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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313470
details
property
value
status
complete
benchmark
OvConsOS_nosorts-noand_Z.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n072.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
10.3027 seconds
cpu usage
36.8525
user time
35.5005
system time
1.35202
max virtual memory
3.755256E7
max residence set size
3895184.0
stage attributes
key
value
starexec-result
WORST_CASE(NON_POLY, ?)
output
36.57/10.26 WORST_CASE(NON_POLY, ?) 36.57/10.26 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 36.57/10.26 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 36.57/10.26 36.57/10.26 36.57/10.26 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(INF, INF). 36.57/10.26 36.57/10.26 (0) CpxTRS 36.57/10.26 (1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 36.57/10.26 (2) TRS for Loop Detection 36.57/10.26 (3) DecreasingLoopProof [LOWER BOUND(ID), 20 ms] 36.57/10.26 (4) BEST 36.57/10.26 (5) proven lower bound 36.57/10.26 (6) LowerBoundPropagationProof [FINISHED, 0 ms] 36.57/10.26 (7) BOUNDS(n^1, INF) 36.57/10.26 (8) TRS for Loop Detection 36.57/10.26 (9) InfiniteLowerBoundProof [FINISHED, 5539 ms] 36.57/10.26 (10) BOUNDS(INF, INF) 36.57/10.26 36.57/10.26 36.57/10.26 ---------------------------------------- 36.57/10.26 36.57/10.26 (0) 36.57/10.26 Obligation: 36.57/10.26 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(INF, INF). 36.57/10.26 36.57/10.26 36.57/10.26 The TRS R consists of the following rules: 36.57/10.26 36.57/10.26 zeros -> cons(0, n__zeros) 36.57/10.26 U11(tt, L) -> U12(tt, activate(L)) 36.57/10.26 U12(tt, L) -> s(length(activate(L))) 36.57/10.26 U21(tt, IL, M, N) -> U22(tt, activate(IL), activate(M), activate(N)) 36.57/10.26 U22(tt, IL, M, N) -> U23(tt, activate(IL), activate(M), activate(N)) 36.57/10.26 U23(tt, IL, M, N) -> cons(activate(N), n__take(activate(M), activate(IL))) 36.57/10.26 length(nil) -> 0 36.57/10.26 length(cons(N, L)) -> U11(tt, activate(L)) 36.57/10.26 take(0, IL) -> nil 36.57/10.26 take(s(M), cons(N, IL)) -> U21(tt, activate(IL), M, N) 36.57/10.26 zeros -> n__zeros 36.57/10.26 take(X1, X2) -> n__take(X1, X2) 36.57/10.26 activate(n__zeros) -> zeros 36.57/10.26 activate(n__take(X1, X2)) -> take(X1, X2) 36.57/10.26 activate(X) -> X 36.57/10.26 36.57/10.26 S is empty. 36.57/10.26 Rewrite Strategy: INNERMOST 36.57/10.26 ---------------------------------------- 36.57/10.26 36.57/10.26 (1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) 36.57/10.26 Transformed a relative TRS into a decreasing-loop problem. 36.57/10.26 ---------------------------------------- 36.57/10.26 36.57/10.26 (2) 36.57/10.26 Obligation: 36.57/10.26 Analyzing the following TRS for decreasing loops: 36.57/10.26 36.57/10.26 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(INF, INF). 36.57/10.26 36.57/10.26 36.57/10.26 The TRS R consists of the following rules: 36.57/10.26 36.57/10.26 zeros -> cons(0, n__zeros) 36.57/10.26 U11(tt, L) -> U12(tt, activate(L)) 36.57/10.26 U12(tt, L) -> s(length(activate(L))) 36.57/10.26 U21(tt, IL, M, N) -> U22(tt, activate(IL), activate(M), activate(N)) 36.57/10.26 U22(tt, IL, M, N) -> U23(tt, activate(IL), activate(M), activate(N)) 36.57/10.26 U23(tt, IL, M, N) -> cons(activate(N), n__take(activate(M), activate(IL))) 36.57/10.26 length(nil) -> 0 36.57/10.26 length(cons(N, L)) -> U11(tt, activate(L)) 36.57/10.26 take(0, IL) -> nil 36.57/10.26 take(s(M), cons(N, IL)) -> U21(tt, activate(IL), M, N) 36.57/10.26 zeros -> n__zeros 36.57/10.26 take(X1, X2) -> n__take(X1, X2) 36.57/10.26 activate(n__zeros) -> zeros 36.57/10.26 activate(n__take(X1, X2)) -> take(X1, X2) 36.57/10.26 activate(X) -> X 36.57/10.26 36.57/10.26 S is empty. 36.57/10.26 Rewrite Strategy: INNERMOST 36.57/10.26 ---------------------------------------- 36.57/10.26 36.57/10.26 (3) DecreasingLoopProof (LOWER BOUND(ID)) 36.57/10.26 The following loop(s) give(s) rise to the lower bound Omega(n^1): 36.57/10.26 36.57/10.26 The rewrite sequence 36.57/10.26 36.57/10.26 activate(n__take(s(M1_0), cons(N2_0, IL3_0))) ->^+ U21(tt, activate(IL3_0), M1_0, N2_0) 36.57/10.26 36.57/10.26 gives rise to a decreasing loop by considering the right hand sides subterm at position [1]. 36.57/10.26 36.57/10.26 The pumping substitution is [IL3_0 / n__take(s(M1_0), cons(N2_0, IL3_0))]. 36.57/10.26 36.57/10.26 The result substitution is [ ]. 36.57/10.26 36.57/10.26 36.57/10.26 36.57/10.26 36.57/10.26 ---------------------------------------- 36.57/10.26
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