YES

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: 2
  enrichment: match
  automaton:
   final states: {33,32,31,30,29,14,12,9,4,1}
   transitions:
    a2() -> 46,54*,35,3,53
    b2() -> 47,55*,34,2,52
    f70() -> 5*
    g0(11,33) -> 31*
    g0(48,3) -> 20*
    g0(46,47) -> 32*
    g0(2,20) -> 16*
    g0(47,32) -> 16*
    g0(8,5) -> 10*
    g0(8,7) -> 29*,13,4
    g0(32,32) -> 16*
    g0(46,55) -> 32*
    g0(17,32) -> 16*
    g0(54,2) -> 32*
    g0(2,32) -> 16*
    g0(32,46) -> 17*
    g0(32,50) -> 16*
    g0(17,50) -> 16*
    g0(32,54) -> 17*
    g0(8,31) -> 29*
    g0(3,47) -> 32*
    g0(50,17) -> 16*
    g0(46,2) -> 32*
    g0(3,55) -> 32*
    g0(5,17) -> 30*,15,14
    g0(49,46) -> 17*
    g0(19,46) -> 20*
    g0(49,54) -> 17*
    g0(11,10) -> 31*,7,9
    g0(19,54) -> 20*
    g0(32,3) -> 17*
    g0(55,51) -> 16*
    g0(11,32) -> 31*
    g0(32,17) -> 16*
    g0(6,32) -> 33*
    g0(17,17) -> 16*
    g0(3,2) -> 32*,15,16,20,10,14,13,12,7,17,9,4,1
    g0(16,46) -> 17*
    g0(16,54) -> 17*
    g0(49,3) -> 17*
    g0(19,3) -> 20*
    g0(47,51) -> 16*
    g0(8,32) -> 29*
    g0(2,51) -> 16*
    g0(48,46) -> 20*
    g0(48,54) -> 20*
    g0(55,20) -> 16*
    g0(54,47) -> 32*
    g0(16,3) -> 17*
    g0(55,32) -> 16*
    g0(50,32) -> 16*
    g0(11,5) -> 13*
    g0(6,5) -> 7*
    g0(54,55) -> 32*
    g0(5,32) -> 30*
    g0(6,13) -> 33*,10,12
    g0(50,50) -> 16*
    g0(6,29) -> 33*
    g0(5,50) -> 30*
    g0(47,20) -> 16*
    e0() -> 8*
    d0() -> 6*
    c0() -> 11*
    f0(45) -> 19*
    f0(30) -> 16*
    f0(15) -> 16*
    f0(32) -> 16*
    f0(44) -> 16*
    f0(18) -> 19*
    g1(46,47) -> 32*,16
    g1(46,55) -> 32*,16
    g1(47,38) -> 16*
    g1(2,38) -> 16*
    g1(37,46) -> 38*
    g1(32,50) -> 16*
    g1(48,35) -> 38*
    g1(37,54) -> 38*
    g1(17,50) -> 16*
    g1(54,34) -> 16*
    g1(49,46) -> 50*,17,41
    g1(49,54) -> 17,50*,41
    g1(40,35) -> 41*
    g1(50,41) -> 16*
    g1(55,51) -> 16*
    g1(35,47) -> 16*
    g1(46,34) -> 16*
    g1(35,55) -> 16*
    g1(37,35) -> 38*
    g1(32,41) -> 16*
    g1(17,41) -> 16*
    g1(47,51) -> 16*
    g1(2,51) -> 16*
    g1(48,46) -> 51*,20,38
    g1(48,54) -> 20,38,51*
    g1(49,35) -> 41*
    g1(54,47) -> 32*,16
    g1(54,55) -> 16*
    g1(55,38) -> 16*
    g1(35,34) -> 16*
    g1(40,46) -> 41*
    g1(50,50) -> 16*
    g1(40,54) -> 41*
    f1(45) -> 48*,19,37
    f1(5) -> 44*,15,39
    f1(54) -> 45*
    f1(44) -> 49*,16,40
    f1(39) -> 40*
    f1(46) -> 45*
    f1(36) -> 37*
    f1(3) -> 45*,18,36
    g2(53,55) -> 16*
    g2(54,52) -> 16*
    g2(53,52) -> 16*
    g2(54,55) -> 32*,16
    4 -> 13*
    9 -> 7*
    12 -> 10*
    14 -> 15*
  problem:
   
  Qed