Termination w.r.t. Q of the following Term Rewriting System could be proven:
Q restricted rewrite system:
The TRS R consists of the following rules:
a(b(x1)) → b(a(x1))
b(a(x1)) → a(a(c(b(x1))))
Q is empty.
↳ QTRS
↳ RFCMatchBoundsTRSProof
Q restricted rewrite system:
The TRS R consists of the following rules:
a(b(x1)) → b(a(x1))
b(a(x1)) → a(a(c(b(x1))))
Q is empty.
Termination of the TRS R could be shown with a Match Bound [6,7] of 3. This implies Q-termination of R.
The following rules were used to construct the certificate:
a(b(x1)) → b(a(x1))
b(a(x1)) → a(a(c(b(x1))))
The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
1, 2, 3, 5, 6, 4, 8, 9, 7, 10, 12, 13, 11, 15, 16, 14, 18, 19, 17
Node 1 is start node and node 2 is final node.
Those nodes are connect through the following edges:
- 1 to 3 labelled b_1(0)
- 1 to 4 labelled a_1(0)
- 1 to 7 labelled a_1(1)
- 2 to 2 labelled #_1(0)
- 3 to 2 labelled a_1(0)
- 3 to 10 labelled b_1(1)
- 3 to 11 labelled a_1(2)
- 5 to 6 labelled c_1(0)
- 6 to 2 labelled b_1(0)
- 6 to 7 labelled a_1(1)
- 4 to 5 labelled a_1(0)
- 8 to 9 labelled c_1(1)
- 9 to 2 labelled b_1(1)
- 9 to 7 labelled a_1(1)
- 9 to 11 labelled b_1(1)
- 9 to 14 labelled a_1(2)
- 7 to 8 labelled a_1(1)
- 10 to 2 labelled a_1(1)
- 10 to 10 labelled b_1(1)
- 10 to 11 labelled a_1(2)
- 12 to 13 labelled c_1(2)
- 13 to 2 labelled b_1(2)
- 13 to 7 labelled a_1(1)
- 13 to 11 labelled b_1(2)
- 13 to 17 labelled a_1(3)
- 11 to 12 labelled a_1(2)
- 15 to 16 labelled c_1(2)
- 16 to 12 labelled b_1(2)
- 14 to 15 labelled a_1(2)
- 18 to 19 labelled c_1(3)
- 19 to 12 labelled b_1(3)
- 17 to 18 labelled a_1(3)