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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313743
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
n111.star.cs.uiowa.edu
space
AProVE_07
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
294.798 seconds
cpu usage
1154.2
user time
1139.32
system time
14.884
max virtual memory
3.8739708E7
max residence set size
1.4893972E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
1141.28/291.50 WORST_CASE(Omega(n^1), ?) 1154.08/294.73 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 1154.08/294.73 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1154.08/294.73 1154.08/294.73 1154.08/294.73 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1154.08/294.73 1154.08/294.73 (0) CpxTRS 1154.08/294.73 (1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 1154.08/294.73 (2) TRS for Loop Detection 1154.08/294.73 (3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 1154.08/294.73 (4) BEST 1154.08/294.73 (5) proven lower bound 1154.08/294.73 (6) LowerBoundPropagationProof [FINISHED, 0 ms] 1154.08/294.73 (7) BOUNDS(n^1, INF) 1154.08/294.73 (8) TRS for Loop Detection 1154.08/294.73 1154.08/294.73 1154.08/294.73 ---------------------------------------- 1154.08/294.73 1154.08/294.73 (0) 1154.08/294.73 Obligation: 1154.08/294.73 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1154.08/294.73 1154.08/294.73 1154.08/294.73 The TRS R consists of the following rules: 1154.08/294.73 1154.08/294.73 eq(0, 0) -> true 1154.08/294.73 eq(0, s(x)) -> false 1154.08/294.73 eq(s(x), 0) -> false 1154.08/294.73 eq(s(x), s(y)) -> eq(x, y) 1154.08/294.73 le(0, y) -> true 1154.08/294.73 le(s(x), 0) -> false 1154.08/294.73 le(s(x), s(y)) -> le(x, y) 1154.08/294.73 app(nil, y) -> y 1154.08/294.73 app(add(n, x), y) -> add(n, app(x, y)) 1154.08/294.73 min(add(n, nil)) -> n 1154.08/294.73 min(add(n, add(m, x))) -> if_min(le(n, m), add(n, add(m, x))) 1154.08/294.73 if_min(true, add(n, add(m, x))) -> min(add(n, x)) 1154.08/294.73 if_min(false, add(n, add(m, x))) -> min(add(m, x)) 1154.08/294.73 head(add(n, x)) -> n 1154.08/294.73 tail(add(n, x)) -> x 1154.08/294.73 tail(nil) -> nil 1154.08/294.73 null(nil) -> true 1154.08/294.73 null(add(n, x)) -> false 1154.08/294.73 rm(n, nil) -> nil 1154.08/294.73 rm(n, add(m, x)) -> if_rm(eq(n, m), n, add(m, x)) 1154.08/294.73 if_rm(true, n, add(m, x)) -> rm(n, x) 1154.08/294.73 if_rm(false, n, add(m, x)) -> add(m, rm(n, x)) 1154.08/294.73 minsort(x) -> mins(x, nil, nil) 1154.08/294.73 mins(x, y, z) -> if(null(x), x, y, z) 1154.08/294.73 if(true, x, y, z) -> z 1154.08/294.73 if(false, x, y, z) -> if2(eq(head(x), min(x)), x, y, z) 1154.08/294.73 if2(true, x, y, z) -> mins(app(rm(head(x), tail(x)), y), nil, app(z, add(head(x), nil))) 1154.08/294.73 if2(false, x, y, z) -> mins(tail(x), add(head(x), y), z) 1154.08/294.73 1154.08/294.73 S is empty. 1154.08/294.73 Rewrite Strategy: INNERMOST 1154.08/294.73 ---------------------------------------- 1154.08/294.73 1154.08/294.73 (1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) 1154.08/294.73 Transformed a relative TRS into a decreasing-loop problem. 1154.08/294.73 ---------------------------------------- 1154.08/294.73 1154.08/294.73 (2) 1154.08/294.73 Obligation: 1154.08/294.73 Analyzing the following TRS for decreasing loops: 1154.08/294.73 1154.08/294.73 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1154.08/294.73 1154.08/294.73 1154.08/294.73 The TRS R consists of the following rules: 1154.08/294.73 1154.08/294.73 eq(0, 0) -> true 1154.08/294.73 eq(0, s(x)) -> false 1154.08/294.73 eq(s(x), 0) -> false 1154.08/294.73 eq(s(x), s(y)) -> eq(x, y) 1154.08/294.73 le(0, y) -> true 1154.08/294.73 le(s(x), 0) -> false 1154.08/294.73 le(s(x), s(y)) -> le(x, y) 1154.08/294.73 app(nil, y) -> y 1154.08/294.73 app(add(n, x), y) -> add(n, app(x, y)) 1154.08/294.73 min(add(n, nil)) -> n 1154.08/294.73 min(add(n, add(m, x))) -> if_min(le(n, m), add(n, add(m, x))) 1154.08/294.73 if_min(true, add(n, add(m, x))) -> min(add(n, x)) 1154.08/294.73 if_min(false, add(n, add(m, x))) -> min(add(m, x)) 1154.08/294.73 head(add(n, x)) -> n 1154.08/294.73 tail(add(n, x)) -> x 1154.08/294.73 tail(nil) -> nil 1154.08/294.73 null(nil) -> true 1154.08/294.73 null(add(n, x)) -> false 1154.08/294.73 rm(n, nil) -> nil 1154.08/294.73 rm(n, add(m, x)) -> if_rm(eq(n, m), n, add(m, x)) 1154.08/294.73 if_rm(true, n, add(m, x)) -> rm(n, x) 1154.08/294.73 if_rm(false, n, add(m, x)) -> add(m, rm(n, x)) 1154.08/294.73 minsort(x) -> mins(x, nil, nil) 1154.08/294.73 mins(x, y, z) -> if(null(x), x, y, z) 1154.08/294.73 if(true, x, y, z) -> z 1154.08/294.73 if(false, x, y, z) -> if2(eq(head(x), min(x)), x, y, z) 1154.08/294.73 if2(true, x, y, z) -> mins(app(rm(head(x), tail(x)), y), nil, app(z, add(head(x), nil)))
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return to Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40