YES
Termination w.r.t. Q proof of ../tpdb/SRS/secret06/matchbox/5.srs
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(c(x1))) → a(a(b(x1)))
a(b(c(x1))) → b(c(b(c(x1))))
a(b(c(x1))) → c(b(c(a(x1))))
Q is empty.
↳ QTRS
↳ RFCMatchBoundsTRSProof
Q restricted rewrite system:
The TRS R consists of the following rules:
a(b(c(x1))) → a(a(b(x1)))
a(b(c(x1))) → b(c(b(c(x1))))
a(b(c(x1))) → c(b(c(a(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(c(x1))) → a(a(b(x1)))
a(b(c(x1))) → b(c(b(c(x1))))
a(b(c(x1))) → c(b(c(a(x1))))
The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
1, 2, 4, 5, 3, 7, 6, 8, 9, 10, 12, 13, 11, 15, 14, 16, 17, 18, 20, 19, 21, 22, 23, 26, 24, 25, 27, 28, 31, 30, 29, 34, 32, 33, 35, 36, 39, 38, 37, 41, 42, 40, 44, 43, 45, 46, 47
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 6 labelled a_1(0)
- 1 to 8 labelled c_1(0)
- 1 to 17 labelled b_1(1)
- 1 to 19 labelled a_1(1)
- 1 to 21 labelled c_1(1)
- 2 to 2 labelled #_1(0)
- 4 to 5 labelled b_1(0)
- 5 to 2 labelled c_1(0)
- 3 to 4 labelled c_1(0)
- 7 to 2 labelled b_1(0)
- 6 to 7 labelled a_1(0)
- 6 to 11 labelled b_1(1)
- 6 to 14 labelled a_1(1)
- 6 to 16 labelled c_1(1)
- 6 to 32 labelled b_1(2)
- 6 to 35 labelled a_1(2)
- 6 to 37 labelled c_1(2)
- 8 to 9 labelled b_1(0)
- 9 to 10 labelled c_1(0)
- 10 to 2 labelled a_1(0)
- 10 to 11 labelled b_1(1)
- 10 to 14 labelled a_1(1)
- 10 to 16 labelled c_1(1)
- 10 to 32 labelled b_1(2)
- 10 to 35 labelled a_1(2)
- 10 to 37 labelled c_1(2)
- 12 to 13 labelled b_1(1)
- 13 to 2 labelled c_1(1)
- 11 to 12 labelled c_1(1)
- 11 to 33 labelled c_1(1)
- 15 to 2 labelled b_1(1)
- 14 to 15 labelled a_1(1)
- 14 to 11 labelled b_1(1)
- 14 to 14 labelled a_1(1)
- 14 to 16 labelled c_1(1)
- 14 to 32 labelled b_1(2)
- 14 to 35 labelled a_1(2)
- 14 to 37 labelled c_1(2)
- 16 to 17 labelled b_1(1)
- 17 to 18 labelled c_1(1)
- 18 to 2 labelled a_1(1)
- 18 to 11 labelled b_1(1)
- 18 to 14 labelled a_1(1)
- 18 to 16 labelled c_1(1)
- 18 to 32 labelled b_1(2)
- 18 to 35 labelled a_1(2)
- 18 to 37 labelled c_1(2)
- 20 to 12 labelled b_1(1)
- 20 to 33 labelled b_1(1)
- 19 to 20 labelled a_1(1)
- 21 to 22 labelled b_1(1)
- 22 to 23 labelled c_1(1)
- 23 to 12 labelled a_1(1)
- 23 to 24 labelled b_1(2)
- 23 to 27 labelled a_1(2)
- 23 to 29 labelled c_1(2)
- 23 to 33 labelled a_1(1)
- 23 to 32 labelled b_1(2)
- 23 to 35 labelled a_1(2)
- 23 to 37 labelled c_1(2)
- 23 to 40 labelled b_1(3)
- 23 to 43 labelled a_1(3)
- 23 to 45 labelled c_1(3)
- 26 to 2 labelled c_1(2)
- 24 to 25 labelled c_1(2)
- 25 to 26 labelled b_1(2)
- 27 to 28 labelled a_1(2)
- 27 to 11 labelled b_1(1)
- 27 to 14 labelled a_1(1)
- 27 to 16 labelled c_1(1)
- 27 to 32 labelled b_1(2)
- 27 to 35 labelled a_1(2)
- 27 to 37 labelled c_1(2)
- 28 to 2 labelled b_1(2)
- 31 to 2 labelled a_1(2)
- 31 to 11 labelled b_1(1)
- 31 to 14 labelled a_1(1)
- 31 to 16 labelled c_1(1)
- 31 to 32 labelled b_1(2)
- 31 to 35 labelled a_1(2)
- 31 to 37 labelled c_1(2)
- 30 to 31 labelled c_1(2)
- 29 to 30 labelled b_1(2)
- 34 to 12 labelled c_1(2)
- 34 to 33 labelled c_1(2)
- 32 to 33 labelled c_1(2)
- 33 to 34 labelled b_1(2)
- 35 to 36 labelled a_1(2)
- 36 to 12 labelled b_1(2)
- 36 to 33 labelled b_1(2)
- 39 to 12 labelled a_1(2)
- 39 to 33 labelled a_1(2)
- 39 to 24 labelled b_1(2)
- 39 to 27 labelled a_1(2)
- 39 to 29 labelled c_1(2)
- 39 to 40 labelled b_1(3)
- 39 to 43 labelled a_1(3)
- 39 to 45 labelled c_1(3)
- 39 to 32 labelled b_1(2)
- 39 to 35 labelled a_1(2)
- 39 to 37 labelled c_1(2)
- 38 to 39 labelled c_1(2)
- 37 to 38 labelled b_1(2)
- 41 to 42 labelled b_1(3)
- 42 to 33 labelled c_1(3)
- 42 to 12 labelled c_1(3)
- 40 to 41 labelled c_1(3)
- 44 to 33 labelled b_1(3)
- 44 to 12 labelled b_1(3)
- 43 to 44 labelled a_1(3)
- 45 to 46 labelled b_1(3)
- 46 to 47 labelled c_1(3)
- 47 to 33 labelled a_1(3)
- 47 to 12 labelled a_1(3)
- 47 to 40 labelled b_1(3)
- 47 to 43 labelled a_1(3)
- 47 to 45 labelled c_1(3)
- 47 to 24 labelled b_1(2)
- 47 to 27 labelled a_1(2)
- 47 to 29 labelled c_1(2)
- 47 to 32 labelled b_1(2)
- 47 to 35 labelled a_1(2)
- 47 to 37 labelled c_1(2)