Spaces
Explore
Communities
Statistics
Reports
Cluster
Status
Help
Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313383
details
property
value
status
complete
benchmark
Ex1_Luc04b_GM.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n071.star.cs.uiowa.edu
space
Mixed_TRS
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.649 seconds
cpu usage
1084.69
user time
1070.74
system time
13.9563
max virtual memory
3.7580116E7
max residence set size
1.5024352E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
1084.45/291.57 WORST_CASE(Omega(n^1), ?) 1084.45/291.58 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 1084.45/291.58 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1084.45/291.58 1084.45/291.58 1084.45/291.58 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1084.45/291.58 1084.45/291.58 (0) CpxTRS 1084.45/291.58 (1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 1084.45/291.58 (2) TRS for Loop Detection 1084.45/291.58 (3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 1084.45/291.58 (4) BEST 1084.45/291.58 (5) proven lower bound 1084.45/291.58 (6) LowerBoundPropagationProof [FINISHED, 0 ms] 1084.45/291.58 (7) BOUNDS(n^1, INF) 1084.45/291.58 (8) TRS for Loop Detection 1084.45/291.58 1084.45/291.58 1084.45/291.58 ---------------------------------------- 1084.45/291.58 1084.45/291.58 (0) 1084.45/291.58 Obligation: 1084.45/291.58 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1084.45/291.58 1084.45/291.58 1084.45/291.58 The TRS R consists of the following rules: 1084.45/291.58 1084.45/291.58 a__nats -> cons(0, incr(nats)) 1084.45/291.58 a__pairs -> cons(0, incr(odds)) 1084.45/291.58 a__odds -> a__incr(a__pairs) 1084.45/291.58 a__incr(cons(X, XS)) -> cons(s(mark(X)), incr(XS)) 1084.45/291.58 a__head(cons(X, XS)) -> mark(X) 1084.45/291.58 a__tail(cons(X, XS)) -> mark(XS) 1084.45/291.58 mark(nats) -> a__nats 1084.45/291.58 mark(pairs) -> a__pairs 1084.45/291.58 mark(odds) -> a__odds 1084.45/291.58 mark(incr(X)) -> a__incr(mark(X)) 1084.45/291.58 mark(head(X)) -> a__head(mark(X)) 1084.45/291.58 mark(tail(X)) -> a__tail(mark(X)) 1084.45/291.58 mark(0) -> 0 1084.45/291.58 mark(s(X)) -> s(mark(X)) 1084.45/291.58 mark(nil) -> nil 1084.45/291.58 mark(cons(X1, X2)) -> cons(mark(X1), X2) 1084.45/291.58 a__nats -> nats 1084.45/291.58 a__pairs -> pairs 1084.45/291.58 a__odds -> odds 1084.45/291.58 a__incr(X) -> incr(X) 1084.45/291.58 a__head(X) -> head(X) 1084.45/291.58 a__tail(X) -> tail(X) 1084.45/291.58 1084.45/291.58 S is empty. 1084.45/291.58 Rewrite Strategy: INNERMOST 1084.45/291.58 ---------------------------------------- 1084.45/291.58 1084.45/291.58 (1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) 1084.45/291.58 Transformed a relative TRS into a decreasing-loop problem. 1084.45/291.58 ---------------------------------------- 1084.45/291.58 1084.45/291.58 (2) 1084.45/291.58 Obligation: 1084.45/291.58 Analyzing the following TRS for decreasing loops: 1084.45/291.58 1084.45/291.58 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1084.45/291.58 1084.45/291.58 1084.45/291.58 The TRS R consists of the following rules: 1084.45/291.58 1084.45/291.58 a__nats -> cons(0, incr(nats)) 1084.45/291.58 a__pairs -> cons(0, incr(odds)) 1084.45/291.58 a__odds -> a__incr(a__pairs) 1084.45/291.58 a__incr(cons(X, XS)) -> cons(s(mark(X)), incr(XS)) 1084.45/291.58 a__head(cons(X, XS)) -> mark(X) 1084.45/291.58 a__tail(cons(X, XS)) -> mark(XS) 1084.45/291.58 mark(nats) -> a__nats 1084.45/291.58 mark(pairs) -> a__pairs 1084.45/291.58 mark(odds) -> a__odds 1084.45/291.58 mark(incr(X)) -> a__incr(mark(X)) 1084.45/291.58 mark(head(X)) -> a__head(mark(X)) 1084.45/291.58 mark(tail(X)) -> a__tail(mark(X)) 1084.45/291.58 mark(0) -> 0 1084.45/291.58 mark(s(X)) -> s(mark(X)) 1084.45/291.58 mark(nil) -> nil 1084.45/291.58 mark(cons(X1, X2)) -> cons(mark(X1), X2) 1084.45/291.58 a__nats -> nats 1084.45/291.58 a__pairs -> pairs 1084.45/291.58 a__odds -> odds 1084.45/291.58 a__incr(X) -> incr(X) 1084.45/291.58 a__head(X) -> head(X) 1084.45/291.58 a__tail(X) -> tail(X) 1084.45/291.58 1084.45/291.58 S is empty. 1084.45/291.58 Rewrite Strategy: INNERMOST 1084.45/291.58 ---------------------------------------- 1084.45/291.58 1084.45/291.58 (3) DecreasingLoopProof (LOWER BOUND(ID)) 1084.45/291.58 The following loop(s) give(s) rise to the lower bound Omega(n^1): 1084.45/291.58 1084.45/291.58 The rewrite sequence 1084.45/291.58 1084.45/291.58 mark(incr(X)) ->^+ a__incr(mark(X))
popout
output may be truncated. 'popout' for the full output.
job log
popout
actions
all output
return to Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40
