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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313813
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
n002.star.cs.uiowa.edu
space
Frederiksen_Glenstrup
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
5.4302 seconds
cpu usage
17.2521
user time
15.8497
system time
1.40238
max virtual memory
1.8949772E7
max residence set size
3859156.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^1))
output
16.81/5.36 WORST_CASE(Omega(n^1), O(n^1)) 16.81/5.38 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 16.81/5.38 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 16.81/5.38 16.81/5.38 16.81/5.38 The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^1). 16.81/5.38 16.81/5.38 (0) CpxRelTRS 16.81/5.38 (1) STerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 195 ms] 16.81/5.38 (2) CpxRelTRS 16.81/5.38 (3) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] 16.81/5.38 (4) CpxWeightedTrs 16.81/5.38 (5) CpxWeightedTrsRenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 16.81/5.38 (6) CpxWeightedTrs 16.81/5.38 (7) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 16.81/5.38 (8) CpxTypedWeightedTrs 16.81/5.38 (9) CompletionProof [UPPER BOUND(ID), 0 ms] 16.81/5.38 (10) CpxTypedWeightedCompleteTrs 16.81/5.38 (11) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 6 ms] 16.81/5.38 (12) CpxRNTS 16.81/5.38 (13) CompleteCoflocoProof [FINISHED, 384 ms] 16.81/5.38 (14) BOUNDS(1, n^1) 16.81/5.38 (15) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 16.81/5.38 (16) TRS for Loop Detection 16.81/5.38 (17) DecreasingLoopProof [LOWER BOUND(ID), 38 ms] 16.81/5.38 (18) BEST 16.81/5.38 (19) proven lower bound 16.81/5.38 (20) LowerBoundPropagationProof [FINISHED, 0 ms] 16.81/5.38 (21) BOUNDS(n^1, INF) 16.81/5.38 (22) TRS for Loop Detection 16.81/5.38 16.81/5.38 16.81/5.38 ---------------------------------------- 16.81/5.38 16.81/5.38 (0) 16.81/5.38 Obligation: 16.81/5.38 The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^1). 16.81/5.38 16.81/5.38 16.81/5.38 The TRS R consists of the following rules: 16.81/5.38 16.81/5.38 merge(Cons(x, xs), Nil) -> Cons(x, xs) 16.81/5.38 merge(Cons(x', xs'), Cons(x, xs)) -> merge[Ite](<=(x', x), Cons(x', xs'), Cons(x, xs)) 16.81/5.38 merge(Nil, ys) -> ys 16.81/5.38 goal(xs, ys) -> merge(xs, ys) 16.81/5.38 16.81/5.38 The (relative) TRS S consists of the following rules: 16.81/5.38 16.81/5.38 <=(S(x), S(y)) -> <=(x, y) 16.81/5.38 <=(0, y) -> True 16.81/5.38 <=(S(x), 0) -> False 16.81/5.38 merge[Ite](False, xs', Cons(x, xs)) -> Cons(x, merge(xs', xs)) 16.81/5.38 merge[Ite](True, Cons(x, xs), ys) -> Cons(x, merge(xs, ys)) 16.81/5.38 16.81/5.38 Rewrite Strategy: INNERMOST 16.81/5.38 ---------------------------------------- 16.81/5.38 16.81/5.38 (1) STerminationProof (BOTH CONCRETE BOUNDS(ID, ID)) 16.81/5.38 proved termination of relative rules 16.81/5.38 ---------------------------------------- 16.81/5.38 16.81/5.38 (2) 16.81/5.38 Obligation: 16.81/5.38 The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^1). 16.81/5.38 16.81/5.38 16.81/5.38 The TRS R consists of the following rules: 16.81/5.38 16.81/5.38 merge(Cons(x, xs), Nil) -> Cons(x, xs) 16.81/5.38 merge(Cons(x', xs'), Cons(x, xs)) -> merge[Ite](<=(x', x), Cons(x', xs'), Cons(x, xs)) 16.81/5.38 merge(Nil, ys) -> ys 16.81/5.38 goal(xs, ys) -> merge(xs, ys) 16.81/5.38 16.81/5.38 The (relative) TRS S consists of the following rules: 16.81/5.38 16.81/5.38 <=(S(x), S(y)) -> <=(x, y) 16.81/5.38 <=(0, y) -> True 16.81/5.38 <=(S(x), 0) -> False 16.81/5.38 merge[Ite](False, xs', Cons(x, xs)) -> Cons(x, merge(xs', xs)) 16.81/5.38 merge[Ite](True, Cons(x, xs), ys) -> Cons(x, merge(xs, ys)) 16.81/5.38 16.81/5.38 Rewrite Strategy: INNERMOST 16.81/5.38 ---------------------------------------- 16.81/5.38 16.81/5.38 (3) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) 16.81/5.38 Transformed relative TRS to weighted TRS 16.81/5.38 ---------------------------------------- 16.81/5.38 16.81/5.38 (4) 16.81/5.38 Obligation: 16.81/5.38 The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^1). 16.81/5.38 16.81/5.38 16.81/5.38 The TRS R consists of the following rules: 16.81/5.38 16.81/5.38 merge(Cons(x, xs), Nil) -> Cons(x, xs) [1] 16.81/5.38 merge(Cons(x', xs'), Cons(x, xs)) -> merge[Ite](<=(x', x), Cons(x', xs'), Cons(x, xs)) [1] 16.81/5.38 merge(Nil, ys) -> ys [1] 16.81/5.38 goal(xs, ys) -> merge(xs, ys) [1] 16.81/5.38 <=(S(x), S(y)) -> <=(x, y) [0]
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