/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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) RFCMatchBoundsTRSProof [EQUIVALENT, 0 ms]
(2) YES


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

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

The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
1, 2, 3, 4, 5, 6, 7, 8, 9, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35

Node 1 is start node and node 2 is final node.

Those nodes are connected through the following edges:

* 1 to 3 labelled b_1(0)* 1 to 4 labelled a_1(0)* 1 to 7 labelled a_1(1)* 2 to 2 labelled #_1(0)* 3 to 2 labelled a_1(0)* 3 to 26 labelled b_1(1)* 3 to 27 labelled a_1(2)* 4 to 5 labelled a_1(0)* 5 to 6 labelled c_1(0)* 6 to 2 labelled b_1(0)* 6 to 7 labelled a_1(1)* 7 to 8 labelled a_1(1)* 8 to 9 labelled c_1(1)* 9 to 2 labelled b_1(1)* 9 to 7 labelled a_1(1)* 9 to 27 labelled b_1(1)* 9 to 30 labelled a_1(2)* 26 to 2 labelled a_1(1)* 26 to 26 labelled b_1(1)* 26 to 27 labelled a_1(2)* 27 to 28 labelled a_1(2)* 28 to 29 labelled c_1(2)* 29 to 2 labelled b_1(2)* 29 to 7 labelled a_1(1)* 29 to 27 labelled b_1(2)* 29 to 33 labelled a_1(3)* 30 to 31 labelled a_1(2)* 31 to 32 labelled c_1(2)* 32 to 28 labelled b_1(2)* 33 to 34 labelled a_1(3)* 34 to 35 labelled c_1(3)* 35 to 28 labelled b_1(3)


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(2)
YES