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Runti Compl Inner Rewri 22807 pair #381904813
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
n078.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.743673086 seconds
cpu usage
1128.09311676
max memory
1.5334027264E10
stage attributes
key
value
output-size
22989
starexec-result
WORST_CASE(Omega(n^2), ?)
output
/export/starexec/sandbox2/solver/bin/starexec_run_complexity /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- WORST_CASE(Omega(n^2), ?) proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). (0) CpxTRS (1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxTRS (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (4) typed CpxTrs (5) OrderProof [LOWER BOUND(ID), 0 ms] (6) typed CpxTrs (7) RewriteLemmaProof [LOWER BOUND(ID), 329 ms] (8) BEST (9) proven lower bound (10) LowerBoundPropagationProof [FINISHED, 0 ms] (11) BOUNDS(n^1, INF) (12) typed CpxTrs (13) RewriteLemmaProof [LOWER BOUND(ID), 133 ms] (14) BEST (15) proven lower bound (16) LowerBoundPropagationProof [FINISHED, 0 ms] (17) BOUNDS(n^2, INF) (18) typed CpxTrs (19) RewriteLemmaProof [LOWER BOUND(ID), 37 ms] (20) typed CpxTrs ---------------------------------------- (0) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). The TRS R consists of the following rules: a__fib(N) -> a__sel(mark(N), a__fib1(s(0), s(0))) a__fib1(X, Y) -> cons(mark(X), fib1(Y, add(X, Y))) a__add(0, X) -> mark(X) a__add(s(X), Y) -> s(a__add(mark(X), mark(Y))) a__sel(0, cons(X, XS)) -> mark(X) a__sel(s(N), cons(X, XS)) -> a__sel(mark(N), mark(XS)) mark(fib(X)) -> a__fib(mark(X)) mark(sel(X1, X2)) -> a__sel(mark(X1), mark(X2)) mark(fib1(X1, X2)) -> a__fib1(mark(X1), mark(X2)) mark(add(X1, X2)) -> a__add(mark(X1), mark(X2)) mark(s(X)) -> s(mark(X)) mark(0) -> 0 mark(cons(X1, X2)) -> cons(mark(X1), X2) a__fib(X) -> fib(X) a__sel(X1, X2) -> sel(X1, X2) a__fib1(X1, X2) -> fib1(X1, X2) a__add(X1, X2) -> add(X1, X2) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (1) RenamingProof (BOTH BOUNDS(ID, ID)) Renamed function symbols to avoid clashes with predefined symbol. ---------------------------------------- (2) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). The TRS R consists of the following rules: a__fib(N) -> a__sel(mark(N), a__fib1(s(0'), s(0'))) a__fib1(X, Y) -> cons(mark(X), fib1(Y, add(X, Y))) a__add(0', X) -> mark(X) a__add(s(X), Y) -> s(a__add(mark(X), mark(Y))) a__sel(0', cons(X, XS)) -> mark(X) a__sel(s(N), cons(X, XS)) -> a__sel(mark(N), mark(XS)) mark(fib(X)) -> a__fib(mark(X)) mark(sel(X1, X2)) -> a__sel(mark(X1), mark(X2)) mark(fib1(X1, X2)) -> a__fib1(mark(X1), mark(X2)) mark(add(X1, X2)) -> a__add(mark(X1), mark(X2)) mark(s(X)) -> s(mark(X)) mark(0') -> 0' mark(cons(X1, X2)) -> cons(mark(X1), X2) a__fib(X) -> fib(X) a__sel(X1, X2) -> sel(X1, X2) a__fib1(X1, X2) -> fib1(X1, X2) a__add(X1, X2) -> add(X1, X2) S is empty. Rewrite Strategy: INNERMOST ----------------------------------------
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