MAYBE

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

Proof:
 Complexity 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
   max_matrix:
    1
    interpretation:
     [q](x0) = x0 + 1,
     
     [e](x0) = x0,
     
     [s](x0) = x0,
     
     [d](x0) = x0,
     
     [0] = 0
    orientation:
     d(0()) = 0 >= 0 = 0()
     
     d(s(x)) = x >= x = s(s(d(x)))
     
     e(0()) = 0 >= 0 = s(0())
     
     e(q(x)) = x + 1 >= x = d(e(x))
    problem:
     strict:
      d(0()) -> 0()
      d(s(x)) -> s(s(d(x)))
      e(0()) -> s(0())
     weak:
      e(q(x)) -> d(e(x))
    Matrix Interpretation Processor:
     dimension: 1
     max_matrix:
      1
      interpretation:
       [q](x0) = x0 + 1,
       
       [e](x0) = x0 + 1,
       
       [s](x0) = x0,
       
       [d](x0) = x0 + 1,
       
       [0] = 0
      orientation:
       d(0()) = 1 >= 0 = 0()
       
       d(s(x)) = x + 1 >= x + 1 = s(s(d(x)))
       
       e(0()) = 1 >= 0 = s(0())
       
       e(q(x)) = x + 2 >= x + 2 = d(e(x))
      problem:
       strict:
        d(s(x)) -> s(s(d(x)))
       weak:
        d(0()) -> 0()
        e(0()) -> s(0())
        e(q(x)) -> d(e(x))
      Open