MAYBE

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

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