/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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished


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:
84, 86, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122

Node 84 is start node and node 86 is final node.

Those nodes are connected through the following edges:

* 84 to 97 labelled a_1(0)* 84 to 99 labelled c_1(0)* 84 to 101 labelled a_1(0)* 84 to 105 labelled a_1(1)* 86 to 86 labelled #_1(0)* 97 to 98 labelled a_1(0)* 97 to 113 labelled a_1(1)* 98 to 86 labelled b_1(0)* 98 to 103 labelled c_1(1)* 98 to 107 labelled a_1(1)* 98 to 117 labelled a_1(2)* 99 to 100 labelled a_1(0)* 100 to 86 labelled c_1(0)* 101 to 102 labelled c_1(0)* 102 to 86 labelled a_1(0)* 102 to 109 labelled a_1(1)* 103 to 104 labelled a_1(1)* 104 to 86 labelled c_1(1)* 105 to 106 labelled c_1(1)* 106 to 98 labelled a_1(1)* 106 to 115 labelled a_1(2)* 106 to 113 labelled a_1(1)* 107 to 108 labelled a_1(1)* 107 to 115 labelled a_1(2)* 108 to 86 labelled b_1(1)* 108 to 111 labelled c_1(2)* 108 to 107 labelled a_1(1)* 108 to 117 labelled a_1(2)* 109 to 110 labelled c_1(1)* 110 to 86 labelled a_1(1)* 110 to 109 labelled a_1(1)* 111 to 112 labelled a_1(2)* 112 to 86 labelled c_1(2)* 113 to 114 labelled c_1(1)* 114 to 107 labelled a_1(1)* 114 to 117 labelled a_1(1), a_1(2)* 115 to 116 labelled c_1(2)* 116 to 107 labelled a_1(2)* 116 to 117 labelled a_1(2)* 116 to 119 labelled a_1(3)* 117 to 118 labelled c_1(2)* 118 to 108 labelled a_1(2)* 118 to 115 labelled a_1(2)* 118 to 121 labelled a_1(3)* 119 to 120 labelled c_1(3)* 120 to 115 labelled a_1(3)* 121 to 122 labelled c_1(3)* 122 to 117 labelled a_1(3)


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(4)
YES