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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433308468
details
property
value
status
complete
benchmark
aprove10.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n156.star.cs.uiowa.edu
space
Secret_07_TRS
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.671 seconds
cpu usage
990.27
user time
980.576
system time
9.69443
max virtual memory
3.8251088E7
max residence set size
1.470998E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^3))
output
989.65/291.55 WORST_CASE(Omega(n^1), O(n^3)) 990.04/291.58 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 990.04/291.58 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 990.04/291.58 990.04/291.58 990.04/291.58 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^3). 990.04/291.58 990.04/291.58 (0) CpxTRS 990.04/291.58 (1) RcToIrcProof [BOTH BOUNDS(ID, ID), 0 ms] 990.04/291.58 (2) CpxTRS 990.04/291.58 (3) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] 990.04/291.58 (4) CpxWeightedTrs 990.04/291.58 (5) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 990.04/291.58 (6) CpxTypedWeightedTrs 990.04/291.58 (7) CompletionProof [UPPER BOUND(ID), 0 ms] 990.04/291.58 (8) CpxTypedWeightedCompleteTrs 990.04/291.58 (9) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] 990.04/291.58 (10) CpxRNTS 990.04/291.58 (11) CompleteCoflocoProof [FINISHED, 3689 ms] 990.04/291.58 (12) BOUNDS(1, n^3) 990.04/291.58 (13) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 990.04/291.58 (14) TRS for Loop Detection 990.04/291.58 (15) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 990.04/291.58 (16) BEST 990.04/291.58 (17) proven lower bound 990.04/291.58 (18) LowerBoundPropagationProof [FINISHED, 0 ms] 990.04/291.58 (19) BOUNDS(n^1, INF) 990.04/291.58 (20) TRS for Loop Detection 990.04/291.58 990.04/291.58 990.04/291.58 ---------------------------------------- 990.04/291.58 990.04/291.58 (0) 990.04/291.58 Obligation: 990.04/291.58 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^3). 990.04/291.58 990.04/291.58 990.04/291.58 The TRS R consists of the following rules: 990.04/291.58 990.04/291.58 lessElements(l, t) -> lessE(l, t, 0) 990.04/291.58 lessE(l, t, n) -> if(le(length(l), n), le(length(toList(t)), n), l, t, n) 990.04/291.58 if(true, b, l, t, n) -> l 990.04/291.58 if(false, true, l, t, n) -> t 990.04/291.58 if(false, false, l, t, n) -> lessE(l, t, s(n)) 990.04/291.58 length(nil) -> 0 990.04/291.58 length(cons(n, l)) -> s(length(l)) 990.04/291.58 toList(leaf) -> nil 990.04/291.58 toList(node(t1, n, t2)) -> append(toList(t1), cons(n, toList(t2))) 990.04/291.58 append(nil, l2) -> l2 990.04/291.58 append(cons(n, l1), l2) -> cons(n, append(l1, l2)) 990.04/291.58 le(s(n), 0) -> false 990.04/291.58 le(0, m) -> true 990.04/291.58 le(s(n), s(m)) -> le(n, m) 990.04/291.58 a -> c 990.04/291.58 a -> d 990.04/291.58 990.04/291.58 S is empty. 990.04/291.58 Rewrite Strategy: FULL 990.04/291.58 ---------------------------------------- 990.04/291.58 990.04/291.58 (1) RcToIrcProof (BOTH BOUNDS(ID, ID)) 990.04/291.58 Converted rc-obligation to irc-obligation. 990.04/291.58 990.04/291.58 The duplicating contexts are: 990.04/291.58 lessE([], t, n) 990.04/291.58 lessE(l, t, []) 990.04/291.58 lessE(l, [], n) 990.04/291.58 990.04/291.58 990.04/291.58 The defined contexts are: 990.04/291.58 if([], x1, x2, x3, x4) 990.04/291.58 le([], x1) 990.04/291.58 if(x0, [], x2, x3, x4) 990.04/291.58 length([]) 990.04/291.58 append([], cons(x1, x2)) 990.04/291.58 append(x0, cons(x1, [])) 990.04/291.58 append([], x1) 990.04/291.58 append(x0, []) 990.04/291.58 990.04/291.58 990.04/291.58 As the TRS is an overlay system and the defined contexts and the duplicating contexts don't overlap, we have rc = irc. 990.04/291.58 ---------------------------------------- 990.04/291.58 990.04/291.58 (2) 990.04/291.58 Obligation: 990.04/291.58 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, n^3). 990.04/291.58 990.04/291.58 990.04/291.58 The TRS R consists of the following rules: 990.04/291.58 990.04/291.58 lessElements(l, t) -> lessE(l, t, 0) 990.04/291.58 lessE(l, t, n) -> if(le(length(l), n), le(length(toList(t)), n), l, t, n) 990.04/291.58 if(true, b, l, t, n) -> l 990.04/291.58 if(false, true, l, t, n) -> t 990.04/291.58 if(false, false, l, t, n) -> lessE(l, t, s(n)) 990.04/291.58 length(nil) -> 0 990.04/291.58 length(cons(n, l)) -> s(length(l)) 990.04/291.58 toList(leaf) -> nil 990.04/291.58 toList(node(t1, n, t2)) -> append(toList(t1), cons(n, toList(t2))) 990.04/291.58 append(nil, l2) -> l2
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