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


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


YES
proof of /export/starexec/sandbox/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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) Strip Symbols Proof [SOUND, 0 ms]
(2) QTRS
(3) RFCMatchBoundsTRSProof [EQUIVALENT, 1 ms]
(4) YES


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

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

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

Q is empty.

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

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

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

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

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

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

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

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

The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
3, 4, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38

Node 3 is start node and node 4 is final node.

Those nodes are connected through the following edges:

* 3 to 23 labelled a_1(0)* 4 to 4 labelled #_1(0)* 23 to 24 labelled b_1(0)* 24 to 25 labelled a_1(0)* 25 to 26 labelled a_1(0)* 26 to 27 labelled b_1(0)* 27 to 28 labelled b_1(0)* 27 to 31 labelled a_1(1)* 28 to 29 labelled a_1(0)* 29 to 30 labelled b_1(0)* 30 to 4 labelled b_1(0)* 30 to 31 labelled a_1(1)* 31 to 32 labelled b_1(1)* 32 to 33 labelled a_1(1)* 33 to 34 labelled a_1(1)* 34 to 35 labelled b_1(1)* 35 to 36 labelled b_1(1)* 35 to 31 labelled a_1(1)* 36 to 37 labelled a_1(1)* 37 to 38 labelled b_1(1)* 38 to 4 labelled b_1(1)* 38 to 31 labelled a_1(1)


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

(4)
YES