YES(?,O(n^1))
TRS:
 {
                    f(x, x, y) -> x,
                    f(x, y, y) -> y,
                  f(x, y, g y) -> x,
  f(f(x, y, z), u, f(x, y, v)) -> f(x, y, f(z, u, v)),
                  f(g x, x, y) -> y
 }
 DUP: We consider a non-duplicating system.
  Trs:
   {
                      f(x, x, y) -> x,
                      f(x, y, y) -> y,
                    f(x, y, g y) -> x,
    f(f(x, y, z), u, f(x, y, v)) -> f(x, y, f(z, u, v)),
                    f(g x, x, y) -> y
   }
  Natural interpretation:
   Strict:
    {
                       f(x, x, y) -> x,
                       f(x, y, y) -> y,
                     f(x, y, g y) -> x,
     f(f(x, y, z), u, f(x, y, v)) -> f(x, y, f(z, u, v)),
                     f(g x, x, y) -> y
    }
   Weak:
    {}
   Interpretation class: stronglylinear
   [g](X0) = + 1*X0 + 5
   [f](X2, X1, X0) = + 1*X0 + 1*X1 + 1*X2 + 3
   
   Qed