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
  Matrix Interpretation Processor: dim=1
   
   usable rules:
    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
   interpretation:
    [+#](x0, x1) = x1 + 4,
    
    [i#](x0) = x0 + 6,
    
    [+](x0, x1) = x0 + 5x1 + 1,
    
    [i](x0) = 4x0,
    
    [0] = 0
   orientation:
    i#(+(x,y)) = x + 5y + 7 >= y + 6 = i#(y)
    
    i#(+(x,y)) = x + 5y + 7 >= x + 6 = i#(x)
    
    i#(+(x,y)) = x + 5y + 7 >= 4y + 4 = +#(i(x),i(y))
    
    +#(x,+(y,z)) = y + 5z + 5 >= y + 4 = +#(x,y)
    
    +#(x,+(y,z)) = y + 5z + 5 >= z + 4 = +#(+(x,y),z)
    
    i(0()) = 0 >= 0 = 0()
    
    +(0(),y) = 5y + 1 >= y = y
    
    +(x,0()) = x + 1 >= x = x
    
    i(i(x)) = 16x >= x = x
    
    +(i(x),x) = 9x + 1 >= 0 = 0()
    
    +(x,i(x)) = 21x + 1 >= 0 = 0()
    
    i(+(x,y)) = 4x + 20y + 4 >= 4x + 20y + 1 = +(i(x),i(y))
    
    +(x,+(y,z)) = x + 5y + 25z + 6 >= x + 5y + 5z + 2 = +(+(x,y),z)
    
    +(+(x,i(y)),y) = x + 25y + 2 >= x = x
    
    +(+(x,y),i(y)) = x + 25y + 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