YES

Problem:
 +(x,0()) -> x
 +(x,s(y)) -> s(+(x,y))
 +(0(),y) -> y
 +(s(x),y) -> s(+(x,y))
 *(k(),0()) -> 0()
 *(k(),s(y)) -> +(k(),*(k(),y))
 +(x,y) -> +(y,x)
 +(+(x,y),z) -> +(x,+(y,z))

Proof:
 AT confluence processor
  Complete TRS T' of input TRS:
  +(x,0()) -> x
  +(x,s(y)) -> s(+(x,y))
  +(0(),y) -> y
  +(s(x),y) -> s(+(x,y))
  *(k(),0()) -> 0()
  *(k(),s(y)) -> +(k(),*(k(),y))
  +(x,y) -> +(y,x)
  +(+(x,y),z) -> +(x,+(y,z))
  
   T' = (P union S) with
  
   TRS P:+(x,y) -> +(y,x)
         +(+(x,y),z) -> +(x,+(y,z))
  
   TRS S:+(x,0()) -> x
         +(x,s(y)) -> s(+(x,y))
         +(0(),y) -> y
         +(s(x),y) -> s(+(x,y))
         *(k(),0()) -> 0()
         *(k(),s(y)) -> +(k(),*(k(),y))
  
  S is left-linear and P is reversible.
  
   CP(S,S) = 
  0() = 0(), s(x) = s(+(x,0())), s(+(0(),x366)) = s(x366), s(+(s(x),x368)) = 
  s(+(x,s(x368))), s(y) = s(+(0(),y)), s(+(x371,0())) = s(x371), s(+(x373,s(y))) = 
  s(+(s(x373),y))
  
   CP(S,P union P^-1) = 
  x = +(0(),x), +(x,y) = +(x,+(y,0())), +(x,z) = +(x,+(0(),z)), y = +(0(),y), 
  +(x,y) = +(+(x,y),0()), s(+(x,x423)) = +(s(x423),x), s(+(+(x,y),x425)) = 
  +(x,+(y,s(x425))), +(s(+(x,x427)),z) = +(x,+(s(x427),z)), s(+(y,x429)) = 
  +(s(x429),y), +(x,s(+(y,x431))) = +(+(x,y),s(x431)), y = +(y,0()), 
  +(y,z) = +(0(),+(y,z)), x = +(x,0()), +(y,z) = +(+(0(),y),z), +(x,z) = 
  +(+(x,0()),z), s(+(x437,y)) = +(y,s(x437)), +(s(+(x439,y)),z) = +(s(x439),+(y,z)), 
  s(+(x441,x)) = +(x,s(x441)), s(+(x443,+(y,z))) = +(+(s(x443),y),z), 
  +(x,s(+(x445,z))) = +(+(x,s(x445)),z)
  
  
   PCP_in(P union P^-1,S) = 
  
  
  We have to check termination of S:
  
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [*](x0, x1) = 4x0 + 4x1,
    
    [+](x0, x1) = x0 + x1 + 5,
    
    [k] = 0,
    
    [0] = 0,
    
    [s](x0) = x0 + 2
   orientation:
    +(x,0()) = x + 5 >= x = x
    
    +(x,s(y)) = x + y + 7 >= x + y + 7 = s(+(x,y))
    
    +(0(),y) = y + 5 >= y = y
    
    +(s(x),y) = x + y + 7 >= x + y + 7 = s(+(x,y))
    
    *(k(),0()) = 0 >= 0 = 0()
    
    *(k(),s(y)) = 4y + 8 >= 4y + 5 = +(k(),*(k(),y))
   problem:
    +(x,s(y)) -> s(+(x,y))
    +(s(x),y) -> s(+(x,y))
    *(k(),0()) -> 0()
   Matrix Interpretation Processor: dim=1
    
    interpretation:
     [*](x0, x1) = 4x0 + 2x1 + 4,
     
     [+](x0, x1) = x0 + x1 + 4,
     
     [k] = 2,
     
     [0] = 2,
     
     [s](x0) = x0 + 1
    orientation:
     +(x,s(y)) = x + y + 5 >= x + y + 5 = s(+(x,y))
     
     +(s(x),y) = x + y + 5 >= x + y + 5 = s(+(x,y))
     
     *(k(),0()) = 16 >= 2 = 0()
    problem:
     +(x,s(y)) -> s(+(x,y))
     +(s(x),y) -> s(+(x,y))
    Matrix Interpretation Processor: dim=1
     
     interpretation:
      [+](x0, x1) = x0 + 4x1 + 5,
      
      [s](x0) = x0 + 1
     orientation:
      +(x,s(y)) = x + 4y + 9 >= x + 4y + 6 = s(+(x,y))
      
      +(s(x),y) = x + 4y + 6 >= x + 4y + 6 = s(+(x,y))
     problem:
      +(s(x),y) -> s(+(x,y))
     Matrix Interpretation Processor: dim=1
      
      interpretation:
       [+](x0, x1) = 6x0 + x1 + 2,
       
       [s](x0) = x0 + 3
      orientation:
       +(s(x),y) = 6x + y + 20 >= 6x + y + 5 = s(+(x,y))
      problem:
       
      Qed