MAYBE

Problem:
 f(c(s(x),y)) -> f(c(x,s(y)))
 f(c(s(x),s(y))) -> g(c(x,y))
 g(c(x,s(y))) -> g(c(s(x),y))
 g(c(s(x),s(y))) -> f(c(x,y))

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