TRS:
 {      a__U11(tt(), V1, V2) -> a__U12(a__isNatKind(V1), V1, V2),
        a__U12(tt(), V1, V2) -> a__U13(a__isNatKind(V2), V1, V2),
        a__U13(tt(), V1, V2) -> a__U14(a__isNatKind(V2), V1, V2),
        a__U14(tt(), V1, V2) -> a__U15(a__isNat(V1), V2),
            a__U15(tt(), V2) -> a__U16(a__isNat(V2)),
                a__U16(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(), V2) -> a__U32(a__isNatKind(V2)),
                a__U32(tt()) -> tt(),
                a__U41(tt()) -> tt(),
             a__U51(tt(), N) -> a__U52(a__isNatKind(N), N),
             a__U52(tt(), N) -> mark(N),
          a__U61(tt(), M, N) -> a__U62(a__isNatKind(M), M, N),
          a__U62(tt(), M, N) -> a__U63(a__isNat(N), M, N),
          a__U63(tt(), M, N) -> a__U64(a__isNatKind(N), M, N),
          a__U64(tt(), M, N) -> s(a__plus(mark(N), mark(M))),
               a__isNat(0()) -> tt(),
      a__isNat(plus(V1, V2)) -> a__U11(a__isNatKind(V1), V1, V2),
             a__isNat(s(V1)) -> a__U21(a__isNatKind(V1), V1),
           a__isNatKind(0()) -> tt(),
  a__isNatKind(plus(V1, V2)) -> a__U31(a__isNatKind(V1), V2),
         a__isNatKind(s(V1)) -> a__U41(a__isNatKind(V1)),
             a__plus(N, 0()) -> a__U51(a__isNat(N), N),
            a__plus(N, s(M)) -> a__U61(a__isNat(M), M, N),
       mark(U11(X1, X2, X3)) -> a__U11(mark(X1), X2, X3),
       mark(U12(X1, X2, X3)) -> a__U12(mark(X1), X2, X3),
          mark(isNatKind(X)) -> a__isNatKind(X),
       mark(U13(X1, X2, X3)) -> a__U13(mark(X1), X2, X3),
       mark(U14(X1, X2, X3)) -> a__U14(mark(X1), X2, X3),
           mark(U15(X1, X2)) -> a__U15(mark(X1), X2),
              mark(isNat(X)) -> a__isNat(X),
                mark(U16(X)) -> a__U16(mark(X)),
           mark(U21(X1, X2)) -> a__U21(mark(X1), X2),
           mark(U22(X1, X2)) -> a__U22(mark(X1), X2),
                mark(U23(X)) -> a__U23(mark(X)),
           mark(U31(X1, X2)) -> a__U31(mark(X1), X2),
                mark(U32(X)) -> a__U32(mark(X)),
                mark(U41(X)) -> a__U41(mark(X)),
           mark(U51(X1, X2)) -> a__U51(mark(X1), X2),
           mark(U52(X1, X2)) -> a__U52(mark(X1), X2),
       mark(U61(X1, X2, X3)) -> a__U61(mark(X1), X2, X3),
       mark(U62(X1, X2, X3)) -> a__U62(mark(X1), X2, X3),
       mark(U63(X1, X2, X3)) -> a__U63(mark(X1), X2, X3),
       mark(U64(X1, X2, X3)) -> a__U64(mark(X1), X2, X3),
          mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)),
                  mark(tt()) -> tt(),
                  mark(s(X)) -> s(mark(X)),
                   mark(0()) -> 0(),
          a__U11(X1, X2, X3) -> U11(X1, X2, X3),
          a__U12(X1, X2, X3) -> U12(X1, X2, X3),
             a__isNatKind(X) -> isNatKind(X),
          a__U13(X1, X2, X3) -> U13(X1, X2, X3),
          a__U14(X1, X2, X3) -> U14(X1, X2, X3),
              a__U15(X1, X2) -> U15(X1, X2),
                 a__isNat(X) -> isNat(X),
                   a__U16(X) -> U16(X),
              a__U21(X1, X2) -> U21(X1, X2),
              a__U22(X1, X2) -> U22(X1, X2),
                   a__U23(X) -> U23(X),
              a__U31(X1, X2) -> U31(X1, X2),
                   a__U32(X) -> U32(X),
                   a__U41(X) -> U41(X),
              a__U51(X1, X2) -> U51(X1, X2),
              a__U52(X1, X2) -> U52(X1, X2),
          a__U61(X1, X2, X3) -> U61(X1, X2, X3),
          a__U62(X1, X2, X3) -> U62(X1, X2, X3),
          a__U63(X1, X2, X3) -> U63(X1, X2, X3),
          a__U64(X1, X2, X3) -> U64(X1, X2, X3),
             a__plus(X1, X2) -> plus(X1, X2)}
 Fail