Spaces
Explore
Communities
Statistics
Reports
Cluster
Status
Help
Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433308133
details
property
value
status
complete
benchmark
Ex3_2_Luc97_GM.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n066.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.57 seconds
cpu usage
340.799
user time
334.734
system time
6.06476
max virtual memory
1.8277336E7
max residence set size
9268604.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
340.73/291.52 WORST_CASE(Omega(n^1), ?) 340.73/291.53 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 340.73/291.53 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 340.73/291.53 340.73/291.53 340.73/291.53 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 340.73/291.53 340.73/291.53 (0) CpxTRS 340.73/291.53 (1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 340.73/291.53 (2) TRS for Loop Detection 340.73/291.53 (3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 340.73/291.53 (4) BEST 340.73/291.53 (5) proven lower bound 340.73/291.53 (6) LowerBoundPropagationProof [FINISHED, 0 ms] 340.73/291.53 (7) BOUNDS(n^1, INF) 340.73/291.53 (8) TRS for Loop Detection 340.73/291.53 340.73/291.53 340.73/291.53 ---------------------------------------- 340.73/291.53 340.73/291.53 (0) 340.73/291.53 Obligation: 340.73/291.53 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 340.73/291.53 340.73/291.53 340.73/291.53 The TRS R consists of the following rules: 340.73/291.53 340.73/291.53 a__dbl(0) -> 0 340.73/291.53 a__dbl(s(X)) -> s(s(dbl(X))) 340.73/291.53 a__dbls(nil) -> nil 340.73/291.53 a__dbls(cons(X, Y)) -> cons(dbl(X), dbls(Y)) 340.73/291.53 a__sel(0, cons(X, Y)) -> mark(X) 340.73/291.53 a__sel(s(X), cons(Y, Z)) -> a__sel(mark(X), mark(Z)) 340.73/291.53 a__indx(nil, X) -> nil 340.73/291.53 a__indx(cons(X, Y), Z) -> cons(sel(X, Z), indx(Y, Z)) 340.73/291.53 a__from(X) -> cons(X, from(s(X))) 340.73/291.53 mark(dbl(X)) -> a__dbl(mark(X)) 340.73/291.53 mark(dbls(X)) -> a__dbls(mark(X)) 340.73/291.53 mark(sel(X1, X2)) -> a__sel(mark(X1), mark(X2)) 340.73/291.53 mark(indx(X1, X2)) -> a__indx(mark(X1), X2) 340.73/291.53 mark(from(X)) -> a__from(X) 340.73/291.53 mark(0) -> 0 340.73/291.53 mark(s(X)) -> s(X) 340.73/291.53 mark(nil) -> nil 340.73/291.53 mark(cons(X1, X2)) -> cons(X1, X2) 340.73/291.53 a__dbl(X) -> dbl(X) 340.73/291.53 a__dbls(X) -> dbls(X) 340.73/291.53 a__sel(X1, X2) -> sel(X1, X2) 340.73/291.53 a__indx(X1, X2) -> indx(X1, X2) 340.73/291.53 a__from(X) -> from(X) 340.73/291.53 340.73/291.53 S is empty. 340.73/291.53 Rewrite Strategy: FULL 340.73/291.53 ---------------------------------------- 340.73/291.53 340.73/291.53 (1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) 340.73/291.53 Transformed a relative TRS into a decreasing-loop problem. 340.73/291.53 ---------------------------------------- 340.73/291.53 340.73/291.53 (2) 340.73/291.53 Obligation: 340.73/291.53 Analyzing the following TRS for decreasing loops: 340.73/291.53 340.73/291.53 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 340.73/291.53 340.73/291.53 340.73/291.53 The TRS R consists of the following rules: 340.73/291.53 340.73/291.53 a__dbl(0) -> 0 340.73/291.53 a__dbl(s(X)) -> s(s(dbl(X))) 340.73/291.53 a__dbls(nil) -> nil 340.73/291.53 a__dbls(cons(X, Y)) -> cons(dbl(X), dbls(Y)) 340.73/291.53 a__sel(0, cons(X, Y)) -> mark(X) 340.73/291.53 a__sel(s(X), cons(Y, Z)) -> a__sel(mark(X), mark(Z)) 340.73/291.53 a__indx(nil, X) -> nil 340.73/291.53 a__indx(cons(X, Y), Z) -> cons(sel(X, Z), indx(Y, Z)) 340.73/291.53 a__from(X) -> cons(X, from(s(X))) 340.73/291.53 mark(dbl(X)) -> a__dbl(mark(X)) 340.73/291.53 mark(dbls(X)) -> a__dbls(mark(X)) 340.73/291.53 mark(sel(X1, X2)) -> a__sel(mark(X1), mark(X2)) 340.73/291.53 mark(indx(X1, X2)) -> a__indx(mark(X1), X2) 340.73/291.53 mark(from(X)) -> a__from(X) 340.73/291.53 mark(0) -> 0 340.73/291.53 mark(s(X)) -> s(X) 340.73/291.53 mark(nil) -> nil 340.73/291.53 mark(cons(X1, X2)) -> cons(X1, X2) 340.73/291.53 a__dbl(X) -> dbl(X) 340.73/291.53 a__dbls(X) -> dbls(X) 340.73/291.53 a__sel(X1, X2) -> sel(X1, X2) 340.73/291.53 a__indx(X1, X2) -> indx(X1, X2) 340.73/291.53 a__from(X) -> from(X) 340.73/291.53 340.73/291.53 S is empty. 340.73/291.53 Rewrite Strategy: FULL 340.73/291.53 ---------------------------------------- 340.73/291.53 340.73/291.53 (3) DecreasingLoopProof (LOWER BOUND(ID)) 340.73/291.53 The following loop(s) give(s) rise to the lower bound Omega(n^1): 340.73/291.53 340.73/291.53 The rewrite sequence
popout
output may be truncated. 'popout' for the full output.
job log
popout
actions
all output
return to Runtime_Complexity_Full_Rewriting 2019-04-01 06.11
