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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433308078
details
property
value
status
complete
benchmark
LengthOfFiniteLists_complete_Z.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n072.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.548 seconds
cpu usage
317.317
user time
314.894
system time
2.42244
max virtual memory
1.8277336E7
max residence set size
5832288.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
317.25/291.50 WORST_CASE(Omega(n^1), ?) 317.25/291.50 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 317.25/291.50 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 317.25/291.50 317.25/291.50 317.25/291.50 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 317.25/291.50 317.25/291.50 (0) CpxTRS 317.25/291.50 (1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 317.25/291.50 (2) TRS for Loop Detection 317.25/291.50 (3) DecreasingLoopProof [LOWER BOUND(ID), 166 ms] 317.25/291.50 (4) BEST 317.25/291.50 (5) proven lower bound 317.25/291.50 (6) LowerBoundPropagationProof [FINISHED, 0 ms] 317.25/291.50 (7) BOUNDS(n^1, INF) 317.25/291.50 (8) TRS for Loop Detection 317.25/291.50 317.25/291.50 317.25/291.50 ---------------------------------------- 317.25/291.50 317.25/291.50 (0) 317.25/291.50 Obligation: 317.25/291.50 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 317.25/291.50 317.25/291.50 317.25/291.50 The TRS R consists of the following rules: 317.25/291.50 317.25/291.50 zeros -> cons(0, n__zeros) 317.25/291.50 U11(tt, V1) -> U12(isNatList(activate(V1))) 317.25/291.50 U12(tt) -> tt 317.25/291.50 U21(tt, V1) -> U22(isNat(activate(V1))) 317.25/291.50 U22(tt) -> tt 317.25/291.50 U31(tt, V) -> U32(isNatList(activate(V))) 317.25/291.50 U32(tt) -> tt 317.25/291.50 U41(tt, V1, V2) -> U42(isNat(activate(V1)), activate(V2)) 317.25/291.50 U42(tt, V2) -> U43(isNatIList(activate(V2))) 317.25/291.50 U43(tt) -> tt 317.25/291.50 U51(tt, V1, V2) -> U52(isNat(activate(V1)), activate(V2)) 317.25/291.50 U52(tt, V2) -> U53(isNatList(activate(V2))) 317.25/291.50 U53(tt) -> tt 317.25/291.50 U61(tt, L) -> s(length(activate(L))) 317.25/291.50 and(tt, X) -> activate(X) 317.25/291.50 isNat(n__0) -> tt 317.25/291.50 isNat(n__length(V1)) -> U11(isNatIListKind(activate(V1)), activate(V1)) 317.25/291.50 isNat(n__s(V1)) -> U21(isNatKind(activate(V1)), activate(V1)) 317.25/291.50 isNatIList(V) -> U31(isNatIListKind(activate(V)), activate(V)) 317.25/291.50 isNatIList(n__zeros) -> tt 317.25/291.50 isNatIList(n__cons(V1, V2)) -> U41(and(isNatKind(activate(V1)), n__isNatIListKind(activate(V2))), activate(V1), activate(V2)) 317.25/291.50 isNatIListKind(n__nil) -> tt 317.25/291.50 isNatIListKind(n__zeros) -> tt 317.25/291.50 isNatIListKind(n__cons(V1, V2)) -> and(isNatKind(activate(V1)), n__isNatIListKind(activate(V2))) 317.25/291.50 isNatKind(n__0) -> tt 317.25/291.50 isNatKind(n__length(V1)) -> isNatIListKind(activate(V1)) 317.25/291.50 isNatKind(n__s(V1)) -> isNatKind(activate(V1)) 317.25/291.50 isNatList(n__nil) -> tt 317.25/291.50 isNatList(n__cons(V1, V2)) -> U51(and(isNatKind(activate(V1)), n__isNatIListKind(activate(V2))), activate(V1), activate(V2)) 317.25/291.50 length(nil) -> 0 317.25/291.50 length(cons(N, L)) -> U61(and(and(isNatList(activate(L)), n__isNatIListKind(activate(L))), n__and(isNat(N), n__isNatKind(N))), activate(L)) 317.25/291.50 zeros -> n__zeros 317.25/291.50 0 -> n__0 317.25/291.50 length(X) -> n__length(X) 317.25/291.50 s(X) -> n__s(X) 317.25/291.50 cons(X1, X2) -> n__cons(X1, X2) 317.25/291.50 isNatIListKind(X) -> n__isNatIListKind(X) 317.25/291.50 nil -> n__nil 317.25/291.50 and(X1, X2) -> n__and(X1, X2) 317.25/291.50 isNatKind(X) -> n__isNatKind(X) 317.25/291.50 activate(n__zeros) -> zeros 317.25/291.50 activate(n__0) -> 0 317.25/291.50 activate(n__length(X)) -> length(X) 317.25/291.50 activate(n__s(X)) -> s(X) 317.25/291.50 activate(n__cons(X1, X2)) -> cons(X1, X2) 317.25/291.50 activate(n__isNatIListKind(X)) -> isNatIListKind(X) 317.25/291.50 activate(n__nil) -> nil 317.25/291.50 activate(n__and(X1, X2)) -> and(X1, X2) 317.25/291.50 activate(n__isNatKind(X)) -> isNatKind(X) 317.25/291.50 activate(X) -> X 317.25/291.50 317.25/291.50 S is empty. 317.25/291.50 Rewrite Strategy: FULL 317.25/291.50 ---------------------------------------- 317.25/291.50 317.25/291.50 (1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) 317.25/291.50 Transformed a relative TRS into a decreasing-loop problem. 317.25/291.50 ---------------------------------------- 317.25/291.50 317.25/291.50 (2) 317.25/291.50 Obligation: 317.25/291.50 Analyzing the following TRS for decreasing loops: 317.25/291.50 317.25/291.50 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 317.25/291.50 317.25/291.50 317.25/291.50 The TRS R consists of the following rules: 317.25/291.50 317.25/291.50 zeros -> cons(0, n__zeros) 317.25/291.50 U11(tt, V1) -> U12(isNatList(activate(V1))) 317.25/291.50 U12(tt) -> tt 317.25/291.50 U21(tt, V1) -> U22(isNat(activate(V1))) 317.25/291.50 U22(tt) -> tt
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return to Runtime_Complexity_Full_Rewriting 2019-04-01 06.11
