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)
   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: 23/25
     DPs:
      +#(f(x),f(y)) -> +#(x,y)
      +#(f(x),+(f(y),z)) -> +#(f(+(x,y)),z)
      +#(f(x),+(f(y),z)) -> +#(x,y)
      +#(+(x,y),z) -> +#(x,+(y,z))
      +#(+(x,y),z) -> +#(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,
       
       [+](x0, x1) = x0 + x1 + 1
      orientation:
       +#(f(x),f(y)) = x + y >= x + y = +#(x,y)
       
       +#(f(x),+(f(y),z)) = x + y + z + 1 >= x + y + z + 1 = +#(f(+(x,y)),z)
       
       +#(f(x),+(f(y),z)) = x + y + z + 1 >= x + y = +#(x,y)
       
       +#(+(x,y),z) = x + y + z + 1 >= x + y + z + 1 = +#(x,+(y,z))
       
       +#(+(x,y),z) = x + y + z + 1 >= y + z = +#(y,z)
       
       +(+(x,y),z) = x + y + z + 2 >= x + y + z + 2 = +(x,+(y,z))
       
       +(f(x),f(y)) = x + y + 1 >= x + y + 1 = f(+(x,y))
       
       +(f(x),+(f(y),z)) = x + y + z + 2 >= x + y + z + 2 = +(f(+(x,y)),z)
      problem:
       DPs:
        +#(f(x),f(y)) -> +#(x,y)
        +#(f(x),+(f(y),z)) -> +#(f(+(x,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) = x1 + 1,
        
        [f](x0) = x0 + 1,
        
        [+](x0, x1) = x1
       orientation:
        +#(f(x),f(y)) = y + 2 >= y + 1 = +#(x,y)
        
        +#(f(x),+(f(y),z)) = z + 1 >= z + 1 = +#(f(+(x,y)),z)
        
        +#(+(x,y),z) = z + 1 >= z + 1 = +#(x,+(y,z))
        
        +(+(x,y),z) = z >= z = +(x,+(y,z))
        
        +(f(x),f(y)) = y + 1 >= y + 1 = f(+(x,y))
        
        +(f(x),+(f(y),z)) = z >= z = +(f(+(x,y)),z)
       problem:
        DPs:
         +#(f(x),+(f(y),z)) -> +#(f(+(x,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,
         
         [f](x0) = 0,
         
         [+](x0, x1) = x0 + 1
        orientation:
         +#(f(x),+(f(y),z)) = 0 >= 0 = +#(f(+(x,y)),z)
         
         +#(+(x,y),z) = x + 1 >= x = +#(x,+(y,z))
         
         +(+(x,y),z) = x + 2 >= x + 1 = +(x,+(y,z))
         
         +(f(x),f(y)) = 1 >= 0 = f(+(x,y))
         
         +(f(x),+(f(y),z)) = 1 >= 1 = +(f(+(x,y)),z)
        problem:
         DPs:
          +#(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) = x1,
          
          [f](x0) = 0,
          
          [+](x0, x1) = x0 + x1 + 1
         orientation:
          +#(f(x),+(f(y),z)) = z + 1 >= z = +#(f(+(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