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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313905
details
property
value
status
complete
benchmark
15.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n107.star.cs.uiowa.edu
space
Beerendonk_07
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.601 seconds
cpu usage
1000.51
user time
988.139
system time
12.3713
max virtual memory
3.7776304E7
max residence set size
1.338652E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^2))
output
1000.18/291.48 WORST_CASE(Omega(n^1), O(n^2)) 1000.25/291.49 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 1000.25/291.49 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1000.25/291.49 1000.25/291.49 1000.25/291.49 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 1000.25/291.49 1000.25/291.49 (0) CpxTRS 1000.25/291.49 (1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] 1000.25/291.49 (2) CpxWeightedTrs 1000.25/291.49 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 1000.25/291.49 (4) CpxTypedWeightedTrs 1000.25/291.49 (5) CompletionProof [UPPER BOUND(ID), 0 ms] 1000.25/291.49 (6) CpxTypedWeightedCompleteTrs 1000.25/291.49 (7) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 4 ms] 1000.25/291.49 (8) CpxRNTS 1000.25/291.49 (9) CompleteCoflocoProof [FINISHED, 580 ms] 1000.25/291.49 (10) BOUNDS(1, n^2) 1000.25/291.49 (11) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 1000.25/291.49 (12) TRS for Loop Detection 1000.25/291.49 (13) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 1000.25/291.49 (14) BEST 1000.25/291.49 (15) proven lower bound 1000.25/291.49 (16) LowerBoundPropagationProof [FINISHED, 0 ms] 1000.25/291.49 (17) BOUNDS(n^1, INF) 1000.25/291.49 (18) TRS for Loop Detection 1000.25/291.49 1000.25/291.49 1000.25/291.49 ---------------------------------------- 1000.25/291.49 1000.25/291.49 (0) 1000.25/291.49 Obligation: 1000.25/291.49 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 1000.25/291.49 1000.25/291.49 1000.25/291.49 The TRS R consists of the following rules: 1000.25/291.49 1000.25/291.49 cond1(true, x, y) -> cond2(gr(x, 0), x, y) 1000.25/291.49 cond2(true, x, y) -> cond1(gr(add(x, y), 0), p(x), y) 1000.25/291.49 cond2(false, x, y) -> cond3(gr(y, 0), x, y) 1000.25/291.49 cond3(true, x, y) -> cond1(gr(add(x, y), 0), x, p(y)) 1000.25/291.49 cond3(false, x, y) -> cond1(gr(add(x, y), 0), x, y) 1000.25/291.49 gr(0, x) -> false 1000.25/291.49 gr(s(x), 0) -> true 1000.25/291.49 gr(s(x), s(y)) -> gr(x, y) 1000.25/291.49 add(0, x) -> x 1000.25/291.49 add(s(x), y) -> s(add(x, y)) 1000.25/291.49 p(0) -> 0 1000.25/291.49 p(s(x)) -> x 1000.25/291.49 1000.25/291.49 S is empty. 1000.25/291.49 Rewrite Strategy: INNERMOST 1000.25/291.49 ---------------------------------------- 1000.25/291.49 1000.25/291.49 (1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) 1000.25/291.49 Transformed relative TRS to weighted TRS 1000.25/291.49 ---------------------------------------- 1000.25/291.49 1000.25/291.49 (2) 1000.25/291.49 Obligation: 1000.25/291.49 The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^2). 1000.25/291.49 1000.25/291.49 1000.25/291.49 The TRS R consists of the following rules: 1000.25/291.49 1000.25/291.49 cond1(true, x, y) -> cond2(gr(x, 0), x, y) [1] 1000.25/291.49 cond2(true, x, y) -> cond1(gr(add(x, y), 0), p(x), y) [1] 1000.25/291.49 cond2(false, x, y) -> cond3(gr(y, 0), x, y) [1] 1000.25/291.49 cond3(true, x, y) -> cond1(gr(add(x, y), 0), x, p(y)) [1] 1000.25/291.49 cond3(false, x, y) -> cond1(gr(add(x, y), 0), x, y) [1] 1000.25/291.49 gr(0, x) -> false [1] 1000.25/291.49 gr(s(x), 0) -> true [1] 1000.25/291.49 gr(s(x), s(y)) -> gr(x, y) [1] 1000.25/291.49 add(0, x) -> x [1] 1000.25/291.49 add(s(x), y) -> s(add(x, y)) [1] 1000.25/291.49 p(0) -> 0 [1] 1000.25/291.49 p(s(x)) -> x [1] 1000.25/291.49 1000.25/291.49 Rewrite Strategy: INNERMOST 1000.25/291.49 ---------------------------------------- 1000.25/291.49 1000.25/291.49 (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) 1000.25/291.49 Infered types. 1000.25/291.49 ---------------------------------------- 1000.25/291.49 1000.25/291.49 (4) 1000.25/291.49 Obligation: 1000.25/291.49 Runtime Complexity Weighted TRS with Types. 1000.25/291.49 The TRS R consists of the following rules: 1000.25/291.49 1000.25/291.49 cond1(true, x, y) -> cond2(gr(x, 0), x, y) [1] 1000.25/291.49 cond2(true, x, y) -> cond1(gr(add(x, y), 0), p(x), y) [1] 1000.25/291.49 cond2(false, x, y) -> cond3(gr(y, 0), x, y) [1] 1000.25/291.49 cond3(true, x, y) -> cond1(gr(add(x, y), 0), x, p(y)) [1] 1000.25/291.49 cond3(false, x, y) -> cond1(gr(add(x, y), 0), x, y) [1] 1000.25/291.49 gr(0, x) -> false [1] 1000.25/291.49 gr(s(x), 0) -> true [1] 1000.25/291.49 gr(s(x), s(y)) -> gr(x, y) [1] 1000.25/291.49 add(0, x) -> x [1] 1000.25/291.49 add(s(x), y) -> s(add(x, y)) [1]
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