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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313721
details
property
value
status
complete
benchmark
otto01.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n138.star.cs.uiowa.edu
space
AProVE_07
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
63.5866 seconds
cpu usage
246.291
user time
238.646
system time
7.6444
max virtual memory
3.79066E7
max residence set size
9943928.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^1))
output
245.92/63.50 WORST_CASE(Omega(n^1), O(n^1)) 245.92/63.51 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 245.92/63.51 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 245.92/63.51 245.92/63.51 245.92/63.51 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 245.92/63.51 245.92/63.51 (0) CpxTRS 245.92/63.51 (1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] 245.92/63.51 (2) CpxWeightedTrs 245.92/63.51 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 2 ms] 245.92/63.51 (4) CpxTypedWeightedTrs 245.92/63.51 (5) CompletionProof [UPPER BOUND(ID), 0 ms] 245.92/63.51 (6) CpxTypedWeightedCompleteTrs 245.92/63.51 (7) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 2 ms] 245.92/63.51 (8) CpxRNTS 245.92/63.51 (9) CompleteCoflocoProof [FINISHED, 4097 ms] 245.92/63.51 (10) BOUNDS(1, n^1) 245.92/63.51 (11) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 245.92/63.51 (12) TRS for Loop Detection 245.92/63.51 (13) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 245.92/63.51 (14) BEST 245.92/63.51 (15) proven lower bound 245.92/63.51 (16) LowerBoundPropagationProof [FINISHED, 0 ms] 245.92/63.51 (17) BOUNDS(n^1, INF) 245.92/63.51 (18) TRS for Loop Detection 245.92/63.51 245.92/63.51 245.92/63.51 ---------------------------------------- 245.92/63.51 245.92/63.51 (0) 245.92/63.51 Obligation: 245.92/63.51 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 245.92/63.51 245.92/63.51 245.92/63.51 The TRS R consists of the following rules: 245.92/63.51 245.92/63.51 min(0, y) -> 0 245.92/63.51 min(s(x), 0) -> 0 245.92/63.51 min(s(x), s(y)) -> min(x, y) 245.92/63.51 len(nil) -> 0 245.92/63.51 len(cons(x, xs)) -> s(len(xs)) 245.92/63.51 sum(x, 0) -> x 245.92/63.51 sum(x, s(y)) -> s(sum(x, y)) 245.92/63.51 le(0, x) -> true 245.92/63.51 le(s(x), 0) -> false 245.92/63.51 le(s(x), s(y)) -> le(x, y) 245.92/63.51 take(0, cons(y, ys)) -> y 245.92/63.51 take(s(x), cons(y, ys)) -> take(x, ys) 245.92/63.51 addList(x, y) -> if(le(0, min(len(x), len(y))), 0, x, y, nil) 245.92/63.51 if(false, c, x, y, z) -> z 245.92/63.51 if(true, c, xs, ys, z) -> if(le(s(c), min(len(xs), len(ys))), s(c), xs, ys, cons(sum(take(c, xs), take(c, ys)), z)) 245.92/63.51 245.92/63.51 S is empty. 245.92/63.51 Rewrite Strategy: INNERMOST 245.92/63.51 ---------------------------------------- 245.92/63.51 245.92/63.51 (1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) 245.92/63.51 Transformed relative TRS to weighted TRS 245.92/63.51 ---------------------------------------- 245.92/63.51 245.92/63.51 (2) 245.92/63.51 Obligation: 245.92/63.51 The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^1). 245.92/63.51 245.92/63.51 245.92/63.51 The TRS R consists of the following rules: 245.92/63.51 245.92/63.51 min(0, y) -> 0 [1] 245.92/63.51 min(s(x), 0) -> 0 [1] 245.92/63.51 min(s(x), s(y)) -> min(x, y) [1] 245.92/63.51 len(nil) -> 0 [1] 245.92/63.51 len(cons(x, xs)) -> s(len(xs)) [1] 245.92/63.51 sum(x, 0) -> x [1] 245.92/63.51 sum(x, s(y)) -> s(sum(x, y)) [1] 245.92/63.51 le(0, x) -> true [1] 245.92/63.51 le(s(x), 0) -> false [1] 245.92/63.51 le(s(x), s(y)) -> le(x, y) [1] 245.92/63.51 take(0, cons(y, ys)) -> y [1] 245.92/63.51 take(s(x), cons(y, ys)) -> take(x, ys) [1] 245.92/63.51 addList(x, y) -> if(le(0, min(len(x), len(y))), 0, x, y, nil) [1] 245.92/63.51 if(false, c, x, y, z) -> z [1] 245.92/63.51 if(true, c, xs, ys, z) -> if(le(s(c), min(len(xs), len(ys))), s(c), xs, ys, cons(sum(take(c, xs), take(c, ys)), z)) [1] 245.92/63.51 245.92/63.51 Rewrite Strategy: INNERMOST 245.92/63.51 ---------------------------------------- 245.92/63.51 245.92/63.51 (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) 245.92/63.51 Infered types. 245.92/63.51 ---------------------------------------- 245.92/63.51 245.92/63.51 (4) 245.92/63.51 Obligation: 245.92/63.51 Runtime Complexity Weighted TRS with Types. 245.92/63.51 The TRS R consists of the following rules: 245.92/63.51 245.92/63.51 min(0, y) -> 0 [1] 245.92/63.51 min(s(x), 0) -> 0 [1] 245.92/63.51 min(s(x), s(y)) -> min(x, y) [1] 245.92/63.51 len(nil) -> 0 [1]
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