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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433308526
details
property
value
status
complete
benchmark
#4.23.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n167.star.cs.uiowa.edu
space
Strategy_removed_AG01
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.623 seconds
cpu usage
411.239
user time
407.479
system time
3.76005
max virtual memory
1.9351776E7
max residence set size
6177292.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^2))
output
411.10/291.56 WORST_CASE(Omega(n^1), O(n^2)) 411.10/291.59 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 411.10/291.59 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 411.10/291.59 411.10/291.59 411.10/291.59 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 411.10/291.59 411.10/291.59 (0) CpxTRS 411.10/291.59 (1) RcToIrcProof [BOTH BOUNDS(ID, ID), 0 ms] 411.10/291.59 (2) CpxTRS 411.10/291.59 (3) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] 411.10/291.59 (4) CpxWeightedTrs 411.10/291.59 (5) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 411.10/291.59 (6) CpxTypedWeightedTrs 411.10/291.59 (7) CompletionProof [UPPER BOUND(ID), 0 ms] 411.10/291.59 (8) CpxTypedWeightedCompleteTrs 411.10/291.59 (9) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] 411.10/291.59 (10) CpxTypedWeightedCompleteTrs 411.10/291.59 (11) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] 411.10/291.59 (12) CpxRNTS 411.10/291.59 (13) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms] 411.10/291.59 (14) CpxRNTS 411.10/291.59 (15) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 0 ms] 411.10/291.59 (16) CpxRNTS 411.10/291.59 (17) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 411.10/291.59 (18) CpxRNTS 411.10/291.59 (19) IntTrsBoundProof [UPPER BOUND(ID), 303 ms] 411.10/291.59 (20) CpxRNTS 411.10/291.59 (21) IntTrsBoundProof [UPPER BOUND(ID), 131 ms] 411.10/291.59 (22) CpxRNTS 411.10/291.59 (23) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 411.10/291.59 (24) CpxRNTS 411.10/291.59 (25) IntTrsBoundProof [UPPER BOUND(ID), 598 ms] 411.10/291.59 (26) CpxRNTS 411.10/291.59 (27) IntTrsBoundProof [UPPER BOUND(ID), 318 ms] 411.10/291.59 (28) CpxRNTS 411.10/291.59 (29) FinalProof [FINISHED, 0 ms] 411.10/291.59 (30) BOUNDS(1, n^2) 411.10/291.59 (31) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 411.10/291.59 (32) CpxTRS 411.10/291.59 (33) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 411.10/291.59 (34) typed CpxTrs 411.10/291.59 (35) OrderProof [LOWER BOUND(ID), 0 ms] 411.10/291.59 (36) typed CpxTrs 411.10/291.59 (37) RewriteLemmaProof [LOWER BOUND(ID), 277 ms] 411.10/291.59 (38) BEST 411.10/291.59 (39) proven lower bound 411.10/291.59 (40) LowerBoundPropagationProof [FINISHED, 0 ms] 411.10/291.59 (41) BOUNDS(n^1, INF) 411.10/291.59 (42) typed CpxTrs 411.10/291.59 (43) RewriteLemmaProof [LOWER BOUND(ID), 211 ms] 411.10/291.59 (44) BOUNDS(1, INF) 411.10/291.59 411.10/291.59 411.10/291.59 ---------------------------------------- 411.10/291.59 411.10/291.59 (0) 411.10/291.59 Obligation: 411.10/291.59 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 411.10/291.59 411.10/291.59 411.10/291.59 The TRS R consists of the following rules: 411.10/291.59 411.10/291.59 quot(0, s(y), s(z)) -> 0 411.10/291.59 quot(s(x), s(y), z) -> quot(x, y, z) 411.10/291.59 plus(0, y) -> y 411.10/291.59 plus(s(x), y) -> s(plus(x, y)) 411.10/291.59 quot(x, 0, s(z)) -> s(quot(x, plus(z, s(0)), s(z))) 411.10/291.59 411.10/291.59 S is empty. 411.10/291.59 Rewrite Strategy: FULL 411.10/291.59 ---------------------------------------- 411.10/291.59 411.10/291.59 (1) RcToIrcProof (BOTH BOUNDS(ID, ID)) 411.10/291.59 Converted rc-obligation to irc-obligation. 411.10/291.59 411.10/291.59 The duplicating contexts are: 411.10/291.59 quot(x, 0, s([])) 411.10/291.59 411.10/291.59 411.10/291.59 The defined contexts are: 411.10/291.59 quot(x0, [], s(x2)) 411.10/291.59 quot(x0, [], x2) 411.10/291.59 411.10/291.59 411.10/291.59 As the TRS is an overlay system and the defined contexts and the duplicating contexts don't overlap, we have rc = irc. 411.10/291.59 ---------------------------------------- 411.10/291.59 411.10/291.59 (2) 411.10/291.59 Obligation: 411.10/291.59 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, n^2). 411.10/291.59 411.10/291.59 411.10/291.59 The TRS R consists of the following rules: 411.10/291.59 411.10/291.59 quot(0, s(y), s(z)) -> 0 411.10/291.59 quot(s(x), s(y), z) -> quot(x, y, z) 411.10/291.59 plus(0, y) -> y 411.10/291.59 plus(s(x), y) -> s(plus(x, y)) 411.10/291.59 quot(x, 0, s(z)) -> s(quot(x, plus(z, s(0)), s(z)))
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