MAYBE

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

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