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	n137.star.cs.uiowa.edu
space	Frederiksen_Others

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	6.36452 seconds
cpu usage	21.4428
user time	20.2788
system time	1.16403
max virtual memory	3.7716488E7
max residence set size	3078756.0

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).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 [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)), 82 ms] (8) CdtProblem (9) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 16 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), 42 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) f1(z0, z1, z2, z3, 0) -> 0 Tuples: F4(S(z0), S(z1), z2, z3, S(z4)) -> c(F2(S(z0), z1, z2, z3, z4)) F4(S(z0), 0, z1, z2, S(z3)) -> c1(F3(z0, 0, z1, z2, z3)) F4(S(z0), S(z1), z2, z3, 0) -> c2 F4(S(z0), 0, z1, z2, 0) -> c3 popout

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

job log

popout

actions

all output return to Runtime Complexity: TRS Innermost