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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313694
details
property
value
status
complete
benchmark
otto06.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n176.star.cs.uiowa.edu
space
AProVE_07
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
294.686 seconds
cpu usage
1131.76
user time
1119.22
system time
12.5347
max virtual memory
3.7907744E7
max residence set size
1.4909576E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^2))
output
1131.48/294.58 WORST_CASE(Omega(n^1), O(n^2)) 1131.48/294.61 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 1131.48/294.61 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1131.48/294.61 1131.48/294.61 1131.48/294.61 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 1131.48/294.61 1131.48/294.61 (0) CpxTRS 1131.48/294.61 (1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] 1131.48/294.61 (2) CpxWeightedTrs 1131.48/294.61 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 1131.48/294.61 (4) CpxTypedWeightedTrs 1131.48/294.61 (5) CompletionProof [UPPER BOUND(ID), 0 ms] 1131.48/294.61 (6) CpxTypedWeightedCompleteTrs 1131.48/294.61 (7) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] 1131.48/294.61 (8) CpxRNTS 1131.48/294.61 (9) CompleteCoflocoProof [FINISHED, 7724 ms] 1131.48/294.61 (10) BOUNDS(1, n^2) 1131.48/294.61 (11) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 1131.48/294.61 (12) TRS for Loop Detection 1131.48/294.61 (13) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 1131.48/294.61 (14) BEST 1131.48/294.61 (15) proven lower bound 1131.48/294.61 (16) LowerBoundPropagationProof [FINISHED, 0 ms] 1131.48/294.61 (17) BOUNDS(n^1, INF) 1131.48/294.61 (18) TRS for Loop Detection 1131.48/294.61 1131.48/294.61 1131.48/294.61 ---------------------------------------- 1131.48/294.61 1131.48/294.61 (0) 1131.48/294.61 Obligation: 1131.48/294.61 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 1131.48/294.61 1131.48/294.61 1131.48/294.61 The TRS R consists of the following rules: 1131.48/294.61 1131.48/294.61 app(x, y) -> helpa(0, plus(length(x), length(y)), x, y) 1131.48/294.61 plus(x, 0) -> x 1131.48/294.61 plus(x, s(y)) -> s(plus(x, y)) 1131.48/294.61 length(nil) -> 0 1131.48/294.61 length(cons(x, y)) -> s(length(y)) 1131.48/294.61 helpa(c, l, ys, zs) -> if(ge(c, l), c, l, ys, zs) 1131.48/294.61 ge(x, 0) -> true 1131.48/294.61 ge(0, s(x)) -> false 1131.48/294.61 ge(s(x), s(y)) -> ge(x, y) 1131.48/294.61 if(true, c, l, ys, zs) -> nil 1131.48/294.61 if(false, c, l, ys, zs) -> helpb(c, l, greater(ys, zs), smaller(ys, zs)) 1131.48/294.61 greater(ys, zs) -> helpc(ge(length(ys), length(zs)), ys, zs) 1131.48/294.61 smaller(ys, zs) -> helpc(ge(length(ys), length(zs)), zs, ys) 1131.48/294.61 helpc(true, ys, zs) -> ys 1131.48/294.61 helpc(false, ys, zs) -> zs 1131.48/294.61 helpb(c, l, cons(y, ys), zs) -> cons(y, helpa(s(c), l, ys, zs)) 1131.48/294.61 1131.48/294.61 S is empty. 1131.48/294.61 Rewrite Strategy: INNERMOST 1131.48/294.61 ---------------------------------------- 1131.48/294.61 1131.48/294.61 (1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) 1131.48/294.61 Transformed relative TRS to weighted TRS 1131.48/294.61 ---------------------------------------- 1131.48/294.61 1131.48/294.61 (2) 1131.48/294.61 Obligation: 1131.48/294.61 The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^2). 1131.48/294.61 1131.48/294.61 1131.48/294.61 The TRS R consists of the following rules: 1131.48/294.61 1131.48/294.61 app(x, y) -> helpa(0, plus(length(x), length(y)), x, y) [1] 1131.48/294.61 plus(x, 0) -> x [1] 1131.48/294.61 plus(x, s(y)) -> s(plus(x, y)) [1] 1131.48/294.61 length(nil) -> 0 [1] 1131.48/294.61 length(cons(x, y)) -> s(length(y)) [1] 1131.48/294.61 helpa(c, l, ys, zs) -> if(ge(c, l), c, l, ys, zs) [1] 1131.48/294.61 ge(x, 0) -> true [1] 1131.48/294.61 ge(0, s(x)) -> false [1] 1131.48/294.61 ge(s(x), s(y)) -> ge(x, y) [1] 1131.48/294.61 if(true, c, l, ys, zs) -> nil [1] 1131.48/294.61 if(false, c, l, ys, zs) -> helpb(c, l, greater(ys, zs), smaller(ys, zs)) [1] 1131.48/294.61 greater(ys, zs) -> helpc(ge(length(ys), length(zs)), ys, zs) [1] 1131.48/294.61 smaller(ys, zs) -> helpc(ge(length(ys), length(zs)), zs, ys) [1] 1131.48/294.61 helpc(true, ys, zs) -> ys [1] 1131.48/294.61 helpc(false, ys, zs) -> zs [1] 1131.48/294.61 helpb(c, l, cons(y, ys), zs) -> cons(y, helpa(s(c), l, ys, zs)) [1] 1131.48/294.61 1131.48/294.61 Rewrite Strategy: INNERMOST 1131.48/294.61 ---------------------------------------- 1131.48/294.61 1131.48/294.61 (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) 1131.48/294.61 Infered types. 1131.48/294.61 ---------------------------------------- 1131.48/294.61 1131.48/294.61 (4) 1131.48/294.61 Obligation: 1131.48/294.61 Runtime Complexity Weighted TRS with Types. 1131.48/294.61 The TRS R consists of the following rules: 1131.48/294.61 1131.48/294.61 app(x, y) -> helpa(0, plus(length(x), length(y)), x, y) [1] 1131.48/294.61 plus(x, 0) -> x [1]
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