SRS Standard pair #516976192

details

property	value
status	complete
benchmark	random-97.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n068.star.cs.uiowa.edu
space	Waldmann_19

run statistics

property	value
solver	AProVE21
configuration	standard
runtime (wallclock)	5.55952000618 seconds
cpu usage	18.657261755
max memory	1.316896768E9

stage attributes

key	value
output-size	17616
starexec-result	YES

output

/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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished


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

(0) QTRS
(1) FlatCCProof [EQUIVALENT, 0 ms]
(2) QTRS
(3) RootLabelingProof [EQUIVALENT, 0 ms]
(4) QTRS
(5) QTRSRRRProof [EQUIVALENT, 54 ms]
(6) QTRS
(7) DependencyPairsProof [EQUIVALENT, 0 ms]
(8) QDP
(9) DependencyGraphProof [EQUIVALENT, 0 ms]
(10) AND
    (11) QDP
        (12) QDPOrderProof [EQUIVALENT, 22 ms]
        (13) QDP
        (14) PisEmptyProof [EQUIVALENT, 0 ms]
        (15) YES
    (16) QDP
        (17) UsableRulesProof [EQUIVALENT, 2 ms]
        (18) QDP
        (19) MNOCProof [EQUIVALENT, 0 ms]
        (20) QDP
        (21) QDPOrderProof [EQUIVALENT, 3 ms]
        (22) QDP
        (23) PisEmptyProof [EQUIVALENT, 0 ms]
        (24) YES
    (25) QDP
        (26) QDPOrderProof [EQUIVALENT, 25 ms]
        (27) QDP
        (28) PisEmptyProof [EQUIVALENT, 0 ms]
        (29) YES


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

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

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

Q is empty.

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

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

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

(2)
Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:

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

Q is empty.

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

(3) RootLabelingProof (EQUIVALENT)
We used plain root labeling [ROOTLAB] with the following heuristic:
LabelAll: All function symbols get labeled

As Q is empty the root labeling was sound AND complete.

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

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

   a_{a_1}(a_{b_1}(b_{b_1}(b_{a_1}(x1)))) -> a_{a_1}(a_{a_1}(a_{b_1}(b_{a_1}(x1))))
   a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(x1)))) -> a_{a_1}(a_{a_1}(a_{b_1}(b_{b_1}(x1))))
   b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x1)))) -> b_{a_1}(a_{b_1}(b_{b_1}(b_{a_1}(x1))))
   b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x1)))) -> b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(x1))))

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