MAYBE

Problem:
 g(c(x1)) -> g(f(c(x1)))
 g(f(c(x1))) -> g(f(f(c(x1))))
 g(g(x1)) -> g(f(g(x1)))
 f(f(g(x1))) -> g(f(x1))

Proof:
 Complexity Transformation Processor:
  strict:
   g(c(x1)) -> g(f(c(x1)))
   g(f(c(x1))) -> g(f(f(c(x1))))
   g(g(x1)) -> g(f(g(x1)))
   f(f(g(x1))) -> g(f(x1))
  weak:
   
  Matrix Interpretation Processor:
   dimension: 1
   max_matrix:
    1
    interpretation:
     [f](x0) = x0 + 1,
     
     [g](x0) = x0 + 1,
     
     [c](x0) = x0
    orientation:
     g(c(x1)) = x1 + 1 >= x1 + 2 = g(f(c(x1)))
     
     g(f(c(x1))) = x1 + 2 >= x1 + 3 = g(f(f(c(x1))))
     
     g(g(x1)) = x1 + 2 >= x1 + 3 = g(f(g(x1)))
     
     f(f(g(x1))) = x1 + 3 >= x1 + 2 = g(f(x1))
    problem:
     strict:
      g(c(x1)) -> g(f(c(x1)))
      g(f(c(x1))) -> g(f(f(c(x1))))
      g(g(x1)) -> g(f(g(x1)))
     weak:
      f(f(g(x1))) -> g(f(x1))
    Matrix Interpretation Processor:
     dimension: 2
     max_matrix:
      [1 1]
      [0 1]
      interpretation:
                 [1 0]  
       [f](x0) = [0 0]x0,
       
                 [1 1]  
       [g](x0) = [0 1]x0,
       
                 [1 0]     [1]
       [c](x0) = [0 0]x0 + [1]
      orientation:
                  [1 0]     [2]    [1 0]     [1]              
       g(c(x1)) = [0 0]x1 + [1] >= [0 0]x1 + [0] = g(f(c(x1)))
       
                     [1 0]     [1]    [1 0]     [1]                 
       g(f(c(x1))) = [0 0]x1 + [0] >= [0 0]x1 + [0] = g(f(f(c(x1))))
       
                  [1 2]      [1 1]                
       g(g(x1)) = [0 1]x1 >= [0 0]x1 = g(f(g(x1)))
       
                     [1 1]      [1 0]             
       f(f(g(x1))) = [0 0]x1 >= [0 0]x1 = g(f(x1))
      problem:
       strict:
        g(f(c(x1))) -> g(f(f(c(x1))))
        g(g(x1)) -> g(f(g(x1)))
       weak:
        g(c(x1)) -> g(f(c(x1)))
        f(f(g(x1))) -> g(f(x1))
      Matrix Interpretation Processor:
       dimension: 3
       max_matrix:
        [1 1 1]
        [0 1 1]
        [0 0 0]
        interpretation:
                   [1 0 0]  
         [f](x0) = [0 0 1]x0
                   [0 0 0]  ,
         
                   [1 1 1]  
         [g](x0) = [0 0 0]x0
                   [0 0 0]  ,
         
                   [1 0 1]     [0]
         [c](x0) = [0 1 1]x0 + [0]
                   [0 0 0]     [1]
        orientation:
                       [1 0 1]     [1]    [1 0 1]                   
         g(f(c(x1))) = [0 0 0]x1 + [0] >= [0 0 0]x1 = g(f(f(c(x1))))
                       [0 0 0]     [0]    [0 0 0]                   
         
                    [1 1 1]      [1 1 1]                
         g(g(x1)) = [0 0 0]x1 >= [0 0 0]x1 = g(f(g(x1)))
                    [0 0 0]      [0 0 0]                
         
                    [1 1 2]     [1]    [1 0 1]     [1]              
         g(c(x1)) = [0 0 0]x1 + [0] >= [0 0 0]x1 + [0] = g(f(c(x1)))
                    [0 0 0]     [0]    [0 0 0]     [0]              
         
                       [1 1 1]      [1 0 1]             
         f(f(g(x1))) = [0 0 0]x1 >= [0 0 0]x1 = g(f(x1))
                       [0 0 0]      [0 0 0]             
        problem:
         strict:
          g(g(x1)) -> g(f(g(x1)))
         weak:
          g(f(c(x1))) -> g(f(f(c(x1))))
          g(c(x1)) -> g(f(c(x1)))
          f(f(g(x1))) -> g(f(x1))
        Open