(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:

727587, 727588, 727589, 727590, 727592, 727591

Node 727587 is start node and node 727588 is final node.

Those nodes are connect through the following edges:

  • 727587 to 727589 labelled a_1(0)
  • 727588 to 727588 labelled #_1(0)
  • 727589 to 727590 labelled b_1(0)
  • 727590 to 727588 labelled a_1(0)
  • 727590 to 727591 labelled a_1(1)
  • 727592 to 727588 labelled a_1(1)
  • 727592 to 727591 labelled a_1(1)
  • 727591 to 727592 labelled b_1(1)

(2) TRUE