details

property	value
status	complete
benchmark	IJCAR_1.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	AProVE_04

run statistics

property	value
solver	AProVE
configuration	rcdcRelativeAlsoLower
runtime (wallclock)	291.722 seconds
cpu usage	1119.9
user time	1107.34
system time	12.5675
max virtual memory	5.6012476E7
max residence set size	1.4717292E7

stage attributes

key	value
starexec-result	WORST_CASE(Omega(n^1), O(n^2))

output

WORST_CASE(Omega(n^1), O(n^2)) proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(n^1, n^2). (0) DCpxTrs (1) DerivationalComplexityToRuntimeComplexityProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxRelTRS (3) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 161 ms] (4) CpxRelTRS (5) RelTrsToWeightedTrsProof [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) NarrowingProof [BOTH BOUNDS(ID, ID), 81 ms] (12) CpxTypedWeightedCompleteTrs (13) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (14) CpxRNTS (15) SimplificationProof [BOTH BOUNDS(ID, ID), 3 ms] (16) CpxRNTS (17) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 0 ms] (18) CpxRNTS (19) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (20) CpxRNTS (21) IntTrsBoundProof [UPPER BOUND(ID), 68 ms] (22) CpxRNTS (23) IntTrsBoundProof [UPPER BOUND(ID), 4 ms] (24) CpxRNTS (25) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (26) CpxRNTS (27) IntTrsBoundProof [UPPER BOUND(ID), 940 ms] (28) CpxRNTS (29) IntTrsBoundProof [UPPER BOUND(ID), 384 ms] (30) CpxRNTS (31) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (32) CpxRNTS (33) IntTrsBoundProof [UPPER BOUND(ID), 150 ms] (34) CpxRNTS (35) IntTrsBoundProof [UPPER BOUND(ID), 285 ms] (36) CpxRNTS (37) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (38) CpxRNTS (39) IntTrsBoundProof [UPPER BOUND(ID), 38 ms] (40) CpxRNTS (41) IntTrsBoundProof [UPPER BOUND(ID), 0 ms] (42) CpxRNTS (43) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (44) CpxRNTS (45) IntTrsBoundProof [UPPER BOUND(ID), 207 ms] (46) CpxRNTS (47) IntTrsBoundProof [UPPER BOUND(ID), 0 ms] (48) CpxRNTS (49) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (50) CpxRNTS (51) IntTrsBoundProof [UPPER BOUND(ID), 136 ms] (52) CpxRNTS (53) IntTrsBoundProof [UPPER BOUND(ID), 0 ms] (54) CpxRNTS (55) FinalProof [FINISHED, 0 ms] (56) BOUNDS(1, n^2) (57) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (58) TRS for Loop Detection (59) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] (60) BEST (61) proven lower bound (62) LowerBoundPropagationProof [FINISHED, 0 ms] (63) BOUNDS(n^1, INF) (64) TRS for Loop Detection ---------------------------------------- (0) Obligation: The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(n^1, n^2). The TRS R consists of the following rules: div(0, y) -> 0 div(x, y) -> quot(x, y, y) quot(0, s(y), z) -> 0 quot(s(x), s(y), z) -> quot(x, y, z) quot(x, 0, s(z)) -> s(div(x, s(z))) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (1) DerivationalComplexityToRuntimeComplexityProof (BOTH BOUNDS(ID, ID)) The following rules have been added to S to convert the given derivational complexity problem to a runtime complexity problem: encArg(0) -> 0 encArg(s(x_1)) -> s(encArg(x_1)) encArg(cons_div(x_1, x_2)) -> div(encArg(x_1), encArg(x_2)) encArg(cons_quot(x_1, x_2, x_3)) -> quot(encArg(x_1), encArg(x_2), encArg(x_3)) popout

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

job log

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actions

all output return to Derivational Complexity: TRS Innermost