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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307607
details
property
value
status
complete
benchmark
mod.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n051.star.cs.uiowa.edu
space
AProVE_09_Inductive
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.588 seconds
cpu usage
301.4
user time
299.745
system time
1.65446
max virtual memory
1.8279384E7
max residence set size
5179240.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
301.23/291.51 WORST_CASE(Omega(n^1), ?) 301.23/291.56 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 301.23/291.56 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 301.23/291.56 301.23/291.56 301.23/291.56 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 301.23/291.56 301.23/291.56 (0) CpxTRS 301.23/291.56 (1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 301.23/291.56 (2) TRS for Loop Detection 301.23/291.56 (3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 301.23/291.56 (4) BEST 301.23/291.56 (5) proven lower bound 301.23/291.56 (6) LowerBoundPropagationProof [FINISHED, 0 ms] 301.23/291.56 (7) BOUNDS(n^1, INF) 301.23/291.56 (8) TRS for Loop Detection 301.23/291.56 301.23/291.56 301.23/291.56 ---------------------------------------- 301.23/291.56 301.23/291.56 (0) 301.23/291.56 Obligation: 301.23/291.56 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 301.23/291.56 301.23/291.56 301.23/291.56 The TRS R consists of the following rules: 301.23/291.56 301.23/291.56 minus(0, y) -> 0 301.23/291.56 minus(s(x), y) -> if(gt(s(x), y), x, y) 301.23/291.56 if(true, x, y) -> s(minus(x, y)) 301.23/291.56 if(false, x, y) -> 0 301.23/291.56 mod(x, 0) -> 0 301.23/291.56 mod(x, s(y)) -> if1(lt(x, s(y)), x, s(y)) 301.23/291.56 if1(true, x, y) -> x 301.23/291.56 if1(false, x, y) -> mod(minus(x, y), y) 301.23/291.56 gt(0, y) -> false 301.23/291.56 gt(s(x), 0) -> true 301.23/291.56 gt(s(x), s(y)) -> gt(x, y) 301.23/291.56 lt(x, 0) -> false 301.23/291.56 lt(0, s(x)) -> true 301.23/291.56 lt(s(x), s(y)) -> lt(x, y) 301.23/291.56 301.23/291.56 S is empty. 301.23/291.56 Rewrite Strategy: FULL 301.23/291.56 ---------------------------------------- 301.23/291.56 301.23/291.56 (1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) 301.23/291.56 Transformed a relative TRS into a decreasing-loop problem. 301.23/291.56 ---------------------------------------- 301.23/291.56 301.23/291.56 (2) 301.23/291.56 Obligation: 301.23/291.56 Analyzing the following TRS for decreasing loops: 301.23/291.56 301.23/291.56 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 301.23/291.56 301.23/291.56 301.23/291.56 The TRS R consists of the following rules: 301.23/291.56 301.23/291.56 minus(0, y) -> 0 301.23/291.56 minus(s(x), y) -> if(gt(s(x), y), x, y) 301.23/291.56 if(true, x, y) -> s(minus(x, y)) 301.23/291.56 if(false, x, y) -> 0 301.23/291.56 mod(x, 0) -> 0 301.23/291.56 mod(x, s(y)) -> if1(lt(x, s(y)), x, s(y)) 301.23/291.56 if1(true, x, y) -> x 301.23/291.56 if1(false, x, y) -> mod(minus(x, y), y) 301.23/291.56 gt(0, y) -> false 301.23/291.56 gt(s(x), 0) -> true 301.23/291.56 gt(s(x), s(y)) -> gt(x, y) 301.23/291.56 lt(x, 0) -> false 301.23/291.56 lt(0, s(x)) -> true 301.23/291.56 lt(s(x), s(y)) -> lt(x, y) 301.23/291.56 301.23/291.56 S is empty. 301.23/291.56 Rewrite Strategy: FULL 301.23/291.56 ---------------------------------------- 301.23/291.56 301.23/291.56 (3) DecreasingLoopProof (LOWER BOUND(ID)) 301.23/291.56 The following loop(s) give(s) rise to the lower bound Omega(n^1): 301.23/291.56 301.23/291.56 The rewrite sequence 301.23/291.56 301.23/291.56 lt(s(x), s(y)) ->^+ lt(x, y) 301.23/291.56 301.23/291.56 gives rise to a decreasing loop by considering the right hand sides subterm at position []. 301.23/291.56 301.23/291.56 The pumping substitution is [x / s(x), y / s(y)]. 301.23/291.56 301.23/291.56 The result substitution is [ ]. 301.23/291.56 301.23/291.56 301.23/291.56 301.23/291.56 301.23/291.56 ---------------------------------------- 301.23/291.56 301.23/291.56 (4) 301.23/291.56 Complex Obligation (BEST) 301.23/291.56 301.23/291.56 ----------------------------------------
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