/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 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, 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 2 is start node and node 22 is final node.

Those nodes are connected through the following edges:

* 2 to 23 labelled a_1(0)* 2 to 25 labelled c_1(0)* 2 to 27 labelled a_1(0)* 2 to 31 labelled a_1(1)* 22 to 22 labelled #_1(0)* 23 to 24 labelled a_1(0)* 23 to 39 labelled a_1(1)* 24 to 22 labelled b_1(0)* 24 to 29 labelled c_1(1)* 24 to 33 labelled a_1(1)* 24 to 43 labelled a_1(2)* 25 to 26 labelled a_1(0)* 26 to 22 labelled c_1(0)* 27 to 28 labelled c_1(0)* 28 to 22 labelled a_1(0)* 28 to 35 labelled a_1(1)* 29 to 30 labelled a_1(1)* 30 to 22 labelled c_1(1)* 31 to 32 labelled c_1(1)* 32 to 24 labelled a_1(1)* 32 to 41 labelled a_1(2)* 32 to 39 labelled a_1(1)* 33 to 34 labelled a_1(1)* 33 to 41 labelled a_1(2)* 34 to 22 labelled b_1(1)* 34 to 37 labelled c_1(2)* 34 to 33 labelled a_1(1)* 34 to 43 labelled a_1(2)* 35 to 36 labelled c_1(1)* 36 to 22 labelled a_1(1)* 36 to 35 labelled a_1(1)* 37 to 38 labelled a_1(2)* 38 to 22 labelled c_1(2)* 39 to 40 labelled c_1(1)* 40 to 33 labelled a_1(1)* 40 to 43 labelled a_1(1), a_1(2)* 41 to 42 labelled c_1(2)* 42 to 33 labelled a_1(2)* 42 to 43 labelled a_1(2)* 42 to 45 labelled a_1(3)* 43 to 44 labelled c_1(2)* 44 to 34 labelled a_1(2)* 44 to 41 labelled a_1(2)* 44 to 47 labelled a_1(3)* 45 to 46 labelled c_1(3)* 46 to 41 labelled a_1(3)* 47 to 48 labelled c_1(3)* 48 to 43 labelled a_1(3)


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(4)
YES