details

property	value
status	complete
benchmark	Ex3_3_25_Bor03_L.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n139.star.cs.uiowa.edu
space	Transformed_CSR_innermost_04

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	1.63017 seconds
cpu usage	3.60021
user time	3.441
system time	0.15921
max virtual memory	1.8277608E7
max residence set size	230540.0

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSRRRProof [EQUIVALENT, 25 ms] (2) QTRS (3) RisEmptyProof [EQUIVALENT, 0 ms] (4) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: app(nil, YS) -> YS app(cons(X), YS) -> cons(X) from(X) -> cons(X) zWadr(nil, YS) -> nil zWadr(XS, nil) -> nil zWadr(cons(X), cons(Y)) -> cons(app(Y, cons(X))) prefix(L) -> cons(nil) The set Q consists of the following terms: app(nil, x0) app(cons(x0), x1) from(x0) zWadr(nil, x0) zWadr(x0, nil) zWadr(cons(x0), cons(x1)) prefix(x0) ---------------------------------------- (1) QTRSRRRProof (EQUIVALENT) Used ordering: Knuth-Bendix order [KBO] with precedence:nil > zWadr_2 > from_1 > prefix_1 > cons_1 > app_2 and weight map: nil=2 cons_1=1 from_1=1 prefix_1=2 app_2=0 zWadr_2=0 The variable weight is 1With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: app(nil, YS) -> YS app(cons(X), YS) -> cons(X) from(X) -> cons(X) zWadr(nil, YS) -> nil zWadr(XS, nil) -> nil zWadr(cons(X), cons(Y)) -> cons(app(Y, cons(X))) prefix(L) -> cons(nil) ---------------------------------------- (2) Obligation: Q restricted rewrite system: R is empty. The set Q consists of the following terms: app(nil, x0) app(cons(x0), x1) from(x0) zWadr(nil, x0) zWadr(x0, nil) zWadr(cons(x0), cons(x1)) prefix(x0) ---------------------------------------- (3) RisEmptyProof (EQUIVALENT) The TRS R is empty. Hence, termination is trivially proven. ---------------------------------------- (4) YES popout

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job log

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actions

all output return to TRS Innermost