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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313466
details
property
value
status
complete
benchmark
Ex1_Luc02b_Z.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n102.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.591 seconds
cpu usage
334.129
user time
330.628
system time
3.50098
max virtual memory
3.7705104E7
max residence set size
5727664.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^2))
output
333.96/291.54 WORST_CASE(Omega(n^1), O(n^2)) 333.96/291.55 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 333.96/291.55 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 333.96/291.55 333.96/291.55 333.96/291.55 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 333.96/291.55 333.96/291.55 (0) CpxTRS 333.96/291.55 (1) CpxTrsToCdtProof [UPPER BOUND(ID), 5 ms] 333.96/291.55 (2) CdtProblem 333.96/291.55 (3) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] 333.96/291.55 (4) CdtProblem 333.96/291.55 (5) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms] 333.96/291.55 (6) CdtProblem 333.96/291.55 (7) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 91 ms] 333.96/291.55 (8) CdtProblem 333.96/291.55 (9) CdtRuleRemovalProof [UPPER BOUND(ADD(n^2)), 34 ms] 333.96/291.55 (10) CdtProblem 333.96/291.55 (11) CdtKnowledgeProof [FINISHED, 0 ms] 333.96/291.55 (12) BOUNDS(1, 1) 333.96/291.55 (13) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 333.96/291.55 (14) TRS for Loop Detection 333.96/291.55 (15) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 333.96/291.55 (16) BEST 333.96/291.55 (17) proven lower bound 333.96/291.55 (18) LowerBoundPropagationProof [FINISHED, 0 ms] 333.96/291.55 (19) BOUNDS(n^1, INF) 333.96/291.55 (20) TRS for Loop Detection 333.96/291.55 333.96/291.55 333.96/291.55 ---------------------------------------- 333.96/291.55 333.96/291.55 (0) 333.96/291.55 Obligation: 333.96/291.55 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 333.96/291.55 333.96/291.55 333.96/291.55 The TRS R consists of the following rules: 333.96/291.55 333.96/291.55 from(X) -> cons(X, n__from(s(X))) 333.96/291.55 first(0, Z) -> nil 333.96/291.55 first(s(X), cons(Y, Z)) -> cons(Y, n__first(X, activate(Z))) 333.96/291.55 sel(0, cons(X, Z)) -> X 333.96/291.55 sel(s(X), cons(Y, Z)) -> sel(X, activate(Z)) 333.96/291.55 from(X) -> n__from(X) 333.96/291.55 first(X1, X2) -> n__first(X1, X2) 333.96/291.55 activate(n__from(X)) -> from(X) 333.96/291.55 activate(n__first(X1, X2)) -> first(X1, X2) 333.96/291.55 activate(X) -> X 333.96/291.55 333.96/291.55 S is empty. 333.96/291.55 Rewrite Strategy: INNERMOST 333.96/291.55 ---------------------------------------- 333.96/291.55 333.96/291.55 (1) CpxTrsToCdtProof (UPPER BOUND(ID)) 333.96/291.55 Converted Cpx (relative) TRS to CDT 333.96/291.55 ---------------------------------------- 333.96/291.55 333.96/291.55 (2) 333.96/291.55 Obligation: 333.96/291.55 Complexity Dependency Tuples Problem 333.96/291.55 333.96/291.55 Rules: 333.96/291.55 from(z0) -> cons(z0, n__from(s(z0))) 333.96/291.55 from(z0) -> n__from(z0) 333.96/291.55 first(0, z0) -> nil 333.96/291.55 first(s(z0), cons(z1, z2)) -> cons(z1, n__first(z0, activate(z2))) 333.96/291.55 first(z0, z1) -> n__first(z0, z1) 333.96/291.55 sel(0, cons(z0, z1)) -> z0 333.96/291.55 sel(s(z0), cons(z1, z2)) -> sel(z0, activate(z2)) 333.96/291.55 activate(n__from(z0)) -> from(z0) 333.96/291.55 activate(n__first(z0, z1)) -> first(z0, z1) 333.96/291.55 activate(z0) -> z0 333.96/291.55 Tuples: 333.96/291.55 FROM(z0) -> c 333.96/291.55 FROM(z0) -> c1 333.96/291.55 FIRST(0, z0) -> c2 333.96/291.55 FIRST(s(z0), cons(z1, z2)) -> c3(ACTIVATE(z2)) 333.96/291.55 FIRST(z0, z1) -> c4 333.96/291.55 SEL(0, cons(z0, z1)) -> c5 333.96/291.55 SEL(s(z0), cons(z1, z2)) -> c6(SEL(z0, activate(z2)), ACTIVATE(z2)) 333.96/291.55 ACTIVATE(n__from(z0)) -> c7(FROM(z0)) 333.96/291.55 ACTIVATE(n__first(z0, z1)) -> c8(FIRST(z0, z1)) 333.96/291.55 ACTIVATE(z0) -> c9 333.96/291.55 S tuples: 333.96/291.55 FROM(z0) -> c 333.96/291.55 FROM(z0) -> c1 333.96/291.55 FIRST(0, z0) -> c2 333.96/291.55 FIRST(s(z0), cons(z1, z2)) -> c3(ACTIVATE(z2)) 333.96/291.55 FIRST(z0, z1) -> c4 333.96/291.55 SEL(0, cons(z0, z1)) -> c5 333.96/291.55 SEL(s(z0), cons(z1, z2)) -> c6(SEL(z0, activate(z2)), ACTIVATE(z2)) 333.96/291.55 ACTIVATE(n__from(z0)) -> c7(FROM(z0)) 333.96/291.55 ACTIVATE(n__first(z0, z1)) -> c8(FIRST(z0, z1)) 333.96/291.55 ACTIVATE(z0) -> c9 333.96/291.55 K tuples:none 333.96/291.55 Defined Rule Symbols: from_1, first_2, sel_2, activate_1 333.96/291.55 333.96/291.55 Defined Pair Symbols: FROM_1, FIRST_2, SEL_2, ACTIVATE_1 333.96/291.55
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