(1) 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:
f(f(X)) → f(a(b(f(X))))
f(a(g(X))) → b(X)
b(X) → a(X)
The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
7474230, 7474231, 7474233, 7474234, 7474232, 7474236, 7474237, 7474235
Node 7474230 is start node and node 7474231 is final node.
Those nodes are connect through the following edges:
- 7474230 to 7474231 labelled a_1(0), b_1(0), a_1(1)
- 7474230 to 7474232 labelled f_1(0)
- 7474231 to 7474231 labelled #_1(0)
- 7474233 to 7474234 labelled b_1(0), a_1(1)
- 7474234 to 7474231 labelled f_1(0), b_1(1), a_1(2)
- 7474234 to 7474235 labelled f_1(1)
- 7474232 to 7474233 labelled a_1(0)
- 7474236 to 7474237 labelled b_1(1), a_1(2)
- 7474237 to 7474231 labelled f_1(1), b_1(1), a_1(2)
- 7474237 to 7474235 labelled f_1(1)
- 7474235 to 7474236 labelled a_1(1)