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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433308219
details
property
value
status
complete
benchmark
LengthOfFiniteLists_complete_noand_C.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n018.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
295.041 seconds
cpu usage
1160.58
user time
1142.83
system time
17.7446
max virtual memory
3.8171488E7
max residence set size
1.4981156E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
1146.86/291.59 WORST_CASE(Omega(n^1), ?) 1160.44/294.97 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 1160.44/294.97 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1160.44/294.97 1160.44/294.97 1160.44/294.97 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1160.44/294.97 1160.44/294.97 (0) CpxTRS 1160.44/294.97 (1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 1160.44/294.97 (2) TRS for Loop Detection 1160.44/294.97 (3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 1160.44/294.97 (4) BEST 1160.44/294.97 (5) proven lower bound 1160.44/294.97 (6) LowerBoundPropagationProof [FINISHED, 0 ms] 1160.44/294.97 (7) BOUNDS(n^1, INF) 1160.44/294.97 (8) TRS for Loop Detection 1160.44/294.97 1160.44/294.97 1160.44/294.97 ---------------------------------------- 1160.44/294.97 1160.44/294.97 (0) 1160.44/294.97 Obligation: 1160.44/294.97 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1160.44/294.97 1160.44/294.97 1160.44/294.97 The TRS R consists of the following rules: 1160.44/294.97 1160.44/294.97 active(zeros) -> mark(cons(0, zeros)) 1160.44/294.97 active(U11(tt, V1)) -> mark(U12(isNatIListKind(V1), V1)) 1160.44/294.97 active(U12(tt, V1)) -> mark(U13(isNatList(V1))) 1160.44/294.97 active(U13(tt)) -> mark(tt) 1160.44/294.97 active(U21(tt, V1)) -> mark(U22(isNatKind(V1), V1)) 1160.44/294.97 active(U22(tt, V1)) -> mark(U23(isNat(V1))) 1160.44/294.97 active(U23(tt)) -> mark(tt) 1160.44/294.97 active(U31(tt, V)) -> mark(U32(isNatIListKind(V), V)) 1160.44/294.97 active(U32(tt, V)) -> mark(U33(isNatList(V))) 1160.44/294.97 active(U33(tt)) -> mark(tt) 1160.44/294.97 active(U41(tt, V1, V2)) -> mark(U42(isNatKind(V1), V1, V2)) 1160.44/294.97 active(U42(tt, V1, V2)) -> mark(U43(isNatIListKind(V2), V1, V2)) 1160.44/294.97 active(U43(tt, V1, V2)) -> mark(U44(isNatIListKind(V2), V1, V2)) 1160.44/294.97 active(U44(tt, V1, V2)) -> mark(U45(isNat(V1), V2)) 1160.44/294.97 active(U45(tt, V2)) -> mark(U46(isNatIList(V2))) 1160.44/294.97 active(U46(tt)) -> mark(tt) 1160.44/294.97 active(U51(tt, V2)) -> mark(U52(isNatIListKind(V2))) 1160.44/294.97 active(U52(tt)) -> mark(tt) 1160.44/294.97 active(U61(tt)) -> mark(tt) 1160.44/294.97 active(U71(tt)) -> mark(tt) 1160.44/294.97 active(U81(tt, V1, V2)) -> mark(U82(isNatKind(V1), V1, V2)) 1160.44/294.97 active(U82(tt, V1, V2)) -> mark(U83(isNatIListKind(V2), V1, V2)) 1160.44/294.97 active(U83(tt, V1, V2)) -> mark(U84(isNatIListKind(V2), V1, V2)) 1160.44/294.97 active(U84(tt, V1, V2)) -> mark(U85(isNat(V1), V2)) 1160.44/294.97 active(U85(tt, V2)) -> mark(U86(isNatList(V2))) 1160.44/294.97 active(U86(tt)) -> mark(tt) 1160.44/294.97 active(U91(tt, L, N)) -> mark(U92(isNatIListKind(L), L, N)) 1160.46/294.97 active(U92(tt, L, N)) -> mark(U93(isNat(N), L, N)) 1160.46/294.97 active(U93(tt, L, N)) -> mark(U94(isNatKind(N), L)) 1160.46/294.97 active(U94(tt, L)) -> mark(s(length(L))) 1160.46/294.97 active(isNat(0)) -> mark(tt) 1160.46/294.97 active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1), V1)) 1160.46/294.97 active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1)) 1160.46/294.97 active(isNatIList(V)) -> mark(U31(isNatIListKind(V), V)) 1160.46/294.97 active(isNatIList(zeros)) -> mark(tt) 1160.46/294.97 active(isNatIList(cons(V1, V2))) -> mark(U41(isNatKind(V1), V1, V2)) 1160.46/294.97 active(isNatIListKind(nil)) -> mark(tt) 1160.46/294.97 active(isNatIListKind(zeros)) -> mark(tt) 1160.46/294.97 active(isNatIListKind(cons(V1, V2))) -> mark(U51(isNatKind(V1), V2)) 1160.46/294.97 active(isNatKind(0)) -> mark(tt) 1160.46/294.97 active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1))) 1160.46/294.97 active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1))) 1160.46/294.97 active(isNatList(nil)) -> mark(tt) 1160.46/294.97 active(isNatList(cons(V1, V2))) -> mark(U81(isNatKind(V1), V1, V2)) 1160.46/294.97 active(length(nil)) -> mark(0) 1160.46/294.97 active(length(cons(N, L))) -> mark(U91(isNatList(L), L, N)) 1160.46/294.97 active(cons(X1, X2)) -> cons(active(X1), X2) 1160.46/294.97 active(U11(X1, X2)) -> U11(active(X1), X2) 1160.46/294.97 active(U12(X1, X2)) -> U12(active(X1), X2) 1160.46/294.97 active(U13(X)) -> U13(active(X)) 1160.46/294.97 active(U21(X1, X2)) -> U21(active(X1), X2) 1160.46/294.97 active(U22(X1, X2)) -> U22(active(X1), X2) 1160.46/294.97 active(U23(X)) -> U23(active(X)) 1160.46/294.97 active(U31(X1, X2)) -> U31(active(X1), X2) 1160.46/294.97 active(U32(X1, X2)) -> U32(active(X1), X2) 1160.46/294.97 active(U33(X)) -> U33(active(X)) 1160.46/294.97 active(U41(X1, X2, X3)) -> U41(active(X1), X2, X3) 1160.46/294.97 active(U42(X1, X2, X3)) -> U42(active(X1), X2, X3) 1160.46/294.97 active(U43(X1, X2, X3)) -> U43(active(X1), X2, X3) 1160.46/294.97 active(U44(X1, X2, X3)) -> U44(active(X1), X2, X3) 1160.46/294.97 active(U45(X1, X2)) -> U45(active(X1), X2) 1160.46/294.97 active(U46(X)) -> U46(active(X)) 1160.46/294.97 active(U51(X1, X2)) -> U51(active(X1), X2) 1160.46/294.97 active(U52(X)) -> U52(active(X)) 1160.46/294.97 active(U61(X)) -> U61(active(X)) 1160.46/294.97 active(U71(X)) -> U71(active(X)) 1160.46/294.97 active(U81(X1, X2, X3)) -> U81(active(X1), X2, X3) 1160.46/294.97 active(U82(X1, X2, X3)) -> U82(active(X1), X2, X3) 1160.46/294.97 active(U83(X1, X2, X3)) -> U83(active(X1), X2, X3) 1160.46/294.97 active(U84(X1, X2, X3)) -> U84(active(X1), X2, X3) 1160.46/294.97 active(U85(X1, X2)) -> U85(active(X1), X2) 1160.46/294.97 active(U86(X)) -> U86(active(X)) 1160.46/294.97 active(U91(X1, X2, X3)) -> U91(active(X1), X2, X3)
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