MAYBE

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

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