details

property	value
status	complete
benchmark	Ex6_Luc98_Z.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n180.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	1.86374 seconds
cpu usage	3.76584
user time	3.57667
system time	0.18917
max virtual memory	1.8343376E7
max residence set size	251460.0

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSRRRProof [EQUIVALENT, 65 ms] (2) QTRS (3) QTRSRRRProof [EQUIVALENT, 0 ms] (4) QTRS (5) QTRSRRRProof [EQUIVALENT, 1 ms] (6) QTRS (7) RisEmptyProof [EQUIVALENT, 0 ms] (8) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: first(0, X) -> nil first(s(X), cons(Y, Z)) -> cons(Y, n__first(X, activate(Z))) from(X) -> cons(X, n__from(s(X))) first(X1, X2) -> n__first(X1, X2) from(X) -> n__from(X) activate(n__first(X1, X2)) -> first(X1, X2) activate(n__from(X)) -> from(X) activate(X) -> X Q is empty. ---------------------------------------- (1) QTRSRRRProof (EQUIVALENT) Used ordering: Polynomial interpretation [POLO]: POL(0) = 0 POL(activate(x_1)) = 2*x_1 POL(cons(x_1, x_2)) = 1 + x_1 + x_2 POL(first(x_1, x_2)) = 2*x_1 + 2*x_2 POL(from(x_1)) = 2 + 2*x_1 POL(n__first(x_1, x_2)) = x_1 + x_2 POL(n__from(x_1)) = 1 + x_1 POL(nil) = 0 POL(s(x_1)) = x_1 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: first(s(X), cons(Y, Z)) -> cons(Y, n__first(X, activate(Z))) from(X) -> n__from(X) ---------------------------------------- (2) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: first(0, X) -> nil from(X) -> cons(X, n__from(s(X))) first(X1, X2) -> n__first(X1, X2) activate(n__first(X1, X2)) -> first(X1, X2) activate(n__from(X)) -> from(X) activate(X) -> X Q is empty. ---------------------------------------- (3) QTRSRRRProof (EQUIVALENT) Used ordering: Polynomial interpretation [POLO]: POL(0) = 0 POL(activate(x_1)) = 1 + 2*x_1 POL(cons(x_1, x_2)) = x_1 + x_2 POL(first(x_1, x_2)) = 2 + 2*x_1 + 2*x_2 POL(from(x_1)) = 1 + 2*x_1 POL(n__first(x_1, x_2)) = 2 + 2*x_1 + x_2 POL(n__from(x_1)) = x_1 POL(nil) = 1 POL(s(x_1)) = 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 from(X) -> cons(X, n__from(s(X))) activate(n__first(X1, X2)) -> first(X1, X2) activate(X) -> X popout

output may be truncated. 'popout' for the full output.

job log

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actions

all output return to TRS Standard