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:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [+](x0, x1) = x0 + x1 + 3,
   
   [i](x0) = 3x0 + 4,
   
   [0] = 5
  orientation:
   i(0()) = 19 >= 5 = 0()
   
   +(0(),y) = y + 8 >= y = y
   
   +(x,0()) = x + 8 >= x = x
   
   i(i(x)) = 9x + 16 >= x = x
   
   +(i(x),x) = 4x + 7 >= 5 = 0()
   
   +(x,i(x)) = 4x + 7 >= 5 = 0()
   
   i(+(x,y)) = 3x + 3y + 13 >= 3x + 3y + 11 = +(i(x),i(y))
   
   +(x,+(y,z)) = x + y + z + 6 >= x + y + z + 6 = +(+(x,y),z)
   
   +(+(x,i(y)),y) = x + 4y + 10 >= x = x
   
   +(+(x,y),i(y)) = x + 4y + 10 >= x = x
  problem:
   +(x,+(y,z)) -> +(+(x,y),z)
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [+](x0, x1) = x0 + 4x1 + 3
   orientation:
    +(x,+(y,z)) = x + 4y + 16z + 15 >= x + 4y + 4z + 6 = +(+(x,y),z)
   problem:
    
   Qed