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

Proof:
 Bounds Processor:
  bound: 1
  enrichment: match
  automaton:
   final states: {20,8,7,6,5}
   transitions:
    i0(17,18) -> 5*
    i0(18,1) -> 5*
    i0(2,18) -> 5*
    i0(18,3) -> 5*
    i0(3,1) -> 5*
    i0(3,3) -> 5*
    i0(18,17) -> 5*
    i0(18,19) -> 5*
    i0(3,17) -> 5*
    i0(19,2) -> 5*
    i0(3,19) -> 5*
    i0(19,4) -> 5*
    i0(4,2) -> 5*
    i0(4,4) -> 5*
    i0(19,18) -> 5*
    i0(4,18) -> 5*
    i0(1,2) -> 5*
    i0(1,4) -> 5*
    i0(17,1) -> 5*
    i0(1,18) -> 5*
    i0(17,3) -> 5*
    i0(2,1) -> 5*
    i0(2,3) -> 5*
    i0(17,17) -> 5*
    i0(17,19) -> 5*
    i0(2,17) -> 5*
    i0(18,2) -> 5*
    i0(2,19) -> 5*
    i0(18,4) -> 5*
    i0(3,2) -> 5*
    i0(3,4) -> 5*
    i0(18,18) -> 5*
    i0(19,1) -> 5*
    i0(3,18) -> 5*
    i0(19,3) -> 5*
    i0(4,1) -> 5*
    i0(4,3) -> 5*
    i0(19,17) -> 5*
    i0(19,19) -> 5*
    i0(4,17) -> 5*
    i0(4,19) -> 5*
    i0(1,1) -> 5*
    i0(1,3) -> 5*
    i0(1,17) -> 5*
    i0(17,2) -> 5*
    i0(1,19) -> 5*
    i0(17,4) -> 5*
    i0(2,2) -> 5*
    i0(2,4) -> 5*
    a0() -> 1*
    b0() -> 2*
    g0(17,18) -> 6*
    g0(18,1) -> 6*
    g0(2,18) -> 6*
    g0(18,3) -> 6*
    g0(3,1) -> 6*
    g0(3,3) -> 6*
    g0(18,17) -> 6*
    g0(18,19) -> 6*
    g0(3,17) -> 6*
    g0(19,2) -> 6*
    g0(3,19) -> 6*
    g0(19,4) -> 6*
    g0(4,2) -> 6*
    g0(4,4) -> 6*
    g0(19,18) -> 6*
    g0(4,18) -> 6*
    g0(1,2) -> 6*
    g0(1,4) -> 6*
    g0(17,1) -> 6*
    g0(1,18) -> 6*
    g0(17,3) -> 6*
    g0(2,1) -> 6*
    g0(2,3) -> 6*
    g0(17,17) -> 6*
    g0(17,19) -> 6*
    g0(2,17) -> 6*
    g0(18,2) -> 6*
    g0(2,19) -> 6*
    g0(18,4) -> 6*
    g0(3,2) -> 6*
    g0(3,4) -> 6*
    g0(18,18) -> 6*
    g0(19,1) -> 6*
    g0(3,18) -> 6*
    g0(19,3) -> 6*
    g0(4,1) -> 6*
    g0(4,3) -> 6*
    g0(19,17) -> 6*
    g0(19,19) -> 6*
    g0(4,17) -> 6*
    g0(4,19) -> 6*
    g0(1,1) -> 6*
    g0(1,3) -> 6*
    g0(1,17) -> 6*
    g0(17,2) -> 6*
    g0(1,19) -> 6*
    g0(17,4) -> 6*
    g0(2,2) -> 6*
    g0(2,4) -> 6*
    h0(17) -> 7*
    h0(2) -> 7*
    h0(19) -> 7*
    h0(4) -> 7*
    h0(1) -> 7*
    h0(18) -> 7*
    h0(3) -> 7*
    s0(17) -> 3*
    s0(2) -> 3*
    s0(19) -> 3*
    s0(4) -> 3*
    s0(1) -> 3*
    s0(18) -> 3*
    s0(3) -> 3*
    f0(17) -> 8*
    f0(2) -> 8*
    f0(19) -> 8*
    f0(4) -> 8*
    f0(1) -> 8*
    f0(18) -> 8*
    f0(3) -> 8*
    c0() -> 4*
    s1(15) -> 16*
    s1(17) -> 3,17*
    s1(2) -> 17*,3,13
    s1(19) -> 3,17*
    s1(4) -> 17*,3,13
    s1(16) -> 8*
    s1(1) -> 17*,3,13
    s1(18) -> 3,17*
    s1(3) -> 17*,3,13
    f1(20) -> 15*
    f1(14) -> 15*
    h1(17) -> 20*,7,14
    h1(13) -> 14*
    g1(18,9) -> 6*
    g1(18,19) -> 6*
    g1(10,9) -> 6*
    g1(10,19) -> 6*
    a1() -> 18*,1,10
    b1() -> 19*,2,9
    i1(18,9) -> 5*
    i1(18,19) -> 5*
    i1(10,9) -> 5*
    i1(10,19) -> 5*
  problem:
   
  Qed