YES

Problem:
 f(x,x) -> f(a(),b())
 b() -> c()

Proof:
 Bounds Processor:
  bound: 2
  enrichment: roof
  automaton:
   final states: {8,4,3,2,1}
   transitions:
    f0(8,1) -> 1*
    f0(3,1) -> 1*
    f0(8,3) -> 1*
    f0(3,3) -> 1*
    f0(4,2) -> 1*
    f0(4,4) -> 1*
    f0(4,8) -> 1*
    f0(1,2) -> 1*
    f0(1,4) -> 1*
    f0(1,8) -> 1*
    f0(2,1) -> 1*
    f0(2,3) -> 1*
    f0(8,2) -> 1*
    f0(3,2) -> 1*
    f0(8,4) -> 1*
    f0(3,4) -> 1*
    f0(8,8) -> 1*
    f0(3,8) -> 1*
    f0(4,1) -> 1*
    f0(4,3) -> 1*
    f0(1,1) -> 1*
    f0(1,3) -> 1*
    f0(2,2) -> 1*
    f0(2,4) -> 1*
    f0(2,8) -> 1*
    a0() -> 2*
    b0() -> 3*
    c0() -> 4*
    c1() -> 8*,4,3
    f1(2,3) -> 1*
    f1(2,8) -> 1*
    a1() -> 2*
    b1() -> 3*
    c2() -> 4,8*,3
  problem:
   
  Qed