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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313465
details
property
value
status
complete
benchmark
MYNAT_nosorts-noand_FR.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n112.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
8.74254 seconds
cpu usage
24.1052
user time
22.8643
system time
1.24092
max virtual memory
1.9010604E7
max residence set size
3574428.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^2), O(n^2))
output
19.29/6.01 WORST_CASE(Omega(n^2), O(n^2)) 19.41/6.04 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 19.41/6.04 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 19.41/6.04 19.41/6.04 19.41/6.04 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^2, n^2). 19.41/6.04 19.41/6.04 (0) CpxTRS 19.41/6.04 (1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] 19.41/6.04 (2) CpxWeightedTrs 19.41/6.04 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 19.41/6.04 (4) CpxTypedWeightedTrs 19.41/6.04 (5) CompletionProof [UPPER BOUND(ID), 0 ms] 19.41/6.04 (6) CpxTypedWeightedCompleteTrs 19.41/6.04 (7) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] 19.41/6.04 (8) CpxRNTS 19.41/6.04 (9) CompleteCoflocoProof [FINISHED, 265 ms] 19.41/6.04 (10) BOUNDS(1, n^2) 19.41/6.04 (11) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 19.41/6.04 (12) CpxTRS 19.41/6.04 (13) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 19.41/6.04 (14) typed CpxTrs 19.41/6.04 (15) OrderProof [LOWER BOUND(ID), 0 ms] 19.41/6.04 (16) typed CpxTrs 19.41/6.04 (17) RewriteLemmaProof [LOWER BOUND(ID), 261 ms] 19.41/6.04 (18) BEST 19.41/6.04 (19) proven lower bound 19.41/6.04 (20) LowerBoundPropagationProof [FINISHED, 0 ms] 19.41/6.04 (21) BOUNDS(n^1, INF) 19.41/6.04 (22) typed CpxTrs 19.41/6.04 (23) RewriteLemmaProof [LOWER BOUND(ID), 80 ms] 19.41/6.04 (24) proven lower bound 19.41/6.04 (25) LowerBoundPropagationProof [FINISHED, 0 ms] 19.41/6.04 (26) BOUNDS(n^2, INF) 19.41/6.04 19.41/6.04 19.41/6.04 ---------------------------------------- 19.41/6.04 19.41/6.04 (0) 19.41/6.04 Obligation: 19.41/6.04 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^2, n^2). 19.41/6.04 19.41/6.04 19.41/6.04 The TRS R consists of the following rules: 19.41/6.04 19.41/6.04 U11(tt, M, N) -> U12(tt, activate(M), activate(N)) 19.41/6.04 U12(tt, M, N) -> s(plus(activate(N), activate(M))) 19.41/6.04 U21(tt, M, N) -> U22(tt, activate(M), activate(N)) 19.41/6.04 U22(tt, M, N) -> plus(x(activate(N), activate(M)), activate(N)) 19.41/6.04 plus(N, 0) -> N 19.41/6.04 plus(N, s(M)) -> U11(tt, M, N) 19.41/6.04 x(N, 0) -> 0 19.41/6.04 x(N, s(M)) -> U21(tt, M, N) 19.41/6.04 activate(X) -> X 19.41/6.04 19.41/6.04 S is empty. 19.41/6.04 Rewrite Strategy: INNERMOST 19.41/6.04 ---------------------------------------- 19.41/6.04 19.41/6.04 (1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) 19.41/6.04 Transformed relative TRS to weighted TRS 19.41/6.04 ---------------------------------------- 19.41/6.04 19.41/6.04 (2) 19.41/6.04 Obligation: 19.41/6.04 The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^2). 19.41/6.04 19.41/6.04 19.41/6.04 The TRS R consists of the following rules: 19.41/6.04 19.41/6.04 U11(tt, M, N) -> U12(tt, activate(M), activate(N)) [1] 19.41/6.04 U12(tt, M, N) -> s(plus(activate(N), activate(M))) [1] 19.41/6.04 U21(tt, M, N) -> U22(tt, activate(M), activate(N)) [1] 19.41/6.04 U22(tt, M, N) -> plus(x(activate(N), activate(M)), activate(N)) [1] 19.41/6.04 plus(N, 0) -> N [1] 19.41/6.04 plus(N, s(M)) -> U11(tt, M, N) [1] 19.41/6.04 x(N, 0) -> 0 [1] 19.41/6.04 x(N, s(M)) -> U21(tt, M, N) [1] 19.41/6.04 activate(X) -> X [1] 19.41/6.04 19.41/6.04 Rewrite Strategy: INNERMOST 19.41/6.04 ---------------------------------------- 19.41/6.04 19.41/6.04 (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) 19.41/6.04 Infered types. 19.41/6.04 ---------------------------------------- 19.41/6.04 19.41/6.04 (4) 19.41/6.04 Obligation: 19.41/6.04 Runtime Complexity Weighted TRS with Types. 19.41/6.04 The TRS R consists of the following rules: 19.41/6.04 19.41/6.04 U11(tt, M, N) -> U12(tt, activate(M), activate(N)) [1] 19.41/6.04 U12(tt, M, N) -> s(plus(activate(N), activate(M))) [1] 19.41/6.04 U21(tt, M, N) -> U22(tt, activate(M), activate(N)) [1] 19.41/6.04 U22(tt, M, N) -> plus(x(activate(N), activate(M)), activate(N)) [1] 19.41/6.04 plus(N, 0) -> N [1] 19.41/6.04 plus(N, s(M)) -> U11(tt, M, N) [1] 19.41/6.04 x(N, 0) -> 0 [1] 19.41/6.04 x(N, s(M)) -> U21(tt, M, N) [1]
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