NO

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

Proof:
 Matrix Interpretation Processor:
  dimension: 1
  interpretation:
   [d](x0) = x0 + 4,
   
   [s](x0) = x0 + 1,
   
   [-](x0, x1) = x0 + 4x1,
   
   [0] = 0
  orientation:
   -(0(),0()) = 0 >= 0 = 0()
   
   -(s(x),0()) = x + 1 >= x + 1 = s(x)
   
   -(x,s(y)) = x + 4y + 4 >= x + 4y + 4 = -(d(x),y)
   
   d(s(x)) = x + 5 >= x = x
   
   -(s(x),s(y)) = x + 4y + 5 >= x + 4y = -(x,y)
   
   -(d(x),y) = x + 4y + 4 >= x + 4y + 4 = -(x,s(y))
  problem:
   -(0(),0()) -> 0()
   -(s(x),0()) -> s(x)
   -(x,s(y)) -> -(d(x),y)
   -(d(x),y) -> -(x,s(y))
  Matrix Interpretation Processor:
   dimension: 1
   interpretation:
    [d](x0) = x0 + 2,
    
    [s](x0) = x0 + 4,
    
    [-](x0, x1) = 4x0 + 2x1,
    
    [0] = 0
   orientation:
    -(0(),0()) = 0 >= 0 = 0()
    
    -(s(x),0()) = 4x + 16 >= x + 4 = s(x)
    
    -(x,s(y)) = 4x + 2y + 8 >= 4x + 2y + 8 = -(d(x),y)
    
    -(d(x),y) = 4x + 2y + 8 >= 4x + 2y + 8 = -(x,s(y))
   problem:
    -(0(),0()) -> 0()
    -(x,s(y)) -> -(d(x),y)
    -(d(x),y) -> -(x,s(y))
   Matrix Interpretation Processor:
    dimension: 1
    interpretation:
     [d](x0) = x0,
     
     [s](x0) = x0,
     
     [-](x0, x1) = x0 + x1,
     
     [0] = 2
    orientation:
     -(0(),0()) = 4 >= 2 = 0()
     
     -(x,s(y)) = x + y >= x + y = -(d(x),y)
     
     -(d(x),y) = x + y >= x + y = -(x,s(y))
    problem:
     -(x,s(y)) -> -(d(x),y)
     -(d(x),y) -> -(x,s(y))
    Unfolding Processor:
     loop length: 2
     terms:
      -(x4,s(x5))
      -(d(x4),x5)
     context: []
     substitution:
      x4 -> x4
      x5 -> x5
     Qed