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	n147.star.cs.uiowa.edu
space	Mixed_TRS

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	9.11661 seconds
cpu usage	26.6506
user time	25.1053
system time	1.5453
max virtual memory	1.907828E7
max residence set size	4081492.0

stage attributes

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

output

WORST_CASE(Omega(n^1), O(n^1)) proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).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)), 35 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 F(0, z0, s(z1), z2) -> c3 F(0, z0, 0, z1) -> c2 ---------------------------------------- (4) popout

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

job log

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actions

all output return to Runtime Complexity: TRS Innermost