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
  TDG 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),z)
    +#(x,+(y,z)) -> +#(+(x,y),z) -> +#(x,+(y,z)) -> +#(x,y)
    +#(x,+(y,z)) -> +#(x,y) -> +#(x,+(y,z)) -> +#(+(x,y),z)
    +#(x,+(y,z)) -> +#(x,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(y)) -> +#(x,+(y,z)) -> +#(x,y)
    i#(+(x,y)) -> i#(y) -> i#(+(x,y)) -> +#(i(x),i(y))
    i#(+(x,y)) -> i#(y) -> i#(+(x,y)) -> i#(x)
    i#(+(x,y)) -> i#(y) -> i#(+(x,y)) -> i#(y)
    i#(+(x,y)) -> i#(x) -> i#(+(x,y)) -> +#(i(x),i(y))
    i#(+(x,y)) -> i#(x) -> i#(+(x,y)) -> i#(x)
    i#(+(x,y)) -> i#(x) -> i#(+(x,y)) -> i#(y)
   SCC Processor:
    #sccs: 2
    #rules: 4
    #arcs: 12/25
    DPs:
     i#(+(x,y)) -> i#(y)
     i#(+(x,y)) -> i#(x)
    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
    Subterm Criterion Processor:
     simple projection:
      pi(i#) = 0
     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
    Subterm Criterion Processor:
     simple projection:
      pi(+#) = 1
     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