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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307926
details
property
value
status
complete
benchmark
cade14.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n136.star.cs.uiowa.edu
space
GTSSK07
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.63 seconds
cpu usage
1120.41
user time
1109.62
system time
10.7892
max virtual memory
5.6800228E7
max residence set size
1.0782272E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^2))
output
1120.18/291.53 WORST_CASE(Omega(n^1), O(n^2)) 1120.20/291.56 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 1120.20/291.56 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1120.20/291.56 1120.20/291.56 1120.20/291.56 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 1120.20/291.56 1120.20/291.56 (0) CpxTRS 1120.20/291.56 (1) RcToIrcProof [BOTH BOUNDS(ID, ID), 0 ms] 1120.20/291.56 (2) CpxTRS 1120.20/291.56 (3) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] 1120.20/291.56 (4) CpxWeightedTrs 1120.20/291.56 (5) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 1120.20/291.56 (6) CpxTypedWeightedTrs 1120.20/291.56 (7) CompletionProof [UPPER BOUND(ID), 0 ms] 1120.20/291.56 (8) CpxTypedWeightedCompleteTrs 1120.20/291.56 (9) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 2 ms] 1120.20/291.56 (10) CpxRNTS 1120.20/291.56 (11) CompleteCoflocoProof [FINISHED, 541 ms] 1120.20/291.56 (12) BOUNDS(1, n^2) 1120.20/291.56 (13) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 1120.20/291.56 (14) TRS for Loop Detection 1120.20/291.56 (15) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 1120.20/291.56 (16) BEST 1120.20/291.56 (17) proven lower bound 1120.20/291.56 (18) LowerBoundPropagationProof [FINISHED, 0 ms] 1120.20/291.56 (19) BOUNDS(n^1, INF) 1120.20/291.56 (20) TRS for Loop Detection 1120.20/291.56 1120.20/291.56 1120.20/291.56 ---------------------------------------- 1120.20/291.56 1120.20/291.56 (0) 1120.20/291.56 Obligation: 1120.20/291.56 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 1120.20/291.56 1120.20/291.56 1120.20/291.56 The TRS R consists of the following rules: 1120.20/291.56 1120.20/291.56 diff(x, y) -> cond1(equal(x, y), x, y) 1120.20/291.56 cond1(true, x, y) -> 0 1120.20/291.56 cond1(false, x, y) -> cond2(gt(x, y), x, y) 1120.20/291.56 cond2(true, x, y) -> s(diff(x, s(y))) 1120.20/291.56 cond2(false, x, y) -> s(diff(s(x), y)) 1120.20/291.56 gt(0, v) -> false 1120.20/291.56 gt(s(u), 0) -> true 1120.20/291.56 gt(s(u), s(v)) -> gt(u, v) 1120.20/291.56 equal(0, 0) -> true 1120.20/291.56 equal(s(x), 0) -> false 1120.20/291.56 equal(0, s(y)) -> false 1120.20/291.56 equal(s(x), s(y)) -> equal(x, y) 1120.20/291.56 1120.20/291.56 S is empty. 1120.20/291.56 Rewrite Strategy: FULL 1120.20/291.56 ---------------------------------------- 1120.20/291.56 1120.20/291.56 (1) RcToIrcProof (BOTH BOUNDS(ID, ID)) 1120.20/291.56 Converted rc-obligation to irc-obligation. 1120.20/291.56 1120.20/291.56 The duplicating contexts are: 1120.20/291.56 diff([], y) 1120.20/291.56 diff(x, []) 1120.20/291.56 cond1(false, [], y) 1120.20/291.56 cond1(false, x, []) 1120.20/291.56 1120.20/291.56 1120.20/291.56 The defined contexts are: 1120.20/291.56 cond2([], x1, x2) 1120.20/291.56 cond1([], x1, x2) 1120.20/291.56 1120.20/291.56 1120.20/291.56 [] just represents basic- or constructor-terms in the following defined contexts: 1120.20/291.56 cond2([], x1, x2) 1120.20/291.56 cond1([], x1, x2) 1120.20/291.56 1120.20/291.56 1120.20/291.56 As the TRS is an overlay system and the defined contexts and the duplicating contexts don't overlap, we have rc = irc. 1120.20/291.56 ---------------------------------------- 1120.20/291.56 1120.20/291.56 (2) 1120.20/291.56 Obligation: 1120.20/291.56 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, n^2). 1120.20/291.56 1120.20/291.56 1120.20/291.56 The TRS R consists of the following rules: 1120.20/291.56 1120.20/291.56 diff(x, y) -> cond1(equal(x, y), x, y) 1120.20/291.56 cond1(true, x, y) -> 0 1120.20/291.56 cond1(false, x, y) -> cond2(gt(x, y), x, y) 1120.20/291.56 cond2(true, x, y) -> s(diff(x, s(y))) 1120.20/291.56 cond2(false, x, y) -> s(diff(s(x), y)) 1120.20/291.56 gt(0, v) -> false 1120.20/291.56 gt(s(u), 0) -> true 1120.20/291.56 gt(s(u), s(v)) -> gt(u, v) 1120.20/291.56 equal(0, 0) -> true 1120.20/291.56 equal(s(x), 0) -> false 1120.20/291.56 equal(0, s(y)) -> false 1120.20/291.56 equal(s(x), s(y)) -> equal(x, y) 1120.20/291.56 1120.20/291.56 S is empty.
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