Problem:
 g(x,x) -> g(a(),b())
 g(c(),g(c(),x)) -> g(e(),g(d(),x))
 g(d(),g(d(),x)) -> g(c(),g(e(),x))
 g(e(),g(e(),x)) -> g(d(),g(c(),x))
 f(g(x,y)) -> g(y,g(f(f(x)),a()))

Proof:
 Bounds Processor:
  bound: 1
  enrichment: match
  automaton:
   final states: {7,6}
   transitions:
    b1() -> 2*
    g0(3,1) -> 6*
    g0(3,3) -> 6*
    g0(3,5) -> 6*
    g0(4,2) -> 6*
    g0(4,4) -> 6*
    g0(5,1) -> 6*
    g0(5,3) -> 6*
    g0(5,5) -> 6*
    g0(1,4) -> 6*
    g0(2,1) -> 6*
    g0(2,3) -> 6*
    g0(2,5) -> 6*
    g0(3,2) -> 6*
    g0(3,4) -> 6*
    g0(4,1) -> 6*
    g0(4,3) -> 6*
    g0(4,5) -> 6*
    g0(5,2) -> 6*
    g0(5,4) -> 6*
    g0(1,1) -> 6*
    g0(1,3) -> 6*
    g0(1,5) -> 6*
    g0(2,2) -> 6*
    g0(2,4) -> 6*
    c0() -> 3*
    e0() -> 4*
    d0() -> 5*
    f0(5) -> 7*
    f0(2) -> 7*
    f0(4) -> 7*
    f0(1) -> 7*
    f0(3) -> 7*
    g1(1,2) -> 6*
    a1() -> 1*
  problem:
   
  Qed