YES
O(n^4)
TRS:
 {
    activate(X) -> X,
   and(tt(), X) -> activate(X),
   plus(N, 0()) -> N,
  plus(N, s(M)) -> s(plus(N, M))
 }
 DUP: We consider a non-duplicating system.
  Trs:
   {
      activate(X) -> X,
     and(tt(), X) -> activate(X),
     plus(N, 0()) -> N,
    plus(N, s(M)) -> s(plus(N, M))
   }
  Matrix Interpretation:
   Interpretation class: triangular
       [X3]    [1 0 0 0][X3]   [0]
       [X2]    [0 0 0 0][X2]   [0]
   [s]([X1]) = [0 0 0 0][X1] + [0]
       [X0]    [0 0 0 1][X0]   [1]
   
         [1]
         [0]
   [0] = [0]
         [1]
   
          [X7]  [X3]    [1 0 0 0][X7]   [1 0 0 1][X3]   [0]
          [X6]  [X2]    [0 1 1 1][X6]   [0 0 0 0][X2]   [0]
   [plus]([X5], [X1]) = [0 0 1 0][X5] + [0 0 0 0][X1] + [0]
          [X4]  [X0]    [0 0 0 1][X4]   [0 0 0 1][X0]   [0]
   
          [1]
          [0]
   [tt] = [0]
          [0]
   
         [X7]  [X3]    [1 0 0 0][X7]   [1 0 0 1][X3]   [1]
         [X6]  [X2]    [0 0 0 0][X6]   [0 1 0 0][X2]   [0]
   [and]([X5], [X1]) = [0 0 0 0][X5] + [0 0 1 0][X1] + [0]
         [X4]  [X0]    [0 0 0 0][X4]   [0 0 0 1][X0]   [0]
   
              [X3]    [1 0 0 0][X3]   [1]
              [X2]    [0 1 0 0][X2]   [0]
   [activate]([X1]) = [0 0 1 0][X1] + [0]
              [X0]    [0 0 0 1][X0]   [0]
   
   
   Qed