YES
O(n^5)
TRS:
 {
  q(f(f(x))) -> p(f(g(x))),
  q(g(g(x))) -> p(g(f(x))),
  p(f(f(x))) -> q(f(g(x))),
  p(g(g(x))) -> q(g(f(x)))
 }
 DUP: We consider a non-duplicating system.
  Trs:
   {
    q(f(f(x))) -> p(f(g(x))),
    q(g(g(x))) -> p(g(f(x))),
    p(f(f(x))) -> q(f(g(x))),
    p(g(g(x))) -> q(g(f(x)))
   }
  Matrix Interpretation:
   Interpretation class: triangular
       [X4]    [1 0 0 0 0][X4]   [0]
       [X3]    [0 0 0 0 0][X3]   [1]
   [p]([X2]) = [0 0 0 0 0][X2] + [0]
       [X1]    [0 0 0 0 0][X1]   [0]
       [X0]    [0 0 0 0 0][X0]   [0]
   
       [X4]    [1 1 0 0 1][X4]   [0]
       [X3]    [0 0 1 0 0][X3]   [0]
   [g]([X2]) = [0 0 0 0 0][X2] + [0]
       [X1]    [0 0 0 0 0][X1]   [0]
       [X0]    [0 0 0 0 0][X0]   [1]
   
       [X4]    [1 1 1 0 0][X4]   [0]
       [X3]    [0 0 0 0 1][X3]   [0]
   [f]([X2]) = [0 0 1 0 0][X2] + [1]
       [X1]    [0 0 0 0 0][X1]   [0]
       [X0]    [0 0 0 0 0][X0]   [0]
   
       [X4]    [1 0 0 0 0][X4]   [0]
       [X3]    [0 0 1 0 1][X3]   [0]
   [q]([X2]) = [0 0 0 0 0][X2] + [0]
       [X1]    [0 0 0 0 0][X1]   [0]
       [X0]    [0 0 0 0 0][X0]   [0]
   
   
   Qed