YES Termination w.r.t. Q proof of /home/cern_httpd/provide/research/cycsrs/tpdb/TPDB-d9b80194f163/SRS_Standard/Zantema_04/z058.srs

(0) Obligation:

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

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

The certificate found is represented by the following graph.

The certificate consists of the following enumerated nodes:

3, 4, 6, 8, 10, 12, 14, 16, 17, 18, 19, 20, 21, 22

Node 3 is start node and node 4 is final node.

Those nodes are connected through the following edges:

  • 3 to 6 labelled a_1(0)
  • 4 to 4 labelled #_1(0)
  • 6 to 8 labelled b_1(0)
  • 8 to 10 labelled b_1(0)
  • 10 to 12 labelled a_1(0)
  • 12 to 14 labelled b_1(0)
  • 12 to 17 labelled a_1(1)
  • 14 to 16 labelled b_1(0)
  • 16 to 4 labelled a_1(0)
  • 17 to 18 labelled b_1(1)
  • 18 to 19 labelled b_1(1)
  • 19 to 20 labelled a_1(1)
  • 20 to 21 labelled b_1(1)
  • 20 to 17 labelled a_1(1)
  • 21 to 22 labelled b_1(1)
  • 22 to 4 labelled a_1(1)

(4) YES