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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307807
details
property
value
status
complete
benchmark
div_notTermin.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n149.star.cs.uiowa.edu
space
AProVE_06
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.558 seconds
cpu usage
316.465
user time
314.124
system time
2.34065
max virtual memory
1.8279388E7
max residence set size
5533524.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
316.39/291.52 WORST_CASE(Omega(n^1), ?) 316.39/291.53 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 316.39/291.53 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 316.39/291.53 316.39/291.53 316.39/291.53 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 316.39/291.53 316.39/291.53 (0) CpxTRS 316.39/291.53 (1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 316.39/291.53 (2) TRS for Loop Detection 316.39/291.53 (3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 316.39/291.53 (4) BEST 316.39/291.53 (5) proven lower bound 316.39/291.53 (6) LowerBoundPropagationProof [FINISHED, 0 ms] 316.39/291.53 (7) BOUNDS(n^1, INF) 316.39/291.53 (8) TRS for Loop Detection 316.39/291.53 316.39/291.53 316.39/291.53 ---------------------------------------- 316.39/291.53 316.39/291.53 (0) 316.39/291.53 Obligation: 316.39/291.53 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 316.39/291.53 316.39/291.53 316.39/291.53 The TRS R consists of the following rules: 316.39/291.53 316.39/291.53 ge(0, 0) -> true 316.39/291.53 ge(s(x), 0) -> ge(x, 0) 316.39/291.53 ge(0, s(0)) -> false 316.39/291.53 ge(0, s(s(x))) -> ge(0, s(x)) 316.39/291.53 ge(s(x), s(y)) -> ge(x, y) 316.39/291.53 minus(0, 0) -> 0 316.39/291.53 minus(0, s(x)) -> minus(0, x) 316.39/291.53 minus(s(x), 0) -> s(minus(x, 0)) 316.39/291.53 minus(s(x), s(y)) -> minus(x, y) 316.39/291.53 plus(0, 0) -> 0 316.39/291.53 plus(0, s(x)) -> s(plus(0, x)) 316.39/291.53 plus(s(x), y) -> s(plus(x, y)) 316.39/291.53 div(x, y) -> ify(ge(y, s(0)), x, y) 316.39/291.53 ify(false, x, y) -> divByZeroError 316.39/291.53 ify(true, x, y) -> if(ge(x, y), x, y) 316.39/291.53 if(false, x, y) -> 0 316.39/291.53 if(true, x, y) -> s(div(minus(x, y), y)) 316.39/291.53 div(plus(x, y), z) -> plus(div(x, z), div(y, z)) 316.39/291.53 316.39/291.53 S is empty. 316.39/291.53 Rewrite Strategy: FULL 316.39/291.53 ---------------------------------------- 316.39/291.53 316.39/291.53 (1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) 316.39/291.53 Transformed a relative TRS into a decreasing-loop problem. 316.39/291.53 ---------------------------------------- 316.39/291.53 316.39/291.53 (2) 316.39/291.53 Obligation: 316.39/291.53 Analyzing the following TRS for decreasing loops: 316.39/291.53 316.39/291.53 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 316.39/291.53 316.39/291.53 316.39/291.53 The TRS R consists of the following rules: 316.39/291.53 316.39/291.53 ge(0, 0) -> true 316.39/291.53 ge(s(x), 0) -> ge(x, 0) 316.39/291.53 ge(0, s(0)) -> false 316.39/291.53 ge(0, s(s(x))) -> ge(0, s(x)) 316.39/291.53 ge(s(x), s(y)) -> ge(x, y) 316.39/291.53 minus(0, 0) -> 0 316.39/291.53 minus(0, s(x)) -> minus(0, x) 316.39/291.53 minus(s(x), 0) -> s(minus(x, 0)) 316.39/291.53 minus(s(x), s(y)) -> minus(x, y) 316.39/291.53 plus(0, 0) -> 0 316.39/291.53 plus(0, s(x)) -> s(plus(0, x)) 316.39/291.53 plus(s(x), y) -> s(plus(x, y)) 316.39/291.53 div(x, y) -> ify(ge(y, s(0)), x, y) 316.39/291.53 ify(false, x, y) -> divByZeroError 316.39/291.53 ify(true, x, y) -> if(ge(x, y), x, y) 316.39/291.53 if(false, x, y) -> 0 316.39/291.53 if(true, x, y) -> s(div(minus(x, y), y)) 316.39/291.53 div(plus(x, y), z) -> plus(div(x, z), div(y, z)) 316.39/291.53 316.39/291.53 S is empty. 316.39/291.53 Rewrite Strategy: FULL 316.39/291.53 ---------------------------------------- 316.39/291.53 316.39/291.53 (3) DecreasingLoopProof (LOWER BOUND(ID)) 316.39/291.53 The following loop(s) give(s) rise to the lower bound Omega(n^1): 316.39/291.53 316.39/291.53 The rewrite sequence 316.39/291.53 316.39/291.53 minus(s(x), 0) ->^+ s(minus(x, 0)) 316.39/291.53 316.39/291.53 gives rise to a decreasing loop by considering the right hand sides subterm at position [0]. 316.39/291.53 316.39/291.53 The pumping substitution is [x / s(x)]. 316.39/291.53 316.39/291.53 The result substitution is [ ]. 316.39/291.53 316.39/291.53
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