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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307931
details
property
value
status
complete
benchmark
cade06.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n147.star.cs.uiowa.edu
space
GTSSK07
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.573 seconds
cpu usage
1020.99
user time
1007.98
system time
13.0093
max virtual memory
5.6802628E7
max residence set size
1.5017624E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^2))
output
1020.63/291.49 WORST_CASE(Omega(n^1), O(n^2)) 1020.63/291.50 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 1020.63/291.50 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1020.63/291.50 1020.63/291.50 1020.63/291.50 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 1020.63/291.50 1020.63/291.50 (0) CpxTRS 1020.63/291.50 (1) RcToIrcProof [BOTH BOUNDS(ID, ID), 0 ms] 1020.63/291.50 (2) CpxTRS 1020.63/291.50 (3) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] 1020.63/291.50 (4) CpxWeightedTrs 1020.63/291.50 (5) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 1020.63/291.50 (6) CpxTypedWeightedTrs 1020.63/291.50 (7) CompletionProof [UPPER BOUND(ID), 0 ms] 1020.63/291.50 (8) CpxTypedWeightedCompleteTrs 1020.63/291.50 (9) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] 1020.63/291.50 (10) CpxRNTS 1020.63/291.50 (11) CompleteCoflocoProof [FINISHED, 1264 ms] 1020.63/291.50 (12) BOUNDS(1, n^2) 1020.63/291.50 (13) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 1020.63/291.50 (14) CpxTRS 1020.63/291.50 (15) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 1020.63/291.50 (16) typed CpxTrs 1020.63/291.50 (17) OrderProof [LOWER BOUND(ID), 0 ms] 1020.63/291.50 (18) typed CpxTrs 1020.63/291.50 (19) RewriteLemmaProof [LOWER BOUND(ID), 292 ms] 1020.63/291.50 (20) BEST 1020.63/291.50 (21) proven lower bound 1020.63/291.50 (22) LowerBoundPropagationProof [FINISHED, 0 ms] 1020.63/291.50 (23) BOUNDS(n^1, INF) 1020.63/291.50 (24) typed CpxTrs 1020.63/291.50 (25) RewriteLemmaProof [LOWER BOUND(ID), 63 ms] 1020.63/291.50 (26) typed CpxTrs 1020.63/291.50 1020.63/291.50 1020.63/291.50 ---------------------------------------- 1020.63/291.50 1020.63/291.50 (0) 1020.63/291.50 Obligation: 1020.63/291.50 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 1020.63/291.50 1020.63/291.50 1020.63/291.50 The TRS R consists of the following rules: 1020.63/291.50 1020.63/291.50 f(true, x, y, z) -> f(gt(x, plus(y, z)), x, s(y), z) 1020.63/291.50 f(true, x, y, z) -> f(gt(x, plus(y, z)), x, y, s(z)) 1020.63/291.50 plus(n, 0) -> n 1020.63/291.50 plus(n, s(m)) -> s(plus(n, m)) 1020.63/291.50 gt(0, v) -> false 1020.63/291.50 gt(s(u), 0) -> true 1020.63/291.50 gt(s(u), s(v)) -> gt(u, v) 1020.63/291.50 1020.63/291.50 S is empty. 1020.63/291.50 Rewrite Strategy: FULL 1020.63/291.50 ---------------------------------------- 1020.63/291.50 1020.63/291.50 (1) RcToIrcProof (BOTH BOUNDS(ID, ID)) 1020.63/291.50 Converted rc-obligation to irc-obligation. 1020.63/291.50 1020.63/291.50 The duplicating contexts are: 1020.63/291.50 f(true, [], y, z) 1020.63/291.50 f(true, x, [], z) 1020.63/291.50 f(true, x, y, []) 1020.63/291.50 1020.63/291.50 1020.63/291.50 The defined contexts are: 1020.63/291.50 f([], x1, x2, s(x3)) 1020.63/291.50 gt(x0, []) 1020.63/291.50 f([], x1, s(x2), x3) 1020.63/291.50 1020.63/291.50 1020.63/291.50 As the TRS is an overlay system and the defined contexts and the duplicating contexts don't overlap, we have rc = irc. 1020.63/291.50 ---------------------------------------- 1020.63/291.50 1020.63/291.50 (2) 1020.63/291.50 Obligation: 1020.63/291.50 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, n^2). 1020.63/291.50 1020.63/291.50 1020.63/291.50 The TRS R consists of the following rules: 1020.63/291.50 1020.63/291.50 f(true, x, y, z) -> f(gt(x, plus(y, z)), x, s(y), z) 1020.63/291.50 f(true, x, y, z) -> f(gt(x, plus(y, z)), x, y, s(z)) 1020.63/291.50 plus(n, 0) -> n 1020.63/291.50 plus(n, s(m)) -> s(plus(n, m)) 1020.63/291.50 gt(0, v) -> false 1020.63/291.50 gt(s(u), 0) -> true 1020.63/291.50 gt(s(u), s(v)) -> gt(u, v) 1020.63/291.50 1020.63/291.50 S is empty. 1020.63/291.50 Rewrite Strategy: INNERMOST 1020.63/291.50 ---------------------------------------- 1020.63/291.50 1020.63/291.50 (3) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) 1020.63/291.50 Transformed relative TRS to weighted TRS 1020.63/291.50 ---------------------------------------- 1020.63/291.50 1020.63/291.50 (4) 1020.63/291.50 Obligation:
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