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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313913
details
property
value
status
complete
benchmark
minsort.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n111.star.cs.uiowa.edu
space
AProVE_09_Inductive
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.584 seconds
cpu usage
1113.73
user time
1100.65
system time
13.0726
max virtual memory
5.6408044E7
max residence set size
1.4966944E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
1113.26/291.49 WORST_CASE(Omega(n^1), ?) 1113.54/291.50 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 1113.54/291.50 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1113.54/291.50 1113.54/291.50 1113.54/291.50 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1113.54/291.50 1113.54/291.50 (0) CpxTRS 1113.54/291.50 (1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 1113.54/291.50 (2) TRS for Loop Detection 1113.54/291.50 (3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 1113.54/291.50 (4) BEST 1113.54/291.50 (5) proven lower bound 1113.54/291.50 (6) LowerBoundPropagationProof [FINISHED, 0 ms] 1113.54/291.50 (7) BOUNDS(n^1, INF) 1113.54/291.50 (8) TRS for Loop Detection 1113.54/291.50 1113.54/291.50 1113.54/291.50 ---------------------------------------- 1113.54/291.50 1113.54/291.50 (0) 1113.54/291.50 Obligation: 1113.54/291.50 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1113.54/291.50 1113.54/291.50 1113.54/291.50 The TRS R consists of the following rules: 1113.54/291.50 1113.54/291.50 le(0, y) -> true 1113.54/291.50 le(s(x), 0) -> false 1113.54/291.50 le(s(x), s(y)) -> le(x, y) 1113.54/291.50 eq(0, 0) -> true 1113.54/291.50 eq(0, s(y)) -> false 1113.54/291.50 eq(s(x), 0) -> false 1113.54/291.50 eq(s(x), s(y)) -> eq(x, y) 1113.54/291.50 minsort(nil) -> nil 1113.54/291.50 minsort(cons(x, xs)) -> cons(min(cons(x, xs)), minsort(rm(min(cons(x, xs)), cons(x, xs)))) 1113.54/291.50 min(nil) -> 0 1113.54/291.50 min(cons(x, nil)) -> x 1113.54/291.50 min(cons(x, cons(y, xs))) -> if1(le(x, y), x, y, xs) 1113.54/291.50 if1(true, x, y, xs) -> min(cons(x, xs)) 1113.54/291.50 if1(false, x, y, xs) -> min(cons(y, xs)) 1113.54/291.50 rm(x, nil) -> nil 1113.54/291.50 rm(x, cons(y, xs)) -> if2(eq(x, y), x, y, xs) 1113.54/291.50 if2(true, x, y, xs) -> rm(x, xs) 1113.54/291.50 if2(false, x, y, xs) -> cons(y, rm(x, xs)) 1113.54/291.50 1113.54/291.50 S is empty. 1113.54/291.50 Rewrite Strategy: INNERMOST 1113.54/291.50 ---------------------------------------- 1113.54/291.50 1113.54/291.50 (1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) 1113.54/291.50 Transformed a relative TRS into a decreasing-loop problem. 1113.54/291.50 ---------------------------------------- 1113.54/291.50 1113.54/291.50 (2) 1113.54/291.50 Obligation: 1113.54/291.50 Analyzing the following TRS for decreasing loops: 1113.54/291.50 1113.54/291.50 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1113.54/291.50 1113.54/291.50 1113.54/291.50 The TRS R consists of the following rules: 1113.54/291.50 1113.54/291.50 le(0, y) -> true 1113.54/291.50 le(s(x), 0) -> false 1113.54/291.50 le(s(x), s(y)) -> le(x, y) 1113.54/291.50 eq(0, 0) -> true 1113.54/291.50 eq(0, s(y)) -> false 1113.54/291.50 eq(s(x), 0) -> false 1113.54/291.50 eq(s(x), s(y)) -> eq(x, y) 1113.54/291.50 minsort(nil) -> nil 1113.54/291.50 minsort(cons(x, xs)) -> cons(min(cons(x, xs)), minsort(rm(min(cons(x, xs)), cons(x, xs)))) 1113.54/291.50 min(nil) -> 0 1113.54/291.50 min(cons(x, nil)) -> x 1113.54/291.50 min(cons(x, cons(y, xs))) -> if1(le(x, y), x, y, xs) 1113.54/291.50 if1(true, x, y, xs) -> min(cons(x, xs)) 1113.54/291.50 if1(false, x, y, xs) -> min(cons(y, xs)) 1113.54/291.50 rm(x, nil) -> nil 1113.54/291.50 rm(x, cons(y, xs)) -> if2(eq(x, y), x, y, xs) 1113.54/291.50 if2(true, x, y, xs) -> rm(x, xs) 1113.54/291.50 if2(false, x, y, xs) -> cons(y, rm(x, xs)) 1113.54/291.50 1113.54/291.50 S is empty. 1113.54/291.50 Rewrite Strategy: INNERMOST 1113.54/291.50 ---------------------------------------- 1113.54/291.50 1113.54/291.50 (3) DecreasingLoopProof (LOWER BOUND(ID)) 1113.54/291.50 The following loop(s) give(s) rise to the lower bound Omega(n^1): 1113.54/291.50 1113.54/291.50 The rewrite sequence 1113.54/291.50 1113.54/291.50 le(s(x), s(y)) ->^+ le(x, y) 1113.54/291.50 1113.54/291.50 gives rise to a decreasing loop by considering the right hand sides subterm at position []. 1113.54/291.50 1113.54/291.50 The pumping substitution is [x / s(x), y / s(y)]. 1113.54/291.50 1113.54/291.50 The result substitution is [ ]. 1113.54/291.50 1113.54/291.50
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