/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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished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(c(c(a(a(a(a(x1)))))))) -> a(a(a(a(a(b(c(c(a(a(b(c(c(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(a(a(a(c(c(b(a(x1)))))))) -> c(c(b(a(a(c(c(b(a(a(a(a(a(x1)))))))))))))

Q is empty.

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

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

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

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

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

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

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

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

The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
7, 8, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 263, 264, 265, 266, 267, 268, 269, 270, 271, 272, 273

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

Those nodes are connected through the following edges:

* 7 to 45 labelled c_1(0)* 8 to 8 labelled #_1(0)* 45 to 46 labelled c_1(0)* 46 to 47 labelled b_1(0)* 47 to 48 labelled a_1(0)* 48 to 49 labelled a_1(0)* 49 to 50 labelled c_1(0)* 50 to 51 labelled c_1(0)* 51 to 52 labelled b_1(0)* 52 to 53 labelled a_1(0)* 52 to 263 labelled c_1(1)* 53 to 54 labelled a_1(0)* 53 to 263 labelled c_1(1)* 54 to 55 labelled a_1(0)* 54 to 263 labelled c_1(1)* 55 to 8 labelled a_1(0)* 55 to 263 labelled c_1(1)* 263 to 264 labelled c_1(1)* 264 to 265 labelled b_1(1)* 265 to 266 labelled a_1(1)* 266 to 267 labelled a_1(1)* 267 to 268 labelled c_1(1)* 268 to 269 labelled c_1(1)* 269 to 270 labelled b_1(1)* 270 to 271 labelled a_1(1)* 270 to 263 labelled c_1(1)* 271 to 272 labelled a_1(1)* 271 to 263 labelled c_1(1)* 272 to 273 labelled a_1(1)* 272 to 263 labelled c_1(1)* 273 to 8 labelled a_1(1)* 273 to 263 labelled c_1(1)


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

(6)
YES