details

property	value
status	complete
benchmark	t011.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n149.star.cs.uiowa.edu
space	HirokawaMiddeldorp_04

run statistics

property	value
solver	AProVE
configuration	rcdcRelativeAlsoLower
runtime (wallclock)	291.547 seconds
cpu usage	325.886
user time	322.926
system time	2.95989
max virtual memory	1.9148236E7
max residence set size	5249912.0

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/sandbox/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(n^1, n^2).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), 157 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), 0 ms] (20) CpxRNTS (21) IntTrsBoundProof [UPPER BOUND(ID), 476 ms] (22) CpxRNTS (23) IntTrsBoundProof [UPPER BOUND(ID), 162 ms] (24) CpxRNTS (25) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (26) CpxRNTS (27) IntTrsBoundProof [UPPER BOUND(ID), 2847 ms] (28) CpxRNTS (29) IntTrsBoundProof [UPPER BOUND(ID), 5225 ms] (30) CpxRNTS (31) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (32) CpxRNTS (33) IntTrsBoundProof [UPPER BOUND(ID), 1197 ms] (34) CpxRNTS (35) IntTrsBoundProof [UPPER BOUND(ID), 808 ms] (36) CpxRNTS (37) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (38) CpxRNTS (39) IntTrsBoundProof [UPPER BOUND(ID), 187 ms] (40) CpxRNTS (41) IntTrsBoundProof [UPPER BOUND(ID), 2 ms] (42) CpxRNTS (43) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (44) CpxRNTS (45) IntTrsBoundProof [UPPER BOUND(ID), 1249 ms] (46) CpxRNTS (47) IntTrsBoundProof [UPPER BOUND(ID), 805 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, 1 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: g(f(x), y) -> f(h(x, y)) h(x, y) -> g(x, f(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(f(x_1)) -> f(encArg(x_1)) encArg(cons_g(x_1, x_2)) -> g(encArg(x_1), encArg(x_2)) encArg(cons_h(x_1, x_2)) -> h(encArg(x_1), encArg(x_2)) encode_g(x_1, x_2) -> g(encArg(x_1), encArg(x_2)) encode_f(x_1) -> f(encArg(x_1)) encode_h(x_1, x_2) -> h(encArg(x_1), encArg(x_2)) ---------------------------------------- (2) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^2). popout

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job log

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actions

all output return to Derivational Complexity: TRS Innermost