SRS Standard pair #487083160

details

property	value
status	complete
benchmark	x02.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n143.star.cs.uiowa.edu
space	Secret_07_SRS

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	27.8663 seconds
cpu usage	102.325
user time	99.3971
system time	2.92743
max virtual memory	8.1129856E7
max residence set size	5059520.0

stage attributes

key	value
starexec-result	YES

output

YES
proof of /export/starexec/sandbox/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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) FlatCCProof [EQUIVALENT, 0 ms]
(2) QTRS
(3) RootLabelingProof [EQUIVALENT, 0 ms]
(4) QTRS
(5) QTRSRRRProof [EQUIVALENT, 199 ms]
(6) QTRS
(7) DependencyPairsProof [EQUIVALENT, 89 ms]
(8) QDP
(9) DependencyGraphProof [EQUIVALENT, 0 ms]
(10) QDP
(11) QDPOrderProof [EQUIVALENT, 4541 ms]
(12) QDP
(13) DependencyGraphProof [EQUIVALENT, 0 ms]
(14) TRUE


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

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

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

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job log

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