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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313566
details
property
value
status
complete
benchmark
2.45.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n143.star.cs.uiowa.edu
space
SK90
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
5.25302 seconds
cpu usage
17.4947
user time
16.4803
system time
1.0144
max virtual memory
1.9040896E7
max residence set size
3318748.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^1))
output
17.29/5.19 WORST_CASE(Omega(n^1), O(n^1)) 17.41/5.20 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 17.41/5.20 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 17.41/5.20 17.41/5.20 17.41/5.20 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 17.41/5.20 17.41/5.20 (0) CpxTRS 17.41/5.20 (1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] 17.41/5.20 (2) CpxWeightedTrs 17.41/5.20 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 17.41/5.20 (4) CpxTypedWeightedTrs 17.41/5.20 (5) CompletionProof [UPPER BOUND(ID), 0 ms] 17.41/5.20 (6) CpxTypedWeightedCompleteTrs 17.41/5.20 (7) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] 17.41/5.20 (8) CpxRNTS 17.41/5.20 (9) CompleteCoflocoProof [FINISHED, 43 ms] 17.41/5.20 (10) BOUNDS(1, n^1) 17.41/5.20 (11) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 17.41/5.20 (12) TRS for Loop Detection 17.41/5.20 (13) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 17.41/5.20 (14) BEST 17.41/5.20 (15) proven lower bound 17.41/5.20 (16) LowerBoundPropagationProof [FINISHED, 0 ms] 17.41/5.20 (17) BOUNDS(n^1, INF) 17.41/5.20 (18) TRS for Loop Detection 17.41/5.20 17.41/5.20 17.41/5.20 ---------------------------------------- 17.41/5.20 17.41/5.20 (0) 17.41/5.20 Obligation: 17.41/5.20 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 17.41/5.20 17.41/5.20 17.41/5.20 The TRS R consists of the following rules: 17.41/5.20 17.41/5.20 admit(x, nil) -> nil 17.41/5.20 admit(x, .(u, .(v, .(w, z)))) -> cond(=(sum(x, u, v), w), .(u, .(v, .(w, admit(carry(x, u, v), z))))) 17.41/5.20 cond(true, y) -> y 17.41/5.20 17.41/5.20 S is empty. 17.41/5.20 Rewrite Strategy: INNERMOST 17.41/5.20 ---------------------------------------- 17.41/5.20 17.41/5.20 (1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) 17.41/5.20 Transformed relative TRS to weighted TRS 17.41/5.20 ---------------------------------------- 17.41/5.20 17.41/5.20 (2) 17.41/5.20 Obligation: 17.41/5.20 The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^1). 17.41/5.20 17.41/5.20 17.41/5.20 The TRS R consists of the following rules: 17.41/5.20 17.41/5.20 admit(x, nil) -> nil [1] 17.41/5.20 admit(x, .(u, .(v, .(w, z)))) -> cond(=(sum(x, u, v), w), .(u, .(v, .(w, admit(carry(x, u, v), z))))) [1] 17.41/5.20 cond(true, y) -> y [1] 17.41/5.20 17.41/5.20 Rewrite Strategy: INNERMOST 17.41/5.20 ---------------------------------------- 17.41/5.20 17.41/5.20 (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) 17.41/5.20 Infered types. 17.41/5.20 ---------------------------------------- 17.41/5.20 17.41/5.20 (4) 17.41/5.20 Obligation: 17.41/5.20 Runtime Complexity Weighted TRS with Types. 17.41/5.20 The TRS R consists of the following rules: 17.41/5.20 17.41/5.20 admit(x, nil) -> nil [1] 17.41/5.20 admit(x, .(u, .(v, .(w, z)))) -> cond(=(sum(x, u, v), w), .(u, .(v, .(w, admit(carry(x, u, v), z))))) [1] 17.41/5.20 cond(true, y) -> y [1] 17.41/5.20 17.41/5.20 The TRS has the following type information: 17.41/5.20 admit :: carry -> nil:. -> nil:. 17.41/5.20 nil :: nil:. 17.41/5.20 . :: w -> nil:. -> nil:. 17.41/5.20 w :: w 17.41/5.20 cond :: =:true -> nil:. -> nil:. 17.41/5.20 = :: sum -> w -> =:true 17.41/5.20 sum :: carry -> w -> w -> sum 17.41/5.20 carry :: carry -> w -> w -> carry 17.41/5.20 true :: =:true 17.41/5.20 17.41/5.20 Rewrite Strategy: INNERMOST 17.41/5.20 ---------------------------------------- 17.41/5.20 17.41/5.20 (5) CompletionProof (UPPER BOUND(ID)) 17.41/5.20 The TRS is a completely defined constructor system, as every type has a constant constructor and the following rules were added: 17.41/5.20 17.41/5.20 admit(v0, v1) -> null_admit [0] 17.41/5.20 cond(v0, v1) -> null_cond [0] 17.41/5.20 17.41/5.20 And the following fresh constants: null_admit, null_cond, const, const1 17.41/5.20 17.41/5.20 ---------------------------------------- 17.41/5.20
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