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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313805
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
n174.star.cs.uiowa.edu
space
Frederiksen_Glenstrup
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.55 seconds
cpu usage
323.592
user time
320.586
system time
3.00666
max virtual memory
1.89467E7
max residence set size
5539828.0
stage attributes
key
value
starexec-result
WORST_CASE(?, O(n^1))
output
323.44/291.49 WORST_CASE(?, O(n^1)) 323.44/291.50 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 323.44/291.50 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 323.44/291.50 323.44/291.50 323.44/291.50 The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, n^1). 323.44/291.50 323.44/291.50 (0) CpxRelTRS 323.44/291.50 (1) STerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 166 ms] 323.44/291.50 (2) CpxRelTRS 323.44/291.50 (3) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] 323.44/291.50 (4) CpxWeightedTrs 323.44/291.50 (5) CpxWeightedTrsRenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 323.44/291.50 (6) CpxWeightedTrs 323.44/291.50 (7) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 323.44/291.50 (8) CpxTypedWeightedTrs 323.44/291.50 (9) CompletionProof [UPPER BOUND(ID), 0 ms] 323.44/291.50 (10) CpxTypedWeightedCompleteTrs 323.44/291.50 (11) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] 323.44/291.50 (12) CpxTypedWeightedCompleteTrs 323.44/291.50 (13) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] 323.44/291.50 (14) CpxRNTS 323.44/291.50 (15) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms] 323.44/291.50 (16) CpxRNTS 323.44/291.50 (17) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 0 ms] 323.44/291.50 (18) CpxRNTS 323.44/291.50 (19) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 323.44/291.50 (20) CpxRNTS 323.44/291.50 (21) IntTrsBoundProof [UPPER BOUND(ID), 368 ms] 323.44/291.50 (22) CpxRNTS 323.44/291.50 (23) IntTrsBoundProof [UPPER BOUND(ID), 89 ms] 323.44/291.50 (24) CpxRNTS 323.44/291.50 (25) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 323.44/291.50 (26) CpxRNTS 323.44/291.50 (27) IntTrsBoundProof [UPPER BOUND(ID), 140 ms] 323.44/291.50 (28) CpxRNTS 323.44/291.50 (29) IntTrsBoundProof [UPPER BOUND(ID), 55 ms] 323.44/291.50 (30) CpxRNTS 323.44/291.50 (31) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 323.44/291.50 (32) CpxRNTS 323.44/291.50 (33) IntTrsBoundProof [UPPER BOUND(ID), 1222 ms] 323.44/291.50 (34) CpxRNTS 323.44/291.50 (35) IntTrsBoundProof [UPPER BOUND(ID), 520 ms] 323.44/291.50 (36) CpxRNTS 323.44/291.50 (37) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 323.44/291.50 (38) CpxRNTS 323.44/291.50 (39) IntTrsBoundProof [UPPER BOUND(ID), 127 ms] 323.44/291.50 (40) CpxRNTS 323.44/291.50 (41) IntTrsBoundProof [UPPER BOUND(ID), 52 ms] 323.44/291.50 (42) CpxRNTS 323.44/291.50 (43) FinalProof [FINISHED, 0 ms] 323.44/291.50 (44) BOUNDS(1, n^1) 323.44/291.50 323.44/291.50 323.44/291.50 ---------------------------------------- 323.44/291.50 323.44/291.50 (0) 323.44/291.50 Obligation: 323.44/291.50 The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, n^1). 323.44/291.50 323.44/291.50 323.44/291.50 The TRS R consists of the following rules: 323.44/291.50 323.44/291.50 ordered(Cons(x', Cons(x, xs))) -> ordered[Ite](<(x', x), Cons(x', Cons(x, xs))) 323.44/291.50 ordered(Cons(x, Nil)) -> True 323.44/291.50 ordered(Nil) -> True 323.44/291.50 notEmpty(Cons(x, xs)) -> True 323.44/291.50 notEmpty(Nil) -> False 323.44/291.50 goal(xs) -> ordered(xs) 323.44/291.50 323.44/291.50 The (relative) TRS S consists of the following rules: 323.44/291.50 323.44/291.50 <(S(x), S(y)) -> <(x, y) 323.44/291.50 <(0, S(y)) -> True 323.44/291.50 <(x, 0) -> False 323.44/291.50 ordered[Ite](True, Cons(x, xs)) -> ordered(xs) 323.44/291.50 ordered[Ite](False, xs) -> False 323.44/291.50 323.44/291.50 Rewrite Strategy: INNERMOST 323.44/291.50 ---------------------------------------- 323.44/291.50 323.44/291.50 (1) STerminationProof (BOTH CONCRETE BOUNDS(ID, ID)) 323.44/291.50 proved termination of relative rules 323.44/291.50 ---------------------------------------- 323.44/291.50 323.44/291.50 (2) 323.44/291.50 Obligation: 323.44/291.50 The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, n^1). 323.44/291.50 323.44/291.50 323.44/291.50 The TRS R consists of the following rules: 323.44/291.50 323.44/291.50 ordered(Cons(x', Cons(x, xs))) -> ordered[Ite](<(x', x), Cons(x', Cons(x, xs))) 323.44/291.50 ordered(Cons(x, Nil)) -> True 323.44/291.50 ordered(Nil) -> True 323.44/291.50 notEmpty(Cons(x, xs)) -> True 323.44/291.50 notEmpty(Nil) -> False 323.44/291.50 goal(xs) -> ordered(xs) 323.44/291.50 323.44/291.50 The (relative) TRS S consists of the following rules:
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