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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313283
details
property
value
status
complete
benchmark
division.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n037.star.cs.uiowa.edu
space
Rubio_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.582 seconds
cpu usage
316.218
user time
313.158
system time
3.05939
max virtual memory
1.914368E7
max residence set size
5185472.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^3))
output
316.07/291.52 WORST_CASE(Omega(n^1), O(n^3)) 316.07/291.54 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 316.07/291.54 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 316.07/291.54 316.07/291.54 316.07/291.54 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^3). 316.07/291.54 316.07/291.54 (0) CpxTRS 316.07/291.54 (1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] 316.07/291.54 (2) CpxWeightedTrs 316.07/291.54 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 316.07/291.54 (4) CpxTypedWeightedTrs 316.07/291.54 (5) CompletionProof [UPPER BOUND(ID), 0 ms] 316.07/291.54 (6) CpxTypedWeightedCompleteTrs 316.07/291.54 (7) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] 316.07/291.54 (8) CpxTypedWeightedCompleteTrs 316.07/291.54 (9) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] 316.07/291.54 (10) CpxRNTS 316.07/291.54 (11) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms] 316.07/291.54 (12) CpxRNTS 316.07/291.54 (13) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 0 ms] 316.07/291.54 (14) CpxRNTS 316.07/291.54 (15) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 316.07/291.54 (16) CpxRNTS 316.07/291.54 (17) IntTrsBoundProof [UPPER BOUND(ID), 402 ms] 316.07/291.54 (18) CpxRNTS 316.07/291.54 (19) IntTrsBoundProof [UPPER BOUND(ID), 150 ms] 316.07/291.54 (20) CpxRNTS 316.07/291.54 (21) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 316.07/291.54 (22) CpxRNTS 316.07/291.54 (23) IntTrsBoundProof [UPPER BOUND(ID), 980 ms] 316.07/291.54 (24) CpxRNTS 316.07/291.54 (25) IntTrsBoundProof [UPPER BOUND(ID), 329 ms] 316.07/291.54 (26) CpxRNTS 316.07/291.54 (27) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 316.07/291.54 (28) CpxRNTS 316.07/291.54 (29) IntTrsBoundProof [UPPER BOUND(ID), 452 ms] 316.07/291.54 (30) CpxRNTS 316.07/291.54 (31) IntTrsBoundProof [UPPER BOUND(ID), 0 ms] 316.07/291.54 (32) CpxRNTS 316.07/291.54 (33) FinalProof [FINISHED, 0 ms] 316.07/291.54 (34) BOUNDS(1, n^3) 316.07/291.54 (35) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 316.07/291.54 (36) TRS for Loop Detection 316.07/291.54 (37) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 316.07/291.54 (38) BEST 316.07/291.54 (39) proven lower bound 316.07/291.54 (40) LowerBoundPropagationProof [FINISHED, 0 ms] 316.07/291.54 (41) BOUNDS(n^1, INF) 316.07/291.54 (42) TRS for Loop Detection 316.07/291.54 316.07/291.54 316.07/291.54 ---------------------------------------- 316.07/291.54 316.07/291.54 (0) 316.07/291.54 Obligation: 316.07/291.54 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^3). 316.07/291.54 316.07/291.54 316.07/291.54 The TRS R consists of the following rules: 316.07/291.54 316.07/291.54 le(0, Y) -> true 316.07/291.54 le(s(X), 0) -> false 316.07/291.54 le(s(X), s(Y)) -> le(X, Y) 316.07/291.54 minus(0, Y) -> 0 316.07/291.54 minus(s(X), Y) -> ifMinus(le(s(X), Y), s(X), Y) 316.07/291.54 ifMinus(true, s(X), Y) -> 0 316.07/291.54 ifMinus(false, s(X), Y) -> s(minus(X, Y)) 316.07/291.54 quot(0, s(Y)) -> 0 316.07/291.54 quot(s(X), s(Y)) -> s(quot(minus(X, Y), s(Y))) 316.07/291.54 316.07/291.54 S is empty. 316.07/291.54 Rewrite Strategy: INNERMOST 316.07/291.54 ---------------------------------------- 316.07/291.54 316.07/291.54 (1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) 316.07/291.54 Transformed relative TRS to weighted TRS 316.07/291.54 ---------------------------------------- 316.07/291.54 316.07/291.54 (2) 316.07/291.54 Obligation: 316.07/291.54 The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^3). 316.07/291.54 316.07/291.54 316.07/291.54 The TRS R consists of the following rules: 316.07/291.54 316.07/291.54 le(0, Y) -> true [1] 316.07/291.54 le(s(X), 0) -> false [1] 316.07/291.54 le(s(X), s(Y)) -> le(X, Y) [1] 316.07/291.54 minus(0, Y) -> 0 [1] 316.07/291.54 minus(s(X), Y) -> ifMinus(le(s(X), Y), s(X), Y) [1] 316.07/291.54 ifMinus(true, s(X), Y) -> 0 [1] 316.07/291.54 ifMinus(false, s(X), Y) -> s(minus(X, Y)) [1] 316.07/291.54 quot(0, s(Y)) -> 0 [1] 316.07/291.54 quot(s(X), s(Y)) -> s(quot(minus(X, Y), s(Y))) [1] 316.07/291.54 316.07/291.54 Rewrite Strategy: INNERMOST 316.07/291.54 ---------------------------------------- 316.07/291.54 316.07/291.54 (3) TypeInferenceProof (BOTH BOUNDS(ID, ID))
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