(3) Strip Symbols Proof (SOUND transformation)
We were given the following TRS:
a(a(a(b(a(b(a(x))))))) → b(a(b(a(b(a(a(a(a(x)))))))))
By stripping symbols from the only rule of the system, we obtained the following TRS [ENDRULLIS]:
a(a(a(b(a(b(x)))))) → b(a(b(a(b(a(a(a(x))))))))
(5) 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:
a(a(a(b(a(b(x)))))) → b(a(b(a(b(a(a(a(x))))))))
The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
7, 8, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37
Node 7 is start node and node 8 is final node.
Those nodes are connected through the following edges:
- 7 to 24 labelled b_1(0)
- 8 to 8 labelled #_1(0)
- 24 to 25 labelled a_1(0)
- 25 to 26 labelled b_1(0)
- 26 to 27 labelled a_1(0)
- 27 to 28 labelled b_1(0)
- 28 to 29 labelled a_1(0)
- 28 to 31 labelled b_1(1)
- 29 to 30 labelled a_1(0)
- 29 to 31 labelled b_1(1)
- 30 to 8 labelled a_1(0)
- 30 to 31 labelled b_1(1)
- 31 to 32 labelled a_1(1)
- 32 to 33 labelled b_1(1)
- 33 to 34 labelled a_1(1)
- 34 to 35 labelled b_1(1)
- 35 to 36 labelled a_1(1)
- 35 to 31 labelled b_1(1)
- 36 to 37 labelled a_1(1)
- 36 to 31 labelled b_1(1)
- 37 to 8 labelled a_1(1)
- 37 to 31 labelled b_1(1)