MAYBE

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

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