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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307803
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
n070.star.cs.uiowa.edu
space
AProVE_07
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.652 seconds
cpu usage
308.605
user time
306.277
system time
2.32839
max virtual memory
1.8279384E7
max residence set size
5214868.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
308.55/291.61 WORST_CASE(Omega(n^1), ?) 308.55/291.62 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 308.55/291.62 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 308.55/291.62 308.55/291.62 308.55/291.62 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 308.55/291.62 308.55/291.62 (0) CpxTRS 308.55/291.62 (1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 308.55/291.62 (2) TRS for Loop Detection 308.55/291.62 (3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 308.55/291.62 (4) BEST 308.55/291.62 (5) proven lower bound 308.55/291.62 (6) LowerBoundPropagationProof [FINISHED, 0 ms] 308.55/291.62 (7) BOUNDS(n^1, INF) 308.55/291.62 (8) TRS for Loop Detection 308.55/291.62 308.55/291.62 308.55/291.62 ---------------------------------------- 308.55/291.62 308.55/291.62 (0) 308.55/291.62 Obligation: 308.55/291.62 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 308.55/291.62 308.55/291.62 308.55/291.62 The TRS R consists of the following rules: 308.55/291.62 308.55/291.62 eq(0, 0) -> true 308.55/291.62 eq(0, s(x)) -> false 308.55/291.62 eq(s(x), 0) -> false 308.55/291.62 eq(s(x), s(y)) -> eq(x, y) 308.55/291.62 le(0, y) -> true 308.55/291.62 le(s(x), 0) -> false 308.55/291.62 le(s(x), s(y)) -> le(x, y) 308.55/291.62 app(nil, y) -> y 308.55/291.62 app(add(n, x), y) -> add(n, app(x, y)) 308.55/291.62 min(add(n, nil)) -> n 308.55/291.62 min(add(n, add(m, x))) -> if_min(le(n, m), add(n, add(m, x))) 308.55/291.62 if_min(true, add(n, add(m, x))) -> min(add(n, x)) 308.55/291.62 if_min(false, add(n, add(m, x))) -> min(add(m, x)) 308.55/291.62 head(add(n, x)) -> n 308.55/291.62 tail(add(n, x)) -> x 308.55/291.62 tail(nil) -> nil 308.55/291.62 null(nil) -> true 308.55/291.62 null(add(n, x)) -> false 308.55/291.62 rm(n, nil) -> nil 308.55/291.62 rm(n, add(m, x)) -> if_rm(eq(n, m), n, add(m, x)) 308.55/291.62 if_rm(true, n, add(m, x)) -> rm(n, x) 308.55/291.62 if_rm(false, n, add(m, x)) -> add(m, rm(n, x)) 308.55/291.62 minsort(x) -> mins(x, nil, nil) 308.55/291.62 mins(x, y, z) -> if(null(x), x, y, z) 308.55/291.62 if(true, x, y, z) -> z 308.55/291.62 if(false, x, y, z) -> if2(eq(head(x), min(x)), x, y, z) 308.55/291.62 if2(true, x, y, z) -> mins(app(rm(head(x), tail(x)), y), nil, app(z, add(head(x), nil))) 308.55/291.62 if2(false, x, y, z) -> mins(tail(x), add(head(x), y), z) 308.55/291.62 308.55/291.62 S is empty. 308.55/291.62 Rewrite Strategy: FULL 308.55/291.62 ---------------------------------------- 308.55/291.62 308.55/291.62 (1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) 308.55/291.62 Transformed a relative TRS into a decreasing-loop problem. 308.55/291.62 ---------------------------------------- 308.55/291.62 308.55/291.62 (2) 308.55/291.62 Obligation: 308.55/291.62 Analyzing the following TRS for decreasing loops: 308.55/291.62 308.55/291.62 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 308.55/291.62 308.55/291.62 308.55/291.62 The TRS R consists of the following rules: 308.55/291.62 308.55/291.62 eq(0, 0) -> true 308.55/291.62 eq(0, s(x)) -> false 308.55/291.62 eq(s(x), 0) -> false 308.55/291.62 eq(s(x), s(y)) -> eq(x, y) 308.55/291.62 le(0, y) -> true 308.55/291.62 le(s(x), 0) -> false 308.55/291.62 le(s(x), s(y)) -> le(x, y) 308.55/291.62 app(nil, y) -> y 308.55/291.62 app(add(n, x), y) -> add(n, app(x, y)) 308.55/291.62 min(add(n, nil)) -> n 308.55/291.62 min(add(n, add(m, x))) -> if_min(le(n, m), add(n, add(m, x))) 308.55/291.62 if_min(true, add(n, add(m, x))) -> min(add(n, x)) 308.55/291.62 if_min(false, add(n, add(m, x))) -> min(add(m, x)) 308.55/291.62 head(add(n, x)) -> n 308.55/291.62 tail(add(n, x)) -> x 308.55/291.62 tail(nil) -> nil 308.55/291.62 null(nil) -> true 308.55/291.62 null(add(n, x)) -> false 308.55/291.62 rm(n, nil) -> nil 308.55/291.62 rm(n, add(m, x)) -> if_rm(eq(n, m), n, add(m, x)) 308.55/291.62 if_rm(true, n, add(m, x)) -> rm(n, x) 308.55/291.62 if_rm(false, n, add(m, x)) -> add(m, rm(n, x)) 308.55/291.62 minsort(x) -> mins(x, nil, nil) 308.55/291.62 mins(x, y, z) -> if(null(x), x, y, z) 308.55/291.62 if(true, x, y, z) -> z 308.55/291.62 if(false, x, y, z) -> if2(eq(head(x), min(x)), x, y, z) 308.55/291.62 if2(true, x, y, z) -> mins(app(rm(head(x), tail(x)), y), nil, app(z, add(head(x), nil)))
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