(0) Obligation:

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

a(b(x)) → b(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(b(x)) → b(b(a(x)))

The certificate found is represented by the following graph.

The certificate consists of the following enumerated nodes:

726966, 726967, 726968, 726969, 726970, 726971

Node 726966 is start node and node 726967 is final node.

Those nodes are connect through the following edges:

  • 726966 to 726968 labelled b_1(0)
  • 726967 to 726967 labelled #_1(0)
  • 726968 to 726969 labelled b_1(0)
  • 726969 to 726967 labelled a_1(0)
  • 726969 to 726970 labelled b_1(1)
  • 726970 to 726971 labelled b_1(1)
  • 726971 to 726967 labelled a_1(1)
  • 726971 to 726970 labelled b_1(1)

(2) TRUE