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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313891
details
property
value
status
complete
benchmark
17.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n031.star.cs.uiowa.edu
space
Beerendonk_07
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.731 seconds
cpu usage
1148.72
user time
1133.86
system time
14.8603
max virtual memory
5.6609104E7
max residence set size
1.46616E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^2))
output
1148.12/291.58 WORST_CASE(Omega(n^1), O(n^2)) 1148.34/291.61 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 1148.34/291.61 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1148.34/291.61 1148.34/291.61 1148.34/291.61 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 1148.34/291.61 1148.34/291.61 (0) CpxTRS 1148.34/291.61 (1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] 1148.34/291.61 (2) CpxWeightedTrs 1148.34/291.61 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 1148.34/291.61 (4) CpxTypedWeightedTrs 1148.34/291.61 (5) CompletionProof [UPPER BOUND(ID), 0 ms] 1148.34/291.61 (6) CpxTypedWeightedCompleteTrs 1148.34/291.61 (7) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] 1148.34/291.61 (8) CpxRNTS 1148.34/291.61 (9) CompleteCoflocoProof [FINISHED, 1105 ms] 1148.34/291.61 (10) BOUNDS(1, n^2) 1148.34/291.61 (11) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 1148.34/291.61 (12) TRS for Loop Detection 1148.34/291.61 (13) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 1148.34/291.61 (14) BEST 1148.34/291.61 (15) proven lower bound 1148.34/291.61 (16) LowerBoundPropagationProof [FINISHED, 0 ms] 1148.34/291.61 (17) BOUNDS(n^1, INF) 1148.34/291.61 (18) TRS for Loop Detection 1148.34/291.61 1148.34/291.61 1148.34/291.61 ---------------------------------------- 1148.34/291.61 1148.34/291.61 (0) 1148.34/291.61 Obligation: 1148.34/291.61 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 1148.34/291.61 1148.34/291.61 1148.34/291.61 The TRS R consists of the following rules: 1148.34/291.61 1148.34/291.61 cond1(true, x, y) -> cond2(gr(x, y), x, y) 1148.34/291.61 cond2(true, x, y) -> cond1(gr(add(x, y), 0), p(x), y) 1148.34/291.61 cond2(false, x, y) -> cond3(eq(x, y), x, y) 1148.34/291.61 cond3(true, x, y) -> cond1(gr(add(x, y), 0), p(x), y) 1148.34/291.61 cond3(false, x, y) -> cond1(gr(add(x, y), 0), x, p(y)) 1148.34/291.61 gr(0, x) -> false 1148.34/291.61 gr(s(x), 0) -> true 1148.34/291.61 gr(s(x), s(y)) -> gr(x, y) 1148.34/291.61 add(0, x) -> x 1148.34/291.61 add(s(x), y) -> s(add(x, y)) 1148.34/291.61 eq(0, 0) -> true 1148.34/291.61 eq(0, s(x)) -> false 1148.34/291.61 eq(s(x), 0) -> false 1148.34/291.61 eq(s(x), s(y)) -> eq(x, y) 1148.34/291.61 p(0) -> 0 1148.34/291.61 p(s(x)) -> x 1148.34/291.61 1148.34/291.61 S is empty. 1148.34/291.61 Rewrite Strategy: INNERMOST 1148.34/291.61 ---------------------------------------- 1148.34/291.61 1148.34/291.61 (1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) 1148.34/291.61 Transformed relative TRS to weighted TRS 1148.34/291.61 ---------------------------------------- 1148.34/291.61 1148.34/291.61 (2) 1148.34/291.61 Obligation: 1148.34/291.61 The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^2). 1148.34/291.61 1148.34/291.61 1148.34/291.61 The TRS R consists of the following rules: 1148.34/291.61 1148.34/291.61 cond1(true, x, y) -> cond2(gr(x, y), x, y) [1] 1148.34/291.61 cond2(true, x, y) -> cond1(gr(add(x, y), 0), p(x), y) [1] 1148.34/291.61 cond2(false, x, y) -> cond3(eq(x, y), x, y) [1] 1148.34/291.61 cond3(true, x, y) -> cond1(gr(add(x, y), 0), p(x), y) [1] 1148.34/291.61 cond3(false, x, y) -> cond1(gr(add(x, y), 0), x, p(y)) [1] 1148.34/291.61 gr(0, x) -> false [1] 1148.34/291.61 gr(s(x), 0) -> true [1] 1148.34/291.61 gr(s(x), s(y)) -> gr(x, y) [1] 1148.34/291.61 add(0, x) -> x [1] 1148.34/291.61 add(s(x), y) -> s(add(x, y)) [1] 1148.34/291.61 eq(0, 0) -> true [1] 1148.34/291.61 eq(0, s(x)) -> false [1] 1148.34/291.61 eq(s(x), 0) -> false [1] 1148.34/291.61 eq(s(x), s(y)) -> eq(x, y) [1] 1148.34/291.61 p(0) -> 0 [1] 1148.34/291.61 p(s(x)) -> x [1] 1148.34/291.61 1148.34/291.61 Rewrite Strategy: INNERMOST 1148.34/291.61 ---------------------------------------- 1148.34/291.61 1148.34/291.61 (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) 1148.34/291.61 Infered types. 1148.34/291.61 ---------------------------------------- 1148.34/291.61 1148.34/291.61 (4) 1148.34/291.61 Obligation: 1148.34/291.61 Runtime Complexity Weighted TRS with Types. 1148.34/291.61 The TRS R consists of the following rules: 1148.34/291.61 1148.34/291.61 cond1(true, x, y) -> cond2(gr(x, y), x, y) [1] 1148.34/291.61 cond2(true, x, y) -> cond1(gr(add(x, y), 0), p(x), y) [1]
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