/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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:

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

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

The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
2, 4, 5, 6, 7, 8, 9, 10, 17, 18, 19, 20, 21, 22, 23, 24, 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 5 labelled a_1(0)* 2 to 7 labelled c_1(0)* 2 to 9 labelled a_1(0)* 2 to 19 labelled a_1(1)* 4 to 4 labelled #_1(0)* 5 to 6 labelled a_1(0)* 5 to 27 labelled a_1(1)* 6 to 4 labelled b_1(0)* 6 to 17 labelled c_1(1)* 6 to 21 labelled a_1(1)* 6 to 31 labelled a_1(2)* 7 to 8 labelled a_1(0)* 8 to 4 labelled c_1(0)* 9 to 10 labelled c_1(0)* 10 to 4 labelled a_1(0)* 10 to 23 labelled a_1(1)* 17 to 18 labelled a_1(1)* 18 to 4 labelled c_1(1)* 19 to 20 labelled c_1(1)* 20 to 6 labelled a_1(1)* 20 to 29 labelled a_1(2)* 20 to 27 labelled a_1(1)* 21 to 22 labelled a_1(1)* 21 to 29 labelled a_1(2)* 22 to 4 labelled b_1(1)* 22 to 25 labelled c_1(2)* 22 to 21 labelled a_1(1)* 22 to 31 labelled a_1(2)* 23 to 24 labelled c_1(1)* 24 to 4 labelled a_1(1)* 24 to 23 labelled a_1(1)* 25 to 26 labelled a_1(2)* 26 to 4 labelled c_1(2)* 27 to 28 labelled c_1(1)* 28 to 21 labelled a_1(1)* 28 to 31 labelled a_1(1), a_1(2)* 29 to 30 labelled c_1(2)* 30 to 21 labelled a_1(2)* 30 to 31 labelled a_1(2)* 30 to 33 labelled a_1(3)* 31 to 32 labelled c_1(2)* 32 to 22 labelled a_1(2)* 32 to 29 labelled a_1(2)* 32 to 35 labelled a_1(3)* 33 to 34 labelled c_1(3)* 34 to 29 labelled a_1(3)* 35 to 36 labelled c_1(3)* 36 to 31 labelled a_1(3)


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(4)
YES