#!/bin/sed -uf

:1;     s/^/b/; t2;     b2
:2;     s/x//;  t3;     b7
:3;     s/b/a/; t4;     b5
:4;     s/^/c/; t3;     b3
:5;     s/a/b/; t5;     b6
:6;     s/c/a/; t6;     b2
:7;     s/b//;  t7;     bN

:N