SRS Standard pair #487089364

details

property	value
status	complete
benchmark	jambox1.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n149.star.cs.uiowa.edu
space	Secret_05_SRS

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	7.67128 seconds
cpu usage	27.0953
user time	25.9178
system time	1.17753
max virtual memory	3.9790024E7
max residence set size	3544548.0

stage attributes

key	value
starexec-result	YES

output

YES
proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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) FlatCCProof [EQUIVALENT, 0 ms]
(4) QTRS
(5) RootLabelingProof [EQUIVALENT, 0 ms]
(6) QTRS
(7) QTRSRRRProof [EQUIVALENT, 39 ms]
(8) QTRS
(9) DependencyPairsProof [EQUIVALENT, 4 ms]
(10) QDP
(11) DependencyGraphProof [EQUIVALENT, 0 ms]
(12) AND
    (13) QDP
        (14) UsableRulesProof [EQUIVALENT, 0 ms]
        (15) QDP
        (16) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (17) YES
    (18) QDP
        (19) QDPOrderProof [EQUIVALENT, 797 ms]
        (20) QDP
        (21) QDPOrderProof [EQUIVALENT, 20 ms]
        (22) QDP
        (23) QDPOrderProof [EQUIVALENT, 5 ms]
        (24) QDP
        (25) PisEmptyProof [EQUIVALENT, 0 ms]
        (26) YES


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

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

   a(c(x1)) -> a(x1)
   a(c(b(c(x1)))) -> c(b(c(c(x1))))
   c(x1) -> 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:

   c(a(x1)) -> a(x1)
   c(b(c(a(x1)))) -> c(c(b(c(x1))))
   c(x1) -> a(a(b(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:

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

Q is empty.

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

(5) 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.

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(6)

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