MAYBE

Problem:
 f(g(a())) -> f(s(g(b())))
 f(f(x)) -> b()
 g(x) -> f(g(x))

Proof:
 RT Transformation Processor:
  strict:
   f(g(a())) -> f(s(g(b())))
   f(f(x)) -> b()
   g(x) -> f(g(x))
  weak:
   
  Matrix Interpretation Processor:
   dimension: 1
   interpretation:
    [s](x0) = x0 + 5,
    
    [b] = 3,
    
    [f](x0) = x0,
    
    [g](x0) = x0 + 8,
    
    [a] = 24
   orientation:
    f(g(a())) = 32 >= 16 = f(s(g(b())))
    
    f(f(x)) = x >= 3 = b()
    
    g(x) = x + 8 >= x + 8 = f(g(x))
   problem:
    strict:
     f(f(x)) -> b()
     g(x) -> f(g(x))
    weak:
     f(g(a())) -> f(s(g(b())))
   Matrix Interpretation Processor:
    dimension: 1
    interpretation:
     [s](x0) = x0 + 7,
     
     [b] = 8,
     
     [f](x0) = x0 + 5,
     
     [g](x0) = x0 + 1,
     
     [a] = 28
    orientation:
     f(f(x)) = x + 10 >= 8 = b()
     
     g(x) = x + 1 >= x + 6 = f(g(x))
     
     f(g(a())) = 34 >= 21 = f(s(g(b())))
    problem:
     strict:
      g(x) -> f(g(x))
     weak:
      f(f(x)) -> b()
      f(g(a())) -> f(s(g(b())))
    Open