YES
O(n^4)
TRS:
 {
        \(x, x) -> e(),
  \(x, .(x, y)) -> y,
      \(e(), x) -> x,
  \(/(x, y), x) -> y,
        /(x, x) -> e(),
      /(x, e()) -> x,
  /(x, \(y, x)) -> y,
  /(.(y, x), x) -> y,
      .(x, e()) -> x,
  .(x, \(x, y)) -> y,
      .(e(), x) -> x,
  .(/(y, x), x) -> y
 }
 DUP: We consider a non-duplicating system.
  Trs:
   {
          \(x, x) -> e(),
    \(x, .(x, y)) -> y,
        \(e(), x) -> x,
    \(/(x, y), x) -> y,
          /(x, x) -> e(),
        /(x, e()) -> x,
    /(x, \(y, x)) -> y,
    /(.(y, x), x) -> y,
        .(x, e()) -> x,
    .(x, \(x, y)) -> y,
        .(e(), x) -> x,
    .(/(y, x), x) -> y
   }
  Matrix Interpretation:
   Interpretation class: triangular
       [X7]  [X3]    [1 0 0 0][X7]   [1 0 0 0][X3]   [1]
       [X6]  [X2]    [0 1 0 0][X6]   [0 1 0 0][X2]   [0]
   [.]([X5], [X1]) = [0 0 1 0][X5] + [0 0 1 0][X1] + [0]
       [X4]  [X0]    [0 0 0 1][X4]   [0 0 0 1][X0]   [0]
   
       [X7]  [X3]    [1 0 0 0][X7]   [1 0 0 0][X3]   [1]
       [X6]  [X2]    [0 1 0 0][X6]   [0 1 0 0][X2]   [0]
   [/]([X5], [X1]) = [0 0 1 0][X5] + [0 0 1 0][X1] + [0]
       [X4]  [X0]    [0 0 0 1][X4]   [0 0 0 1][X0]   [1]
   
       [X7]  [X3]    [1 0 0 1][X7]   [1 0 0 0][X3]   [1]
       [X6]  [X2]    [0 1 0 0][X6]   [0 1 0 0][X2]   [0]
   [\]([X5], [X1]) = [0 0 1 0][X5] + [0 0 1 0][X1] + [0]
       [X4]  [X0]    [0 0 0 1][X4]   [0 0 0 1][X0]   [0]
   
         [0]
         [0]
   [e] = [0]
         [0]
   
   
   Qed