/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 0 ms]
(4) 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) 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:

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

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

The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
2, 4, 12, 13, 14, 15, 16, 17, 18, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36

Node 2 is start node and node 4 is final node.

Those nodes are connected through the following edges:

* 2 to 12 labelled b_1(0)* 2 to 15 labelled c_1(0)* 2 to 16 labelled a_1(0)* 2 to 25 labelled c_1(1)* 4 to 4 labelled #_1(0)* 12 to 13 labelled a_1(0)* 13 to 14 labelled b_1(0)* 13 to 26 labelled c_1(1)* 14 to 4 labelled a_1(0)* 14 to 28 labelled b_1(1)* 14 to 31 labelled a_1(1)* 14 to 34 labelled c_1(2)* 15 to 4 labelled c_1(0)* 16 to 17 labelled b_1(0)* 16 to 27 labelled c_1(1)* 17 to 18 labelled c_1(0)* 18 to 4 labelled a_1(0)* 18 to 28 labelled b_1(1)* 18 to 31 labelled a_1(1)* 18 to 34 labelled c_1(2)* 25 to 12 labelled c_1(1)* 26 to 14 labelled c_1(1)* 27 to 17 labelled c_1(1)* 28 to 29 labelled a_1(1)* 29 to 30 labelled b_1(1)* 29 to 35 labelled c_1(2)* 30 to 4 labelled a_1(1)* 30 to 28 labelled b_1(1)* 30 to 31 labelled a_1(1)* 30 to 34 labelled c_1(2)* 31 to 32 labelled b_1(1)* 31 to 36 labelled c_1(2)* 32 to 33 labelled c_1(1)* 33 to 4 labelled a_1(1)* 33 to 28 labelled b_1(1)* 33 to 31 labelled a_1(1)* 33 to 34 labelled c_1(2)* 34 to 28 labelled c_1(2)* 35 to 30 labelled c_1(2)* 36 to 32 labelled c_1(2)


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(4)
YES