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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313472
details
property
value
status
complete
benchmark
PEANO_nosorts_GM.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n181.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
293.819 seconds
cpu usage
1131.88
user time
1120.56
system time
11.3216
max virtual memory
3.7246672E7
max residence set size
1.4997404E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^2), ?)
output
1122.80/291.53 WORST_CASE(Omega(n^2), ?) 1131.45/293.71 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 1131.45/293.71 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1131.45/293.71 1131.45/293.71 1131.45/293.71 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). 1131.45/293.71 1131.45/293.71 (0) CpxTRS 1131.45/293.71 (1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 1131.45/293.71 (2) CpxTRS 1131.45/293.71 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 1131.45/293.71 (4) typed CpxTrs 1131.45/293.71 (5) OrderProof [LOWER BOUND(ID), 0 ms] 1131.45/293.71 (6) typed CpxTrs 1131.45/293.71 (7) RewriteLemmaProof [LOWER BOUND(ID), 504 ms] 1131.45/293.71 (8) BEST 1131.45/293.71 (9) proven lower bound 1131.45/293.71 (10) LowerBoundPropagationProof [FINISHED, 0 ms] 1131.45/293.71 (11) BOUNDS(n^1, INF) 1131.45/293.71 (12) typed CpxTrs 1131.45/293.71 (13) RewriteLemmaProof [LOWER BOUND(ID), 676 ms] 1131.45/293.71 (14) BEST 1131.45/293.71 (15) proven lower bound 1131.45/293.71 (16) LowerBoundPropagationProof [FINISHED, 0 ms] 1131.45/293.71 (17) BOUNDS(n^2, INF) 1131.45/293.71 (18) typed CpxTrs 1131.45/293.71 (19) RewriteLemmaProof [LOWER BOUND(ID), 21 ms] 1131.45/293.71 (20) BOUNDS(1, INF) 1131.45/293.71 1131.45/293.71 1131.45/293.71 ---------------------------------------- 1131.45/293.71 1131.45/293.71 (0) 1131.45/293.71 Obligation: 1131.45/293.71 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). 1131.45/293.71 1131.45/293.71 1131.45/293.71 The TRS R consists of the following rules: 1131.45/293.71 1131.45/293.71 a__and(tt, X) -> mark(X) 1131.45/293.71 a__plus(N, 0) -> mark(N) 1131.45/293.71 a__plus(N, s(M)) -> s(a__plus(mark(N), mark(M))) 1131.45/293.71 mark(and(X1, X2)) -> a__and(mark(X1), X2) 1131.45/293.71 mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)) 1131.45/293.71 mark(tt) -> tt 1131.45/293.71 mark(0) -> 0 1131.45/293.71 mark(s(X)) -> s(mark(X)) 1131.45/293.71 a__and(X1, X2) -> and(X1, X2) 1131.45/293.71 a__plus(X1, X2) -> plus(X1, X2) 1131.45/293.71 1131.45/293.71 S is empty. 1131.45/293.71 Rewrite Strategy: INNERMOST 1131.45/293.71 ---------------------------------------- 1131.45/293.71 1131.45/293.71 (1) RenamingProof (BOTH BOUNDS(ID, ID)) 1131.45/293.71 Renamed function symbols to avoid clashes with predefined symbol. 1131.45/293.71 ---------------------------------------- 1131.45/293.71 1131.45/293.71 (2) 1131.45/293.71 Obligation: 1131.45/293.71 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). 1131.45/293.71 1131.45/293.71 1131.45/293.71 The TRS R consists of the following rules: 1131.45/293.71 1131.45/293.71 a__and(tt, X) -> mark(X) 1131.45/293.71 a__plus(N, 0') -> mark(N) 1131.45/293.71 a__plus(N, s(M)) -> s(a__plus(mark(N), mark(M))) 1131.45/293.71 mark(and(X1, X2)) -> a__and(mark(X1), X2) 1131.45/293.71 mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)) 1131.45/293.71 mark(tt) -> tt 1131.45/293.71 mark(0') -> 0' 1131.45/293.71 mark(s(X)) -> s(mark(X)) 1131.45/293.71 a__and(X1, X2) -> and(X1, X2) 1131.45/293.71 a__plus(X1, X2) -> plus(X1, X2) 1131.45/293.71 1131.45/293.71 S is empty. 1131.45/293.71 Rewrite Strategy: INNERMOST 1131.45/293.71 ---------------------------------------- 1131.45/293.71 1131.45/293.71 (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) 1131.45/293.71 Infered types. 1131.45/293.71 ---------------------------------------- 1131.45/293.71 1131.45/293.71 (4) 1131.45/293.71 Obligation: 1131.45/293.71 Innermost TRS: 1131.45/293.71 Rules: 1131.45/293.71 a__and(tt, X) -> mark(X) 1131.45/293.71 a__plus(N, 0') -> mark(N) 1131.45/293.71 a__plus(N, s(M)) -> s(a__plus(mark(N), mark(M))) 1131.45/293.71 mark(and(X1, X2)) -> a__and(mark(X1), X2) 1131.45/293.71 mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)) 1131.45/293.71 mark(tt) -> tt 1131.45/293.71 mark(0') -> 0' 1131.45/293.71 mark(s(X)) -> s(mark(X)) 1131.45/293.71 a__and(X1, X2) -> and(X1, X2) 1131.45/293.71 a__plus(X1, X2) -> plus(X1, X2) 1131.45/293.71 1131.45/293.71 Types:
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