/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty


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

(0) QTRS
(1) RFCMatchBoundsTRSProof [EQUIVALENT, 27 ms]
(2) YES


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

   a(l(x1)) -> l(a(x1))
   a(c(x1)) -> c(a(x1))
   c(a(r(x1))) -> r(a(x1))
   l(r(a(x1))) -> a(l(c(c(r(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:

   a(l(x1)) -> l(a(x1))
   a(c(x1)) -> c(a(x1))
   c(a(r(x1))) -> r(a(x1))
   l(r(a(x1))) -> a(l(c(c(r(x1)))))

The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
1, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 19, 24, 25, 26, 27, 55, 56, 57, 58, 59, 60, 61

Node 1 is start node and node 3 is final node.

Those nodes are connected through the following edges:

* 1 to 4 labelled l_1(0), c_1(0), r_1(0)* 1 to 5 labelled a_1(0)* 1 to 9 labelled l_1(1)* 1 to 10 labelled r_1(1)* 1 to 13 labelled a_1(1)* 1 to 19 labelled l_1(2)* 3 to 3 labelled #_1(0)* 4 to 3 labelled a_1(0)* 4 to 10 labelled l_1(1), c_1(1), r_1(1)* 4 to 24 labelled a_1(2)* 4 to 55 labelled l_1(3)* 5 to 6 labelled l_1(0)* 6 to 7 labelled c_1(0)* 7 to 8 labelled c_1(0)* 8 to 3 labelled r_1(0)* 9 to 6 labelled a_1(1)* 9 to 11 labelled c_1(1)* 10 to 3 labelled a_1(1)* 10 to 10 labelled l_1(1), c_1(1), r_1(1)* 10 to 24 labelled a_1(2)* 10 to 55 labelled l_1(3)* 11 to 7 labelled a_1(1)* 11 to 12 labelled c_1(1)* 11 to 10 labelled r_1(1)* 12 to 8 labelled a_1(1)* 13 to 14 labelled l_1(1)* 14 to 15 labelled c_1(1)* 15 to 16 labelled c_1(1)* 16 to 3 labelled r_1(1)* 16 to 24 labelled r_1(1)* 19 to 14 labelled a_1(2)* 19 to 56 labelled c_1(2)* 24 to 25 labelled l_1(2)* 25 to 26 labelled c_1(2)* 26 to 27 labelled c_1(2)* 27 to 3 labelled r_1(2)* 27 to 24 labelled r_1(2)* 55 to 25 labelled a_1(3)* 55 to 57 labelled c_1(3)* 56 to 15 labelled a_1(2)* 56 to 58 labelled c_1(2)* 56 to 60 labelled r_1(2)* 56 to 4 labelled r_1(2)* 57 to 26 labelled a_1(3)* 57 to 59 labelled c_1(3)* 57 to 61 labelled r_1(3)* 58 to 16 labelled a_1(2)* 59 to 27 labelled a_1(3)* 60 to 3 labelled a_1(2)* 60 to 10 labelled l_1(1), c_1(1), r_1(1)* 60 to 24 labelled a_1(2)* 60 to 55 labelled l_1(3)* 61 to 3 labelled a_1(3)* 61 to 24 labelled a_1(3), a_1(2)* 61 to 10 labelled l_1(1), c_1(1), r_1(1)* 61 to 55 labelled l_1(3)


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(2)
YES