YES
O(n^5)
TRS:
 {
   if(true(), X, Y) -> X,
  if(false(), X, Y) -> activate(Y),
               f(X) -> if(X, c(), n__f(true())),
               f(X) -> n__f(X),
        activate(X) -> X,
  activate(n__f(X)) -> f(X)
 }
 DUP: We consider a non-duplicating system.
  Trs:
   {
     if(true(), X, Y) -> X,
    if(false(), X, Y) -> activate(Y),
                 f(X) -> if(X, c(), n__f(true())),
                 f(X) -> n__f(X),
          activate(X) -> X,
    activate(n__f(X)) -> f(X)
   }
  Matrix Interpretation:
   Interpretation class: triangular
             [3]
             [0]
   [false] = [0]
             [1]
             [0]
   
              [X4]    [1 2 3 0 0][X4]   [3]
              [X3]    [0 1 2 2 0][X3]   [0]
   [activate]([X2]) = [0 0 1 0 2][X2] + [0]
              [X1]    [0 0 0 1 0][X1]   [0]
              [X0]    [0 0 0 0 1][X0]   [0]
   
       [X4]    [1 0 3 1 0][X4]   [2]
       [X3]    [0 1 2 0 2][X3]   [0]
   [f]([X2]) = [0 0 1 0 0][X2] + [0]
       [X1]    [0 0 0 0 0][X1]   [0]
       [X0]    [0 0 0 0 0][X0]   [0]
   
            [0]
            [0]
   [true] = [0]
            [1]
            [0]
   
          [X4]    [1 0 3 1 0][X4]   [0]
          [X3]    [0 1 1 0 2][X3]   [0]
   [n__f]([X2]) = [0 0 1 0 0][X2] + [0]
          [X1]    [0 0 0 0 0][X1]   [0]
          [X0]    [0 0 0 0 0][X0]   [0]
   
         [0]
         [0]
   [c] = [0]
         [0]
         [0]
   
        [X14]  [X9]  [X4]    [1 0 0 1 0][X14]   [1 0 0 2 0][X9]   [1 2 3 2 0][X4]   [0]
        [X13]  [X8]  [X3]    [0 0 0 0 0][X13]   [0 1 2 2 2][X8]   [0 1 2 2 2][X3]   [0]
   [if]([X12], [X7], [X2]) = [0 0 0 0 0][X12] + [0 0 1 2 2][X7] + [0 0 1 2 3][X2] + [0]
        [X11]  [X6]  [X1]    [0 0 0 0 0][X11]   [0 0 0 1 2][X6]   [0 0 0 1 0][X1]   [0]
        [X10]  [X5]  [X0]    [0 0 0 0 0][X10]   [0 0 0 0 1][X5]   [0 0 0 0 1][X0]   [0]
   
   
   Qed