details

property	value
status	complete
benchmark	2.29.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n139.star.cs.uiowa.edu
space	SK90

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	4.39848 seconds
cpu usage	14.4775
user time	13.4684
system time	1.00913
max virtual memory	1.8911108E7
max residence set size	3612572.0

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/sandbox2/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).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)), 14 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: prime(0) -> false prime(s(0)) -> false prime(s(s(x))) -> prime1(s(s(x)), s(x)) prime1(x, 0) -> false prime1(x, s(0)) -> true prime1(x, s(s(y))) -> and(not(divp(s(s(y)), x)), prime1(x, s(y))) divp(x, y) -> =(rem(x, y), 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: prime(0) -> false prime(s(0)) -> false prime(s(s(z0))) -> prime1(s(s(z0)), s(z0)) prime1(z0, 0) -> false prime1(z0, s(0)) -> true prime1(z0, s(s(z1))) -> and(not(divp(s(s(z1)), z0)), prime1(z0, s(z1))) divp(z0, z1) -> =(rem(z0, z1), 0) Tuples: PRIME(0) -> c PRIME(s(0)) -> c1 PRIME(s(s(z0))) -> c2(PRIME1(s(s(z0)), s(z0))) PRIME1(z0, 0) -> c3 PRIME1(z0, s(0)) -> c4 PRIME1(z0, s(s(z1))) -> c5(DIVP(s(s(z1)), z0), PRIME1(z0, s(z1))) DIVP(z0, z1) -> c6 S tuples: PRIME(0) -> c PRIME(s(0)) -> c1 PRIME(s(s(z0))) -> c2(PRIME1(s(s(z0)), s(z0))) PRIME1(z0, 0) -> c3 PRIME1(z0, s(0)) -> c4 PRIME1(z0, s(s(z1))) -> c5(DIVP(s(s(z1)), z0), PRIME1(z0, s(z1))) DIVP(z0, z1) -> c6 K tuples:none Defined Rule Symbols: prime_1, prime1_2, divp_2 Defined Pair Symbols: PRIME_1, PRIME1_2, DIVP_2 Compound Symbols: c, c1, c2_1, c3, c4, c5_2, c6 ---------------------------------------- (3) CdtLeafRemovalProof (ComplexityIfPolyImplication) Removed 1 leading nodes: PRIME(s(s(z0))) -> c2(PRIME1(s(s(z0)), s(z0))) Removed 5 trailing nodes: PRIME(0) -> c DIVP(z0, z1) -> c6 PRIME1(z0, 0) -> c3 popout

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actions

all output return to Runtime Complexity: TRS Innermost