MAYBE

Problem:
 f(0(x1)) -> s(0(x1))
 d(0(x1)) -> 0(x1)
 d(s(x1)) -> s(s(d(x1)))
 f(s(x1)) -> d(f(x1))

Proof:
 Complexity Transformation Processor:
  strict:
   f(0(x1)) -> s(0(x1))
   d(0(x1)) -> 0(x1)
   d(s(x1)) -> s(s(d(x1)))
   f(s(x1)) -> d(f(x1))
  weak:
   
  Matrix Interpretation Processor:
   dimension: 1
   max_matrix:
    1
    interpretation:
     [d](x0) = x0,
     
     [s](x0) = x0 + 1,
     
     [f](x0) = x0,
     
     [0](x0) = x0
    orientation:
     f(0(x1)) = x1 >= x1 + 1 = s(0(x1))
     
     d(0(x1)) = x1 >= x1 = 0(x1)
     
     d(s(x1)) = x1 + 1 >= x1 + 2 = s(s(d(x1)))
     
     f(s(x1)) = x1 + 1 >= x1 = d(f(x1))
    problem:
     strict:
      f(0(x1)) -> s(0(x1))
      d(0(x1)) -> 0(x1)
      d(s(x1)) -> s(s(d(x1)))
     weak:
      f(s(x1)) -> d(f(x1))
    Matrix Interpretation Processor:
     dimension: 1
     max_matrix:
      1
      interpretation:
       [d](x0) = x0,
       
       [s](x0) = x0,
       
       [f](x0) = x0 + 1,
       
       [0](x0) = x0
      orientation:
       f(0(x1)) = x1 + 1 >= x1 = s(0(x1))
       
       d(0(x1)) = x1 >= x1 = 0(x1)
       
       d(s(x1)) = x1 >= x1 = s(s(d(x1)))
       
       f(s(x1)) = x1 + 1 >= x1 + 1 = d(f(x1))
      problem:
       strict:
        d(0(x1)) -> 0(x1)
        d(s(x1)) -> s(s(d(x1)))
       weak:
        f(0(x1)) -> s(0(x1))
        f(s(x1)) -> d(f(x1))
      Matrix Interpretation Processor:
       dimension: 1
       max_matrix:
        1
        interpretation:
         [d](x0) = x0 + 1,
         
         [s](x0) = x0 + 1,
         
         [f](x0) = x0 + 1,
         
         [0](x0) = x0
        orientation:
         d(0(x1)) = x1 + 1 >= x1 = 0(x1)
         
         d(s(x1)) = x1 + 2 >= x1 + 3 = s(s(d(x1)))
         
         f(0(x1)) = x1 + 1 >= x1 + 1 = s(0(x1))
         
         f(s(x1)) = x1 + 2 >= x1 + 2 = d(f(x1))
        problem:
         strict:
          d(s(x1)) -> s(s(d(x1)))
         weak:
          d(0(x1)) -> 0(x1)
          f(0(x1)) -> s(0(x1))
          f(s(x1)) -> d(f(x1))
        Open