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)
  Restore Modifier:
   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)
   SCC Processor:
    #sccs: 1
    #rules: 5
    #arcs: 25/25
    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)
    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)
     Matrix Interpretation Processor:
      dimension: 1
      interpretation:
       [+#](x0, x1) = x0 + 1,
       
       [f](x0) = 0,
       
       [+](x0, x1) = x0 + x1 + 1
      orientation:
       +#(+(x,y),z) = x + y + 2 >= y + 1 = +#(y,z)
       
       +#(+(x,y),z) = x + y + 2 >= x + 1 = +#(x,+(y,z))
       
       +(+(x,y),z) = x + y + z + 2 >= x + y + z + 2 = +(x,+(y,z))
       
       +(f(x),f(y)) = 1 >= 0 = f(+(x,y))
       
       +(f(x),+(f(y),z)) = z + 2 >= z + 1 = +(f(+(x,y)),z)
      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