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) = x0 + 4x1,
    
    [+](x0, x1) = x0 + 2x1 + 3,
    
    [s](x0) = x0 + 4,
    
    [p](x0) = x0 + 1
   orientation:
    +(x201,p(x200)) = 2x200 + x201 + 5 >= 2x200 + x201 + 4 = p(+(x201,x200))
    
    s(p(x204)) = x204 + 5 >= x204 = x204
    
    -(x206,p(x205)) = 4x205 + x206 + 4 >= 4x205 + x206 + 4 = s(-(x206,x205))
    
    p(s(x209)) = x209 + 5 >= x209 = x209
    
    +(x211,s(x210)) = 2x210 + x211 + 11 >= 2x210 + x211 + 7 = s(+(x211,x210))
    
    -(x216,s(x215)) = 4x215 + x216 + 16 >= 4x215 + x216 + 1 = p(-(x216,x215))
   problem:
    -(x206,p(x205)) -> s(-(x206,x205))
   Matrix Interpretation Processor: dim=1
    
    interpretation:
     [-](x0, x1) = x0 + 4x1 + 2,
     
     [s](x0) = x0,
     
     [p](x0) = 4x0 + 1
    orientation:
     -(x206,p(x205)) = 16x205 + x206 + 6 >= 4x205 + x206 + 2 = s(-(x206,x205))
    problem:
     
    Qed