Spaces
Explore
Communities
Statistics
Reports
Cluster
Status
Help
Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307769
details
property
value
status
complete
benchmark
thiemann41.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n106.star.cs.uiowa.edu
space
AProVE_07
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.819 seconds
cpu usage
1104.74
user time
1092.54
system time
12.1972
max virtual memory
5.5884336E7
max residence set size
1.3245988E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
1104.28/291.72 WORST_CASE(Omega(n^1), ?) 1104.28/291.74 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 1104.28/291.74 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1104.28/291.74 1104.28/291.74 1104.28/291.74 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1104.28/291.74 1104.28/291.74 (0) CpxTRS 1104.28/291.74 (1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 1104.28/291.74 (2) TRS for Loop Detection 1104.28/291.74 (3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 1104.28/291.74 (4) BEST 1104.28/291.74 (5) proven lower bound 1104.28/291.74 (6) LowerBoundPropagationProof [FINISHED, 0 ms] 1104.28/291.74 (7) BOUNDS(n^1, INF) 1104.28/291.74 (8) TRS for Loop Detection 1104.28/291.74 1104.28/291.74 1104.28/291.74 ---------------------------------------- 1104.28/291.74 1104.28/291.74 (0) 1104.28/291.74 Obligation: 1104.28/291.74 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1104.28/291.74 1104.28/291.74 1104.28/291.74 The TRS R consists of the following rules: 1104.28/291.74 1104.28/291.74 times(x, y) -> sum(generate(x, y)) 1104.28/291.74 generate(x, y) -> gen(x, y, 0) 1104.28/291.74 gen(x, y, z) -> if(ge(z, x), x, y, z) 1104.28/291.74 if(true, x, y, z) -> nil 1104.28/291.74 if(false, x, y, z) -> cons(y, gen(x, y, s(z))) 1104.28/291.74 sum(nil) -> 0 1104.28/291.74 sum(cons(0, xs)) -> sum(xs) 1104.28/291.74 sum(cons(s(x), xs)) -> s(sum(cons(x, xs))) 1104.28/291.74 ge(x, 0) -> true 1104.28/291.74 ge(0, s(y)) -> false 1104.28/291.74 ge(s(x), s(y)) -> ge(x, y) 1104.28/291.74 1104.28/291.74 S is empty. 1104.28/291.74 Rewrite Strategy: FULL 1104.28/291.74 ---------------------------------------- 1104.28/291.74 1104.28/291.74 (1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) 1104.28/291.74 Transformed a relative TRS into a decreasing-loop problem. 1104.28/291.74 ---------------------------------------- 1104.28/291.74 1104.28/291.74 (2) 1104.28/291.74 Obligation: 1104.28/291.74 Analyzing the following TRS for decreasing loops: 1104.28/291.74 1104.28/291.74 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1104.28/291.74 1104.28/291.74 1104.28/291.74 The TRS R consists of the following rules: 1104.28/291.74 1104.28/291.74 times(x, y) -> sum(generate(x, y)) 1104.28/291.74 generate(x, y) -> gen(x, y, 0) 1104.28/291.74 gen(x, y, z) -> if(ge(z, x), x, y, z) 1104.28/291.74 if(true, x, y, z) -> nil 1104.28/291.74 if(false, x, y, z) -> cons(y, gen(x, y, s(z))) 1104.28/291.74 sum(nil) -> 0 1104.28/291.74 sum(cons(0, xs)) -> sum(xs) 1104.28/291.74 sum(cons(s(x), xs)) -> s(sum(cons(x, xs))) 1104.28/291.74 ge(x, 0) -> true 1104.28/291.74 ge(0, s(y)) -> false 1104.28/291.74 ge(s(x), s(y)) -> ge(x, y) 1104.28/291.74 1104.28/291.74 S is empty. 1104.28/291.74 Rewrite Strategy: FULL 1104.28/291.74 ---------------------------------------- 1104.28/291.74 1104.28/291.74 (3) DecreasingLoopProof (LOWER BOUND(ID)) 1104.28/291.74 The following loop(s) give(s) rise to the lower bound Omega(n^1): 1104.28/291.74 1104.28/291.74 The rewrite sequence 1104.28/291.74 1104.28/291.74 sum(cons(0, xs)) ->^+ sum(xs) 1104.28/291.74 1104.28/291.74 gives rise to a decreasing loop by considering the right hand sides subterm at position []. 1104.28/291.74 1104.28/291.74 The pumping substitution is [xs / cons(0, xs)]. 1104.28/291.74 1104.28/291.74 The result substitution is [ ]. 1104.28/291.74 1104.28/291.74 1104.28/291.74 1104.28/291.74 1104.28/291.74 ---------------------------------------- 1104.28/291.74 1104.28/291.74 (4) 1104.28/291.74 Complex Obligation (BEST) 1104.28/291.74 1104.28/291.74 ---------------------------------------- 1104.28/291.74 1104.28/291.74 (5) 1104.28/291.74 Obligation: 1104.28/291.74 Proved the lower bound n^1 for the following obligation: 1104.28/291.74 1104.28/291.74 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF).
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
