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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313900
details
property
value
status
complete
benchmark
6.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n130.star.cs.uiowa.edu
space
Beerendonk_07
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.641 seconds
cpu usage
366.985
user time
363.685
system time
3.30003
max virtual memory
5.7197212E7
max residence set size
5184608.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^2))
output
366.83/291.57 WORST_CASE(Omega(n^1), O(n^2)) 366.87/291.59 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 366.87/291.59 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 366.87/291.59 366.87/291.59 366.87/291.59 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 366.87/291.59 366.87/291.59 (0) CpxTRS 366.87/291.59 (1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] 366.87/291.59 (2) CpxWeightedTrs 366.87/291.59 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 366.87/291.59 (4) CpxTypedWeightedTrs 366.87/291.59 (5) CompletionProof [UPPER BOUND(ID), 0 ms] 366.87/291.59 (6) CpxTypedWeightedCompleteTrs 366.87/291.59 (7) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] 366.87/291.59 (8) CpxTypedWeightedCompleteTrs 366.87/291.59 (9) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] 366.87/291.59 (10) CpxRNTS 366.87/291.59 (11) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms] 366.87/291.59 (12) CpxRNTS 366.87/291.59 (13) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 0 ms] 366.87/291.59 (14) CpxRNTS 366.87/291.59 (15) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 366.87/291.59 (16) CpxRNTS 366.87/291.59 (17) IntTrsBoundProof [UPPER BOUND(ID), 265 ms] 366.87/291.59 (18) CpxRNTS 366.87/291.59 (19) IntTrsBoundProof [UPPER BOUND(ID), 109 ms] 366.87/291.59 (20) CpxRNTS 366.87/291.59 (21) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 366.87/291.59 (22) CpxRNTS 366.87/291.59 (23) IntTrsBoundProof [UPPER BOUND(ID), 190 ms] 366.87/291.59 (24) CpxRNTS 366.87/291.59 (25) IntTrsBoundProof [UPPER BOUND(ID), 55 ms] 366.87/291.59 (26) CpxRNTS 366.87/291.59 (27) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 366.87/291.59 (28) CpxRNTS 366.87/291.59 (29) IntTrsBoundProof [UPPER BOUND(ID), 402 ms] 366.87/291.59 (30) CpxRNTS 366.87/291.59 (31) IntTrsBoundProof [UPPER BOUND(ID), 164 ms] 366.87/291.59 (32) CpxRNTS 366.87/291.59 (33) FinalProof [FINISHED, 0 ms] 366.87/291.59 (34) BOUNDS(1, n^2) 366.87/291.59 (35) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 366.87/291.59 (36) TRS for Loop Detection 366.87/291.59 (37) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 366.87/291.59 (38) BEST 366.87/291.59 (39) proven lower bound 366.87/291.59 (40) LowerBoundPropagationProof [FINISHED, 0 ms] 366.87/291.59 (41) BOUNDS(n^1, INF) 366.87/291.59 (42) TRS for Loop Detection 366.87/291.59 366.87/291.59 366.87/291.59 ---------------------------------------- 366.87/291.59 366.87/291.59 (0) 366.87/291.59 Obligation: 366.87/291.59 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 366.87/291.59 366.87/291.59 366.87/291.59 The TRS R consists of the following rules: 366.87/291.59 366.87/291.59 cond(true, x) -> cond(odd(x), p(x)) 366.87/291.59 odd(0) -> false 366.87/291.59 odd(s(0)) -> true 366.87/291.59 odd(s(s(x))) -> odd(x) 366.87/291.59 p(0) -> 0 366.87/291.59 p(s(x)) -> x 366.87/291.59 366.87/291.59 S is empty. 366.87/291.59 Rewrite Strategy: INNERMOST 366.87/291.59 ---------------------------------------- 366.87/291.59 366.87/291.59 (1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) 366.87/291.59 Transformed relative TRS to weighted TRS 366.87/291.59 ---------------------------------------- 366.87/291.59 366.87/291.59 (2) 366.87/291.59 Obligation: 366.87/291.59 The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^2). 366.87/291.59 366.87/291.59 366.87/291.59 The TRS R consists of the following rules: 366.87/291.59 366.87/291.59 cond(true, x) -> cond(odd(x), p(x)) [1] 366.87/291.59 odd(0) -> false [1] 366.87/291.59 odd(s(0)) -> true [1] 366.87/291.59 odd(s(s(x))) -> odd(x) [1] 366.87/291.59 p(0) -> 0 [1] 366.87/291.59 p(s(x)) -> x [1] 366.87/291.59 366.87/291.59 Rewrite Strategy: INNERMOST 366.87/291.59 ---------------------------------------- 366.87/291.59 366.87/291.59 (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) 366.87/291.59 Infered types. 366.87/291.59 ---------------------------------------- 366.87/291.59 366.87/291.59 (4) 366.87/291.59 Obligation: 366.87/291.59 Runtime Complexity Weighted TRS with Types.
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