SRS Standard pair #516974842

details

property	value
status	complete
benchmark	size-12-alpha-3-num-561.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n077.star.cs.uiowa.edu
space	Waldmann_07_size12

run statistics

property	value
solver	AProVE21
configuration	standard
runtime (wallclock)	5.35104393959 seconds
cpu usage	18.152738165
max memory	1.330884608E9

stage attributes

key	value
output-size	16332
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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished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) FlatCCProof [EQUIVALENT, 0 ms]
(2) QTRS
(3) RootLabelingProof [EQUIVALENT, 0 ms]
(4) QTRS
(5) QTRSRRRProof [EQUIVALENT, 77 ms]
(6) QTRS
(7) DependencyPairsProof [EQUIVALENT, 6 ms]
(8) QDP
(9) DependencyGraphProof [EQUIVALENT, 1 ms]
(10) AND
    (11) QDP
        (12) UsableRulesProof [EQUIVALENT, 0 ms]
        (13) QDP
        (14) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (15) YES
    (16) QDP
        (17) UsableRulesProof [EQUIVALENT, 0 ms]
        (18) QDP
        (19) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (20) YES
    (21) QDP
        (22) QDPOrderProof [EQUIVALENT, 23 ms]
        (23) QDP
        (24) PisEmptyProof [EQUIVALENT, 0 ms]
        (25) YES


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

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

   a(b(x1)) -> x1
   a(c(x1)) -> c(c(x1))
   b(c(x1)) -> a(b(a(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(x1))) -> a(x1)
   b(a(b(x1))) -> b(x1)
   c(a(b(x1))) -> c(x1)
   a(a(c(x1))) -> a(c(c(x1)))
   b(a(c(x1))) -> b(c(c(x1)))
   c(a(c(x1))) -> c(c(c(x1)))
   a(b(c(x1))) -> a(a(b(a(b(x1)))))
   b(b(c(x1))) -> b(a(b(a(b(x1)))))
   c(b(c(x1))) -> c(a(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_{a_1}(x1))) -> a_{a_1}(x1)
   a_{a_1}(a_{b_1}(b_{b_1}(x1))) -> a_{b_1}(x1)
   a_{a_1}(a_{b_1}(b_{c_1}(x1))) -> a_{c_1}(x1)
   b_{a_1}(a_{b_1}(b_{a_1}(x1))) -> b_{a_1}(x1)
   b_{a_1}(a_{b_1}(b_{b_1}(x1))) -> b_{b_1}(x1)
   b_{a_1}(a_{b_1}(b_{c_1}(x1))) -> b_{c_1}(x1)

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