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Runti Compl Inner Rewri 22807 pair #381904220
details
property
value
status
complete
benchmark
thiemann21.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n056.star.cs.uiowa.edu
space
AProVE_07
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.527001143 seconds
cpu usage
1136.17965434
max memory
1.541832704E10
stage attributes
key
value
output-size
29157
starexec-result
WORST_CASE(Omega(n^1), ?)
output
/export/starexec/sandbox/solver/bin/starexec_run_complexity /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- WORST_CASE(Omega(n^1), ?) proof of /export/starexec/sandbox/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). (0) CpxTRS (1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxTRS (3) SlicingProof [LOWER BOUND(ID), 0 ms] (4) CpxTRS (5) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (6) typed CpxTrs (7) OrderProof [LOWER BOUND(ID), 0 ms] (8) typed CpxTrs (9) RewriteLemmaProof [LOWER BOUND(ID), 334 ms] (10) BEST (11) proven lower bound (12) LowerBoundPropagationProof [FINISHED, 0 ms] (13) BOUNDS(n^1, INF) (14) typed CpxTrs (15) RewriteLemmaProof [LOWER BOUND(ID), 84 ms] (16) typed CpxTrs (17) RewriteLemmaProof [LOWER BOUND(ID), 33 ms] (18) typed CpxTrs ---------------------------------------- (0) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). The TRS R consists of the following rules: eq(0, 0) -> true eq(0, s(y)) -> false eq(s(x), 0) -> false eq(s(x), s(y)) -> eq(x, y) lt(0, s(y)) -> true lt(x, 0) -> false lt(s(x), s(y)) -> lt(x, y) bin2s(nil) -> 0 bin2s(cons(x, xs)) -> bin2ss(x, xs) bin2ss(x, nil) -> x bin2ss(x, cons(0, xs)) -> bin2ss(double(x), xs) bin2ss(x, cons(1, xs)) -> bin2ss(s(double(x)), xs) half(0) -> 0 half(s(0)) -> 0 half(s(s(x))) -> s(half(x)) log(0) -> 0 log(s(0)) -> 0 log(s(s(x))) -> s(log(half(s(s(x))))) more(nil) -> nil more(cons(xs, ys)) -> cons(cons(0, xs), cons(cons(1, xs), cons(xs, ys))) s2bin(x) -> s2bin1(x, 0, cons(nil, nil)) s2bin1(x, y, lists) -> if1(lt(y, log(x)), x, y, lists) if1(true, x, y, lists) -> s2bin1(x, s(y), more(lists)) if1(false, x, y, lists) -> s2bin2(x, lists) s2bin2(x, nil) -> bug_list_not s2bin2(x, cons(xs, ys)) -> if2(eq(x, bin2s(xs)), x, xs, ys) if2(true, x, xs, ys) -> xs if2(false, x, xs, ys) -> s2bin2(x, ys) 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^1, INF). The TRS R consists of the following rules: eq(0', 0') -> true eq(0', s(y)) -> false eq(s(x), 0') -> false eq(s(x), s(y)) -> eq(x, y) lt(0', s(y)) -> true lt(x, 0') -> false lt(s(x), s(y)) -> lt(x, y) bin2s(nil) -> 0' bin2s(cons(x, xs)) -> bin2ss(x, xs) bin2ss(x, nil) -> x bin2ss(x, cons(0', xs)) -> bin2ss(double(x), xs) bin2ss(x, cons(1', xs)) -> bin2ss(s(double(x)), xs) half(0') -> 0'
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