YES

Problem:
 +(+(x,y),z) -> +(x,+(y,z))
 +(f(x),f(y)) -> f(+(x,y))
 +(f(x),+(f(y),z)) -> +(f(+(x,y)),z)

Proof:
 DP Processor:
  DPs:
   +#(+(x,y),z) -> +#(y,z)
   +#(+(x,y),z) -> +#(x,+(y,z))
   +#(f(x),f(y)) -> +#(x,y)
   +#(f(x),+(f(y),z)) -> +#(x,y)
   +#(f(x),+(f(y),z)) -> +#(f(+(x,y)),z)
  TRS:
   +(+(x,y),z) -> +(x,+(y,z))
   +(f(x),f(y)) -> f(+(x,y))
   +(f(x),+(f(y),z)) -> +(f(+(x,y)),z)
  EDG Processor:
   DPs:
    +#(+(x,y),z) -> +#(y,z)
    +#(+(x,y),z) -> +#(x,+(y,z))
    +#(f(x),f(y)) -> +#(x,y)
    +#(f(x),+(f(y),z)) -> +#(x,y)
    +#(f(x),+(f(y),z)) -> +#(f(+(x,y)),z)
   TRS:
    +(+(x,y),z) -> +(x,+(y,z))
    +(f(x),f(y)) -> f(+(x,y))
    +(f(x),+(f(y),z)) -> +(f(+(x,y)),z)
   graph:
    +#(f(x),f(y)) -> +#(x,y) -> +#(+(x,y),z) -> +#(y,z)
    +#(f(x),f(y)) -> +#(x,y) -> +#(+(x,y),z) -> +#(x,+(y,z))
    +#(f(x),f(y)) -> +#(x,y) -> +#(f(x),f(y)) -> +#(x,y)
    +#(f(x),f(y)) -> +#(x,y) -> +#(f(x),+(f(y),z)) -> +#(x,y)
    +#(f(x),f(y)) -> +#(x,y) ->
    +#(f(x),+(f(y),z)) -> +#(f(+(x,y)),z)
    +#(f(x),+(f(y),z)) -> +#(f(+(x,y)),z) ->
    +#(f(x),f(y)) -> +#(x,y)
    +#(f(x),+(f(y),z)) -> +#(f(+(x,y)),z) ->
    +#(f(x),+(f(y),z)) -> +#(x,y)
    +#(f(x),+(f(y),z)) -> +#(f(+(x,y)),z) ->
    +#(f(x),+(f(y),z)) -> +#(f(+(x,y)),z)
    +#(f(x),+(f(y),z)) -> +#(x,y) -> +#(+(x,y),z) -> +#(y,z)
    +#(f(x),+(f(y),z)) -> +#(x,y) -> +#(+(x,y),z) -> +#(x,+(y,z))
    +#(f(x),+(f(y),z)) -> +#(x,y) -> +#(f(x),f(y)) -> +#(x,y)
    +#(f(x),+(f(y),z)) -> +#(x,y) -> +#(f(x),+(f(y),z)) -> +#(x,y)
    +#(f(x),+(f(y),z)) -> +#(x,y) -> +#(f(x),+(f(y),z)) -> +#(f(+(x,y)),z)
    +#(+(x,y),z) -> +#(y,z) -> +#(+(x,y),z) -> +#(y,z)
    +#(+(x,y),z) -> +#(y,z) -> +#(+(x,y),z) -> +#(x,+(y,z))
    +#(+(x,y),z) -> +#(y,z) -> +#(f(x),f(y)) -> +#(x,y)
    +#(+(x,y),z) -> +#(y,z) -> +#(f(x),+(f(y),z)) -> +#(x,y)
    +#(+(x,y),z) -> +#(y,z) -> +#(f(x),+(f(y),z)) -> +#(f(+(x,y)),z)
    +#(+(x,y),z) -> +#(x,+(y,z)) -> +#(+(x,y),z) -> +#(y,z)
    +#(+(x,y),z) -> +#(x,+(y,z)) -> +#(+(x,y),z) -> +#(x,+(y,z))
    +#(+(x,y),z) -> +#(x,+(y,z)) -> +#(f(x),f(y)) -> +#(x,y)
    +#(+(x,y),z) -> +#(x,+(y,z)) -> +#(f(x),+(f(y),z)) -> +#(x,y)
    +#(+(x,y),z) -> +#(x,+(y,z)) -> +#(f(x),+(f(y),z)) -> +#(f(+(x,y)),z)
   KBO Processor:
    argument filtering:
     pi(+) = [0,1]
     pi(f) = [0]
     pi(+#) = [0,1]
    weight function:
     w0 = 1
     w(+#) = w(f) = w(+) = 1
    precedence:
     +# ~ f ~ +
    problem:
     DPs:
      
     TRS:
      +(+(x,y),z) -> +(x,+(y,z))
      +(f(x),f(y)) -> f(+(x,y))
      +(f(x),+(f(y),z)) -> +(f(+(x,y)),z)
    Qed