details

property	value
status	complete
benchmark	2.45.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n148.star.cs.uiowa.edu
space	SK90

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	6.80108 seconds
cpu usage	23.8572
user time	22.534
system time	1.32323
max virtual memory	1.8770216E7
max residence set size	3715648.0

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). (0) CpxTRS (1) RcToIrcProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxTRS (3) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms] (4) CdtProblem (5) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (6) CdtProblem (7) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (8) CdtProblem (9) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms] (10) CdtProblem (11) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 62 ms] (12) CdtProblem (13) SIsEmptyProof [BOTH BOUNDS(ID, ID), 0 ms] (14) BOUNDS(1, 1) (15) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (16) TRS for Loop Detection (17) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] (18) BEST (19) proven lower bound (20) LowerBoundPropagationProof [FINISHED, 0 ms] (21) BOUNDS(n^1, INF) (22) TRS for Loop Detection ---------------------------------------- (0) Obligation: The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). The TRS R consists of the following rules: admit(x, nil) -> nil admit(x, .(u, .(v, .(w, z)))) -> cond(=(sum(x, u, v), w), .(u, .(v, .(w, admit(carry(x, u, v), z))))) cond(true, y) -> y S is empty. Rewrite Strategy: FULL ---------------------------------------- (1) RcToIrcProof (BOTH BOUNDS(ID, ID)) Converted rc-obligation to irc-obligation. The duplicating contexts are: admit([], .(u, .(v, .(w, z)))) admit(x, .([], .(v, .(w, z)))) admit(x, .(u, .([], .(w, z)))) The defined contexts are: cond(=(sum(x0, x1, x2), w), .(x3, .(x4, .(w, [])))) As the TRS is an overlay system and the defined contexts and the duplicating contexts don't overlap, we have rc = irc. ---------------------------------------- (2) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, n^1). The TRS R consists of the following rules: admit(x, nil) -> nil admit(x, .(u, .(v, .(w, z)))) -> cond(=(sum(x, u, v), w), .(u, .(v, .(w, admit(carry(x, u, v), z))))) cond(true, y) -> y S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (3) CpxTrsToCdtProof (UPPER BOUND(ID)) Converted Cpx (relative) TRS to CDT ---------------------------------------- (4) Obligation: Complexity Dependency Tuples Problem Rules: admit(z0, nil) -> nil admit(z0, .(z1, .(z2, .(w, z3)))) -> cond(=(sum(z0, z1, z2), w), .(z1, .(z2, .(w, admit(carry(z0, z1, z2), z3))))) cond(true, z0) -> z0 Tuples: ADMIT(z0, nil) -> c ADMIT(z0, .(z1, .(z2, .(w, z3)))) -> c1(COND(=(sum(z0, z1, z2), w), .(z1, .(z2, .(w, admit(carry(z0, z1, z2), z3))))), ADMIT(carry(z0, z1, z2), z3)) COND(true, z0) -> c2 S tuples: ADMIT(z0, nil) -> c ADMIT(z0, .(z1, .(z2, .(w, z3)))) -> c1(COND(=(sum(z0, z1, z2), w), .(z1, .(z2, .(w, admit(carry(z0, z1, z2), z3))))), ADMIT(carry(z0, z1, z2), z3)) COND(true, z0) -> c2 popout

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actions

all output return to Runtime Complexity: TRS