YES

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

Proof:
 Bounds Processor:
  bound: 2
  enrichment: top
  automaton:
   final states: {15,14,11,10,7}
   transitions:
    f0(7,14) -> 7*
    f0(14,10) -> 7*
    f0(14,14) -> 7*
    f0(15,7) -> 7*
    f0(10,7) -> 7*
    f0(15,11) -> 7*
    f0(10,11) -> 7*
    f0(15,15) -> 7*
    f0(10,15) -> 7*
    f0(11,10) -> 7*
    f0(11,14) -> 7*
    f0(7,7) -> 7*
    f0(7,11) -> 7*
    f0(7,15) -> 7*
    f0(14,7) -> 7*
    f0(14,11) -> 7*
    f0(14,15) -> 7*
    f0(15,10) -> 7*
    f0(10,10) -> 7*
    f0(15,14) -> 7*
    f0(10,14) -> 7*
    f0(11,7) -> 7*
    f0(11,11) -> 7*
    f0(11,15) -> 7*
    f0(7,10) -> 7*
    g0(15) -> 7*
    g0(10) -> 7*
    g0(7) -> 7*
    g0(14) -> 7*
    g0(11) -> 7*
    a0() -> 7*
    h0(11,15,10) -> 7*
    h0(11,7,7) -> 7*
    h0(11,11,7) -> 7*
    h0(11,15,7) -> 7*
    h0(15,7,15) -> 7*
    h0(10,7,15) -> 7*
    h0(15,11,15) -> 7*
    h0(7,10,10) -> 7*
    h0(10,11,15) -> 7*
    h0(14,7,14) -> 7*
    h0(15,15,15) -> 7*
    h0(7,14,10) -> 7*
    h0(10,15,15) -> 7*
    h0(14,11,14) -> 7*
    h0(14,15,14) -> 7*
    h0(7,10,7) -> 7*
    h0(14,7,11) -> 7*
    h0(7,14,7) -> 7*
    h0(14,11,11) -> 7*
    h0(14,15,11) -> 7*
    h0(11,10,15) -> 7*
    h0(11,14,15) -> 7*
    h0(15,10,14) -> 7*
    h0(10,10,14) -> 7*
    h0(15,14,14) -> 7*
    h0(10,14,14) -> 7*
    h0(15,10,11) -> 7*
    h0(10,10,11) -> 7*
    h0(7,7,15) -> 7*
    h0(15,14,11) -> 7*
    h0(10,14,11) -> 7*
    h0(14,10,10) -> 7*
    h0(7,11,15) -> 7*
    h0(11,7,14) -> 7*
    h0(14,14,10) -> 7*
    h0(7,15,15) -> 7*
    h0(11,11,14) -> 7*
    h0(14,10,7) -> 7*
    h0(11,15,14) -> 7*
    h0(11,7,11) -> 7*
    h0(14,14,7) -> 7*
    h0(11,11,11) -> 7*
    h0(15,7,10) -> 7*
    h0(10,7,10) -> 7*
    h0(11,15,11) -> 7*
    h0(15,11,10) -> 7*
    h0(10,11,10) -> 7*
    h0(15,15,10) -> 7*
    h0(10,15,10) -> 7*
    h0(7,10,14) -> 7*
    h0(15,7,7) -> 7*
    h0(10,7,7) -> 7*
    h0(7,14,14) -> 7*
    h0(15,11,7) -> 7*
    h0(10,11,7) -> 7*
    h0(15,15,7) -> 7*
    h0(10,15,7) -> 7*
    h0(7,10,11) -> 7*
    h0(14,7,15) -> 7*
    h0(7,14,11) -> 7*
    h0(11,10,10) -> 7*
    h0(14,11,15) -> 7*
    h0(11,14,10) -> 7*
    h0(14,15,15) -> 7*
    h0(11,10,7) -> 7*
    h0(11,14,7) -> 7*
    h0(7,7,10) -> 7*
    h0(15,10,15) -> 7*
    h0(10,10,15) -> 7*
    h0(7,11,10) -> 7*
    h0(15,14,15) -> 7*
    h0(10,14,15) -> 7*
    h0(14,10,14) -> 7*
    h0(7,15,10) -> 7*
    h0(7,7,7) -> 7*
    h0(14,14,14) -> 7*
    h0(7,11,7) -> 7*
    h0(14,10,11) -> 7*
    h0(7,15,7) -> 7*
    h0(11,7,15) -> 7*
    h0(14,14,11) -> 7*
    h0(11,11,15) -> 7*
    h0(15,7,14) -> 7*
    h0(10,7,14) -> 7*
    h0(11,15,15) -> 7*
    h0(15,11,14) -> 7*
    h0(10,11,14) -> 7*
    h0(15,15,14) -> 7*
    h0(10,15,14) -> 7*
    h0(15,7,11) -> 7*
    h0(10,7,11) -> 7*
    h0(15,11,11) -> 7*
    h0(10,11,11) -> 7*
    h0(14,7,10) -> 7*
    h0(15,15,11) -> 7*
    h0(10,15,11) -> 7*
    h0(14,11,10) -> 7*
    h0(7,10,15) -> 7*
    h0(14,15,10) -> 7*
    h0(7,14,15) -> 7*
    h0(11,10,14) -> 7*
    h0(14,7,7) -> 7*
    h0(11,14,14) -> 7*
    h0(14,11,7) -> 7*
    h0(14,15,7) -> 7*
    h0(11,10,11) -> 7*
    h0(11,14,11) -> 7*
    h0(15,10,10) -> 7*
    h0(10,10,10) -> 7*
    h0(7,7,14) -> 7*
    h0(15,14,10) -> 7*
    h0(10,14,10) -> 7*
    h0(7,11,14) -> 7*
    h0(15,10,7) -> 7*
    h0(10,10,7) -> 7*
    h0(7,15,14) -> 7*
    h0(7,7,11) -> 7*
    h0(15,14,7) -> 7*
    h0(10,14,7) -> 7*
    h0(7,11,11) -> 7*
    h0(11,7,10) -> 7*
    h0(14,10,15) -> 7*
    h0(7,15,11) -> 7*
    h0(11,11,10) -> 7*
    h0(14,14,15) -> 7*
    b0() -> 7*
    i0(15) -> 7*
    i0(10) -> 7*
    i0(7) -> 7*
    i0(14) -> 7*
    i0(11) -> 7*
    g1(15) -> 7*
    g1(10) -> 7*
    g1(7) -> 7*
    g1(14) -> 7*
    g1(11) -> 7*
    f1(7,14) -> 7*
    f1(14,10) -> 7*
    f1(14,14) -> 7*
    f1(15,7) -> 7*
    f1(10,7) -> 7*
    f1(15,11) -> 7*
    f1(10,11) -> 7*
    f1(15,15) -> 7*
    f1(10,15) -> 7*
    f1(11,10) -> 7*
    f1(11,14) -> 7*
    f1(7,7) -> 7*
    f1(7,11) -> 7*
    f1(7,15) -> 7*
    f1(14,7) -> 7*
    f1(14,11) -> 7*
    f1(14,15) -> 7*
    f1(15,10) -> 7*
    f1(10,10) -> 7*
    f1(15,14) -> 7*
    f1(10,14) -> 7*
    f1(11,7) -> 7*
    f1(11,11) -> 7*
    f1(11,15) -> 7*
    f1(7,10) -> 7*
    h1(14,9,14) -> 7*
    h1(14,11,14) -> 7*
    h1(14,15,14) -> 7*
    h1(8,9,10) -> 7*
    h1(8,11,10) -> 7*
    h1(14,9,8) -> 7*
    h1(8,15,10) -> 7*
    h1(14,11,8) -> 7*
    h1(14,15,8) -> 7*
    h1(10,9,10) -> 7*
    h1(10,11,10) -> 7*
    h1(10,15,10) -> 7*
    h1(8,9,14) -> 7*
    h1(8,11,14) -> 7*
    h1(8,15,14) -> 7*
    h1(8,9,8) -> 7*
    h1(8,11,8) -> 7*
    h1(8,15,8) -> 7*
    h1(10,9,14) -> 7*
    h1(10,11,14) -> 7*
    h1(10,15,14) -> 7*
    h1(14,9,10) -> 7*
    h1(14,11,10) -> 7*
    h1(14,15,10) -> 7*
    h1(10,9,8) -> 7*
    h1(10,11,8) -> 7*
    h1(10,15,8) -> 7*
    a1() -> 10*,7,8
    b1() -> 11*,7,9
    h2(14,13,14) -> 7*
    h2(14,15,14) -> 7*
    h2(12,13,12) -> 7*
    h2(12,15,12) -> 7*
    h2(14,13,12) -> 7*
    h2(14,15,12) -> 7*
    h2(12,13,14) -> 7*
    h2(12,15,14) -> 7*
    a2() -> 10,14*,8,7,12
    b2() -> 11,15*,9,7,13
    10 -> 7*
    11 -> 7*
    14 -> 7*
    15 -> 7*
  problem:
   
  Qed