MAYBE

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

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