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

Q is empty.


QTRS
  ↳ RFCMatchBoundsTRSProof

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

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

Q is empty.

Termination of the TRS R could be shown with a Match Bound [6,7] of 4. This implies Q-termination of R.
The following rules were used to construct the certificate:

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

The certificate found is represented by the following graph.

The certificate consists of the following enumerated nodes:

1, 2, 4, 3, 6, 7, 5, 9, 10, 8, 12, 11, 14, 13, 16, 15, 18, 19, 17, 21, 22, 20, 24, 23, 26, 25, 28, 27, 30, 31, 29, 33, 32, 35, 34, 37, 38, 36, 40, 41, 39, 43, 42, 45, 44, 47, 46, 49, 50, 48, 52, 53, 51, 55, 56, 54, 58, 59, 57, 61, 60, 63, 62, 65, 64, 67, 66, 69, 68, 71, 70, 73, 72, 75, 76, 74, 78, 79, 77, 81, 82, 80, 90, 89, 92, 91, 94, 93, 96, 95, 98, 99, 97, 101, 100

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

Those nodes are connect through the following edges: