MAYBE

Problem:
 a(b(x1)) -> d(x1)
 b(a(x1)) -> a(b(x1))
 d(c(x1)) -> f(a(b(b(c(x1)))))
 d(f(x1)) -> f(a(b(x1)))
 a(f(x1)) -> a(x1)

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