YES

Problem:
 f(f(x,y,z),u,f(x,y,v)) -> f(x,y,f(z,u,v))
 f(x,y,y) -> y
 f(x,y,g(y)) -> x
 f(x,x,y) -> x
 f(g(x),x,y) -> y

Proof:
 DP Processor:
  DPs:
   f#(f(x,y,z),u,f(x,y,v)) -> f#(z,u,v)
   f#(f(x,y,z),u,f(x,y,v)) -> f#(x,y,f(z,u,v))
  TRS:
   f(f(x,y,z),u,f(x,y,v)) -> f(x,y,f(z,u,v))
   f(x,y,y) -> y
   f(x,y,g(y)) -> x
   f(x,x,y) -> x
   f(g(x),x,y) -> y
  Restore Modifier:
   DPs:
    f#(f(x,y,z),u,f(x,y,v)) -> f#(z,u,v)
    f#(f(x,y,z),u,f(x,y,v)) -> f#(x,y,f(z,u,v))
   TRS:
    f(f(x,y,z),u,f(x,y,v)) -> f(x,y,f(z,u,v))
    f(x,y,y) -> y
    f(x,y,g(y)) -> x
    f(x,x,y) -> x
    f(g(x),x,y) -> y
   SCC Processor:
    #sccs: 1
    #rules: 2
    #arcs: 4/4
    DPs:
     f#(f(x,y,z),u,f(x,y,v)) -> f#(z,u,v)
     f#(f(x,y,z),u,f(x,y,v)) -> f#(x,y,f(z,u,v))
    TRS:
     f(f(x,y,z),u,f(x,y,v)) -> f(x,y,f(z,u,v))
     f(x,y,y) -> y
     f(x,y,g(y)) -> x
     f(x,x,y) -> x
     f(g(x),x,y) -> y
    Matrix Interpretation Processor:
     dimension: 1
     interpretation:
      [f#](x0, x1, x2) = x0 + 1,
      
      [g](x0) = 0,
      
      [f](x0, x1, x2) = x0 + x2 + 1
     orientation:
      f#(f(x,y,z),u,f(x,y,v)) = x + z + 2 >= z + 1 = f#(z,u,v)
      
      f#(f(x,y,z),u,f(x,y,v)) = x + z + 2 >= x + 1 = f#(x,y,f(z,u,v))
      
      f(f(x,y,z),u,f(x,y,v)) = v + 2x + z + 3 >= v + x + z + 2 = f(x,y,f(z,u,v))
      
      f(x,y,y) = x + y + 1 >= y = y
      
      f(x,y,g(y)) = x + 1 >= x = x
      
      f(x,x,y) = x + y + 1 >= x = x
      
      f(g(x),x,y) = y + 1 >= y = y
     problem:
      DPs:
       
      TRS:
       f(f(x,y,z),u,f(x,y,v)) -> f(x,y,f(z,u,v))
       f(x,y,y) -> y
       f(x,y,g(y)) -> x
       f(x,x,y) -> x
       f(g(x),x,y) -> y
     Qed