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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307824
details
property
value
status
complete
benchmark
prov.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n005.star.cs.uiowa.edu
space
Rubio_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
4.73254 seconds
cpu usage
13.9755
user time
13.0383
system time
0.937187
max virtual memory
1.8743776E7
max residence set size
3305588.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^1))
output
13.65/4.67 WORST_CASE(Omega(n^1), O(n^1)) 13.83/4.69 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 13.83/4.69 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 13.83/4.69 13.83/4.69 13.83/4.69 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 13.83/4.69 13.83/4.69 (0) CpxTRS 13.83/4.69 (1) RcToIrcProof [BOTH BOUNDS(ID, ID), 0 ms] 13.83/4.69 (2) CpxTRS 13.83/4.69 (3) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] 13.83/4.69 (4) CpxWeightedTrs 13.83/4.69 (5) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 13.83/4.69 (6) CpxTypedWeightedTrs 13.83/4.69 (7) CompletionProof [UPPER BOUND(ID), 0 ms] 13.83/4.69 (8) CpxTypedWeightedCompleteTrs 13.83/4.69 (9) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] 13.83/4.69 (10) CpxRNTS 13.83/4.69 (11) CompleteCoflocoProof [FINISHED, 136 ms] 13.83/4.69 (12) BOUNDS(1, n^1) 13.83/4.69 (13) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 13.83/4.69 (14) CpxTRS 13.83/4.69 (15) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 13.83/4.69 (16) typed CpxTrs 13.83/4.69 (17) OrderProof [LOWER BOUND(ID), 0 ms] 13.83/4.69 (18) typed CpxTrs 13.83/4.69 (19) RewriteLemmaProof [LOWER BOUND(ID), 499 ms] 13.83/4.69 (20) BEST 13.83/4.69 (21) proven lower bound 13.83/4.69 (22) LowerBoundPropagationProof [FINISHED, 0 ms] 13.83/4.69 (23) BOUNDS(n^1, INF) 13.83/4.69 (24) typed CpxTrs 13.83/4.69 13.83/4.69 13.83/4.69 ---------------------------------------- 13.83/4.69 13.83/4.69 (0) 13.83/4.69 Obligation: 13.83/4.69 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 13.83/4.69 13.83/4.69 13.83/4.69 The TRS R consists of the following rules: 13.83/4.69 13.83/4.69 ackin(s(X), s(Y)) -> u21(ackin(s(X), Y), X) 13.83/4.69 u21(ackout(X), Y) -> u22(ackin(Y, X)) 13.83/4.69 13.83/4.69 S is empty. 13.83/4.69 Rewrite Strategy: FULL 13.83/4.69 ---------------------------------------- 13.83/4.69 13.83/4.69 (1) RcToIrcProof (BOTH BOUNDS(ID, ID)) 13.83/4.69 Converted rc-obligation to irc-obligation. 13.83/4.69 13.83/4.69 The duplicating contexts are: 13.83/4.69 ackin(s([]), s(Y)) 13.83/4.69 13.83/4.69 13.83/4.69 The defined contexts are: 13.83/4.69 u21([], x1) 13.83/4.69 ackin(x0, []) 13.83/4.69 ackin(s(x0), []) 13.83/4.69 13.83/4.69 13.83/4.69 As the TRS is an overlay system and the defined contexts and the duplicating contexts don't overlap, we have rc = irc. 13.83/4.69 ---------------------------------------- 13.83/4.69 13.83/4.69 (2) 13.83/4.69 Obligation: 13.83/4.69 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, n^1). 13.83/4.69 13.83/4.69 13.83/4.69 The TRS R consists of the following rules: 13.83/4.69 13.83/4.69 ackin(s(X), s(Y)) -> u21(ackin(s(X), Y), X) 13.83/4.69 u21(ackout(X), Y) -> u22(ackin(Y, X)) 13.83/4.69 13.83/4.69 S is empty. 13.83/4.69 Rewrite Strategy: INNERMOST 13.83/4.69 ---------------------------------------- 13.83/4.69 13.83/4.69 (3) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) 13.83/4.69 Transformed relative TRS to weighted TRS 13.83/4.69 ---------------------------------------- 13.83/4.69 13.83/4.69 (4) 13.83/4.69 Obligation: 13.83/4.69 The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^1). 13.83/4.69 13.83/4.69 13.83/4.69 The TRS R consists of the following rules: 13.83/4.69 13.83/4.69 ackin(s(X), s(Y)) -> u21(ackin(s(X), Y), X) [1] 13.83/4.69 u21(ackout(X), Y) -> u22(ackin(Y, X)) [1] 13.83/4.69 13.83/4.69 Rewrite Strategy: INNERMOST 13.83/4.69 ---------------------------------------- 13.83/4.69 13.83/4.69 (5) TypeInferenceProof (BOTH BOUNDS(ID, ID)) 13.83/4.69 Infered types. 13.83/4.69 ----------------------------------------
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