(0) Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:
a__zeros → cons(0, zeros)
a__U11(tt, L) → s(a__length(mark(L)))
a__and(tt, X) → mark(X)
a__isNat(0) → tt
a__isNat(length(V1)) → a__isNatList(V1)
a__isNat(s(V1)) → a__isNat(V1)
a__isNatIList(V) → a__isNatList(V)
a__isNatIList(zeros) → tt
a__isNatIList(cons(V1, V2)) → a__and(a__isNat(V1), isNatIList(V2))
a__isNatList(nil) → tt
a__isNatList(cons(V1, V2)) → a__and(a__isNat(V1), isNatList(V2))
a__length(nil) → 0
a__length(cons(N, L)) → a__U11(a__and(a__isNatList(L), isNat(N)), L)
mark(zeros) → a__zeros
mark(U11(X1, X2)) → a__U11(mark(X1), X2)
mark(length(X)) → a__length(mark(X))
mark(and(X1, X2)) → a__and(mark(X1), X2)
mark(isNat(X)) → a__isNat(X)
mark(isNatList(X)) → a__isNatList(X)
mark(isNatIList(X)) → a__isNatIList(X)
mark(cons(X1, X2)) → cons(mark(X1), X2)
mark(0) → 0
mark(tt) → tt
mark(s(X)) → s(mark(X))
mark(nil) → nil
a__zeros → zeros
a__U11(X1, X2) → U11(X1, X2)
a__length(X) → length(X)
a__and(X1, X2) → and(X1, X2)
a__isNat(X) → isNat(X)
a__isNatList(X) → isNatList(X)
a__isNatIList(X) → isNatIList(X)
Q is empty.