details

property	value
status	complete
benchmark	Ex2_Luc03b_L.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n144.star.cs.uiowa.edu
space	Transformed_CSR_innermost_04

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	1.67075 seconds
cpu usage	3.5712
user time	3.42354
system time	0.147656
max virtual memory	1.8408912E7
max residence set size	229656.0

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSRRRProof [EQUIVALENT, 31 ms] (2) QTRS (3) RisEmptyProof [EQUIVALENT, 0 ms] (4) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: fst(0, Z) -> nil fst(s, cons(Y)) -> cons(Y) from(X) -> cons(X) add(0, X) -> X add(s, Y) -> s len(nil) -> 0 len(cons(X)) -> s The set Q consists of the following terms: fst(0, x0) fst(s, cons(x0)) from(x0) add(0, x0) add(s, x0) len(nil) len(cons(x0)) ---------------------------------------- (1) QTRSRRRProof (EQUIVALENT) Used ordering: Knuth-Bendix order [KBO] with precedence:nil > len_1 > s > add_2 > from_1 > cons_1 > 0 > fst_2 and weight map: 0=2 nil=1 s=3 cons_1=1 from_1=2 len_1=1 fst_2=0 add_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: fst(0, Z) -> nil fst(s, cons(Y)) -> cons(Y) from(X) -> cons(X) add(0, X) -> X add(s, Y) -> s len(nil) -> 0 len(cons(X)) -> s ---------------------------------------- (2) Obligation: Q restricted rewrite system: R is empty. The set Q consists of the following terms: fst(0, x0) fst(s, cons(x0)) from(x0) add(0, x0) add(s, x0) len(nil) len(cons(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