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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307608
details
property
value
status
complete
benchmark
divhard.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n134.star.cs.uiowa.edu
space
AProVE_09_Inductive
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.565 seconds
cpu usage
303.688
user time
301.522
system time
2.16609
max virtual memory
1.8279384E7
max residence set size
5195212.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
303.59/291.52 WORST_CASE(Omega(n^1), ?) 303.59/291.52 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 303.59/291.52 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 303.59/291.52 303.59/291.52 303.59/291.52 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 303.59/291.52 303.59/291.52 (0) CpxTRS 303.59/291.52 (1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 303.59/291.52 (2) TRS for Loop Detection 303.59/291.52 (3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 303.59/291.52 (4) BEST 303.59/291.52 (5) proven lower bound 303.59/291.52 (6) LowerBoundPropagationProof [FINISHED, 0 ms] 303.59/291.52 (7) BOUNDS(n^1, INF) 303.59/291.52 (8) TRS for Loop Detection 303.59/291.52 303.59/291.52 303.59/291.52 ---------------------------------------- 303.59/291.52 303.59/291.52 (0) 303.59/291.52 Obligation: 303.59/291.52 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 303.59/291.52 303.59/291.52 303.59/291.52 The TRS R consists of the following rules: 303.59/291.52 303.59/291.52 minus(x, y) -> if(gt(x, y), x, y) 303.59/291.52 if(true, x, y) -> s(minus(p(x), y)) 303.59/291.52 if(false, x, y) -> 0 303.59/291.52 p(0) -> 0 303.59/291.52 p(s(x)) -> x 303.59/291.52 ge(x, 0) -> true 303.59/291.52 ge(0, s(x)) -> false 303.59/291.52 ge(s(x), s(y)) -> ge(x, y) 303.59/291.52 gt(0, y) -> false 303.59/291.52 gt(s(x), 0) -> true 303.59/291.52 gt(s(x), s(y)) -> gt(x, y) 303.59/291.52 div(x, y) -> if1(ge(x, y), x, y) 303.59/291.52 if1(true, x, y) -> if2(gt(y, 0), x, y) 303.59/291.52 if1(false, x, y) -> 0 303.59/291.52 if2(true, x, y) -> s(div(minus(x, y), y)) 303.59/291.52 if2(false, x, y) -> 0 303.59/291.52 303.59/291.52 S is empty. 303.59/291.52 Rewrite Strategy: FULL 303.59/291.52 ---------------------------------------- 303.59/291.52 303.59/291.52 (1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) 303.59/291.52 Transformed a relative TRS into a decreasing-loop problem. 303.59/291.52 ---------------------------------------- 303.59/291.52 303.59/291.52 (2) 303.59/291.52 Obligation: 303.59/291.52 Analyzing the following TRS for decreasing loops: 303.59/291.52 303.59/291.52 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 303.59/291.52 303.59/291.52 303.59/291.52 The TRS R consists of the following rules: 303.59/291.52 303.59/291.52 minus(x, y) -> if(gt(x, y), x, y) 303.59/291.52 if(true, x, y) -> s(minus(p(x), y)) 303.59/291.52 if(false, x, y) -> 0 303.59/291.52 p(0) -> 0 303.59/291.52 p(s(x)) -> x 303.59/291.52 ge(x, 0) -> true 303.59/291.52 ge(0, s(x)) -> false 303.59/291.52 ge(s(x), s(y)) -> ge(x, y) 303.59/291.52 gt(0, y) -> false 303.59/291.52 gt(s(x), 0) -> true 303.59/291.52 gt(s(x), s(y)) -> gt(x, y) 303.59/291.52 div(x, y) -> if1(ge(x, y), x, y) 303.59/291.52 if1(true, x, y) -> if2(gt(y, 0), x, y) 303.59/291.52 if1(false, x, y) -> 0 303.59/291.52 if2(true, x, y) -> s(div(minus(x, y), y)) 303.59/291.52 if2(false, x, y) -> 0 303.59/291.52 303.59/291.52 S is empty. 303.59/291.52 Rewrite Strategy: FULL 303.59/291.52 ---------------------------------------- 303.59/291.52 303.59/291.52 (3) DecreasingLoopProof (LOWER BOUND(ID)) 303.59/291.52 The following loop(s) give(s) rise to the lower bound Omega(n^1): 303.59/291.52 303.59/291.52 The rewrite sequence 303.59/291.52 303.59/291.52 gt(s(x), s(y)) ->^+ gt(x, y) 303.59/291.52 303.59/291.52 gives rise to a decreasing loop by considering the right hand sides subterm at position []. 303.59/291.52 303.59/291.52 The pumping substitution is [x / s(x), y / s(y)]. 303.59/291.52 303.59/291.52 The result substitution is [ ]. 303.59/291.52 303.59/291.52 303.59/291.52 303.59/291.52 303.59/291.52 ---------------------------------------- 303.59/291.52
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