Spaces
Explore
Communities
Statistics
Reports
Cluster
Status
Help
Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313415
details
property
value
status
complete
benchmark
Ex8_BLR02_GM.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n139.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.574 seconds
cpu usage
1119.6
user time
1108.54
system time
11.0608
max virtual memory
5.5628284E7
max residence set size
1.4895704E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^2), ?)
output
1119.38/291.50 WORST_CASE(Omega(n^2), ?) 1119.38/291.51 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 1119.38/291.51 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1119.38/291.51 1119.38/291.51 1119.38/291.51 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). 1119.38/291.51 1119.38/291.51 (0) CpxTRS 1119.38/291.51 (1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 1119.38/291.51 (2) CpxTRS 1119.38/291.51 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 1119.38/291.51 (4) typed CpxTrs 1119.38/291.51 (5) OrderProof [LOWER BOUND(ID), 0 ms] 1119.38/291.51 (6) typed CpxTrs 1119.38/291.51 (7) RewriteLemmaProof [LOWER BOUND(ID), 274 ms] 1119.38/291.51 (8) BEST 1119.38/291.51 (9) proven lower bound 1119.38/291.51 (10) LowerBoundPropagationProof [FINISHED, 0 ms] 1119.38/291.51 (11) BOUNDS(n^1, INF) 1119.38/291.51 (12) typed CpxTrs 1119.38/291.51 (13) RewriteLemmaProof [LOWER BOUND(ID), 98 ms] 1119.38/291.51 (14) BEST 1119.38/291.51 (15) proven lower bound 1119.38/291.51 (16) LowerBoundPropagationProof [FINISHED, 0 ms] 1119.38/291.51 (17) BOUNDS(n^2, INF) 1119.38/291.51 (18) typed CpxTrs 1119.38/291.51 (19) RewriteLemmaProof [LOWER BOUND(ID), 58 ms] 1119.38/291.51 (20) typed CpxTrs 1119.38/291.51 1119.38/291.51 1119.38/291.51 ---------------------------------------- 1119.38/291.51 1119.38/291.51 (0) 1119.38/291.51 Obligation: 1119.38/291.51 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). 1119.38/291.51 1119.38/291.51 1119.38/291.51 The TRS R consists of the following rules: 1119.38/291.51 1119.38/291.51 a__fib(N) -> a__sel(mark(N), a__fib1(s(0), s(0))) 1119.38/291.51 a__fib1(X, Y) -> cons(mark(X), fib1(Y, add(X, Y))) 1119.38/291.51 a__add(0, X) -> mark(X) 1119.38/291.51 a__add(s(X), Y) -> s(a__add(mark(X), mark(Y))) 1119.38/291.51 a__sel(0, cons(X, XS)) -> mark(X) 1119.38/291.51 a__sel(s(N), cons(X, XS)) -> a__sel(mark(N), mark(XS)) 1119.38/291.51 mark(fib(X)) -> a__fib(mark(X)) 1119.38/291.51 mark(sel(X1, X2)) -> a__sel(mark(X1), mark(X2)) 1119.38/291.51 mark(fib1(X1, X2)) -> a__fib1(mark(X1), mark(X2)) 1119.38/291.51 mark(add(X1, X2)) -> a__add(mark(X1), mark(X2)) 1119.38/291.51 mark(s(X)) -> s(mark(X)) 1119.38/291.51 mark(0) -> 0 1119.38/291.51 mark(cons(X1, X2)) -> cons(mark(X1), X2) 1119.38/291.51 a__fib(X) -> fib(X) 1119.38/291.51 a__sel(X1, X2) -> sel(X1, X2) 1119.38/291.51 a__fib1(X1, X2) -> fib1(X1, X2) 1119.38/291.51 a__add(X1, X2) -> add(X1, X2) 1119.38/291.51 1119.38/291.51 S is empty. 1119.38/291.51 Rewrite Strategy: INNERMOST 1119.38/291.51 ---------------------------------------- 1119.38/291.51 1119.38/291.51 (1) RenamingProof (BOTH BOUNDS(ID, ID)) 1119.38/291.51 Renamed function symbols to avoid clashes with predefined symbol. 1119.38/291.51 ---------------------------------------- 1119.38/291.51 1119.38/291.51 (2) 1119.38/291.51 Obligation: 1119.38/291.51 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). 1119.38/291.51 1119.38/291.51 1119.38/291.51 The TRS R consists of the following rules: 1119.38/291.51 1119.38/291.51 a__fib(N) -> a__sel(mark(N), a__fib1(s(0'), s(0'))) 1119.38/291.51 a__fib1(X, Y) -> cons(mark(X), fib1(Y, add(X, Y))) 1119.38/291.51 a__add(0', X) -> mark(X) 1119.38/291.51 a__add(s(X), Y) -> s(a__add(mark(X), mark(Y))) 1119.38/291.51 a__sel(0', cons(X, XS)) -> mark(X) 1119.38/291.51 a__sel(s(N), cons(X, XS)) -> a__sel(mark(N), mark(XS)) 1119.38/291.51 mark(fib(X)) -> a__fib(mark(X)) 1119.38/291.51 mark(sel(X1, X2)) -> a__sel(mark(X1), mark(X2)) 1119.38/291.51 mark(fib1(X1, X2)) -> a__fib1(mark(X1), mark(X2)) 1119.38/291.51 mark(add(X1, X2)) -> a__add(mark(X1), mark(X2)) 1119.38/291.51 mark(s(X)) -> s(mark(X)) 1119.38/291.51 mark(0') -> 0' 1119.38/291.51 mark(cons(X1, X2)) -> cons(mark(X1), X2) 1119.38/291.51 a__fib(X) -> fib(X) 1119.38/291.51 a__sel(X1, X2) -> sel(X1, X2) 1119.38/291.51 a__fib1(X1, X2) -> fib1(X1, X2) 1119.38/291.51 a__add(X1, X2) -> add(X1, X2) 1119.38/291.51 1119.38/291.51 S is empty. 1119.38/291.51 Rewrite Strategy: INNERMOST 1119.38/291.51 ---------------------------------------- 1119.38/291.51 1119.38/291.51 (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) 1119.38/291.51 Infered types. 1119.38/291.51 ---------------------------------------- 1119.38/291.51 1119.38/291.51 (4) 1119.38/291.51 Obligation:
popout
output may be truncated. 'popout' for the full output.
job log
popout
actions
all output
return to Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40
