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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313530
details
property
value
status
complete
benchmark
Ex4_DLMMU04_GM.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n030.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
299.15 seconds
cpu usage
1153.02
user time
1142.58
system time
10.4477
max virtual memory
3.7926372E7
max residence set size
1.5148428E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
1152.57/298.99 WORST_CASE(Omega(n^1), ?) 1152.57/299.06 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 1152.57/299.06 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1152.57/299.06 1152.57/299.06 1152.57/299.06 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1152.57/299.06 1152.57/299.06 (0) CpxTRS 1152.57/299.06 (1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 1152.57/299.06 (2) TRS for Loop Detection 1152.57/299.06 (3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 1152.57/299.06 (4) BEST 1152.57/299.06 (5) proven lower bound 1152.57/299.06 (6) LowerBoundPropagationProof [FINISHED, 0 ms] 1152.57/299.06 (7) BOUNDS(n^1, INF) 1152.57/299.06 (8) TRS for Loop Detection 1152.57/299.06 1152.57/299.06 1152.57/299.06 ---------------------------------------- 1152.57/299.06 1152.57/299.06 (0) 1152.57/299.06 Obligation: 1152.57/299.06 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1152.57/299.06 1152.57/299.06 1152.57/299.06 The TRS R consists of the following rules: 1152.57/299.06 1152.57/299.06 a__and(tt, T) -> mark(T) 1152.57/299.06 a__isNatIList(IL) -> a__isNatList(IL) 1152.57/299.06 a__isNat(0) -> tt 1152.57/299.06 a__isNat(s(N)) -> a__isNat(N) 1152.57/299.06 a__isNat(length(L)) -> a__isNatList(L) 1152.57/299.06 a__isNatIList(zeros) -> tt 1152.57/299.06 a__isNatIList(cons(N, IL)) -> a__and(a__isNat(N), a__isNatIList(IL)) 1152.57/299.06 a__isNatList(nil) -> tt 1152.57/299.06 a__isNatList(cons(N, L)) -> a__and(a__isNat(N), a__isNatList(L)) 1152.57/299.06 a__isNatList(take(N, IL)) -> a__and(a__isNat(N), a__isNatIList(IL)) 1152.57/299.06 a__zeros -> cons(0, zeros) 1152.57/299.06 a__take(0, IL) -> a__uTake1(a__isNatIList(IL)) 1152.57/299.06 a__uTake1(tt) -> nil 1152.57/299.06 a__take(s(M), cons(N, IL)) -> a__uTake2(a__and(a__isNat(M), a__and(a__isNat(N), a__isNatIList(IL))), M, N, IL) 1152.57/299.06 a__uTake2(tt, M, N, IL) -> cons(mark(N), take(M, IL)) 1152.57/299.06 a__length(cons(N, L)) -> a__uLength(a__and(a__isNat(N), a__isNatList(L)), L) 1152.57/299.06 a__uLength(tt, L) -> s(a__length(mark(L))) 1152.57/299.06 mark(and(X1, X2)) -> a__and(mark(X1), mark(X2)) 1152.57/299.06 mark(isNatIList(X)) -> a__isNatIList(X) 1152.57/299.06 mark(isNatList(X)) -> a__isNatList(X) 1152.57/299.06 mark(isNat(X)) -> a__isNat(X) 1152.57/299.06 mark(length(X)) -> a__length(mark(X)) 1152.57/299.06 mark(zeros) -> a__zeros 1152.57/299.06 mark(take(X1, X2)) -> a__take(mark(X1), mark(X2)) 1152.57/299.06 mark(uTake1(X)) -> a__uTake1(mark(X)) 1152.57/299.06 mark(uTake2(X1, X2, X3, X4)) -> a__uTake2(mark(X1), X2, X3, X4) 1152.57/299.06 mark(uLength(X1, X2)) -> a__uLength(mark(X1), X2) 1152.57/299.06 mark(tt) -> tt 1152.57/299.06 mark(0) -> 0 1152.57/299.06 mark(s(X)) -> s(mark(X)) 1152.57/299.06 mark(cons(X1, X2)) -> cons(mark(X1), X2) 1152.57/299.06 mark(nil) -> nil 1152.57/299.06 a__and(X1, X2) -> and(X1, X2) 1152.57/299.06 a__isNatIList(X) -> isNatIList(X) 1152.57/299.06 a__isNatList(X) -> isNatList(X) 1152.57/299.06 a__isNat(X) -> isNat(X) 1152.57/299.06 a__length(X) -> length(X) 1152.57/299.06 a__zeros -> zeros 1152.57/299.06 a__take(X1, X2) -> take(X1, X2) 1152.57/299.06 a__uTake1(X) -> uTake1(X) 1152.57/299.06 a__uTake2(X1, X2, X3, X4) -> uTake2(X1, X2, X3, X4) 1152.57/299.06 a__uLength(X1, X2) -> uLength(X1, X2) 1152.57/299.06 1152.57/299.06 S is empty. 1152.57/299.06 Rewrite Strategy: INNERMOST 1152.57/299.06 ---------------------------------------- 1152.57/299.06 1152.57/299.06 (1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) 1152.57/299.06 Transformed a relative TRS into a decreasing-loop problem. 1152.57/299.06 ---------------------------------------- 1152.57/299.06 1152.57/299.06 (2) 1152.57/299.06 Obligation: 1152.57/299.06 Analyzing the following TRS for decreasing loops: 1152.57/299.06 1152.57/299.06 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1152.57/299.06 1152.57/299.06 1152.57/299.06 The TRS R consists of the following rules: 1152.57/299.06 1152.57/299.06 a__and(tt, T) -> mark(T) 1152.57/299.06 a__isNatIList(IL) -> a__isNatList(IL) 1152.57/299.06 a__isNat(0) -> tt 1152.57/299.06 a__isNat(s(N)) -> a__isNat(N) 1152.57/299.06 a__isNat(length(L)) -> a__isNatList(L) 1152.57/299.06 a__isNatIList(zeros) -> tt 1152.57/299.06 a__isNatIList(cons(N, IL)) -> a__and(a__isNat(N), a__isNatIList(IL)) 1152.57/299.06 a__isNatList(nil) -> tt 1152.57/299.06 a__isNatList(cons(N, L)) -> a__and(a__isNat(N), a__isNatList(L)) 1152.57/299.06 a__isNatList(take(N, IL)) -> a__and(a__isNat(N), a__isNatIList(IL)) 1152.57/299.06 a__zeros -> cons(0, zeros) 1152.57/299.06 a__take(0, IL) -> a__uTake1(a__isNatIList(IL)) 1152.57/299.06 a__uTake1(tt) -> nil
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return to Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40