YES

Problem:
 f(b(a(),z)) -> z
 b(y,b(a(),z)) -> b(f(c(y,y,a())),b(f(z),a()))
 f(f(f(c(z,x,a())))) -> b(f(x),z)

Proof:
 DP Processor:
  DPs:
   b#(y,b(a(),z)) -> f#(z)
   b#(y,b(a(),z)) -> b#(f(z),a())
   b#(y,b(a(),z)) -> f#(c(y,y,a()))
   b#(y,b(a(),z)) -> b#(f(c(y,y,a())),b(f(z),a()))
   f#(f(f(c(z,x,a())))) -> f#(x)
   f#(f(f(c(z,x,a())))) -> b#(f(x),z)
  TRS:
   f(b(a(),z)) -> z
   b(y,b(a(),z)) -> b(f(c(y,y,a())),b(f(z),a()))
   f(f(f(c(z,x,a())))) -> b(f(x),z)
  EDG Processor:
   DPs:
    b#(y,b(a(),z)) -> f#(z)
    b#(y,b(a(),z)) -> b#(f(z),a())
    b#(y,b(a(),z)) -> f#(c(y,y,a()))
    b#(y,b(a(),z)) -> b#(f(c(y,y,a())),b(f(z),a()))
    f#(f(f(c(z,x,a())))) -> f#(x)
    f#(f(f(c(z,x,a())))) -> b#(f(x),z)
   TRS:
    f(b(a(),z)) -> z
    b(y,b(a(),z)) -> b(f(c(y,y,a())),b(f(z),a()))
    f(f(f(c(z,x,a())))) -> b(f(x),z)
   graph:
    b#(y,b(a(),z)) -> b#(f(c(y,y,a())),b(f(z),a())) ->
    b#(y,b(a(),z)) -> f#(z)
    b#(y,b(a(),z)) -> b#(f(c(y,y,a())),b(f(z),a())) ->
    b#(y,b(a(),z)) -> b#(f(z),a())
    b#(y,b(a(),z)) -> b#(f(c(y,y,a())),b(f(z),a())) ->
    b#(y,b(a(),z)) -> f#(c(y,y,a()))
    b#(y,b(a(),z)) -> b#(f(c(y,y,a())),b(f(z),a())) ->
    b#(y,b(a(),z)) -> b#(f(c(y,y,a())),b(f(z),a()))
    b#(y,b(a(),z)) -> f#(z) -> f#(f(f(c(z,x,a())))) -> f#(x)
    b#(y,b(a(),z)) -> f#(z) -> f#(f(f(c(z,x,a())))) -> b#(f(x),z)
    f#(f(f(c(z,x,a())))) -> b#(f(x),z) -> b#(y,b(a(),z)) -> f#(z)
    f#(f(f(c(z,x,a())))) -> b#(f(x),z) ->
    b#(y,b(a(),z)) -> b#(f(z),a())
    f#(f(f(c(z,x,a())))) -> b#(f(x),z) ->
    b#(y,b(a(),z)) -> f#(c(y,y,a()))
    f#(f(f(c(z,x,a())))) -> b#(f(x),z) ->
    b#(y,b(a(),z)) -> b#(f(c(y,y,a())),b(f(z),a()))
    f#(f(f(c(z,x,a())))) -> f#(x) -> f#(f(f(c(z,x,a())))) -> f#(x)
    f#(f(f(c(z,x,a())))) -> f#(x) -> f#(f(f(c(z,x,a())))) -> b#(f(x),z)
   SCC Processor:
    #sccs: 1
    #rules: 4
    #arcs: 12/36
    DPs:
     b#(y,b(a(),z)) -> b#(f(c(y,y,a())),b(f(z),a()))
     b#(y,b(a(),z)) -> f#(z)
     f#(f(f(c(z,x,a())))) -> b#(f(x),z)
     f#(f(f(c(z,x,a())))) -> f#(x)
    TRS:
     f(b(a(),z)) -> z
     b(y,b(a(),z)) -> b(f(c(y,y,a())),b(f(z),a()))
     f(f(f(c(z,x,a())))) -> b(f(x),z)
    Matrix Interpretation Processor:
     dimension: 1
     interpretation:
      [b#](x0, x1) = x1 + 1,
      
      [f#](x0) = x0 + 1,
      
      [c](x0, x1, x2) = x0 + x1 + 1,
      
      [f](x0) = x0,
      
      [b](x0, x1) = x1,
      
      [a] = 0
     orientation:
      b#(y,b(a(),z)) = z + 1 >= 1 = b#(f(c(y,y,a())),b(f(z),a()))
      
      b#(y,b(a(),z)) = z + 1 >= z + 1 = f#(z)
      
      f#(f(f(c(z,x,a())))) = x + z + 2 >= z + 1 = b#(f(x),z)
      
      f#(f(f(c(z,x,a())))) = x + z + 2 >= x + 1 = f#(x)
      
      f(b(a(),z)) = z >= z = z
      
      b(y,b(a(),z)) = z >= 0 = b(f(c(y,y,a())),b(f(z),a()))
      
      f(f(f(c(z,x,a())))) = x + z + 1 >= z = b(f(x),z)
     problem:
      DPs:
       b#(y,b(a(),z)) -> b#(f(c(y,y,a())),b(f(z),a()))
       b#(y,b(a(),z)) -> f#(z)
      TRS:
       f(b(a(),z)) -> z
       b(y,b(a(),z)) -> b(f(c(y,y,a())),b(f(z),a()))
       f(f(f(c(z,x,a())))) -> b(f(x),z)
     Matrix Interpretation Processor:
      dimension: 1
      interpretation:
       [b#](x0, x1) = 1,
       
       [f#](x0) = 0,
       
       [c](x0, x1, x2) = x0,
       
       [f](x0) = x0,
       
       [b](x0, x1) = x1,
       
       [a] = 0
      orientation:
       b#(y,b(a(),z)) = 1 >= 1 = b#(f(c(y,y,a())),b(f(z),a()))
       
       b#(y,b(a(),z)) = 1 >= 0 = f#(z)
       
       f(b(a(),z)) = z >= z = z
       
       b(y,b(a(),z)) = z >= 0 = b(f(c(y,y,a())),b(f(z),a()))
       
       f(f(f(c(z,x,a())))) = z >= z = b(f(x),z)
      problem:
       DPs:
        b#(y,b(a(),z)) -> b#(f(c(y,y,a())),b(f(z),a()))
       TRS:
        f(b(a(),z)) -> z
        b(y,b(a(),z)) -> b(f(c(y,y,a())),b(f(z),a()))
        f(f(f(c(z,x,a())))) -> b(f(x),z)
      Bounds Processor:
       bound: 3
       enrichment: roof
       automaton:
        final states: {7}
        transitions:
         b{#,2}(26,24) -> 7*
         c0(6,6,6) -> 6*
         b3(28,27) -> 29*
         b3(31,29) -> 6,14,19
         b1(14,6) -> 6*
         b1(17,15) -> 6*
         b1(14,13) -> 15*
         f3(30) -> 31*
         f3(18) -> 28*
         f1(16) -> 17*
         f1(6) -> 14*
         c3(22,22,27) -> 30*
         c1(6,6,13) -> 16*
         a3() -> 27*
         a1() -> 13*
         b{#,1}(17,15) -> 7*
         b2(22,20) -> 6*
         b2(19,18) -> 20*
         b2(26,24) -> 6,14
         b2(23,18) -> 24*
         b{#,0}(6,6) -> 7*
         f2(25) -> 26*
         f2(21) -> 22*
         f2(6) -> 19*
         f2(13) -> 23*
         b0(6,6) -> 6*
         c2(17,17,18) -> 25*
         c2(14,14,18) -> 21*
         a0() -> 6*
         a2() -> 18*
         f0(6) -> 6*
         6 -> 19,14
       problem:
        DPs:
         
        TRS:
         f(b(a(),z)) -> z
         b(y,b(a(),z)) -> b(f(c(y,y,a())),b(f(z),a()))
         f(f(f(c(z,x,a())))) -> b(f(x),z)
       Qed