YES

Problem:
 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()))
 g(x,g(y,g(x,y))) -> g(a(),g(x,g(y,b())))

Proof:
 Bounds Processor:
  bound: 1
  enrichment: roof
  automaton:
   final states: {41,40,39,38,37,16,11,9,6,1}
   transitions:
    f70() -> 2*
    g0(5,52) -> 36*
    g0(37,20) -> 36*
    g0(52,24) -> 36*
    g0(17,18) -> 36*,21,19
    g0(12,18) -> 36*,21,19
    g0(7,18) -> 36*,21,19
    g0(17,20) -> 36*,21,19
    g0(37,24) -> 36*
    g0(52,28) -> 36*
    g0(12,20) -> 36*,21,19
    g0(2,18) -> 36*,21,19
    g0(7,20) -> 36*,21,19
    g0(2,20) -> 36*,21,19
    g0(17,24) -> 36*,19,21
    g0(37,28) -> 36*
    g0(12,24) -> 36*,19,21
    g0(7,24) -> 36*,21,19
    g0(2,24) -> 36*,19,21
    g0(17,28) -> 36*,21,19
    g0(8,7) -> 37*,4,6
    g0(12,28) -> 36*,21,19
    g0(7,28) -> 36*,21,19
    g0(2,28) -> 36*,21,19
    g0(28,17) -> 18*
    g0(18,17) -> 18*
    g0(12,36) -> 39*
    g0(8,17) -> 28*
    g0(3,17) -> 24*
    g0(52,50) -> 18*
    g0(52,52) -> 36*
    g0(37,50) -> 18*
    g0(37,52) -> 36*
    g0(17,50) -> 18*
    g0(54,18) -> 36*
    g0(12,50) -> 18*
    g0(49,18) -> 36*
    g0(17,52) -> 36*
    g0(7,50) -> 18*
    g0(14,12) -> 15*
    g0(54,20) -> 36*
    g0(12,52) -> 36*
    g0(2,50) -> 18*
    g0(39,18) -> 36*
    g0(49,20) -> 36*
    g0(7,52) -> 36*
    g0(2,52) -> 36*
    g0(12,54) -> 39*
    g0(29,18) -> 36*,21,19
    g0(39,20) -> 36*
    g0(24,18) -> 36*,21,19
    g0(54,24) -> 36*
    g0(29,20) -> 36*,21,19
    g0(19,18) -> 36*,21,19
    g0(49,24) -> 36*
    g0(24,20) -> 36*,21,19
    g0(19,20) -> 36*,21,19
    g0(39,24) -> 36*
    g0(4,18) -> 36*,21,19
    g0(54,28) -> 36*
    g0(8,39) -> 37*
    g0(29,24) -> 36*,21,19
    g0(49,28) -> 36*
    g0(53,49) -> 15*
    g0(3,39) -> 40*
    g0(4,20) -> 36*,21,19
    g0(24,24) -> 36*,21,19
    g0(19,24) -> 36*,21,19
    g0(39,28) -> 36*
    g0(3,41) -> 40*
    g0(29,28) -> 36*,21,19
    g0(4,24) -> 36*,21,19
    g0(24,28) -> 36*,21,19
    g0(55,15) -> 14*
    g0(19,28) -> 36*,21,19
    g0(49,36) -> 39*
    g0(50,17) -> 18*
    g0(4,28) -> 36*,21,19
    g0(40,17) -> 18*
    g0(15,15) -> 14*
    g0(20,17) -> 18*
    g0(10,17) -> 18*
    g0(5,17) -> 20*
    g0(54,50) -> 18*
    g0(49,50) -> 18*
    g0(54,52) -> 36*
    g0(49,52) -> 36*
    g0(39,50) -> 18*
    g0(39,52) -> 36*
    g0(29,50) -> 18*
    g0(49,54) -> 39*
    g0(24,50) -> 18*
    g0(29,52) -> 36*
    g0(19,50) -> 18*
    g0(24,52) -> 36*
    g0(19,52) -> 36*
    g0(4,50) -> 18*
    g0(41,18) -> 36*
    g0(36,18) -> 36*
    g0(4,52) -> 36*
    g0(41,20) -> 36*
    g0(36,20) -> 36*
    g0(41,24) -> 36*
    g0(5,37) -> 41*
    g0(36,24) -> 36*
    g0(5,39) -> 41*
    g0(41,28) -> 36*
    g0(36,28) -> 36*
    g0(55,55) -> 14*
    g0(52,17) -> 18*
    g0(37,17) -> 18*
    g0(15,55) -> 14*
    g0(17,17) -> 18*
    g0(12,17) -> 18*
    g0(2,15) -> 38*,13,11
    g0(7,17) -> 18*
    g0(12,19) -> 39*,7,6,4,1,10,9,16
    g0(2,17) -> 18*
    g0(12,21) -> 40*,7,9
    g0(8,2) -> 10*
    g0(53,12) -> 15*
    g0(3,2) -> 4*
    g0(41,50) -> 18*
    g0(36,50) -> 18*
    g0(41,52) -> 36*
    g0(36,52) -> 36*
    g0(12,29) -> 39*,7,6,4,16,9,1,10
    g0(3,10) -> 40*,7,9
    g0(28,18) -> 36*,21,19
    g0(18,18) -> 36*,21,19
    g0(28,20) -> 36*,21,19
    g0(18,20) -> 36*,21,19
    g0(8,18) -> 36*,21,19
    g0(3,18) -> 36*,19,21
    g0(28,24) -> 36*,21,19
    g0(8,20) -> 36*,21,19
    g0(3,20) -> 36*,19,21
    g0(18,24) -> 36*,21,19
    g0(8,24) -> 36*,21,19
    g0(28,28) -> 36*,21,19
    g0(18,28) -> 36*,21,19
    g0(54,17) -> 18*
    g0(49,17) -> 18*
    g0(3,28) -> 36*,21,19
    g0(39,17) -> 18*
    g0(49,19) -> 39*
    g0(29,17) -> 18*
    g0(49,21) -> 40*
    g0(24,17) -> 18*
    g0(19,17) -> 18*
    g0(2,55) -> 38*
    g0(4,17) -> 18*
    g0(8,40) -> 37*
    g0(49,29) -> 39*
    g0(5,2) -> 7*
    g0(5,4) -> 41*,10,1
    g0(28,50) -> 18*
    g0(28,52) -> 36*
    g0(18,50) -> 18*
    g0(50,18) -> 36*
    g0(18,52) -> 36*
    g0(8,50) -> 28*
    g0(3,50) -> 24*
    g0(40,18) -> 36*
    g0(50,20) -> 36*
    g0(8,52) -> 36*
    g0(3,52) -> 36*
    g0(40,20) -> 36*
    g0(20,18) -> 36*,21,19
    g0(50,24) -> 36*
    g0(10,18) -> 36*,21,19
    g0(20,20) -> 36*,21,19
    g0(40,24) -> 36*
    g0(5,18) -> 36*,21,19
    g0(10,20) -> 36*,21,19
    g0(50,28) -> 36*
    g0(20,24) -> 36*,21,19
    g0(40,28) -> 36*
    g0(10,24) -> 36*,21,19
    g0(5,24) -> 36*,19,21
    g0(20,28) -> 36*,21,19
    g0(10,28) -> 36*,21,19
    g0(14,49) -> 15*
    g0(5,28) -> 29*
    g0(41,17) -> 18*
    g0(36,17) -> 18*
    g0(50,50) -> 18*
    g0(50,52) -> 36*
    g0(40,50) -> 18*
    g0(40,52) -> 36*
    g0(20,50) -> 18*
    g0(52,18) -> 36*
    g0(20,52) -> 36*
    g0(10,50) -> 18*
    g0(5,50) -> 20*
    g0(52,20) -> 36*
    g0(10,52) -> 36*
    g0(37,18) -> 36*
    e0() -> 5*
    d0() -> 3*
    c0() -> 8*
    f0(2) -> 13*
    f0(51) -> 14*
    f0(38) -> 14*
    f0(13) -> 14*
    a0() -> 12*
    b0() -> 17*
    g1(42,48) -> 39*
    g1(17,46) -> 47*
    g1(42,54) -> 39*
    g1(17,50) -> 52*,18,47
    g1(12,52) -> 36,54*,48
    g1(53,49) -> 55*,15,45
    g1(44,42) -> 45*
    g1(49,48) -> 39*
    g1(49,52) -> 36,54*,48
    g1(49,54) -> 39*
    g1(55,45) -> 14*
    g1(15,45) -> 14*
    g1(55,55) -> 14*
    g1(15,55) -> 14*
    g1(12,47) -> 48*
    g1(53,42) -> 45*
    g1(49,47) -> 48*
    g1(44,49) -> 45*
    g1(50,46) -> 47*
    g1(50,50) -> 52*,18,47
    a1() -> 49*,12,42
    b1() -> 50*,17,46
    f1(2) -> 51*,13,43
    f1(51) -> 53*,14,44
    f1(43) -> 44*
    1 -> 10*
    6 -> 4*
    9 -> 7*
    11 -> 13*
    19 -> 21*
    21 -> 19*
  problem:
   
  Qed