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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433308316
details
property
value
status
complete
benchmark
LengthOfFiniteLists_complete_noand_GM.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n070.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.677 seconds
cpu usage
625.708
user time
619.508
system time
6.19952
max virtual memory
1.8277336E7
max residence set size
1.024272E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
625.50/291.61 WORST_CASE(Omega(n^1), ?) 625.50/291.62 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 625.50/291.62 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 625.50/291.62 625.50/291.62 625.50/291.62 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 625.50/291.62 625.50/291.62 (0) CpxTRS 625.50/291.62 (1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 625.50/291.62 (2) TRS for Loop Detection 625.50/291.62 (3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 625.50/291.62 (4) BEST 625.50/291.62 (5) proven lower bound 625.50/291.62 (6) LowerBoundPropagationProof [FINISHED, 0 ms] 625.50/291.62 (7) BOUNDS(n^1, INF) 625.50/291.62 (8) TRS for Loop Detection 625.50/291.62 625.50/291.62 625.50/291.62 ---------------------------------------- 625.50/291.62 625.50/291.62 (0) 625.50/291.62 Obligation: 625.50/291.62 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 625.50/291.62 625.50/291.62 625.50/291.62 The TRS R consists of the following rules: 625.50/291.62 625.50/291.62 a__zeros -> cons(0, zeros) 625.50/291.62 a__U11(tt, V1) -> a__U12(a__isNatIListKind(V1), V1) 625.50/291.62 a__U12(tt, V1) -> a__U13(a__isNatList(V1)) 625.50/291.62 a__U13(tt) -> tt 625.50/291.62 a__U21(tt, V1) -> a__U22(a__isNatKind(V1), V1) 625.50/291.62 a__U22(tt, V1) -> a__U23(a__isNat(V1)) 625.50/291.62 a__U23(tt) -> tt 625.50/291.62 a__U31(tt, V) -> a__U32(a__isNatIListKind(V), V) 625.50/291.62 a__U32(tt, V) -> a__U33(a__isNatList(V)) 625.50/291.62 a__U33(tt) -> tt 625.50/291.62 a__U41(tt, V1, V2) -> a__U42(a__isNatKind(V1), V1, V2) 625.50/291.62 a__U42(tt, V1, V2) -> a__U43(a__isNatIListKind(V2), V1, V2) 625.50/291.62 a__U43(tt, V1, V2) -> a__U44(a__isNatIListKind(V2), V1, V2) 625.50/291.62 a__U44(tt, V1, V2) -> a__U45(a__isNat(V1), V2) 625.50/291.62 a__U45(tt, V2) -> a__U46(a__isNatIList(V2)) 625.50/291.62 a__U46(tt) -> tt 625.50/291.62 a__U51(tt, V2) -> a__U52(a__isNatIListKind(V2)) 625.50/291.62 a__U52(tt) -> tt 625.50/291.62 a__U61(tt) -> tt 625.50/291.62 a__U71(tt) -> tt 625.50/291.62 a__U81(tt, V1, V2) -> a__U82(a__isNatKind(V1), V1, V2) 625.50/291.62 a__U82(tt, V1, V2) -> a__U83(a__isNatIListKind(V2), V1, V2) 625.50/291.62 a__U83(tt, V1, V2) -> a__U84(a__isNatIListKind(V2), V1, V2) 625.50/291.62 a__U84(tt, V1, V2) -> a__U85(a__isNat(V1), V2) 625.50/291.62 a__U85(tt, V2) -> a__U86(a__isNatList(V2)) 625.50/291.62 a__U86(tt) -> tt 625.50/291.62 a__U91(tt, L, N) -> a__U92(a__isNatIListKind(L), L, N) 625.50/291.62 a__U92(tt, L, N) -> a__U93(a__isNat(N), L, N) 625.50/291.62 a__U93(tt, L, N) -> a__U94(a__isNatKind(N), L) 625.50/291.62 a__U94(tt, L) -> s(a__length(mark(L))) 625.50/291.62 a__isNat(0) -> tt 625.50/291.62 a__isNat(length(V1)) -> a__U11(a__isNatIListKind(V1), V1) 625.50/291.62 a__isNat(s(V1)) -> a__U21(a__isNatKind(V1), V1) 625.50/291.62 a__isNatIList(V) -> a__U31(a__isNatIListKind(V), V) 625.50/291.62 a__isNatIList(zeros) -> tt 625.50/291.62 a__isNatIList(cons(V1, V2)) -> a__U41(a__isNatKind(V1), V1, V2) 625.50/291.62 a__isNatIListKind(nil) -> tt 625.50/291.62 a__isNatIListKind(zeros) -> tt 625.50/291.62 a__isNatIListKind(cons(V1, V2)) -> a__U51(a__isNatKind(V1), V2) 625.50/291.62 a__isNatKind(0) -> tt 625.50/291.62 a__isNatKind(length(V1)) -> a__U61(a__isNatIListKind(V1)) 625.50/291.62 a__isNatKind(s(V1)) -> a__U71(a__isNatKind(V1)) 625.50/291.62 a__isNatList(nil) -> tt 625.50/291.62 a__isNatList(cons(V1, V2)) -> a__U81(a__isNatKind(V1), V1, V2) 625.50/291.62 a__length(nil) -> 0 625.50/291.62 a__length(cons(N, L)) -> a__U91(a__isNatList(L), L, N) 625.50/291.62 mark(zeros) -> a__zeros 625.50/291.62 mark(U11(X1, X2)) -> a__U11(mark(X1), X2) 625.50/291.62 mark(U12(X1, X2)) -> a__U12(mark(X1), X2) 625.50/291.62 mark(isNatIListKind(X)) -> a__isNatIListKind(X) 625.50/291.62 mark(U13(X)) -> a__U13(mark(X)) 625.50/291.62 mark(isNatList(X)) -> a__isNatList(X) 625.50/291.62 mark(U21(X1, X2)) -> a__U21(mark(X1), X2) 625.50/291.62 mark(U22(X1, X2)) -> a__U22(mark(X1), X2) 625.50/291.62 mark(isNatKind(X)) -> a__isNatKind(X) 625.50/291.62 mark(U23(X)) -> a__U23(mark(X)) 625.50/291.62 mark(isNat(X)) -> a__isNat(X) 625.50/291.62 mark(U31(X1, X2)) -> a__U31(mark(X1), X2) 625.50/291.62 mark(U32(X1, X2)) -> a__U32(mark(X1), X2) 625.50/291.62 mark(U33(X)) -> a__U33(mark(X)) 625.50/291.62 mark(U41(X1, X2, X3)) -> a__U41(mark(X1), X2, X3) 625.50/291.62 mark(U42(X1, X2, X3)) -> a__U42(mark(X1), X2, X3) 625.50/291.62 mark(U43(X1, X2, X3)) -> a__U43(mark(X1), X2, X3) 625.50/291.62 mark(U44(X1, X2, X3)) -> a__U44(mark(X1), X2, X3) 625.50/291.62 mark(U45(X1, X2)) -> a__U45(mark(X1), X2) 625.50/291.62 mark(U46(X)) -> a__U46(mark(X)) 625.50/291.62 mark(isNatIList(X)) -> a__isNatIList(X) 625.50/291.62 mark(U51(X1, X2)) -> a__U51(mark(X1), X2) 625.50/291.62 mark(U52(X)) -> a__U52(mark(X)) 625.50/291.62 mark(U61(X)) -> a__U61(mark(X)) 625.50/291.62 mark(U71(X)) -> a__U71(mark(X)) 625.50/291.62 mark(U81(X1, X2, X3)) -> a__U81(mark(X1), X2, X3) 625.50/291.62 mark(U82(X1, X2, X3)) -> a__U82(mark(X1), X2, X3)
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