YES

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

Proof:
 DP Processor:
  DPs:
   b#(b(y,z),c(a(),a(),a())) -> c#(z,y,z)
   b#(b(y,z),c(a(),a(),a())) -> f#(c(z,y,z))
   c#(y,x,f(z)) -> b#(z,x)
   c#(y,x,f(z)) -> f#(b(z,x))
   c#(y,x,f(z)) -> b#(f(b(z,x)),z)
  TRS:
   b(b(y,z),c(a(),a(),a())) -> f(c(z,y,z))
   f(b(b(a(),z),c(a(),x,y))) -> z
   c(y,x,f(z)) -> b(f(b(z,x)),z)
  TDG Processor:
   DPs:
    b#(b(y,z),c(a(),a(),a())) -> c#(z,y,z)
    b#(b(y,z),c(a(),a(),a())) -> f#(c(z,y,z))
    c#(y,x,f(z)) -> b#(z,x)
    c#(y,x,f(z)) -> f#(b(z,x))
    c#(y,x,f(z)) -> b#(f(b(z,x)),z)
   TRS:
    b(b(y,z),c(a(),a(),a())) -> f(c(z,y,z))
    f(b(b(a(),z),c(a(),x,y))) -> z
    c(y,x,f(z)) -> b(f(b(z,x)),z)
   graph:
    c#(y,x,f(z)) -> b#(f(b(z,x)),z) ->
    b#(b(y,z),c(a(),a(),a())) -> f#(c(z,y,z))
    c#(y,x,f(z)) -> b#(f(b(z,x)),z) ->
    b#(b(y,z),c(a(),a(),a())) -> c#(z,y,z)
    c#(y,x,f(z)) -> b#(z,x) -> b#(b(y,z),c(a(),a(),a())) -> f#(c(z,y,z))
    c#(y,x,f(z)) -> b#(z,x) ->
    b#(b(y,z),c(a(),a(),a())) -> c#(z,y,z)
    b#(b(y,z),c(a(),a(),a())) -> c#(z,y,z) ->
    c#(y,x,f(z)) -> b#(f(b(z,x)),z)
    b#(b(y,z),c(a(),a(),a())) -> c#(z,y,z) ->
    c#(y,x,f(z)) -> f#(b(z,x))
    b#(b(y,z),c(a(),a(),a())) -> c#(z,y,z) -> c#(y,x,f(z)) -> b#(z,x)
   SCC Processor:
    #sccs: 1
    #rules: 3
    #arcs: 7/25
    DPs:
     c#(y,x,f(z)) -> b#(f(b(z,x)),z)
     b#(b(y,z),c(a(),a(),a())) -> c#(z,y,z)
     c#(y,x,f(z)) -> b#(z,x)
    TRS:
     b(b(y,z),c(a(),a(),a())) -> f(c(z,y,z))
     f(b(b(a(),z),c(a(),x,y))) -> z
     c(y,x,f(z)) -> b(f(b(z,x)),z)
    Arctic Interpretation Processor:
     dimension: 1
     usable rules:
      b(b(y,z),c(a(),a(),a())) -> f(c(z,y,z))
      f(b(b(a(),z),c(a(),x,y))) -> z
      c(y,x,f(z)) -> b(f(b(z,x)),z)
     interpretation:
      [b#](x0, x1) = x0 + x1,
      
      [a] = 0,
      
      [f](x0) = x0 + 0,
      
      [c#](x0, x1, x2) = x0 + 2x1 + 2x2,
      
      [b](x0, x1) = 2x0 + 2x1 + 2,
      
      [c](x0, x1, x2) = 4x1 + 4x2
     orientation:
      c#(y,x,f(z)) = 2x + y + 2z + 2 >= 2x + 2z + 2 = b#(f(b(z,x)),z)
      
      b#(b(y,z),c(a(),a(),a())) = 2y + 2z + 4 >= 2y + 2z = c#(z,y,z)
      
      c#(y,x,f(z)) = 2x + y + 2z + 2 >= x + z = b#(z,x)
      
      b(b(y,z),c(a(),a(),a())) = 4y + 4z + 6 >= 4y + 4z + 0 = f(c(z,y,z))
      
      f(b(b(a(),z),c(a(),x,y))) = 6x + 6y + 4z + 4 >= z = z
      
      c(y,x,f(z)) = 4x + 4z + 4 >= 4x + 4z + 4 = b(f(b(z,x)),z)
     problem:
      DPs:
       c#(y,x,f(z)) -> b#(f(b(z,x)),z)
       b#(b(y,z),c(a(),a(),a())) -> c#(z,y,z)
      TRS:
       b(b(y,z),c(a(),a(),a())) -> f(c(z,y,z))
       f(b(b(a(),z),c(a(),x,y))) -> z
       c(y,x,f(z)) -> b(f(b(z,x)),z)
     Restore Modifier:
      DPs:
       c#(y,x,f(z)) -> b#(f(b(z,x)),z)
       b#(b(y,z),c(a(),a(),a())) -> c#(z,y,z)
      TRS:
       b(b(y,z),c(a(),a(),a())) -> f(c(z,y,z))
       f(b(b(a(),z),c(a(),x,y))) -> z
       c(y,x,f(z)) -> b(f(b(z,x)),z)
      Arctic Interpretation Processor:
       dimension: 1
       usable rules:
        b(b(y,z),c(a(),a(),a())) -> f(c(z,y,z))
        f(b(b(a(),z),c(a(),x,y))) -> z
        c(y,x,f(z)) -> b(f(b(z,x)),z)
       interpretation:
        [b#](x0, x1) = 1x0 + x1 + 2,
        
        [a] = 0,
        
        [f](x0) = -2x0 + 0,
        
        [c#](x0, x1, x2) = x0 + 1x1 + 2x2 + 3,
        
        [b](x0, x1) = 1x0 + 2x1 + 2,
        
        [c](x0, x1, x2) = 5x0 + 1x1 + 4x2 + 0
       orientation:
        c#(y,x,f(z)) = 1x + y + z + 3 >= 1x + z + 2 = b#(f(b(z,x)),z)
        
        b#(b(y,z),c(a(),a(),a())) = 2y + 3z + 5 >= 1y + 2z + 3 = c#(z,y,z)
        
        b(b(y,z),c(a(),a(),a())) = 2y + 3z + 7 >= -1y + 3z + 0 = f(c(z,y,z))
        
        f(b(b(a(),z),c(a(),x,y))) = 1x + 4y + 1z + 5 >= z = z
        
        c(y,x,f(z)) = 1x + 5y + 2z + 4 >= 1x + 2z + 2 = b(f(b(z,x)),z)
       problem:
        DPs:
         c#(y,x,f(z)) -> b#(f(b(z,x)),z)
        TRS:
         b(b(y,z),c(a(),a(),a())) -> f(c(z,y,z))
         f(b(b(a(),z),c(a(),x,y))) -> z
         c(y,x,f(z)) -> b(f(b(z,x)),z)
       Restore Modifier:
        DPs:
         c#(y,x,f(z)) -> b#(f(b(z,x)),z)
        TRS:
         b(b(y,z),c(a(),a(),a())) -> f(c(z,y,z))
         f(b(b(a(),z),c(a(),x,y))) -> z
         c(y,x,f(z)) -> b(f(b(z,x)),z)
        SCC Processor:
         #sccs: 0
         #rules: 0
         #arcs: 4/1