details

property	value
status	complete
benchmark	thiemann02.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n151.star.cs.uiowa.edu
space	AProVE_07

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	292.949 seconds
cpu usage	1147.18
user time	1134.94
system time	12.2409
max virtual memory	3.8487648E7
max residence set size	1.4700076E7

stage attributes

key	value
starexec-result	WORST_CASE(Omega(n^1), ?)

output

WORST_CASE(Omega(n^1), ?) proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). (0) CpxTRS (1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (2) TRS for Loop Detection (3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] (4) BEST (5) proven lower bound (6) LowerBoundPropagationProof [FINISHED, 0 ms] (7) BOUNDS(n^1, INF) (8) TRS for Loop Detection ---------------------------------------- (0) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). The TRS R consists of the following rules: eq(0, 0) -> true eq(0, s(x)) -> false eq(s(x), 0) -> false eq(s(x), s(y)) -> eq(x, y) le(0, y) -> true le(s(x), 0) -> false le(s(x), s(y)) -> le(x, y) app(nil, y) -> y app(add(n, x), y) -> add(n, app(x, y)) min(add(n, nil)) -> n min(add(n, add(m, x))) -> if_min(le(n, m), add(n, add(m, x))) if_min(true, add(n, add(m, x))) -> min(add(n, x)) if_min(false, add(n, add(m, x))) -> min(add(m, x)) head(add(n, x)) -> n tail(add(n, x)) -> x tail(nil) -> nil null(nil) -> true null(add(n, x)) -> false rm(n, nil) -> nil rm(n, add(m, x)) -> if_rm(eq(n, m), n, add(m, x)) if_rm(true, n, add(m, x)) -> rm(n, x) if_rm(false, n, add(m, x)) -> add(m, rm(n, x)) minsort(x) -> mins(x, nil, nil) mins(x, y, z) -> if(null(x), x, y, z) if(true, x, y, z) -> z if(false, x, y, z) -> if2(eq(head(x), min(x)), x, y, z) if2(true, x, y, z) -> mins(app(rm(head(x), tail(x)), y), nil, app(z, add(head(x), nil))) if2(false, x, y, z) -> mins(tail(x), add(head(x), y), z) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) Transformed a relative TRS into a decreasing-loop problem. ---------------------------------------- (2) Obligation: Analyzing the following TRS for decreasing loops: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). The TRS R consists of the following rules: eq(0, 0) -> true eq(0, s(x)) -> false eq(s(x), 0) -> false eq(s(x), s(y)) -> eq(x, y) le(0, y) -> true le(s(x), 0) -> false le(s(x), s(y)) -> le(x, y) app(nil, y) -> y app(add(n, x), y) -> add(n, app(x, y)) min(add(n, nil)) -> n min(add(n, add(m, x))) -> if_min(le(n, m), add(n, add(m, x))) if_min(true, add(n, add(m, x))) -> min(add(n, x)) if_min(false, add(n, add(m, x))) -> min(add(m, x)) head(add(n, x)) -> n tail(add(n, x)) -> x tail(nil) -> nil null(nil) -> true null(add(n, x)) -> false rm(n, nil) -> nil rm(n, add(m, x)) -> if_rm(eq(n, m), n, add(m, x)) if_rm(true, n, add(m, x)) -> rm(n, x) if_rm(false, n, add(m, x)) -> add(m, rm(n, x)) minsort(x) -> mins(x, nil, nil) mins(x, y, z) -> if(null(x), x, y, z) if(true, x, y, z) -> z if(false, x, y, z) -> if2(eq(head(x), min(x)), x, y, z) if2(true, x, y, z) -> mins(app(rm(head(x), tail(x)), y), nil, app(z, add(head(x), nil))) popout

output may be truncated. 'popout' for the full output.

job log

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actions

all output return to Runtime Complexity: TRS Innermost