TRS:
 {      a__U11(tt(), V1, V2) -> a__U12(a__isNat(V1), V2),
            a__U12(tt(), V2) -> a__U13(a__isNat(V2)),
                a__U13(tt()) -> tt(),
            a__U21(tt(), V1) -> a__U22(a__isNat(V1)),
                a__U22(tt()) -> tt(),
        a__U31(tt(), V1, V2) -> a__U32(a__isNat(V1), V2),
            a__U32(tt(), V2) -> a__U33(a__isNat(V2)),
                a__U33(tt()) -> tt(),
             a__U41(tt(), N) -> mark(N),
          a__U51(tt(), M, N) -> s(a__plus(mark(N), mark(M))),
                a__U61(tt()) -> 0(),
          a__U71(tt(), M, N) -> a__plus(a__x(mark(N), mark(M)), mark(N)),
             a__and(tt(), X) -> mark(X),
               a__isNat(0()) -> tt(),
      a__isNat(plus(V1, V2)) -> a__U11(a__and(a__isNatKind(V1), isNatKind(V2)), V1, V2),
             a__isNat(s(V1)) -> a__U21(a__isNatKind(V1), V1),
         a__isNat(x(V1, V2)) -> a__U31(a__and(a__isNatKind(V1), isNatKind(V2)), V1, V2),
           a__isNatKind(0()) -> tt(),
  a__isNatKind(plus(V1, V2)) -> a__and(a__isNatKind(V1), isNatKind(V2)),
         a__isNatKind(s(V1)) -> a__isNatKind(V1),
     a__isNatKind(x(V1, V2)) -> a__and(a__isNatKind(V1), isNatKind(V2)),
             a__plus(N, 0()) -> a__U41(a__and(a__isNat(N), isNatKind(N)), N),
            a__plus(N, s(M)) -> a__U51(a__and(a__and(a__isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N),
                a__x(N, 0()) -> a__U61(a__and(a__isNat(N), isNatKind(N))),
               a__x(N, s(M)) -> a__U71(a__and(a__and(a__isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N),
       mark(U11(X1, X2, X3)) -> a__U11(mark(X1), X2, X3),
           mark(U12(X1, X2)) -> a__U12(mark(X1), X2),
              mark(isNat(X)) -> a__isNat(X),
                mark(U13(X)) -> a__U13(mark(X)),
           mark(U21(X1, X2)) -> a__U21(mark(X1), X2),
                mark(U22(X)) -> a__U22(mark(X)),
       mark(U31(X1, X2, X3)) -> a__U31(mark(X1), X2, X3),
           mark(U32(X1, X2)) -> a__U32(mark(X1), X2),
                mark(U33(X)) -> a__U33(mark(X)),
           mark(U41(X1, X2)) -> a__U41(mark(X1), X2),
       mark(U51(X1, X2, X3)) -> a__U51(mark(X1), X2, X3),
          mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)),
                mark(U61(X)) -> a__U61(mark(X)),
       mark(U71(X1, X2, X3)) -> a__U71(mark(X1), X2, X3),
             mark(x(X1, X2)) -> a__x(mark(X1), mark(X2)),
           mark(and(X1, X2)) -> a__and(mark(X1), X2),
          mark(isNatKind(X)) -> a__isNatKind(X),
                  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) -> U12(X1, X2),
                 a__isNat(X) -> isNat(X),
                   a__U13(X) -> U13(X),
              a__U21(X1, X2) -> U21(X1, X2),
                   a__U22(X) -> U22(X),
          a__U31(X1, X2, X3) -> U31(X1, X2, X3),
              a__U32(X1, X2) -> U32(X1, X2),
                   a__U33(X) -> U33(X),
              a__U41(X1, X2) -> U41(X1, X2),
          a__U51(X1, X2, X3) -> U51(X1, X2, X3),
             a__plus(X1, X2) -> plus(X1, X2),
                   a__U61(X) -> U61(X),
          a__U71(X1, X2, X3) -> U71(X1, X2, X3),
                a__x(X1, X2) -> x(X1, X2),
              a__and(X1, X2) -> and(X1, X2),
             a__isNatKind(X) -> isNatKind(X)}
 Fail