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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313884
details
property
value
status
complete
benchmark
10.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n005.star.cs.uiowa.edu
space
Beerendonk_07
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.623 seconds
cpu usage
472.043
user time
466.959
system time
5.08337
max virtual memory
3.81676E7
max residence set size
6179844.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^2))
output
471.81/291.54 WORST_CASE(Omega(n^1), O(n^2)) 471.81/291.55 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 471.81/291.55 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 471.81/291.55 471.81/291.55 471.81/291.55 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 471.81/291.55 471.81/291.55 (0) CpxTRS 471.81/291.55 (1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] 471.81/291.55 (2) CpxWeightedTrs 471.81/291.55 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 471.81/291.55 (4) CpxTypedWeightedTrs 471.81/291.55 (5) CompletionProof [UPPER BOUND(ID), 0 ms] 471.81/291.55 (6) CpxTypedWeightedCompleteTrs 471.81/291.55 (7) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 1 ms] 471.81/291.55 (8) CpxRNTS 471.81/291.55 (9) CompleteCoflocoProof [FINISHED, 1076 ms] 471.81/291.55 (10) BOUNDS(1, n^2) 471.81/291.55 (11) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 471.81/291.55 (12) TRS for Loop Detection 471.81/291.55 (13) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 471.81/291.55 (14) BEST 471.81/291.55 (15) proven lower bound 471.81/291.55 (16) LowerBoundPropagationProof [FINISHED, 0 ms] 471.81/291.55 (17) BOUNDS(n^1, INF) 471.81/291.55 (18) TRS for Loop Detection 471.81/291.55 471.81/291.55 471.81/291.55 ---------------------------------------- 471.81/291.55 471.81/291.55 (0) 471.81/291.55 Obligation: 471.81/291.55 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 471.81/291.55 471.81/291.55 471.81/291.55 The TRS R consists of the following rules: 471.81/291.55 471.81/291.55 cond1(true, x) -> cond2(even(x), x) 471.81/291.55 cond2(true, x) -> cond1(neq(x, 0), div2(x)) 471.81/291.55 cond2(false, x) -> cond1(neq(x, 0), p(x)) 471.81/291.55 neq(0, 0) -> false 471.81/291.55 neq(0, s(x)) -> true 471.81/291.55 neq(s(x), 0) -> true 471.81/291.55 neq(s(x), s(y)) -> neq(x, y) 471.81/291.55 even(0) -> true 471.81/291.55 even(s(0)) -> false 471.81/291.55 even(s(s(x))) -> even(x) 471.81/291.55 div2(0) -> 0 471.81/291.55 div2(s(0)) -> 0 471.81/291.55 div2(s(s(x))) -> s(div2(x)) 471.81/291.55 p(0) -> 0 471.81/291.55 p(s(x)) -> x 471.81/291.55 471.81/291.55 S is empty. 471.81/291.55 Rewrite Strategy: INNERMOST 471.81/291.55 ---------------------------------------- 471.81/291.55 471.81/291.55 (1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) 471.81/291.55 Transformed relative TRS to weighted TRS 471.81/291.55 ---------------------------------------- 471.81/291.55 471.81/291.55 (2) 471.81/291.55 Obligation: 471.81/291.55 The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^2). 471.81/291.55 471.81/291.55 471.81/291.55 The TRS R consists of the following rules: 471.81/291.55 471.81/291.55 cond1(true, x) -> cond2(even(x), x) [1] 471.81/291.55 cond2(true, x) -> cond1(neq(x, 0), div2(x)) [1] 471.81/291.55 cond2(false, x) -> cond1(neq(x, 0), p(x)) [1] 471.81/291.55 neq(0, 0) -> false [1] 471.81/291.55 neq(0, s(x)) -> true [1] 471.81/291.55 neq(s(x), 0) -> true [1] 471.81/291.55 neq(s(x), s(y)) -> neq(x, y) [1] 471.81/291.55 even(0) -> true [1] 471.81/291.55 even(s(0)) -> false [1] 471.81/291.55 even(s(s(x))) -> even(x) [1] 471.81/291.55 div2(0) -> 0 [1] 471.81/291.55 div2(s(0)) -> 0 [1] 471.81/291.55 div2(s(s(x))) -> s(div2(x)) [1] 471.81/291.55 p(0) -> 0 [1] 471.81/291.55 p(s(x)) -> x [1] 471.81/291.55 471.81/291.55 Rewrite Strategy: INNERMOST 471.81/291.55 ---------------------------------------- 471.81/291.55 471.81/291.55 (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) 471.81/291.55 Infered types. 471.81/291.55 ---------------------------------------- 471.81/291.55 471.81/291.55 (4) 471.81/291.55 Obligation: 471.81/291.55 Runtime Complexity Weighted TRS with Types. 471.81/291.55 The TRS R consists of the following rules: 471.81/291.55 471.81/291.55 cond1(true, x) -> cond2(even(x), x) [1] 471.81/291.55 cond2(true, x) -> cond1(neq(x, 0), div2(x)) [1] 471.81/291.55 cond2(false, x) -> cond1(neq(x, 0), p(x)) [1] 471.81/291.55 neq(0, 0) -> false [1]
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