MAYBE

Problem:
 d(0()) -> 0()
 d(s(x)) -> s(s(d(x)))
 e(0()) -> s(0())
 e(q(x)) -> d(e(x))

Proof:
 RT Transformation Processor:
  strict:
   d(0()) -> 0()
   d(s(x)) -> s(s(d(x)))
   e(0()) -> s(0())
   e(q(x)) -> d(e(x))
  weak:
   
  Matrix Interpretation Processor:
   dimension: 1
   interpretation:
    [q](x0) = x0 + 5,
    
    [e](x0) = x0,
    
    [s](x0) = x0,
    
    [d](x0) = x0 + 4,
    
    [0] = 0
   orientation:
    d(0()) = 4 >= 0 = 0()
    
    d(s(x)) = x + 4 >= x + 4 = s(s(d(x)))
    
    e(0()) = 0 >= 0 = s(0())
    
    e(q(x)) = x + 5 >= x + 4 = d(e(x))
   problem:
    strict:
     d(s(x)) -> s(s(d(x)))
     e(0()) -> s(0())
    weak:
     d(0()) -> 0()
     e(q(x)) -> d(e(x))
   Matrix Interpretation Processor:
    dimension: 1
    interpretation:
     [q](x0) = x0,
     
     [e](x0) = x0 + 17,
     
     [s](x0) = x0,
     
     [d](x0) = x0,
     
     [0] = 0
    orientation:
     d(s(x)) = x >= x = s(s(d(x)))
     
     e(0()) = 17 >= 0 = s(0())
     
     d(0()) = 0 >= 0 = 0()
     
     e(q(x)) = x + 17 >= x + 17 = d(e(x))
    problem:
     strict:
      d(s(x)) -> s(s(d(x)))
     weak:
      e(0()) -> s(0())
      d(0()) -> 0()
      e(q(x)) -> d(e(x))
    Open