The confluence property of ground (i.e., variable-free) term rewrite systems (GTRS) is well-known to be decidable. This was proved independently in [DTHL87,DHLT90] and in [Oya87] using tree automata techniques and ground tree transducer techniques (originated from this problem), yielding EXPTIME decision procedures (PSPACE for strings). Since then, it has been a well-known longstanding open question whether this bound is optimal (see, e.g., [RTA01]). In [CGN01] we gave the first polynomial-time algorithm for deciding the confluence of GTRS. Later in [Tiw02] this result was extended, using abstract congruent closure techniques, to linear-shallow TRS. Here, we give a new and much simpler proof of the latter result.