MAYBE

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

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