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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313416
details
property
value
status
complete
benchmark
Ex7_BLR02_Z.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n112.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.651 seconds
cpu usage
331.826
user time
328.161
system time
3.66477
max virtual memory
1.921108E7
max residence set size
5677816.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^2))
output
331.49/291.61 WORST_CASE(Omega(n^1), O(n^2)) 331.49/291.62 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 331.49/291.62 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 331.49/291.62 331.49/291.62 331.49/291.62 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 331.49/291.62 331.49/291.62 (0) CpxTRS 331.49/291.62 (1) CpxTrsToCdtProof [UPPER BOUND(ID), 1 ms] 331.49/291.62 (2) CdtProblem 331.49/291.62 (3) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] 331.49/291.62 (4) CdtProblem 331.49/291.62 (5) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] 331.49/291.62 (6) CdtProblem 331.49/291.62 (7) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms] 331.49/291.62 (8) CdtProblem 331.49/291.62 (9) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms] 331.49/291.62 (10) CdtProblem 331.49/291.62 (11) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 83 ms] 331.49/291.62 (12) CdtProblem 331.49/291.62 (13) CdtRuleRemovalProof [UPPER BOUND(ADD(n^2)), 32 ms] 331.49/291.62 (14) CdtProblem 331.49/291.62 (15) CdtKnowledgeProof [FINISHED, 0 ms] 331.49/291.62 (16) BOUNDS(1, 1) 331.49/291.62 (17) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 331.49/291.62 (18) TRS for Loop Detection 331.49/291.62 (19) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 331.49/291.62 (20) BEST 331.49/291.62 (21) proven lower bound 331.49/291.62 (22) LowerBoundPropagationProof [FINISHED, 0 ms] 331.49/291.62 (23) BOUNDS(n^1, INF) 331.49/291.62 (24) TRS for Loop Detection 331.49/291.62 331.49/291.62 331.49/291.62 ---------------------------------------- 331.49/291.62 331.49/291.62 (0) 331.49/291.62 Obligation: 331.49/291.62 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 331.49/291.62 331.49/291.62 331.49/291.62 The TRS R consists of the following rules: 331.49/291.62 331.49/291.62 from(X) -> cons(X, n__from(s(X))) 331.49/291.62 head(cons(X, XS)) -> X 331.49/291.62 2nd(cons(X, XS)) -> head(activate(XS)) 331.49/291.62 take(0, XS) -> nil 331.49/291.62 take(s(N), cons(X, XS)) -> cons(X, n__take(N, activate(XS))) 331.49/291.62 sel(0, cons(X, XS)) -> X 331.49/291.62 sel(s(N), cons(X, XS)) -> sel(N, activate(XS)) 331.49/291.62 from(X) -> n__from(X) 331.49/291.62 take(X1, X2) -> n__take(X1, X2) 331.49/291.62 activate(n__from(X)) -> from(X) 331.49/291.62 activate(n__take(X1, X2)) -> take(X1, X2) 331.49/291.62 activate(X) -> X 331.49/291.62 331.49/291.62 S is empty. 331.49/291.62 Rewrite Strategy: INNERMOST 331.49/291.62 ---------------------------------------- 331.49/291.62 331.49/291.62 (1) CpxTrsToCdtProof (UPPER BOUND(ID)) 331.49/291.62 Converted Cpx (relative) TRS to CDT 331.49/291.62 ---------------------------------------- 331.49/291.62 331.49/291.62 (2) 331.49/291.62 Obligation: 331.49/291.62 Complexity Dependency Tuples Problem 331.76/291.62 331.76/291.62 Rules: 331.76/291.62 from(z0) -> cons(z0, n__from(s(z0))) 331.76/291.62 from(z0) -> n__from(z0) 331.76/291.62 head(cons(z0, z1)) -> z0 331.76/291.62 2nd(cons(z0, z1)) -> head(activate(z1)) 331.76/291.62 take(0, z0) -> nil 331.76/291.62 take(s(z0), cons(z1, z2)) -> cons(z1, n__take(z0, activate(z2))) 331.76/291.62 take(z0, z1) -> n__take(z0, z1) 331.76/291.62 sel(0, cons(z0, z1)) -> z0 331.76/291.62 sel(s(z0), cons(z1, z2)) -> sel(z0, activate(z2)) 331.76/291.62 activate(n__from(z0)) -> from(z0) 331.76/291.62 activate(n__take(z0, z1)) -> take(z0, z1) 331.76/291.62 activate(z0) -> z0 331.76/291.62 Tuples: 331.76/291.62 FROM(z0) -> c 331.76/291.62 FROM(z0) -> c1 331.76/291.62 HEAD(cons(z0, z1)) -> c2 331.76/291.62 2ND(cons(z0, z1)) -> c3(HEAD(activate(z1)), ACTIVATE(z1)) 331.76/291.62 TAKE(0, z0) -> c4 331.76/291.62 TAKE(s(z0), cons(z1, z2)) -> c5(ACTIVATE(z2)) 331.76/291.62 TAKE(z0, z1) -> c6 331.76/291.62 SEL(0, cons(z0, z1)) -> c7 331.76/291.62 SEL(s(z0), cons(z1, z2)) -> c8(SEL(z0, activate(z2)), ACTIVATE(z2)) 331.76/291.62 ACTIVATE(n__from(z0)) -> c9(FROM(z0)) 331.76/291.62 ACTIVATE(n__take(z0, z1)) -> c10(TAKE(z0, z1)) 331.76/291.62 ACTIVATE(z0) -> c11 331.76/291.62 S tuples: 331.76/291.62 FROM(z0) -> c 331.76/291.62 FROM(z0) -> c1 331.76/291.62 HEAD(cons(z0, z1)) -> c2 331.76/291.62 2ND(cons(z0, z1)) -> c3(HEAD(activate(z1)), ACTIVATE(z1)) 331.76/291.62 TAKE(0, z0) -> c4
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