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)
   Matrix Interpretation Processor:
    dimension: 1
    interpretation:
     [+#](x0, x1) = x0 + x1,
     
     [f](x0) = x0 + 1,
     
     [+](x0, x1) = x0 + x1
    orientation:
     +#(+(x,y),z) = x + y + z >= y + z = +#(y,z)
     
     +#(+(x,y),z) = x + y + z >= x + y + z = +#(x,+(y,z))
     
     +#(f(x),f(y)) = x + y + 2 >= x + y = +#(x,y)
     
     +#(f(x),+(f(y),z)) = x + y + z + 2 >= x + y = +#(x,y)
     
     +#(f(x),+(f(y),z)) = x + y + z + 2 >= x + y + z + 1 = +#(f(+(x,y)),z)
     
     +(+(x,y),z) = x + y + z >= x + y + z = +(x,+(y,z))
     
     +(f(x),f(y)) = x + y + 2 >= x + y + 1 = f(+(x,y))
     
     +(f(x),+(f(y),z)) = x + y + z + 2 >= x + y + z + 1 = +(f(+(x,y)),z)
    problem:
     DPs:
      +#(+(x,y),z) -> +#(y,z)
      +#(+(x,y),z) -> +#(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)
    Subterm Criterion Processor:
     simple projection:
      pi(+#) = 0
     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