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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313756
details
property
value
status
complete
benchmark
#3.12.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n074.star.cs.uiowa.edu
space
AG01
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
3.94563 seconds
cpu usage
12.356
user time
11.6495
system time
0.706506
max virtual memory
1.8940992E7
max residence set size
1644596.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^3), O(n^3))
output
12.24/3.89 WORST_CASE(Omega(n^3), O(n^3)) 12.24/3.90 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 12.24/3.90 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 12.24/3.90 12.24/3.90 12.24/3.90 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^3, n^3). 12.24/3.90 12.24/3.90 (0) CpxTRS 12.24/3.90 (1) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms] 12.24/3.90 (2) CdtProblem 12.24/3.90 (3) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] 12.24/3.90 (4) CdtProblem 12.24/3.90 (5) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms] 12.24/3.90 (6) CdtProblem 12.24/3.90 (7) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 49 ms] 12.24/3.90 (8) CdtProblem 12.24/3.90 (9) CdtRuleRemovalProof [UPPER BOUND(ADD(n^2)), 35 ms] 12.24/3.90 (10) CdtProblem 12.24/3.90 (11) CdtRuleRemovalProof [UPPER BOUND(ADD(n^3)), 69 ms] 12.24/3.90 (12) CdtProblem 12.24/3.90 (13) SIsEmptyProof [BOTH BOUNDS(ID, ID), 0 ms] 12.24/3.90 (14) BOUNDS(1, 1) 12.24/3.90 (15) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 12.24/3.90 (16) CpxTRS 12.24/3.90 (17) SlicingProof [LOWER BOUND(ID), 0 ms] 12.24/3.90 (18) CpxTRS 12.24/3.90 (19) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 12.24/3.90 (20) typed CpxTrs 12.24/3.90 (21) OrderProof [LOWER BOUND(ID), 0 ms] 12.24/3.90 (22) typed CpxTrs 12.24/3.90 (23) RewriteLemmaProof [LOWER BOUND(ID), 282 ms] 12.24/3.90 (24) BEST 12.24/3.90 (25) proven lower bound 12.24/3.90 (26) LowerBoundPropagationProof [FINISHED, 0 ms] 12.24/3.90 (27) BOUNDS(n^1, INF) 12.24/3.90 (28) typed CpxTrs 12.24/3.90 (29) RewriteLemmaProof [LOWER BOUND(ID), 59 ms] 12.24/3.90 (30) BEST 12.24/3.90 (31) proven lower bound 12.24/3.90 (32) LowerBoundPropagationProof [FINISHED, 0 ms] 12.24/3.90 (33) BOUNDS(n^2, INF) 12.24/3.90 (34) typed CpxTrs 12.24/3.90 (35) RewriteLemmaProof [LOWER BOUND(ID), 0 ms] 12.24/3.90 (36) proven lower bound 12.24/3.90 (37) LowerBoundPropagationProof [FINISHED, 0 ms] 12.24/3.90 (38) BOUNDS(n^3, INF) 12.24/3.90 12.24/3.90 12.24/3.90 ---------------------------------------- 12.24/3.90 12.24/3.90 (0) 12.24/3.90 Obligation: 12.24/3.90 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^3, n^3). 12.24/3.90 12.24/3.90 12.24/3.90 The TRS R consists of the following rules: 12.24/3.90 12.24/3.90 app(nil, y) -> y 12.24/3.90 app(add(n, x), y) -> add(n, app(x, y)) 12.24/3.90 reverse(nil) -> nil 12.24/3.90 reverse(add(n, x)) -> app(reverse(x), add(n, nil)) 12.24/3.90 shuffle(nil) -> nil 12.24/3.90 shuffle(add(n, x)) -> add(n, shuffle(reverse(x))) 12.24/3.90 12.24/3.90 S is empty. 12.24/3.90 Rewrite Strategy: INNERMOST 12.24/3.90 ---------------------------------------- 12.24/3.90 12.24/3.90 (1) CpxTrsToCdtProof (UPPER BOUND(ID)) 12.24/3.90 Converted Cpx (relative) TRS to CDT 12.24/3.90 ---------------------------------------- 12.24/3.90 12.24/3.90 (2) 12.24/3.90 Obligation: 12.24/3.90 Complexity Dependency Tuples Problem 12.24/3.90 12.24/3.90 Rules: 12.24/3.90 app(nil, z0) -> z0 12.24/3.90 app(add(z0, z1), z2) -> add(z0, app(z1, z2)) 12.24/3.90 reverse(nil) -> nil 12.24/3.90 reverse(add(z0, z1)) -> app(reverse(z1), add(z0, nil)) 12.24/3.90 shuffle(nil) -> nil 12.24/3.90 shuffle(add(z0, z1)) -> add(z0, shuffle(reverse(z1))) 12.24/3.90 Tuples: 12.24/3.90 APP(nil, z0) -> c 12.24/3.90 APP(add(z0, z1), z2) -> c1(APP(z1, z2)) 12.24/3.90 REVERSE(nil) -> c2 12.24/3.90 REVERSE(add(z0, z1)) -> c3(APP(reverse(z1), add(z0, nil)), REVERSE(z1)) 12.24/3.90 SHUFFLE(nil) -> c4 12.24/3.90 SHUFFLE(add(z0, z1)) -> c5(SHUFFLE(reverse(z1)), REVERSE(z1)) 12.24/3.90 S tuples: 12.24/3.90 APP(nil, z0) -> c 12.24/3.90 APP(add(z0, z1), z2) -> c1(APP(z1, z2)) 12.24/3.90 REVERSE(nil) -> c2 12.24/3.90 REVERSE(add(z0, z1)) -> c3(APP(reverse(z1), add(z0, nil)), REVERSE(z1)) 12.24/3.90 SHUFFLE(nil) -> c4 12.24/3.90 SHUFFLE(add(z0, z1)) -> c5(SHUFFLE(reverse(z1)), REVERSE(z1)) 12.24/3.90 K tuples:none 12.24/3.90 Defined Rule Symbols: app_2, reverse_1, shuffle_1 12.24/3.90
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return to Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40