MAYBE

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

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