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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313483
details
property
value
status
complete
benchmark
OvConsOS_complete_GM.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n005.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
294.574 seconds
cpu usage
1061.33
user time
1049.39
system time
11.933
max virtual memory
1.8845312E7
max residence set size
1.5168728E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
1049.70/291.60 WORST_CASE(Omega(n^1), ?) 1060.99/294.50 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 1060.99/294.50 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1060.99/294.50 1060.99/294.50 1060.99/294.50 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1060.99/294.50 1060.99/294.50 (0) CpxTRS 1060.99/294.50 (1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 1060.99/294.50 (2) TRS for Loop Detection 1060.99/294.50 (3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 1060.99/294.50 (4) BEST 1060.99/294.50 (5) proven lower bound 1060.99/294.50 (6) LowerBoundPropagationProof [FINISHED, 0 ms] 1060.99/294.50 (7) BOUNDS(n^1, INF) 1060.99/294.50 (8) TRS for Loop Detection 1060.99/294.50 1060.99/294.50 1060.99/294.50 ---------------------------------------- 1060.99/294.50 1060.99/294.50 (0) 1060.99/294.50 Obligation: 1060.99/294.50 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1060.99/294.50 1060.99/294.50 1060.99/294.50 The TRS R consists of the following rules: 1060.99/294.50 1060.99/294.50 a__zeros -> cons(0, zeros) 1060.99/294.50 a__U11(tt, V1) -> a__U12(a__isNatList(V1)) 1060.99/294.50 a__U12(tt) -> tt 1060.99/294.50 a__U21(tt, V1) -> a__U22(a__isNat(V1)) 1060.99/294.50 a__U22(tt) -> tt 1060.99/294.50 a__U31(tt, V) -> a__U32(a__isNatList(V)) 1060.99/294.50 a__U32(tt) -> tt 1060.99/294.50 a__U41(tt, V1, V2) -> a__U42(a__isNat(V1), V2) 1060.99/294.50 a__U42(tt, V2) -> a__U43(a__isNatIList(V2)) 1060.99/294.50 a__U43(tt) -> tt 1060.99/294.50 a__U51(tt, V1, V2) -> a__U52(a__isNat(V1), V2) 1060.99/294.50 a__U52(tt, V2) -> a__U53(a__isNatList(V2)) 1060.99/294.50 a__U53(tt) -> tt 1060.99/294.50 a__U61(tt, V1, V2) -> a__U62(a__isNat(V1), V2) 1060.99/294.50 a__U62(tt, V2) -> a__U63(a__isNatIList(V2)) 1060.99/294.50 a__U63(tt) -> tt 1060.99/294.50 a__U71(tt, L) -> s(a__length(mark(L))) 1060.99/294.50 a__U81(tt) -> nil 1060.99/294.50 a__U91(tt, IL, M, N) -> cons(mark(N), take(M, IL)) 1060.99/294.50 a__and(tt, X) -> mark(X) 1060.99/294.50 a__isNat(0) -> tt 1060.99/294.50 a__isNat(length(V1)) -> a__U11(a__isNatIListKind(V1), V1) 1060.99/294.50 a__isNat(s(V1)) -> a__U21(a__isNatKind(V1), V1) 1060.99/294.50 a__isNatIList(V) -> a__U31(a__isNatIListKind(V), V) 1060.99/294.50 a__isNatIList(zeros) -> tt 1060.99/294.50 a__isNatIList(cons(V1, V2)) -> a__U41(a__and(a__isNatKind(V1), isNatIListKind(V2)), V1, V2) 1060.99/294.50 a__isNatIListKind(nil) -> tt 1060.99/294.50 a__isNatIListKind(zeros) -> tt 1060.99/294.50 a__isNatIListKind(cons(V1, V2)) -> a__and(a__isNatKind(V1), isNatIListKind(V2)) 1060.99/294.50 a__isNatIListKind(take(V1, V2)) -> a__and(a__isNatKind(V1), isNatIListKind(V2)) 1060.99/294.50 a__isNatKind(0) -> tt 1060.99/294.50 a__isNatKind(length(V1)) -> a__isNatIListKind(V1) 1060.99/294.50 a__isNatKind(s(V1)) -> a__isNatKind(V1) 1060.99/294.50 a__isNatList(nil) -> tt 1060.99/294.50 a__isNatList(cons(V1, V2)) -> a__U51(a__and(a__isNatKind(V1), isNatIListKind(V2)), V1, V2) 1060.99/294.50 a__isNatList(take(V1, V2)) -> a__U61(a__and(a__isNatKind(V1), isNatIListKind(V2)), V1, V2) 1060.99/294.50 a__length(nil) -> 0 1060.99/294.50 a__length(cons(N, L)) -> a__U71(a__and(a__and(a__isNatList(L), isNatIListKind(L)), and(isNat(N), isNatKind(N))), L) 1060.99/294.50 a__take(0, IL) -> a__U81(a__and(a__isNatIList(IL), isNatIListKind(IL))) 1060.99/294.50 a__take(s(M), cons(N, IL)) -> a__U91(a__and(a__and(a__isNatIList(IL), isNatIListKind(IL)), and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N)))), IL, M, N) 1060.99/294.50 mark(zeros) -> a__zeros 1060.99/294.50 mark(U11(X1, X2)) -> a__U11(mark(X1), X2) 1060.99/294.50 mark(U12(X)) -> a__U12(mark(X)) 1060.99/294.50 mark(isNatList(X)) -> a__isNatList(X) 1060.99/294.50 mark(U21(X1, X2)) -> a__U21(mark(X1), X2) 1060.99/294.50 mark(U22(X)) -> a__U22(mark(X)) 1060.99/294.50 mark(isNat(X)) -> a__isNat(X) 1060.99/294.50 mark(U31(X1, X2)) -> a__U31(mark(X1), X2) 1060.99/294.50 mark(U32(X)) -> a__U32(mark(X)) 1060.99/294.50 mark(U41(X1, X2, X3)) -> a__U41(mark(X1), X2, X3) 1060.99/294.50 mark(U42(X1, X2)) -> a__U42(mark(X1), X2) 1060.99/294.50 mark(U43(X)) -> a__U43(mark(X)) 1060.99/294.50 mark(isNatIList(X)) -> a__isNatIList(X) 1060.99/294.50 mark(U51(X1, X2, X3)) -> a__U51(mark(X1), X2, X3) 1060.99/294.50 mark(U52(X1, X2)) -> a__U52(mark(X1), X2) 1060.99/294.50 mark(U53(X)) -> a__U53(mark(X)) 1060.99/294.50 mark(U61(X1, X2, X3)) -> a__U61(mark(X1), X2, X3) 1060.99/294.50 mark(U62(X1, X2)) -> a__U62(mark(X1), X2) 1060.99/294.50 mark(U63(X)) -> a__U63(mark(X)) 1060.99/294.50 mark(U71(X1, X2)) -> a__U71(mark(X1), X2) 1060.99/294.50 mark(length(X)) -> a__length(mark(X)) 1060.99/294.50 mark(U81(X)) -> a__U81(mark(X)) 1060.99/294.50 mark(U91(X1, X2, X3, X4)) -> a__U91(mark(X1), X2, X3, X4) 1060.99/294.50 mark(take(X1, X2)) -> a__take(mark(X1), mark(X2)) 1060.99/294.50 mark(and(X1, X2)) -> a__and(mark(X1), X2) 1060.99/294.50 mark(isNatIListKind(X)) -> a__isNatIListKind(X) 1060.99/294.50 mark(isNatKind(X)) -> a__isNatKind(X) 1060.99/294.50 mark(cons(X1, X2)) -> cons(mark(X1), X2) 1060.99/294.50 mark(0) -> 0 1060.99/294.50 mark(tt) -> tt 1060.99/294.50 mark(s(X)) -> s(mark(X)) 1060.99/294.50 mark(nil) -> nil 1060.99/294.50 a__zeros -> zeros
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return to Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40