YES(?,O(n^2))
TRS:
 {
  U12(tt(), M, N) -> s plus(activate N, activate M),
       activate X -> X,
  U11(tt(), M, N) -> U12(tt(), activate M, activate N),
     plus(N, s M) -> U11(tt(), M, N),
     plus(N, 0()) -> N
 }
 DUP: We consider a non-duplicating system.
  Trs:
   {
    U12(tt(), M, N) -> s plus(activate N, activate M),
         activate X -> X,
    U11(tt(), M, N) -> U12(tt(), activate M, activate N),
       plus(N, s M) -> U11(tt(), M, N),
       plus(N, 0()) -> N
   }
  Matrix Interpretation:
   Interpretation class: triangular
         [0]
   [0] = [2]
   
          [X3]  [X1]    [1 0][X3]   [1 3][X1]   [0]
   [plus]([X2], [X0]) = [0 1][X2] + [0 1][X0] + [0]
   
       [X1]    [1 0][X1]   [0]
   [s]([X0]) = [0 1][X0] + [3]
   
         [X5]  [X3]  [X1]    [1 3][X5]   [1 3][X3]   [1 0][X1]   [1]
   [U11]([X4], [X2], [X0]) = [0 1][X4] + [0 1][X2] + [0 1][X0] + [2]
   
              [X1]    [1 0][X1]   [1]
   [activate]([X0]) = [0 1][X0] + [0]
   
          [2]
   [tt] = [1]
   
         [X5]  [X3]  [X1]    [1 1][X5]   [1 3][X3]   [1 0][X1]   [0]
   [U12]([X4], [X2], [X0]) = [0 1][X4] + [0 1][X2] + [0 1][X0] + [2]
   
   
   Qed