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Runtime Complexity: TRS Innermost pair #487112368
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
n144.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
6.04599 seconds
cpu usage
20.4613
user time
19.256
system time
1.20536
max virtual memory
3.7509308E7
max residence set size
3430712.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^2), O(n^2))
output
WORST_CASE(Omega(n^2), O(n^2)) proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^2, n^2). (0) CpxTRS (1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxWeightedTrs (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (4) CpxTypedWeightedTrs (5) CompletionProof [UPPER BOUND(ID), 0 ms] (6) CpxTypedWeightedCompleteTrs (7) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (8) CpxRNTS (9) CompleteCoflocoProof [FINISHED, 249 ms] (10) BOUNDS(1, n^2) (11) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (12) CpxTRS (13) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (14) typed CpxTrs (15) OrderProof [LOWER BOUND(ID), 0 ms] (16) typed CpxTrs (17) RewriteLemmaProof [LOWER BOUND(ID), 247 ms] (18) BEST (19) proven lower bound (20) LowerBoundPropagationProof [FINISHED, 0 ms] (21) BOUNDS(n^1, INF) (22) typed CpxTrs (23) RewriteLemmaProof [LOWER BOUND(ID), 42 ms] (24) proven lower bound (25) LowerBoundPropagationProof [FINISHED, 0 ms] (26) BOUNDS(n^2, INF) ---------------------------------------- (0) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^2, n^2). The TRS R consists of the following rules: U11(tt, M, N) -> U12(tt, activate(M), activate(N)) U12(tt, M, N) -> s(plus(activate(N), activate(M))) U21(tt, M, N) -> U22(tt, activate(M), activate(N)) U22(tt, M, N) -> plus(x(activate(N), activate(M)), activate(N)) plus(N, 0) -> N plus(N, s(M)) -> U11(tt, M, N) x(N, 0) -> 0 x(N, s(M)) -> U21(tt, M, N) activate(X) -> X S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) Transformed relative TRS to weighted TRS ---------------------------------------- (2) Obligation: The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^2). The TRS R consists of the following rules: U11(tt, M, N) -> U12(tt, activate(M), activate(N)) [1] U12(tt, M, N) -> s(plus(activate(N), activate(M))) [1] U21(tt, M, N) -> U22(tt, activate(M), activate(N)) [1] U22(tt, M, N) -> plus(x(activate(N), activate(M)), activate(N)) [1] plus(N, 0) -> N [1] plus(N, s(M)) -> U11(tt, M, N) [1] x(N, 0) -> 0 [1] x(N, s(M)) -> U21(tt, M, N) [1] activate(X) -> X [1] Rewrite Strategy: INNERMOST ---------------------------------------- (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (4) Obligation: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: U11(tt, M, N) -> U12(tt, activate(M), activate(N)) [1] U12(tt, M, N) -> s(plus(activate(N), activate(M))) [1] U21(tt, M, N) -> U22(tt, activate(M), activate(N)) [1] U22(tt, M, N) -> plus(x(activate(N), activate(M)), activate(N)) [1] plus(N, 0) -> N [1] plus(N, s(M)) -> U11(tt, M, N) [1] x(N, 0) -> 0 [1] x(N, s(M)) -> U21(tt, M, N) [1]
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