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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313753
details
property
value
status
complete
benchmark
#3.10.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n106.star.cs.uiowa.edu
space
AG01
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.773 seconds
cpu usage
1124.97
user time
1117.12
system time
7.84907
max virtual memory
5.6802628E7
max residence set size
6604476.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^4))
output
1124.61/291.69 WORST_CASE(Omega(n^1), O(n^4)) 1124.61/291.70 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 1124.61/291.70 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1124.61/291.70 1124.61/291.70 1124.61/291.70 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^4). 1124.61/291.70 1124.61/291.70 (0) CpxTRS 1124.61/291.70 (1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] 1124.61/291.70 (2) CpxWeightedTrs 1124.61/291.70 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 1124.61/291.70 (4) CpxTypedWeightedTrs 1124.61/291.70 (5) CompletionProof [UPPER BOUND(ID), 0 ms] 1124.61/291.70 (6) CpxTypedWeightedCompleteTrs 1124.61/291.70 (7) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] 1124.61/291.70 (8) CpxRNTS 1124.61/291.70 (9) CompleteCoflocoProof [FINISHED, 8211 ms] 1124.61/291.70 (10) BOUNDS(1, n^4) 1124.61/291.70 (11) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 1124.61/291.70 (12) TRS for Loop Detection 1124.61/291.70 (13) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 1124.61/291.70 (14) BEST 1124.61/291.70 (15) proven lower bound 1124.61/291.70 (16) LowerBoundPropagationProof [FINISHED, 0 ms] 1124.61/291.70 (17) BOUNDS(n^1, INF) 1124.61/291.70 (18) TRS for Loop Detection 1124.61/291.70 1124.61/291.70 1124.61/291.70 ---------------------------------------- 1124.61/291.70 1124.61/291.70 (0) 1124.61/291.70 Obligation: 1124.61/291.70 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^4). 1124.61/291.70 1124.61/291.70 1124.61/291.70 The TRS R consists of the following rules: 1124.61/291.70 1124.61/291.70 eq(0, 0) -> true 1124.61/291.70 eq(0, s(x)) -> false 1124.61/291.70 eq(s(x), 0) -> false 1124.61/291.70 eq(s(x), s(y)) -> eq(x, y) 1124.61/291.70 le(0, y) -> true 1124.61/291.70 le(s(x), 0) -> false 1124.61/291.70 le(s(x), s(y)) -> le(x, y) 1124.61/291.70 app(nil, y) -> y 1124.61/291.70 app(add(n, x), y) -> add(n, app(x, y)) 1124.61/291.70 min(add(n, nil)) -> n 1124.61/291.70 min(add(n, add(m, x))) -> if_min(le(n, m), add(n, add(m, x))) 1124.61/291.70 if_min(true, add(n, add(m, x))) -> min(add(n, x)) 1124.61/291.70 if_min(false, add(n, add(m, x))) -> min(add(m, x)) 1124.61/291.70 rm(n, nil) -> nil 1124.61/291.70 rm(n, add(m, x)) -> if_rm(eq(n, m), n, add(m, x)) 1124.61/291.70 if_rm(true, n, add(m, x)) -> rm(n, x) 1124.61/291.70 if_rm(false, n, add(m, x)) -> add(m, rm(n, x)) 1124.61/291.70 minsort(nil, nil) -> nil 1124.61/291.70 minsort(add(n, x), y) -> if_minsort(eq(n, min(add(n, x))), add(n, x), y) 1124.61/291.70 if_minsort(true, add(n, x), y) -> add(n, minsort(app(rm(n, x), y), nil)) 1124.61/291.70 if_minsort(false, add(n, x), y) -> minsort(x, add(n, y)) 1124.61/291.70 1124.61/291.70 S is empty. 1124.61/291.70 Rewrite Strategy: INNERMOST 1124.61/291.70 ---------------------------------------- 1124.61/291.70 1124.61/291.70 (1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) 1124.61/291.70 Transformed relative TRS to weighted TRS 1124.61/291.70 ---------------------------------------- 1124.61/291.70 1124.61/291.70 (2) 1124.61/291.70 Obligation: 1124.61/291.70 The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^4). 1124.61/291.70 1124.61/291.70 1124.61/291.70 The TRS R consists of the following rules: 1124.61/291.70 1124.61/291.70 eq(0, 0) -> true [1] 1124.61/291.70 eq(0, s(x)) -> false [1] 1124.61/291.70 eq(s(x), 0) -> false [1] 1124.61/291.70 eq(s(x), s(y)) -> eq(x, y) [1] 1124.61/291.70 le(0, y) -> true [1] 1124.61/291.70 le(s(x), 0) -> false [1] 1124.61/291.70 le(s(x), s(y)) -> le(x, y) [1] 1124.61/291.70 app(nil, y) -> y [1] 1124.61/291.70 app(add(n, x), y) -> add(n, app(x, y)) [1] 1124.61/291.70 min(add(n, nil)) -> n [1] 1124.61/291.70 min(add(n, add(m, x))) -> if_min(le(n, m), add(n, add(m, x))) [1] 1124.61/291.70 if_min(true, add(n, add(m, x))) -> min(add(n, x)) [1] 1124.61/291.70 if_min(false, add(n, add(m, x))) -> min(add(m, x)) [1] 1124.61/291.70 rm(n, nil) -> nil [1] 1124.61/291.70 rm(n, add(m, x)) -> if_rm(eq(n, m), n, add(m, x)) [1] 1124.61/291.70 if_rm(true, n, add(m, x)) -> rm(n, x) [1] 1124.61/291.70 if_rm(false, n, add(m, x)) -> add(m, rm(n, x)) [1] 1124.61/291.70 minsort(nil, nil) -> nil [1] 1124.61/291.70 minsort(add(n, x), y) -> if_minsort(eq(n, min(add(n, x))), add(n, x), y) [1] 1124.61/291.70 if_minsort(true, add(n, x), y) -> add(n, minsort(app(rm(n, x), y), nil)) [1] 1124.61/291.70 if_minsort(false, add(n, x), y) -> minsort(x, add(n, y)) [1] 1124.61/291.70 1124.61/291.70 Rewrite Strategy: INNERMOST 1124.61/291.70 ---------------------------------------- 1124.61/291.70 1124.61/291.70 (3) TypeInferenceProof (BOTH BOUNDS(ID, ID))
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