MAYBE

Problem:
 a(x1) -> b(x1)
 a(a(x1)) -> a(b(a(x1)))
 a(b(x1)) -> b(b(b(x1)))
 a(a(a(x1))) -> a(a(b(a(a(x1)))))
 a(a(b(x1))) -> a(b(b(a(b(x1)))))
 a(b(a(x1))) -> b(a(b(b(a(x1)))))
 a(b(b(x1))) -> b(b(b(b(b(x1)))))
 b(a(x1)) -> b(b(b(x1)))
 a(b(a(x1))) -> a(b(b(a(b(x1)))))
 b(a(a(x1))) -> b(a(b(b(a(x1)))))
 b(b(a(x1))) -> b(b(b(b(b(x1)))))

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