MAYBE We are left with following problem, upon which TcT provides the certificate MAYBE. Strict Trs: { a__zeros() -> cons(0(), zeros()) , a__zeros() -> zeros() , a__U11(X1, X2) -> U11(X1, X2) , a__U11(tt(), L) -> s(a__length(mark(L))) , a__length(X) -> length(X) , a__length(cons(N, L)) -> a__U11(a__and(a__isNatList(L), isNat(N)), L) , a__length(nil()) -> 0() , mark(cons(X1, X2)) -> cons(mark(X1), X2) , mark(0()) -> 0() , mark(zeros()) -> a__zeros() , mark(tt()) -> tt() , mark(s(X)) -> s(mark(X)) , mark(length(X)) -> a__length(mark(X)) , mark(isNatIList(X)) -> a__isNatIList(X) , mark(nil()) -> nil() , mark(isNatList(X)) -> a__isNatList(X) , mark(isNat(X)) -> a__isNat(X) , mark(U11(X1, X2)) -> a__U11(mark(X1), X2) , mark(and(X1, X2)) -> a__and(mark(X1), X2) , a__and(X1, X2) -> and(X1, X2) , a__and(tt(), X) -> mark(X) , a__isNat(X) -> isNat(X) , a__isNat(0()) -> tt() , a__isNat(s(V1)) -> a__isNat(V1) , a__isNat(length(V1)) -> a__isNatList(V1) , a__isNatList(X) -> isNatList(X) , a__isNatList(cons(V1, V2)) -> a__and(a__isNat(V1), isNatList(V2)) , a__isNatList(nil()) -> tt() , a__isNatIList(V) -> a__isNatList(V) , a__isNatIList(X) -> isNatIList(X) , a__isNatIList(cons(V1, V2)) -> a__and(a__isNat(V1), isNatIList(V2)) , a__isNatIList(zeros()) -> tt() } Obligation: innermost runtime complexity Answer: MAYBE The input cannot be shown compatible Arrrr..