details

property	value
status	complete
benchmark	elimdupl.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	Rubio_04

run statistics

property	value
solver	AProVE
configuration	rcdcRelativeAlsoLower
runtime (wallclock)	291.519 seconds
cpu usage	636.911
user time	632.259
system time	4.65231
max virtual memory	5.661916E7
max residence set size	5759852.0

stage attributes

key	value
starexec-result	WORST_CASE(Omega(n^1), O(n^3))

output

WORST_CASE(Omega(n^1), O(n^3)) 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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(n^1, n^3). (0) DCpxTrs (1) DerivationalComplexityToRuntimeComplexityProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxRelTRS (3) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 186 ms] (4) CpxRelTRS (5) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms] (6) CdtProblem (7) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms] (8) CdtProblem (9) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms] (10) CdtProblem (11) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms] (12) CdtProblem (13) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 3 ms] (14) CdtProblem (15) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 195 ms] (16) CdtProblem (17) CdtRuleRemovalProof [UPPER BOUND(ADD(n^2)), 419 ms] (18) CdtProblem (19) CdtRuleRemovalProof [UPPER BOUND(ADD(n^2)), 565 ms] (20) CdtProblem (21) CdtRuleRemovalProof [UPPER BOUND(ADD(n^3)), 2887 ms] (22) CdtProblem (23) CdtRuleRemovalProof [UPPER BOUND(ADD(n^3)), 2780 ms] (24) CdtProblem (25) CdtRuleRemovalProof [UPPER BOUND(ADD(n^3)), 2630 ms] (26) CdtProblem (27) CdtRuleRemovalProof [UPPER BOUND(ADD(n^3)), 2522 ms] (28) CdtProblem (29) CdtRuleRemovalProof [UPPER BOUND(ADD(n^3)), 2366 ms] (30) CdtProblem (31) SIsEmptyProof [BOTH BOUNDS(ID, ID), 0 ms] (32) BOUNDS(1, 1) (33) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (34) CpxRelTRS (35) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (36) typed CpxTrs (37) OrderProof [LOWER BOUND(ID), 0 ms] (38) typed CpxTrs (39) RewriteLemmaProof [LOWER BOUND(ID), 305 ms] (40) BEST (41) proven lower bound (42) LowerBoundPropagationProof [FINISHED, 0 ms] (43) BOUNDS(n^1, INF) (44) typed CpxTrs (45) RewriteLemmaProof [LOWER BOUND(ID), 358 ms] (46) BOUNDS(1, INF) ---------------------------------------- (0) Obligation: The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(n^1, n^3). The TRS R consists of the following rules: eq(0, 0) -> true eq(0, s(X)) -> false eq(s(X), 0) -> false eq(s(X), s(Y)) -> eq(X, Y) rm(N, nil) -> nil rm(N, add(M, X)) -> ifrm(eq(N, M), N, add(M, X)) ifrm(true, N, add(M, X)) -> rm(N, X) ifrm(false, N, add(M, X)) -> add(M, rm(N, X)) purge(nil) -> nil purge(add(N, X)) -> add(N, purge(rm(N, X))) 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(true) -> true encArg(s(x_1)) -> s(encArg(x_1)) encArg(false) -> false encArg(nil) -> nil encArg(add(x_1, x_2)) -> add(encArg(x_1), encArg(x_2)) encArg(cons_eq(x_1, x_2)) -> eq(encArg(x_1), encArg(x_2)) encArg(cons_rm(x_1, x_2)) -> rm(encArg(x_1), encArg(x_2)) encArg(cons_ifrm(x_1, x_2, x_3)) -> ifrm(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_purge(x_1)) -> purge(encArg(x_1)) encode_eq(x_1, x_2) -> eq(encArg(x_1), encArg(x_2)) encode_0 -> 0 encode_true -> true encode_s(x_1) -> s(encArg(x_1)) encode_false -> false encode_rm(x_1, x_2) -> rm(encArg(x_1), encArg(x_2)) encode_nil -> nil 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