MAYBE

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

Proof:
 RT Transformation Processor:
  strict:
   d(0()) -> 0()
   d(s(x)) -> s(s(d(x)))
   e(0(),x) -> x
   e(s(x),y) -> e(x,d(y))
  weak:
   
  Matrix Interpretation Processor:
   dimension: 1
   interpretation:
    [e](x0, x1) = x0 + x1 + 30,
    
    [s](x0) = x0 + 1,
    
    [d](x0) = x0,
    
    [0] = 4
   orientation:
    d(0()) = 4 >= 4 = 0()
    
    d(s(x)) = x + 1 >= x + 2 = s(s(d(x)))
    
    e(0(),x) = x + 34 >= x = x
    
    e(s(x),y) = x + y + 31 >= x + y + 30 = e(x,d(y))
   problem:
    strict:
     d(0()) -> 0()
     d(s(x)) -> s(s(d(x)))
    weak:
     e(0(),x) -> x
     e(s(x),y) -> e(x,d(y))
   Matrix Interpretation Processor:
    dimension: 1
    interpretation:
     [e](x0, x1) = x0 + x1,
     
     [s](x0) = x0 + 16,
     
     [d](x0) = x0 + 16,
     
     [0] = 16
    orientation:
     d(0()) = 32 >= 16 = 0()
     
     d(s(x)) = x + 32 >= x + 48 = s(s(d(x)))
     
     e(0(),x) = x + 16 >= x = x
     
     e(s(x),y) = x + y + 16 >= x + y + 16 = e(x,d(y))
    problem:
     strict:
      d(s(x)) -> s(s(d(x)))
     weak:
      d(0()) -> 0()
      e(0(),x) -> x
      e(s(x),y) -> e(x,d(y))
    Open