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: roof
  automaton:
   final states: {33,32,31,30,29,14,12,9,4,1}
   transitions:
    f70() -> 5*
    g0(11,33) -> 31*
    g0(2,20) -> 16*
    g0(8,5) -> 10*
    g0(8,7) -> 29*,13,4
    g0(32,32) -> 16*
    g0(17,32) -> 16*
    g0(2,32) -> 16*
    g0(44,2) -> 32*
    g0(47,44) -> 20*
    g0(32,44) -> 17*
    g0(47,52) -> 20*
    g0(32,52) -> 17*
    g0(2,48) -> 16*
    g0(8,31) -> 29*
    g0(49,32) -> 16*
    g0(3,45) -> 32*
    g0(3,53) -> 32*
    g0(5,17) -> 30*,15,14
    g0(19,44) -> 20*
    g0(11,10) -> 31*,7,9
    g0(19,52) -> 20*
    g0(47,3) -> 20*
    g0(32,3) -> 17*
    g0(5,49) -> 30*
    g0(11,32) -> 31*
    g0(32,17) -> 16*
    g0(6,32) -> 33*
    g0(17,17) -> 16*
    g0(46,44) -> 17*
    g0(16,44) -> 17*
    g0(3,2) -> 32*,15,16,20,10,14,13,12,7,17,9,4,1
    g0(46,52) -> 17*
    g0(16,52) -> 17*
    g0(53,20) -> 16*
    g0(52,45) -> 32*
    g0(19,3) -> 20*
    g0(53,32) -> 16*
    g0(52,53) -> 32*
    g0(32,49) -> 16*
    g0(17,49) -> 16*
    g0(49,17) -> 16*
    g0(8,32) -> 29*
    g0(53,48) -> 16*
    g0(45,20) -> 16*
    g0(46,3) -> 17*
    g0(44,45) -> 32*
    g0(49,49) -> 16*
    g0(16,3) -> 17*
    g0(11,5) -> 13*
    g0(45,32) -> 16*
    g0(6,5) -> 7*
    g0(44,53) -> 32*
    g0(5,32) -> 30*
    g0(52,2) -> 32*
    g0(6,13) -> 33*,10,12
    g0(45,48) -> 16*
    g0(6,29) -> 33*
    a0() -> 3*
    b0() -> 2*
    e0() -> 8*
    d0() -> 6*
    c0() -> 11*
    f0(30) -> 16*
    f0(15) -> 16*
    f0(5) -> 15*
    f0(52) -> 18*
    f0(42) -> 16*
    f0(32) -> 16*
    f0(44) -> 18*
    f0(43) -> 19*
    f0(18) -> 19*
    f0(3) -> 18*
    g1(52,34) -> 16*
    g1(47,44) -> 48*,20,38
    g1(37,44) -> 38*
    g1(2,38) -> 16*
    g1(47,52) -> 20,48*,38
    g1(37,52) -> 38*
    g1(2,48) -> 16*
    g1(44,34) -> 16*
    g1(40,35) -> 41*
    g1(35,45) -> 16*
    g1(35,53) -> 16*
    g1(46,44) -> 49*,17,41
    g1(46,52) -> 17,49*,41
    g1(47,35) -> 38*
    g1(37,35) -> 38*
    g1(52,45) -> 32*,16
    g1(32,41) -> 16*
    g1(17,41) -> 16*
    g1(52,53) -> 32*,16
    g1(32,49) -> 16*
    g1(17,49) -> 16*
    g1(53,38) -> 16*
    g1(53,48) -> 16*
    g1(49,41) -> 16*
    g1(44,45) -> 32*,16
    g1(49,49) -> 16*
    g1(44,53) -> 32*,16
    g1(35,34) -> 16*
    g1(45,38) -> 16*
    g1(40,44) -> 41*
    g1(45,48) -> 16*
    g1(40,52) -> 41*
    g1(46,35) -> 41*
    f1(5) -> 42*,15,39
    f1(52) -> 18,43*
    f1(42) -> 46*,16,40
    f1(44) -> 18,43*
    f1(39) -> 40*
    f1(36) -> 37*
    f1(43) -> 47*,19,37
    f1(3) -> 43*,18,36
    a1() -> 44*,3,35
    b1() -> 45*,2,34
    g2(51,53) -> 16*
    g2(52,50) -> 16*
    g2(51,50) -> 16*
    g2(52,53) -> 32*,16
    a2() -> 44,52*,35,3,51
    b2() -> 45,53*,34,2,50
    4 -> 13*
    9 -> 7*
    12 -> 10*
    14 -> 15*
  problem:
   
  Qed