(1) RFCMatchBoundsTRSProof (EQUIVALENT transformation)
Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 3. This implies Q-termination of R.
The following rules were used to construct the certificate:
f(a) → f(c(a))
f(c(X)) → X
f(c(a)) → f(d(b))
f(a) → f(d(a))
f(d(X)) → X
f(c(b)) → f(d(a))
e(g(X)) → e(X)
The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
2, 4, 5, 7, 10, 12, 13, 14, 19, 20, 21, 22
Node 2 is start node and node 4 is final node.
Those nodes are connected through the following edges:
- 2 to 5 labelled f_1(0)
- 2 to 4 labelled f_1(0), a(0), c_1(0), d_1(0), b(0), e_1(0), g_1(0), f_1(1), a(1), c_1(1), d_1(1), b(1), e_1(1), g_1(1), a(2), b(2), b(3)
- 2 to 10 labelled f_1(0)
- 2 to 13 labelled f_1(1)
- 2 to 19 labelled f_1(1)
- 2 to 21 labelled f_1(2)
- 4 to 4 labelled #_1(0)
- 5 to 7 labelled c_1(0)
- 7 to 4 labelled a(0)
- 10 to 12 labelled d_1(0)
- 12 to 4 labelled b(0), a(0)
- 13 to 14 labelled c_1(1)
- 14 to 4 labelled a(1)
- 19 to 20 labelled d_1(1)
- 20 to 4 labelled b(1), a(1)
- 21 to 22 labelled d_1(2)
- 22 to 4 labelled b(2)