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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307925
details
property
value
status
complete
benchmark
cade11.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n092.star.cs.uiowa.edu
space
GTSSK07
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.568 seconds
cpu usage
882.979
user time
877.836
system time
5.14286
max virtual memory
3.7920896E7
max residence set size
5747972.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^2))
output
882.75/291.49 WORST_CASE(Omega(n^1), O(n^2)) 882.82/291.51 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 882.82/291.51 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 882.82/291.51 882.82/291.51 882.82/291.51 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 882.82/291.51 882.82/291.51 (0) CpxTRS 882.82/291.51 (1) RcToIrcProof [BOTH BOUNDS(ID, ID), 0 ms] 882.82/291.51 (2) CpxTRS 882.82/291.51 (3) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] 882.82/291.51 (4) CpxWeightedTrs 882.82/291.51 (5) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 882.82/291.51 (6) CpxTypedWeightedTrs 882.82/291.51 (7) CompletionProof [UPPER BOUND(ID), 0 ms] 882.82/291.51 (8) CpxTypedWeightedCompleteTrs 882.82/291.51 (9) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 4 ms] 882.82/291.51 (10) CpxRNTS 882.82/291.51 (11) CompleteCoflocoProof [FINISHED, 278 ms] 882.82/291.51 (12) BOUNDS(1, n^2) 882.82/291.51 (13) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 882.82/291.51 (14) TRS for Loop Detection 882.82/291.51 (15) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 882.82/291.51 (16) BEST 882.82/291.51 (17) proven lower bound 882.82/291.51 (18) LowerBoundPropagationProof [FINISHED, 0 ms] 882.82/291.51 (19) BOUNDS(n^1, INF) 882.82/291.51 (20) TRS for Loop Detection 882.82/291.51 882.82/291.51 882.82/291.51 ---------------------------------------- 882.82/291.51 882.82/291.51 (0) 882.82/291.51 Obligation: 882.82/291.51 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 882.82/291.51 882.82/291.51 882.82/291.51 The TRS R consists of the following rules: 882.82/291.51 882.82/291.51 f(true, x, y) -> f(gt(x, y), s(x), s(s(y))) 882.82/291.51 gt(0, v) -> false 882.82/291.51 gt(s(u), 0) -> true 882.82/291.51 gt(s(u), s(v)) -> gt(u, v) 882.82/291.51 882.82/291.51 S is empty. 882.82/291.51 Rewrite Strategy: FULL 882.82/291.51 ---------------------------------------- 882.82/291.51 882.82/291.51 (1) RcToIrcProof (BOTH BOUNDS(ID, ID)) 882.82/291.51 Converted rc-obligation to irc-obligation. 882.82/291.51 882.82/291.51 The duplicating contexts are: 882.82/291.51 f(true, [], y) 882.82/291.51 f(true, x, []) 882.82/291.51 882.82/291.51 882.82/291.51 The defined contexts are: 882.82/291.51 f([], s(x1), s(s(x2))) 882.82/291.51 882.82/291.51 882.82/291.51 [] just represents basic- or constructor-terms in the following defined contexts: 882.82/291.51 f([], s(x1), s(s(x2))) 882.82/291.51 882.82/291.51 882.82/291.51 As the TRS is an overlay system and the defined contexts and the duplicating contexts don't overlap, we have rc = irc. 882.82/291.51 ---------------------------------------- 882.82/291.51 882.82/291.51 (2) 882.82/291.51 Obligation: 882.82/291.51 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, n^2). 882.82/291.51 882.82/291.51 882.82/291.51 The TRS R consists of the following rules: 882.82/291.51 882.82/291.51 f(true, x, y) -> f(gt(x, y), s(x), s(s(y))) 882.82/291.51 gt(0, v) -> false 882.82/291.51 gt(s(u), 0) -> true 882.82/291.51 gt(s(u), s(v)) -> gt(u, v) 882.82/291.51 882.82/291.51 S is empty. 882.82/291.51 Rewrite Strategy: INNERMOST 882.82/291.51 ---------------------------------------- 882.82/291.51 882.82/291.51 (3) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) 882.82/291.51 Transformed relative TRS to weighted TRS 882.82/291.51 ---------------------------------------- 882.82/291.51 882.82/291.51 (4) 882.82/291.51 Obligation: 882.82/291.51 The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^2). 882.82/291.51 882.82/291.51 882.82/291.51 The TRS R consists of the following rules: 882.82/291.51 882.82/291.51 f(true, x, y) -> f(gt(x, y), s(x), s(s(y))) [1] 882.82/291.51 gt(0, v) -> false [1] 882.82/291.51 gt(s(u), 0) -> true [1] 882.82/291.51 gt(s(u), s(v)) -> gt(u, v) [1] 882.82/291.51 882.82/291.51 Rewrite Strategy: INNERMOST
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