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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313563
details
property
value
status
complete
benchmark
#4.34.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n138.star.cs.uiowa.edu
space
Strategy_removed_AG01
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.597 seconds
cpu usage
464.213
user time
459.384
system time
4.82935
max virtual memory
3.7571064E7
max residence set size
6978488.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^2))
output
464.05/291.53 WORST_CASE(Omega(n^1), O(n^2)) 464.05/291.54 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 464.05/291.54 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 464.05/291.54 464.05/291.54 464.05/291.54 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 464.05/291.54 464.05/291.54 (0) CpxTRS 464.05/291.54 (1) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms] 464.05/291.54 (2) CdtProblem 464.05/291.54 (3) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] 464.05/291.54 (4) CdtProblem 464.05/291.54 (5) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] 464.05/291.54 (6) CdtProblem 464.05/291.54 (7) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 87 ms] 464.05/291.54 (8) CdtProblem 464.05/291.54 (9) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 15 ms] 464.05/291.54 (10) CdtProblem 464.05/291.54 (11) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] 464.05/291.54 (12) CdtProblem 464.05/291.54 (13) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] 464.05/291.54 (14) CdtProblem 464.05/291.54 (15) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] 464.05/291.54 (16) CdtProblem 464.05/291.54 (17) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] 464.05/291.54 (18) CdtProblem 464.05/291.54 (19) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] 464.05/291.54 (20) CdtProblem 464.05/291.54 (21) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] 464.05/291.54 (22) CdtProblem 464.05/291.54 (23) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] 464.05/291.54 (24) CdtProblem 464.05/291.54 (25) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] 464.05/291.54 (26) CdtProblem 464.05/291.54 (27) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] 464.05/291.54 (28) CdtProblem 464.05/291.54 (29) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] 464.05/291.54 (30) CdtProblem 464.05/291.54 (31) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] 464.05/291.54 (32) CdtProblem 464.05/291.54 (33) CdtRuleRemovalProof [UPPER BOUND(ADD(n^2)), 1884 ms] 464.05/291.54 (34) CdtProblem 464.05/291.54 (35) SIsEmptyProof [BOTH BOUNDS(ID, ID), 0 ms] 464.05/291.54 (36) BOUNDS(1, 1) 464.05/291.54 (37) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 464.05/291.54 (38) CpxTRS 464.05/291.54 (39) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 464.05/291.54 (40) typed CpxTrs 464.05/291.54 (41) OrderProof [LOWER BOUND(ID), 0 ms] 464.05/291.54 (42) typed CpxTrs 464.05/291.54 (43) RewriteLemmaProof [LOWER BOUND(ID), 190 ms] 464.05/291.54 (44) BEST 464.05/291.54 (45) proven lower bound 464.05/291.54 (46) LowerBoundPropagationProof [FINISHED, 0 ms] 464.05/291.54 (47) BOUNDS(n^1, INF) 464.05/291.54 (48) typed CpxTrs 464.05/291.54 464.05/291.54 464.05/291.54 ---------------------------------------- 464.05/291.54 464.05/291.54 (0) 464.05/291.54 Obligation: 464.05/291.54 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 464.05/291.54 464.05/291.54 464.05/291.54 The TRS R consists of the following rules: 464.05/291.54 464.05/291.54 f(0) -> true 464.05/291.54 f(1) -> false 464.05/291.54 f(s(x)) -> f(x) 464.05/291.54 if(true, x, y) -> x 464.05/291.54 if(false, x, y) -> y 464.05/291.54 g(s(x), s(y)) -> if(f(x), s(x), s(y)) 464.05/291.54 g(x, c(y)) -> g(x, g(s(c(y)), y)) 464.05/291.54 464.05/291.54 S is empty. 464.05/291.54 Rewrite Strategy: INNERMOST 464.05/291.54 ---------------------------------------- 464.05/291.54 464.05/291.54 (1) CpxTrsToCdtProof (UPPER BOUND(ID)) 464.05/291.54 Converted Cpx (relative) TRS to CDT 464.05/291.54 ---------------------------------------- 464.05/291.54 464.05/291.54 (2) 464.05/291.54 Obligation: 464.05/291.54 Complexity Dependency Tuples Problem 464.05/291.54 464.05/291.54 Rules: 464.05/291.54 f(0) -> true 464.05/291.54 f(1) -> false 464.05/291.54 f(s(z0)) -> f(z0) 464.05/291.54 if(true, z0, z1) -> z0 464.05/291.54 if(false, z0, z1) -> z1 464.05/291.54 g(s(z0), s(z1)) -> if(f(z0), s(z0), s(z1)) 464.05/291.54 g(z0, c(z1)) -> g(z0, g(s(c(z1)), z1)) 464.05/291.54 Tuples: 464.05/291.54 F(0) -> c1 464.05/291.54 F(1) -> c2 464.05/291.54 F(s(z0)) -> c3(F(z0)) 464.05/291.54 IF(true, z0, z1) -> c4
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