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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313895
details
property
value
status
complete
benchmark
5.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n055.star.cs.uiowa.edu
space
Beerendonk_07
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
293.946 seconds
cpu usage
1120.21
user time
1105.91
system time
14.2992
max virtual memory
3.8639064E7
max residence set size
1.53071E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^2))
output
1110.69/291.48 WORST_CASE(Omega(n^1), O(n^2)) 1119.72/293.76 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 1119.72/293.76 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1119.72/293.76 1119.72/293.76 1119.72/293.76 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 1119.72/293.76 1119.72/293.76 (0) CpxTRS 1119.72/293.76 (1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] 1119.72/293.76 (2) CpxWeightedTrs 1119.72/293.76 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 1119.72/293.76 (4) CpxTypedWeightedTrs 1119.72/293.76 (5) CompletionProof [UPPER BOUND(ID), 0 ms] 1119.72/293.76 (6) CpxTypedWeightedCompleteTrs 1119.72/293.76 (7) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] 1119.72/293.76 (8) CpxTypedWeightedCompleteTrs 1119.72/293.76 (9) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] 1119.72/293.76 (10) CpxRNTS 1119.72/293.76 (11) InliningProof [UPPER BOUND(ID), 1034 ms] 1119.72/293.76 (12) CpxRNTS 1119.72/293.76 (13) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms] 1119.72/293.76 (14) CpxRNTS 1119.72/293.76 (15) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 1 ms] 1119.72/293.76 (16) CpxRNTS 1119.72/293.76 (17) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 1119.72/293.76 (18) CpxRNTS 1119.72/293.76 (19) IntTrsBoundProof [UPPER BOUND(ID), 250 ms] 1119.72/293.76 (20) CpxRNTS 1119.72/293.76 (21) IntTrsBoundProof [UPPER BOUND(ID), 80 ms] 1119.72/293.76 (22) CpxRNTS 1119.72/293.76 (23) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 1119.72/293.76 (24) CpxRNTS 1119.72/293.76 (25) IntTrsBoundProof [UPPER BOUND(ID), 120 ms] 1119.72/293.76 (26) CpxRNTS 1119.72/293.76 (27) IntTrsBoundProof [UPPER BOUND(ID), 13 ms] 1119.72/293.76 (28) CpxRNTS 1119.72/293.76 (29) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 1119.72/293.76 (30) CpxRNTS 1119.72/293.76 (31) IntTrsBoundProof [UPPER BOUND(ID), 293 ms] 1119.72/293.76 (32) CpxRNTS 1119.72/293.76 (33) IntTrsBoundProof [UPPER BOUND(ID), 97 ms] 1119.72/293.76 (34) CpxRNTS 1119.72/293.76 (35) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 1119.72/293.76 (36) CpxRNTS 1119.72/293.76 (37) IntTrsBoundProof [UPPER BOUND(ID), 260 ms] 1119.72/293.76 (38) CpxRNTS 1119.72/293.76 (39) IntTrsBoundProof [UPPER BOUND(ID), 96 ms] 1119.72/293.76 (40) CpxRNTS 1119.72/293.76 (41) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 1119.72/293.76 (42) CpxRNTS 1119.72/293.76 (43) IntTrsBoundProof [UPPER BOUND(ID), 1725 ms] 1119.72/293.76 (44) CpxRNTS 1119.72/293.76 (45) IntTrsBoundProof [UPPER BOUND(ID), 2131 ms] 1119.72/293.76 (46) CpxRNTS 1119.72/293.76 (47) FinalProof [FINISHED, 0 ms] 1119.72/293.76 (48) BOUNDS(1, n^2) 1119.72/293.76 (49) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 1119.72/293.76 (50) TRS for Loop Detection 1119.72/293.76 (51) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 1119.72/293.76 (52) BEST 1119.72/293.76 (53) proven lower bound 1119.72/293.76 (54) LowerBoundPropagationProof [FINISHED, 0 ms] 1119.72/293.76 (55) BOUNDS(n^1, INF) 1119.72/293.76 (56) TRS for Loop Detection 1119.72/293.76 1119.72/293.76 1119.72/293.76 ---------------------------------------- 1119.72/293.76 1119.72/293.76 (0) 1119.72/293.76 Obligation: 1119.72/293.76 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 1119.72/293.76 1119.72/293.76 1119.72/293.76 The TRS R consists of the following rules: 1119.72/293.76 1119.72/293.76 cond(true, x) -> cond(and(even(x), gr(x, 0)), p(x)) 1119.72/293.76 and(x, false) -> false 1119.72/293.76 and(false, x) -> false 1119.72/293.76 and(true, true) -> true 1119.72/293.76 even(0) -> true 1119.72/293.76 even(s(0)) -> false 1119.72/293.76 even(s(s(x))) -> even(x) 1119.72/293.76 gr(0, x) -> false 1119.72/293.76 gr(s(x), 0) -> true 1119.72/293.76 gr(s(x), s(y)) -> gr(x, y) 1119.72/293.76 p(0) -> 0 1119.72/293.76 p(s(x)) -> x 1119.72/293.76 1119.72/293.76 S is empty. 1119.72/293.76 Rewrite Strategy: INNERMOST 1119.72/293.76 ---------------------------------------- 1119.72/293.76 1119.72/293.76 (1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) 1119.72/293.76 Transformed relative TRS to weighted TRS 1119.72/293.76 ---------------------------------------- 1119.72/293.76 1119.72/293.76 (2) 1119.72/293.76 Obligation: 1119.72/293.76 The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^2). 1119.72/293.76
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