/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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) QTRSRoofMatchBoundsTAProof [EQUIVALENT, 0 ms]
(4) YES


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

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

   f(X) -> g

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:

   f(X) -> g'(X)

Q is empty.

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

(3) QTRSRoofMatchBoundsTAProof (EQUIVALENT)
The TRS R could be shown to be Match-Bounded [TAB_LEFTLINEAR,TAB_NONLEFTLINEAR] by  1. Therefore it terminates.

The compatible tree automaton used to show the Match-Boundedness is represented by: 
final states : [0, 1]
transitions: 
f0(0) -> 0
f0(1) -> 0
g'0(0) -> 1
g'0(1) -> 1
g'1(0) -> 0
g'1(1) -> 0

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

(4)
YES