/export/starexec/sandbox2/solver/bin/starexec_run_standard /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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YES
proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished


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, 0 ms]
(4) YES


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

   a(b(x1)) -> b(a(x1))
   b(a(x1)) -> a(c(b(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(a(x1)) -> a(b(x1))
   a(b(x1)) -> b(c(a(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 2. This implies Q-termination of R.
The following rules were used to construct the certificate:

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

The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
3, 4, 8, 9, 10, 11, 12, 13, 14, 15

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

Those nodes are connected through the following edges:

* 3 to 8 labelled a_1(0)* 3 to 9 labelled b_1(0)* 3 to 11 labelled b_1(1)* 4 to 4 labelled #_1(0)* 8 to 4 labelled b_1(0)* 8 to 13 labelled a_1(1)* 8 to 14 labelled b_1(2)* 9 to 10 labelled c_1(0)* 10 to 4 labelled a_1(0)* 10 to 11 labelled b_1(1)* 11 to 12 labelled c_1(1)* 12 to 4 labelled a_1(1)* 12 to 11 labelled b_1(1)* 12 to 14 labelled a_1(1)* 13 to 4 labelled b_1(1)* 13 to 13 labelled a_1(1)* 13 to 14 labelled b_1(2)* 14 to 15 labelled c_1(2)* 15 to 4 labelled a_1(2)* 15 to 11 labelled b_1(1)* 15 to 14 labelled a_1(2)


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(4)
YES