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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307973
details
property
value
status
complete
benchmark
OvConsOS_complete-noand_Z.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n091.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.646 seconds
cpu usage
446.711
user time
444.574
system time
2.13691
max virtual memory
1.8279848E7
max residence set size
5463000.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
446.63/291.59 WORST_CASE(Omega(n^1), ?) 446.63/291.60 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 446.63/291.60 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 446.63/291.60 446.63/291.60 446.63/291.60 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 446.63/291.60 446.63/291.60 (0) CpxTRS 446.63/291.60 (1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 446.63/291.60 (2) TRS for Loop Detection 446.63/291.60 (3) DecreasingLoopProof [LOWER BOUND(ID), 363 ms] 446.63/291.60 (4) BEST 446.63/291.60 (5) proven lower bound 446.63/291.60 (6) LowerBoundPropagationProof [FINISHED, 0 ms] 446.63/291.60 (7) BOUNDS(n^1, INF) 446.63/291.60 (8) TRS for Loop Detection 446.63/291.60 446.63/291.60 446.63/291.60 ---------------------------------------- 446.63/291.60 446.63/291.60 (0) 446.63/291.60 Obligation: 446.63/291.60 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 446.63/291.60 446.63/291.60 446.63/291.60 The TRS R consists of the following rules: 446.63/291.60 446.63/291.60 zeros -> cons(0, n__zeros) 446.63/291.60 U101(tt, V1, V2) -> U102(isNatKind(activate(V1)), activate(V1), activate(V2)) 446.63/291.60 U102(tt, V1, V2) -> U103(isNatIListKind(activate(V2)), activate(V1), activate(V2)) 446.63/291.60 U103(tt, V1, V2) -> U104(isNatIListKind(activate(V2)), activate(V1), activate(V2)) 446.63/291.60 U104(tt, V1, V2) -> U105(isNat(activate(V1)), activate(V2)) 446.63/291.60 U105(tt, V2) -> U106(isNatIList(activate(V2))) 446.63/291.60 U106(tt) -> tt 446.63/291.60 U11(tt, V1) -> U12(isNatIListKind(activate(V1)), activate(V1)) 446.63/291.60 U111(tt, L, N) -> U112(isNatIListKind(activate(L)), activate(L), activate(N)) 446.63/291.60 U112(tt, L, N) -> U113(isNat(activate(N)), activate(L), activate(N)) 446.63/291.60 U113(tt, L, N) -> U114(isNatKind(activate(N)), activate(L)) 446.63/291.60 U114(tt, L) -> s(length(activate(L))) 446.63/291.60 U12(tt, V1) -> U13(isNatList(activate(V1))) 446.63/291.60 U121(tt, IL) -> U122(isNatIListKind(activate(IL))) 446.63/291.60 U122(tt) -> nil 446.63/291.60 U13(tt) -> tt 446.63/291.60 U131(tt, IL, M, N) -> U132(isNatIListKind(activate(IL)), activate(IL), activate(M), activate(N)) 446.63/291.60 U132(tt, IL, M, N) -> U133(isNat(activate(M)), activate(IL), activate(M), activate(N)) 446.63/291.60 U133(tt, IL, M, N) -> U134(isNatKind(activate(M)), activate(IL), activate(M), activate(N)) 446.63/291.60 U134(tt, IL, M, N) -> U135(isNat(activate(N)), activate(IL), activate(M), activate(N)) 446.63/291.60 U135(tt, IL, M, N) -> U136(isNatKind(activate(N)), activate(IL), activate(M), activate(N)) 446.63/291.60 U136(tt, IL, M, N) -> cons(activate(N), n__take(activate(M), activate(IL))) 446.63/291.60 U21(tt, V1) -> U22(isNatKind(activate(V1)), activate(V1)) 446.63/291.60 U22(tt, V1) -> U23(isNat(activate(V1))) 446.63/291.60 U23(tt) -> tt 446.63/291.60 U31(tt, V) -> U32(isNatIListKind(activate(V)), activate(V)) 446.63/291.60 U32(tt, V) -> U33(isNatList(activate(V))) 446.63/291.60 U33(tt) -> tt 446.63/291.60 U41(tt, V1, V2) -> U42(isNatKind(activate(V1)), activate(V1), activate(V2)) 446.63/291.60 U42(tt, V1, V2) -> U43(isNatIListKind(activate(V2)), activate(V1), activate(V2)) 446.63/291.60 U43(tt, V1, V2) -> U44(isNatIListKind(activate(V2)), activate(V1), activate(V2)) 446.63/291.60 U44(tt, V1, V2) -> U45(isNat(activate(V1)), activate(V2)) 446.63/291.60 U45(tt, V2) -> U46(isNatIList(activate(V2))) 446.63/291.60 U46(tt) -> tt 446.63/291.60 U51(tt, V2) -> U52(isNatIListKind(activate(V2))) 446.63/291.60 U52(tt) -> tt 446.63/291.60 U61(tt, V2) -> U62(isNatIListKind(activate(V2))) 446.63/291.60 U62(tt) -> tt 446.63/291.60 U71(tt) -> tt 446.63/291.60 U81(tt) -> tt 446.63/291.60 U91(tt, V1, V2) -> U92(isNatKind(activate(V1)), activate(V1), activate(V2)) 446.63/291.60 U92(tt, V1, V2) -> U93(isNatIListKind(activate(V2)), activate(V1), activate(V2)) 446.63/291.60 U93(tt, V1, V2) -> U94(isNatIListKind(activate(V2)), activate(V1), activate(V2)) 446.63/291.60 U94(tt, V1, V2) -> U95(isNat(activate(V1)), activate(V2)) 446.63/291.60 U95(tt, V2) -> U96(isNatList(activate(V2))) 446.63/291.60 U96(tt) -> tt 446.63/291.60 isNat(n__0) -> tt 446.63/291.60 isNat(n__length(V1)) -> U11(isNatIListKind(activate(V1)), activate(V1)) 446.63/291.60 isNat(n__s(V1)) -> U21(isNatKind(activate(V1)), activate(V1)) 446.63/291.60 isNatIList(V) -> U31(isNatIListKind(activate(V)), activate(V)) 446.63/291.60 isNatIList(n__zeros) -> tt 446.63/291.60 isNatIList(n__cons(V1, V2)) -> U41(isNatKind(activate(V1)), activate(V1), activate(V2)) 446.63/291.60 isNatIListKind(n__nil) -> tt 446.63/291.60 isNatIListKind(n__zeros) -> tt 446.63/291.60 isNatIListKind(n__cons(V1, V2)) -> U51(isNatKind(activate(V1)), activate(V2)) 446.63/291.60 isNatIListKind(n__take(V1, V2)) -> U61(isNatKind(activate(V1)), activate(V2)) 446.63/291.60 isNatKind(n__0) -> tt 446.63/291.60 isNatKind(n__length(V1)) -> U71(isNatIListKind(activate(V1))) 446.63/291.60 isNatKind(n__s(V1)) -> U81(isNatKind(activate(V1))) 446.63/291.60 isNatList(n__nil) -> tt 446.63/291.60 isNatList(n__cons(V1, V2)) -> U91(isNatKind(activate(V1)), activate(V1), activate(V2)) 446.63/291.60 isNatList(n__take(V1, V2)) -> U101(isNatKind(activate(V1)), activate(V1), activate(V2)) 446.63/291.60 length(nil) -> 0 446.63/291.60 length(cons(N, L)) -> U111(isNatList(activate(L)), activate(L), N) 446.63/291.60 take(0, IL) -> U121(isNatIList(IL), IL) 446.63/291.60 take(s(M), cons(N, IL)) -> U131(isNatIList(activate(IL)), activate(IL), M, N) 446.63/291.60 zeros -> n__zeros 446.63/291.60 take(X1, X2) -> n__take(X1, X2) 446.63/291.60 0 -> n__0 446.63/291.60 length(X) -> n__length(X) 446.63/291.60 s(X) -> n__s(X) 446.63/291.60 cons(X1, X2) -> n__cons(X1, X2) 446.63/291.60 nil -> n__nil
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