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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313503
details
property
value
status
complete
benchmark
ExSec4_2_DLMMU04_Z.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n182.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
4.57564 seconds
cpu usage
14.4427
user time
13.4707
system time
0.972005
max virtual memory
1.897794E7
max residence set size
3034580.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^1))
output
14.18/4.49 WORST_CASE(Omega(n^1), O(n^1)) 14.18/4.51 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 14.18/4.51 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 14.18/4.51 14.18/4.51 14.18/4.51 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 14.18/4.51 14.18/4.51 (0) CpxTRS 14.18/4.51 (1) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms] 14.18/4.51 (2) CdtProblem 14.18/4.51 (3) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] 14.18/4.51 (4) CdtProblem 14.18/4.51 (5) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] 14.18/4.51 (6) CdtProblem 14.18/4.51 (7) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms] 14.18/4.51 (8) CdtProblem 14.18/4.51 (9) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms] 14.18/4.51 (10) CdtProblem 14.18/4.51 (11) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 55 ms] 14.18/4.51 (12) CdtProblem 14.18/4.51 (13) SIsEmptyProof [BOTH BOUNDS(ID, ID), 0 ms] 14.18/4.51 (14) BOUNDS(1, 1) 14.18/4.51 (15) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 14.18/4.51 (16) TRS for Loop Detection 14.18/4.51 (17) DecreasingLoopProof [LOWER BOUND(ID), 25 ms] 14.18/4.51 (18) BEST 14.18/4.51 (19) proven lower bound 14.18/4.51 (20) LowerBoundPropagationProof [FINISHED, 0 ms] 14.18/4.51 (21) BOUNDS(n^1, INF) 14.18/4.51 (22) TRS for Loop Detection 14.18/4.51 14.18/4.51 14.18/4.51 ---------------------------------------- 14.18/4.51 14.18/4.51 (0) 14.18/4.51 Obligation: 14.18/4.51 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 14.18/4.51 14.18/4.51 14.18/4.51 The TRS R consists of the following rules: 14.18/4.51 14.18/4.51 natsFrom(N) -> cons(N, n__natsFrom(s(N))) 14.18/4.51 fst(pair(XS, YS)) -> XS 14.18/4.51 snd(pair(XS, YS)) -> YS 14.18/4.51 splitAt(0, XS) -> pair(nil, XS) 14.18/4.51 splitAt(s(N), cons(X, XS)) -> u(splitAt(N, activate(XS)), N, X, activate(XS)) 14.18/4.51 u(pair(YS, ZS), N, X, XS) -> pair(cons(activate(X), YS), ZS) 14.18/4.51 head(cons(N, XS)) -> N 14.18/4.51 tail(cons(N, XS)) -> activate(XS) 14.18/4.51 sel(N, XS) -> head(afterNth(N, XS)) 14.18/4.51 take(N, XS) -> fst(splitAt(N, XS)) 14.18/4.51 afterNth(N, XS) -> snd(splitAt(N, XS)) 14.18/4.51 natsFrom(X) -> n__natsFrom(X) 14.18/4.51 activate(n__natsFrom(X)) -> natsFrom(X) 14.18/4.51 activate(X) -> X 14.18/4.51 14.18/4.51 S is empty. 14.18/4.51 Rewrite Strategy: INNERMOST 14.18/4.51 ---------------------------------------- 14.18/4.51 14.18/4.51 (1) CpxTrsToCdtProof (UPPER BOUND(ID)) 14.18/4.51 Converted Cpx (relative) TRS to CDT 14.18/4.51 ---------------------------------------- 14.18/4.51 14.18/4.51 (2) 14.18/4.51 Obligation: 14.18/4.51 Complexity Dependency Tuples Problem 14.18/4.51 14.18/4.51 Rules: 14.18/4.51 natsFrom(z0) -> cons(z0, n__natsFrom(s(z0))) 14.18/4.51 natsFrom(z0) -> n__natsFrom(z0) 14.18/4.51 fst(pair(z0, z1)) -> z0 14.18/4.51 snd(pair(z0, z1)) -> z1 14.18/4.51 splitAt(0, z0) -> pair(nil, z0) 14.18/4.51 splitAt(s(z0), cons(z1, z2)) -> u(splitAt(z0, activate(z2)), z0, z1, activate(z2)) 14.18/4.51 u(pair(z0, z1), z2, z3, z4) -> pair(cons(activate(z3), z0), z1) 14.18/4.51 head(cons(z0, z1)) -> z0 14.18/4.51 tail(cons(z0, z1)) -> activate(z1) 14.18/4.51 sel(z0, z1) -> head(afterNth(z0, z1)) 14.18/4.51 take(z0, z1) -> fst(splitAt(z0, z1)) 14.18/4.51 afterNth(z0, z1) -> snd(splitAt(z0, z1)) 14.18/4.51 activate(n__natsFrom(z0)) -> natsFrom(z0) 14.18/4.51 activate(z0) -> z0 14.18/4.51 Tuples: 14.18/4.51 NATSFROM(z0) -> c 14.18/4.51 NATSFROM(z0) -> c1 14.18/4.51 FST(pair(z0, z1)) -> c2 14.18/4.51 SND(pair(z0, z1)) -> c3 14.18/4.51 SPLITAT(0, z0) -> c4 14.18/4.51 SPLITAT(s(z0), cons(z1, z2)) -> c5(U(splitAt(z0, activate(z2)), z0, z1, activate(z2)), SPLITAT(z0, activate(z2)), ACTIVATE(z2), ACTIVATE(z2)) 14.18/4.51 U(pair(z0, z1), z2, z3, z4) -> c6(ACTIVATE(z3)) 14.18/4.51 HEAD(cons(z0, z1)) -> c7 14.18/4.51 TAIL(cons(z0, z1)) -> c8(ACTIVATE(z1)) 14.18/4.51 SEL(z0, z1) -> c9(HEAD(afterNth(z0, z1)), AFTERNTH(z0, z1)) 14.18/4.51 TAKE(z0, z1) -> c10(FST(splitAt(z0, z1)), SPLITAT(z0, z1)) 14.18/4.51 AFTERNTH(z0, z1) -> c11(SND(splitAt(z0, z1)), SPLITAT(z0, z1)) 14.18/4.51 ACTIVATE(n__natsFrom(z0)) -> c12(NATSFROM(z0)) 14.18/4.51 ACTIVATE(z0) -> c13 14.18/4.51 S tuples: 14.18/4.51 NATSFROM(z0) -> c
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