details

property	value
status	complete
benchmark	boolprog.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n051.star.cs.uiowa.edu
space	Frederiksen_Others

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	7.20279383659 seconds
cpu usage	25.583913255
max memory	4.380737536E9

stage attributes

key	value
output-size	22403
starexec-result	WORST_CASE(Omega(n^1), O(n^1))

output

/export/starexec/sandbox2/solver/bin/starexec_run_complexity /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- WORST_CASE(Omega(n^1), O(n^1)) proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). (0) CpxTRS (1) CpxTrsToCdtProof [UPPER BOUND(ID), 10 ms] (2) CdtProblem (3) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (4) CdtProblem (5) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms] (6) CdtProblem (7) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 92 ms] (8) CdtProblem (9) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 25 ms] (10) CdtProblem (11) CdtKnowledgeProof [FINISHED, 0 ms] (12) BOUNDS(1, 1) (13) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (14) TRS for Loop Detection (15) DecreasingLoopProof [LOWER BOUND(ID), 57 ms] (16) BEST (17) proven lower bound (18) LowerBoundPropagationProof [FINISHED, 0 ms] (19) BOUNDS(n^1, INF) (20) TRS for Loop Detection ---------------------------------------- (0) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). The TRS R consists of the following rules: f4(S(x''), S(x'), x3, x4, S(x)) -> f2(S(x''), x', x3, x4, x) f4(S(x'), 0, x3, x4, S(x)) -> f3(x', 0, x3, x4, x) f2(x1, x2, S(x''), S(x'), S(x)) -> f5(x1, x2, S(x''), x', x) f2(x1, x2, S(x'), 0, S(x)) -> f3(x1, x2, x', 0, x) f4(S(x'), S(x), x3, x4, 0) -> 0 f4(S(x), 0, x3, x4, 0) -> 0 f2(x1, x2, S(x'), S(x), 0) -> 0 f2(x1, x2, S(x), 0, 0) -> 0 f0(x1, S(x'), x3, S(x), x5) -> f1(x', S(x'), x, S(x), S(x)) f0(x1, S(x), x3, 0, x5) -> 0 f6(x1, x2, x3, x4, S(x)) -> f0(x1, x2, x4, x3, x) f5(x1, x2, x3, x4, S(x)) -> f6(x2, x1, x3, x4, x) f3(x1, x2, x3, x4, S(x)) -> f4(x1, x2, x4, x3, x) f1(x1, x2, x3, x4, S(x)) -> f2(x2, x1, x3, x4, x) f6(x1, x2, x3, x4, 0) -> 0 f5(x1, x2, x3, x4, 0) -> 0 f4(0, x2, x3, x4, x5) -> 0 f3(x1, x2, x3, x4, 0) -> 0 f2(x1, x2, 0, x4, x5) -> 0 f1(x1, x2, x3, x4, 0) -> 0 f0(x1, 0, x3, x4, x5) -> 0 S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (1) CpxTrsToCdtProof (UPPER BOUND(ID)) Converted Cpx (relative) TRS to CDT ---------------------------------------- (2) Obligation: Complexity Dependency Tuples Problem Rules: f4(S(z0), S(z1), z2, z3, S(z4)) -> f2(S(z0), z1, z2, z3, z4) f4(S(z0), 0, z1, z2, S(z3)) -> f3(z0, 0, z1, z2, z3) f4(S(z0), S(z1), z2, z3, 0) -> 0 f4(S(z0), 0, z1, z2, 0) -> 0 f4(0, z0, z1, z2, z3) -> 0 f2(z0, z1, S(z2), S(z3), S(z4)) -> f5(z0, z1, S(z2), z3, z4) f2(z0, z1, S(z2), 0, S(z3)) -> f3(z0, z1, z2, 0, z3) f2(z0, z1, S(z2), S(z3), 0) -> 0 f2(z0, z1, S(z2), 0, 0) -> 0 f2(z0, z1, 0, z2, z3) -> 0 f0(z0, S(z1), z2, S(z3), z4) -> f1(z1, S(z1), z3, S(z3), S(z3)) f0(z0, S(z1), z2, 0, z3) -> 0 f0(z0, 0, z1, z2, z3) -> 0 f6(z0, z1, z2, z3, S(z4)) -> f0(z0, z1, z3, z2, z4) f6(z0, z1, z2, z3, 0) -> 0 f5(z0, z1, z2, z3, S(z4)) -> f6(z1, z0, z2, z3, z4) f5(z0, z1, z2, z3, 0) -> 0 f3(z0, z1, z2, z3, S(z4)) -> f4(z0, z1, z3, z2, z4) f3(z0, z1, z2, z3, 0) -> 0 f1(z0, z1, z2, z3, S(z4)) -> f2(z1, z0, z2, z3, z4) popout

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

job log

popout

actions

all output return to Runti Compl Inner Rewri 22807