/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 8 ms]
(4) YES


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

   a(c(b(x1))) -> b(a(b(a(x1))))
   b(x1) -> c(a(c(x1)))
   a(a(x1)) -> a(b(c(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(c(a(x1))) -> a(b(a(b(x1))))
   b(x1) -> c(a(c(x1)))
   a(a(x1)) -> a(c(b(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 3. This implies Q-termination of R.
The following rules were used to construct the certificate:

   b(c(a(x1))) -> a(b(a(b(x1))))
   b(x1) -> c(a(c(x1)))
   a(a(x1)) -> a(c(b(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, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48

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 11 labelled c_1(0)* 3 to 13 labelled a_1(0)* 4 to 4 labelled #_1(0)* 8 to 9 labelled b_1(0)* 8 to 21 labelled c_1(1)* 9 to 10 labelled a_1(0)* 9 to 39 labelled a_1(1)* 10 to 4 labelled b_1(0)* 10 to 23 labelled c_1(1)* 10 to 27 labelled a_1(1)* 11 to 12 labelled a_1(0)* 12 to 4 labelled c_1(0)* 13 to 14 labelled c_1(0)* 14 to 15 labelled b_1(0)* 14 to 25 labelled c_1(1)* 15 to 4 labelled a_1(0)* 15 to 30 labelled a_1(1)* 21 to 22 labelled a_1(1)* 22 to 9 labelled c_1(1)* 23 to 24 labelled a_1(1)* 24 to 4 labelled c_1(1)* 25 to 26 labelled a_1(1)* 26 to 15 labelled c_1(1)* 27 to 28 labelled b_1(1)* 27 to 33 labelled c_1(2)* 28 to 29 labelled a_1(1)* 28 to 44 labelled a_1(2)* 29 to 4 labelled b_1(1)* 29 to 35 labelled c_1(2)* 29 to 27 labelled a_1(1)* 30 to 31 labelled c_1(1)* 31 to 32 labelled b_1(1)* 31 to 37 labelled c_1(2)* 32 to 4 labelled a_1(1)* 32 to 30 labelled a_1(1)* 33 to 34 labelled a_1(2)* 34 to 28 labelled c_1(2)* 35 to 36 labelled a_1(2)* 36 to 4 labelled c_1(2)* 37 to 38 labelled a_1(2)* 38 to 32 labelled c_1(2)* 39 to 40 labelled c_1(1)* 40 to 41 labelled b_1(1)* 40 to 42 labelled c_1(2)* 41 to 27 labelled a_1(1)* 42 to 43 labelled a_1(2)* 43 to 41 labelled c_1(2)* 44 to 45 labelled c_1(2)* 45 to 46 labelled b_1(2)* 45 to 47 labelled c_1(3)* 46 to 27 labelled a_1(2)* 47 to 48 labelled a_1(3)* 48 to 46 labelled c_1(3)


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(4)
YES