details

property	value
status	complete
benchmark	ordered_better.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n149.star.cs.uiowa.edu
space	Frederiksen_Glenstrup

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	291.533 seconds
cpu usage	321.269
user time	318.43
system time	2.83873
max virtual memory	1.8946272E7
max residence set size	5563636.0

stage attributes

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

output

WORST_CASE(?, 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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, n^1). (0) CpxRelTRS (1) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 181 ms] (2) CpxRelTRS (3) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms] (4) CdtProblem (5) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms] (6) CdtProblem (7) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms] (8) CdtProblem (9) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 39 ms] (10) CdtProblem (11) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 8 ms] (12) CdtProblem (13) SIsEmptyProof [BOTH BOUNDS(ID, ID), 0 ms] (14) BOUNDS(1, 1) ---------------------------------------- (0) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, n^1). The TRS R consists of the following rules: ordered(Cons(x', Cons(x, xs))) -> ordered[Ite](<(x', x), Cons(x', Cons(x, xs))) ordered(Cons(x, Nil)) -> True ordered(Nil) -> True notEmpty(Cons(x, xs)) -> True notEmpty(Nil) -> False goal(xs) -> ordered(xs) The (relative) TRS S consists of the following rules: <(S(x), S(y)) -> <(x, y) <(0, S(y)) -> True <(x, 0) -> False ordered[Ite](True, Cons(x, xs)) -> ordered(xs) ordered[Ite](False, xs) -> False Rewrite Strategy: INNERMOST ---------------------------------------- (1) SInnermostTerminationProof (BOTH CONCRETE BOUNDS(ID, ID)) proved innermost termination of relative rules ---------------------------------------- (2) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, n^1). The TRS R consists of the following rules: ordered(Cons(x', Cons(x, xs))) -> ordered[Ite](<(x', x), Cons(x', Cons(x, xs))) ordered(Cons(x, Nil)) -> True ordered(Nil) -> True notEmpty(Cons(x, xs)) -> True notEmpty(Nil) -> False goal(xs) -> ordered(xs) The (relative) TRS S consists of the following rules: <(S(x), S(y)) -> <(x, y) <(0, S(y)) -> True <(x, 0) -> False ordered[Ite](True, Cons(x, xs)) -> ordered(xs) ordered[Ite](False, xs) -> False Rewrite Strategy: INNERMOST ---------------------------------------- (3) CpxTrsToCdtProof (UPPER BOUND(ID)) Converted Cpx (relative) TRS to CDT ---------------------------------------- (4) Obligation: Complexity Dependency Tuples Problem Rules: <(S(z0), S(z1)) -> <(z0, z1) <(0, S(z0)) -> True <(z0, 0) -> False ordered[Ite](True, Cons(z0, z1)) -> ordered(z1) ordered[Ite](False, z0) -> False ordered(Cons(z0, Cons(z1, z2))) -> ordered[Ite](<(z0, z1), Cons(z0, Cons(z1, z2))) ordered(Cons(z0, Nil)) -> True ordered(Nil) -> True notEmpty(Cons(z0, z1)) -> True notEmpty(Nil) -> False goal(z0) -> ordered(z0) popout

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

job log

popout

actions

all output return to Runtime Complexity: TRS Innermost