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

Q is empty.


QTRS
  ↳ RFCMatchBoundsTRSProof

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

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

The certificate found is represented by the following graph.

The certificate consists of the following enumerated nodes:

1, 2, 5, 3, 4, 7, 6, 9, 10, 8, 13, 11, 12, 15, 14, 17, 18, 16, 20, 19, 22, 23, 21, 26, 24, 25, 28, 27, 30, 31, 29, 34, 32, 33, 36, 35, 38, 39, 37, 42, 40, 41, 44, 43, 46, 47, 45

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

Those nodes are connect through the following edges: