(1) Strip Symbols Proof (SOUND transformation)
We were given the following TRS:
b(a(b(b(a(b(a(x))))))) → a(b(a(a(b(b(a(b(b(a(x))))))))))
By stripping symbols from the only rule of the system, we obtained the following TRS [ENDRULLIS]:
b(a(b(b(a(b(x)))))) → a(b(a(a(b(b(a(b(b(x)))))))))
(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(a(b(b(a(b(x)))))) → a(b(a(a(b(b(a(b(b(x)))))))))
The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
1, 6, 10, 12, 14, 16, 18, 20, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32
Node 1 is start node and node 6 is final node.
Those nodes are connected through the following edges:
- 1 to 10 labelled a_1(0)
- 6 to 6 labelled #_1(0)
- 10 to 12 labelled b_1(0)
- 12 to 14 labelled a_1(0)
- 14 to 16 labelled a_1(0)
- 16 to 18 labelled b_1(0)
- 18 to 20 labelled b_1(0)
- 18 to 25 labelled a_1(1)
- 20 to 23 labelled a_1(0)
- 23 to 24 labelled b_1(0)
- 24 to 6 labelled b_1(0)
- 24 to 25 labelled a_1(1)
- 25 to 26 labelled b_1(1)
- 26 to 27 labelled a_1(1)
- 27 to 28 labelled a_1(1)
- 28 to 29 labelled b_1(1)
- 29 to 30 labelled b_1(1)
- 29 to 25 labelled a_1(1)
- 30 to 31 labelled a_1(1)
- 31 to 32 labelled b_1(1)
- 32 to 6 labelled b_1(1)
- 32 to 25 labelled a_1(1)