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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313586
details
property
value
status
complete
benchmark
2.39.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
SK90
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
3.75934 seconds
cpu usage
11.6645
user time
10.9548
system time
0.709678
max virtual memory
1.9077876E7
max residence set size
1985556.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^2), O(n^2))
output
11.35/3.70 WORST_CASE(Omega(n^2), O(n^2)) 11.35/3.71 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 11.35/3.71 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 11.35/3.71 11.35/3.71 11.35/3.71 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^2, n^2). 11.35/3.71 11.35/3.71 (0) CpxTRS 11.35/3.71 (1) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms] 11.35/3.71 (2) CdtProblem 11.35/3.71 (3) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] 11.35/3.71 (4) CdtProblem 11.35/3.71 (5) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms] 11.35/3.71 (6) CdtProblem 11.35/3.71 (7) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 49 ms] 11.35/3.71 (8) CdtProblem 11.35/3.71 (9) CdtRuleRemovalProof [UPPER BOUND(ADD(n^2)), 43 ms] 11.35/3.71 (10) CdtProblem 11.35/3.71 (11) SIsEmptyProof [BOTH BOUNDS(ID, ID), 0 ms] 11.35/3.71 (12) BOUNDS(1, 1) 11.35/3.71 (13) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 11.35/3.71 (14) CpxTRS 11.35/3.71 (15) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 11.35/3.71 (16) typed CpxTrs 11.35/3.71 (17) OrderProof [LOWER BOUND(ID), 0 ms] 11.35/3.71 (18) typed CpxTrs 11.35/3.71 (19) RewriteLemmaProof [LOWER BOUND(ID), 307 ms] 11.35/3.71 (20) BEST 11.35/3.71 (21) proven lower bound 11.35/3.71 (22) LowerBoundPropagationProof [FINISHED, 0 ms] 11.35/3.71 (23) BOUNDS(n^1, INF) 11.35/3.71 (24) typed CpxTrs 11.35/3.71 (25) RewriteLemmaProof [LOWER BOUND(ID), 49 ms] 11.35/3.71 (26) proven lower bound 11.35/3.71 (27) LowerBoundPropagationProof [FINISHED, 0 ms] 11.35/3.71 (28) BOUNDS(n^2, INF) 11.35/3.71 11.35/3.71 11.35/3.71 ---------------------------------------- 11.35/3.71 11.35/3.71 (0) 11.35/3.71 Obligation: 11.35/3.71 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^2, n^2). 11.35/3.71 11.35/3.71 11.35/3.71 The TRS R consists of the following rules: 11.35/3.71 11.35/3.71 rev(nil) -> nil 11.35/3.71 rev(.(x, y)) -> ++(rev(y), .(x, nil)) 11.35/3.71 car(.(x, y)) -> x 11.35/3.71 cdr(.(x, y)) -> y 11.35/3.71 null(nil) -> true 11.35/3.71 null(.(x, y)) -> false 11.35/3.71 ++(nil, y) -> y 11.35/3.71 ++(.(x, y), z) -> .(x, ++(y, z)) 11.35/3.71 11.35/3.71 S is empty. 11.35/3.71 Rewrite Strategy: INNERMOST 11.35/3.71 ---------------------------------------- 11.35/3.71 11.35/3.71 (1) CpxTrsToCdtProof (UPPER BOUND(ID)) 11.35/3.71 Converted Cpx (relative) TRS to CDT 11.35/3.71 ---------------------------------------- 11.35/3.71 11.35/3.71 (2) 11.35/3.71 Obligation: 11.35/3.71 Complexity Dependency Tuples Problem 11.35/3.71 11.35/3.71 Rules: 11.35/3.71 rev(nil) -> nil 11.35/3.71 rev(.(z0, z1)) -> ++(rev(z1), .(z0, nil)) 11.35/3.72 car(.(z0, z1)) -> z0 11.35/3.72 cdr(.(z0, z1)) -> z1 11.35/3.72 null(nil) -> true 11.35/3.72 null(.(z0, z1)) -> false 11.35/3.72 ++(nil, z0) -> z0 11.35/3.72 ++(.(z0, z1), z2) -> .(z0, ++(z1, z2)) 11.35/3.72 Tuples: 11.35/3.72 REV(nil) -> c 11.35/3.72 REV(.(z0, z1)) -> c1(++'(rev(z1), .(z0, nil)), REV(z1)) 11.35/3.72 CAR(.(z0, z1)) -> c2 11.35/3.72 CDR(.(z0, z1)) -> c3 11.35/3.72 NULL(nil) -> c4 11.35/3.72 NULL(.(z0, z1)) -> c5 11.35/3.72 ++'(nil, z0) -> c6 11.35/3.72 ++'(.(z0, z1), z2) -> c7(++'(z1, z2)) 11.35/3.72 S tuples: 11.35/3.72 REV(nil) -> c 11.35/3.72 REV(.(z0, z1)) -> c1(++'(rev(z1), .(z0, nil)), REV(z1)) 11.35/3.72 CAR(.(z0, z1)) -> c2 11.35/3.72 CDR(.(z0, z1)) -> c3 11.35/3.72 NULL(nil) -> c4 11.35/3.72 NULL(.(z0, z1)) -> c5 11.35/3.72 ++'(nil, z0) -> c6 11.35/3.72 ++'(.(z0, z1), z2) -> c7(++'(z1, z2)) 11.35/3.72 K tuples:none 11.35/3.72 Defined Rule Symbols: rev_1, car_1, cdr_1, null_1, ++_2 11.35/3.72 11.35/3.72 Defined Pair Symbols: REV_1, CAR_1, CDR_1, NULL_1, ++'_2 11.35/3.72
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