details

property	value
status	complete
benchmark	Ex15_Luc98_GM.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n151.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	7.37994 seconds
cpu usage	18.8452
user time	17.6205
system time	1.22468
max virtual memory	3.7248668E7
max residence set size	3824224.0

stage attributes

key	value
starexec-result	WORST_CASE(Omega(n^1), O(n^1))

output

WORST_CASE(Omega(n^1), O(n^1)) proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). (0) CpxTRS (1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxWeightedTrs (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (4) CpxTypedWeightedTrs (5) CompletionProof [UPPER BOUND(ID), 0 ms] (6) CpxTypedWeightedCompleteTrs (7) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 5 ms] (8) CpxRNTS (9) CompleteCoflocoProof [FINISHED, 483 ms] (10) BOUNDS(1, n^1) (11) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (12) CpxTRS (13) SlicingProof [LOWER BOUND(ID), 0 ms] (14) CpxTRS (15) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (16) typed CpxTrs (17) OrderProof [LOWER BOUND(ID), 0 ms] (18) typed CpxTrs (19) RewriteLemmaProof [LOWER BOUND(ID), 1690 ms] (20) proven lower bound (21) LowerBoundPropagationProof [FINISHED, 0 ms] (22) BOUNDS(n^1, INF) ---------------------------------------- (0) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). The TRS R consists of the following rules: a__and(true, X) -> mark(X) a__and(false, Y) -> false a__if(true, X, Y) -> mark(X) a__if(false, X, Y) -> mark(Y) a__add(0, X) -> mark(X) a__add(s(X), Y) -> s(add(X, Y)) a__first(0, X) -> nil a__first(s(X), cons(Y, Z)) -> cons(Y, first(X, Z)) a__from(X) -> cons(X, from(s(X))) mark(and(X1, X2)) -> a__and(mark(X1), X2) mark(if(X1, X2, X3)) -> a__if(mark(X1), X2, X3) mark(add(X1, X2)) -> a__add(mark(X1), X2) mark(first(X1, X2)) -> a__first(mark(X1), mark(X2)) mark(from(X)) -> a__from(X) mark(true) -> true mark(false) -> false mark(0) -> 0 mark(s(X)) -> s(X) mark(nil) -> nil mark(cons(X1, X2)) -> cons(X1, X2) a__and(X1, X2) -> and(X1, X2) a__if(X1, X2, X3) -> if(X1, X2, X3) a__add(X1, X2) -> add(X1, X2) a__first(X1, X2) -> first(X1, X2) a__from(X) -> from(X) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) Transformed relative TRS to weighted TRS ---------------------------------------- (2) Obligation: The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^1). The TRS R consists of the following rules: a__and(true, X) -> mark(X) [1] a__and(false, Y) -> false [1] a__if(true, X, Y) -> mark(X) [1] a__if(false, X, Y) -> mark(Y) [1] a__add(0, X) -> mark(X) [1] a__add(s(X), Y) -> s(add(X, Y)) [1] a__first(0, X) -> nil [1] a__first(s(X), cons(Y, Z)) -> cons(Y, first(X, Z)) [1] a__from(X) -> cons(X, from(s(X))) [1] mark(and(X1, X2)) -> a__and(mark(X1), X2) [1] mark(if(X1, X2, X3)) -> a__if(mark(X1), X2, X3) [1] mark(add(X1, X2)) -> a__add(mark(X1), X2) [1] mark(first(X1, X2)) -> a__first(mark(X1), mark(X2)) [1] mark(from(X)) -> a__from(X) [1] mark(true) -> true [1] mark(false) -> false [1] mark(0) -> 0 [1] mark(s(X)) -> s(X) [1] popout

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

job log

popout

actions

all output return to Runtime Complexity: TRS Innermost