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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313550
details
property
value
status
complete
benchmark
#4.27.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n031.star.cs.uiowa.edu
space
Strategy_removed_AG01
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.633 seconds
cpu usage
320.863
user time
318.247
system time
2.61628
max virtual memory
3.8034472E7
max residence set size
5425868.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^2))
output
320.67/291.57 WORST_CASE(Omega(n^1), O(n^2)) 320.67/291.59 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 320.67/291.59 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 320.67/291.59 320.67/291.59 320.67/291.59 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 320.67/291.59 320.67/291.59 (0) CpxTRS 320.67/291.59 (1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] 320.67/291.59 (2) CpxWeightedTrs 320.67/291.59 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 320.67/291.59 (4) CpxTypedWeightedTrs 320.67/291.59 (5) CompletionProof [UPPER BOUND(ID), 0 ms] 320.67/291.59 (6) CpxTypedWeightedCompleteTrs 320.67/291.59 (7) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] 320.67/291.59 (8) CpxTypedWeightedCompleteTrs 320.67/291.59 (9) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 1 ms] 320.67/291.59 (10) CpxRNTS 320.67/291.59 (11) InliningProof [UPPER BOUND(ID), 0 ms] 320.67/291.59 (12) CpxRNTS 320.67/291.59 (13) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms] 320.67/291.59 (14) CpxRNTS 320.67/291.59 (15) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 0 ms] 320.67/291.59 (16) CpxRNTS 320.67/291.59 (17) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 320.67/291.59 (18) CpxRNTS 320.67/291.59 (19) IntTrsBoundProof [UPPER BOUND(ID), 374 ms] 320.67/291.59 (20) CpxRNTS 320.67/291.59 (21) IntTrsBoundProof [UPPER BOUND(ID), 168 ms] 320.67/291.59 (22) CpxRNTS 320.67/291.59 (23) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 320.67/291.59 (24) CpxRNTS 320.67/291.59 (25) IntTrsBoundProof [UPPER BOUND(ID), 320 ms] 320.67/291.59 (26) CpxRNTS 320.67/291.59 (27) IntTrsBoundProof [UPPER BOUND(ID), 73 ms] 320.67/291.59 (28) CpxRNTS 320.67/291.59 (29) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 320.67/291.59 (30) CpxRNTS 320.67/291.59 (31) IntTrsBoundProof [UPPER BOUND(ID), 148 ms] 320.67/291.59 (32) CpxRNTS 320.67/291.59 (33) IntTrsBoundProof [UPPER BOUND(ID), 52 ms] 320.67/291.59 (34) CpxRNTS 320.67/291.59 (35) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 320.67/291.59 (36) CpxRNTS 320.67/291.59 (37) IntTrsBoundProof [UPPER BOUND(ID), 462 ms] 320.67/291.59 (38) CpxRNTS 320.67/291.59 (39) IntTrsBoundProof [UPPER BOUND(ID), 146 ms] 320.67/291.59 (40) CpxRNTS 320.67/291.59 (41) FinalProof [FINISHED, 0 ms] 320.67/291.59 (42) BOUNDS(1, n^2) 320.67/291.59 (43) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 320.67/291.59 (44) TRS for Loop Detection 320.67/291.59 (45) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 320.67/291.59 (46) BEST 320.67/291.59 (47) proven lower bound 320.67/291.59 (48) LowerBoundPropagationProof [FINISHED, 0 ms] 320.67/291.59 (49) BOUNDS(n^1, INF) 320.67/291.59 (50) TRS for Loop Detection 320.67/291.59 320.67/291.59 320.67/291.59 ---------------------------------------- 320.67/291.59 320.67/291.59 (0) 320.67/291.59 Obligation: 320.67/291.59 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 320.67/291.59 320.67/291.59 320.67/291.59 The TRS R consists of the following rules: 320.67/291.59 320.67/291.59 p(0) -> 0 320.67/291.59 p(s(x)) -> x 320.67/291.59 le(0, y) -> true 320.67/291.59 le(s(x), 0) -> false 320.67/291.59 le(s(x), s(y)) -> le(x, y) 320.67/291.59 minus(x, 0) -> x 320.67/291.59 minus(x, s(y)) -> if(le(x, s(y)), 0, p(minus(x, p(s(y))))) 320.67/291.59 if(true, x, y) -> x 320.67/291.59 if(false, x, y) -> y 320.67/291.59 320.67/291.59 S is empty. 320.67/291.59 Rewrite Strategy: INNERMOST 320.67/291.59 ---------------------------------------- 320.67/291.59 320.67/291.59 (1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) 320.67/291.59 Transformed relative TRS to weighted TRS 320.67/291.59 ---------------------------------------- 320.67/291.59 320.67/291.59 (2) 320.67/291.59 Obligation: 320.67/291.59 The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^2). 320.67/291.59 320.67/291.59 320.67/291.59 The TRS R consists of the following rules: 320.67/291.59 320.67/291.59 p(0) -> 0 [1] 320.67/291.59 p(s(x)) -> x [1] 320.67/291.59 le(0, y) -> true [1] 320.67/291.59 le(s(x), 0) -> false [1] 320.67/291.59 le(s(x), s(y)) -> le(x, y) [1] 320.67/291.59 minus(x, 0) -> x [1]
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