/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 0 ms]
(4) YES


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

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

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

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

Q is empty.

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

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

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

The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 27, 28, 29, 30, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79

Node 11 is start node and node 12 is final node.

Those nodes are connected through the following edges:

* 11 to 13 labelled a_1(0)* 11 to 16 labelled c_1(0)* 11 to 18 labelled a_1(0)* 12 to 12 labelled #_1(0)* 13 to 14 labelled b_1(0)* 13 to 27 labelled c_1(1)* 14 to 15 labelled a_1(0)* 14 to 70 labelled a_1(1)* 15 to 12 labelled b_1(0)* 15 to 29 labelled c_1(1)* 15 to 58 labelled a_1(1)* 16 to 17 labelled a_1(0)* 17 to 12 labelled c_1(0)* 18 to 19 labelled c_1(0)* 19 to 20 labelled b_1(0)* 19 to 56 labelled c_1(1)* 20 to 12 labelled a_1(0)* 20 to 61 labelled a_1(1)* 27 to 28 labelled a_1(1)* 28 to 14 labelled c_1(1)* 29 to 30 labelled a_1(1)* 30 to 12 labelled c_1(1)* 56 to 57 labelled a_1(1)* 57 to 20 labelled c_1(1)* 58 to 59 labelled b_1(1)* 58 to 64 labelled c_1(2)* 59 to 60 labelled a_1(1)* 59 to 75 labelled a_1(2)* 60 to 12 labelled b_1(1)* 60 to 66 labelled c_1(2)* 60 to 58 labelled a_1(1)* 61 to 62 labelled c_1(1)* 62 to 63 labelled b_1(1)* 62 to 68 labelled c_1(2)* 63 to 12 labelled a_1(1)* 63 to 61 labelled a_1(1)* 64 to 65 labelled a_1(2)* 65 to 59 labelled c_1(2)* 66 to 67 labelled a_1(2)* 67 to 12 labelled c_1(2)* 68 to 69 labelled a_1(2)* 69 to 63 labelled c_1(2)* 70 to 71 labelled c_1(1)* 71 to 72 labelled b_1(1)* 71 to 73 labelled c_1(2)* 72 to 58 labelled a_1(1)* 73 to 74 labelled a_1(2)* 74 to 72 labelled c_1(2)* 75 to 76 labelled c_1(2)* 76 to 77 labelled b_1(2)* 76 to 78 labelled c_1(3)* 77 to 58 labelled a_1(2)* 78 to 79 labelled a_1(3)* 79 to 77 labelled c_1(3)


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

(4)
YES