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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307946
details
property
value
status
complete
benchmark
test10.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n070.star.cs.uiowa.edu
space
Strategy_removed_mixed_05
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
8.7042 seconds
cpu usage
20.6398
user time
19.0966
system time
1.54319
max virtual memory
1.8811124E7
max residence set size
4087996.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^1))
output
20.54/6.28 WORST_CASE(Omega(n^1), O(n^1)) 20.54/6.29 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 20.54/6.29 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 20.54/6.29 20.54/6.29 20.54/6.29 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 20.54/6.29 20.54/6.29 (0) CpxTRS 20.54/6.29 (1) NestedDefinedSymbolProof [UPPER BOUND(ID), 0 ms] 20.54/6.29 (2) CpxTRS 20.54/6.29 (3) RcToIrcProof [BOTH BOUNDS(ID, ID), 0 ms] 20.54/6.29 (4) CpxTRS 20.54/6.29 (5) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] 20.54/6.29 (6) CpxWeightedTrs 20.54/6.29 (7) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 20.54/6.29 (8) CpxTypedWeightedTrs 20.54/6.29 (9) CompletionProof [UPPER BOUND(ID), 0 ms] 20.54/6.29 (10) CpxTypedWeightedCompleteTrs 20.54/6.29 (11) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] 20.54/6.29 (12) CpxTypedWeightedCompleteTrs 20.54/6.29 (13) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] 20.54/6.29 (14) CpxRNTS 20.54/6.29 (15) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms] 20.54/6.29 (16) CpxRNTS 20.54/6.29 (17) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 0 ms] 20.54/6.29 (18) CpxRNTS 20.54/6.29 (19) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 20.54/6.29 (20) CpxRNTS 20.54/6.29 (21) IntTrsBoundProof [UPPER BOUND(ID), 190 ms] 20.54/6.29 (22) CpxRNTS 20.54/6.29 (23) IntTrsBoundProof [UPPER BOUND(ID), 96 ms] 20.54/6.29 (24) CpxRNTS 20.54/6.29 (25) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 20.54/6.29 (26) CpxRNTS 20.54/6.29 (27) IntTrsBoundProof [UPPER BOUND(ID), 271 ms] 20.54/6.29 (28) CpxRNTS 20.54/6.29 (29) IntTrsBoundProof [UPPER BOUND(ID), 53 ms] 20.54/6.29 (30) CpxRNTS 20.54/6.29 (31) FinalProof [FINISHED, 0 ms] 20.54/6.29 (32) BOUNDS(1, n^1) 20.54/6.29 (33) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 20.54/6.29 (34) CpxTRS 20.54/6.29 (35) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 20.54/6.29 (36) typed CpxTrs 20.54/6.29 (37) OrderProof [LOWER BOUND(ID), 0 ms] 20.54/6.29 (38) typed CpxTrs 20.54/6.29 (39) RewriteLemmaProof [LOWER BOUND(ID), 404 ms] 20.54/6.29 (40) BEST 20.54/6.29 (41) proven lower bound 20.54/6.29 (42) LowerBoundPropagationProof [FINISHED, 0 ms] 20.54/6.29 (43) BOUNDS(n^1, INF) 20.54/6.29 (44) typed CpxTrs 20.54/6.29 20.54/6.29 20.54/6.29 ---------------------------------------- 20.54/6.29 20.54/6.29 (0) 20.54/6.29 Obligation: 20.54/6.29 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 20.54/6.29 20.54/6.29 20.54/6.29 The TRS R consists of the following rules: 20.54/6.29 20.54/6.29 h(X, Z) -> f(X, s(X), Z) 20.54/6.29 f(X, Y, g(X, Y)) -> h(0, g(X, Y)) 20.54/6.29 g(0, Y) -> 0 20.54/6.29 g(X, s(Y)) -> g(X, Y) 20.54/6.29 20.54/6.29 S is empty. 20.54/6.29 Rewrite Strategy: FULL 20.54/6.29 ---------------------------------------- 20.54/6.29 20.54/6.29 (1) NestedDefinedSymbolProof (UPPER BOUND(ID)) 20.54/6.29 The TRS does not nest defined symbols. 20.54/6.29 Hence, the left-hand sides of the following rules are not basic-reachable and can be removed: 20.54/6.29 f(X, Y, g(X, Y)) -> h(0, g(X, Y)) 20.54/6.29 20.54/6.29 ---------------------------------------- 20.54/6.29 20.54/6.29 (2) 20.54/6.29 Obligation: 20.54/6.29 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, n^1). 20.54/6.29 20.54/6.29 20.54/6.29 The TRS R consists of the following rules: 20.54/6.29 20.54/6.29 h(X, Z) -> f(X, s(X), Z) 20.54/6.29 g(0, Y) -> 0 20.54/6.29 g(X, s(Y)) -> g(X, Y) 20.54/6.29 20.54/6.29 S is empty. 20.54/6.29 Rewrite Strategy: FULL 20.54/6.29 ---------------------------------------- 20.54/6.29 20.54/6.29 (3) RcToIrcProof (BOTH BOUNDS(ID, ID)) 20.54/6.29 Converted rc-obligation to irc-obligation. 20.54/6.29 20.54/6.29 As the TRS does not nest defined symbols, we have rc = irc. 20.54/6.29 ---------------------------------------- 20.54/6.29
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