TRS:
 {       a__U11(tt(), N) -> mark(N),
      a__U21(tt(), M, N) -> s(a__plus(mark(N), mark(M))),
            a__U31(tt()) -> 0(),
      a__U41(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__and(a__isNat(V1), isNat(V2)),
         a__isNat(s(V1)) -> a__isNat(V1),
     a__isNat(x(V1, V2)) -> a__and(a__isNat(V1), isNat(V2)),
         a__plus(N, 0()) -> a__U11(a__isNat(N), N),
        a__plus(N, s(M)) -> a__U21(a__and(a__isNat(M), isNat(N)), M, N),
            a__x(N, 0()) -> a__U31(a__isNat(N)),
           a__x(N, s(M)) -> a__U41(a__and(a__isNat(M), isNat(N)), M, N),
       mark(U11(X1, X2)) -> a__U11(mark(X1), X2),
   mark(U21(X1, X2, X3)) -> a__U21(mark(X1), X2, X3),
      mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)),
            mark(U31(X)) -> a__U31(mark(X)),
   mark(U41(X1, X2, X3)) -> a__U41(mark(X1), X2, X3),
         mark(x(X1, X2)) -> a__x(mark(X1), mark(X2)),
       mark(and(X1, X2)) -> a__and(mark(X1), X2),
          mark(isNat(X)) -> a__isNat(X),
              mark(tt()) -> tt(),
              mark(s(X)) -> s(mark(X)),
               mark(0()) -> 0(),
          a__U11(X1, X2) -> U11(X1, X2),
      a__U21(X1, X2, X3) -> U21(X1, X2, X3),
         a__plus(X1, X2) -> plus(X1, X2),
               a__U31(X) -> U31(X),
      a__U41(X1, X2, X3) -> U41(X1, X2, X3),
            a__x(X1, X2) -> x(X1, X2),
          a__and(X1, X2) -> and(X1, X2),
             a__isNat(X) -> isNat(X)}
 Fail