YES

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

Proof:
 Bounds Processor:
  bound: 1
  enrichment: match
  automaton:
   final states: {5,4,1}
   transitions:
    c1() -> 4,5*,2
    f0(3,5) -> 1*
    f0(3,2) -> 1*
    a0() -> 3*
    b0() -> 2*
    c0() -> 5*,2,4
  problem:
   
  Qed