YES(?,O(n^1))

Problem:
 f(f(x,y,z),u,f(x,y,v)) -> f(x,y,f(z,u,v))
 f(x,y,y) -> y
 f(x,y,g(y)) -> x
 f(x,x,y) -> x
 f(g(x),x,y) -> y

Proof:
 Matrix Interpretation Processor:
  dimension: 1
  interpretation:
   [g](x0) = x0,
   
   [f](x0, x1, x2) = x0 + x1 + x2 + 8
  orientation:
   f(f(x,y,z),u,f(x,y,v)) = u + v + 2x + 2y + z + 24 >= u + v + x + y + z + 16 = f(x,y,f(z,u,v))
   
   f(x,y,y) = x + 2y + 8 >= y = y
   
   f(x,y,g(y)) = x + 2y + 8 >= x = x
   
   f(x,x,y) = 2x + y + 8 >= x = x
   
   f(g(x),x,y) = 2x + y + 8 >= y = y
  problem:
   
  Qed