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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433308201
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
n168.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
293.06 seconds
cpu usage
1125.19
user time
1113.27
system time
11.9153
max virtual memory
3.724416E7
max residence set size
1.4782296E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^2), ?)
output
1119.12/291.47 WORST_CASE(Omega(n^2), ?) 1125.01/292.98 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 1125.01/292.98 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1125.01/292.98 1125.01/292.98 1125.01/292.98 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). 1125.01/292.98 1125.01/292.98 (0) CpxTRS 1125.01/292.98 (1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 1125.01/292.98 (2) CpxTRS 1125.01/292.98 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 1125.01/292.98 (4) typed CpxTrs 1125.01/292.98 (5) OrderProof [LOWER BOUND(ID), 0 ms] 1125.01/292.98 (6) typed CpxTrs 1125.01/292.98 (7) RewriteLemmaProof [LOWER BOUND(ID), 532 ms] 1125.01/292.98 (8) BEST 1125.01/292.98 (9) proven lower bound 1125.01/292.98 (10) LowerBoundPropagationProof [FINISHED, 0 ms] 1125.01/292.98 (11) BOUNDS(n^1, INF) 1125.01/292.98 (12) typed CpxTrs 1125.01/292.98 (13) RewriteLemmaProof [LOWER BOUND(ID), 756 ms] 1125.01/292.98 (14) BEST 1125.01/292.98 (15) proven lower bound 1125.01/292.98 (16) LowerBoundPropagationProof [FINISHED, 0 ms] 1125.01/292.98 (17) BOUNDS(n^2, INF) 1125.01/292.98 (18) typed CpxTrs 1125.01/292.98 (19) RewriteLemmaProof [LOWER BOUND(ID), 42 ms] 1125.01/292.98 (20) BOUNDS(1, INF) 1125.01/292.98 1125.01/292.98 1125.01/292.98 ---------------------------------------- 1125.01/292.98 1125.01/292.98 (0) 1125.01/292.98 Obligation: 1125.01/292.98 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). 1125.01/292.98 1125.01/292.98 1125.01/292.98 The TRS R consists of the following rules: 1125.01/292.98 1125.01/292.98 a__and(tt, X) -> mark(X) 1125.01/292.98 a__plus(N, 0) -> mark(N) 1125.01/292.98 a__plus(N, s(M)) -> s(a__plus(mark(N), mark(M))) 1125.01/292.98 mark(and(X1, X2)) -> a__and(mark(X1), X2) 1125.01/292.98 mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)) 1125.01/292.98 mark(tt) -> tt 1125.01/292.98 mark(0) -> 0 1125.01/292.98 mark(s(X)) -> s(mark(X)) 1125.01/292.98 a__and(X1, X2) -> and(X1, X2) 1125.01/292.98 a__plus(X1, X2) -> plus(X1, X2) 1125.01/292.98 1125.01/292.98 S is empty. 1125.01/292.98 Rewrite Strategy: FULL 1125.01/292.98 ---------------------------------------- 1125.01/292.98 1125.01/292.98 (1) RenamingProof (BOTH BOUNDS(ID, ID)) 1125.01/292.98 Renamed function symbols to avoid clashes with predefined symbol. 1125.01/292.98 ---------------------------------------- 1125.01/292.98 1125.01/292.98 (2) 1125.01/292.98 Obligation: 1125.01/292.98 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). 1125.01/292.98 1125.01/292.98 1125.01/292.98 The TRS R consists of the following rules: 1125.01/292.98 1125.01/292.98 a__and(tt, X) -> mark(X) 1125.01/292.98 a__plus(N, 0') -> mark(N) 1125.01/292.98 a__plus(N, s(M)) -> s(a__plus(mark(N), mark(M))) 1125.01/292.98 mark(and(X1, X2)) -> a__and(mark(X1), X2) 1125.01/292.98 mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)) 1125.01/292.98 mark(tt) -> tt 1125.01/292.98 mark(0') -> 0' 1125.01/292.98 mark(s(X)) -> s(mark(X)) 1125.01/292.98 a__and(X1, X2) -> and(X1, X2) 1125.01/292.98 a__plus(X1, X2) -> plus(X1, X2) 1125.01/292.98 1125.01/292.98 S is empty. 1125.01/292.98 Rewrite Strategy: FULL 1125.01/292.98 ---------------------------------------- 1125.01/292.98 1125.01/292.98 (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) 1125.01/292.98 Infered types. 1125.01/292.98 ---------------------------------------- 1125.01/292.98 1125.01/292.98 (4) 1125.01/292.98 Obligation: 1125.01/292.98 TRS: 1125.01/292.98 Rules: 1125.01/292.98 a__and(tt, X) -> mark(X) 1125.01/292.98 a__plus(N, 0') -> mark(N) 1125.01/292.98 a__plus(N, s(M)) -> s(a__plus(mark(N), mark(M))) 1125.01/292.98 mark(and(X1, X2)) -> a__and(mark(X1), X2) 1125.01/292.98 mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)) 1125.01/292.98 mark(tt) -> tt 1125.01/292.98 mark(0') -> 0' 1125.01/292.98 mark(s(X)) -> s(mark(X)) 1125.01/292.98 a__and(X1, X2) -> and(X1, X2) 1125.01/292.98 a__plus(X1, X2) -> plus(X1, X2) 1125.01/292.98 1125.01/292.98 Types:
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