MAYBE

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

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