/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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) RFCMatchBoundsTRSProof [EQUIVALENT, 2 ms]
(4) YES


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

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

   0(1(2(3(4(x1))))) -> 0(2(3(1(4(x1)))))
   0(5(1(2(3(4(x1)))))) -> 0(1(2(5(3(4(x1))))))
   0(5(1(2(3(4(x1)))))) -> 0(5(2(1(3(4(x1))))))
   0(5(1(2(3(4(x1)))))) -> 5(0(2(3(1(4(x1))))))
   0(5(2(3(1(4(x1)))))) -> 0(1(5(2(3(4(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:

   4(3(2(1(0(x1))))) -> 4(1(3(2(0(x1)))))
   4(3(2(1(5(0(x1)))))) -> 4(3(5(2(1(0(x1))))))
   4(3(2(1(5(0(x1)))))) -> 4(3(1(2(5(0(x1))))))
   4(3(2(1(5(0(x1)))))) -> 4(1(3(2(0(5(x1))))))
   4(1(3(2(5(0(x1)))))) -> 4(3(2(5(1(0(x1))))))

Q is empty.

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

(3) RFCMatchBoundsTRSProof (EQUIVALENT)
Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 0. This implies Q-termination of R.
The following rules were used to construct the certificate:

   4(3(2(1(0(x1))))) -> 4(1(3(2(0(x1)))))
   4(3(2(1(5(0(x1)))))) -> 4(3(5(2(1(0(x1))))))
   4(3(2(1(5(0(x1)))))) -> 4(3(1(2(5(0(x1))))))
   4(3(2(1(5(0(x1)))))) -> 4(1(3(2(0(5(x1))))))
   4(1(3(2(5(0(x1)))))) -> 4(3(2(5(1(0(x1))))))

The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42

Node 22 is start node and node 23 is final node.

Those nodes are connected through the following edges:

* 22 to 24 labelled 4_1(0)* 22 to 28 labelled 4_1(0)* 22 to 33 labelled 4_1(0)* 22 to 38 labelled 4_1(0)* 23 to 23 labelled #_1(0), 5_1(0)* 24 to 25 labelled 1_1(0)* 25 to 26 labelled 3_1(0)* 26 to 27 labelled 2_1(0)* 27 to 23 labelled 0_1(0)* 28 to 29 labelled 3_1(0)* 29 to 30 labelled 5_1(0)* 30 to 31 labelled 2_1(0)* 31 to 32 labelled 1_1(0)* 32 to 23 labelled 0_1(0)* 33 to 34 labelled 3_1(0)* 34 to 35 labelled 1_1(0)* 35 to 36 labelled 2_1(0)* 36 to 37 labelled 5_1(0)* 37 to 23 labelled 0_1(0)* 38 to 39 labelled 3_1(0)* 39 to 40 labelled 2_1(0)* 40 to 41 labelled 5_1(0)* 41 to 42 labelled 1_1(0)* 42 to 23 labelled 0_1(0)


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

(4)
YES