MAYBE

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

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