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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313275
details
property
value
status
complete
benchmark
tpa2.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n071.star.cs.uiowa.edu
space
Secret_05_TRS
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.66 seconds
cpu usage
369.669
user time
366.125
system time
3.54438
max virtual memory
3.830626E7
max residence set size
5645236.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^2))
output
369.29/291.54 WORST_CASE(Omega(n^1), O(n^2)) 369.38/291.56 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 369.38/291.56 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 369.38/291.56 369.38/291.56 369.38/291.56 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 369.38/291.56 369.38/291.56 (0) CpxTRS 369.38/291.56 (1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] 369.38/291.56 (2) CpxWeightedTrs 369.38/291.56 (3) CpxWeightedTrsRenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 369.38/291.56 (4) CpxWeightedTrs 369.38/291.56 (5) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 369.38/291.56 (6) CpxTypedWeightedTrs 369.38/291.56 (7) CompletionProof [UPPER BOUND(ID), 0 ms] 369.38/291.56 (8) CpxTypedWeightedCompleteTrs 369.38/291.56 (9) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] 369.38/291.56 (10) CpxTypedWeightedCompleteTrs 369.38/291.56 (11) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] 369.38/291.56 (12) CpxRNTS 369.38/291.56 (13) InliningProof [UPPER BOUND(ID), 473 ms] 369.38/291.56 (14) CpxRNTS 369.38/291.56 (15) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms] 369.38/291.56 (16) CpxRNTS 369.38/291.56 (17) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 0 ms] 369.38/291.56 (18) CpxRNTS 369.38/291.56 (19) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 369.38/291.56 (20) CpxRNTS 369.38/291.56 (21) IntTrsBoundProof [UPPER BOUND(ID), 393 ms] 369.38/291.56 (22) CpxRNTS 369.38/291.56 (23) IntTrsBoundProof [UPPER BOUND(ID), 119 ms] 369.38/291.56 (24) CpxRNTS 369.38/291.56 (25) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 369.38/291.56 (26) CpxRNTS 369.38/291.56 (27) IntTrsBoundProof [UPPER BOUND(ID), 169 ms] 369.38/291.56 (28) CpxRNTS 369.38/291.56 (29) IntTrsBoundProof [UPPER BOUND(ID), 42 ms] 369.38/291.56 (30) CpxRNTS 369.38/291.56 (31) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 369.38/291.56 (32) CpxRNTS 369.38/291.56 (33) IntTrsBoundProof [UPPER BOUND(ID), 1084 ms] 369.38/291.56 (34) CpxRNTS 369.38/291.56 (35) IntTrsBoundProof [UPPER BOUND(ID), 1157 ms] 369.38/291.56 (36) CpxRNTS 369.38/291.56 (37) FinalProof [FINISHED, 0 ms] 369.38/291.56 (38) BOUNDS(1, n^2) 369.38/291.56 (39) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 369.38/291.56 (40) TRS for Loop Detection 369.38/291.56 (41) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 369.38/291.56 (42) BEST 369.38/291.56 (43) proven lower bound 369.38/291.56 (44) LowerBoundPropagationProof [FINISHED, 0 ms] 369.38/291.56 (45) BOUNDS(n^1, INF) 369.38/291.56 (46) TRS for Loop Detection 369.38/291.56 369.38/291.56 369.38/291.56 ---------------------------------------- 369.38/291.56 369.38/291.56 (0) 369.38/291.56 Obligation: 369.38/291.56 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 369.38/291.56 369.38/291.56 369.38/291.56 The TRS R consists of the following rules: 369.38/291.56 369.38/291.56 -(x, 0) -> x 369.38/291.56 -(s(x), s(y)) -> -(x, y) 369.38/291.56 p(s(x)) -> x 369.38/291.56 f(s(x), y) -> f(p(-(s(x), y)), p(-(y, s(x)))) 369.38/291.56 f(x, s(y)) -> f(p(-(x, s(y))), p(-(s(y), x))) 369.38/291.56 369.38/291.56 S is empty. 369.38/291.56 Rewrite Strategy: INNERMOST 369.38/291.56 ---------------------------------------- 369.38/291.56 369.38/291.56 (1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) 369.38/291.56 Transformed relative TRS to weighted TRS 369.38/291.56 ---------------------------------------- 369.38/291.56 369.38/291.56 (2) 369.38/291.56 Obligation: 369.38/291.56 The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^2). 369.38/291.56 369.38/291.56 369.38/291.56 The TRS R consists of the following rules: 369.38/291.56 369.38/291.56 -(x, 0) -> x [1] 369.38/291.56 -(s(x), s(y)) -> -(x, y) [1] 369.38/291.56 p(s(x)) -> x [1] 369.38/291.56 f(s(x), y) -> f(p(-(s(x), y)), p(-(y, s(x)))) [1] 369.38/291.56 f(x, s(y)) -> f(p(-(x, s(y))), p(-(s(y), x))) [1] 369.38/291.56 369.38/291.56 Rewrite Strategy: INNERMOST 369.38/291.56 ---------------------------------------- 369.38/291.56 369.38/291.56 (3) CpxWeightedTrsRenamingProof (BOTH BOUNDS(ID, ID)) 369.38/291.56 Renamed defined symbols to avoid conflicts with arithmetic symbols: 369.38/291.56 369.38/291.56 - => minus 369.38/291.56
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