/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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) RFCMatchBoundsTRSProof [EQUIVALENT, 1 ms]
(4) YES


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

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

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

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

Q is empty.

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

(3) RFCMatchBoundsTRSProof (EQUIVALENT)
Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 2. This implies Q-termination of R.
The following rules were used to construct the certificate:

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

The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
2, 4, 13, 14, 15, 16, 17, 18, 19, 20

Node 2 is start node and node 4 is final node.

Those nodes are connected through the following edges:

* 2 to 13 labelled a_1(0)* 2 to 14 labelled b_1(0)* 2 to 16 labelled b_1(1)* 4 to 4 labelled #_1(0)* 13 to 4 labelled b_1(0)* 13 to 18 labelled a_1(1)* 13 to 19 labelled b_1(2)* 14 to 15 labelled c_1(0)* 15 to 4 labelled a_1(0)* 15 to 16 labelled b_1(1)* 16 to 17 labelled c_1(1)* 17 to 4 labelled a_1(1)* 17 to 16 labelled b_1(1)* 17 to 19 labelled a_1(1)* 18 to 4 labelled b_1(1)* 18 to 18 labelled a_1(1)* 18 to 19 labelled b_1(2)* 19 to 20 labelled c_1(2)* 20 to 4 labelled a_1(2)* 20 to 16 labelled b_1(1)* 20 to 19 labelled a_1(2)


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

(4)
YES