/export/starexec/sandbox2/solver/bin/starexec_run_standard /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


--------------------------------------------------------------------------------


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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished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) Strip Symbols Proof [SOUND, 0 ms]
(2) QTRS
(3) RFCMatchBoundsTRSProof [EQUIVALENT, 0 ms]
(4) YES


----------------------------------------

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

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

Q is empty.

----------------------------------------

(1) Strip Symbols Proof (SOUND)
We were given the following TRS:

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

By stripping symbols from the only rule of the system, we obtained the following TRS [ENDRULLIS]: 

   b(a(a(b(b(a(a(x))))))) -> a(a(b(b(a(a(b(a(a(b(x))))))))))

----------------------------------------

(2)
Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:

   b(a(a(b(b(a(a(x))))))) -> a(a(b(b(a(a(b(a(a(b(x))))))))))

Q is empty.

----------------------------------------

(3) RFCMatchBoundsTRSProof (EQUIVALENT)
Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 1. This implies Q-termination of R.
The following rules were used to construct the certificate:

   b(a(a(b(b(a(a(x))))))) -> a(a(b(b(a(a(b(a(a(b(x))))))))))

The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
5, 6, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56

Node 5 is start node and node 6 is final node.

Those nodes are connected through the following edges:

* 5 to 39 labelled a_1(0)* 6 to 6 labelled #_1(0)* 39 to 40 labelled a_1(0)* 40 to 41 labelled b_1(0)* 41 to 42 labelled b_1(0)* 42 to 43 labelled a_1(0)* 43 to 44 labelled a_1(0)* 44 to 45 labelled b_1(0)* 44 to 48 labelled a_1(1)* 45 to 46 labelled a_1(0)* 46 to 47 labelled a_1(0)* 47 to 6 labelled b_1(0)* 47 to 48 labelled a_1(1)* 48 to 49 labelled a_1(1)* 49 to 50 labelled b_1(1)* 50 to 51 labelled b_1(1)* 51 to 52 labelled a_1(1)* 52 to 53 labelled a_1(1)* 53 to 54 labelled b_1(1)* 53 to 48 labelled a_1(1)* 54 to 55 labelled a_1(1)* 55 to 56 labelled a_1(1)* 56 to 6 labelled b_1(1)* 56 to 48 labelled a_1(1)


----------------------------------------

(4)
YES