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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433308289
details
property
value
status
complete
benchmark
OvConsOS_complete_Z.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n067.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.591 seconds
cpu usage
359.184
user time
356.522
system time
2.66201
max virtual memory
1.8277336E7
max residence set size
5882148.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
358.89/291.52 WORST_CASE(Omega(n^1), ?) 359.00/291.56 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 359.00/291.56 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 359.00/291.56 359.00/291.56 359.00/291.56 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 359.00/291.56 359.00/291.56 (0) CpxTRS 359.00/291.56 (1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 359.00/291.56 (2) TRS for Loop Detection 359.00/291.56 (3) DecreasingLoopProof [LOWER BOUND(ID), 190 ms] 359.00/291.56 (4) BEST 359.00/291.56 (5) proven lower bound 359.00/291.56 (6) LowerBoundPropagationProof [FINISHED, 0 ms] 359.00/291.56 (7) BOUNDS(n^1, INF) 359.00/291.56 (8) TRS for Loop Detection 359.00/291.56 359.00/291.56 359.00/291.56 ---------------------------------------- 359.00/291.56 359.00/291.56 (0) 359.00/291.56 Obligation: 359.00/291.56 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 359.00/291.56 359.00/291.56 359.00/291.56 The TRS R consists of the following rules: 359.00/291.56 359.00/291.56 zeros -> cons(0, n__zeros) 359.00/291.56 U11(tt, V1) -> U12(isNatList(activate(V1))) 359.00/291.56 U12(tt) -> tt 359.00/291.56 U21(tt, V1) -> U22(isNat(activate(V1))) 359.00/291.56 U22(tt) -> tt 359.00/291.56 U31(tt, V) -> U32(isNatList(activate(V))) 359.00/291.56 U32(tt) -> tt 359.00/291.56 U41(tt, V1, V2) -> U42(isNat(activate(V1)), activate(V2)) 359.00/291.56 U42(tt, V2) -> U43(isNatIList(activate(V2))) 359.00/291.56 U43(tt) -> tt 359.00/291.56 U51(tt, V1, V2) -> U52(isNat(activate(V1)), activate(V2)) 359.00/291.56 U52(tt, V2) -> U53(isNatList(activate(V2))) 359.00/291.56 U53(tt) -> tt 359.00/291.56 U61(tt, V1, V2) -> U62(isNat(activate(V1)), activate(V2)) 359.00/291.56 U62(tt, V2) -> U63(isNatIList(activate(V2))) 359.00/291.56 U63(tt) -> tt 359.00/291.56 U71(tt, L) -> s(length(activate(L))) 359.00/291.56 U81(tt) -> nil 359.00/291.56 U91(tt, IL, M, N) -> cons(activate(N), n__take(activate(M), activate(IL))) 359.00/291.56 and(tt, X) -> activate(X) 359.00/291.56 isNat(n__0) -> tt 359.00/291.56 isNat(n__length(V1)) -> U11(isNatIListKind(activate(V1)), activate(V1)) 359.00/291.56 isNat(n__s(V1)) -> U21(isNatKind(activate(V1)), activate(V1)) 359.00/291.56 isNatIList(V) -> U31(isNatIListKind(activate(V)), activate(V)) 359.00/291.56 isNatIList(n__zeros) -> tt 359.00/291.56 isNatIList(n__cons(V1, V2)) -> U41(and(isNatKind(activate(V1)), n__isNatIListKind(activate(V2))), activate(V1), activate(V2)) 359.00/291.56 isNatIListKind(n__nil) -> tt 359.00/291.56 isNatIListKind(n__zeros) -> tt 359.00/291.56 isNatIListKind(n__cons(V1, V2)) -> and(isNatKind(activate(V1)), n__isNatIListKind(activate(V2))) 359.00/291.56 isNatIListKind(n__take(V1, V2)) -> and(isNatKind(activate(V1)), n__isNatIListKind(activate(V2))) 359.00/291.56 isNatKind(n__0) -> tt 359.00/291.56 isNatKind(n__length(V1)) -> isNatIListKind(activate(V1)) 359.00/291.56 isNatKind(n__s(V1)) -> isNatKind(activate(V1)) 359.00/291.56 isNatList(n__nil) -> tt 359.00/291.56 isNatList(n__cons(V1, V2)) -> U51(and(isNatKind(activate(V1)), n__isNatIListKind(activate(V2))), activate(V1), activate(V2)) 359.00/291.56 isNatList(n__take(V1, V2)) -> U61(and(isNatKind(activate(V1)), n__isNatIListKind(activate(V2))), activate(V1), activate(V2)) 359.00/291.56 length(nil) -> 0 359.00/291.56 length(cons(N, L)) -> U71(and(and(isNatList(activate(L)), n__isNatIListKind(activate(L))), n__and(isNat(N), n__isNatKind(N))), activate(L)) 359.00/291.56 take(0, IL) -> U81(and(isNatIList(IL), n__isNatIListKind(IL))) 359.00/291.56 take(s(M), cons(N, IL)) -> U91(and(and(isNatIList(activate(IL)), n__isNatIListKind(activate(IL))), n__and(and(isNat(M), n__isNatKind(M)), n__and(isNat(N), n__isNatKind(N)))), activate(IL), M, N) 359.00/291.56 zeros -> n__zeros 359.00/291.56 take(X1, X2) -> n__take(X1, X2) 359.00/291.56 0 -> n__0 359.00/291.56 length(X) -> n__length(X) 359.00/291.56 s(X) -> n__s(X) 359.00/291.56 cons(X1, X2) -> n__cons(X1, X2) 359.00/291.56 isNatIListKind(X) -> n__isNatIListKind(X) 359.00/291.56 nil -> n__nil 359.00/291.56 and(X1, X2) -> n__and(X1, X2) 359.00/291.56 isNatKind(X) -> n__isNatKind(X) 359.00/291.56 activate(n__zeros) -> zeros 359.00/291.56 activate(n__take(X1, X2)) -> take(X1, X2) 359.00/291.56 activate(n__0) -> 0 359.00/291.56 activate(n__length(X)) -> length(X) 359.00/291.56 activate(n__s(X)) -> s(X) 359.00/291.56 activate(n__cons(X1, X2)) -> cons(X1, X2) 359.00/291.56 activate(n__isNatIListKind(X)) -> isNatIListKind(X) 359.00/291.56 activate(n__nil) -> nil 359.00/291.56 activate(n__and(X1, X2)) -> and(X1, X2) 359.00/291.56 activate(n__isNatKind(X)) -> isNatKind(X) 359.00/291.56 activate(X) -> X 359.00/291.56 359.00/291.56 S is empty. 359.00/291.56 Rewrite Strategy: FULL 359.00/291.56 ---------------------------------------- 359.00/291.56 359.00/291.56 (1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) 359.00/291.56 Transformed a relative TRS into a decreasing-loop problem. 359.00/291.56 ---------------------------------------- 359.00/291.56 359.00/291.56 (2) 359.00/291.56 Obligation: 359.00/291.56 Analyzing the following TRS for decreasing loops:
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