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

Proof:
 Bounds Processor:
  bound: 1
  enrichment: match
  automaton:
   final states: {5,4,3}
   transitions:
    h0(1,2) -> 3*
    h0(2,1) -> 3*
    h0(1,1) -> 3*
    h0(2,2) -> 3*
    a0() -> 1*
    b0() -> 2*
    g0(1,2) -> 4*
    g0(2,1) -> 4*
    g0(1,1) -> 4*
    g0(2,2) -> 4*
    f0(2) -> 5*
    f0(1) -> 5*
    h1(1,2) -> 3*
    a1() -> 1*
    b1() -> 2*
  problem:
   
  Qed