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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433308083
details
property
value
status
complete
benchmark
LISTUTILITIES_nokinds_C.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n148.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
10.6902 seconds
cpu usage
38.1129
user time
36.1501
system time
1.96276
max virtual memory
1.961276E7
max residence set size
3946420.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^1))
output
37.74/10.63 WORST_CASE(Omega(n^1), O(n^1)) 37.74/10.64 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 37.74/10.64 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 37.74/10.64 37.74/10.64 37.74/10.64 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 37.74/10.64 37.74/10.64 (0) CpxTRS 37.74/10.64 (1) NestedDefinedSymbolProof [UPPER BOUND(ID), 0 ms] 37.74/10.64 (2) CpxTRS 37.74/10.64 (3) RcToIrcProof [BOTH BOUNDS(ID, ID), 0 ms] 37.74/10.64 (4) CpxTRS 37.74/10.64 (5) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms] 37.74/10.64 (6) CdtProblem 37.74/10.64 (7) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] 37.74/10.64 (8) CdtProblem 37.74/10.64 (9) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] 37.74/10.64 (10) CdtProblem 37.74/10.64 (11) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms] 37.74/10.64 (12) CdtProblem 37.74/10.64 (13) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 173 ms] 37.74/10.64 (14) CdtProblem 37.74/10.64 (15) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 42 ms] 37.74/10.64 (16) CdtProblem 37.74/10.64 (17) SIsEmptyProof [BOTH BOUNDS(ID, ID), 0 ms] 37.74/10.64 (18) BOUNDS(1, 1) 37.74/10.64 (19) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 37.74/10.64 (20) TRS for Loop Detection 37.74/10.64 (21) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 37.74/10.64 (22) BEST 37.74/10.64 (23) proven lower bound 37.74/10.64 (24) LowerBoundPropagationProof [FINISHED, 0 ms] 37.74/10.64 (25) BOUNDS(n^1, INF) 37.74/10.64 (26) TRS for Loop Detection 37.74/10.64 37.74/10.64 37.74/10.64 ---------------------------------------- 37.74/10.64 37.74/10.64 (0) 37.74/10.64 Obligation: 37.74/10.64 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 37.74/10.64 37.74/10.64 37.74/10.64 The TRS R consists of the following rules: 37.74/10.64 37.74/10.64 active(U101(tt, N, XS)) -> mark(fst(splitAt(N, XS))) 37.74/10.64 active(U11(tt, N, XS)) -> mark(snd(splitAt(N, XS))) 37.74/10.64 active(U21(tt, X)) -> mark(X) 37.74/10.64 active(U31(tt, N)) -> mark(N) 37.74/10.64 active(U41(tt, N)) -> mark(cons(N, natsFrom(s(N)))) 37.74/10.64 active(U51(tt, N, XS)) -> mark(head(afterNth(N, XS))) 37.74/10.64 active(U61(tt, Y)) -> mark(Y) 37.74/10.64 active(U71(tt, XS)) -> mark(pair(nil, XS)) 37.74/10.64 active(U81(tt, N, X, XS)) -> mark(U82(splitAt(N, XS), X)) 37.74/10.64 active(U82(pair(YS, ZS), X)) -> mark(pair(cons(X, YS), ZS)) 37.74/10.64 active(U91(tt, XS)) -> mark(XS) 37.74/10.64 active(afterNth(N, XS)) -> mark(U11(and(isNatural(N), isLNat(XS)), N, XS)) 37.74/10.64 active(and(tt, X)) -> mark(X) 37.74/10.64 active(fst(pair(X, Y))) -> mark(U21(and(isLNat(X), isLNat(Y)), X)) 37.74/10.64 active(head(cons(N, XS))) -> mark(U31(and(isNatural(N), isLNat(XS)), N)) 37.74/10.64 active(isLNat(nil)) -> mark(tt) 37.74/10.64 active(isLNat(afterNth(V1, V2))) -> mark(and(isNatural(V1), isLNat(V2))) 37.74/10.64 active(isLNat(cons(V1, V2))) -> mark(and(isNatural(V1), isLNat(V2))) 37.74/10.64 active(isLNat(fst(V1))) -> mark(isPLNat(V1)) 37.74/10.64 active(isLNat(natsFrom(V1))) -> mark(isNatural(V1)) 37.74/10.64 active(isLNat(snd(V1))) -> mark(isPLNat(V1)) 37.74/10.64 active(isLNat(tail(V1))) -> mark(isLNat(V1)) 37.74/10.64 active(isLNat(take(V1, V2))) -> mark(and(isNatural(V1), isLNat(V2))) 37.74/10.64 active(isNatural(0)) -> mark(tt) 37.74/10.64 active(isNatural(head(V1))) -> mark(isLNat(V1)) 37.74/10.64 active(isNatural(s(V1))) -> mark(isNatural(V1)) 37.74/10.64 active(isNatural(sel(V1, V2))) -> mark(and(isNatural(V1), isLNat(V2))) 37.74/10.64 active(isPLNat(pair(V1, V2))) -> mark(and(isLNat(V1), isLNat(V2))) 37.74/10.64 active(isPLNat(splitAt(V1, V2))) -> mark(and(isNatural(V1), isLNat(V2))) 37.74/10.64 active(natsFrom(N)) -> mark(U41(isNatural(N), N)) 37.74/10.64 active(sel(N, XS)) -> mark(U51(and(isNatural(N), isLNat(XS)), N, XS)) 37.74/10.64 active(snd(pair(X, Y))) -> mark(U61(and(isLNat(X), isLNat(Y)), Y)) 37.74/10.64 active(splitAt(0, XS)) -> mark(U71(isLNat(XS), XS)) 37.74/10.64 active(splitAt(s(N), cons(X, XS))) -> mark(U81(and(isNatural(N), and(isNatural(X), isLNat(XS))), N, X, XS)) 37.74/10.64 active(tail(cons(N, XS))) -> mark(U91(and(isNatural(N), isLNat(XS)), XS)) 37.74/10.64 active(take(N, XS)) -> mark(U101(and(isNatural(N), isLNat(XS)), N, XS)) 37.74/10.64 active(U101(X1, X2, X3)) -> U101(active(X1), X2, X3) 37.74/10.64 active(fst(X)) -> fst(active(X)) 37.74/10.64 active(splitAt(X1, X2)) -> splitAt(active(X1), X2) 37.74/10.64 active(splitAt(X1, X2)) -> splitAt(X1, active(X2)) 37.74/10.64 active(U11(X1, X2, X3)) -> U11(active(X1), X2, X3) 37.74/10.64 active(snd(X)) -> snd(active(X)) 37.74/10.64 active(U21(X1, X2)) -> U21(active(X1), X2) 37.74/10.64 active(U31(X1, X2)) -> U31(active(X1), X2) 37.74/10.64 active(U41(X1, X2)) -> U41(active(X1), X2) 37.74/10.64 active(cons(X1, X2)) -> cons(active(X1), X2) 37.74/10.64 active(natsFrom(X)) -> natsFrom(active(X)) 37.74/10.64 active(s(X)) -> s(active(X)) 37.74/10.64 active(U51(X1, X2, X3)) -> U51(active(X1), X2, X3) 37.74/10.64 active(head(X)) -> head(active(X)) 37.74/10.64 active(afterNth(X1, X2)) -> afterNth(active(X1), X2) 37.74/10.64 active(afterNth(X1, X2)) -> afterNth(X1, active(X2)) 37.74/10.64 active(U61(X1, X2)) -> U61(active(X1), X2) 37.74/10.64 active(U71(X1, X2)) -> U71(active(X1), X2) 37.74/10.64 active(pair(X1, X2)) -> pair(active(X1), X2)
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