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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307738
details
property
value
status
complete
benchmark
thiemann14.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n174.star.cs.uiowa.edu
space
AProVE_07
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.561 seconds
cpu usage
321.104
user time
318.883
system time
2.22083
max virtual memory
1.8281276E7
max residence set size
5547024.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^2), ?)
output
320.93/291.50 WORST_CASE(Omega(n^2), ?) 320.93/291.51 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 320.93/291.51 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 320.93/291.51 320.93/291.51 320.93/291.51 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). 320.93/291.51 320.93/291.51 (0) CpxTRS 320.93/291.51 (1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 320.93/291.51 (2) CpxTRS 320.93/291.51 (3) SlicingProof [LOWER BOUND(ID), 0 ms] 320.93/291.51 (4) CpxTRS 320.93/291.51 (5) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 320.93/291.51 (6) typed CpxTrs 320.93/291.51 (7) OrderProof [LOWER BOUND(ID), 0 ms] 320.93/291.51 (8) typed CpxTrs 320.93/291.51 (9) RewriteLemmaProof [LOWER BOUND(ID), 257 ms] 320.93/291.51 (10) BEST 320.93/291.51 (11) proven lower bound 320.93/291.51 (12) LowerBoundPropagationProof [FINISHED, 0 ms] 320.93/291.51 (13) BOUNDS(n^1, INF) 320.93/291.51 (14) typed CpxTrs 320.93/291.51 (15) RewriteLemmaProof [LOWER BOUND(ID), 608 ms] 320.93/291.51 (16) typed CpxTrs 320.93/291.51 (17) RewriteLemmaProof [LOWER BOUND(ID), 261 ms] 320.93/291.51 (18) BEST 320.93/291.51 (19) proven lower bound 320.93/291.51 (20) LowerBoundPropagationProof [FINISHED, 0 ms] 320.93/291.51 (21) BOUNDS(n^2, INF) 320.93/291.51 (22) typed CpxTrs 320.93/291.51 320.93/291.51 320.93/291.51 ---------------------------------------- 320.93/291.51 320.93/291.51 (0) 320.93/291.51 Obligation: 320.93/291.51 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). 320.93/291.51 320.93/291.51 320.93/291.51 The TRS R consists of the following rules: 320.93/291.51 320.93/291.51 empty(nil) -> true 320.93/291.51 empty(cons(x, y)) -> false 320.93/291.51 tail(nil) -> nil 320.93/291.51 tail(cons(x, y)) -> y 320.93/291.51 head(cons(x, y)) -> x 320.93/291.51 zero(0) -> true 320.93/291.51 zero(s(x)) -> false 320.93/291.51 p(0) -> 0 320.93/291.51 p(s(0)) -> 0 320.93/291.51 p(s(s(x))) -> s(p(s(x))) 320.93/291.51 intlist(x) -> if_intlist(empty(x), x) 320.93/291.51 if_intlist(true, x) -> nil 320.93/291.51 if_intlist(false, x) -> cons(s(head(x)), intlist(tail(x))) 320.93/291.51 int(x, y) -> if_int(zero(x), zero(y), x, y) 320.93/291.51 if_int(true, b, x, y) -> if1(b, x, y) 320.93/291.51 if_int(false, b, x, y) -> if2(b, x, y) 320.93/291.51 if1(true, x, y) -> cons(0, nil) 320.93/291.51 if1(false, x, y) -> cons(0, int(s(0), y)) 320.93/291.51 if2(true, x, y) -> nil 320.93/291.51 if2(false, x, y) -> intlist(int(p(x), p(y))) 320.93/291.51 320.93/291.51 S is empty. 320.93/291.51 Rewrite Strategy: FULL 320.93/291.51 ---------------------------------------- 320.93/291.51 320.93/291.51 (1) RenamingProof (BOTH BOUNDS(ID, ID)) 320.93/291.51 Renamed function symbols to avoid clashes with predefined symbol. 320.93/291.51 ---------------------------------------- 320.93/291.51 320.93/291.51 (2) 320.93/291.51 Obligation: 320.93/291.51 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). 320.93/291.51 320.93/291.51 320.93/291.51 The TRS R consists of the following rules: 320.93/291.51 320.93/291.51 empty(nil) -> true 320.93/291.51 empty(cons(x, y)) -> false 320.93/291.51 tail(nil) -> nil 320.93/291.51 tail(cons(x, y)) -> y 320.93/291.51 head(cons(x, y)) -> x 320.93/291.51 zero(0') -> true 320.93/291.51 zero(s(x)) -> false 320.93/291.51 p(0') -> 0' 320.93/291.51 p(s(0')) -> 0' 320.93/291.51 p(s(s(x))) -> s(p(s(x))) 320.93/291.51 intlist(x) -> if_intlist(empty(x), x) 320.93/291.51 if_intlist(true, x) -> nil 320.93/291.51 if_intlist(false, x) -> cons(s(head(x)), intlist(tail(x))) 320.93/291.51 int(x, y) -> if_int(zero(x), zero(y), x, y) 320.93/291.51 if_int(true, b, x, y) -> if1(b, x, y) 320.93/291.51 if_int(false, b, x, y) -> if2(b, x, y) 320.93/291.51 if1(true, x, y) -> cons(0', nil) 320.93/291.51 if1(false, x, y) -> cons(0', int(s(0'), y)) 320.93/291.51 if2(true, x, y) -> nil 320.93/291.51 if2(false, x, y) -> intlist(int(p(x), p(y))) 320.93/291.51 320.93/291.51 S is empty. 320.93/291.51 Rewrite Strategy: FULL
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