/export/starexec/sandbox/solver/bin/starexec_run_standard /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files


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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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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) QTRS Reverse [EQUIVALENT, 0 ms]
(2) QTRS
(3) RFCMatchBoundsTRSProof [EQUIVALENT, 10 ms]
(4) YES


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(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.

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(1) QTRS Reverse (EQUIVALENT)
We applied the QTRS Reverse Processor [REVERSE].
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(2)
Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:

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

Q is empty.

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(3) 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:

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

The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
3, 4, 10, 11, 12, 13, 14, 15, 17, 19, 21, 22, 27, 29, 31, 33, 34, 37, 39, 41, 43, 44, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84

Node 3 is start node and node 4 is final node.

Those nodes are connected through the following edges:

* 3 to 10 labelled a_1(0)* 4 to 4 labelled #_1(0)* 10 to 11 labelled a_1(0)* 11 to 12 labelled a_1(0)* 12 to 13 labelled b_1(0)* 12 to 27 labelled a_1(1)* 13 to 14 labelled b_1(0)* 13 to 15 labelled a_1(1)* 14 to 4 labelled b_1(0)* 14 to 15 labelled a_1(1)* 15 to 17 labelled a_1(1)* 17 to 19 labelled a_1(1)* 19 to 21 labelled b_1(1)* 19 to 37 labelled a_1(2)* 21 to 22 labelled b_1(1)* 21 to 15 labelled a_1(1)* 22 to 4 labelled b_1(1)* 22 to 15 labelled a_1(1)* 27 to 29 labelled a_1(1)* 29 to 31 labelled a_1(1)* 31 to 33 labelled b_1(1)* 33 to 34 labelled b_1(1)* 33 to 50 labelled a_1(2)* 34 to 17 labelled b_1(1)* 37 to 39 labelled a_1(2)* 39 to 41 labelled a_1(2)* 41 to 43 labelled b_1(2)* 43 to 44 labelled b_1(2)* 43 to 50 labelled a_1(2)* 44 to 17 labelled b_1(2)* 50 to 51 labelled a_1(2)* 51 to 52 labelled a_1(2)* 52 to 53 labelled b_1(2)* 53 to 54 labelled b_1(2)* 53 to 55 labelled a_1(3)* 54 to 37 labelled b_1(2)* 55 to 56 labelled a_1(3)* 56 to 57 labelled a_1(3)* 57 to 58 labelled b_1(3)* 57 to 80 labelled a_1(4)* 58 to 59 labelled b_1(3)* 59 to 41 labelled b_1(3)* 59 to 75 labelled a_1(3)* 75 to 76 labelled a_1(3)* 76 to 77 labelled a_1(3)* 77 to 78 labelled b_1(3)* 78 to 79 labelled b_1(3)* 79 to 51 labelled b_1(3)* 80 to 81 labelled a_1(4)* 81 to 82 labelled a_1(4)* 82 to 83 labelled b_1(4)* 83 to 84 labelled b_1(4)* 84 to 76 labelled b_1(4)


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(4)
YES