details

property	value
status	complete
benchmark	04.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	Various_04

run statistics

property	value
solver	AProVE
configuration	rcdcRelativeAlsoLower
runtime (wallclock)	291.636 seconds
cpu usage	969.733
user time	960.269
system time	9.46448
max virtual memory	3.8378512E7
max residence set size	1.4408824E7

stage attributes

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

output

WORST_CASE(?, O(n^1)) 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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(1, n^1). (0) DCpxTrs (1) DerivationalComplexityToRuntimeComplexityProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxRelTRS (3) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 949 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), 3 ms] (10) CdtProblem (11) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms] (12) CdtProblem (13) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 23 ms] (14) CdtProblem (15) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 110 ms] (16) CdtProblem (17) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (18) CdtProblem (19) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (20) CdtProblem (21) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (22) CdtProblem (23) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 2249 ms] (24) CdtProblem (25) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 2111 ms] (26) CdtProblem (27) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 1978 ms] (28) CdtProblem (29) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 2096 ms] (30) CdtProblem (31) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 2047 ms] (32) CdtProblem (33) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 2084 ms] (34) CdtProblem (35) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 2105 ms] (36) CdtProblem (37) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 2064 ms] (38) CdtProblem (39) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 2057 ms] (40) CdtProblem (41) SIsEmptyProof [BOTH BOUNDS(ID, ID), 0 ms] (42) BOUNDS(1, 1) ---------------------------------------- (0) Obligation: The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(1, n^1). The TRS R consists of the following rules: f1 -> g1 f1 -> g2 f2 -> g1 f2 -> g2 g1 -> h1 g1 -> h2 g2 -> h1 g2 -> h2 h1 -> i h2 -> i e1(h1, h2, x, y, z) -> e2(x, x, y, z, z) e1(x1, x1, x, y, z) -> e5(x1, x, y, z) e2(f1, x, y, z, f2) -> e3(x, y, x, y, y, z, y, z, x, y, z) e2(x, x, y, z, z) -> e6(x, y, z) e2(i, x, y, z, i) -> e6(x, y, z) e3(x1, x1, x2, x2, x3, x3, x4, x4, x, y, z) -> e4(x1, x1, x2, x2, x3, x3, x4, x4, x, y, z) e3(x, y, x, y, y, z, y, z, x, y, z) -> e6(x, y, z) e4(g1, x1, g2, x1, g1, x1, g2, x1, x, y, z) -> e1(x1, x1, x, y, z) e4(i, x1, i, x1, i, x1, i, x1, x, y, z) -> e5(x1, x, y, z) e4(x, x, x, x, x, x, x, x, x, x, x) -> e6(x, x, x) e5(i, x, y, z) -> e6(x, y, 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(i) -> i encArg(e6(x_1, x_2, x_3)) -> e6(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_f1) -> f1 encArg(cons_f2) -> f2 encArg(cons_g1) -> g1 encArg(cons_g2) -> g2 encArg(cons_h1) -> h1 encArg(cons_h2) -> h2 encArg(cons_e1(x_1, x_2, x_3, x_4, x_5)) -> e1(encArg(x_1), encArg(x_2), encArg(x_3), encArg(x_4), encArg(x_5)) encArg(cons_e2(x_1, x_2, x_3, x_4, x_5)) -> e2(encArg(x_1), encArg(x_2), encArg(x_3), encArg(x_4), encArg(x_5)) popout

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

job log

popout

actions

all output return to Derivational Complexity: TRS Innermost