details

property	value
status	complete
benchmark	2.55.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n144.star.cs.uiowa.edu
space	SK90

run statistics

property	value
solver	AProVE
configuration	rcdcRelativeAlsoLower
runtime (wallclock)	291.538 seconds
cpu usage	315.762
user time	312.988
system time	2.77427
max virtual memory	1.8948976E7
max residence set size	5357664.0

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(n^1, n^2).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), 176 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), 0 ms] (12) CpxTypedWeightedCompleteTrs (13) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (14) CpxRNTS (15) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms] (16) CpxRNTS (17) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 0 ms] (18) CpxRNTS (19) ResultPropagationProof [UPPER BOUND(ID), 2 ms] (20) CpxRNTS (21) IntTrsBoundProof [UPPER BOUND(ID), 273 ms] (22) CpxRNTS (23) IntTrsBoundProof [UPPER BOUND(ID), 66 ms] (24) CpxRNTS (25) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (26) CpxRNTS (27) IntTrsBoundProof [UPPER BOUND(ID), 1186 ms] (28) CpxRNTS (29) IntTrsBoundProof [UPPER BOUND(ID), 1714 ms] (30) CpxRNTS (31) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (32) CpxRNTS (33) IntTrsBoundProof [UPPER BOUND(ID), 160 ms] (34) CpxRNTS (35) IntTrsBoundProof [UPPER BOUND(ID), 0 ms] (36) CpxRNTS (37) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (38) CpxRNTS (39) IntTrsBoundProof [UPPER BOUND(ID), 697 ms] (40) CpxRNTS (41) IntTrsBoundProof [UPPER BOUND(ID), 392 ms] (42) CpxRNTS (43) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (44) CpxRNTS (45) IntTrsBoundProof [UPPER BOUND(ID), 128 ms] (46) CpxRNTS (47) IntTrsBoundProof [UPPER BOUND(ID), 0 ms] (48) CpxRNTS (49) FinalProof [FINISHED, 0 ms] (50) BOUNDS(1, n^2) (51) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (52) TRS for Loop Detection (53) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] (54) BEST (55) proven lower bound (56) LowerBoundPropagationProof [FINISHED, 0 ms] (57) BOUNDS(n^1, INF) (58) 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: f(x, g(x)) -> x f(x, h(y)) -> f(h(x), y) 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(g(x_1)) -> g(encArg(x_1)) encArg(h(x_1)) -> h(encArg(x_1)) encArg(cons_f(x_1, x_2)) -> f(encArg(x_1), encArg(x_2)) encode_f(x_1, x_2) -> f(encArg(x_1), encArg(x_2)) encode_g(x_1) -> g(encArg(x_1)) encode_h(x_1) -> h(encArg(x_1)) ---------------------------------------- (2) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^2). popout

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

job log

popout

actions

all output return to Derivational Complexity: TRS Innermost