TRS Standard pair #487068353

details

property	value
status	complete
benchmark	t000.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n178.star.cs.uiowa.edu
space	HirokawaMiddeldorp_04

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	2.53943 seconds
cpu usage	5.75105
user time	5.55738
system time	0.193664
max virtual memory	1.8413804E7
max residence set size	313736.0

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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) QTRSRRRProof [EQUIVALENT, 43 ms]
(2) QTRS
(3) RisEmptyProof [EQUIVALENT, 0 ms]
(4) YES


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

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

   +(0, 0) -> 0
   +(0, 1) -> 1
   +(0, 2) -> 2
   +(0, 3) -> 3
   +(0, 4) -> 4
   +(0, 5) -> 5
   +(0, 6) -> 6
   +(0, 7) -> 7
   +(0, 8) -> 8
   +(0, 9) -> 9
   +(1, 0) -> 1
   +(1, 1) -> 2
   +(1, 2) -> 3
   +(1, 3) -> 4
   +(1, 4) -> 5
   +(1, 5) -> 6
   +(1, 6) -> 7
   +(1, 7) -> 8
   +(1, 8) -> 9
   +(1, 9) -> c(1, 0)
   +(2, 0) -> 2
   +(2, 1) -> 3
   +(2, 2) -> 4
   +(2, 3) -> 5
   +(2, 4) -> 6
   +(2, 5) -> 7
   +(2, 6) -> 8
   +(2, 7) -> 9
   +(2, 8) -> c(1, 0)
   +(2, 9) -> c(1, 1)
   +(3, 0) -> 3
   +(3, 1) -> 4
   +(3, 2) -> 5
   +(3, 3) -> 6
   +(3, 4) -> 7
   +(3, 5) -> 8
   +(3, 6) -> 9
   +(3, 7) -> c(1, 0)
   +(3, 8) -> c(1, 1)
   +(3, 9) -> c(1, 2)
   +(4, 0) -> 4
   +(4, 1) -> 5
   +(4, 2) -> 6
   +(4, 3) -> 7
   +(4, 4) -> 8
   +(4, 5) -> 9
   +(4, 6) -> c(1, 0)
   +(4, 7) -> c(1, 1)
   +(4, 8) -> c(1, 2)
   +(4, 9) -> c(1, 3)
   +(5, 0) -> 5
   +(5, 1) -> 6
   +(5, 2) -> 7
   +(5, 3) -> 8
   +(5, 4) -> 9
   +(5, 5) -> c(1, 0)
   +(5, 6) -> c(1, 1)
   +(5, 7) -> c(1, 2)
   +(5, 8) -> c(1, 3)
   +(5, 9) -> c(1, 4)
   +(6, 0) -> 6
   +(6, 1) -> 7
   +(6, 2) -> 8
   +(6, 3) -> 9
   +(6, 4) -> c(1, 0)
   +(6, 5) -> c(1, 1)
   +(6, 6) -> c(1, 2)
   +(6, 7) -> c(1, 3)
   +(6, 8) -> c(1, 4)
   +(6, 9) -> c(1, 5)
   +(7, 0) -> 7
   +(7, 1) -> 8
   +(7, 2) -> 9
   +(7, 3) -> c(1, 0)
   +(7, 4) -> c(1, 1)
   +(7, 5) -> c(1, 2)
   +(7, 6) -> c(1, 3)
   +(7, 7) -> c(1, 4)
   +(7, 8) -> c(1, 5)

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