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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313327
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
n122.star.cs.uiowa.edu
space
Secret_06_TRS
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
295.119 seconds
cpu usage
1125.39
user time
1110.75
system time
14.6427
max virtual memory
5.9471556E7
max residence set size
1.5609948E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
1123.10/294.49 WORST_CASE(Omega(n^1), ?) 1125.18/294.99 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 1125.18/294.99 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1125.18/294.99 1125.18/294.99 1125.18/294.99 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1125.18/294.99 1125.18/294.99 (0) CpxTRS 1125.18/294.99 (1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 1125.18/294.99 (2) TRS for Loop Detection 1125.18/294.99 (3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 1125.18/294.99 (4) BEST 1125.18/294.99 (5) proven lower bound 1125.18/294.99 (6) LowerBoundPropagationProof [FINISHED, 0 ms] 1125.18/294.99 (7) BOUNDS(n^1, INF) 1125.18/294.99 (8) TRS for Loop Detection 1125.18/294.99 1125.18/294.99 1125.18/294.99 ---------------------------------------- 1125.18/294.99 1125.18/294.99 (0) 1125.18/294.99 Obligation: 1125.18/294.99 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1125.18/294.99 1125.18/294.99 1125.18/294.99 The TRS R consists of the following rules: 1125.18/294.99 1125.18/294.99 isEmpty(cons(x, xs)) -> false 1125.18/294.99 isEmpty(nil) -> true 1125.18/294.99 isZero(0) -> true 1125.18/294.99 isZero(s(x)) -> false 1125.18/294.99 head(cons(x, xs)) -> x 1125.18/294.99 tail(cons(x, xs)) -> xs 1125.18/294.99 tail(nil) -> nil 1125.18/294.99 append(nil, x) -> cons(x, nil) 1125.18/294.99 append(cons(y, ys), x) -> cons(y, append(ys, x)) 1125.18/294.99 p(s(s(x))) -> s(p(s(x))) 1125.18/294.99 p(s(0)) -> 0 1125.18/294.99 p(0) -> 0 1125.18/294.99 inc(s(x)) -> s(inc(x)) 1125.18/294.99 inc(0) -> s(0) 1125.18/294.99 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))) 1125.18/294.99 if(true, true, b, xs, ys, xs2, ys2, zs, zs2) -> zs 1125.18/294.99 if(true, false, b, xs, ys, xs2, ys2, zs, zs2) -> differentLengthError 1125.18/294.99 if(false, true, b, xs, ys, xs2, ys2, zs, zs2) -> differentLengthError 1125.18/294.99 if(false, false, false, xs, ys, xs2, ys2, zs, zs2) -> addLists(xs2, ys2, zs) 1125.18/294.99 if(false, false, true, xs, ys, xs2, ys2, zs, zs2) -> addLists(xs, ys, zs2) 1125.18/294.99 addList(xs, ys) -> addLists(xs, ys, nil) 1125.18/294.99 1125.18/294.99 S is empty. 1125.18/294.99 Rewrite Strategy: INNERMOST 1125.18/294.99 ---------------------------------------- 1125.18/294.99 1125.18/294.99 (1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) 1125.18/294.99 Transformed a relative TRS into a decreasing-loop problem. 1125.18/294.99 ---------------------------------------- 1125.18/294.99 1125.18/294.99 (2) 1125.18/294.99 Obligation: 1125.18/294.99 Analyzing the following TRS for decreasing loops: 1125.18/294.99 1125.18/294.99 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1125.18/294.99 1125.18/294.99 1125.18/294.99 The TRS R consists of the following rules: 1125.18/294.99 1125.18/294.99 isEmpty(cons(x, xs)) -> false 1125.18/294.99 isEmpty(nil) -> true 1125.18/294.99 isZero(0) -> true 1125.18/294.99 isZero(s(x)) -> false 1125.18/294.99 head(cons(x, xs)) -> x 1125.18/294.99 tail(cons(x, xs)) -> xs 1125.18/294.99 tail(nil) -> nil 1125.18/294.99 append(nil, x) -> cons(x, nil) 1125.18/294.99 append(cons(y, ys), x) -> cons(y, append(ys, x)) 1125.18/294.99 p(s(s(x))) -> s(p(s(x))) 1125.18/294.99 p(s(0)) -> 0 1125.18/294.99 p(0) -> 0 1125.18/294.99 inc(s(x)) -> s(inc(x)) 1125.18/294.99 inc(0) -> s(0) 1125.18/294.99 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))) 1125.18/294.99 if(true, true, b, xs, ys, xs2, ys2, zs, zs2) -> zs 1125.18/294.99 if(true, false, b, xs, ys, xs2, ys2, zs, zs2) -> differentLengthError 1125.18/294.99 if(false, true, b, xs, ys, xs2, ys2, zs, zs2) -> differentLengthError 1125.18/294.99 if(false, false, false, xs, ys, xs2, ys2, zs, zs2) -> addLists(xs2, ys2, zs) 1125.18/294.99 if(false, false, true, xs, ys, xs2, ys2, zs, zs2) -> addLists(xs, ys, zs2) 1125.18/294.99 addList(xs, ys) -> addLists(xs, ys, nil) 1125.18/294.99 1125.18/294.99 S is empty. 1125.18/294.99 Rewrite Strategy: INNERMOST 1125.18/294.99 ---------------------------------------- 1125.18/294.99 1125.18/294.99 (3) DecreasingLoopProof (LOWER BOUND(ID)) 1125.18/294.99 The following loop(s) give(s) rise to the lower bound Omega(n^1): 1125.18/294.99 1125.18/294.99 The rewrite sequence 1125.18/294.99 1125.18/294.99 append(cons(y, ys), x) ->^+ cons(y, append(ys, x)) 1125.18/294.99 1125.18/294.99 gives rise to a decreasing loop by considering the right hand sides subterm at position [1].
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