MAYBE

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

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