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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313697
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
n087.star.cs.uiowa.edu
space
AProVE_07
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
294.004 seconds
cpu usage
1137.31
user time
1123.19
system time
14.1154
max virtual memory
3.805482E7
max residence set size
1.491644E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
1127.48/291.52 WORST_CASE(Omega(n^1), ?) 1136.85/293.92 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 1136.85/293.92 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1136.85/293.92 1136.85/293.92 1136.85/293.92 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1136.85/293.92 1136.85/293.92 (0) CpxTRS 1136.85/293.92 (1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 1136.85/293.92 (2) CpxTRS 1136.85/293.92 (3) SlicingProof [LOWER BOUND(ID), 0 ms] 1136.85/293.92 (4) CpxTRS 1136.85/293.92 (5) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 1136.85/293.92 (6) typed CpxTrs 1136.85/293.92 (7) OrderProof [LOWER BOUND(ID), 0 ms] 1136.85/293.92 (8) typed CpxTrs 1136.85/293.92 (9) RewriteLemmaProof [LOWER BOUND(ID), 333 ms] 1136.85/293.92 (10) BEST 1136.85/293.92 (11) proven lower bound 1136.85/293.92 (12) LowerBoundPropagationProof [FINISHED, 0 ms] 1136.85/293.92 (13) BOUNDS(n^1, INF) 1136.85/293.92 (14) typed CpxTrs 1136.85/293.92 (15) RewriteLemmaProof [LOWER BOUND(ID), 41 ms] 1136.85/293.92 (16) typed CpxTrs 1136.85/293.92 (17) RewriteLemmaProof [LOWER BOUND(ID), 53 ms] 1136.85/293.92 (18) typed CpxTrs 1136.85/293.92 1136.85/293.92 1136.85/293.92 ---------------------------------------- 1136.85/293.92 1136.85/293.92 (0) 1136.85/293.92 Obligation: 1136.85/293.92 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1136.85/293.92 1136.85/293.92 1136.85/293.92 The TRS R consists of the following rules: 1136.85/293.92 1136.85/293.92 eq(0, 0) -> true 1136.85/293.92 eq(0, s(y)) -> false 1136.85/293.92 eq(s(x), 0) -> false 1136.85/293.92 eq(s(x), s(y)) -> eq(x, y) 1136.85/293.92 lt(0, s(y)) -> true 1136.85/293.92 lt(x, 0) -> false 1136.85/293.92 lt(s(x), s(y)) -> lt(x, y) 1136.85/293.92 bin2s(nil) -> 0 1136.85/293.92 bin2s(cons(x, xs)) -> bin2ss(x, xs) 1136.85/293.92 bin2ss(x, nil) -> x 1136.85/293.92 bin2ss(x, cons(0, xs)) -> bin2ss(double(x), xs) 1136.85/293.92 bin2ss(x, cons(1, xs)) -> bin2ss(s(double(x)), xs) 1136.85/293.92 half(0) -> 0 1136.85/293.92 half(s(0)) -> 0 1136.85/293.92 half(s(s(x))) -> s(half(x)) 1136.85/293.92 log(0) -> 0 1136.85/293.92 log(s(0)) -> 0 1136.85/293.92 log(s(s(x))) -> s(log(half(s(s(x))))) 1136.85/293.92 more(nil) -> nil 1136.85/293.92 more(cons(xs, ys)) -> cons(cons(0, xs), cons(cons(1, xs), cons(xs, ys))) 1136.85/293.92 s2bin(x) -> s2bin1(x, 0, cons(nil, nil)) 1136.85/293.92 s2bin1(x, y, lists) -> if1(lt(y, log(x)), x, y, lists) 1136.85/293.92 if1(true, x, y, lists) -> s2bin1(x, s(y), more(lists)) 1136.85/293.92 if1(false, x, y, lists) -> s2bin2(x, lists) 1136.85/293.92 s2bin2(x, nil) -> bug_list_not 1136.85/293.92 s2bin2(x, cons(xs, ys)) -> if2(eq(x, bin2s(xs)), x, xs, ys) 1136.85/293.92 if2(true, x, xs, ys) -> xs 1136.85/293.92 if2(false, x, xs, ys) -> s2bin2(x, ys) 1136.85/293.92 1136.85/293.92 S is empty. 1136.85/293.92 Rewrite Strategy: INNERMOST 1136.85/293.92 ---------------------------------------- 1136.85/293.92 1136.85/293.92 (1) RenamingProof (BOTH BOUNDS(ID, ID)) 1136.85/293.92 Renamed function symbols to avoid clashes with predefined symbol. 1136.85/293.92 ---------------------------------------- 1136.85/293.92 1136.85/293.92 (2) 1136.85/293.92 Obligation: 1136.85/293.92 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1136.85/293.92 1136.85/293.92 1136.85/293.92 The TRS R consists of the following rules: 1136.85/293.92 1136.85/293.92 eq(0', 0') -> true 1136.85/293.92 eq(0', s(y)) -> false 1136.85/293.92 eq(s(x), 0') -> false 1136.85/293.92 eq(s(x), s(y)) -> eq(x, y) 1136.85/293.92 lt(0', s(y)) -> true 1136.85/293.92 lt(x, 0') -> false 1136.85/293.92 lt(s(x), s(y)) -> lt(x, y) 1136.85/293.92 bin2s(nil) -> 0' 1136.85/293.92 bin2s(cons(x, xs)) -> bin2ss(x, xs) 1136.85/293.92 bin2ss(x, nil) -> x 1136.85/293.92 bin2ss(x, cons(0', xs)) -> bin2ss(double(x), xs) 1136.85/293.92 bin2ss(x, cons(1', xs)) -> bin2ss(s(double(x)), xs) 1136.85/293.92 half(0') -> 0' 1136.85/293.92 half(s(0')) -> 0' 1136.85/293.92 half(s(s(x))) -> s(half(x)) 1136.85/293.92 log(0') -> 0' 1136.85/293.92 log(s(0')) -> 0' 1136.85/293.92 log(s(s(x))) -> s(log(half(s(s(x))))) 1136.85/293.92 more(nil) -> nil
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