details

property	value
status	complete
benchmark	gexgcd.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	Frederiksen_Others

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	7.22506 seconds
cpu usage	24.9001
user time	23.2915
system time	1.60865
max virtual memory	1.9512668E7
max residence set size	3872376.0

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^1). (0) CpxRelTRS (1) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 151 ms] (2) CpxRelTRS (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) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 2 ms] (10) CdtProblem (11) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms] (12) CdtProblem (13) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 176 ms] (14) CdtProblem (15) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 92 ms] (16) CdtProblem (17) CdtKnowledgeProof [BOTH BOUNDS(ID, ID), 0 ms] (18) CdtProblem (19) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 63 ms] (20) CdtProblem (21) CdtKnowledgeProof [FINISHED, 0 ms] (22) BOUNDS(1, 1) (23) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (24) CpxRelTRS (25) SlicingProof [LOWER BOUND(ID), 74 ms] (26) CpxRelTRS (27) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (28) typed CpxTrs (29) OrderProof [LOWER BOUND(ID), 0 ms] (30) typed CpxTrs (31) RewriteLemmaProof [LOWER BOUND(ID), 284 ms] (32) typed CpxTrs (33) RewriteLemmaProof [LOWER BOUND(ID), 171 ms] (34) BEST (35) proven lower bound (36) LowerBoundPropagationProof [FINISHED, 0 ms] (37) BOUNDS(n^1, INF) (38) typed CpxTrs (39) RewriteLemmaProof [LOWER BOUND(ID), 150 ms] (40) typed CpxTrs (41) RewriteLemmaProof [LOWER BOUND(ID), 142 ms] (42) typed CpxTrs (43) RewriteLemmaProof [LOWER BOUND(ID), 138 ms] (44) typed CpxTrs (45) RewriteLemmaProof [LOWER BOUND(ID), 93 ms] (46) typed CpxTrs ---------------------------------------- (0) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^1). The TRS R consists of the following rules: m2(S(0), b, res, True) -> False m2(S(S(x)), b, res, True) -> True m2(0, b, res, True) -> False m3(S(0), b, res, t) -> False m3(S(S(x)), b, res, t) -> True m3(0, b, res, t) -> False l8(res, y, res', True, mtmp, t) -> res l5(x, y, res, tmp, mtmp, True) -> 0 help1(S(0)) -> False help1(S(S(x))) -> True e4(a, b, res, False) -> False e4(a, b, res, True) -> True e2(a, b, res, False) -> False l15(x, y, res, tmp, False, t) -> l16(x, y, gcd(y, 0), tmp, False, t) l15(x, y, res, tmp, True, t) -> l16(x, y, gcd(y, S(0)), tmp, True, t) l13(x, y, res, tmp, False, t) -> l16(x, y, gcd(0, y), tmp, False, t) l13(x, y, res, tmp, True, t) -> l16(x, y, gcd(S(0), y), tmp, True, t) m4(S(x'), S(x), res, t) -> m5(S(x'), S(x), monus(x', x), t) m2(a, b, res, False) -> m4(a, b, res, False) l8(x, y, res, False, mtmp, t) -> l10(x, y, res, False, mtmp, t) l5(x, y, res, tmp, mtmp, False) -> l7(x, y, res, tmp, mtmp, False) l2(x, y, res, tmp, mtmp, False) -> l3(x, y, res, tmp, mtmp, False) l2(x, y, res, tmp, mtmp, True) -> res l11(x, y, res, tmp, mtmp, False) -> l14(x, y, res, tmp, mtmp, False) l11(x, y, res, tmp, mtmp, True) -> l12(x, y, res, tmp, mtmp, True) help1(0) -> False e2(a, b, res, True) -> e3(a, b, res, True) bool2Nat(False) -> 0 bool2Nat(True) -> S(0) m1(a, x, res, t) -> m2(a, x, res, False) l9(res, y, res', tmp, mtmp, t) -> res l6(x, y, res, tmp, mtmp, t) -> 0 l4(x', x, res, tmp, mtmp, t) -> l5(x', x, res, tmp, mtmp, False) l1(x, y, res, tmp, mtmp, t) -> l2(x, y, res, tmp, mtmp, False) e7(a, b, res, t) -> False popout

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

job log

popout

actions

all output return to Runtime Complexity: TRS Innermost