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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307927
details
property
value
status
complete
benchmark
cade16.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n134.star.cs.uiowa.edu
space
GTSSK07
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.63 seconds
cpu usage
1131.77
user time
1117.28
system time
14.4938
max virtual memory
5.7199612E7
max residence set size
1.5139308E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^2))
output
1131.39/291.51 WORST_CASE(Omega(n^1), O(n^2)) 1131.39/291.53 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 1131.39/291.53 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1131.39/291.53 1131.39/291.53 1131.39/291.53 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 1131.39/291.53 1131.39/291.53 (0) CpxTRS 1131.39/291.53 (1) RcToIrcProof [BOTH BOUNDS(ID, ID), 0 ms] 1131.39/291.53 (2) CpxTRS 1131.39/291.53 (3) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] 1131.39/291.53 (4) CpxWeightedTrs 1131.39/291.53 (5) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 1131.39/291.53 (6) CpxTypedWeightedTrs 1131.39/291.53 (7) CompletionProof [UPPER BOUND(ID), 0 ms] 1131.39/291.53 (8) CpxTypedWeightedCompleteTrs 1131.39/291.53 (9) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] 1131.39/291.53 (10) CpxRNTS 1131.39/291.53 (11) CompleteCoflocoProof [FINISHED, 380 ms] 1131.39/291.53 (12) BOUNDS(1, n^2) 1131.39/291.53 (13) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 1131.39/291.53 (14) CpxTRS 1131.39/291.53 (15) SlicingProof [LOWER BOUND(ID), 0 ms] 1131.39/291.53 (16) CpxTRS 1131.39/291.53 (17) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 1131.39/291.53 (18) typed CpxTrs 1131.39/291.53 (19) OrderProof [LOWER BOUND(ID), 0 ms] 1131.39/291.53 (20) typed CpxTrs 1131.39/291.53 (21) RewriteLemmaProof [LOWER BOUND(ID), 292 ms] 1131.39/291.53 (22) BEST 1131.39/291.53 (23) proven lower bound 1131.39/291.53 (24) LowerBoundPropagationProof [FINISHED, 0 ms] 1131.39/291.53 (25) BOUNDS(n^1, INF) 1131.39/291.53 (26) typed CpxTrs 1131.39/291.53 (27) RewriteLemmaProof [LOWER BOUND(ID), 60 ms] 1131.39/291.53 (28) typed CpxTrs 1131.39/291.53 1131.39/291.53 1131.39/291.53 ---------------------------------------- 1131.39/291.53 1131.39/291.53 (0) 1131.39/291.53 Obligation: 1131.39/291.53 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 1131.39/291.53 1131.39/291.53 1131.39/291.53 The TRS R consists of the following rules: 1131.39/291.53 1131.39/291.53 nthtail(n, l) -> cond(ge(n, length(l)), n, l) 1131.39/291.53 cond(true, n, l) -> l 1131.39/291.53 cond(false, n, l) -> tail(nthtail(s(n), l)) 1131.39/291.53 tail(nil) -> nil 1131.39/291.53 tail(cons(x, l)) -> l 1131.39/291.53 length(nil) -> 0 1131.39/291.53 length(cons(x, l)) -> s(length(l)) 1131.39/291.53 ge(u, 0) -> true 1131.39/291.53 ge(0, s(v)) -> false 1131.39/291.53 ge(s(u), s(v)) -> ge(u, v) 1131.39/291.53 1131.39/291.53 S is empty. 1131.39/291.53 Rewrite Strategy: FULL 1131.39/291.53 ---------------------------------------- 1131.39/291.53 1131.39/291.53 (1) RcToIrcProof (BOTH BOUNDS(ID, ID)) 1131.39/291.53 Converted rc-obligation to irc-obligation. 1131.39/291.53 1131.39/291.53 The duplicating contexts are: 1131.39/291.53 nthtail([], l) 1131.39/291.53 nthtail(n, []) 1131.39/291.53 1131.39/291.53 1131.39/291.53 The defined contexts are: 1131.39/291.53 tail([]) 1131.39/291.53 cond([], x1, x2) 1131.39/291.53 ge(x0, []) 1131.39/291.53 1131.39/291.53 1131.39/291.53 As the TRS is an overlay system and the defined contexts and the duplicating contexts don't overlap, we have rc = irc. 1131.39/291.53 ---------------------------------------- 1131.39/291.53 1131.39/291.53 (2) 1131.39/291.53 Obligation: 1131.39/291.53 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, n^2). 1131.39/291.53 1131.39/291.53 1131.39/291.53 The TRS R consists of the following rules: 1131.39/291.53 1131.39/291.53 nthtail(n, l) -> cond(ge(n, length(l)), n, l) 1131.39/291.53 cond(true, n, l) -> l 1131.39/291.53 cond(false, n, l) -> tail(nthtail(s(n), l)) 1131.39/291.53 tail(nil) -> nil 1131.39/291.53 tail(cons(x, l)) -> l 1131.39/291.53 length(nil) -> 0 1131.39/291.53 length(cons(x, l)) -> s(length(l)) 1131.39/291.53 ge(u, 0) -> true 1131.39/291.53 ge(0, s(v)) -> false 1131.39/291.53 ge(s(u), s(v)) -> ge(u, v) 1131.39/291.53 1131.39/291.53 S is empty. 1131.39/291.53 Rewrite Strategy: INNERMOST 1131.39/291.53 ----------------------------------------
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