MAYBE
MAYBE
TRS:
 {
                 U12(mark(X)) -> mark(U12(X)),
                   U12(ok(X)) -> ok(U12(X)),
                 isNat(ok(X)) -> ok(isNat(X)),
               active(U12(X)) -> U12(active(X)),
            active(U12(tt())) -> mark(tt()),
         active(isNat(s(V1))) -> mark(U21(isNat(V1))),
  active(isNat(plus(V1, V2))) -> mark(U11(isNat(V1), V2)),
           active(isNat(0())) -> mark(tt()),
     active(isNat(x(V1, V2))) -> mark(U31(isNat(V1), V2)),
          active(U11(X1, X2)) -> U11(active(X1), X2),
        active(U11(tt(), V2)) -> mark(U12(isNat(V2))),
               active(U21(X)) -> U21(active(X)),
            active(U21(tt())) -> mark(tt()),
               active(U32(X)) -> U32(active(X)),
            active(U32(tt())) -> mark(tt()),
          active(U31(X1, X2)) -> U31(active(X1), X2),
        active(U31(tt(), V2)) -> mark(U32(isNat(V2))),
          active(U41(X1, X2)) -> U41(active(X1), X2),
         active(U41(tt(), N)) -> mark(N),
      active(U52(X1, X2, X3)) -> U52(active(X1), X2, X3),
      active(U52(tt(), M, N)) -> mark(s(plus(N, M))),
      active(U51(X1, X2, X3)) -> U51(active(X1), X2, X3),
      active(U51(tt(), M, N)) -> mark(U52(isNat(N), M, N)),
                 active(s(X)) -> s(active(X)),
        active(plus(N, s(M))) -> mark(U51(isNat(M), M, N)),
         active(plus(N, 0())) -> mark(U41(isNat(N), N)),
         active(plus(X1, X2)) -> plus(X1, active(X2)),
         active(plus(X1, X2)) -> plus(active(X1), X2),
               active(U61(X)) -> U61(active(X)),
            active(U61(tt())) -> mark(0()),
      active(U72(X1, X2, X3)) -> U72(active(X1), X2, X3),
      active(U72(tt(), M, N)) -> mark(plus(x(N, M), N)),
      active(U71(X1, X2, X3)) -> U71(active(X1), X2, X3),
      active(U71(tt(), M, N)) -> mark(U72(isNat(N), M, N)),
           active(x(N, s(M))) -> mark(U71(isNat(M), M, N)),
            active(x(N, 0())) -> mark(U61(isNat(N))),
            active(x(X1, X2)) -> x(X1, active(X2)),
            active(x(X1, X2)) -> x(active(X1), X2),
            U11(mark(X1), X2) -> mark(U11(X1, X2)),
          U11(ok(X1), ok(X2)) -> ok(U11(X1, X2)),
                 U21(mark(X)) -> mark(U21(X)),
                   U21(ok(X)) -> ok(U21(X)),
                 U32(mark(X)) -> mark(U32(X)),
                   U32(ok(X)) -> ok(U32(X)),
            U31(mark(X1), X2) -> mark(U31(X1, X2)),
          U31(ok(X1), ok(X2)) -> ok(U31(X1, X2)),
            U41(mark(X1), X2) -> mark(U41(X1, X2)),
          U41(ok(X1), ok(X2)) -> ok(U41(X1, X2)),
        U52(mark(X1), X2, X3) -> mark(U52(X1, X2, X3)),
  U52(ok(X1), ok(X2), ok(X3)) -> ok(U52(X1, X2, X3)),
        U51(mark(X1), X2, X3) -> mark(U51(X1, X2, X3)),
  U51(ok(X1), ok(X2), ok(X3)) -> ok(U51(X1, X2, X3)),
                   s(mark(X)) -> mark(s(X)),
                     s(ok(X)) -> ok(s(X)),
           plus(X1, mark(X2)) -> mark(plus(X1, X2)),
           plus(mark(X1), X2) -> mark(plus(X1, X2)),
         plus(ok(X1), ok(X2)) -> ok(plus(X1, X2)),
                 U61(mark(X)) -> mark(U61(X)),
                   U61(ok(X)) -> ok(U61(X)),
        U72(mark(X1), X2, X3) -> mark(U72(X1, X2, X3)),
  U72(ok(X1), ok(X2), ok(X3)) -> ok(U72(X1, X2, X3)),
        U71(mark(X1), X2, X3) -> mark(U71(X1, X2, X3)),
  U71(ok(X1), ok(X2), ok(X3)) -> ok(U71(X1, X2, X3)),
              x(X1, mark(X2)) -> mark(x(X1, X2)),
              x(mark(X1), X2) -> mark(x(X1, X2)),
            x(ok(X1), ok(X2)) -> ok(x(X1, X2)),
               proper(U12(X)) -> U12(proper(X)),
             proper(isNat(X)) -> isNat(proper(X)),
          proper(U11(X1, X2)) -> U11(proper(X1), proper(X2)),
                 proper(tt()) -> ok(tt()),
               proper(U21(X)) -> U21(proper(X)),
               proper(U32(X)) -> U32(proper(X)),
          proper(U31(X1, X2)) -> U31(proper(X1), proper(X2)),
          proper(U41(X1, X2)) -> U41(proper(X1), proper(X2)),
      proper(U52(X1, X2, X3)) -> U52(proper(X1), proper(X2), proper(X3)),
      proper(U51(X1, X2, X3)) -> U51(proper(X1), proper(X2), proper(X3)),
                 proper(s(X)) -> s(proper(X)),
         proper(plus(X1, X2)) -> plus(proper(X1), proper(X2)),
                  proper(0()) -> ok(0()),
               proper(U61(X)) -> U61(proper(X)),
      proper(U72(X1, X2, X3)) -> U72(proper(X1), proper(X2), proper(X3)),
      proper(U71(X1, X2, X3)) -> U71(proper(X1), proper(X2), proper(X3)),
            proper(x(X1, X2)) -> x(proper(X1), proper(X2)),
                 top(mark(X)) -> top(proper(X)),
                   top(ok(X)) -> top(active(X))
 }
 DUP: We consider a duplicating system.
  Trs:
   {
                   U12(mark(X)) -> mark(U12(X)),
                     U12(ok(X)) -> ok(U12(X)),
                   isNat(ok(X)) -> ok(isNat(X)),
                 active(U12(X)) -> U12(active(X)),
              active(U12(tt())) -> mark(tt()),
           active(isNat(s(V1))) -> mark(U21(isNat(V1))),
    active(isNat(plus(V1, V2))) -> mark(U11(isNat(V1), V2)),
             active(isNat(0())) -> mark(tt()),
       active(isNat(x(V1, V2))) -> mark(U31(isNat(V1), V2)),
            active(U11(X1, X2)) -> U11(active(X1), X2),
          active(U11(tt(), V2)) -> mark(U12(isNat(V2))),
                 active(U21(X)) -> U21(active(X)),
              active(U21(tt())) -> mark(tt()),
                 active(U32(X)) -> U32(active(X)),
              active(U32(tt())) -> mark(tt()),
            active(U31(X1, X2)) -> U31(active(X1), X2),
          active(U31(tt(), V2)) -> mark(U32(isNat(V2))),
            active(U41(X1, X2)) -> U41(active(X1), X2),
           active(U41(tt(), N)) -> mark(N),
        active(U52(X1, X2, X3)) -> U52(active(X1), X2, X3),
        active(U52(tt(), M, N)) -> mark(s(plus(N, M))),
        active(U51(X1, X2, X3)) -> U51(active(X1), X2, X3),
        active(U51(tt(), M, N)) -> mark(U52(isNat(N), M, N)),
                   active(s(X)) -> s(active(X)),
          active(plus(N, s(M))) -> mark(U51(isNat(M), M, N)),
           active(plus(N, 0())) -> mark(U41(isNat(N), N)),
           active(plus(X1, X2)) -> plus(X1, active(X2)),
           active(plus(X1, X2)) -> plus(active(X1), X2),
                 active(U61(X)) -> U61(active(X)),
              active(U61(tt())) -> mark(0()),
        active(U72(X1, X2, X3)) -> U72(active(X1), X2, X3),
        active(U72(tt(), M, N)) -> mark(plus(x(N, M), N)),
        active(U71(X1, X2, X3)) -> U71(active(X1), X2, X3),
        active(U71(tt(), M, N)) -> mark(U72(isNat(N), M, N)),
             active(x(N, s(M))) -> mark(U71(isNat(M), M, N)),
              active(x(N, 0())) -> mark(U61(isNat(N))),
              active(x(X1, X2)) -> x(X1, active(X2)),
              active(x(X1, X2)) -> x(active(X1), X2),
              U11(mark(X1), X2) -> mark(U11(X1, X2)),
            U11(ok(X1), ok(X2)) -> ok(U11(X1, X2)),
                   U21(mark(X)) -> mark(U21(X)),
                     U21(ok(X)) -> ok(U21(X)),
                   U32(mark(X)) -> mark(U32(X)),
                     U32(ok(X)) -> ok(U32(X)),
              U31(mark(X1), X2) -> mark(U31(X1, X2)),
            U31(ok(X1), ok(X2)) -> ok(U31(X1, X2)),
              U41(mark(X1), X2) -> mark(U41(X1, X2)),
            U41(ok(X1), ok(X2)) -> ok(U41(X1, X2)),
          U52(mark(X1), X2, X3) -> mark(U52(X1, X2, X3)),
    U52(ok(X1), ok(X2), ok(X3)) -> ok(U52(X1, X2, X3)),
          U51(mark(X1), X2, X3) -> mark(U51(X1, X2, X3)),
    U51(ok(X1), ok(X2), ok(X3)) -> ok(U51(X1, X2, X3)),
                     s(mark(X)) -> mark(s(X)),
                       s(ok(X)) -> ok(s(X)),
             plus(X1, mark(X2)) -> mark(plus(X1, X2)),
             plus(mark(X1), X2) -> mark(plus(X1, X2)),
           plus(ok(X1), ok(X2)) -> ok(plus(X1, X2)),
                   U61(mark(X)) -> mark(U61(X)),
                     U61(ok(X)) -> ok(U61(X)),
          U72(mark(X1), X2, X3) -> mark(U72(X1, X2, X3)),
    U72(ok(X1), ok(X2), ok(X3)) -> ok(U72(X1, X2, X3)),
          U71(mark(X1), X2, X3) -> mark(U71(X1, X2, X3)),
    U71(ok(X1), ok(X2), ok(X3)) -> ok(U71(X1, X2, X3)),
                x(X1, mark(X2)) -> mark(x(X1, X2)),
                x(mark(X1), X2) -> mark(x(X1, X2)),
              x(ok(X1), ok(X2)) -> ok(x(X1, X2)),
                 proper(U12(X)) -> U12(proper(X)),
               proper(isNat(X)) -> isNat(proper(X)),
            proper(U11(X1, X2)) -> U11(proper(X1), proper(X2)),
                   proper(tt()) -> ok(tt()),
                 proper(U21(X)) -> U21(proper(X)),
                 proper(U32(X)) -> U32(proper(X)),
            proper(U31(X1, X2)) -> U31(proper(X1), proper(X2)),
            proper(U41(X1, X2)) -> U41(proper(X1), proper(X2)),
        proper(U52(X1, X2, X3)) -> U52(proper(X1), proper(X2), proper(X3)),
        proper(U51(X1, X2, X3)) -> U51(proper(X1), proper(X2), proper(X3)),
                   proper(s(X)) -> s(proper(X)),
           proper(plus(X1, X2)) -> plus(proper(X1), proper(X2)),
                    proper(0()) -> ok(0()),
                 proper(U61(X)) -> U61(proper(X)),
        proper(U72(X1, X2, X3)) -> U72(proper(X1), proper(X2), proper(X3)),
        proper(U71(X1, X2, X3)) -> U71(proper(X1), proper(X2), proper(X3)),
              proper(x(X1, X2)) -> x(proper(X1), proper(X2)),
                   top(mark(X)) -> top(proper(X)),
                     top(ok(X)) -> top(active(X))
   }
  Fail