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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433308372
details
property
value
status
complete
benchmark
LengthOfFiniteLists_nokinds_GM.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n099.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.667 seconds
cpu usage
323.731
user time
320.014
system time
3.71625
max virtual memory
1.8279384E7
max residence set size
6971756.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
323.38/291.53 WORST_CASE(Omega(n^1), ?) 323.67/291.63 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 323.67/291.63 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 323.67/291.63 323.67/291.63 323.67/291.63 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 323.67/291.63 323.67/291.63 (0) CpxTRS 323.67/291.63 (1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 323.67/291.63 (2) TRS for Loop Detection 323.67/291.63 (3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 323.67/291.63 (4) BEST 323.67/291.63 (5) proven lower bound 323.67/291.63 (6) LowerBoundPropagationProof [FINISHED, 0 ms] 323.67/291.63 (7) BOUNDS(n^1, INF) 323.67/291.63 (8) TRS for Loop Detection 323.67/291.63 323.67/291.63 323.67/291.63 ---------------------------------------- 323.67/291.63 323.67/291.63 (0) 323.67/291.63 Obligation: 323.67/291.63 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 323.67/291.63 323.67/291.63 323.67/291.63 The TRS R consists of the following rules: 323.67/291.63 323.67/291.63 a__zeros -> cons(0, zeros) 323.67/291.63 a__U11(tt, L) -> s(a__length(mark(L))) 323.67/291.63 a__and(tt, X) -> mark(X) 323.67/291.63 a__isNat(0) -> tt 323.67/291.63 a__isNat(length(V1)) -> a__isNatList(V1) 323.67/291.63 a__isNat(s(V1)) -> a__isNat(V1) 323.67/291.63 a__isNatIList(V) -> a__isNatList(V) 323.67/291.63 a__isNatIList(zeros) -> tt 323.67/291.63 a__isNatIList(cons(V1, V2)) -> a__and(a__isNat(V1), isNatIList(V2)) 323.67/291.63 a__isNatList(nil) -> tt 323.67/291.63 a__isNatList(cons(V1, V2)) -> a__and(a__isNat(V1), isNatList(V2)) 323.67/291.63 a__length(nil) -> 0 323.67/291.63 a__length(cons(N, L)) -> a__U11(a__and(a__isNatList(L), isNat(N)), L) 323.67/291.63 mark(zeros) -> a__zeros 323.67/291.63 mark(U11(X1, X2)) -> a__U11(mark(X1), X2) 323.67/291.63 mark(length(X)) -> a__length(mark(X)) 323.67/291.63 mark(and(X1, X2)) -> a__and(mark(X1), X2) 323.67/291.63 mark(isNat(X)) -> a__isNat(X) 323.67/291.63 mark(isNatList(X)) -> a__isNatList(X) 323.67/291.63 mark(isNatIList(X)) -> a__isNatIList(X) 323.67/291.63 mark(cons(X1, X2)) -> cons(mark(X1), X2) 323.67/291.63 mark(0) -> 0 323.67/291.63 mark(tt) -> tt 323.67/291.63 mark(s(X)) -> s(mark(X)) 323.67/291.63 mark(nil) -> nil 323.67/291.63 a__zeros -> zeros 323.67/291.63 a__U11(X1, X2) -> U11(X1, X2) 323.67/291.63 a__length(X) -> length(X) 323.67/291.63 a__and(X1, X2) -> and(X1, X2) 323.67/291.63 a__isNat(X) -> isNat(X) 323.67/291.63 a__isNatList(X) -> isNatList(X) 323.67/291.63 a__isNatIList(X) -> isNatIList(X) 323.67/291.63 323.67/291.63 S is empty. 323.67/291.63 Rewrite Strategy: FULL 323.67/291.63 ---------------------------------------- 323.67/291.63 323.67/291.63 (1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) 323.67/291.63 Transformed a relative TRS into a decreasing-loop problem. 323.67/291.63 ---------------------------------------- 323.67/291.63 323.67/291.63 (2) 323.67/291.63 Obligation: 323.67/291.63 Analyzing the following TRS for decreasing loops: 323.67/291.63 323.67/291.63 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 323.67/291.63 323.67/291.63 323.67/291.63 The TRS R consists of the following rules: 323.67/291.63 323.67/291.63 a__zeros -> cons(0, zeros) 323.67/291.63 a__U11(tt, L) -> s(a__length(mark(L))) 323.67/291.63 a__and(tt, X) -> mark(X) 323.67/291.63 a__isNat(0) -> tt 323.67/291.63 a__isNat(length(V1)) -> a__isNatList(V1) 323.67/291.63 a__isNat(s(V1)) -> a__isNat(V1) 323.67/291.63 a__isNatIList(V) -> a__isNatList(V) 323.67/291.63 a__isNatIList(zeros) -> tt 323.67/291.63 a__isNatIList(cons(V1, V2)) -> a__and(a__isNat(V1), isNatIList(V2)) 323.67/291.63 a__isNatList(nil) -> tt 323.67/291.63 a__isNatList(cons(V1, V2)) -> a__and(a__isNat(V1), isNatList(V2)) 323.67/291.63 a__length(nil) -> 0 323.67/291.63 a__length(cons(N, L)) -> a__U11(a__and(a__isNatList(L), isNat(N)), L) 323.67/291.63 mark(zeros) -> a__zeros 323.67/291.63 mark(U11(X1, X2)) -> a__U11(mark(X1), X2) 323.67/291.63 mark(length(X)) -> a__length(mark(X)) 323.67/291.63 mark(and(X1, X2)) -> a__and(mark(X1), X2) 323.67/291.63 mark(isNat(X)) -> a__isNat(X) 323.67/291.63 mark(isNatList(X)) -> a__isNatList(X) 323.67/291.63 mark(isNatIList(X)) -> a__isNatIList(X) 323.67/291.63 mark(cons(X1, X2)) -> cons(mark(X1), X2) 323.67/291.63 mark(0) -> 0 323.67/291.63 mark(tt) -> tt
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