(M)), activate(IL), activate(M), activate(N)),
U131(tt(), IL, M, N) -> U132(isNatIListKind(activate(IL)), activate(IL), activate(M), activate(N)),
U133(tt(), IL, M, N) -> U134(isNatKind(activate(M)), activate(IL), activate(M), activate(N)),
U134(tt(), IL, M, N) -> U135(isNat(activate(N)), activate(IL), activate(M), activate(N)),
U135(tt(), IL, M, N) -> U136(isNatKind(activate(N)), activate(IL), activate(M), activate(N)),
U136(tt(), IL, M, N) -> cons(activate(N), n__take(activate(M), activate(IL))),
U22(tt(), V1) -> U23(isNat(activate(V1))),
U21(tt(), V1) -> U22(isNatKind(activate(V1)), activate(V1)),
U23(tt()) -> tt(),
U32(tt(), V) -> U33(isNatList(activate(V))),
U31(tt(), V) -> U32(isNatIListKind(activate(V)), activate(V)),
U33(tt()) -> tt(),
U42(tt(), V1, V2) -> U43(isNatIListKind(activate(V2)), activate(V1), activate(V2)),
U41(tt(), V1, V2) -> U42(isNatKind(activate(V1)), activate(V1), activate(V2)),
U43(tt(), V1, V2) -> U44(isNatIListKind(activate(V2)), activate(V1), activate(V2)),
U44(tt(), V1, V2) -> U45(isNat(activate(V1)), activate(V2)),
U45(tt(), V2) -> U46(isNatIList(activate(V2))),
U46(tt()) -> tt(),
U52(tt()) -> tt(),
U51(tt(), V2) -> U52(isNatIListKind(activate(V2))),
U62(tt()) -> tt(),
U61(tt(), V2) -> U62(isNatIListKind(activate(V2))),
U71(tt()) -> tt(),
U81(tt()) -> tt(),
U92(tt(), V1, V2) -> U93(isNatIListKind(activate(V2)), activate(V1), activate(V2)),
U91(tt(), V1, V2) -> U92(isNatKind(activate(V1)), activate(V1), activate(V2)),
U93(tt(), V1, V2) -> U94(isNatIListKind(activate(V2)), activate(V1), activate(V2)),
U94(tt(), V1, V2) -> U95(isNat(activate(V1)), activate(V2)),
U95(tt(), V2) -> U96(isNatList(activate(V2))),
U96(tt()) -> tt(),
take(X1, X2) -> n__take(X1, X2),
take(0(), IL) -> U121(isNatIList(IL), IL),
take(s(M), cons(N, IL)) -> U131(isNatIList(activate(IL)), activate(IL), M, N)}
Fail