details

property	value
status	complete
benchmark	perfect.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n027.star.cs.uiowa.edu
space	Mixed_TRS

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	5.56392812729 seconds
cpu usage	18.950868573
max memory	4.159803392E9

stage attributes

key	value
output-size	9855
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).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), 0 ms] (2) CdtProblem (3) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms] (4) CdtProblem (5) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (6) CdtProblem (7) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms] (8) CdtProblem (9) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 22 ms] (10) CdtProblem (11) SIsEmptyProof [BOTH BOUNDS(ID, ID), 0 ms] (12) BOUNDS(1, 1) (13) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (14) TRS for Loop Detection (15) DecreasingLoopProof [LOWER BOUND(ID), 0 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: perfectp(0) -> false perfectp(s(x)) -> f(x, s(0), s(x), s(x)) f(0, y, 0, u) -> true f(0, y, s(z), u) -> false f(s(x), 0, z, u) -> f(x, u, minus(z, s(x)), u) f(s(x), s(y), z, u) -> if(le(x, y), f(s(x), minus(y, x), z, u), f(x, u, z, u)) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (1) CpxTrsToCdtProof (UPPER BOUND(ID)) Converted Cpx (relative) TRS to CDT ---------------------------------------- (2) Obligation: Complexity Dependency Tuples Problem Rules: perfectp(0) -> false perfectp(s(z0)) -> f(z0, s(0), s(z0), s(z0)) f(0, z0, 0, z1) -> true f(0, z0, s(z1), z2) -> false f(s(z0), 0, z1, z2) -> f(z0, z2, minus(z1, s(z0)), z2) f(s(z0), s(z1), z2, z3) -> if(le(z0, z1), f(s(z0), minus(z1, z0), z2, z3), f(z0, z3, z2, z3)) Tuples: PERFECTP(0) -> c PERFECTP(s(z0)) -> c1(F(z0, s(0), s(z0), s(z0))) F(0, z0, 0, z1) -> c2 F(0, z0, s(z1), z2) -> c3 F(s(z0), 0, z1, z2) -> c4(F(z0, z2, minus(z1, s(z0)), z2)) F(s(z0), s(z1), z2, z3) -> c5(F(s(z0), minus(z1, z0), z2, z3), F(z0, z3, z2, z3)) S tuples: PERFECTP(0) -> c PERFECTP(s(z0)) -> c1(F(z0, s(0), s(z0), s(z0))) F(0, z0, 0, z1) -> c2 F(0, z0, s(z1), z2) -> c3 F(s(z0), 0, z1, z2) -> c4(F(z0, z2, minus(z1, s(z0)), z2)) F(s(z0), s(z1), z2, z3) -> c5(F(s(z0), minus(z1, z0), z2, z3), F(z0, z3, z2, z3)) K tuples:none Defined Rule Symbols: perfectp_1, f_4 Defined Pair Symbols: PERFECTP_1, F_4 Compound Symbols: c, c1_1, c2, c3, c4_1, c5_2 ---------------------------------------- (3) CdtLeafRemovalProof (ComplexityIfPolyImplication) Removed 1 leading nodes: PERFECTP(s(z0)) -> c1(F(z0, s(0), s(z0), s(z0))) Removed 3 trailing nodes: PERFECTP(0) -> c popout

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

job log

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actions

all output return to Runti Compl Inner Rewri 22807