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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433308360
details
property
value
status
complete
benchmark
OvConsOS_nosorts-noand_FR.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n045.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
263.561 seconds
cpu usage
1035.68
user time
1023.58
system time
12.0964
max virtual memory
3.8712292E7
max residence set size
1.4877456E7
stage attributes
key
value
starexec-result
WORST_CASE(NON_POLY, ?)
output
1034.98/263.39 WORST_CASE(NON_POLY, ?) 1035.51/263.48 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 1035.51/263.48 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1035.51/263.48 1035.51/263.48 1035.51/263.48 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(INF, INF). 1035.51/263.48 1035.51/263.48 (0) CpxTRS 1035.51/263.48 (1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 1035.51/263.48 (2) TRS for Loop Detection 1035.51/263.48 (3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 1035.51/263.48 (4) BEST 1035.51/263.48 (5) proven lower bound 1035.51/263.48 (6) LowerBoundPropagationProof [FINISHED, 0 ms] 1035.51/263.48 (7) BOUNDS(n^1, INF) 1035.51/263.48 (8) TRS for Loop Detection 1035.51/263.48 (9) InfiniteLowerBoundProof [FINISHED, 145.2 s] 1035.51/263.48 (10) BOUNDS(INF, INF) 1035.51/263.48 1035.51/263.48 1035.51/263.48 ---------------------------------------- 1035.51/263.48 1035.51/263.48 (0) 1035.51/263.48 Obligation: 1035.51/263.48 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(INF, INF). 1035.51/263.48 1035.51/263.48 1035.51/263.48 The TRS R consists of the following rules: 1035.51/263.48 1035.51/263.48 zeros -> cons(0, n__zeros) 1035.51/263.48 U11(tt, L) -> U12(tt, activate(L)) 1035.51/263.48 U12(tt, L) -> s(length(activate(L))) 1035.51/263.48 U21(tt, IL, M, N) -> U22(tt, activate(IL), activate(M), activate(N)) 1035.51/263.48 U22(tt, IL, M, N) -> U23(tt, activate(IL), activate(M), activate(N)) 1035.51/263.48 U23(tt, IL, M, N) -> cons(activate(N), n__take(activate(M), activate(IL))) 1035.51/263.48 length(nil) -> 0 1035.51/263.48 length(cons(N, L)) -> U11(tt, activate(L)) 1035.51/263.48 take(0, IL) -> nil 1035.51/263.48 take(s(M), cons(N, IL)) -> U21(tt, activate(IL), M, N) 1035.51/263.48 zeros -> n__zeros 1035.51/263.48 take(X1, X2) -> n__take(X1, X2) 1035.51/263.48 activate(n__zeros) -> zeros 1035.51/263.48 activate(n__take(X1, X2)) -> take(activate(X1), activate(X2)) 1035.51/263.48 activate(X) -> X 1035.51/263.48 1035.51/263.48 S is empty. 1035.51/263.48 Rewrite Strategy: FULL 1035.51/263.48 ---------------------------------------- 1035.51/263.48 1035.51/263.48 (1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) 1035.51/263.48 Transformed a relative TRS into a decreasing-loop problem. 1035.51/263.48 ---------------------------------------- 1035.51/263.48 1035.51/263.48 (2) 1035.51/263.48 Obligation: 1035.51/263.48 Analyzing the following TRS for decreasing loops: 1035.51/263.48 1035.51/263.48 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(INF, INF). 1035.51/263.48 1035.51/263.48 1035.51/263.48 The TRS R consists of the following rules: 1035.51/263.48 1035.51/263.48 zeros -> cons(0, n__zeros) 1035.51/263.48 U11(tt, L) -> U12(tt, activate(L)) 1035.51/263.48 U12(tt, L) -> s(length(activate(L))) 1035.51/263.48 U21(tt, IL, M, N) -> U22(tt, activate(IL), activate(M), activate(N)) 1035.51/263.48 U22(tt, IL, M, N) -> U23(tt, activate(IL), activate(M), activate(N)) 1035.51/263.48 U23(tt, IL, M, N) -> cons(activate(N), n__take(activate(M), activate(IL))) 1035.51/263.48 length(nil) -> 0 1035.51/263.48 length(cons(N, L)) -> U11(tt, activate(L)) 1035.51/263.48 take(0, IL) -> nil 1035.51/263.48 take(s(M), cons(N, IL)) -> U21(tt, activate(IL), M, N) 1035.51/263.48 zeros -> n__zeros 1035.51/263.48 take(X1, X2) -> n__take(X1, X2) 1035.51/263.48 activate(n__zeros) -> zeros 1035.51/263.48 activate(n__take(X1, X2)) -> take(activate(X1), activate(X2)) 1035.51/263.48 activate(X) -> X 1035.51/263.48 1035.51/263.48 S is empty. 1035.51/263.48 Rewrite Strategy: FULL 1035.51/263.48 ---------------------------------------- 1035.51/263.48 1035.51/263.48 (3) DecreasingLoopProof (LOWER BOUND(ID)) 1035.51/263.48 The following loop(s) give(s) rise to the lower bound Omega(n^1): 1035.51/263.48 1035.51/263.48 The rewrite sequence 1035.51/263.48 1035.51/263.48 activate(n__take(X1, X2)) ->^+ take(activate(X1), activate(X2)) 1035.51/263.48 1035.51/263.48 gives rise to a decreasing loop by considering the right hand sides subterm at position [0]. 1035.51/263.48 1035.51/263.48 The pumping substitution is [X1 / n__take(X1, X2)]. 1035.51/263.48 1035.51/263.48 The result substitution is [ ]. 1035.51/263.48 1035.51/263.48 1035.51/263.48 1035.51/263.48 1035.51/263.48 ---------------------------------------- 1035.51/263.48
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