YES

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:
 Bounds Processor:
  bound: 0
  enrichment: match
  automaton:
   final states: {7,6,2,1}
   transitions:
    f0(7,2,7) -> 6*
    f0(2,2,7) -> 6*
    f0(7,7,6) -> 6*
    f0(2,7,6) -> 6*
    f0(7,7,3) -> 6*
    f0(2,7,3) -> 6*
    f0(7,2,2) -> 6*
    f0(2,2,2) -> 6*,1,3
    f0(7,7,7) -> 6*
    f0(2,7,7) -> 6*
    f0(7,2,6) -> 6*
    f0(2,2,6) -> 6*
    f0(7,2,3) -> 6*
    f0(2,2,3) -> 6*,3,1
    f0(7,7,2) -> 6*
    f0(2,7,2) -> 6*
    f20() -> 7*,1,3,2
    1 -> 3*
    2 -> 6,3,1
    3 -> 1*
    7 -> 6*
  problem:
   
  Qed