details

property	value
status	complete
benchmark	mergelists.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n140.star.cs.uiowa.edu
space	Frederiksen_Glenstrup

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	6.13698 seconds
cpu usage	18.7047
user time	17.4192
system time	1.28554
max virtual memory	1.9213028E7
max residence set size	3732092.0

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^1). (0) CpxRelTRS (1) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 164 ms] (2) CpxRelTRS (3) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (4) CpxWeightedTrs (5) CpxWeightedTrsRenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (6) CpxWeightedTrs (7) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (8) CpxTypedWeightedTrs (9) CompletionProof [UPPER BOUND(ID), 0 ms] (10) CpxTypedWeightedCompleteTrs (11) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (12) CpxRNTS (13) CompleteCoflocoProof [FINISHED, 154 ms] (14) BOUNDS(1, n^1) (15) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (16) CpxRelTRS (17) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (18) typed CpxTrs (19) OrderProof [LOWER BOUND(ID), 1 ms] (20) typed CpxTrs (21) RewriteLemmaProof [LOWER BOUND(ID), 286 ms] (22) typed CpxTrs (23) RewriteLemmaProof [LOWER BOUND(ID), 43 ms] (24) proven lower bound (25) LowerBoundPropagationProof [FINISHED, 0 ms] (26) BOUNDS(n^1, INF) ---------------------------------------- (0) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^1). The TRS R consists of the following rules: merge(Cons(x, xs), Nil) -> Cons(x, xs) merge(Cons(x', xs'), Cons(x, xs)) -> merge[Ite](<=(x', x), Cons(x', xs'), Cons(x, xs)) merge(Nil, ys) -> ys goal(xs, ys) -> merge(xs, ys) The (relative) TRS S consists of the following rules: <=(S(x), S(y)) -> <=(x, y) <=(0, y) -> True <=(S(x), 0) -> False merge[Ite](False, xs', Cons(x, xs)) -> Cons(x, merge(xs', xs)) merge[Ite](True, Cons(x, xs), ys) -> Cons(x, merge(xs, ys)) Rewrite Strategy: INNERMOST ---------------------------------------- (1) SInnermostTerminationProof (BOTH CONCRETE BOUNDS(ID, ID)) proved innermost termination of relative rules ---------------------------------------- (2) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^1). The TRS R consists of the following rules: merge(Cons(x, xs), Nil) -> Cons(x, xs) merge(Cons(x', xs'), Cons(x, xs)) -> merge[Ite](<=(x', x), Cons(x', xs'), Cons(x, xs)) merge(Nil, ys) -> ys goal(xs, ys) -> merge(xs, ys) The (relative) TRS S consists of the following rules: <=(S(x), S(y)) -> <=(x, y) <=(0, y) -> True <=(S(x), 0) -> False merge[Ite](False, xs', Cons(x, xs)) -> Cons(x, merge(xs', xs)) merge[Ite](True, Cons(x, xs), ys) -> Cons(x, merge(xs, ys)) Rewrite Strategy: INNERMOST ---------------------------------------- (3) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) Transformed relative TRS to weighted TRS ---------------------------------------- (4) 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: merge(Cons(x, xs), Nil) -> Cons(x, xs) [1] popout

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actions

all output return to Runtime Complexity: TRS Innermost