SRS Standard pair #516968902

details

property	value
status	complete
benchmark	z081.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n177.star.cs.uiowa.edu
space	Zantema_04

run statistics

property	value
solver	AProVE21
configuration	standard
runtime (wallclock)	4.88145589828 seconds
cpu usage	16.124446691
max memory	1.303830528E9

stage attributes

key	value
output-size	3988
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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished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) QTRSRRRProof [EQUIVALENT, 88 ms]
(2) QTRS
(3) DependencyPairsProof [EQUIVALENT, 0 ms]
(4) QDP
(5) DependencyGraphProof [EQUIVALENT, 0 ms]
(6) QDP
(7) MRRProof [EQUIVALENT, 33 ms]
(8) QDP
(9) PisEmptyProof [EQUIVALENT, 0 ms]
(10) YES


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

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

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

Q is empty.

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

(1) QTRSRRRProof (EQUIVALENT)
Used ordering:
Polynomial interpretation [POLO]:

   POL(a(x_1)) = x_1
   POL(b(x_1)) = 1 + x_1
   POL(c(x_1)) = 1 + x_1
   POL(d(x_1)) = 2 + x_1
With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:

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




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

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

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

Q is empty.

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

(3) DependencyPairsProof (EQUIVALENT)
Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem.
----------------------------------------

(4)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   C(d(x1)) -> D(c(x1))
   C(d(x1)) -> C(x1)
   C(d(b(x1))) -> D(c(c(x1)))
   C(d(b(x1))) -> C(c(x1))
   C(d(b(x1))) -> C(x1)
   C(b(x1)) -> D(a(x1))

The TRS R consists of the following rules:

   c(d(x1)) -> d(c(x1))
   c(d(b(x1))) -> d(c(c(x1)))

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