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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433308276
details
property
value
status
complete
benchmark
LengthOfFiniteLists_nosorts_noand_GM.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n092.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
4.93752 seconds
cpu usage
15.9028
user time
15.1598
system time
0.743053
max virtual memory
1.8786436E7
max residence set size
1867140.0
stage attributes
key
value
starexec-result
WORST_CASE(NON_POLY, ?)
output
15.39/4.83 WORST_CASE(NON_POLY, ?) 15.39/4.84 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 15.39/4.84 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 15.39/4.84 15.39/4.84 15.39/4.84 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(INF, INF). 15.39/4.84 15.39/4.84 (0) CpxTRS 15.39/4.84 (1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 15.39/4.84 (2) TRS for Loop Detection 15.39/4.84 (3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 15.39/4.84 (4) BEST 15.39/4.84 (5) proven lower bound 15.39/4.84 (6) LowerBoundPropagationProof [FINISHED, 0 ms] 15.39/4.84 (7) BOUNDS(n^1, INF) 15.39/4.84 (8) TRS for Loop Detection 15.39/4.84 (9) InfiniteLowerBoundProof [FINISHED, 1931 ms] 15.39/4.84 (10) BOUNDS(INF, INF) 15.39/4.84 15.39/4.84 15.39/4.84 ---------------------------------------- 15.39/4.84 15.39/4.84 (0) 15.39/4.84 Obligation: 15.39/4.84 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(INF, INF). 15.39/4.84 15.39/4.84 15.39/4.84 The TRS R consists of the following rules: 15.39/4.84 15.39/4.84 a__zeros -> cons(0, zeros) 15.39/4.84 a__U11(tt, L) -> a__U12(tt, L) 15.39/4.84 a__U12(tt, L) -> s(a__length(mark(L))) 15.39/4.84 a__length(nil) -> 0 15.39/4.84 a__length(cons(N, L)) -> a__U11(tt, L) 15.39/4.84 mark(zeros) -> a__zeros 15.39/4.84 mark(U11(X1, X2)) -> a__U11(mark(X1), X2) 15.39/4.84 mark(U12(X1, X2)) -> a__U12(mark(X1), X2) 15.39/4.84 mark(length(X)) -> a__length(mark(X)) 15.39/4.84 mark(cons(X1, X2)) -> cons(mark(X1), X2) 15.39/4.84 mark(0) -> 0 15.39/4.84 mark(tt) -> tt 15.39/4.84 mark(s(X)) -> s(mark(X)) 15.39/4.84 mark(nil) -> nil 15.39/4.84 a__zeros -> zeros 15.39/4.84 a__U11(X1, X2) -> U11(X1, X2) 15.39/4.84 a__U12(X1, X2) -> U12(X1, X2) 15.39/4.84 a__length(X) -> length(X) 15.39/4.84 15.39/4.84 S is empty. 15.39/4.84 Rewrite Strategy: FULL 15.39/4.84 ---------------------------------------- 15.39/4.84 15.39/4.84 (1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) 15.39/4.84 Transformed a relative TRS into a decreasing-loop problem. 15.39/4.84 ---------------------------------------- 15.39/4.84 15.39/4.84 (2) 15.39/4.84 Obligation: 15.39/4.84 Analyzing the following TRS for decreasing loops: 15.39/4.84 15.39/4.84 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(INF, INF). 15.39/4.84 15.39/4.84 15.39/4.84 The TRS R consists of the following rules: 15.39/4.84 15.39/4.84 a__zeros -> cons(0, zeros) 15.39/4.84 a__U11(tt, L) -> a__U12(tt, L) 15.39/4.84 a__U12(tt, L) -> s(a__length(mark(L))) 15.39/4.84 a__length(nil) -> 0 15.39/4.84 a__length(cons(N, L)) -> a__U11(tt, L) 15.39/4.84 mark(zeros) -> a__zeros 15.39/4.84 mark(U11(X1, X2)) -> a__U11(mark(X1), X2) 15.39/4.84 mark(U12(X1, X2)) -> a__U12(mark(X1), X2) 15.39/4.84 mark(length(X)) -> a__length(mark(X)) 15.39/4.84 mark(cons(X1, X2)) -> cons(mark(X1), X2) 15.39/4.84 mark(0) -> 0 15.39/4.84 mark(tt) -> tt 15.39/4.84 mark(s(X)) -> s(mark(X)) 15.39/4.84 mark(nil) -> nil 15.39/4.84 a__zeros -> zeros 15.39/4.84 a__U11(X1, X2) -> U11(X1, X2) 15.39/4.84 a__U12(X1, X2) -> U12(X1, X2) 15.39/4.84 a__length(X) -> length(X) 15.39/4.84 15.39/4.84 S is empty. 15.39/4.84 Rewrite Strategy: FULL 15.39/4.84 ---------------------------------------- 15.39/4.84 15.39/4.84 (3) DecreasingLoopProof (LOWER BOUND(ID)) 15.39/4.84 The following loop(s) give(s) rise to the lower bound Omega(n^1): 15.39/4.84 15.39/4.84 The rewrite sequence 15.39/4.84 15.39/4.84 mark(length(X)) ->^+ a__length(mark(X)) 15.39/4.84 15.39/4.84 gives rise to a decreasing loop by considering the right hand sides subterm at position [0]. 15.39/4.84 15.39/4.84 The pumping substitution is [X / length(X)]. 15.39/4.84 15.39/4.84 The result substitution is [ ].
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