(VAR V1 V V2 L X N X1 X2)
(RULES 
zeros -> cons(0,n__zeros)
U11(tt,V1) -> U12(isNatList(activate(V1)))
U12(tt) -> tt
U21(tt,V1) -> U22(isNat(activate(V1)))
U22(tt) -> tt
U31(tt,V) -> U32(isNatList(activate(V)))
U32(tt) -> tt
U41(tt,V1,V2) -> U42(isNat(activate(V1)),activate(V2))
U42(tt,V2) -> U43(isNatIList(activate(V2)))
U43(tt) -> tt
U51(tt,V1,V2) -> U52(isNat(activate(V1)),activate(V2))
U52(tt,V2) -> U53(isNatList(activate(V2)))
U53(tt) -> tt
U61(tt,L) -> s(length(activate(L)))
and(tt,X) -> activate(X)
isNat(n__0) -> tt
isNat(n__length(V1)) -> U11(isNatIListKind(activate(V1)),activate(V1))
isNat(n__s(V1)) -> U21(isNatKind(activate(V1)),activate(V1))
isNatIList(V) -> U31(isNatIListKind(activate(V)),activate(V))
isNatIList(n__zeros) -> tt
isNatIList(n__cons(V1,V2)) -> U41(and(isNatKind(activate(V1)),n__isNatIListKind(activate(V2))),activate(V1),activate(V2))
isNatIListKind(n__nil) -> tt
isNatIListKind(n__zeros) -> tt
isNatIListKind(n__cons(V1,V2)) -> and(isNatKind(activate(V1)),n__isNatIListKind(activate(V2)))
isNatKind(n__0) -> tt
isNatKind(n__length(V1)) -> isNatIListKind(activate(V1))
isNatKind(n__s(V1)) -> isNatKind(activate(V1))
isNatList(n__nil) -> tt
isNatList(n__cons(V1,V2)) -> U51(and(isNatKind(activate(V1)),n__isNatIListKind(activate(V2))),activate(V1),activate(V2))
length(nil) -> 0
length(cons(N,L)) -> U61(and(and(isNatList(activate(L)),n__isNatIListKind(activate(L))),n__and(isNat(N),n__isNatKind(N))),activate(L))
zeros -> n__zeros
0 -> n__0
length(X) -> n__length(X)
s(X) -> n__s(X)
cons(X1,X2) -> n__cons(X1,X2)
isNatIListKind(X) -> n__isNatIListKind(X)
nil -> n__nil
and(X1,X2) -> n__and(X1,X2)
isNatKind(X) -> n__isNatKind(X)
activate(n__zeros) -> zeros
activate(n__0) -> 0
activate(n__length(X)) -> length(X)
activate(n__s(X)) -> s(X)
activate(n__cons(X1,X2)) -> cons(X1,X2)
activate(n__isNatIListKind(X)) -> isNatIListKind(X)
activate(n__nil) -> nil
activate(n__and(X1,X2)) -> and(X1,X2)
activate(n__isNatKind(X)) -> isNatKind(X)
activate(X) -> X
)