MAYBE

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

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