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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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:

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

Q is empty.

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

(1) RFCMatchBoundsTRSProof (EQUIVALENT)
Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 4. This implies Q-termination of R.
The following rules were used to construct the certificate:

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

The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
1, 2, 5, 8, 9, 11, 13, 16, 18, 20, 22, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 50, 51, 52, 53, 54, 60, 61, 62, 63, 64

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

Those nodes are connected through the following edges:

* 1 to 5 labelled b_1(0)* 2 to 2 labelled #_1(0)* 5 to 8 labelled b_1(0)* 8 to 9 labelled b_1(0)* 9 to 11 labelled a_1(0)* 9 to 25 labelled b_1(1)* 11 to 13 labelled a_1(0)* 11 to 16 labelled b_1(1)* 13 to 2 labelled a_1(0)* 13 to 16 labelled b_1(1)* 16 to 18 labelled b_1(1)* 18 to 20 labelled b_1(1)* 20 to 22 labelled a_1(1)* 20 to 30 labelled b_1(2)* 22 to 24 labelled a_1(1)* 22 to 16 labelled b_1(1)* 24 to 2 labelled a_1(1)* 24 to 16 labelled b_1(1)* 25 to 26 labelled b_1(1)* 26 to 27 labelled b_1(1)* 27 to 28 labelled a_1(1)* 28 to 29 labelled a_1(1)* 28 to 35 labelled b_1(2)* 29 to 18 labelled a_1(1)* 30 to 31 labelled b_1(2)* 31 to 32 labelled b_1(2)* 32 to 33 labelled a_1(2)* 33 to 34 labelled a_1(2)* 33 to 35 labelled b_1(2)* 34 to 18 labelled a_1(2)* 35 to 36 labelled b_1(2)* 36 to 37 labelled b_1(2)* 37 to 38 labelled a_1(2)* 38 to 39 labelled a_1(2)* 38 to 40 labelled b_1(3)* 39 to 30 labelled a_1(2)* 40 to 41 labelled b_1(3)* 41 to 42 labelled b_1(3)* 42 to 43 labelled a_1(3)* 42 to 60 labelled b_1(4)* 43 to 44 labelled a_1(3)* 44 to 32 labelled a_1(3)* 44 to 50 labelled b_1(3)* 50 to 51 labelled b_1(3)* 51 to 52 labelled b_1(3)* 52 to 53 labelled a_1(3)* 53 to 54 labelled a_1(3)* 54 to 36 labelled a_1(3)* 60 to 61 labelled b_1(4)* 61 to 62 labelled b_1(4)* 62 to 63 labelled a_1(4)* 63 to 64 labelled a_1(4)* 64 to 51 labelled a_1(4)


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

(2)
YES