YES

Problem:
 i(0()) -> 0()
 +(0(),y) -> y
 +(x,0()) -> x
 i(i(x)) -> x
 +(i(x),x) -> 0()
 +(x,i(x)) -> 0()
 i(+(x,y)) -> +(i(x),i(y))
 +(x,+(y,z)) -> +(+(x,y),z)
 +(+(x,i(y)),y) -> x
 +(+(x,y),i(y)) -> x

Proof:
 DP Processor:
  DPs:
   i#(+(x,y)) -> i#(y)
   i#(+(x,y)) -> i#(x)
   i#(+(x,y)) -> +#(i(x),i(y))
   +#(x,+(y,z)) -> +#(x,y)
   +#(x,+(y,z)) -> +#(+(x,y),z)
  TRS:
   i(0()) -> 0()
   +(0(),y) -> y
   +(x,0()) -> x
   i(i(x)) -> x
   +(i(x),x) -> 0()
   +(x,i(x)) -> 0()
   i(+(x,y)) -> +(i(x),i(y))
   +(x,+(y,z)) -> +(+(x,y),z)
   +(+(x,i(y)),y) -> x
   +(+(x,y),i(y)) -> x
  EDG Processor:
   DPs:
    i#(+(x,y)) -> i#(y)
    i#(+(x,y)) -> i#(x)
    i#(+(x,y)) -> +#(i(x),i(y))
    +#(x,+(y,z)) -> +#(x,y)
    +#(x,+(y,z)) -> +#(+(x,y),z)
   TRS:
    i(0()) -> 0()
    +(0(),y) -> y
    +(x,0()) -> x
    i(i(x)) -> x
    +(i(x),x) -> 0()
    +(x,i(x)) -> 0()
    i(+(x,y)) -> +(i(x),i(y))
    +(x,+(y,z)) -> +(+(x,y),z)
    +(+(x,i(y)),y) -> x
    +(+(x,y),i(y)) -> x
   graph:
    +#(x,+(y,z)) -> +#(+(x,y),z) -> +#(x,+(y,z)) -> +#(x,y)
    +#(x,+(y,z)) -> +#(+(x,y),z) -> +#(x,+(y,z)) -> +#(+(x,y),z)
    +#(x,+(y,z)) -> +#(x,y) -> +#(x,+(y,z)) -> +#(x,y)
    +#(x,+(y,z)) -> +#(x,y) -> +#(x,+(y,z)) -> +#(+(x,y),z)
    i#(+(x,y)) -> +#(i(x),i(y)) -> +#(x,+(y,z)) -> +#(x,y)
    i#(+(x,y)) -> +#(i(x),i(y)) -> +#(x,+(y,z)) -> +#(+(x,y),z)
    i#(+(x,y)) -> i#(x) -> i#(+(x,y)) -> i#(y)
    i#(+(x,y)) -> i#(x) -> i#(+(x,y)) -> i#(x)
    i#(+(x,y)) -> i#(x) -> i#(+(x,y)) -> +#(i(x),i(y))
    i#(+(x,y)) -> i#(y) -> i#(+(x,y)) -> i#(y)
    i#(+(x,y)) -> i#(y) -> i#(+(x,y)) -> i#(x)
    i#(+(x,y)) -> i#(y) -> i#(+(x,y)) -> +#(i(x),i(y))
   Restore Modifier:
    DPs:
     i#(+(x,y)) -> i#(y)
     i#(+(x,y)) -> i#(x)
     i#(+(x,y)) -> +#(i(x),i(y))
     +#(x,+(y,z)) -> +#(x,y)
     +#(x,+(y,z)) -> +#(+(x,y),z)
    TRS:
     i(0()) -> 0()
     +(0(),y) -> y
     +(x,0()) -> x
     i(i(x)) -> x
     +(i(x),x) -> 0()
     +(x,i(x)) -> 0()
     i(+(x,y)) -> +(i(x),i(y))
     +(x,+(y,z)) -> +(+(x,y),z)
     +(+(x,i(y)),y) -> x
     +(+(x,y),i(y)) -> x
    SCC Processor:
     #sccs: 2
     #rules: 4
     #arcs: 12/25
     DPs:
      i#(+(x,y)) -> i#(x)
      i#(+(x,y)) -> i#(y)
     TRS:
      i(0()) -> 0()
      +(0(),y) -> y
      +(x,0()) -> x
      i(i(x)) -> x
      +(i(x),x) -> 0()
      +(x,i(x)) -> 0()
      i(+(x,y)) -> +(i(x),i(y))
      +(x,+(y,z)) -> +(+(x,y),z)
      +(+(x,i(y)),y) -> x
      +(+(x,y),i(y)) -> x
     Matrix Interpretation Processor:
      dimension: 1
      interpretation:
       [i#](x0) = x0 + 1,
       
       [+](x0, x1) = x0 + x1 + 1,
       
       [i](x0) = x0,
       
       [0] = 1
      orientation:
       i#(+(x,y)) = x + y + 2 >= x + 1 = i#(x)
       
       i#(+(x,y)) = x + y + 2 >= y + 1 = i#(y)
       
       i(0()) = 1 >= 1 = 0()
       
       +(0(),y) = y + 2 >= y = y
       
       +(x,0()) = x + 2 >= x = x
       
       i(i(x)) = x >= x = x
       
       +(i(x),x) = 2x + 1 >= 1 = 0()
       
       +(x,i(x)) = 2x + 1 >= 1 = 0()
       
       i(+(x,y)) = x + y + 1 >= x + y + 1 = +(i(x),i(y))
       
       +(x,+(y,z)) = x + y + z + 2 >= x + y + z + 2 = +(+(x,y),z)
       
       +(+(x,i(y)),y) = x + 2y + 2 >= x = x
       
       +(+(x,y),i(y)) = x + 2y + 2 >= x = x
      problem:
       DPs:
        
       TRS:
        i(0()) -> 0()
        +(0(),y) -> y
        +(x,0()) -> x
        i(i(x)) -> x
        +(i(x),x) -> 0()
        +(x,i(x)) -> 0()
        i(+(x,y)) -> +(i(x),i(y))
        +(x,+(y,z)) -> +(+(x,y),z)
        +(+(x,i(y)),y) -> x
        +(+(x,y),i(y)) -> x
      Qed
     
     DPs:
      +#(x,+(y,z)) -> +#(+(x,y),z)
      +#(x,+(y,z)) -> +#(x,y)
     TRS:
      i(0()) -> 0()
      +(0(),y) -> y
      +(x,0()) -> x
      i(i(x)) -> x
      +(i(x),x) -> 0()
      +(x,i(x)) -> 0()
      i(+(x,y)) -> +(i(x),i(y))
      +(x,+(y,z)) -> +(+(x,y),z)
      +(+(x,i(y)),y) -> x
      +(+(x,y),i(y)) -> x
     Matrix Interpretation Processor:
      dimension: 1
      interpretation:
       [+#](x0, x1) = x1 + 1,
       
       [+](x0, x1) = x0 + x1 + 1,
       
       [i](x0) = x0,
       
       [0] = 1
      orientation:
       +#(x,+(y,z)) = y + z + 2 >= z + 1 = +#(+(x,y),z)
       
       +#(x,+(y,z)) = y + z + 2 >= y + 1 = +#(x,y)
       
       i(0()) = 1 >= 1 = 0()
       
       +(0(),y) = y + 2 >= y = y
       
       +(x,0()) = x + 2 >= x = x
       
       i(i(x)) = x >= x = x
       
       +(i(x),x) = 2x + 1 >= 1 = 0()
       
       +(x,i(x)) = 2x + 1 >= 1 = 0()
       
       i(+(x,y)) = x + y + 1 >= x + y + 1 = +(i(x),i(y))
       
       +(x,+(y,z)) = x + y + z + 2 >= x + y + z + 2 = +(+(x,y),z)
       
       +(+(x,i(y)),y) = x + 2y + 2 >= x = x
       
       +(+(x,y),i(y)) = x + 2y + 2 >= x = x
      problem:
       DPs:
        
       TRS:
        i(0()) -> 0()
        +(0(),y) -> y
        +(x,0()) -> x
        i(i(x)) -> x
        +(i(x),x) -> 0()
        +(x,i(x)) -> 0()
        i(+(x,y)) -> +(i(x),i(y))
        +(x,+(y,z)) -> +(+(x,y),z)
        +(+(x,i(y)),y) -> x
        +(+(x,y),i(y)) -> x
      Qed