TRS:
 {                     a__zeros() -> cons(0(), zeros()),
                 a__U11(tt(), V1) -> a__U12(a__isNatIListKind(V1), V1),
                 a__U12(tt(), V1) -> a__U13(a__isNatList(V1)),
                     a__U13(tt()) -> tt(),
                 a__U21(tt(), V1) -> a__U22(a__isNatKind(V1), V1),
                 a__U22(tt(), V1) -> a__U23(a__isNat(V1)),
                     a__U23(tt()) -> tt(),
                  a__U31(tt(), V) -> a__U32(a__isNatIListKind(V), V),
                  a__U32(tt(), V) -> a__U33(a__isNatList(V)),
                     a__U33(tt()) -> tt(),
             a__U41(tt(), V1, V2) -> a__U42(a__isNatKind(V1), V1, V2),
             a__U42(tt(), V1, V2) -> a__U43(a__isNatIListKind(V2), V1, V2),
             a__U43(tt(), V1, V2) -> a__U44(a__isNatIListKind(V2), V1, V2),
             a__U44(tt(), V1, V2) -> a__U45(a__isNat(V1), V2),
                 a__U45(tt(), V2) -> a__U46(a__isNatIList(V2)),
                     a__U46(tt()) -> tt(),
                 a__U51(tt(), V2) -> a__U52(a__isNatIListKind(V2)),
                     a__U52(tt()) -> tt(),
                     a__U61(tt()) -> tt(),
                     a__U71(tt()) -> tt(),
             a__U81(tt(), V1, V2) -> a__U82(a__isNatKind(V1), V1, V2),
             a__U82(tt(), V1, V2) -> a__U83(a__isNatIListKind(V2), V1, V2),
             a__U83(tt(), V1, V2) -> a__U84(a__isNatIListKind(V2), V1, V2),
             a__U84(tt(), V1, V2) -> a__U85(a__isNat(V1), V2),
                 a__U85(tt(), V2) -> a__U86(a__isNatList(V2)),
                     a__U86(tt()) -> tt(),
               a__U91(tt(), L, N) -> a__U92(a__isNatIListKind(L), L, N),
               a__U92(tt(), L, N) -> a__U93(a__isNat(N), L, N),
               a__U93(tt(), L, N) -> a__U94(a__isNatKind(N), L),
                  a__U94(tt(), L) -> s(a__length(mark(L))),
                    a__isNat(0()) -> tt(),
             a__isNat(length(V1)) -> a__U11(a__isNatIListKind(V1), V1),
                  a__isNat(s(V1)) -> a__U21(a__isNatKind(V1), V1),
                 a__isNatIList(V) -> a__U31(a__isNatIListKind(V), V),
           a__isNatIList(zeros()) -> tt(),
      a__isNatIList(cons(V1, V2)) -> a__U41(a__isNatKind(V1), V1, V2),
         a__isNatIListKind(nil()) -> tt(),
       a__isNatIListKind(zeros()) -> tt(),
  a__isNatIListKind(cons(V1, V2)) -> a__U51(a__isNatKind(V1), V2),
                a__isNatKind(0()) -> tt(),
         a__isNatKind(length(V1)) -> a__U61(a__isNatIListKind(V1)),
              a__isNatKind(s(V1)) -> a__U71(a__isNatKind(V1)),
              a__isNatList(nil()) -> tt(),
       a__isNatList(cons(V1, V2)) -> a__U81(a__isNatKind(V1), V1, V2),
                 a__length(nil()) -> 0(),
            a__length(cons(N, L)) -> a__U91(a__isNatList(L), L, N),
                    mark(zeros()) -> a__zeros(),
                mark(U11(X1, X2)) -> a__U11(mark(X1), X2),
                mark(U12(X1, X2)) -> a__U12(mark(X1), X2),
          mark(isNatIListKind(X)) -> a__isNatIListKind(X),
                     mark(U13(X)) -> a__U13(mark(X)),
               mark(isNatList(X)) -> a__isNatList(X),
                mark(U21(X1, X2)) -> a__U21(mark(X1), X2),
                mark(U22(X1, X2)) -> a__U22(mark(X1), X2),
               mark(isNatKind(X)) -> a__isNatKind(X),
                     mark(U23(X)) -> a__U23(mark(X)),
                   mark(isNat(X)) -> a__isNat(X),
                mark(U31(X1, X2)) -> a__U31(mark(X1), X2),
                mark(U32(X1, X2)) -> a__U32(mark(X1), X2),
                     mark(U33(X)) -> a__U33(mark(X)),
            mark(U41(X1, X2, X3)) -> a__U41(mark(X1), X2, X3),
            mark(U42(X1, X2, X3)) -> a__U42(mark(X1), X2, X3),
            mark(U43(X1, X2, X3)) -> a__U43(mark(X1), X2, X3),
            mark(U44(X1, X2, X3)) -> a__U44(mark(X1), X2, X3),
                mark(U45(X1, X2)) -> a__U45(mark(X1), X2),
                     mark(U46(X)) -> a__U46(mark(X)),
              mark(isNatIList(X)) -> a__isNatIList(X),
                mark(U51(X1, X2)) -> a__U51(mark(X1), X2),
                     mark(U52(X)) -> a__U52(mark(X)),
                     mark(U61(X)) -> a__U61(mark(X)),
                     mark(U71(X)) -> a__U71(mark(X)),
            mark(U81(X1, X2, X3)) -> a__U81(mark(X1), X2, X3),
            mark(U82(X1, X2, X3)) -> a__U82(mark(X1), X2, X3),
            mark(U83(X1, X2, X3)) -> a__U83(mark(X1), X2, X3),
            mark(U84(X1, X2, X3)) -> a__U84(mark(X1), X2, X3),
                mark(U85(X1, X2)) -> a__U85(mark(X1), X2),
                     mark(U86(X)) -> a__U86(mark(X)),
            mark(U91(X1, X2, X3)) -> a__U91(mark(X1), X2, X3),
            mark(U92(X1, X2, X3)) -> a__U92(mark(X1), X2, X3),
            mark(U93(X1, X2, X3)) -> a__U93(mark(X1), X2, X3),
                mark(U94(X1, X2)) -> a__U94(mark(X1), X2),
                  mark(length(X)) -> a__length(mark(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__U12(X1, X2) -> U12(X1, X2),
             a__isNatIListKind(X) -> isNatIListKind(X),
                        a__U13(X) -> U13(X),
                  a__isNatList(X) -> isNatList(X),
                   a__U21(X1, X2) -> U21(X1, X2),
                   a__U22(X1, X2) -> U22(X1, X2),
                  a__isNatKind(X) -> isNatKind(X),
                        a__U23(X) -> U23(X),
                      a__isNat(X) -> isNat(X),
                   a__U31(X1, X2) -> U31(X1, X2),
                   a__U32(X1, X2) -> U32(X1, X2),
                        a__U33(X) -> U33(X),
               a__U41(X1, X2, X3) -> U41(X1, X2, X3),
               a__U42(X1, X2, X3) -> U42(X1, X2, X3),
               a__U43(X1, X2, X3) -> U43(X1, X2, X3),
               a__U44(X1, X2, X3) -> U44(X1, X2, X3),
                   a__U45(X1, X2) -> U45(X1, X2),
                        a__U46(X) -> U46(X),
                 a__isNatIList(X) -> isNatIList(X),
                   a__U51(X1, X2) -> U51(X1, X2),
                        a__U52(X) -> U52(X),
                        a__U61(X) -> U61(X),
                        a__U71(X) -> U71(X),
               a__U81(X1, X2, X3) -> U81(X1, X2, X3),
               a__U82(X1, X2, X3) -> U82(X1, X2, X3),
               a__U83(X1, X2, X3) -> U83(X1, X2, X3),
               a__U84(X1, X2, X3) -> U84(X1, X2, X3),
                   a__U85(X1, X2) -> U85(X1, X2),
                        a__U86(X) -> U86(X),
               a__U91(X1, X2, X3) -> U91(X1, X2, X3),
               a__U92(X1, X2, X3) -> U92(X1, X2, X3),
               a__U93(X1, X2, X3) -> U93(X1, X2, X3),
                   a__U94(X1, X2) -> U94(X1, X2),
                     a__length(X) -> length(X)}
 Fail