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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307746
details
property
value
status
complete
benchmark
thiemann34.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n135.star.cs.uiowa.edu
space
AProVE_07
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.657 seconds
cpu usage
1103.09
user time
1090.89
system time
12.1997
max virtual memory
3.7826976E7
max residence set size
1.2219288E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^2))
output
1097.33/291.52 WORST_CASE(Omega(n^1), O(n^2)) 1097.33/291.57 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 1097.33/291.57 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1097.33/291.57 1097.33/291.57 1097.33/291.57 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 1097.33/291.57 1097.33/291.57 (0) CpxTRS 1097.33/291.57 (1) RcToIrcProof [BOTH BOUNDS(ID, ID), 0 ms] 1097.33/291.57 (2) CpxTRS 1097.33/291.57 (3) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] 1097.33/291.57 (4) CpxWeightedTrs 1097.33/291.57 (5) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 1097.33/291.57 (6) CpxTypedWeightedTrs 1097.33/291.57 (7) CompletionProof [UPPER BOUND(ID), 0 ms] 1097.33/291.57 (8) CpxTypedWeightedCompleteTrs 1097.33/291.57 (9) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] 1097.33/291.57 (10) CpxRNTS 1097.33/291.57 (11) CompleteCoflocoProof [FINISHED, 807 ms] 1097.33/291.57 (12) BOUNDS(1, n^2) 1097.33/291.57 (13) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 1097.33/291.57 (14) TRS for Loop Detection 1097.33/291.57 (15) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 1097.33/291.57 (16) BEST 1097.33/291.57 (17) proven lower bound 1097.33/291.57 (18) LowerBoundPropagationProof [FINISHED, 0 ms] 1097.33/291.57 (19) BOUNDS(n^1, INF) 1097.33/291.57 (20) TRS for Loop Detection 1097.33/291.57 1097.33/291.57 1097.33/291.57 ---------------------------------------- 1097.33/291.57 1097.33/291.57 (0) 1097.33/291.57 Obligation: 1097.33/291.57 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 1097.33/291.57 1097.33/291.57 1097.33/291.57 The TRS R consists of the following rules: 1097.33/291.57 1097.33/291.57 gt(s(x), 0) -> true 1097.33/291.57 gt(0, y) -> false 1097.33/291.57 gt(s(x), s(y)) -> gt(x, y) 1097.33/291.57 divides(x, y) -> div(x, y, y) 1097.33/291.57 div(0, 0, z) -> true 1097.33/291.57 div(0, s(x), z) -> false 1097.33/291.57 div(s(x), 0, s(z)) -> div(s(x), s(z), s(z)) 1097.33/291.57 div(s(x), s(y), z) -> div(x, y, z) 1097.33/291.57 prime(x) -> test(x, s(s(0))) 1097.33/291.57 test(x, y) -> if1(gt(x, y), x, y) 1097.33/291.57 if1(true, x, y) -> if2(divides(x, y), x, y) 1097.33/291.57 if1(false, x, y) -> true 1097.33/291.57 if2(true, x, y) -> false 1097.33/291.57 if2(false, x, y) -> test(x, s(y)) 1097.33/291.57 1097.33/291.57 S is empty. 1097.33/291.57 Rewrite Strategy: FULL 1097.33/291.57 ---------------------------------------- 1097.33/291.57 1097.33/291.57 (1) RcToIrcProof (BOTH BOUNDS(ID, ID)) 1097.33/291.57 Converted rc-obligation to irc-obligation. 1097.33/291.57 1097.33/291.57 The duplicating contexts are: 1097.33/291.57 divides(x, []) 1097.33/291.57 div(s(x), 0, s([])) 1097.33/291.57 test([], y) 1097.33/291.57 test(x, []) 1097.33/291.57 if1(true, [], y) 1097.33/291.57 if1(true, x, []) 1097.33/291.57 1097.33/291.57 1097.33/291.57 The defined contexts are: 1097.33/291.57 if2([], x1, x2) 1097.33/291.57 if1([], x1, x2) 1097.33/291.57 1097.33/291.57 1097.33/291.57 [] just represents basic- or constructor-terms in the following defined contexts: 1097.33/291.57 if2([], x1, x2) 1097.33/291.57 if1([], x1, x2) 1097.33/291.57 1097.33/291.57 1097.33/291.57 As the TRS is an overlay system and the defined contexts and the duplicating contexts don't overlap, we have rc = irc. 1097.33/291.57 ---------------------------------------- 1097.33/291.57 1097.33/291.57 (2) 1097.33/291.57 Obligation: 1097.33/291.57 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, n^2). 1097.33/291.57 1097.33/291.57 1097.33/291.57 The TRS R consists of the following rules: 1097.33/291.57 1097.33/291.57 gt(s(x), 0) -> true 1097.33/291.57 gt(0, y) -> false 1097.33/291.57 gt(s(x), s(y)) -> gt(x, y) 1097.33/291.57 divides(x, y) -> div(x, y, y) 1097.33/291.57 div(0, 0, z) -> true 1097.33/291.57 div(0, s(x), z) -> false 1097.33/291.57 div(s(x), 0, s(z)) -> div(s(x), s(z), s(z)) 1097.33/291.57 div(s(x), s(y), z) -> div(x, y, z) 1097.33/291.57 prime(x) -> test(x, s(s(0))) 1097.33/291.57 test(x, y) -> if1(gt(x, y), x, y)
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