YES

Problem:
 +(0(),y) -> y
 +(s(x),y) -> s(+(x,y))
 inc(x) -> s(x)
 +(x,y) -> +(y,x)
 inc(+(x,y)) -> +(inc(x),y)

Proof:
 AT confluence processor
  Complete TRS T' of input TRS:
  +(0(),y) -> y
  +(s(x),y) -> s(+(x,y))
  inc(x) -> s(x)
  inc(+(x,y)) -> +(inc(x),y)
  +(y,0()) -> y
  +(y,s(x)) -> s(+(y,x))
  +(x,y) -> +(y,x)
  
   T' = (P union S) with
  
   TRS P:+(x,y) -> +(y,x)
  
   TRS S:+(0(),y) -> y
         +(s(x),y) -> s(+(x,y))
         inc(x) -> s(x)
         inc(+(x,y)) -> +(inc(x),y)
         +(y,0()) -> y
         +(y,s(x)) -> s(+(y,x))
  
  S is linear and P is reversible.
  
   CP(S,S) = 
  inc(y) = +(inc(0()),y), 0() = 0(), s(x) = s(+(0(),x)), inc(s(+(x358,y))) = 
  +(inc(s(x358)),y), s(+(x360,0())) = s(x360), s(+(x362,s(x))) = s(+(s(x362),x)), 
  s(+(x,y)) = +(inc(x),y), +(inc(x365),x366) = s(+(x365,x366)), s(x) = 
  s(+(x,0())), inc(x) = +(inc(x),0()), s(+(0(),x371)) = s(x371), s(+(s(x),x373)) = 
  s(+(x,s(x373))), inc(s(+(x,x375))) = +(inc(x),s(x375))
  
   CP(S,P union P^-1) = 
  y = +(y,0()), x = +(x,0()), s(+(x396,y)) = +(y,s(x396)), s(+(x398,x)) = 
  +(x,s(x398)), x = +(0(),x), y = +(0(),y), s(+(x,x403)) = +(s(x403),x), 
  s(+(y,x405)) = +(s(x405),y)
  
   CP(P union P^-1,S) = 
  +(y,0()) = y, +(y,s(x)) = s(+(x,y)), inc(+(y,x)) = +(inc(x),y), +(0(),y) = 
  y, +(s(x),y) = s(+(y,x))
  
  
  We have to check termination of S:
  
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [+](x0, x1) = 4x0 + x1 + 1,
    
    [inc](x0) = 2x0,
    
    [0] = 0,
    
    [s](x0) = x0
   orientation:
    +(0(),y) = y + 1 >= y = y
    
    +(s(x),y) = 4x + y + 1 >= 4x + y + 1 = s(+(x,y))
    
    inc(x) = 2x >= x = s(x)
    
    inc(+(x,y)) = 8x + 2y + 2 >= 8x + y + 1 = +(inc(x),y)
    
    +(y,0()) = 4y + 1 >= y = y
    
    +(y,s(x)) = x + 4y + 1 >= x + 4y + 1 = s(+(y,x))
   problem:
    +(s(x),y) -> s(+(x,y))
    inc(x) -> s(x)
    +(y,s(x)) -> s(+(y,x))
   Matrix Interpretation Processor: dim=1
    
    interpretation:
     [+](x0, x1) = x0 + 2x1 + 7,
     
     [inc](x0) = 4x0 + 2,
     
     [s](x0) = x0 + 2
    orientation:
     +(s(x),y) = x + 2y + 9 >= x + 2y + 9 = s(+(x,y))
     
     inc(x) = 4x + 2 >= x + 2 = s(x)
     
     +(y,s(x)) = 2x + y + 11 >= 2x + y + 9 = s(+(y,x))
    problem:
     +(s(x),y) -> s(+(x,y))
     inc(x) -> s(x)
    Matrix Interpretation Processor: dim=1
     
     interpretation:
      [+](x0, x1) = x0 + x1,
      
      [inc](x0) = x0 + 1,
      
      [s](x0) = x0
     orientation:
      +(s(x),y) = x + y >= x + y = s(+(x,y))
      
      inc(x) = x + 1 >= x = s(x)
     problem:
      +(s(x),y) -> s(+(x,y))
     Matrix Interpretation Processor: dim=1
      
      interpretation:
       [+](x0, x1) = 4x0 + x1,
       
       [s](x0) = x0 + 5
      orientation:
       +(s(x),y) = 4x + y + 20 >= 4x + y + 5 = s(+(x,y))
      problem:
       
      Qed