Spaces
Explore
Communities
Statistics
Reports
Cluster
Status
Help
Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313745
details
property
value
status
complete
benchmark
#3.49.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n101.star.cs.uiowa.edu
space
AG01
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.528 seconds
cpu usage
911.098
user time
904.511
system time
6.58723
max virtual memory
3.7828328E7
max residence set size
7365288.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
910.87/291.46 WORST_CASE(Omega(n^1), ?) 910.96/291.46 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 910.96/291.46 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 910.96/291.46 910.96/291.46 910.96/291.46 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 910.96/291.46 910.96/291.46 (0) CpxTRS 910.96/291.46 (1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 910.96/291.46 (2) TRS for Loop Detection 910.96/291.46 (3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 910.96/291.46 (4) BEST 910.96/291.46 (5) proven lower bound 910.96/291.46 (6) LowerBoundPropagationProof [FINISHED, 0 ms] 910.96/291.46 (7) BOUNDS(n^1, INF) 910.96/291.46 (8) TRS for Loop Detection 910.96/291.46 910.96/291.46 910.96/291.46 ---------------------------------------- 910.96/291.46 910.96/291.46 (0) 910.96/291.46 Obligation: 910.96/291.46 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 910.96/291.46 910.96/291.46 910.96/291.46 The TRS R consists of the following rules: 910.96/291.46 910.96/291.46 f(c(s(x), y)) -> f(c(x, s(y))) 910.96/291.46 f(c(s(x), s(y))) -> g(c(x, y)) 910.96/291.46 g(c(x, s(y))) -> g(c(s(x), y)) 910.96/291.46 g(c(s(x), s(y))) -> f(c(x, y)) 910.96/291.46 910.96/291.46 S is empty. 910.96/291.46 Rewrite Strategy: INNERMOST 910.96/291.46 ---------------------------------------- 910.96/291.46 910.96/291.46 (1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) 910.96/291.46 Transformed a relative TRS into a decreasing-loop problem. 910.96/291.46 ---------------------------------------- 910.96/291.46 910.96/291.46 (2) 910.96/291.46 Obligation: 910.96/291.46 Analyzing the following TRS for decreasing loops: 910.96/291.46 910.96/291.46 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 910.96/291.46 910.96/291.46 910.96/291.46 The TRS R consists of the following rules: 910.96/291.46 910.96/291.46 f(c(s(x), y)) -> f(c(x, s(y))) 910.96/291.46 f(c(s(x), s(y))) -> g(c(x, y)) 910.96/291.46 g(c(x, s(y))) -> g(c(s(x), y)) 910.96/291.46 g(c(s(x), s(y))) -> f(c(x, y)) 910.96/291.46 910.96/291.46 S is empty. 910.96/291.46 Rewrite Strategy: INNERMOST 910.96/291.46 ---------------------------------------- 910.96/291.46 910.96/291.46 (3) DecreasingLoopProof (LOWER BOUND(ID)) 910.96/291.46 The following loop(s) give(s) rise to the lower bound Omega(n^1): 910.96/291.46 910.96/291.46 The rewrite sequence 910.96/291.46 910.96/291.46 g(c(x, s(y))) ->^+ g(c(s(x), y)) 910.96/291.46 910.96/291.46 gives rise to a decreasing loop by considering the right hand sides subterm at position []. 910.96/291.46 910.96/291.46 The pumping substitution is [y / s(y)]. 910.96/291.46 910.96/291.46 The result substitution is [x / s(x)]. 910.96/291.46 910.96/291.46 910.96/291.46 910.96/291.46 910.96/291.46 ---------------------------------------- 910.96/291.46 910.96/291.46 (4) 910.96/291.46 Complex Obligation (BEST) 910.96/291.46 910.96/291.46 ---------------------------------------- 910.96/291.46 910.96/291.46 (5) 910.96/291.46 Obligation: 910.96/291.46 Proved the lower bound n^1 for the following obligation: 910.96/291.46 910.96/291.46 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 910.96/291.46 910.96/291.46 910.96/291.46 The TRS R consists of the following rules: 910.96/291.46 910.96/291.46 f(c(s(x), y)) -> f(c(x, s(y))) 910.96/291.46 f(c(s(x), s(y))) -> g(c(x, y)) 910.96/291.46 g(c(x, s(y))) -> g(c(s(x), y)) 910.96/291.46 g(c(s(x), s(y))) -> f(c(x, y)) 910.96/291.46 910.96/291.46 S is empty. 910.96/291.46 Rewrite Strategy: INNERMOST 910.96/291.46 ---------------------------------------- 910.96/291.46 910.96/291.46 (6) LowerBoundPropagationProof (FINISHED)
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
