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:
 DP Processor:
  DPs:
   g#(x,x) -> g#(a(),b())
   g#(c(),g(c(),x)) -> g#(d(),x)
   g#(c(),g(c(),x)) -> g#(e(),g(d(),x))
   g#(d(),g(d(),x)) -> g#(e(),x)
   g#(d(),g(d(),x)) -> g#(c(),g(e(),x))
   g#(e(),g(e(),x)) -> g#(c(),x)
   g#(e(),g(e(),x)) -> g#(d(),g(c(),x))
   f#(g(x,y)) -> f#(x)
   f#(g(x,y)) -> f#(f(x))
   f#(g(x,y)) -> g#(f(f(x)),a())
   f#(g(x,y)) -> g#(y,g(f(f(x)),a()))
  TRS:
   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()))
  EDG Processor:
   DPs:
    g#(x,x) -> g#(a(),b())
    g#(c(),g(c(),x)) -> g#(d(),x)
    g#(c(),g(c(),x)) -> g#(e(),g(d(),x))
    g#(d(),g(d(),x)) -> g#(e(),x)
    g#(d(),g(d(),x)) -> g#(c(),g(e(),x))
    g#(e(),g(e(),x)) -> g#(c(),x)
    g#(e(),g(e(),x)) -> g#(d(),g(c(),x))
    f#(g(x,y)) -> f#(x)
    f#(g(x,y)) -> f#(f(x))
    f#(g(x,y)) -> g#(f(f(x)),a())
    f#(g(x,y)) -> g#(y,g(f(f(x)),a()))
   TRS:
    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()))
   graph:
    f#(g(x,y)) -> f#(f(x)) -> f#(g(x,y)) -> f#(x)
    f#(g(x,y)) -> f#(f(x)) -> f#(g(x,y)) -> f#(f(x))
    f#(g(x,y)) -> f#(f(x)) -> f#(g(x,y)) -> g#(f(f(x)),a())
    f#(g(x,y)) -> f#(f(x)) -> f#(g(x,y)) -> g#(y,g(f(f(x)),a()))
    f#(g(x,y)) -> f#(x) -> f#(g(x,y)) -> f#(x)
    f#(g(x,y)) -> f#(x) -> f#(g(x,y)) -> f#(f(x))
    f#(g(x,y)) -> f#(x) -> f#(g(x,y)) -> g#(f(f(x)),a())
    f#(g(x,y)) -> f#(x) -> f#(g(x,y)) -> g#(y,g(f(f(x)),a()))
    f#(g(x,y)) -> g#(f(f(x)),a()) -> g#(x,x) -> g#(a(),b())
    f#(g(x,y)) -> g#(y,g(f(f(x)),a())) -> g#(x,x) -> g#(a(),b())
    f#(g(x,y)) -> g#(y,g(f(f(x)),a())) ->
    g#(c(),g(c(),x)) -> g#(d(),x)
    f#(g(x,y)) -> g#(y,g(f(f(x)),a())) ->
    g#(c(),g(c(),x)) -> g#(e(),g(d(),x))
    f#(g(x,y)) -> g#(y,g(f(f(x)),a())) ->
    g#(d(),g(d(),x)) -> g#(e(),x)
    f#(g(x,y)) -> g#(y,g(f(f(x)),a())) ->
    g#(d(),g(d(),x)) -> g#(c(),g(e(),x))
    f#(g(x,y)) -> g#(y,g(f(f(x)),a())) ->
    g#(e(),g(e(),x)) -> g#(c(),x)
    f#(g(x,y)) -> g#(y,g(f(f(x)),a())) ->
    g#(e(),g(e(),x)) -> g#(d(),g(c(),x))
    g#(d(),g(d(),x)) -> g#(e(),x) -> g#(x,x) -> g#(a(),b())
    g#(d(),g(d(),x)) -> g#(e(),x) -> g#(e(),g(e(),x)) -> g#(c(),x)
    g#(d(),g(d(),x)) -> g#(e(),x) ->
    g#(e(),g(e(),x)) -> g#(d(),g(c(),x))
    g#(d(),g(d(),x)) -> g#(c(),g(e(),x)) ->
    g#(x,x) -> g#(a(),b())
    g#(d(),g(d(),x)) -> g#(c(),g(e(),x)) ->
    g#(c(),g(c(),x)) -> g#(d(),x)
    g#(d(),g(d(),x)) -> g#(c(),g(e(),x)) ->
    g#(c(),g(c(),x)) -> g#(e(),g(d(),x))
    g#(e(),g(e(),x)) -> g#(d(),g(c(),x)) ->
    g#(x,x) -> g#(a(),b())
    g#(e(),g(e(),x)) -> g#(d(),g(c(),x)) ->
    g#(d(),g(d(),x)) -> g#(e(),x)
    g#(e(),g(e(),x)) -> g#(d(),g(c(),x)) ->
    g#(d(),g(d(),x)) -> g#(c(),g(e(),x))
    g#(e(),g(e(),x)) -> g#(c(),x) -> g#(x,x) -> g#(a(),b())
    g#(e(),g(e(),x)) -> g#(c(),x) -> g#(c(),g(c(),x)) -> g#(d(),x)
    g#(e(),g(e(),x)) -> g#(c(),x) ->
    g#(c(),g(c(),x)) -> g#(e(),g(d(),x))
    g#(c(),g(c(),x)) -> g#(d(),x) -> g#(x,x) -> g#(a(),b())
    g#(c(),g(c(),x)) -> g#(d(),x) -> g#(d(),g(d(),x)) -> g#(e(),x)
    g#(c(),g(c(),x)) -> g#(d(),x) ->
    g#(d(),g(d(),x)) -> g#(c(),g(e(),x))
    g#(c(),g(c(),x)) -> g#(e(),g(d(),x)) ->
    g#(x,x) -> g#(a(),b())
    g#(c(),g(c(),x)) -> g#(e(),g(d(),x)) ->
    g#(e(),g(e(),x)) -> g#(c(),x)
    g#(c(),g(c(),x)) -> g#(e(),g(d(),x)) -> g#(e(),g(e(),x)) -> g#(d(),g(c(),x))
   SCC Processor:
    #sccs: 2
    #rules: 8
    #arcs: 34/121
    DPs:
     f#(g(x,y)) -> f#(f(x))
     f#(g(x,y)) -> f#(x)
    TRS:
     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()))
    Bounds Processor:
     bound: 2
     enrichment: match
     automaton:
      final states: {27,26,25,24,23,22,17,15,12,8,5,4,1}
      transitions:
       b2() -> 59*,6,46
       f90() -> 2*
       f{#,0}(25) -> 22*
       f{#,0}(42) -> 22*
       f{#,0}(27) -> 22*
       f{#,0}(44) -> 22*
       f{#,0}(3) -> 22*,4,1
       f0(25) -> 18*
       f0(42) -> 18*
       f0(27) -> 18*
       f0(44) -> 18*
       f0(3) -> 18*
       g0(25,58) -> 20*
       g0(42,28) -> 25*
       g0(6,43) -> 18*
       g0(27,28) -> 18*
       g0(18,7) -> 19*
       g0(6,45) -> 18*
       g0(3,7) -> 20*
       g0(2,28) -> 25*
       g0(28,19) -> 18*
       g0(14,2) -> 16*
       g0(9,2) -> 10*
       g0(28,27) -> 18*
       g0(59,20) -> 18*
       g0(42,58) -> 20*
       g0(27,58) -> 19,20,28*
       g0(9,16) -> 23*,13,15
       g0(59,28) -> 18*
       g0(44,28) -> 25*
       g0(28,45) -> 18*
       g0(25,7) -> 20*
       g0(9,24) -> 23*
       g0(19,28) -> 18*
       g0(45,19) -> 18*
       g0(45,27) -> 18*
       g0(14,42) -> 16*
       g0(11,2) -> 13*
       g0(9,42) -> 10*
       g0(14,44) -> 16*
       g0(9,44) -> 10*
       g0(11,10) -> 24*,16,8
       g0(44,58) -> 28*,19,20
       g0(45,45) -> 18*
       g0(42,7) -> 20*
       g0(6,20) -> 18*
       g0(27,7) -> 28*,19,20
       g0(11,26) -> 24*
       g0(6,28) -> 18*
       g0(42,19) -> 25*
       g0(27,19) -> 18*
       g0(42,27) -> 25*
       g0(2,19) -> 25*,3,17
       g0(11,42) -> 13*
       g0(27,27) -> 18*
       g0(11,44) -> 13*
       g0(2,27) -> 25*
       g0(42,45) -> 25*
       g0(44,7) -> 28*,19,20
       g0(27,45) -> 18*
       g0(28,28) -> 18*
       g0(2,45) -> 25*
       g0(14,13) -> 26*,10,12
       g0(44,19) -> 25*
       g0(59,27) -> 18*
       g0(19,19) -> 18*
       g0(44,27) -> 25*
       g0(14,23) -> 26*
       g0(19,27) -> 18*
       g0(14,27) -> 26*
       g0(9,27) -> 23*
       g0(59,43) -> 18*
       g0(59,45) -> 18*
       g0(18,58) -> 19*
       g0(44,45) -> 25*
       g0(3,58) -> 20*
       g0(45,28) -> 18*
       g0(19,45) -> 18*
       g0(11,27) -> 24*
       g0(6,27) -> 18*
       e0() -> 11*
       d0() -> 9*
       c0() -> 14*
       g1(6,37) -> 18*
       g1(6,43) -> 18*
       g1(6,45) -> 18*
       g1(42,58) -> 20,43*,37
       g1(28,37) -> 18*
       g1(28,43) -> 18*
       g1(2,58) -> 37*
       g1(28,45) -> 18*
       g1(58,59) -> 27*
       g1(45,37) -> 18*
       g1(44,58) -> 28,20,19,37,45*
       g1(45,43) -> 18*
       g1(45,45) -> 18*
       g1(42,7) -> 43*,20,37
       g1(2,7) -> 37*
       g1(58,6) -> 27*
       g1(27,37) -> 18*
       g1(27,43) -> 18*
       g1(44,7) -> 43,28,45*,20,19,37
       g1(27,45) -> 18*
       g1(7,59) -> 27*
       g1(59,37) -> 18*
       g1(59,43) -> 18*
       g1(59,45) -> 18*
       g1(19,37) -> 18*
       g1(19,43) -> 18*
       g1(19,45) -> 18*
       g1(7,6) -> 5,16,15,8,12,17,13,10,19,20,3,27*,18
       f1(42) -> 42,44*,18
       f1(7) -> 2*
       f1(2) -> 42*,3,2
       f1(44) -> 18,44*
       f1(58) -> 2*
       f{#,1}(42) -> 22*
       f{#,1}(7) -> 4,1,22*
       f{#,1}(2) -> 4,1,22*
       f{#,1}(44) -> 22*
       f{#,1}(58) -> 22*
       g2(47,46) -> 18*
       g2(58,59) -> 27*,18
       g2(47,59) -> 18*
       g2(58,46) -> 18*
       a2() -> 58*,7,47
       1 -> 4*
       8 -> 16*
       12 -> 10*
       15 -> 13*
       17 -> 3*
     problem:
      DPs:
       
      TRS:
       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()))
     Qed
    
    DPs:
     g#(e(),g(e(),x)) -> g#(d(),g(c(),x))
     g#(d(),g(d(),x)) -> g#(c(),g(e(),x))
     g#(c(),g(c(),x)) -> g#(e(),g(d(),x))
     g#(e(),g(e(),x)) -> g#(c(),x)
     g#(c(),g(c(),x)) -> g#(d(),x)
     g#(d(),g(d(),x)) -> g#(e(),x)
    TRS:
     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()))
    Matrix Interpretation Processor:
     dimension: 1
     interpretation:
      [g#](x0, x1) = x1,
      
      [f](x0) = x0 + 1,
      
      [d] = 0,
      
      [e] = 0,
      
      [c] = 0,
      
      [b] = 0,
      
      [a] = 0,
      
      [g](x0, x1) = x1 + 1
     orientation:
      g#(e(),g(e(),x)) = x + 1 >= x + 1 = g#(d(),g(c(),x))
      
      g#(d(),g(d(),x)) = x + 1 >= x + 1 = g#(c(),g(e(),x))
      
      g#(c(),g(c(),x)) = x + 1 >= x + 1 = g#(e(),g(d(),x))
      
      g#(e(),g(e(),x)) = x + 1 >= x = g#(c(),x)
      
      g#(c(),g(c(),x)) = x + 1 >= x = g#(d(),x)
      
      g#(d(),g(d(),x)) = x + 1 >= x = g#(e(),x)
      
      g(x,x) = x + 1 >= 1 = g(a(),b())
      
      g(c(),g(c(),x)) = x + 2 >= x + 2 = g(e(),g(d(),x))
      
      g(d(),g(d(),x)) = x + 2 >= x + 2 = g(c(),g(e(),x))
      
      g(e(),g(e(),x)) = x + 2 >= x + 2 = g(d(),g(c(),x))
      
      f(g(x,y)) = y + 2 >= 2 = g(y,g(f(f(x)),a()))
     problem:
      DPs:
       g#(e(),g(e(),x)) -> g#(d(),g(c(),x))
       g#(d(),g(d(),x)) -> g#(c(),g(e(),x))
       g#(c(),g(c(),x)) -> g#(e(),g(d(),x))
      TRS:
       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()))
     Bounds Processor:
      bound: 2
      enrichment: match
      automaton:
       final states: {36,35,34,33,32,17,16,15,14,11,9,6,1}
       transitions:
        g2(56,55) -> 19*
        g2(57,58) -> 34*,19
        g2(56,58) -> 19*
        g2(57,55) -> 19*
        a2() -> 49,57*,38,13,56
        b2() -> 50,58*,37,12,55
        f270() -> 2*
        g{#,0}(7,10) -> 9*
        g{#,0}(7,34) -> 9*
        g{#,0}(3,35) -> 6*
        g{#,0}(3,8) -> 6*
        g{#,0}(7,33) -> 9*
        g{#,0}(3,34) -> 6*
        g{#,0}(5,4) -> 1*
        g{#,0}(5,34) -> 1*
        g{#,0}(5,36) -> 1*
        f0(47) -> 19*
        f0(32) -> 19*
        f0(34) -> 19*
        f0(21) -> 22*
        f0(48) -> 22*
        f0(18) -> 19*
        g0(51,49) -> 20*
        g0(2,20) -> 32*,18,17
        g0(51,57) -> 20*
        g0(58,23) -> 19*
        g0(12,34) -> 19*
        g0(7,34) -> 36*
        g0(2,34) -> 32*
        g0(57,50) -> 34*
        g0(49,12) -> 34*
        g0(57,58) -> 34*
        g0(12,54) -> 19*
        g0(34,20) -> 19*
        g0(3,35) -> 33*
        g0(53,53) -> 19*
        g0(34,34) -> 19*
        g0(50,23) -> 19*
        g0(49,50) -> 34*
        g0(49,58) -> 34*
        g0(52,13) -> 23*
        g0(22,13) -> 23*
        g0(20,53) -> 19*
        g0(12,23) -> 19*
        g0(3,2) -> 4*
        g0(3,8) -> 33*,10,15
        g0(53,20) -> 19*
        g0(13,12) -> 34*,18,23,19,17,15,20,16,14,8,10,4,11
        g0(7,33) -> 36*
        g0(52,49) -> 23*
        g0(58,34) -> 19*
        g0(53,34) -> 19*
        g0(22,49) -> 23*
        g0(34,13) -> 20*
        g0(52,57) -> 23*
        g0(19,13) -> 20*
        g0(22,57) -> 23*
        g0(2,53) -> 32*
        g0(3,34) -> 33*
        g0(5,2) -> 10*
        g0(58,54) -> 19*
        g0(5,4) -> 35*,8,16
        g0(13,50) -> 34*
        g0(13,58) -> 34*
        g0(20,20) -> 19*
        g0(34,49) -> 20*
        g0(51,13) -> 20*
        g0(50,34) -> 19*
        g0(19,49) -> 20*
        g0(34,53) -> 19*
        g0(20,34) -> 19*
        g0(34,57) -> 20*
        g0(5,34) -> 35*
        g0(19,57) -> 20*
        g0(5,36) -> 35*
        g0(57,12) -> 34*
        g0(7,2) -> 8*
        g0(50,54) -> 19*
        g0(7,10) -> 36*,4,14
        e0() -> 7*
        d0() -> 5*
        c0() -> 3*
        g1(51,49) -> 53*,20,44
        g1(51,57) -> 20,53*,44
        g1(52,38) -> 41*
        g1(57,50) -> 34*,19
        g1(57,58) -> 19*
        g1(58,41) -> 19*
        g1(38,37) -> 19*
        g1(12,54) -> 19*
        g1(43,49) -> 44*
        g1(53,53) -> 19*
        g1(43,57) -> 44*
        g1(34,44) -> 19*
        g1(49,50) -> 34*,19
        g1(49,58) -> 34*,19
        g1(50,41) -> 19*
        g1(40,49) -> 41*
        g1(51,38) -> 44*
        g1(40,57) -> 41*
        g1(20,53) -> 19*
        g1(57,37) -> 19*
        g1(12,41) -> 19*
        g1(52,49) -> 54*,23,41
        g1(52,57) -> 23,54*,41
        g1(43,38) -> 44*
        g1(53,44) -> 19*
        g1(58,54) -> 19*
        g1(38,50) -> 19*
        g1(49,37) -> 19*
        g1(38,58) -> 19*
        g1(34,53) -> 19*
        g1(40,38) -> 41*
        g1(20,44) -> 19*
        g1(50,54) -> 19*
        f1(57) -> 48*
        f1(47) -> 51*,19,43
        f1(42) -> 43*
        f1(2) -> 47*,18,42
        f1(49) -> 48*
        f1(39) -> 40*
        f1(48) -> 52*,22,40
        f1(13) -> 48*,21,39
        14 -> 4*
        15 -> 10*
        16 -> 8*
        17 -> 18*
      problem:
       DPs:
        
       TRS:
        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()))
      Qed