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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307879
details
property
value
status
complete
benchmark
addList.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n126.star.cs.uiowa.edu
space
Secret_06_TRS
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.565 seconds
cpu usage
596.301
user time
594.421
system time
1.87952
max virtual memory
1.827924E7
max residence set size
5277800.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
596.18/291.52 WORST_CASE(Omega(n^1), ?) 596.18/291.52 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 596.18/291.52 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 596.18/291.52 596.18/291.52 596.18/291.52 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 596.18/291.52 596.18/291.52 (0) CpxTRS 596.18/291.52 (1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 596.18/291.52 (2) TRS for Loop Detection 596.18/291.52 (3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 596.18/291.52 (4) BEST 596.18/291.52 (5) proven lower bound 596.18/291.52 (6) LowerBoundPropagationProof [FINISHED, 0 ms] 596.18/291.52 (7) BOUNDS(n^1, INF) 596.18/291.52 (8) TRS for Loop Detection 596.18/291.52 596.18/291.52 596.18/291.52 ---------------------------------------- 596.18/291.52 596.18/291.52 (0) 596.18/291.52 Obligation: 596.18/291.52 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 596.18/291.52 596.18/291.52 596.18/291.52 The TRS R consists of the following rules: 596.18/291.52 596.18/291.52 isEmpty(cons(x, xs)) -> false 596.18/291.52 isEmpty(nil) -> true 596.18/291.52 isZero(0) -> true 596.18/291.52 isZero(s(x)) -> false 596.18/291.52 head(cons(x, xs)) -> x 596.18/291.52 tail(cons(x, xs)) -> xs 596.18/291.52 tail(nil) -> nil 596.18/291.52 append(nil, x) -> cons(x, nil) 596.18/291.52 append(cons(y, ys), x) -> cons(y, append(ys, x)) 596.18/291.52 p(s(s(x))) -> s(p(s(x))) 596.18/291.52 p(s(0)) -> 0 596.18/291.52 p(0) -> 0 596.18/291.52 inc(s(x)) -> s(inc(x)) 596.18/291.52 inc(0) -> s(0) 596.18/291.52 addLists(xs, ys, zs) -> if(isEmpty(xs), isEmpty(ys), isZero(head(xs)), tail(xs), tail(ys), cons(p(head(xs)), tail(xs)), cons(inc(head(ys)), tail(ys)), zs, append(zs, head(ys))) 596.18/291.52 if(true, true, b, xs, ys, xs2, ys2, zs, zs2) -> zs 596.18/291.52 if(true, false, b, xs, ys, xs2, ys2, zs, zs2) -> differentLengthError 596.18/291.52 if(false, true, b, xs, ys, xs2, ys2, zs, zs2) -> differentLengthError 596.18/291.52 if(false, false, false, xs, ys, xs2, ys2, zs, zs2) -> addLists(xs2, ys2, zs) 596.18/291.52 if(false, false, true, xs, ys, xs2, ys2, zs, zs2) -> addLists(xs, ys, zs2) 596.18/291.52 addList(xs, ys) -> addLists(xs, ys, nil) 596.18/291.52 596.18/291.52 S is empty. 596.18/291.52 Rewrite Strategy: FULL 596.18/291.52 ---------------------------------------- 596.18/291.52 596.18/291.52 (1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) 596.18/291.52 Transformed a relative TRS into a decreasing-loop problem. 596.18/291.52 ---------------------------------------- 596.18/291.52 596.18/291.52 (2) 596.18/291.52 Obligation: 596.18/291.52 Analyzing the following TRS for decreasing loops: 596.18/291.52 596.18/291.52 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 596.18/291.52 596.18/291.52 596.18/291.52 The TRS R consists of the following rules: 596.18/291.52 596.18/291.52 isEmpty(cons(x, xs)) -> false 596.18/291.52 isEmpty(nil) -> true 596.18/291.52 isZero(0) -> true 596.18/291.52 isZero(s(x)) -> false 596.18/291.52 head(cons(x, xs)) -> x 596.18/291.52 tail(cons(x, xs)) -> xs 596.18/291.52 tail(nil) -> nil 596.18/291.52 append(nil, x) -> cons(x, nil) 596.18/291.52 append(cons(y, ys), x) -> cons(y, append(ys, x)) 596.18/291.52 p(s(s(x))) -> s(p(s(x))) 596.18/291.52 p(s(0)) -> 0 596.18/291.52 p(0) -> 0 596.18/291.52 inc(s(x)) -> s(inc(x)) 596.18/291.52 inc(0) -> s(0) 596.18/291.52 addLists(xs, ys, zs) -> if(isEmpty(xs), isEmpty(ys), isZero(head(xs)), tail(xs), tail(ys), cons(p(head(xs)), tail(xs)), cons(inc(head(ys)), tail(ys)), zs, append(zs, head(ys))) 596.18/291.52 if(true, true, b, xs, ys, xs2, ys2, zs, zs2) -> zs 596.18/291.52 if(true, false, b, xs, ys, xs2, ys2, zs, zs2) -> differentLengthError 596.18/291.52 if(false, true, b, xs, ys, xs2, ys2, zs, zs2) -> differentLengthError 596.18/291.52 if(false, false, false, xs, ys, xs2, ys2, zs, zs2) -> addLists(xs2, ys2, zs) 596.18/291.52 if(false, false, true, xs, ys, xs2, ys2, zs, zs2) -> addLists(xs, ys, zs2) 596.18/291.52 addList(xs, ys) -> addLists(xs, ys, nil) 596.18/291.52 596.18/291.52 S is empty. 596.18/291.52 Rewrite Strategy: FULL 596.18/291.52 ---------------------------------------- 596.18/291.52 596.18/291.52 (3) DecreasingLoopProof (LOWER BOUND(ID)) 596.18/291.52 The following loop(s) give(s) rise to the lower bound Omega(n^1): 596.18/291.52 596.18/291.52 The rewrite sequence 596.18/291.52 596.18/291.52 append(cons(y, ys), x) ->^+ cons(y, append(ys, x)) 596.18/291.52 596.18/291.52 gives rise to a decreasing loop by considering the right hand sides subterm at position [1].
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