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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307760
details
property
value
status
complete
benchmark
wiehe11.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n018.star.cs.uiowa.edu
space
AProVE_07
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.595 seconds
cpu usage
341.662
user time
338.918
system time
2.74374
max virtual memory
1.8279384E7
max residence set size
6105532.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
341.60/291.54 WORST_CASE(Omega(n^1), ?) 341.60/291.55 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 341.60/291.55 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 341.60/291.55 341.60/291.55 341.60/291.55 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 341.60/291.55 341.60/291.55 (0) CpxTRS 341.60/291.55 (1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 341.60/291.55 (2) TRS for Loop Detection 341.60/291.55 (3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 341.60/291.55 (4) BEST 341.60/291.55 (5) proven lower bound 341.60/291.55 (6) LowerBoundPropagationProof [FINISHED, 0 ms] 341.60/291.55 (7) BOUNDS(n^1, INF) 341.60/291.55 (8) TRS for Loop Detection 341.60/291.55 341.60/291.55 341.60/291.55 ---------------------------------------- 341.60/291.55 341.60/291.55 (0) 341.60/291.55 Obligation: 341.60/291.55 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 341.60/291.55 341.60/291.55 341.60/291.55 The TRS R consists of the following rules: 341.60/291.55 341.60/291.55 minus(x, 0) -> x 341.60/291.55 minus(s(x), s(y)) -> minus(x, y) 341.60/291.55 quot(0, s(y)) -> 0 341.60/291.55 quot(s(x), s(y)) -> s(quot(minus(x, y), s(y))) 341.60/291.55 plus(0, y) -> y 341.60/291.55 plus(s(x), y) -> s(plus(x, y)) 341.60/291.55 minus(minus(x, y), z) -> minus(x, plus(y, z)) 341.60/291.55 app(nil, k) -> k 341.60/291.55 app(l, nil) -> l 341.60/291.55 app(cons(x, l), k) -> cons(x, app(l, k)) 341.60/291.55 sum(cons(x, nil)) -> cons(x, nil) 341.60/291.55 sum(cons(x, cons(y, l))) -> sum(cons(plus(x, y), l)) 341.60/291.55 sum(app(l, cons(x, cons(y, k)))) -> sum(app(l, sum(cons(x, cons(y, k))))) 341.60/291.55 plus(s(x), s(y)) -> s(s(plus(if(gt(x, y), x, y), if(not(gt(x, y)), id(x), id(y))))) 341.60/291.55 plus(s(x), x) -> plus(if(gt(x, x), id(x), id(x)), s(x)) 341.60/291.55 plus(zero, y) -> y 341.60/291.55 plus(id(x), s(y)) -> s(plus(x, if(gt(s(y), y), y, s(y)))) 341.60/291.55 id(x) -> x 341.60/291.55 if(true, x, y) -> x 341.60/291.55 if(false, x, y) -> y 341.60/291.55 not(x) -> if(x, false, true) 341.60/291.55 gt(s(x), zero) -> true 341.60/291.55 gt(zero, y) -> false 341.60/291.55 gt(s(x), s(y)) -> gt(x, y) 341.60/291.55 341.60/291.55 S is empty. 341.60/291.55 Rewrite Strategy: FULL 341.60/291.55 ---------------------------------------- 341.60/291.55 341.60/291.55 (1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) 341.60/291.55 Transformed a relative TRS into a decreasing-loop problem. 341.60/291.55 ---------------------------------------- 341.60/291.55 341.60/291.55 (2) 341.60/291.55 Obligation: 341.60/291.55 Analyzing the following TRS for decreasing loops: 341.60/291.55 341.60/291.55 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 341.60/291.55 341.60/291.55 341.60/291.55 The TRS R consists of the following rules: 341.60/291.55 341.60/291.55 minus(x, 0) -> x 341.60/291.55 minus(s(x), s(y)) -> minus(x, y) 341.60/291.55 quot(0, s(y)) -> 0 341.60/291.55 quot(s(x), s(y)) -> s(quot(minus(x, y), s(y))) 341.60/291.55 plus(0, y) -> y 341.60/291.55 plus(s(x), y) -> s(plus(x, y)) 341.60/291.55 minus(minus(x, y), z) -> minus(x, plus(y, z)) 341.60/291.55 app(nil, k) -> k 341.60/291.55 app(l, nil) -> l 341.60/291.55 app(cons(x, l), k) -> cons(x, app(l, k)) 341.60/291.55 sum(cons(x, nil)) -> cons(x, nil) 341.60/291.55 sum(cons(x, cons(y, l))) -> sum(cons(plus(x, y), l)) 341.60/291.55 sum(app(l, cons(x, cons(y, k)))) -> sum(app(l, sum(cons(x, cons(y, k))))) 341.60/291.55 plus(s(x), s(y)) -> s(s(plus(if(gt(x, y), x, y), if(not(gt(x, y)), id(x), id(y))))) 341.60/291.55 plus(s(x), x) -> plus(if(gt(x, x), id(x), id(x)), s(x)) 341.60/291.55 plus(zero, y) -> y 341.60/291.55 plus(id(x), s(y)) -> s(plus(x, if(gt(s(y), y), y, s(y)))) 341.60/291.55 id(x) -> x 341.60/291.55 if(true, x, y) -> x 341.60/291.55 if(false, x, y) -> y 341.60/291.55 not(x) -> if(x, false, true) 341.60/291.55 gt(s(x), zero) -> true 341.60/291.55 gt(zero, y) -> false 341.60/291.55 gt(s(x), s(y)) -> gt(x, y) 341.60/291.55 341.60/291.55 S is empty. 341.60/291.55 Rewrite Strategy: FULL 341.60/291.55 ---------------------------------------- 341.60/291.55 341.60/291.55 (3) DecreasingLoopProof (LOWER BOUND(ID)) 341.60/291.55 The following loop(s) give(s) rise to the lower bound Omega(n^1):
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