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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307767
details
property
value
status
complete
benchmark
otto02.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n075.star.cs.uiowa.edu
space
AProVE_07
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.533 seconds
cpu usage
314.18
user time
312.254
system time
1.92579
max virtual memory
1.8281628E7
max residence set size
5338300.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
314.11/291.50 WORST_CASE(Omega(n^1), ?) 314.11/291.50 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 314.11/291.50 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 314.11/291.50 314.11/291.50 314.11/291.50 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 314.11/291.50 314.11/291.50 (0) CpxTRS 314.11/291.50 (1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 314.11/291.50 (2) TRS for Loop Detection 314.11/291.50 (3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 314.11/291.50 (4) BEST 314.11/291.50 (5) proven lower bound 314.11/291.50 (6) LowerBoundPropagationProof [FINISHED, 0 ms] 314.11/291.50 (7) BOUNDS(n^1, INF) 314.11/291.50 (8) TRS for Loop Detection 314.11/291.50 314.11/291.50 314.11/291.50 ---------------------------------------- 314.11/291.50 314.11/291.50 (0) 314.11/291.50 Obligation: 314.11/291.50 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 314.11/291.50 314.11/291.50 314.11/291.50 The TRS R consists of the following rules: 314.11/291.50 314.11/291.50 app(x, y) -> helpa(0, plus(length(x), length(y)), x, y) 314.11/291.50 plus(x, 0) -> x 314.11/291.50 plus(x, s(y)) -> s(plus(x, y)) 314.11/291.50 length(nil) -> 0 314.11/291.50 length(cons(x, y)) -> s(length(y)) 314.11/291.50 helpa(c, l, ys, zs) -> if(ge(c, l), c, l, ys, zs) 314.11/291.50 ge(x, 0) -> true 314.11/291.50 ge(0, s(x)) -> false 314.11/291.50 ge(s(x), s(y)) -> ge(x, y) 314.11/291.50 if(true, c, l, ys, zs) -> nil 314.11/291.50 if(false, c, l, ys, zs) -> helpb(c, l, ys, zs) 314.11/291.50 take(0, cons(x, xs), ys) -> x 314.11/291.50 take(0, nil, cons(y, ys)) -> y 314.11/291.50 take(s(c), cons(x, xs), ys) -> take(c, xs, ys) 314.11/291.50 take(s(c), nil, cons(y, ys)) -> take(c, nil, ys) 314.11/291.50 helpb(c, l, ys, zs) -> cons(take(c, ys, zs), helpa(s(c), l, ys, zs)) 314.11/291.50 314.11/291.50 S is empty. 314.11/291.50 Rewrite Strategy: FULL 314.11/291.50 ---------------------------------------- 314.11/291.50 314.11/291.50 (1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) 314.11/291.50 Transformed a relative TRS into a decreasing-loop problem. 314.11/291.50 ---------------------------------------- 314.11/291.50 314.11/291.50 (2) 314.11/291.50 Obligation: 314.11/291.50 Analyzing the following TRS for decreasing loops: 314.11/291.50 314.11/291.50 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 314.11/291.50 314.11/291.50 314.11/291.50 The TRS R consists of the following rules: 314.11/291.50 314.11/291.50 app(x, y) -> helpa(0, plus(length(x), length(y)), x, y) 314.11/291.50 plus(x, 0) -> x 314.11/291.50 plus(x, s(y)) -> s(plus(x, y)) 314.11/291.50 length(nil) -> 0 314.11/291.50 length(cons(x, y)) -> s(length(y)) 314.11/291.50 helpa(c, l, ys, zs) -> if(ge(c, l), c, l, ys, zs) 314.11/291.50 ge(x, 0) -> true 314.11/291.50 ge(0, s(x)) -> false 314.11/291.50 ge(s(x), s(y)) -> ge(x, y) 314.11/291.50 if(true, c, l, ys, zs) -> nil 314.11/291.50 if(false, c, l, ys, zs) -> helpb(c, l, ys, zs) 314.11/291.50 take(0, cons(x, xs), ys) -> x 314.11/291.50 take(0, nil, cons(y, ys)) -> y 314.11/291.50 take(s(c), cons(x, xs), ys) -> take(c, xs, ys) 314.11/291.50 take(s(c), nil, cons(y, ys)) -> take(c, nil, ys) 314.11/291.50 helpb(c, l, ys, zs) -> cons(take(c, ys, zs), helpa(s(c), l, ys, zs)) 314.11/291.50 314.11/291.50 S is empty. 314.11/291.50 Rewrite Strategy: FULL 314.11/291.50 ---------------------------------------- 314.11/291.50 314.11/291.50 (3) DecreasingLoopProof (LOWER BOUND(ID)) 314.11/291.50 The following loop(s) give(s) rise to the lower bound Omega(n^1): 314.11/291.50 314.11/291.50 The rewrite sequence 314.11/291.50 314.11/291.50 plus(x, s(y)) ->^+ s(plus(x, y)) 314.11/291.50 314.11/291.50 gives rise to a decreasing loop by considering the right hand sides subterm at position [0]. 314.11/291.50 314.11/291.50 The pumping substitution is [y / s(y)]. 314.11/291.50 314.11/291.50 The result substitution is [ ]. 314.11/291.50 314.11/291.50 314.11/291.50 314.11/291.50 314.11/291.50 ---------------------------------------- 314.11/291.50
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