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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433308213
details
property
value
status
complete
benchmark
ExIntrod_GM01_GM.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n123.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.65 seconds
cpu usage
1081.8
user time
1067.71
system time
14.0904
max virtual memory
3.730892E7
max residence set size
1.493296E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
1081.63/291.56 WORST_CASE(Omega(n^1), ?) 1081.63/291.56 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 1081.63/291.56 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1081.63/291.56 1081.63/291.56 1081.63/291.56 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1081.63/291.56 1081.63/291.56 (0) CpxTRS 1081.63/291.56 (1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 1081.63/291.56 (2) CpxTRS 1081.63/291.56 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 1081.63/291.56 (4) typed CpxTrs 1081.63/291.56 (5) OrderProof [LOWER BOUND(ID), 4 ms] 1081.63/291.56 (6) typed CpxTrs 1081.63/291.56 (7) RewriteLemmaProof [LOWER BOUND(ID), 550 ms] 1081.63/291.56 (8) BEST 1081.63/291.56 (9) proven lower bound 1081.63/291.56 (10) LowerBoundPropagationProof [FINISHED, 0 ms] 1081.63/291.56 (11) BOUNDS(n^1, INF) 1081.63/291.56 (12) typed CpxTrs 1081.63/291.56 1081.63/291.56 1081.63/291.56 ---------------------------------------- 1081.63/291.56 1081.63/291.56 (0) 1081.63/291.56 Obligation: 1081.63/291.56 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1081.63/291.56 1081.63/291.56 1081.63/291.56 The TRS R consists of the following rules: 1081.63/291.56 1081.63/291.56 a__incr(nil) -> nil 1081.63/291.56 a__incr(cons(X, L)) -> cons(s(mark(X)), incr(L)) 1081.63/291.56 a__adx(nil) -> nil 1081.63/291.56 a__adx(cons(X, L)) -> a__incr(cons(mark(X), adx(L))) 1081.63/291.56 a__nats -> a__adx(a__zeros) 1081.63/291.56 a__zeros -> cons(0, zeros) 1081.63/291.57 a__head(cons(X, L)) -> mark(X) 1081.63/291.57 a__tail(cons(X, L)) -> mark(L) 1081.63/291.57 mark(incr(X)) -> a__incr(mark(X)) 1081.63/291.57 mark(adx(X)) -> a__adx(mark(X)) 1081.63/291.57 mark(nats) -> a__nats 1081.63/291.57 mark(zeros) -> a__zeros 1081.63/291.57 mark(head(X)) -> a__head(mark(X)) 1081.63/291.57 mark(tail(X)) -> a__tail(mark(X)) 1081.63/291.57 mark(nil) -> nil 1081.63/291.57 mark(cons(X1, X2)) -> cons(mark(X1), X2) 1081.63/291.57 mark(s(X)) -> s(mark(X)) 1081.63/291.57 mark(0) -> 0 1081.63/291.57 a__incr(X) -> incr(X) 1081.63/291.57 a__adx(X) -> adx(X) 1081.63/291.57 a__nats -> nats 1081.63/291.57 a__zeros -> zeros 1081.63/291.57 a__head(X) -> head(X) 1081.63/291.57 a__tail(X) -> tail(X) 1081.63/291.57 1081.63/291.57 S is empty. 1081.63/291.57 Rewrite Strategy: FULL 1081.63/291.57 ---------------------------------------- 1081.63/291.57 1081.63/291.57 (1) RenamingProof (BOTH BOUNDS(ID, ID)) 1081.63/291.57 Renamed function symbols to avoid clashes with predefined symbol. 1081.63/291.57 ---------------------------------------- 1081.63/291.57 1081.63/291.57 (2) 1081.63/291.57 Obligation: 1081.63/291.57 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1081.63/291.57 1081.63/291.57 1081.63/291.57 The TRS R consists of the following rules: 1081.63/291.57 1081.63/291.57 a__incr(nil) -> nil 1081.63/291.57 a__incr(cons(X, L)) -> cons(s(mark(X)), incr(L)) 1081.63/291.57 a__adx(nil) -> nil 1081.63/291.57 a__adx(cons(X, L)) -> a__incr(cons(mark(X), adx(L))) 1081.63/291.57 a__nats -> a__adx(a__zeros) 1081.63/291.57 a__zeros -> cons(0', zeros) 1081.63/291.57 a__head(cons(X, L)) -> mark(X) 1081.63/291.57 a__tail(cons(X, L)) -> mark(L) 1081.63/291.57 mark(incr(X)) -> a__incr(mark(X)) 1081.63/291.57 mark(adx(X)) -> a__adx(mark(X)) 1081.63/291.57 mark(nats) -> a__nats 1081.63/291.57 mark(zeros) -> a__zeros 1081.63/291.57 mark(head(X)) -> a__head(mark(X)) 1081.63/291.57 mark(tail(X)) -> a__tail(mark(X)) 1081.63/291.57 mark(nil) -> nil 1081.63/291.57 mark(cons(X1, X2)) -> cons(mark(X1), X2) 1081.63/291.57 mark(s(X)) -> s(mark(X)) 1081.63/291.57 mark(0') -> 0' 1081.63/291.57 a__incr(X) -> incr(X) 1081.63/291.57 a__adx(X) -> adx(X) 1081.63/291.57 a__nats -> nats 1081.63/291.57 a__zeros -> zeros 1081.63/291.57 a__head(X) -> head(X) 1081.63/291.57 a__tail(X) -> tail(X) 1081.63/291.57 1081.63/291.57 S is empty. 1081.63/291.57 Rewrite Strategy: FULL 1081.63/291.57 ---------------------------------------- 1081.63/291.57
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