MAYBE

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

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