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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313888
details
property
value
status
complete
benchmark
20.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n012.star.cs.uiowa.edu
space
Beerendonk_07
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
16.5527 seconds
cpu usage
60.5414
user time
57.6884
system time
2.85294
max virtual memory
1.9125564E7
max residence set size
4484964.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^1))
output
60.40/16.49 WORST_CASE(Omega(n^1), O(n^1)) 60.40/16.50 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 60.40/16.50 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 60.40/16.50 60.40/16.50 60.40/16.50 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 60.40/16.50 60.40/16.50 (0) CpxTRS 60.40/16.50 (1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] 60.40/16.50 (2) CpxWeightedTrs 60.40/16.50 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 60.40/16.50 (4) CpxTypedWeightedTrs 60.40/16.50 (5) CompletionProof [UPPER BOUND(ID), 0 ms] 60.40/16.50 (6) CpxTypedWeightedCompleteTrs 60.40/16.50 (7) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 3 ms] 60.40/16.50 (8) CpxRNTS 60.40/16.50 (9) CompleteCoflocoProof [FINISHED, 574 ms] 60.40/16.50 (10) BOUNDS(1, n^1) 60.40/16.50 (11) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 60.40/16.50 (12) CpxTRS 60.40/16.50 (13) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 60.40/16.50 (14) typed CpxTrs 60.40/16.50 (15) OrderProof [LOWER BOUND(ID), 0 ms] 60.40/16.50 (16) typed CpxTrs 60.40/16.50 (17) RewriteLemmaProof [LOWER BOUND(ID), 297 ms] 60.40/16.50 (18) BEST 60.40/16.50 (19) proven lower bound 60.40/16.50 (20) LowerBoundPropagationProof [FINISHED, 0 ms] 60.40/16.50 (21) BOUNDS(n^1, INF) 60.40/16.50 (22) typed CpxTrs 60.40/16.50 (23) RewriteLemmaProof [LOWER BOUND(ID), 72 ms] 60.40/16.50 (24) typed CpxTrs 60.40/16.50 60.40/16.50 60.40/16.50 ---------------------------------------- 60.40/16.50 60.40/16.50 (0) 60.40/16.50 Obligation: 60.40/16.50 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 60.40/16.50 60.40/16.50 60.40/16.50 The TRS R consists of the following rules: 60.40/16.50 60.40/16.50 cond1(true, x, y) -> cond2(gr(y, 0), x, y) 60.40/16.50 cond2(true, x, y) -> cond2(gr(y, 0), p(x), p(y)) 60.40/16.50 cond2(false, x, y) -> cond1(and(eq(x, y), gr(x, 0)), x, y) 60.40/16.50 gr(0, x) -> false 60.40/16.50 gr(s(x), 0) -> true 60.40/16.50 gr(s(x), s(y)) -> gr(x, y) 60.40/16.50 p(0) -> 0 60.40/16.50 p(s(x)) -> x 60.40/16.50 eq(0, 0) -> true 60.40/16.50 eq(s(x), 0) -> false 60.40/16.50 eq(0, s(x)) -> false 60.40/16.50 eq(s(x), s(y)) -> eq(x, y) 60.40/16.50 and(true, true) -> true 60.40/16.50 and(false, x) -> false 60.40/16.50 and(x, false) -> false 60.40/16.50 60.40/16.50 S is empty. 60.40/16.50 Rewrite Strategy: INNERMOST 60.40/16.50 ---------------------------------------- 60.40/16.50 60.40/16.50 (1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) 60.40/16.50 Transformed relative TRS to weighted TRS 60.40/16.50 ---------------------------------------- 60.40/16.50 60.40/16.50 (2) 60.40/16.50 Obligation: 60.40/16.50 The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^1). 60.40/16.50 60.40/16.50 60.40/16.50 The TRS R consists of the following rules: 60.40/16.50 60.40/16.50 cond1(true, x, y) -> cond2(gr(y, 0), x, y) [1] 60.40/16.50 cond2(true, x, y) -> cond2(gr(y, 0), p(x), p(y)) [1] 60.40/16.50 cond2(false, x, y) -> cond1(and(eq(x, y), gr(x, 0)), x, y) [1] 60.40/16.50 gr(0, x) -> false [1] 60.40/16.50 gr(s(x), 0) -> true [1] 60.40/16.50 gr(s(x), s(y)) -> gr(x, y) [1] 60.40/16.50 p(0) -> 0 [1] 60.40/16.50 p(s(x)) -> x [1] 60.40/16.50 eq(0, 0) -> true [1] 60.40/16.50 eq(s(x), 0) -> false [1] 60.40/16.50 eq(0, s(x)) -> false [1] 60.40/16.50 eq(s(x), s(y)) -> eq(x, y) [1] 60.40/16.50 and(true, true) -> true [1] 60.40/16.50 and(false, x) -> false [1] 60.40/16.50 and(x, false) -> false [1] 60.40/16.50 60.40/16.50 Rewrite Strategy: INNERMOST 60.40/16.50 ---------------------------------------- 60.40/16.50 60.40/16.50 (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) 60.40/16.50 Infered types. 60.40/16.50 ---------------------------------------- 60.40/16.50 60.40/16.50 (4) 60.40/16.50 Obligation: 60.40/16.50 Runtime Complexity Weighted TRS with Types.
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