(3) Strip Symbols Proof (SOUND transformation)
We were given the following TRS:
b(a(b(b(a(a(x)))))) → a(b(b(a(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(x))))) → a(b(b(a(a(b(b(x)))))))
(5) RFCMatchBoundsTRSProof (EQUIVALENT transformation)
Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 2. This implies Q-termination of R.
The following rules were used to construct the certificate:
b(a(b(b(a(x))))) → a(b(b(a(a(b(b(x)))))))
The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
1, 2, 9, 10, 11, 12, 13, 14, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59
Node 1 is start node and node 2 is final node.
Those nodes are connected through the following edges:
- 1 to 9 labelled a_1(0)
- 2 to 2 labelled #_1(0)
- 9 to 10 labelled b_1(0)
- 10 to 11 labelled b_1(0)
- 11 to 12 labelled a_1(0)
- 12 to 13 labelled a_1(0)
- 13 to 14 labelled b_1(0)
- 13 to 48 labelled a_1(1)
- 14 to 2 labelled b_1(0)
- 14 to 42 labelled a_1(1)
- 42 to 43 labelled b_1(1)
- 43 to 44 labelled b_1(1)
- 44 to 45 labelled a_1(1)
- 45 to 46 labelled a_1(1)
- 46 to 47 labelled b_1(1)
- 46 to 54 labelled a_1(2)
- 47 to 2 labelled b_1(1)
- 47 to 42 labelled a_1(1)
- 48 to 49 labelled b_1(1)
- 49 to 50 labelled b_1(1)
- 50 to 51 labelled a_1(1)
- 51 to 52 labelled a_1(1)
- 52 to 53 labelled b_1(1)
- 52 to 54 labelled a_1(2)
- 53 to 45 labelled b_1(1)
- 53 to 42 labelled a_1(1)
- 54 to 55 labelled b_1(2)
- 55 to 56 labelled b_1(2)
- 56 to 57 labelled a_1(2)
- 57 to 58 labelled a_1(2)
- 58 to 59 labelled b_1(2)
- 58 to 54 labelled a_1(2)
- 59 to 45 labelled b_1(2)
- 59 to 42 labelled a_1(1)