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	n030.star.cs.uiowa.edu
space	AProVE_07

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	292.637046814 seconds
cpu usage	1147.77194795
max memory	1.5466037248E10

stage attributes

key	value
output-size	6838
starexec-result	WORST_CASE(Omega(n^1), ?)

output

/export/starexec/sandbox2/solver/bin/starexec_run_complexity /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- WORST_CASE(Omega(n^1), ?) proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF).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) popout

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

job log

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actions

all output return to Runti Compl Inner Rewri 22807