Spaces
Explore
Communities
Statistics
Reports
Cluster
Status
Help
Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313517
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
n115.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
296.81 seconds
cpu usage
1165.71
user time
1155.6
system time
10.1166
max virtual memory
3.8323492E7
max residence set size
1.5242108E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
1144.99/291.57 WORST_CASE(Omega(n^1), ?) 1165.45/296.72 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 1165.45/296.72 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1165.45/296.72 1165.45/296.72 1165.45/296.72 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1165.45/296.72 1165.45/296.72 (0) CpxTRS 1165.45/296.72 (1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 1165.45/296.72 (2) TRS for Loop Detection 1165.45/296.72 (3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 1165.45/296.72 (4) BEST 1165.45/296.72 (5) proven lower bound 1165.45/296.72 (6) LowerBoundPropagationProof [FINISHED, 0 ms] 1165.45/296.72 (7) BOUNDS(n^1, INF) 1165.45/296.72 (8) TRS for Loop Detection 1165.45/296.72 1165.45/296.72 1165.45/296.72 ---------------------------------------- 1165.45/296.72 1165.45/296.72 (0) 1165.45/296.72 Obligation: 1165.45/296.72 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1165.45/296.72 1165.45/296.72 1165.45/296.72 The TRS R consists of the following rules: 1165.45/296.72 1165.45/296.72 a__zeros -> cons(0, zeros) 1165.45/296.72 a__U11(tt, V1) -> a__U12(a__isNatIListKind(V1), V1) 1165.45/296.72 a__U12(tt, V1) -> a__U13(a__isNatList(V1)) 1165.45/296.72 a__U13(tt) -> tt 1165.45/296.72 a__U21(tt, V1) -> a__U22(a__isNatKind(V1), V1) 1165.45/296.72 a__U22(tt, V1) -> a__U23(a__isNat(V1)) 1165.45/296.72 a__U23(tt) -> tt 1165.45/296.72 a__U31(tt, V) -> a__U32(a__isNatIListKind(V), V) 1165.45/296.72 a__U32(tt, V) -> a__U33(a__isNatList(V)) 1165.45/296.72 a__U33(tt) -> tt 1165.45/296.72 a__U41(tt, V1, V2) -> a__U42(a__isNatKind(V1), V1, V2) 1165.45/296.72 a__U42(tt, V1, V2) -> a__U43(a__isNatIListKind(V2), V1, V2) 1165.45/296.72 a__U43(tt, V1, V2) -> a__U44(a__isNatIListKind(V2), V1, V2) 1165.45/296.72 a__U44(tt, V1, V2) -> a__U45(a__isNat(V1), V2) 1165.45/296.72 a__U45(tt, V2) -> a__U46(a__isNatIList(V2)) 1165.45/296.72 a__U46(tt) -> tt 1165.45/296.72 a__U51(tt, V2) -> a__U52(a__isNatIListKind(V2)) 1165.45/296.72 a__U52(tt) -> tt 1165.45/296.72 a__U61(tt) -> tt 1165.45/296.72 a__U71(tt) -> tt 1165.45/296.72 a__U81(tt, V1, V2) -> a__U82(a__isNatKind(V1), V1, V2) 1165.45/296.72 a__U82(tt, V1, V2) -> a__U83(a__isNatIListKind(V2), V1, V2) 1165.45/296.72 a__U83(tt, V1, V2) -> a__U84(a__isNatIListKind(V2), V1, V2) 1165.45/296.72 a__U84(tt, V1, V2) -> a__U85(a__isNat(V1), V2) 1165.45/296.72 a__U85(tt, V2) -> a__U86(a__isNatList(V2)) 1165.45/296.72 a__U86(tt) -> tt 1165.45/296.72 a__U91(tt, L, N) -> a__U92(a__isNatIListKind(L), L, N) 1165.45/296.72 a__U92(tt, L, N) -> a__U93(a__isNat(N), L, N) 1165.45/296.72 a__U93(tt, L, N) -> a__U94(a__isNatKind(N), L) 1165.45/296.72 a__U94(tt, L) -> s(a__length(mark(L))) 1165.45/296.72 a__isNat(0) -> tt 1165.45/296.72 a__isNat(length(V1)) -> a__U11(a__isNatIListKind(V1), V1) 1165.45/296.72 a__isNat(s(V1)) -> a__U21(a__isNatKind(V1), V1) 1165.45/296.72 a__isNatIList(V) -> a__U31(a__isNatIListKind(V), V) 1165.45/296.72 a__isNatIList(zeros) -> tt 1165.45/296.72 a__isNatIList(cons(V1, V2)) -> a__U41(a__isNatKind(V1), V1, V2) 1165.45/296.72 a__isNatIListKind(nil) -> tt 1165.45/296.72 a__isNatIListKind(zeros) -> tt 1165.45/296.72 a__isNatIListKind(cons(V1, V2)) -> a__U51(a__isNatKind(V1), V2) 1165.45/296.72 a__isNatKind(0) -> tt 1165.45/296.72 a__isNatKind(length(V1)) -> a__U61(a__isNatIListKind(V1)) 1165.45/296.72 a__isNatKind(s(V1)) -> a__U71(a__isNatKind(V1)) 1165.45/296.72 a__isNatList(nil) -> tt 1165.45/296.72 a__isNatList(cons(V1, V2)) -> a__U81(a__isNatKind(V1), V1, V2) 1165.45/296.72 a__length(nil) -> 0 1165.45/296.72 a__length(cons(N, L)) -> a__U91(a__isNatList(L), L, N) 1165.45/296.72 mark(zeros) -> a__zeros 1165.45/296.72 mark(U11(X1, X2)) -> a__U11(mark(X1), X2) 1165.45/296.72 mark(U12(X1, X2)) -> a__U12(mark(X1), X2) 1165.45/296.72 mark(isNatIListKind(X)) -> a__isNatIListKind(X) 1165.45/296.72 mark(U13(X)) -> a__U13(mark(X)) 1165.45/296.72 mark(isNatList(X)) -> a__isNatList(X) 1165.45/296.72 mark(U21(X1, X2)) -> a__U21(mark(X1), X2) 1165.45/296.72 mark(U22(X1, X2)) -> a__U22(mark(X1), X2) 1165.45/296.72 mark(isNatKind(X)) -> a__isNatKind(X) 1165.45/296.72 mark(U23(X)) -> a__U23(mark(X)) 1165.45/296.72 mark(isNat(X)) -> a__isNat(X) 1165.45/296.72 mark(U31(X1, X2)) -> a__U31(mark(X1), X2) 1165.45/296.72 mark(U32(X1, X2)) -> a__U32(mark(X1), X2) 1165.45/296.72 mark(U33(X)) -> a__U33(mark(X)) 1165.45/296.72 mark(U41(X1, X2, X3)) -> a__U41(mark(X1), X2, X3) 1165.45/296.72 mark(U42(X1, X2, X3)) -> a__U42(mark(X1), X2, X3) 1165.45/296.72 mark(U43(X1, X2, X3)) -> a__U43(mark(X1), X2, X3) 1165.45/296.72 mark(U44(X1, X2, X3)) -> a__U44(mark(X1), X2, X3) 1165.45/296.72 mark(U45(X1, X2)) -> a__U45(mark(X1), X2) 1165.45/296.72 mark(U46(X)) -> a__U46(mark(X)) 1165.45/296.72 mark(isNatIList(X)) -> a__isNatIList(X) 1165.45/296.72 mark(U51(X1, X2)) -> a__U51(mark(X1), X2) 1165.45/296.72 mark(U52(X)) -> a__U52(mark(X)) 1165.45/296.72 mark(U61(X)) -> a__U61(mark(X)) 1165.45/296.72 mark(U71(X)) -> a__U71(mark(X)) 1165.45/296.72 mark(U81(X1, X2, X3)) -> a__U81(mark(X1), X2, X3) 1165.45/296.72 mark(U82(X1, X2, X3)) -> a__U82(mark(X1), X2, X3)
popout
output may be truncated. 'popout' for the full output.
job log
popout
actions
all output
return to Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40