MAYBE
MAYBE
TRS:
 {
        U12(mark(X1), X2, X3) -> mark(U12(X1, X2, X3)),
  U12(ok(X1), ok(X2), ok(X3)) -> ok(U12(X1, X2, X3)),
      active(U12(X1, X2, X3)) -> U12(active(X1), X2, X3),
      active(U12(tt(), M, N)) -> mark(s(plus(N, M))),
      active(U11(X1, X2, X3)) -> U11(active(X1), X2, X3),
      active(U11(tt(), M, N)) -> mark(U12(tt(), M, N)),
                 active(s(X)) -> s(active(X)),
        active(plus(N, s(M))) -> mark(U11(tt(), M, N)),
         active(plus(N, 0())) -> mark(N),
         active(plus(X1, X2)) -> plus(X1, active(X2)),
         active(plus(X1, X2)) -> plus(active(X1), X2),
        U11(mark(X1), X2, X3) -> mark(U11(X1, X2, X3)),
  U11(ok(X1), ok(X2), ok(X3)) -> ok(U11(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)),
      proper(U12(X1, X2, X3)) -> U12(proper(X1), proper(X2), proper(X3)),
                 proper(tt()) -> ok(tt()),
      proper(U11(X1, X2, X3)) -> U11(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()),
                 top(mark(X)) -> top(proper(X)),
                   top(ok(X)) -> top(active(X))
 }
 DUP: We consider a non-duplicating system.
  Trs:
   {
          U12(mark(X1), X2, X3) -> mark(U12(X1, X2, X3)),
    U12(ok(X1), ok(X2), ok(X3)) -> ok(U12(X1, X2, X3)),
        active(U12(X1, X2, X3)) -> U12(active(X1), X2, X3),
        active(U12(tt(), M, N)) -> mark(s(plus(N, M))),
        active(U11(X1, X2, X3)) -> U11(active(X1), X2, X3),
        active(U11(tt(), M, N)) -> mark(U12(tt(), M, N)),
                   active(s(X)) -> s(active(X)),
          active(plus(N, s(M))) -> mark(U11(tt(), M, N)),
           active(plus(N, 0())) -> mark(N),
           active(plus(X1, X2)) -> plus(X1, active(X2)),
           active(plus(X1, X2)) -> plus(active(X1), X2),
          U11(mark(X1), X2, X3) -> mark(U11(X1, X2, X3)),
    U11(ok(X1), ok(X2), ok(X3)) -> ok(U11(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)),
        proper(U12(X1, X2, X3)) -> U12(proper(X1), proper(X2), proper(X3)),
                   proper(tt()) -> ok(tt()),
        proper(U11(X1, X2, X3)) -> U11(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()),
                   top(mark(X)) -> top(proper(X)),
                     top(ok(X)) -> top(active(X))
   }
  Fail