YES(?,O(n^1))

Problem:
 f(x,x) -> a()
 f(g(x),y) -> f(x,y)

Proof:
 Bounds Processor:
  bound: 2
  enrichment: match
  automaton:
   final states: {4,3}
   transitions:
    f0(4,2) -> 3*
    f0(4,4) -> 3*
    f0(1,2) -> 3*
    f0(1,4) -> 3*
    f0(2,1) -> 3*
    f0(4,1) -> 3*
    f0(1,1) -> 3*
    f0(2,2) -> 3*
    f0(2,4) -> 3*
    a0() -> 1*
    g0(2) -> 2*
    g0(4) -> 2*
    g0(1) -> 2*
    f1(4,2) -> 3*
    f1(4,4) -> 3*
    f1(1,2) -> 3*
    f1(1,4) -> 3*
    f1(2,1) -> 3*
    f1(4,1) -> 3*
    f1(1,1) -> 3*
    f1(2,2) -> 3*
    f1(2,4) -> 3*
    a1() -> 4*,1,3
    a2() -> 1,4*,3
  problem:
   
  Qed