/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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(b(x1)) -> b(a(a(x1)))
   b(c(x1)) -> c(b(x1))
   a(a(x1)) -> a(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(a(x1)) -> a(a(b(x1)))
   c(b(x1)) -> b(c(x1))
   a(a(x1)) -> a(c(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(a(x1)) -> a(a(b(x1)))
   c(b(x1)) -> b(c(x1))
   a(a(x1)) -> a(c(a(x1)))

The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146

Node 123 is start node and node 124 is final node.

Those nodes are connected through the following edges:

* 123 to 125 labelled a_1(0)* 123 to 127 labelled b_1(0)* 123 to 128 labelled a_1(0)* 123 to 130 labelled a_1(1)* 124 to 124 labelled #_1(0)* 125 to 126 labelled a_1(0)* 125 to 137 labelled a_1(1)* 126 to 124 labelled b_1(0)* 126 to 132 labelled a_1(1)* 126 to 141 labelled a_1(2)* 127 to 124 labelled c_1(0)* 127 to 134 labelled b_1(1)* 128 to 129 labelled c_1(0)* 129 to 124 labelled a_1(0)* 129 to 135 labelled a_1(1)* 130 to 131 labelled c_1(1)* 131 to 126 labelled a_1(1)* 131 to 139 labelled a_1(2)* 131 to 137 labelled a_1(1)* 132 to 133 labelled a_1(1)* 132 to 139 labelled a_1(2)* 133 to 124 labelled b_1(1)* 133 to 132 labelled a_1(1)* 133 to 141 labelled a_1(2)* 134 to 124 labelled c_1(1)* 134 to 134 labelled b_1(1)* 135 to 136 labelled c_1(1)* 136 to 124 labelled a_1(1)* 136 to 135 labelled a_1(1)* 137 to 138 labelled c_1(1)* 138 to 132 labelled a_1(1)* 138 to 141 labelled a_1(1), a_1(2)* 139 to 140 labelled c_1(2)* 140 to 132 labelled a_1(2)* 140 to 141 labelled a_1(2)* 140 to 143 labelled a_1(3)* 141 to 142 labelled c_1(2)* 142 to 133 labelled a_1(2)* 142 to 139 labelled a_1(2)* 142 to 145 labelled a_1(3)* 143 to 144 labelled c_1(3)* 144 to 139 labelled a_1(3)* 145 to 146 labelled c_1(3)* 146 to 141 labelled a_1(3)


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

(4)
YES