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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313817
details
property
value
status
complete
benchmark
ordered.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n051.star.cs.uiowa.edu
space
Frederiksen_Glenstrup
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
5.07092 seconds
cpu usage
16.4117
user time
15.1962
system time
1.21555
max virtual memory
3.67046E7
max residence set size
3554024.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^1))
output
15.95/5.00 WORST_CASE(Omega(n^1), O(n^1)) 15.95/5.01 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 15.95/5.01 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 15.95/5.01 15.95/5.01 15.95/5.01 The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^1). 15.95/5.01 15.95/5.01 (0) CpxRelTRS 15.95/5.01 (1) STerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 212 ms] 15.95/5.01 (2) CpxRelTRS 15.95/5.01 (3) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] 15.95/5.01 (4) CpxWeightedTrs 15.95/5.01 (5) CpxWeightedTrsRenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 15.95/5.01 (6) CpxWeightedTrs 15.95/5.01 (7) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 15.95/5.01 (8) CpxTypedWeightedTrs 15.95/5.01 (9) CompletionProof [UPPER BOUND(ID), 0 ms] 15.95/5.01 (10) CpxTypedWeightedCompleteTrs 15.95/5.01 (11) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] 15.95/5.01 (12) CpxRNTS 15.95/5.01 (13) CompleteCoflocoProof [FINISHED, 234 ms] 15.95/5.01 (14) BOUNDS(1, n^1) 15.95/5.01 (15) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 15.95/5.01 (16) TRS for Loop Detection 15.95/5.01 (17) DecreasingLoopProof [LOWER BOUND(ID), 25 ms] 15.95/5.01 (18) BEST 15.95/5.01 (19) proven lower bound 15.95/5.01 (20) LowerBoundPropagationProof [FINISHED, 0 ms] 15.95/5.01 (21) BOUNDS(n^1, INF) 15.95/5.01 (22) TRS for Loop Detection 15.95/5.01 15.95/5.01 15.95/5.01 ---------------------------------------- 15.95/5.01 15.95/5.01 (0) 15.95/5.01 Obligation: 15.95/5.01 The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^1). 15.95/5.01 15.95/5.01 15.95/5.01 The TRS R consists of the following rules: 15.95/5.01 15.95/5.01 ordered(Cons(x', Cons(x, xs))) -> ordered[Ite](<(x', x), Cons(x', Cons(x, xs))) 15.95/5.01 ordered(Cons(x, Nil)) -> True 15.95/5.01 ordered(Nil) -> True 15.95/5.01 notEmpty(Cons(x, xs)) -> True 15.95/5.01 notEmpty(Nil) -> False 15.95/5.01 goal(xs) -> ordered(xs) 15.95/5.01 15.95/5.01 The (relative) TRS S consists of the following rules: 15.95/5.01 15.95/5.01 <(S(x), S(y)) -> <(x, y) 15.95/5.01 <(0, S(y)) -> True 15.95/5.01 <(x, 0) -> False 15.95/5.01 ordered[Ite](True, Cons(x', Cons(x, xs))) -> ordered(xs) 15.95/5.01 ordered[Ite](False, xs) -> False 15.95/5.01 15.95/5.01 Rewrite Strategy: INNERMOST 15.95/5.01 ---------------------------------------- 15.95/5.01 15.95/5.01 (1) STerminationProof (BOTH CONCRETE BOUNDS(ID, ID)) 15.95/5.01 proved termination of relative rules 15.95/5.01 ---------------------------------------- 15.95/5.01 15.95/5.01 (2) 15.95/5.01 Obligation: 15.95/5.01 The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^1). 15.95/5.01 15.95/5.01 15.95/5.01 The TRS R consists of the following rules: 15.95/5.01 15.95/5.01 ordered(Cons(x', Cons(x, xs))) -> ordered[Ite](<(x', x), Cons(x', Cons(x, xs))) 15.95/5.01 ordered(Cons(x, Nil)) -> True 15.95/5.01 ordered(Nil) -> True 15.95/5.01 notEmpty(Cons(x, xs)) -> True 15.95/5.01 notEmpty(Nil) -> False 15.95/5.01 goal(xs) -> ordered(xs) 15.95/5.01 15.95/5.01 The (relative) TRS S consists of the following rules: 15.95/5.01 15.95/5.01 <(S(x), S(y)) -> <(x, y) 15.95/5.01 <(0, S(y)) -> True 15.95/5.01 <(x, 0) -> False 15.95/5.01 ordered[Ite](True, Cons(x', Cons(x, xs))) -> ordered(xs) 15.95/5.01 ordered[Ite](False, xs) -> False 15.95/5.01 15.95/5.01 Rewrite Strategy: INNERMOST 15.95/5.01 ---------------------------------------- 15.95/5.01 15.95/5.01 (3) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) 15.95/5.01 Transformed relative TRS to weighted TRS 15.95/5.01 ---------------------------------------- 15.95/5.01 15.95/5.01 (4) 15.95/5.01 Obligation: 15.95/5.01 The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^1). 15.95/5.01 15.95/5.01 15.95/5.01 The TRS R consists of the following rules: 15.95/5.01 15.95/5.01 ordered(Cons(x', Cons(x, xs))) -> ordered[Ite](<(x', x), Cons(x', Cons(x, xs))) [1]
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