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(a(b(x1))) → b(b(a(a(x1))))
b(a(x1)) → a(c(b(x1)))

Q is empty.


QTRS
  ↳ RFCMatchBoundsTRSProof

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

a(a(b(x1))) → b(b(a(a(x1))))
b(a(x1)) → a(c(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(a(b(x1))) → b(b(a(a(x1))))
b(a(x1)) → a(c(b(x1)))

The certificate found is represented by the following graph.

The certificate consists of the following enumerated nodes:

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24

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

Those nodes are connect through the following edges: