(0) Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:
a(b(a(a(b(b(x)))))) → a(a(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(a(b(a(x)))))) → a(b(b(a(b(a(a(x)))))))
Q is empty.
(3) Strip Symbols Proof (SOUND transformation)
We were given the following TRS:
b(b(a(a(b(a(x)))))) → a(b(b(a(b(a(a(x)))))))
By stripping symbols from the only rule of the system, we obtained the following TRS [ENDRULLIS]:
b(b(a(a(b(x))))) → a(b(b(a(b(a(x))))))
(4) Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:
b(b(a(a(b(x))))) → a(b(b(a(b(a(x))))))
Q is empty.
(5) 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:
b(b(a(a(b(x))))) → a(b(b(a(b(a(x))))))
The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
3, 4, 14, 15, 16, 17, 18
Node 3 is start node and node 4 is final node.
Those nodes are connected through the following edges:
- 3 to 14 labelled a_1(0)
- 4 to 4 labelled #_1(0)
- 14 to 15 labelled b_1(0)
- 15 to 16 labelled b_1(0)
- 16 to 17 labelled a_1(0)
- 17 to 18 labelled b_1(0)
- 18 to 4 labelled a_1(0)
(6) YES