TRS Relative pair #487081929

details

property	value
status	complete
benchmark	rt1-4.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n145.star.cs.uiowa.edu
space	Relative_05

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	1.84284 seconds
cpu usage	4.49158
user time	4.2641
system time	0.227483
max virtual memory	1.8677216E7
max residence set size	368556.0

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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 of the given RelTRS could be proven:

(0) RelTRS
(1) RelTRSRRRProof [EQUIVALENT, 76 ms]
(2) RelTRS
(3) RIsEmptyProof [EQUIVALENT, 0 ms]
(4) YES


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

(0)
Obligation:
Relative term rewrite system:
The relative TRS consists of the following R rules:

   f(el(x), y) -> f(x, el(y))

The relative TRS consists of the following S rules:

   f(x, y) -> f(l(x), y)
   f(x, y) -> f(x, r(y))
   l(el(x)) -> el(l(x))
   el(r(x)) -> r(el(x))


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

(1) RelTRSRRRProof (EQUIVALENT)
We used the following monotonic ordering for rule removal:
f/2(YES,YES)
el/1(YES)
l/1)YES(
r/1)YES(

Quasi precedence:
f_2 > el_1


Status:
f_2: [1,2]
el_1: [1]

With this ordering the following rules can be removed [MATRO] because they are oriented strictly:
Rules from R:

   f(el(x), y) -> f(x, el(y))
Rules from S:
none




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

(2)
Obligation:
Relative term rewrite system:
R is empty.
The relative TRS consists of the following S rules:

   f(x, y) -> f(l(x), y)
   f(x, y) -> f(x, r(y))
   l(el(x)) -> el(l(x))
   el(r(x)) -> r(el(x))


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

(3) RIsEmptyProof (EQUIVALENT)
The TRS R is empty. Hence, termination is trivially proven.
----------------------------------------

(4)
YES

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