YES

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

Proof:
 Church Rosser Transformation Processor (critical pair closing system, Thm 2.11):
  +(x201,p(x200)) -> p(+(x201,x200))
  s(p(x204)) -> x204
  -(x206,p(x205)) -> s(-(x206,x205))
  p(s(x209)) -> x209
  +(x211,s(x210)) -> s(+(x211,x210))
  -(x216,s(x215)) -> p(-(x216,x215))
  critical peaks: joinable
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [-](x0, x1) = 4x0 + 2x1 + 2,
    
    [s](x0) = x0 + 2,
    
    [+](x0, x1) = x0 + x1 + 3,
    
    [p](x0) = x0 + 1
   orientation:
    +(x201,p(x200)) = x200 + x201 + 4 >= x200 + x201 + 4 = p(+(x201,x200))
    
    s(p(x204)) = x204 + 3 >= x204 = x204
    
    -(x206,p(x205)) = 2x205 + 4x206 + 4 >= 2x205 + 4x206 + 4 = s(-(x206,x205))
    
    p(s(x209)) = x209 + 3 >= x209 = x209
    
    +(x211,s(x210)) = x210 + x211 + 5 >= x210 + x211 + 5 = s(+(x211,x210))
    
    -(x216,s(x215)) = 2x215 + 4x216 + 6 >= 2x215 + 4x216 + 3 = p(-(x216,x215))
   problem:
    +(x201,p(x200)) -> p(+(x201,x200))
    -(x206,p(x205)) -> s(-(x206,x205))
    +(x211,s(x210)) -> s(+(x211,x210))
   Matrix Interpretation Processor: dim=1
    
    interpretation:
     [-](x0, x1) = 2x0 + x1 + 2,
     
     [s](x0) = x0,
     
     [+](x0, x1) = x0 + 4x1 + 4,
     
     [p](x0) = x0 + 4
    orientation:
     +(x201,p(x200)) = 4x200 + x201 + 20 >= 4x200 + x201 + 8 = p(+(x201,x200))
     
     -(x206,p(x205)) = x205 + 2x206 + 6 >= x205 + 2x206 + 2 = s(-(x206,x205))
     
     +(x211,s(x210)) = 4x210 + x211 + 4 >= 4x210 + x211 + 4 = s(+(x211,x210))
    problem:
     +(x211,s(x210)) -> s(+(x211,x210))
    Matrix Interpretation Processor: dim=1
     
     interpretation:
      [s](x0) = x0 + 1,
      
      [+](x0, x1) = x0 + 4x1 + 7
     orientation:
      +(x211,s(x210)) = 4x210 + x211 + 11 >= 4x210 + x211 + 8 = s(+(x211,x210))
     problem:
      
     Qed