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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313679
details
property
value
status
complete
benchmark
AAECC-ring.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n178.star.cs.uiowa.edu
space
AProVE_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.897 seconds
cpu usage
1098.98
user time
1074.7
system time
24.2759
max virtual memory
3.9233588E7
max residence set size
1.4867724E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
1098.01/291.61 WORST_CASE(Omega(n^1), ?) 1098.86/291.81 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 1098.86/291.81 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1098.86/291.81 1098.86/291.81 1098.86/291.81 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1098.86/291.81 1098.86/291.81 (0) CpxTRS 1098.86/291.81 (1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 1098.86/291.81 (2) CpxTRS 1098.86/291.81 (3) SlicingProof [LOWER BOUND(ID), 0 ms] 1098.86/291.81 (4) CpxTRS 1098.86/291.81 (5) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 1098.86/291.81 (6) typed CpxTrs 1098.86/291.81 (7) OrderProof [LOWER BOUND(ID), 0 ms] 1098.86/291.81 (8) typed CpxTrs 1098.86/291.81 (9) RewriteLemmaProof [LOWER BOUND(ID), 342 ms] 1098.86/291.81 (10) BEST 1098.86/291.81 (11) proven lower bound 1098.86/291.81 (12) LowerBoundPropagationProof [FINISHED, 0 ms] 1098.86/291.81 (13) BOUNDS(n^1, INF) 1098.86/291.81 (14) typed CpxTrs 1098.86/291.81 (15) RewriteLemmaProof [LOWER BOUND(ID), 82 ms] 1098.86/291.81 (16) typed CpxTrs 1098.86/291.81 (17) RewriteLemmaProof [LOWER BOUND(ID), 45 ms] 1098.86/291.81 (18) typed CpxTrs 1098.86/291.81 (19) RewriteLemmaProof [LOWER BOUND(ID), 54 ms] 1098.86/291.81 (20) typed CpxTrs 1098.86/291.81 (21) RewriteLemmaProof [LOWER BOUND(ID), 55 ms] 1098.86/291.81 (22) typed CpxTrs 1098.86/291.81 (23) RewriteLemmaProof [LOWER BOUND(ID), 2231 ms] 1098.86/291.81 (24) typed CpxTrs 1098.86/291.81 1098.86/291.81 1098.86/291.81 ---------------------------------------- 1098.86/291.81 1098.86/291.81 (0) 1098.86/291.81 Obligation: 1098.86/291.81 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1098.86/291.81 1098.86/291.81 1098.86/291.81 The TRS R consists of the following rules: 1098.86/291.81 1098.86/291.81 fstsplit(0, x) -> nil 1098.86/291.81 fstsplit(s(n), nil) -> nil 1098.86/291.81 fstsplit(s(n), cons(h, t)) -> cons(h, fstsplit(n, t)) 1098.86/291.81 sndsplit(0, x) -> x 1098.86/291.81 sndsplit(s(n), nil) -> nil 1098.86/291.81 sndsplit(s(n), cons(h, t)) -> sndsplit(n, t) 1098.86/291.81 empty(nil) -> true 1098.86/291.81 empty(cons(h, t)) -> false 1098.86/291.81 leq(0, m) -> true 1098.86/291.81 leq(s(n), 0) -> false 1098.86/291.81 leq(s(n), s(m)) -> leq(n, m) 1098.86/291.81 length(nil) -> 0 1098.86/291.81 length(cons(h, t)) -> s(length(t)) 1098.86/291.81 app(nil, x) -> x 1098.86/291.81 app(cons(h, t), x) -> cons(h, app(t, x)) 1098.86/291.81 map_f(pid, nil) -> nil 1098.86/291.81 map_f(pid, cons(h, t)) -> app(f(pid, h), map_f(pid, t)) 1098.86/291.81 head(cons(h, t)) -> h 1098.86/291.81 tail(cons(h, t)) -> t 1098.86/291.81 ring(st_1, in_2, st_2, in_3, st_3, m) -> if_1(st_1, in_2, st_2, in_3, st_3, m, empty(fstsplit(m, st_1))) 1098.86/291.81 if_1(st_1, in_2, st_2, in_3, st_3, m, false) -> ring(sndsplit(m, st_1), cons(fstsplit(m, st_1), in_2), st_2, in_3, st_3, m) 1098.86/291.81 ring(st_1, in_2, st_2, in_3, st_3, m) -> if_2(st_1, in_2, st_2, in_3, st_3, m, leq(m, length(st_2))) 1098.86/291.81 if_2(st_1, in_2, st_2, in_3, st_3, m, true) -> if_3(st_1, in_2, st_2, in_3, st_3, m, empty(fstsplit(m, st_2))) 1098.86/291.81 if_3(st_1, in_2, st_2, in_3, st_3, m, false) -> ring(st_1, in_2, sndsplit(m, st_2), cons(fstsplit(m, st_2), in_3), st_3, m) 1098.86/291.81 if_2(st_1, in_2, st_2, in_3, st_3, m, false) -> if_4(st_1, in_2, st_2, in_3, st_3, m, empty(fstsplit(m, app(map_f(two, head(in_2)), st_2)))) 1098.86/291.81 if_4(st_1, in_2, st_2, in_3, st_3, m, false) -> ring(st_1, tail(in_2), sndsplit(m, app(map_f(two, head(in_2)), st_2)), cons(fstsplit(m, app(map_f(two, head(in_2)), st_2)), in_3), st_3, m) 1098.86/291.81 ring(st_1, in_2, st_2, in_3, st_3, m) -> if_5(st_1, in_2, st_2, in_3, st_3, m, empty(map_f(two, head(in_2)))) 1098.86/291.81 if_5(st_1, in_2, st_2, in_3, st_3, m, true) -> ring(st_1, tail(in_2), st_2, in_3, st_3, m) 1098.86/291.81 ring(st_1, in_2, st_2, in_3, st_3, m) -> if_6(st_1, in_2, st_2, in_3, st_3, m, leq(m, length(st_3))) 1098.86/291.81 if_6(st_1, in_2, st_2, in_3, st_3, m, true) -> if_7(st_1, in_2, st_2, in_3, st_3, m, empty(fstsplit(m, st_3))) 1098.86/291.81 if_7(st_1, in_2, st_2, in_3, st_3, m, false) -> ring(st_1, in_2, st_2, in_3, sndsplit(m, st_3), m) 1098.86/291.81 if_6(st_1, in_2, st_2, in_3, st_3, m, false) -> if_8(st_1, in_2, st_2, in_3, st_3, m, empty(fstsplit(m, app(map_f(three, head(in_3)), st_3)))) 1098.86/291.81 if_8(st_1, in_2, st_2, in_3, st_3, m, false) -> ring(st_1, in_2, st_2, tail(in_3), sndsplit(m, app(map_f(three, head(in_3)), st_3)), m) 1098.86/291.81 ring(st_1, in_2, st_2, in_3, st_3, m) -> if_9(st_1, in_2, st_2, in_3, st_3, m, empty(map_f(three, head(in_3)))) 1098.86/291.81 if_9(st_1, in_2, st_2, in_3, st_3, m, true) -> ring(st_1, in_2, st_2, tail(in_3), st_3, m) 1098.86/291.81 1098.86/291.81 S is empty. 1098.86/291.81 Rewrite Strategy: INNERMOST 1098.86/291.81 ---------------------------------------- 1098.86/291.81 1098.86/291.81 (1) RenamingProof (BOTH BOUNDS(ID, ID)) 1098.86/291.81 Renamed function symbols to avoid clashes with predefined symbol. 1098.86/291.81 ---------------------------------------- 1098.86/291.81 1098.86/291.81 (2) 1098.86/291.81 Obligation: 1098.86/291.81 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1098.86/291.81 1098.86/291.81 1098.86/291.81 The TRS R consists of the following rules: 1098.86/291.81 1098.86/291.81 fstsplit(0', x) -> nil 1098.86/291.81 fstsplit(s(n), nil) -> nil 1098.86/291.81 fstsplit(s(n), cons(h, t)) -> cons(h, fstsplit(n, t)) 1098.86/291.81 sndsplit(0', x) -> x 1098.86/291.81 sndsplit(s(n), nil) -> nil 1098.86/291.81 sndsplit(s(n), cons(h, t)) -> sndsplit(n, t)
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return to Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40