/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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished


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

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


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(0)
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(c(x1))
   a(a(x1)) -> a(c(b(a(x1))))

Q is empty.

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(1) 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(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:
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, 27, 28, 29

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)* 1 to 6 labelled c_1(0)* 1 to 7 labelled a_1(0)* 2 to 2 labelled #_1(0)* 3 to 4 labelled b_1(0)* 3 to 10 labelled c_1(1)* 4 to 5 labelled a_1(0)* 4 to 22 labelled a_1(1)* 5 to 2 labelled b_1(0)* 5 to 11 labelled c_1(1)* 5 to 13 labelled a_1(1)* 6 to 2 labelled c_1(0)* 7 to 8 labelled c_1(0)* 8 to 9 labelled b_1(0)* 8 to 12 labelled c_1(1)* 9 to 2 labelled a_1(0)* 9 to 16 labelled a_1(1)* 10 to 4 labelled c_1(1)* 11 to 2 labelled c_1(1)* 12 to 9 labelled c_1(1)* 13 to 14 labelled b_1(1)* 13 to 19 labelled c_1(2)* 14 to 15 labelled a_1(1)* 14 to 26 labelled a_1(2)* 15 to 2 labelled b_1(1)* 15 to 20 labelled c_1(2)* 15 to 13 labelled a_1(1)* 16 to 17 labelled c_1(1)* 17 to 18 labelled b_1(1)* 17 to 21 labelled c_1(2)* 18 to 2 labelled a_1(1)* 18 to 16 labelled a_1(1)* 19 to 14 labelled c_1(2)* 20 to 2 labelled c_1(2)* 21 to 18 labelled c_1(2)* 22 to 23 labelled c_1(1)* 23 to 24 labelled b_1(1)* 23 to 25 labelled c_1(2)* 24 to 13 labelled a_1(1)* 25 to 24 labelled c_1(2)* 26 to 27 labelled c_1(2)* 27 to 28 labelled b_1(2)* 27 to 29 labelled c_1(3)* 28 to 13 labelled a_1(2)* 29 to 28 labelled c_1(3)


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(2)
YES