YES Termination w.r.t. Q proof of /home/cern_httpd/provide/research/cycsrs/tpdb/TPDB-d9b80194f163/SRS_Standard/Zantema_04/z056.srs

(0) Obligation:

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

b(a(b(a(b(b(x)))))) → a(b(a(b(b(b(a(x)))))))

Q is empty.

(1) QTRS Reverse (EQUIVALENT transformation)

We applied the QTRS Reverse Processor [REVERSE].

(2) Obligation:

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

b(b(a(b(a(b(x)))))) → a(b(b(b(a(b(a(x)))))))

Q is empty.

(3) 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:

b(b(a(b(a(b(x)))))) → a(b(b(b(a(b(a(x)))))))

The certificate found is represented by the following graph.

The certificate consists of the following enumerated nodes:

1, 2, 5, 7, 8, 9, 10, 11, 23, 24, 25, 26, 27, 28

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

Those nodes are connected through the following edges:

  • 1 to 5 labelled a_1(0)
  • 2 to 2 labelled #_1(0)
  • 5 to 7 labelled b_1(0)
  • 7 to 8 labelled b_1(0)
  • 7 to 23 labelled a_1(1)
  • 8 to 9 labelled b_1(0)
  • 9 to 10 labelled a_1(0)
  • 10 to 11 labelled b_1(0)
  • 11 to 2 labelled a_1(0)
  • 23 to 24 labelled b_1(1)
  • 24 to 25 labelled b_1(1)
  • 24 to 23 labelled a_1(1)
  • 25 to 26 labelled b_1(1)
  • 26 to 27 labelled a_1(1)
  • 27 to 28 labelled b_1(1)
  • 28 to 2 labelled a_1(1)

(4) YES