MAYBE

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

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