Termination w.r.t. Q of the following Term Rewriting System could be proven:

Q restricted rewrite system:
The TRS R consists of the following rules:

a(l(x1)) → l(a(x1))
r(a(a(x1))) → a(a(r(x1)))
b(l(x1)) → b(a(r(x1)))
r(b(x1)) → l(b(x1))

Q is empty.


↳ QTRS
  ↳ RFCMatchBoundsTRSProof

Q restricted rewrite system:
The TRS R consists of the following rules:

a(l(x1)) → l(a(x1))
r(a(a(x1))) → a(a(r(x1)))
b(l(x1)) → b(a(r(x1)))
r(b(x1)) → l(b(x1))

Q is empty.

Termination of the TRS R could be shown with a Match Bound [6,7] of 3. This implies Q-termination of R.
The following rules were used to construct the certificate:

a(l(x1)) → l(a(x1))
r(a(a(x1))) → a(a(r(x1)))
b(l(x1)) → b(a(r(x1)))
r(b(x1)) → l(b(x1))

The certificate found is represented by the following graph.

The certificate consists of the following enumerated nodes:

1, 2, 3, 5, 4, 6, 8, 7, 9, 10, 11, 13, 12, 14, 16, 15, 17, 19, 18

Node 1 is start node and node 2 is final node.

Those nodes are connect through the following edges: