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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313588
details
property
value
status
complete
benchmark
4.27.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n125.star.cs.uiowa.edu
space
SK90
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.527 seconds
cpu usage
971.268
user time
964.575
system time
6.6933
max virtual memory
3.73798E7
max residence set size
8516088.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
971.06/291.46 WORST_CASE(Omega(n^1), ?) 971.06/291.47 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 971.06/291.47 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 971.06/291.47 971.06/291.47 971.06/291.47 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 971.06/291.47 971.06/291.47 (0) CpxTRS 971.06/291.47 (1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 971.06/291.47 (2) TRS for Loop Detection 971.06/291.47 (3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 971.06/291.47 (4) BEST 971.06/291.47 (5) proven lower bound 971.06/291.47 (6) LowerBoundPropagationProof [FINISHED, 0 ms] 971.06/291.47 (7) BOUNDS(n^1, INF) 971.06/291.47 (8) TRS for Loop Detection 971.06/291.47 971.06/291.47 971.06/291.47 ---------------------------------------- 971.06/291.47 971.06/291.47 (0) 971.06/291.47 Obligation: 971.06/291.47 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 971.06/291.47 971.06/291.47 971.06/291.47 The TRS R consists of the following rules: 971.06/291.47 971.06/291.47 int(0, 0) -> .(0, nil) 971.06/291.47 int(0, s(y)) -> .(0, int(s(0), s(y))) 971.06/291.47 int(s(x), 0) -> nil 971.06/291.47 int(s(x), s(y)) -> int_list(int(x, y)) 971.06/291.47 int_list(nil) -> nil 971.06/291.47 int_list(.(x, y)) -> .(s(x), int_list(y)) 971.06/291.47 971.06/291.47 S is empty. 971.06/291.47 Rewrite Strategy: INNERMOST 971.06/291.47 ---------------------------------------- 971.06/291.47 971.06/291.47 (1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) 971.06/291.47 Transformed a relative TRS into a decreasing-loop problem. 971.06/291.47 ---------------------------------------- 971.06/291.47 971.06/291.47 (2) 971.06/291.47 Obligation: 971.06/291.47 Analyzing the following TRS for decreasing loops: 971.06/291.47 971.06/291.47 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 971.06/291.47 971.06/291.47 971.06/291.47 The TRS R consists of the following rules: 971.06/291.47 971.06/291.47 int(0, 0) -> .(0, nil) 971.06/291.47 int(0, s(y)) -> .(0, int(s(0), s(y))) 971.06/291.47 int(s(x), 0) -> nil 971.06/291.47 int(s(x), s(y)) -> int_list(int(x, y)) 971.06/291.47 int_list(nil) -> nil 971.06/291.47 int_list(.(x, y)) -> .(s(x), int_list(y)) 971.06/291.47 971.06/291.47 S is empty. 971.06/291.47 Rewrite Strategy: INNERMOST 971.06/291.47 ---------------------------------------- 971.06/291.47 971.06/291.47 (3) DecreasingLoopProof (LOWER BOUND(ID)) 971.06/291.47 The following loop(s) give(s) rise to the lower bound Omega(n^1): 971.06/291.47 971.06/291.47 The rewrite sequence 971.06/291.47 971.06/291.47 int_list(.(x, y)) ->^+ .(s(x), int_list(y)) 971.06/291.47 971.06/291.47 gives rise to a decreasing loop by considering the right hand sides subterm at position [1]. 971.06/291.47 971.06/291.47 The pumping substitution is [y / .(x, y)]. 971.06/291.47 971.06/291.47 The result substitution is [ ]. 971.06/291.47 971.06/291.47 971.06/291.47 971.06/291.47 971.06/291.47 ---------------------------------------- 971.06/291.47 971.06/291.47 (4) 971.06/291.47 Complex Obligation (BEST) 971.06/291.47 971.06/291.47 ---------------------------------------- 971.06/291.47 971.06/291.47 (5) 971.06/291.47 Obligation: 971.06/291.47 Proved the lower bound n^1 for the following obligation: 971.06/291.47 971.06/291.47 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 971.06/291.47 971.06/291.47 971.06/291.47 The TRS R consists of the following rules: 971.06/291.47 971.06/291.47 int(0, 0) -> .(0, nil) 971.06/291.47 int(0, s(y)) -> .(0, int(s(0), s(y))) 971.06/291.47 int(s(x), 0) -> nil 971.06/291.47 int(s(x), s(y)) -> int_list(int(x, y)) 971.06/291.47 int_list(nil) -> nil 971.06/291.47 int_list(.(x, y)) -> .(s(x), int_list(y))
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