MAYBE

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

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