(0) Obligation:

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

a(b(x)) → a(c(b(x)))

Q is empty.

(1) RFCMatchBoundsTRSProof (EQUIVALENT transformation)

Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 0. This implies Q-termination of R.
The following rules were used to construct the certificate:

a(b(x)) → a(c(b(x)))

The certificate found is represented by the following graph.

The certificate consists of the following enumerated nodes:

9111662, 9111663, 9111664, 9111665

Node 9111662 is start node and node 9111663 is final node.

Those nodes are connect through the following edges:

  • 9111662 to 9111664 labelled a_1(0)
  • 9111663 to 9111663 labelled #_1(0)
  • 9111664 to 9111665 labelled c_1(0)
  • 9111665 to 9111663 labelled b_1(0)

(2) TRUE