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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313901
details
property
value
status
complete
benchmark
21.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n180.star.cs.uiowa.edu
space
Beerendonk_07
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.638 seconds
cpu usage
1110.15
user time
1098.09
system time
12.0542
max virtual memory
1.9338944E7
max residence set size
1.5056252E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^2))
output
1109.65/291.54 WORST_CASE(Omega(n^1), O(n^2)) 1109.65/291.56 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 1109.65/291.56 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1109.65/291.56 1109.65/291.56 1109.65/291.56 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 1109.65/291.56 1109.65/291.56 (0) CpxTRS 1109.65/291.56 (1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] 1109.65/291.56 (2) CpxWeightedTrs 1109.65/291.56 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 1109.65/291.56 (4) CpxTypedWeightedTrs 1109.65/291.56 (5) CompletionProof [UPPER BOUND(ID), 0 ms] 1109.65/291.56 (6) CpxTypedWeightedCompleteTrs 1109.65/291.56 (7) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] 1109.65/291.56 (8) CpxRNTS 1109.65/291.56 (9) CompleteCoflocoProof [FINISHED, 1734 ms] 1109.65/291.56 (10) BOUNDS(1, n^2) 1109.65/291.56 (11) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 1109.65/291.56 (12) CpxTRS 1109.65/291.56 (13) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 1109.65/291.56 (14) typed CpxTrs 1109.65/291.56 (15) OrderProof [LOWER BOUND(ID), 0 ms] 1109.65/291.56 (16) typed CpxTrs 1109.65/291.56 (17) RewriteLemmaProof [LOWER BOUND(ID), 287 ms] 1109.65/291.56 (18) BEST 1109.65/291.56 (19) proven lower bound 1109.65/291.56 (20) LowerBoundPropagationProof [FINISHED, 0 ms] 1109.65/291.56 (21) BOUNDS(n^1, INF) 1109.65/291.56 (22) typed CpxTrs 1109.65/291.56 (23) RewriteLemmaProof [LOWER BOUND(ID), 90 ms] 1109.65/291.56 (24) typed CpxTrs 1109.65/291.56 1109.65/291.56 1109.65/291.56 ---------------------------------------- 1109.65/291.56 1109.65/291.56 (0) 1109.65/291.56 Obligation: 1109.65/291.56 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 1109.65/291.56 1109.65/291.56 1109.65/291.56 The TRS R consists of the following rules: 1109.65/291.56 1109.65/291.56 cond1(true, x, y, z) -> cond2(gr(y, z), x, y, z) 1109.65/291.56 cond2(true, x, y, z) -> cond2(gr(y, z), p(x), p(y), z) 1109.65/291.56 cond2(false, x, y, z) -> cond1(and(eq(x, y), gr(x, z)), x, y, z) 1109.65/291.56 gr(0, x) -> false 1109.65/291.56 gr(s(x), 0) -> true 1109.65/291.56 gr(s(x), s(y)) -> gr(x, y) 1109.65/291.56 p(0) -> 0 1109.65/291.56 p(s(x)) -> x 1109.65/291.56 eq(0, 0) -> true 1109.65/291.56 eq(s(x), 0) -> false 1109.65/291.56 eq(0, s(x)) -> false 1109.65/291.56 eq(s(x), s(y)) -> eq(x, y) 1109.65/291.56 and(true, true) -> true 1109.65/291.56 and(false, x) -> false 1109.65/291.56 and(x, false) -> false 1109.65/291.56 1109.65/291.56 S is empty. 1109.65/291.56 Rewrite Strategy: INNERMOST 1109.65/291.56 ---------------------------------------- 1109.65/291.56 1109.65/291.56 (1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) 1109.65/291.56 Transformed relative TRS to weighted TRS 1109.65/291.56 ---------------------------------------- 1109.65/291.56 1109.65/291.56 (2) 1109.65/291.56 Obligation: 1109.65/291.56 The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^2). 1109.65/291.56 1109.65/291.56 1109.65/291.56 The TRS R consists of the following rules: 1109.65/291.56 1109.65/291.56 cond1(true, x, y, z) -> cond2(gr(y, z), x, y, z) [1] 1109.65/291.56 cond2(true, x, y, z) -> cond2(gr(y, z), p(x), p(y), z) [1] 1109.65/291.56 cond2(false, x, y, z) -> cond1(and(eq(x, y), gr(x, z)), x, y, z) [1] 1109.65/291.56 gr(0, x) -> false [1] 1109.65/291.56 gr(s(x), 0) -> true [1] 1109.65/291.56 gr(s(x), s(y)) -> gr(x, y) [1] 1109.65/291.56 p(0) -> 0 [1] 1109.65/291.56 p(s(x)) -> x [1] 1109.65/291.56 eq(0, 0) -> true [1] 1109.65/291.56 eq(s(x), 0) -> false [1] 1109.65/291.56 eq(0, s(x)) -> false [1] 1109.65/291.56 eq(s(x), s(y)) -> eq(x, y) [1] 1109.65/291.56 and(true, true) -> true [1] 1109.65/291.56 and(false, x) -> false [1] 1109.65/291.56 and(x, false) -> false [1] 1109.65/291.56 1109.65/291.56 Rewrite Strategy: INNERMOST 1109.65/291.56 ---------------------------------------- 1109.65/291.56 1109.65/291.56 (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) 1109.65/291.56 Infered types. 1109.65/291.56 ---------------------------------------- 1109.65/291.56 1109.65/291.56 (4) 1109.65/291.56 Obligation: 1109.65/291.56 Runtime Complexity Weighted TRS with Types.
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