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(h(0()))) -> g(d(1()))
 g(c(1())) -> g(d(h(0())))
 g(h(x)) -> g(x)

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(h(0()))) -> g(d(1()))
   g(c(1())) -> g(d(h(0())))
   g(h(x)) -> g(x)
  weak:
   
  Matrix Interpretation Processor:
   dimension: 1
   max_matrix:
    1
    interpretation:
     [1] = 1,
     
     [h](x0) = x0 + 1,
     
     [0] = 0,
     
     [g](x0) = x0 + 1,
     
     [d](x0) = x0,
     
     [c](x0) = x0 + 1,
     
     [f](x0) = x0 + 1
    orientation:
     f(f(x)) = x + 2 >= x + 3 = f(c(f(x)))
     
     f(f(x)) = x + 2 >= x + 2 = f(d(f(x)))
     
     g(c(x)) = x + 2 >= x = x
     
     g(d(x)) = x + 1 >= x = x
     
     g(c(h(0()))) = 3 >= 2 = g(d(1()))
     
     g(c(1())) = 3 >= 2 = g(d(h(0())))
     
     g(h(x)) = x + 2 >= x + 1 = g(x)
    problem:
     strict:
      f(f(x)) -> f(c(f(x)))
      f(f(x)) -> f(d(f(x)))
     weak:
      g(c(x)) -> x
      g(d(x)) -> x
      g(c(h(0()))) -> g(d(1()))
      g(c(1())) -> g(d(h(0())))
      g(h(x)) -> g(x)
    Open