details

property	value
status	complete
benchmark	Ex6_Luc98.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n148.star.cs.uiowa.edu
space	CSR_04

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	2.01765 seconds
cpu usage	3.20284
user time	3.04335
system time	0.159498
max virtual memory	1.8341556E7
max residence set size	207564.0

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination of the given CSR could be proven: (0) CSR (1) CSRRRRProof [EQUIVALENT, 41 ms] (2) CSR (3) RisEmptyProof [EQUIVALENT, 0 ms] (4) YES ---------------------------------------- (0) Obligation: Context-sensitive rewrite system: The TRS R consists of the following rules: first(0, X) -> nil first(s(X), cons(Y, Z)) -> cons(Y, first(X, Z)) from(X) -> cons(X, from(s(X))) The replacement map contains the following entries: first: {1, 2} 0: empty set nil: empty set s: {1} cons: {1} from: {1} ---------------------------------------- (1) CSRRRRProof (EQUIVALENT) The following CSR is given: Context-sensitive rewrite system: The TRS R consists of the following rules: first(0, X) -> nil first(s(X), cons(Y, Z)) -> cons(Y, first(X, Z)) from(X) -> cons(X, from(s(X))) The replacement map contains the following entries: first: {1, 2} 0: empty set nil: empty set s: {1} cons: {1} from: {1} Used ordering: Polynomial interpretation [POLO]: POL(0) = 1 POL(cons(x_1, x_2)) = x_1 POL(first(x_1, x_2)) = 2 + 2*x_1 + x_2 POL(from(x_1)) = 1 + x_1 POL(nil) = 0 POL(s(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: first(0, X) -> nil first(s(X), cons(Y, Z)) -> cons(Y, first(X, Z)) from(X) -> cons(X, from(s(X))) ---------------------------------------- (2) Obligation: Context-sensitive rewrite system: R is empty. ---------------------------------------- (3) RisEmptyProof (EQUIVALENT) The CSR 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 Contextsensitive