Spaces
Explore
Communities
Statistics
Reports
Cluster
Status
Help
Runti Compl Inner Rewri 22807 pair #381904936
details
property
value
status
complete
benchmark
mergelists.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n042.star.cs.uiowa.edu
space
Frederiksen_Glenstrup
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
5.27572798729 seconds
cpu usage
17.157792965
max memory
3.705270272E9
stage attributes
key
value
output-size
16363
starexec-result
WORST_CASE(Omega(n^1), O(n^1))
output
/export/starexec/sandbox/solver/bin/starexec_run_complexity /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- WORST_CASE(Omega(n^1), O(n^1)) proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^1). (0) CpxRelTRS (1) STerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 175 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)), 54 ms] (10) CdtProblem (11) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 13 ms] (12) CdtProblem (13) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 0 ms] (14) CdtProblem (15) SIsEmptyProof [BOTH BOUNDS(ID, ID), 0 ms] (16) BOUNDS(1, 1) (17) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (18) TRS for Loop Detection (19) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] (20) BEST (21) proven lower bound (22) LowerBoundPropagationProof [FINISHED, 0 ms] (23) BOUNDS(n^1, INF) (24) TRS for Loop Detection ---------------------------------------- (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: merge(Cons(x, xs), Nil) -> Cons(x, xs) merge(Cons(x', xs'), Cons(x, xs)) -> merge[Ite](<=(x', x), Cons(x', xs'), Cons(x, xs)) merge(Nil, ys) -> ys goal(xs, ys) -> merge(xs, ys) The (relative) TRS S consists of the following rules: <=(S(x), S(y)) -> <=(x, y) <=(0, y) -> True <=(S(x), 0) -> False merge[Ite](False, xs', Cons(x, xs)) -> Cons(x, merge(xs', xs)) merge[Ite](True, Cons(x, xs), ys) -> Cons(x, merge(xs, ys)) Rewrite Strategy: INNERMOST ---------------------------------------- (1) STerminationProof (BOTH CONCRETE BOUNDS(ID, ID)) proved termination of relative rules ---------------------------------------- (2) 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: merge(Cons(x, xs), Nil) -> Cons(x, xs) merge(Cons(x', xs'), Cons(x, xs)) -> merge[Ite](<=(x', x), Cons(x', xs'), Cons(x, xs)) merge(Nil, ys) -> ys goal(xs, ys) -> merge(xs, ys) The (relative) TRS S consists of the following rules: <=(S(x), S(y)) -> <=(x, y) <=(0, y) -> True <=(S(x), 0) -> False merge[Ite](False, xs', Cons(x, xs)) -> Cons(x, merge(xs', xs)) merge[Ite](True, Cons(x, xs), ys) -> Cons(x, merge(xs, ys)) Rewrite Strategy: INNERMOST ---------------------------------------- (3) CpxTrsToCdtProof (UPPER BOUND(ID)) Converted Cpx (relative) TRS to CDT ---------------------------------------- (4) Obligation: Complexity Dependency Tuples Problem
popout
output may be truncated. 'popout' for the full output.
job log
popout
actions
all output
return to Runti Compl Inner Rewri 22807