MAYBE

Problem:
 a(b(x1)) -> b(d(x1))
 a(c(x1)) -> d(d(d(x1)))
 b(d(x1)) -> a(c(b(x1)))
 c(f(x1)) -> d(d(c(x1)))
 d(d(x1)) -> f(x1)
 f(f(x1)) -> a(x1)

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