YES
proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


Termination w.r.t. Q of the given QTRS could be proven:

(0) QTRS
(1) RFCMatchBoundsTRSProof [EQUIVALENT, 0 ms]
(2) YES


----------------------------------------

(0)
Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:

   c(a(b(a(b(x1))))) -> a(b(a(b(b(a(b(b(c(a(b(c(a(x1)))))))))))))

Q is empty.

----------------------------------------

(1) RFCMatchBoundsTRSProof (EQUIVALENT)
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:

   c(a(b(a(b(x1))))) -> a(b(a(b(b(a(b(b(c(a(b(c(a(x1)))))))))))))

The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 41, 42, 43, 44, 45, 46, 47, 49, 51, 53, 55, 57, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76

Node 1 is start node and node 2 is final node.

Those nodes are connected through the following edges:

* 1 to 3 labelled a_1(0)* 2 to 2 labelled #_1(0)* 3 to 4 labelled b_1(0)* 4 to 5 labelled a_1(0)* 5 to 6 labelled b_1(0)* 6 to 7 labelled b_1(0)* 7 to 8 labelled a_1(0)* 8 to 9 labelled b_1(0)* 9 to 10 labelled b_1(0)* 10 to 11 labelled c_1(0)* 10 to 41 labelled a_1(1)* 11 to 12 labelled a_1(0)* 12 to 13 labelled b_1(0)* 13 to 14 labelled c_1(0)* 13 to 15 labelled a_1(1)* 14 to 2 labelled a_1(0)* 15 to 16 labelled b_1(1)* 16 to 17 labelled a_1(1)* 17 to 18 labelled b_1(1)* 18 to 19 labelled b_1(1)* 19 to 20 labelled a_1(1)* 20 to 21 labelled b_1(1)* 21 to 22 labelled b_1(1)* 22 to 23 labelled c_1(1)* 22 to 65 labelled a_1(2)* 23 to 24 labelled a_1(1)* 24 to 25 labelled b_1(1)* 25 to 26 labelled c_1(1)* 25 to 15 labelled a_1(1)* 26 to 2 labelled a_1(1)* 41 to 42 labelled b_1(1)* 42 to 43 labelled a_1(1)* 43 to 44 labelled b_1(1)* 44 to 45 labelled b_1(1)* 45 to 46 labelled a_1(1)* 46 to 47 labelled b_1(1)* 47 to 49 labelled b_1(1)* 49 to 51 labelled c_1(1)* 51 to 53 labelled a_1(1)* 53 to 55 labelled b_1(1)* 55 to 57 labelled c_1(1)* 57 to 16 labelled a_1(1)* 65 to 66 labelled b_1(2)* 66 to 67 labelled a_1(2)* 67 to 68 labelled b_1(2)* 68 to 69 labelled b_1(2)* 69 to 70 labelled a_1(2)* 70 to 71 labelled b_1(2)* 71 to 72 labelled b_1(2)* 72 to 73 labelled c_1(2)* 73 to 74 labelled a_1(2)* 74 to 75 labelled b_1(2)* 75 to 76 labelled c_1(2)* 76 to 16 labelled a_1(2)


----------------------------------------

(2)
YES