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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433308516
details
property
value
status
complete
benchmark
#4.22.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n103.star.cs.uiowa.edu
space
Strategy_removed_AG01
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
5.92997 seconds
cpu usage
18.0371
user time
16.8088
system time
1.22831
max virtual memory
1.874562E7
max residence set size
3612132.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^1))
output
17.32/5.55 WORST_CASE(Omega(n^1), O(n^1)) 17.64/5.56 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 17.64/5.56 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 17.64/5.56 17.64/5.56 17.64/5.56 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 17.64/5.56 17.64/5.56 (0) CpxTRS 17.64/5.56 (1) RcToIrcProof [BOTH BOUNDS(ID, ID), 0 ms] 17.64/5.56 (2) CpxTRS 17.64/5.56 (3) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] 17.64/5.56 (4) CpxWeightedTrs 17.64/5.56 (5) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 17.64/5.56 (6) CpxTypedWeightedTrs 17.64/5.56 (7) CompletionProof [UPPER BOUND(ID), 0 ms] 17.64/5.56 (8) CpxTypedWeightedCompleteTrs 17.64/5.56 (9) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] 17.64/5.56 (10) CpxTypedWeightedCompleteTrs 17.64/5.56 (11) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] 17.64/5.56 (12) CpxRNTS 17.64/5.56 (13) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms] 17.64/5.56 (14) CpxRNTS 17.64/5.56 (15) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 0 ms] 17.64/5.56 (16) CpxRNTS 17.64/5.56 (17) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 17.64/5.56 (18) CpxRNTS 17.64/5.56 (19) IntTrsBoundProof [UPPER BOUND(ID), 514 ms] 17.64/5.56 (20) CpxRNTS 17.64/5.56 (21) IntTrsBoundProof [UPPER BOUND(ID), 189 ms] 17.64/5.56 (22) CpxRNTS 17.64/5.56 (23) FinalProof [FINISHED, 0 ms] 17.64/5.56 (24) BOUNDS(1, n^1) 17.64/5.56 (25) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 17.64/5.56 (26) CpxTRS 17.64/5.56 (27) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 17.64/5.56 (28) typed CpxTrs 17.64/5.56 (29) OrderProof [LOWER BOUND(ID), 0 ms] 17.64/5.56 (30) typed CpxTrs 17.64/5.56 (31) RewriteLemmaProof [LOWER BOUND(ID), 420 ms] 17.64/5.56 (32) proven lower bound 17.64/5.56 (33) LowerBoundPropagationProof [FINISHED, 0 ms] 17.64/5.56 (34) BOUNDS(n^1, INF) 17.64/5.56 17.64/5.56 17.64/5.56 ---------------------------------------- 17.64/5.56 17.64/5.56 (0) 17.64/5.56 Obligation: 17.64/5.56 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 17.64/5.56 17.64/5.56 17.64/5.56 The TRS R consists of the following rules: 17.64/5.56 17.64/5.56 quot(0, s(y), s(z)) -> 0 17.64/5.56 quot(s(x), s(y), z) -> quot(x, y, z) 17.64/5.56 quot(x, 0, s(z)) -> s(quot(x, s(z), s(z))) 17.64/5.56 17.64/5.56 S is empty. 17.64/5.56 Rewrite Strategy: FULL 17.64/5.56 ---------------------------------------- 17.64/5.56 17.64/5.56 (1) RcToIrcProof (BOTH BOUNDS(ID, ID)) 17.64/5.56 Converted rc-obligation to irc-obligation. 17.64/5.56 17.64/5.56 As the TRS does not nest defined symbols, we have rc = irc. 17.64/5.56 ---------------------------------------- 17.64/5.56 17.64/5.56 (2) 17.64/5.56 Obligation: 17.64/5.56 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, n^1). 17.64/5.56 17.64/5.56 17.64/5.56 The TRS R consists of the following rules: 17.64/5.56 17.64/5.56 quot(0, s(y), s(z)) -> 0 17.64/5.56 quot(s(x), s(y), z) -> quot(x, y, z) 17.64/5.56 quot(x, 0, s(z)) -> s(quot(x, s(z), s(z))) 17.64/5.56 17.64/5.56 S is empty. 17.64/5.56 Rewrite Strategy: INNERMOST 17.64/5.56 ---------------------------------------- 17.64/5.56 17.64/5.56 (3) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) 17.64/5.56 Transformed relative TRS to weighted TRS 17.64/5.56 ---------------------------------------- 17.64/5.56 17.64/5.56 (4) 17.64/5.56 Obligation: 17.64/5.56 The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^1). 17.64/5.56 17.64/5.56 17.64/5.56 The TRS R consists of the following rules: 17.64/5.56 17.64/5.56 quot(0, s(y), s(z)) -> 0 [1] 17.64/5.56 quot(s(x), s(y), z) -> quot(x, y, z) [1] 17.64/5.56 quot(x, 0, s(z)) -> s(quot(x, s(z), s(z))) [1] 17.64/5.56 17.64/5.56 Rewrite Strategy: INNERMOST 17.64/5.56 ---------------------------------------- 17.64/5.56
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