SRS Standard pair #516976360

details

property	value
status	complete
benchmark	random-402.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n175.star.cs.uiowa.edu
space	Waldmann_19

run statistics

property	value
solver	AProVE21
configuration	standard
runtime (wallclock)	6.69785094261 seconds
cpu usage	15.864107499
max memory	1.326620672E9

stage attributes

key	value
output-size	15441
starexec-result	YES

output

/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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished


Termination w.r.t. Q of the given QTRS could be proven:

(0) QTRS
(1) QTRS Reverse [EQUIVALENT, 0 ms]
(2) QTRS
(3) FlatCCProof [EQUIVALENT, 0 ms]
(4) QTRS
(5) RootLabelingProof [EQUIVALENT, 0 ms]
(6) QTRS
(7) QTRSRRRProof [EQUIVALENT, 45 ms]
(8) QTRS
(9) DependencyPairsProof [EQUIVALENT, 0 ms]
(10) QDP
(11) DependencyGraphProof [EQUIVALENT, 0 ms]
(12) AND
    (13) QDP
        (14) QDPOrderProof [EQUIVALENT, 78 ms]
        (15) QDP
        (16) PisEmptyProof [EQUIVALENT, 0 ms]
        (17) YES
    (18) QDP
        (19) UsableRulesProof [EQUIVALENT, 0 ms]
        (20) QDP
        (21) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (22) YES
    (23) QDP
        (24) UsableRulesProof [EQUIVALENT, 0 ms]
        (25) QDP
        (26) MNOCProof [EQUIVALENT, 0 ms]
        (27) QDP
        (28) QDPOrderProof [EQUIVALENT, 9 ms]
        (29) QDP
        (30) PisEmptyProof [EQUIVALENT, 0 ms]
        (31) YES


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

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

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

Q is empty.

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

(3) FlatCCProof (EQUIVALENT)
We used flat context closure [ROOTLAB]
As Q is empty the flat context closure was sound AND complete.

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

(4)
Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:

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

Q is empty.

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