/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


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

Q is empty.

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

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

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

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

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

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

The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137

Node 91 is start node and node 92 is final node.

Those nodes are connected through the following edges:

* 91 to 93 labelled b_1(0)* 92 to 92 labelled #_1(0)* 93 to 94 labelled a_1(0)* 94 to 95 labelled b_1(0)* 95 to 96 labelled a_1(0)* 96 to 97 labelled b_1(0)* 97 to 98 labelled a_1(0)* 98 to 99 labelled b_1(0)* 99 to 100 labelled a_1(0)* 99 to 127 labelled b_1(1)* 100 to 101 labelled a_1(0)* 100 to 127 labelled b_1(1)* 101 to 102 labelled a_1(0)* 101 to 127 labelled b_1(1)* 102 to 103 labelled a_1(0)* 102 to 127 labelled b_1(1)* 103 to 92 labelled a_1(0)* 103 to 127 labelled b_1(1)* 127 to 128 labelled a_1(1)* 128 to 129 labelled b_1(1)* 129 to 130 labelled a_1(1)* 130 to 131 labelled b_1(1)* 131 to 132 labelled a_1(1)* 132 to 133 labelled b_1(1)* 133 to 134 labelled a_1(1)* 133 to 127 labelled b_1(1)* 134 to 135 labelled a_1(1)* 134 to 127 labelled b_1(1)* 135 to 136 labelled a_1(1)* 135 to 127 labelled b_1(1)* 136 to 137 labelled a_1(1)* 136 to 127 labelled b_1(1)* 137 to 92 labelled a_1(1)* 137 to 127 labelled b_1(1)


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

(6)
YES