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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307740
details
property
value
status
complete
benchmark
thiemann01.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n099.star.cs.uiowa.edu
space
AProVE_07
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.669 seconds
cpu usage
307.778
user time
305.884
system time
1.89391
max virtual memory
1.8281752E7
max residence set size
5392256.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
307.60/291.58 WORST_CASE(Omega(n^1), ?) 307.60/291.64 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 307.60/291.64 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 307.60/291.64 307.60/291.64 307.60/291.64 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 307.60/291.64 307.60/291.64 (0) CpxTRS 307.60/291.64 (1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 307.60/291.64 (2) TRS for Loop Detection 307.60/291.64 (3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 307.60/291.64 (4) BEST 307.60/291.64 (5) proven lower bound 307.60/291.64 (6) LowerBoundPropagationProof [FINISHED, 0 ms] 307.60/291.64 (7) BOUNDS(n^1, INF) 307.60/291.64 (8) TRS for Loop Detection 307.60/291.64 307.60/291.64 307.60/291.64 ---------------------------------------- 307.60/291.64 307.60/291.64 (0) 307.60/291.64 Obligation: 307.60/291.64 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 307.60/291.64 307.60/291.64 307.60/291.64 The TRS R consists of the following rules: 307.60/291.64 307.60/291.64 minus(0, y) -> 0 307.60/291.64 minus(x, 0) -> x 307.60/291.64 minus(s(x), s(y)) -> minus(x, y) 307.60/291.64 plus(0, y) -> y 307.60/291.64 plus(s(x), y) -> plus(x, s(y)) 307.60/291.64 zero(s(x)) -> false 307.60/291.64 zero(0) -> true 307.60/291.64 p(s(x)) -> x 307.60/291.64 div(x, y) -> quot(x, y, 0) 307.60/291.64 quot(x, y, z) -> if(zero(x), x, y, plus(z, s(0))) 307.60/291.64 if(true, x, y, z) -> p(z) 307.60/291.64 if(false, x, s(y), z) -> quot(minus(x, s(y)), s(y), z) 307.60/291.64 307.60/291.64 S is empty. 307.60/291.64 Rewrite Strategy: FULL 307.60/291.64 ---------------------------------------- 307.60/291.64 307.60/291.64 (1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) 307.60/291.64 Transformed a relative TRS into a decreasing-loop problem. 307.60/291.64 ---------------------------------------- 307.60/291.64 307.60/291.64 (2) 307.60/291.64 Obligation: 307.60/291.64 Analyzing the following TRS for decreasing loops: 307.60/291.64 307.60/291.64 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 307.60/291.64 307.60/291.64 307.60/291.64 The TRS R consists of the following rules: 307.60/291.64 307.60/291.64 minus(0, y) -> 0 307.60/291.64 minus(x, 0) -> x 307.60/291.64 minus(s(x), s(y)) -> minus(x, y) 307.60/291.64 plus(0, y) -> y 307.60/291.64 plus(s(x), y) -> plus(x, s(y)) 307.60/291.64 zero(s(x)) -> false 307.60/291.64 zero(0) -> true 307.60/291.64 p(s(x)) -> x 307.60/291.64 div(x, y) -> quot(x, y, 0) 307.60/291.64 quot(x, y, z) -> if(zero(x), x, y, plus(z, s(0))) 307.60/291.64 if(true, x, y, z) -> p(z) 307.60/291.64 if(false, x, s(y), z) -> quot(minus(x, s(y)), s(y), z) 307.60/291.64 307.60/291.64 S is empty. 307.60/291.64 Rewrite Strategy: FULL 307.60/291.64 ---------------------------------------- 307.60/291.64 307.60/291.64 (3) DecreasingLoopProof (LOWER BOUND(ID)) 307.60/291.64 The following loop(s) give(s) rise to the lower bound Omega(n^1): 307.60/291.64 307.60/291.64 The rewrite sequence 307.60/291.64 307.60/291.64 minus(s(x), s(y)) ->^+ minus(x, y) 307.60/291.64 307.60/291.64 gives rise to a decreasing loop by considering the right hand sides subterm at position []. 307.60/291.64 307.60/291.64 The pumping substitution is [x / s(x), y / s(y)]. 307.60/291.64 307.60/291.64 The result substitution is [ ]. 307.60/291.64 307.60/291.64 307.60/291.64 307.60/291.64 307.60/291.64 ---------------------------------------- 307.60/291.64 307.60/291.64 (4) 307.60/291.64 Complex Obligation (BEST) 307.60/291.64 307.60/291.64 ---------------------------------------- 307.60/291.64 307.60/291.64 (5) 307.60/291.64 Obligation: 307.60/291.64 Proved the lower bound n^1 for the following obligation:
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