details

property	value
status	complete
benchmark	24.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	Beerendonk_07

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	17.6967 seconds
cpu usage	63.8047
user time	60.9794
system time	2.82531
max virtual memory	1.9263492E7
max residence set size	4350052.0

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/sandbox2/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).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) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (8) CpxTypedWeightedCompleteTrs (9) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (10) CpxRNTS (11) InliningProof [UPPER BOUND(ID), 585 ms] (12) CpxRNTS (13) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms] (14) CpxRNTS (15) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 0 ms] (16) CpxRNTS (17) ResultPropagationProof [UPPER BOUND(ID), 2 ms] (18) CpxRNTS (19) IntTrsBoundProof [UPPER BOUND(ID), 180 ms] (20) CpxRNTS (21) IntTrsBoundProof [UPPER BOUND(ID), 47 ms] (22) CpxRNTS (23) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (24) CpxRNTS (25) IntTrsBoundProof [UPPER BOUND(ID), 30 ms] (26) CpxRNTS (27) IntTrsBoundProof [UPPER BOUND(ID), 52 ms] (28) CpxRNTS (29) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (30) CpxRNTS (31) IntTrsBoundProof [UPPER BOUND(ID), 111 ms] (32) CpxRNTS (33) IntTrsBoundProof [UPPER BOUND(ID), 104 ms] (34) CpxRNTS (35) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (36) CpxRNTS (37) IntTrsBoundProof [UPPER BOUND(ID), 3301 ms] (38) CpxRNTS (39) IntTrsBoundProof [UPPER BOUND(ID), 1496 ms] (40) CpxRNTS (41) FinalProof [FINISHED, 0 ms] (42) BOUNDS(1, n^1) (43) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (44) TRS for Loop Detection (45) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] (46) BEST (47) proven lower bound (48) LowerBoundPropagationProof [FINISHED, 0 ms] (49) BOUNDS(n^1, INF) (50) TRS for Loop Detection ---------------------------------------- (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: cond1(true, x, y) -> cond2(gr(x, y), x, y) cond2(true, x, y) -> cond3(gr(x, 0), x, y) cond2(false, x, y) -> cond4(gr(y, 0), x, y) cond3(true, x, y) -> cond3(gr(x, 0), p(x), y) cond3(false, x, y) -> cond1(and(gr(x, 0), gr(y, 0)), x, y) cond4(true, x, y) -> cond4(gr(y, 0), x, p(y)) cond4(false, x, y) -> cond1(and(gr(x, 0), gr(y, 0)), x, y) gr(0, x) -> false gr(s(x), 0) -> true gr(s(x), s(y)) -> gr(x, y) and(true, true) -> true and(false, x) -> false and(x, false) -> false p(0) -> 0 p(s(x)) -> 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: popout

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

job log

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actions

all output return to Runtime Complexity: TRS Innermost