MAYBE

Problem:
 f(f(x)) -> f(c(f(x)))
 f(f(x)) -> f(d(f(x)))
 g(c(x)) -> x
 g(d(x)) -> x
 g(c(0())) -> g(d(1()))
 g(c(1())) -> g(d(0()))

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