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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313537
details
property
value
status
complete
benchmark
polycounter-10.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n135.star.cs.uiowa.edu
space
TCT_12
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
295.886 seconds
cpu usage
1166.43
user time
1146.27
system time
20.1624
max virtual memory
5.916214E7
max residence set size
1.4283244E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
1166.12/295.76 WORST_CASE(Omega(n^1), ?) 1166.12/295.78 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 1166.12/295.78 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1166.12/295.78 1166.12/295.78 1166.12/295.78 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1166.12/295.78 1166.12/295.78 (0) CpxTRS 1166.12/295.78 (1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 1166.12/295.78 (2) TRS for Loop Detection 1166.12/295.78 (3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 1166.12/295.78 (4) BEST 1166.12/295.78 (5) proven lower bound 1166.12/295.78 (6) LowerBoundPropagationProof [FINISHED, 0 ms] 1166.12/295.78 (7) BOUNDS(n^1, INF) 1166.12/295.78 (8) TRS for Loop Detection 1166.12/295.78 1166.12/295.78 1166.12/295.78 ---------------------------------------- 1166.12/295.78 1166.12/295.78 (0) 1166.12/295.78 Obligation: 1166.12/295.78 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1166.12/295.78 1166.12/295.78 1166.12/295.78 The TRS R consists of the following rules: 1166.12/295.78 1166.12/295.78 f(s(x1), x2, x3, x4, x5, x6, x7, x8, x9, x10) -> f(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) 1166.12/295.78 f(0, s(x2), x3, x4, x5, x6, x7, x8, x9, x10) -> f(x2, x2, x3, x4, x5, x6, x7, x8, x9, x10) 1166.12/295.78 f(0, 0, s(x3), x4, x5, x6, x7, x8, x9, x10) -> f(x3, x3, x3, x4, x5, x6, x7, x8, x9, x10) 1166.12/295.78 f(0, 0, 0, s(x4), x5, x6, x7, x8, x9, x10) -> f(x4, x4, x4, x4, x5, x6, x7, x8, x9, x10) 1166.12/295.78 f(0, 0, 0, 0, s(x5), x6, x7, x8, x9, x10) -> f(x5, x5, x5, x5, x5, x6, x7, x8, x9, x10) 1166.12/295.78 f(0, 0, 0, 0, 0, s(x6), x7, x8, x9, x10) -> f(x6, x6, x6, x6, x6, x6, x7, x8, x9, x10) 1166.12/295.78 f(0, 0, 0, 0, 0, 0, s(x7), x8, x9, x10) -> f(x7, x7, x7, x7, x7, x7, x7, x8, x9, x10) 1166.12/295.78 f(0, 0, 0, 0, 0, 0, 0, s(x8), x9, x10) -> f(x8, x8, x8, x8, x8, x8, x8, x8, x9, x10) 1166.12/295.78 f(0, 0, 0, 0, 0, 0, 0, 0, s(x9), x10) -> f(x9, x9, x9, x9, x9, x9, x9, x9, x9, x10) 1166.12/295.78 f(0, 0, 0, 0, 0, 0, 0, 0, 0, s(x10)) -> f(x10, x10, x10, x10, x10, x10, x10, x10, x10, x10) 1166.12/295.78 f(0, 0, 0, 0, 0, 0, 0, 0, 0, 0) -> 0 1166.12/295.78 1166.12/295.78 S is empty. 1166.12/295.78 Rewrite Strategy: INNERMOST 1166.12/295.78 ---------------------------------------- 1166.12/295.78 1166.12/295.78 (1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) 1166.12/295.78 Transformed a relative TRS into a decreasing-loop problem. 1166.12/295.78 ---------------------------------------- 1166.12/295.78 1166.12/295.78 (2) 1166.12/295.78 Obligation: 1166.12/295.78 Analyzing the following TRS for decreasing loops: 1166.12/295.78 1166.12/295.78 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1166.12/295.78 1166.12/295.78 1166.12/295.78 The TRS R consists of the following rules: 1166.12/295.78 1166.12/295.78 f(s(x1), x2, x3, x4, x5, x6, x7, x8, x9, x10) -> f(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) 1166.12/295.78 f(0, s(x2), x3, x4, x5, x6, x7, x8, x9, x10) -> f(x2, x2, x3, x4, x5, x6, x7, x8, x9, x10) 1166.12/295.78 f(0, 0, s(x3), x4, x5, x6, x7, x8, x9, x10) -> f(x3, x3, x3, x4, x5, x6, x7, x8, x9, x10) 1166.12/295.78 f(0, 0, 0, s(x4), x5, x6, x7, x8, x9, x10) -> f(x4, x4, x4, x4, x5, x6, x7, x8, x9, x10) 1166.12/295.78 f(0, 0, 0, 0, s(x5), x6, x7, x8, x9, x10) -> f(x5, x5, x5, x5, x5, x6, x7, x8, x9, x10) 1166.12/295.78 f(0, 0, 0, 0, 0, s(x6), x7, x8, x9, x10) -> f(x6, x6, x6, x6, x6, x6, x7, x8, x9, x10) 1166.12/295.78 f(0, 0, 0, 0, 0, 0, s(x7), x8, x9, x10) -> f(x7, x7, x7, x7, x7, x7, x7, x8, x9, x10) 1166.12/295.78 f(0, 0, 0, 0, 0, 0, 0, s(x8), x9, x10) -> f(x8, x8, x8, x8, x8, x8, x8, x8, x9, x10) 1166.12/295.78 f(0, 0, 0, 0, 0, 0, 0, 0, s(x9), x10) -> f(x9, x9, x9, x9, x9, x9, x9, x9, x9, x10) 1166.12/295.78 f(0, 0, 0, 0, 0, 0, 0, 0, 0, s(x10)) -> f(x10, x10, x10, x10, x10, x10, x10, x10, x10, x10) 1166.12/295.78 f(0, 0, 0, 0, 0, 0, 0, 0, 0, 0) -> 0 1166.12/295.78 1166.12/295.78 S is empty. 1166.12/295.78 Rewrite Strategy: INNERMOST 1166.12/295.78 ---------------------------------------- 1166.12/295.78 1166.12/295.78 (3) DecreasingLoopProof (LOWER BOUND(ID)) 1166.12/295.78 The following loop(s) give(s) rise to the lower bound Omega(n^1): 1166.12/295.78 1166.12/295.78 The rewrite sequence 1166.12/295.78 1166.12/295.78 f(s(x1), x2, x3, x4, x5, x6, x7, x8, x9, x10) ->^+ f(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) 1166.12/295.78 1166.12/295.78 gives rise to a decreasing loop by considering the right hand sides subterm at position []. 1166.12/295.78 1166.12/295.78 The pumping substitution is [x1 / s(x1)]. 1166.12/295.78 1166.12/295.78 The result substitution is [ ]. 1166.12/295.78 1166.12/295.78 1166.12/295.78 1166.12/295.78 1166.12/295.78 ---------------------------------------- 1166.12/295.78 1166.12/295.78 (4) 1166.12/295.78 Complex Obligation (BEST) 1166.12/295.78 1166.12/295.78 ---------------------------------------- 1166.12/295.78 1166.12/295.78 (5) 1166.12/295.78 Obligation: 1166.12/295.78 Proved the lower bound n^1 for the following obligation: 1166.12/295.78 1166.12/295.78 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF).
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