TRS:
 {      a__U11(tt(), V2) -> a__U12(a__isNat(V2)),
            a__U12(tt()) -> tt(),
            a__U21(tt()) -> tt(),
        a__U31(tt(), V2) -> a__U32(a__isNat(V2)),
            a__U32(tt()) -> tt(),
         a__U41(tt(), N) -> mark(N),
      a__U51(tt(), M, N) -> a__U52(a__isNat(N), M, N),
      a__U52(tt(), M, N) -> s(a__plus(mark(N), mark(M))),
            a__U61(tt()) -> 0(),
      a__U71(tt(), M, N) -> a__U72(a__isNat(N), M, N),
      a__U72(tt(), M, N) -> a__plus(a__x(mark(N), mark(M)), mark(N)),
           a__isNat(0()) -> tt(),
  a__isNat(plus(V1, V2)) -> a__U11(a__isNat(V1), V2),
         a__isNat(s(V1)) -> a__U21(a__isNat(V1)),
     a__isNat(x(V1, V2)) -> a__U31(a__isNat(V1), V2),
         a__plus(N, 0()) -> a__U41(a__isNat(N), N),
        a__plus(N, s(M)) -> a__U51(a__isNat(M), M, N),
            a__x(N, 0()) -> a__U61(a__isNat(N)),
           a__x(N, s(M)) -> a__U71(a__isNat(M), M, N),
       mark(U11(X1, X2)) -> a__U11(mark(X1), X2),
            mark(U12(X)) -> a__U12(mark(X)),
          mark(isNat(X)) -> a__isNat(X),
            mark(U21(X)) -> a__U21(mark(X)),
       mark(U31(X1, X2)) -> a__U31(mark(X1), X2),
            mark(U32(X)) -> a__U32(mark(X)),
       mark(U41(X1, X2)) -> a__U41(mark(X1), X2),
   mark(U51(X1, X2, X3)) -> a__U51(mark(X1), X2, X3),
   mark(U52(X1, X2, X3)) -> a__U52(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(U72(X1, X2, X3)) -> a__U72(mark(X1), X2, X3),
         mark(x(X1, X2)) -> a__x(mark(X1), mark(X2)),
              mark(tt()) -> tt(),
              mark(s(X)) -> s(mark(X)),
               mark(0()) -> 0(),
          a__U11(X1, X2) -> U11(X1, X2),
               a__U12(X) -> U12(X),
             a__isNat(X) -> isNat(X),
               a__U21(X) -> U21(X),
          a__U31(X1, X2) -> U31(X1, X2),
               a__U32(X) -> U32(X),
          a__U41(X1, X2) -> U41(X1, X2),
      a__U51(X1, X2, X3) -> U51(X1, X2, X3),
      a__U52(X1, X2, X3) -> U52(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__U72(X1, X2, X3) -> U72(X1, X2, X3),
            a__x(X1, X2) -> x(X1, X2)}
 Fail