MAYBE

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

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