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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished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


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

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

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

Q is empty.

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

(1) QTRS Reverse (EQUIVALENT)
We applied the QTRS Reverse Processor [REVERSE].
----------------------------------------

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

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

Q is empty.

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

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

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

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

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

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

(4)
Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:

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

Q is empty.

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

(5) 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:

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

The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
7, 8, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82

Node 7 is start node and node 8 is final node.

Those nodes are connected through the following edges:

* 7 to 52 labelled b_1(0)* 8 to 8 labelled #_1(0)* 52 to 53 labelled a_1(0)* 53 to 54 labelled a_1(0)* 54 to 55 labelled b_1(0)* 55 to 56 labelled a_1(0)* 56 to 57 labelled b_1(0)* 57 to 58 labelled a_1(0)* 57 to 73 labelled b_1(1)* 58 to 59 labelled b_1(0)* 59 to 60 labelled a_1(0)* 59 to 73 labelled b_1(1)* 60 to 61 labelled b_1(0)* 61 to 8 labelled a_1(0)* 61 to 73 labelled b_1(1)* 73 to 74 labelled a_1(1)* 74 to 75 labelled a_1(1)* 75 to 76 labelled b_1(1)* 76 to 77 labelled a_1(1)* 77 to 78 labelled b_1(1)* 78 to 79 labelled a_1(1)* 78 to 73 labelled b_1(1)* 79 to 80 labelled b_1(1)* 80 to 81 labelled a_1(1)* 80 to 73 labelled b_1(1)* 81 to 82 labelled b_1(1)* 82 to 8 labelled a_1(1)* 82 to 73 labelled b_1(1)


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

(6)
YES