Spaces
Explore
Communities
Statistics
Reports
Cluster
Status
Help
Runtime Complexity: TRS Innermost pair #487112058
details
property
value
status
complete
benchmark
parting02_doublelist.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n139.star.cs.uiowa.edu
space
AProVE_08
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.736 seconds
cpu usage
1102.5
user time
1087.64
system time
14.8671
max virtual memory
3.751792E7
max residence set size
1.5148648E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
WORST_CASE(Omega(n^1), ?) proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). (0) CpxTRS (1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxTRS (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (4) typed CpxTrs (5) OrderProof [LOWER BOUND(ID), 0 ms] (6) typed CpxTrs (7) RewriteLemmaProof [LOWER BOUND(ID), 292 ms] (8) BEST (9) proven lower bound (10) LowerBoundPropagationProof [FINISHED, 0 ms] (11) BOUNDS(n^1, INF) (12) typed CpxTrs (13) RewriteLemmaProof [LOWER BOUND(ID), 30 ms] (14) typed CpxTrs (15) RewriteLemmaProof [LOWER BOUND(ID), 59 ms] (16) BOUNDS(1, INF) ---------------------------------------- (0) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). The TRS R consists of the following rules: double(0) -> 0 double(s(x)) -> s(s(double(x))) del(x, nil) -> nil del(x, cons(y, xs)) -> if(eq(x, y), x, y, xs) if(true, x, y, xs) -> xs if(false, x, y, xs) -> cons(y, del(x, xs)) eq(0, 0) -> true eq(0, s(y)) -> false eq(s(x), 0) -> false eq(s(x), s(y)) -> eq(x, y) first(nil) -> 0 first(cons(x, xs)) -> x doublelist(nil) -> nil doublelist(cons(x, xs)) -> cons(double(x), doublelist(del(first(cons(x, xs)), cons(x, xs)))) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (1) RenamingProof (BOTH BOUNDS(ID, ID)) Renamed function symbols to avoid clashes with predefined symbol. ---------------------------------------- (2) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). The TRS R consists of the following rules: double(0') -> 0' double(s(x)) -> s(s(double(x))) del(x, nil) -> nil del(x, cons(y, xs)) -> if(eq(x, y), x, y, xs) if(true, x, y, xs) -> xs if(false, x, y, xs) -> cons(y, del(x, xs)) eq(0', 0') -> true eq(0', s(y)) -> false eq(s(x), 0') -> false eq(s(x), s(y)) -> eq(x, y) first(nil) -> 0' first(cons(x, xs)) -> x doublelist(nil) -> nil doublelist(cons(x, xs)) -> cons(double(x), doublelist(del(first(cons(x, xs)), cons(x, xs)))) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (4) Obligation: Innermost TRS: Rules: double(0') -> 0' double(s(x)) -> s(s(double(x))) del(x, nil) -> nil del(x, cons(y, xs)) -> if(eq(x, y), x, y, xs) if(true, x, y, xs) -> xs if(false, x, y, xs) -> cons(y, del(x, xs)) eq(0', 0') -> true eq(0', s(y)) -> false
popout
output may be truncated. 'popout' for the full output.
job log
popout
actions
all output
return to Runtime Complexity: TRS Innermost