(0) Obligation:

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

a(a(x)) → a(b(a(x)))

Q is empty.

(1) RFCMatchBoundsTRSProof (EQUIVALENT transformation)

Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 1. This implies Q-termination of R.
The following rules were used to construct the certificate:

a(a(x)) → a(b(a(x)))

The certificate found is represented by the following graph.

The certificate consists of the following enumerated nodes:

9114429, 9114430, 9114431, 9114432, 9114433, 9114434

Node 9114429 is start node and node 9114430 is final node.

Those nodes are connect through the following edges:

  • 9114429 to 9114431 labelled a_1(0)
  • 9114430 to 9114430 labelled #_1(0)
  • 9114431 to 9114432 labelled b_1(0)
  • 9114432 to 9114430 labelled a_1(0)
  • 9114432 to 9114433 labelled a_1(1)
  • 9114433 to 9114434 labelled b_1(1)
  • 9114434 to 9114430 labelled a_1(1)
  • 9114434 to 9114433 labelled a_1(1)

(2) TRUE