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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313387
details
property
value
status
complete
benchmark
fossacs.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n059.star.cs.uiowa.edu
space
Mixed_TRS
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.619 seconds
cpu usage
1089.71
user time
1082.01
system time
7.70404
max virtual memory
1.9398824E7
max residence set size
7786664.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
1089.43/291.53 WORST_CASE(Omega(n^1), ?) 1089.43/291.55 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 1089.43/291.55 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1089.43/291.55 1089.43/291.55 1089.43/291.55 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1089.43/291.55 1089.43/291.55 (0) CpxTRS 1089.43/291.55 (1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 1089.43/291.55 (2) TRS for Loop Detection 1089.43/291.55 (3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 1089.43/291.55 (4) BEST 1089.43/291.55 (5) proven lower bound 1089.43/291.55 (6) LowerBoundPropagationProof [FINISHED, 0 ms] 1089.43/291.55 (7) BOUNDS(n^1, INF) 1089.43/291.55 (8) TRS for Loop Detection 1089.43/291.55 1089.43/291.55 1089.43/291.55 ---------------------------------------- 1089.43/291.55 1089.43/291.55 (0) 1089.43/291.55 Obligation: 1089.43/291.55 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1089.43/291.55 1089.43/291.55 1089.43/291.55 The TRS R consists of the following rules: 1089.43/291.55 1089.43/291.55 f(node(s(n), xs)) -> f(addchild(select(xs), node(n, xs))) 1089.43/291.55 select(cons(ap, xs)) -> ap 1089.43/291.55 select(cons(ap, xs)) -> select(xs) 1089.43/291.55 addchild(node(y, ys), node(n, xs)) -> node(y, cons(node(n, xs), ys)) 1089.43/291.55 1089.43/291.55 S is empty. 1089.43/291.55 Rewrite Strategy: INNERMOST 1089.43/291.55 ---------------------------------------- 1089.43/291.55 1089.43/291.55 (1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) 1089.43/291.55 Transformed a relative TRS into a decreasing-loop problem. 1089.43/291.55 ---------------------------------------- 1089.43/291.55 1089.43/291.55 (2) 1089.43/291.55 Obligation: 1089.43/291.55 Analyzing the following TRS for decreasing loops: 1089.43/291.55 1089.43/291.55 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1089.43/291.55 1089.43/291.55 1089.43/291.55 The TRS R consists of the following rules: 1089.43/291.55 1089.43/291.55 f(node(s(n), xs)) -> f(addchild(select(xs), node(n, xs))) 1089.43/291.55 select(cons(ap, xs)) -> ap 1089.43/291.55 select(cons(ap, xs)) -> select(xs) 1089.43/291.55 addchild(node(y, ys), node(n, xs)) -> node(y, cons(node(n, xs), ys)) 1089.43/291.55 1089.43/291.55 S is empty. 1089.43/291.55 Rewrite Strategy: INNERMOST 1089.43/291.55 ---------------------------------------- 1089.43/291.55 1089.43/291.55 (3) DecreasingLoopProof (LOWER BOUND(ID)) 1089.43/291.55 The following loop(s) give(s) rise to the lower bound Omega(n^1): 1089.43/291.55 1089.43/291.55 The rewrite sequence 1089.43/291.55 1089.43/291.55 select(cons(ap, xs)) ->^+ select(xs) 1089.43/291.55 1089.43/291.55 gives rise to a decreasing loop by considering the right hand sides subterm at position []. 1089.43/291.55 1089.43/291.55 The pumping substitution is [xs / cons(ap, xs)]. 1089.43/291.55 1089.43/291.55 The result substitution is [ ]. 1089.43/291.55 1089.43/291.55 1089.43/291.55 1089.43/291.55 1089.43/291.55 ---------------------------------------- 1089.43/291.55 1089.43/291.55 (4) 1089.43/291.55 Complex Obligation (BEST) 1089.43/291.55 1089.43/291.55 ---------------------------------------- 1089.43/291.55 1089.43/291.55 (5) 1089.43/291.55 Obligation: 1089.43/291.55 Proved the lower bound n^1 for the following obligation: 1089.43/291.55 1089.43/291.55 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1089.43/291.55 1089.43/291.55 1089.43/291.55 The TRS R consists of the following rules: 1089.43/291.55 1089.43/291.55 f(node(s(n), xs)) -> f(addchild(select(xs), node(n, xs))) 1089.43/291.55 select(cons(ap, xs)) -> ap 1089.43/291.55 select(cons(ap, xs)) -> select(xs) 1089.43/291.55 addchild(node(y, ys), node(n, xs)) -> node(y, cons(node(n, xs), ys)) 1089.43/291.55 1089.43/291.55 S is empty. 1089.43/291.55 Rewrite Strategy: INNERMOST 1089.43/291.55 ---------------------------------------- 1089.43/291.55 1089.43/291.55 (6) LowerBoundPropagationProof (FINISHED)
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