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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313340
details
property
value
status
complete
benchmark
mappplus.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n180.star.cs.uiowa.edu
space
hoca
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.652 seconds
cpu usage
323.822
user time
320.207
system time
3.61567
max virtual memory
1.9538032E7
max residence set size
6425900.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^2))
output
323.65/291.58 WORST_CASE(Omega(n^1), O(n^2)) 323.65/291.60 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 323.65/291.60 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 323.65/291.60 323.65/291.60 323.65/291.60 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 323.65/291.60 323.65/291.60 (0) CpxTRS 323.65/291.60 (1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] 323.65/291.60 (2) CpxWeightedTrs 323.65/291.60 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 323.65/291.60 (4) CpxTypedWeightedTrs 323.65/291.60 (5) CompletionProof [UPPER BOUND(ID), 0 ms] 323.65/291.60 (6) CpxTypedWeightedCompleteTrs 323.65/291.60 (7) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] 323.65/291.60 (8) CpxTypedWeightedCompleteTrs 323.65/291.60 (9) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 1 ms] 323.65/291.60 (10) CpxRNTS 323.65/291.60 (11) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms] 323.65/291.60 (12) CpxRNTS 323.65/291.60 (13) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 3 ms] 323.65/291.60 (14) CpxRNTS 323.65/291.60 (15) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 323.65/291.60 (16) CpxRNTS 323.65/291.60 (17) IntTrsBoundProof [UPPER BOUND(ID), 284 ms] 323.65/291.60 (18) CpxRNTS 323.65/291.60 (19) IntTrsBoundProof [UPPER BOUND(ID), 98 ms] 323.65/291.60 (20) CpxRNTS 323.65/291.60 (21) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 323.65/291.60 (22) CpxRNTS 323.65/291.60 (23) IntTrsBoundProof [UPPER BOUND(ID), 356 ms] 323.65/291.60 (24) CpxRNTS 323.65/291.60 (25) IntTrsBoundProof [UPPER BOUND(ID), 117 ms] 323.65/291.60 (26) CpxRNTS 323.65/291.60 (27) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 323.65/291.60 (28) CpxRNTS 323.65/291.60 (29) IntTrsBoundProof [UPPER BOUND(ID), 850 ms] 323.65/291.60 (30) CpxRNTS 323.65/291.60 (31) IntTrsBoundProof [UPPER BOUND(ID), 0 ms] 323.65/291.60 (32) CpxRNTS 323.65/291.60 (33) FinalProof [FINISHED, 0 ms] 323.65/291.60 (34) BOUNDS(1, n^2) 323.65/291.60 (35) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 323.65/291.60 (36) TRS for Loop Detection 323.65/291.60 (37) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 323.65/291.60 (38) BEST 323.65/291.60 (39) proven lower bound 323.65/291.60 (40) LowerBoundPropagationProof [FINISHED, 0 ms] 323.65/291.60 (41) BOUNDS(n^1, INF) 323.65/291.60 (42) TRS for Loop Detection 323.65/291.60 323.65/291.60 323.65/291.60 ---------------------------------------- 323.65/291.60 323.65/291.60 (0) 323.65/291.60 Obligation: 323.65/291.60 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 323.65/291.60 323.65/291.60 323.65/291.60 The TRS R consists of the following rules: 323.65/291.60 323.65/291.60 plus_x#1(0, x8) -> x8 323.65/291.60 plus_x#1(S(x12), x14) -> S(plus_x#1(x12, x14)) 323.65/291.60 map#2(plus_x(x2), Nil) -> Nil 323.65/291.60 map#2(plus_x(x6), Cons(x4, x2)) -> Cons(plus_x#1(x6, x4), map#2(plus_x(x6), x2)) 323.65/291.60 main(x5, x12) -> map#2(plus_x(x12), x5) 323.65/291.60 323.65/291.60 S is empty. 323.65/291.60 Rewrite Strategy: INNERMOST 323.65/291.60 ---------------------------------------- 323.65/291.60 323.65/291.60 (1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) 323.65/291.60 Transformed relative TRS to weighted TRS 323.65/291.60 ---------------------------------------- 323.65/291.60 323.65/291.60 (2) 323.65/291.60 Obligation: 323.65/291.60 The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^2). 323.65/291.60 323.65/291.60 323.65/291.60 The TRS R consists of the following rules: 323.65/291.60 323.65/291.60 plus_x#1(0, x8) -> x8 [1] 323.65/291.60 plus_x#1(S(x12), x14) -> S(plus_x#1(x12, x14)) [1] 323.65/291.60 map#2(plus_x(x2), Nil) -> Nil [1] 323.65/291.60 map#2(plus_x(x6), Cons(x4, x2)) -> Cons(plus_x#1(x6, x4), map#2(plus_x(x6), x2)) [1] 323.65/291.60 main(x5, x12) -> map#2(plus_x(x12), x5) [1] 323.65/291.60 323.65/291.60 Rewrite Strategy: INNERMOST 323.65/291.60 ---------------------------------------- 323.65/291.60 323.65/291.60 (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) 323.65/291.60 Infered types. 323.65/291.60 ---------------------------------------- 323.65/291.60 323.65/291.60 (4) 323.65/291.60 Obligation: 323.65/291.60 Runtime Complexity Weighted TRS with Types. 323.65/291.60 The TRS R consists of the following rules: 323.65/291.60
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