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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313479
details
property
value
status
complete
benchmark
PEANO_nosorts_noand_GM.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n132.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.613 seconds
cpu usage
1118.9
user time
1105.85
system time
13.0463
max virtual memory
3.7255968E7
max residence set size
1.5133764E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^2), ?)
output
1118.46/291.46 WORST_CASE(Omega(n^2), ?) 1118.46/291.48 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 1118.46/291.48 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1118.46/291.48 1118.46/291.48 1118.46/291.48 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). 1118.46/291.48 1118.46/291.48 (0) CpxTRS 1118.46/291.48 (1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 1118.46/291.48 (2) CpxTRS 1118.46/291.48 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 8 ms] 1118.46/291.48 (4) typed CpxTrs 1118.46/291.48 (5) OrderProof [LOWER BOUND(ID), 0 ms] 1118.46/291.48 (6) typed CpxTrs 1118.46/291.48 (7) RewriteLemmaProof [LOWER BOUND(ID), 670 ms] 1118.46/291.48 (8) BEST 1118.46/291.48 (9) proven lower bound 1118.46/291.48 (10) LowerBoundPropagationProof [FINISHED, 0 ms] 1118.46/291.48 (11) BOUNDS(n^1, INF) 1118.46/291.48 (12) typed CpxTrs 1118.46/291.48 (13) RewriteLemmaProof [LOWER BOUND(ID), 137 ms] 1118.46/291.48 (14) BEST 1118.46/291.48 (15) proven lower bound 1118.46/291.48 (16) LowerBoundPropagationProof [FINISHED, 0 ms] 1118.46/291.48 (17) BOUNDS(n^2, INF) 1118.46/291.48 (18) typed CpxTrs 1118.46/291.48 (19) RewriteLemmaProof [LOWER BOUND(ID), 155 ms] 1118.46/291.48 (20) typed CpxTrs 1118.46/291.48 (21) RewriteLemmaProof [LOWER BOUND(ID), 141 ms] 1118.46/291.48 (22) typed CpxTrs 1118.46/291.48 (23) RewriteLemmaProof [LOWER BOUND(ID), 34 ms] 1118.46/291.48 (24) typed CpxTrs 1118.46/291.48 (25) RewriteLemmaProof [LOWER BOUND(ID), 95 ms] 1118.46/291.48 (26) typed CpxTrs 1118.46/291.48 (27) RewriteLemmaProof [LOWER BOUND(ID), 138 ms] 1118.46/291.48 (28) BOUNDS(1, INF) 1118.46/291.48 1118.46/291.48 1118.46/291.48 ---------------------------------------- 1118.46/291.48 1118.46/291.48 (0) 1118.46/291.48 Obligation: 1118.46/291.48 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). 1118.46/291.48 1118.46/291.48 1118.46/291.48 The TRS R consists of the following rules: 1118.46/291.48 1118.46/291.48 a__U11(tt, M, N) -> a__U12(tt, M, N) 1118.46/291.48 a__U12(tt, M, N) -> s(a__plus(mark(N), mark(M))) 1118.46/291.48 a__plus(N, 0) -> mark(N) 1118.46/291.48 a__plus(N, s(M)) -> a__U11(tt, M, N) 1118.46/291.48 mark(U11(X1, X2, X3)) -> a__U11(mark(X1), X2, X3) 1118.46/291.48 mark(U12(X1, X2, X3)) -> a__U12(mark(X1), X2, X3) 1118.46/291.48 mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)) 1118.46/291.48 mark(tt) -> tt 1118.46/291.48 mark(s(X)) -> s(mark(X)) 1118.46/291.48 mark(0) -> 0 1118.46/291.48 a__U11(X1, X2, X3) -> U11(X1, X2, X3) 1118.46/291.48 a__U12(X1, X2, X3) -> U12(X1, X2, X3) 1118.46/291.48 a__plus(X1, X2) -> plus(X1, X2) 1118.46/291.48 1118.46/291.48 S is empty. 1118.46/291.48 Rewrite Strategy: INNERMOST 1118.46/291.48 ---------------------------------------- 1118.46/291.48 1118.46/291.48 (1) RenamingProof (BOTH BOUNDS(ID, ID)) 1118.46/291.48 Renamed function symbols to avoid clashes with predefined symbol. 1118.46/291.48 ---------------------------------------- 1118.46/291.48 1118.46/291.48 (2) 1118.46/291.48 Obligation: 1118.46/291.48 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). 1118.46/291.48 1118.46/291.48 1118.46/291.48 The TRS R consists of the following rules: 1118.46/291.48 1118.46/291.48 a__U11(tt, M, N) -> a__U12(tt, M, N) 1118.46/291.48 a__U12(tt, M, N) -> s(a__plus(mark(N), mark(M))) 1118.46/291.48 a__plus(N, 0') -> mark(N) 1118.46/291.48 a__plus(N, s(M)) -> a__U11(tt, M, N) 1118.46/291.48 mark(U11(X1, X2, X3)) -> a__U11(mark(X1), X2, X3) 1118.46/291.48 mark(U12(X1, X2, X3)) -> a__U12(mark(X1), X2, X3) 1118.46/291.48 mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)) 1118.46/291.48 mark(tt) -> tt 1118.46/291.48 mark(s(X)) -> s(mark(X)) 1118.46/291.48 mark(0') -> 0' 1118.46/291.48 a__U11(X1, X2, X3) -> U11(X1, X2, X3) 1118.46/291.48 a__U12(X1, X2, X3) -> U12(X1, X2, X3) 1118.46/291.48 a__plus(X1, X2) -> plus(X1, X2) 1118.46/291.48 1118.46/291.48 S is empty. 1118.46/291.48 Rewrite Strategy: INNERMOST 1118.46/291.48 ---------------------------------------- 1118.46/291.48 1118.46/291.48 (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) 1118.46/291.48 Infered types. 1118.46/291.48 ---------------------------------------- 1118.46/291.48 1118.46/291.48 (4) 1118.46/291.48 Obligation:
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