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

Proof:
 Church Rosser Transformation Processor (critical pair closing system, Thm 2.11):
  +(0(),x62) -> x62
  +(x63,0()) -> x63
  +(x65,s(x64)) -> s(+(x65,x64))
  +(s(x67),x66) -> s(+(x67,x66))
  critical peaks: joinable
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [s](x0) = x0,
    
    [+](x0, x1) = x0 + 4x1 + 4,
    
    [0] = 2
   orientation:
    +(0(),x62) = 4x62 + 6 >= x62 = x62
    
    +(x63,0()) = x63 + 12 >= x63 = x63
    
    +(x65,s(x64)) = 4x64 + x65 + 4 >= 4x64 + x65 + 4 = s(+(x65,x64))
    
    +(s(x67),x66) = 4x66 + x67 + 4 >= 4x66 + x67 + 4 = s(+(x67,x66))
   problem:
    +(x65,s(x64)) -> s(+(x65,x64))
    +(s(x67),x66) -> s(+(x67,x66))
   Matrix Interpretation Processor: dim=1
    
    interpretation:
     [s](x0) = x0 + 1,
     
     [+](x0, x1) = 2x0 + x1 + 5
    orientation:
     +(x65,s(x64)) = x64 + 2x65 + 6 >= x64 + 2x65 + 6 = s(+(x65,x64))
     
     +(s(x67),x66) = x66 + 2x67 + 7 >= x66 + 2x67 + 6 = s(+(x67,x66))
    problem:
     +(x65,s(x64)) -> s(+(x65,x64))
    Matrix Interpretation Processor: dim=1
     
     interpretation:
      [s](x0) = x0 + 1,
      
      [+](x0, x1) = x0 + 2x1 + 5
     orientation:
      +(x65,s(x64)) = 2x64 + x65 + 7 >= 2x64 + x65 + 6 = s(+(x65,x64))
     problem:
      
     Qed