YES Termination w.r.t. Q proof of /home/cern_httpd/provide/research/cycsrs/tpdb/TPDB-d9b80194f163/SRS_Standard/Zantema_04/z061.srs

Termination w.r.t. Q of the given QTRS could be proven:

0 QTRS
↳1 QTRS Reverse (⇔, 0 ms)
↳2 QTRS
↳3 RFCMatchBoundsTRSProof (⇔, 0 ms)
↳4 YES

(0) Obligation:

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

b(b(c(a(b(c(x)))))) → a(b(b(c(b(c(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:

c(b(a(c(b(b(x)))))) → a(c(b(c(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 0. This implies Q-termination of R.
The following rules were used to construct the certificate:

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

The certificate found is represented by the following graph.

The certificate consists of the following enumerated nodes:

3, 4, 5, 7, 9, 11, 13, 15

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

Those nodes are connected through the following edges:

  • 3 to 5 labelled a_1(0)
  • 4 to 4 labelled #_1(0)
  • 5 to 7 labelled c_1(0)
  • 7 to 9 labelled b_1(0)
  • 9 to 11 labelled c_1(0)
  • 11 to 13 labelled b_1(0)
  • 13 to 15 labelled b_1(0)
  • 15 to 4 labelled a_1(0)

(4) YES