YES

Problem:
 f(x,y,z) -> g(x,y,z)
 g(0(),1(),x) -> f(x,x,x)
 a() -> b()
 a() -> c()

Proof:
 Bounds Processor:
  bound: 3
  enrichment: roof
  automaton:
   final states: {8,10,9}
   transitions:
    c1() -> 8*
    b1() -> 8*
    f1(8,8,8) -> 8*
    f1(9,9,9) -> 8*
    f1(10,10,10) -> 8*
    g1(10,9,9) -> 8*
    g1(8,8,8) -> 8*
    g1(8,10,8) -> 8*
    g1(8,9,10) -> 8*
    g1(9,9,8) -> 8*
    g1(9,8,10) -> 8*
    g1(9,10,10) -> 8*
    g1(10,8,8) -> 8*
    g1(8,8,9) -> 8*
    g1(10,10,8) -> 8*
    g1(8,10,9) -> 8*
    g1(10,9,10) -> 8*
    g1(9,9,9) -> 8*
    g1(10,8,9) -> 8*
    g1(10,10,9) -> 8*
    g1(8,9,8) -> 8*
    g1(8,8,10) -> 8*
    g1(8,10,10) -> 8*
    g1(9,8,8) -> 8*
    g1(9,10,8) -> 8*
    g1(9,9,10) -> 8*
    g1(10,9,8) -> 8*
    g1(8,9,9) -> 8*
    g1(10,8,10) -> 8*
    g1(10,10,10) -> 8*
    g1(9,8,9) -> 8*
    g1(9,10,9) -> 8*
    f2(8,8,8) -> 8*
    f2(9,9,9) -> 8*
    f2(10,10,10) -> 8*
    g2(8,8,8) -> 8*
    g2(9,9,9) -> 8*
    g2(10,10,10) -> 8*
    g3(8,8,8) -> 8*
    g3(9,9,9) -> 8*
    g3(10,10,10) -> 8*
    f0(8,8,8) -> 8*
    f0(8,10,8) -> 8*
    f0(8,9,10) -> 8*
    f0(9,9,8) -> 8*
    f0(9,8,10) -> 8*
    f0(9,10,10) -> 8*
    f0(10,8,8) -> 8*
    f0(8,8,9) -> 8*
    f0(10,10,8) -> 8*
    f0(8,10,9) -> 8*
    f0(10,9,10) -> 8*
    f0(9,9,9) -> 8*
    f0(10,8,9) -> 8*
    f0(10,10,9) -> 8*
    f0(8,9,8) -> 8*
    f0(8,8,10) -> 8*
    f0(8,10,10) -> 8*
    f0(9,8,8) -> 8*
    f0(9,10,8) -> 8*
    f0(9,9,10) -> 8*
    f0(10,9,8) -> 8*
    f0(8,9,9) -> 8*
    f0(10,8,10) -> 8*
    f0(10,10,10) -> 8*
    f0(9,8,9) -> 8*
    f0(9,10,9) -> 8*
    f0(10,9,9) -> 8*
    g0(8,8,8) -> 8*
    g0(8,10,8) -> 8*
    g0(8,9,10) -> 8*
    g0(9,9,8) -> 8*
    g0(9,8,10) -> 8*
    g0(9,10,10) -> 8*
    g0(10,8,8) -> 8*
    g0(8,8,9) -> 8*
    g0(10,10,8) -> 8*
    g0(8,10,9) -> 8*
    g0(10,9,10) -> 8*
    g0(9,9,9) -> 8*
    g0(10,8,9) -> 8*
    g0(10,10,9) -> 8*
    g0(8,9,8) -> 8*
    g0(8,8,10) -> 8*
    g0(8,10,10) -> 8*
    g0(9,8,8) -> 8*
    g0(9,10,8) -> 8*
    g0(9,9,10) -> 8*
    g0(10,9,8) -> 8*
    g0(8,9,9) -> 8*
    g0(10,8,10) -> 8*
    g0(10,10,10) -> 8*
    g0(9,8,9) -> 8*
    g0(9,10,9) -> 8*
    g0(10,9,9) -> 8*
    00() -> 9*
    10() -> 10*
    a0() -> 8*
    b0() -> 8*
    c0() -> 8*
  problem:
   
  Qed