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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313352
details
property
value
status
complete
benchmark
t001.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n182.star.cs.uiowa.edu
space
HirokawaMiddeldorp_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.688 seconds
cpu usage
841.361
user time
827.493
system time
13.868
max virtual memory
5.6800228E7
max residence set size
1.505866E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
841.19/291.59 WORST_CASE(Omega(n^1), ?) 841.19/291.60 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 841.19/291.60 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 841.19/291.60 841.19/291.60 841.19/291.60 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 841.19/291.60 841.19/291.60 (0) CpxTRS 841.19/291.60 (1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 841.19/291.60 (2) TRS for Loop Detection 841.19/291.60 (3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 841.19/291.60 (4) BEST 841.19/291.60 (5) proven lower bound 841.19/291.60 (6) LowerBoundPropagationProof [FINISHED, 0 ms] 841.19/291.60 (7) BOUNDS(n^1, INF) 841.19/291.60 (8) TRS for Loop Detection 841.19/291.60 841.19/291.60 841.19/291.60 ---------------------------------------- 841.19/291.60 841.19/291.60 (0) 841.19/291.60 Obligation: 841.19/291.60 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 841.19/291.60 841.19/291.60 841.19/291.60 The TRS R consists of the following rules: 841.19/291.60 841.19/291.60 -(x, 0) -> x 841.19/291.60 -(s(x), s(y)) -> -(x, y) 841.19/291.60 *(x, 0) -> 0 841.19/291.60 *(x, s(y)) -> +(*(x, y), x) 841.19/291.60 if(true, x, y) -> x 841.19/291.60 if(false, x, y) -> y 841.19/291.60 odd(0) -> false 841.19/291.60 odd(s(0)) -> true 841.19/291.60 odd(s(s(x))) -> odd(x) 841.19/291.60 half(0) -> 0 841.19/291.60 half(s(0)) -> 0 841.19/291.60 half(s(s(x))) -> s(half(x)) 841.19/291.60 if(true, x, y) -> true 841.19/291.60 if(false, x, y) -> false 841.19/291.60 pow(x, y) -> f(x, y, s(0)) 841.19/291.60 f(x, 0, z) -> z 841.19/291.60 f(x, s(y), z) -> if(odd(s(y)), f(x, y, *(x, z)), f(*(x, x), half(s(y)), z)) 841.19/291.60 841.19/291.60 S is empty. 841.19/291.60 Rewrite Strategy: INNERMOST 841.19/291.60 ---------------------------------------- 841.19/291.60 841.19/291.60 (1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) 841.19/291.60 Transformed a relative TRS into a decreasing-loop problem. 841.19/291.60 ---------------------------------------- 841.19/291.60 841.19/291.60 (2) 841.19/291.60 Obligation: 841.19/291.60 Analyzing the following TRS for decreasing loops: 841.19/291.60 841.19/291.60 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 841.19/291.60 841.19/291.60 841.19/291.60 The TRS R consists of the following rules: 841.19/291.60 841.19/291.60 -(x, 0) -> x 841.19/291.60 -(s(x), s(y)) -> -(x, y) 841.19/291.60 *(x, 0) -> 0 841.19/291.60 *(x, s(y)) -> +(*(x, y), x) 841.19/291.60 if(true, x, y) -> x 841.19/291.60 if(false, x, y) -> y 841.19/291.60 odd(0) -> false 841.19/291.60 odd(s(0)) -> true 841.19/291.60 odd(s(s(x))) -> odd(x) 841.19/291.60 half(0) -> 0 841.19/291.60 half(s(0)) -> 0 841.19/291.60 half(s(s(x))) -> s(half(x)) 841.19/291.60 if(true, x, y) -> true 841.19/291.60 if(false, x, y) -> false 841.19/291.60 pow(x, y) -> f(x, y, s(0)) 841.19/291.60 f(x, 0, z) -> z 841.19/291.60 f(x, s(y), z) -> if(odd(s(y)), f(x, y, *(x, z)), f(*(x, x), half(s(y)), z)) 841.19/291.60 841.19/291.60 S is empty. 841.19/291.60 Rewrite Strategy: INNERMOST 841.19/291.60 ---------------------------------------- 841.19/291.60 841.19/291.60 (3) DecreasingLoopProof (LOWER BOUND(ID)) 841.19/291.60 The following loop(s) give(s) rise to the lower bound Omega(n^1): 841.19/291.60 841.19/291.60 The rewrite sequence 841.19/291.60 841.19/291.60 -(s(x), s(y)) ->^+ -(x, y) 841.19/291.60 841.19/291.60 gives rise to a decreasing loop by considering the right hand sides subterm at position []. 841.19/291.60 841.19/291.60 The pumping substitution is [x / s(x), y / s(y)]. 841.19/291.60 841.19/291.60 The result substitution is [ ]. 841.19/291.60 841.19/291.60 841.19/291.60 841.19/291.60
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