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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313737
details
property
value
status
complete
benchmark
otto10.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n018.star.cs.uiowa.edu
space
AProVE_07
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.597 seconds
cpu usage
1140.59
user time
1123.69
system time
16.8942
max virtual memory
5.7396904E7
max residence set size
1.5042228E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
1140.33/291.51 WORST_CASE(Omega(n^1), ?) 1140.50/291.53 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 1140.50/291.53 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1140.50/291.53 1140.50/291.53 1140.50/291.53 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1140.50/291.53 1140.50/291.53 (0) CpxTRS 1140.50/291.53 (1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 1140.50/291.53 (2) CpxTRS 1140.50/291.53 (3) SlicingProof [LOWER BOUND(ID), 0 ms] 1140.50/291.53 (4) CpxTRS 1140.50/291.53 (5) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 1140.50/291.53 (6) typed CpxTrs 1140.50/291.53 (7) OrderProof [LOWER BOUND(ID), 0 ms] 1140.50/291.53 (8) typed CpxTrs 1140.50/291.53 (9) RewriteLemmaProof [LOWER BOUND(ID), 286 ms] 1140.50/291.53 (10) BEST 1140.50/291.53 (11) proven lower bound 1140.50/291.53 (12) LowerBoundPropagationProof [FINISHED, 0 ms] 1140.50/291.53 (13) BOUNDS(n^1, INF) 1140.50/291.53 (14) typed CpxTrs 1140.50/291.53 (15) RewriteLemmaProof [LOWER BOUND(ID), 75 ms] 1140.50/291.53 (16) typed CpxTrs 1140.50/291.53 (17) RewriteLemmaProof [LOWER BOUND(ID), 32 ms] 1140.50/291.53 (18) typed CpxTrs 1140.50/291.53 1140.50/291.53 1140.50/291.53 ---------------------------------------- 1140.50/291.53 1140.50/291.53 (0) 1140.50/291.53 Obligation: 1140.50/291.53 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1140.50/291.53 1140.50/291.53 1140.50/291.53 The TRS R consists of the following rules: 1140.50/291.53 1140.50/291.53 ge(x, 0) -> true 1140.50/291.53 ge(0, s(y)) -> false 1140.50/291.53 ge(s(x), s(y)) -> ge(x, y) 1140.50/291.53 rev(x) -> if(x, eq(0, length(x)), nil, 0, length(x)) 1140.50/291.53 if(x, true, z, c, l) -> z 1140.50/291.53 if(x, false, z, c, l) -> help(s(c), l, x, z) 1140.50/291.53 help(c, l, cons(x, y), z) -> if(append(y, cons(x, nil)), ge(c, l), cons(x, z), c, l) 1140.50/291.53 append(nil, y) -> y 1140.50/291.53 append(cons(x, y), z) -> cons(x, append(y, z)) 1140.50/291.53 length(nil) -> 0 1140.50/291.53 length(cons(x, y)) -> s(length(y)) 1140.50/291.53 1140.50/291.53 S is empty. 1140.50/291.53 Rewrite Strategy: INNERMOST 1140.50/291.53 ---------------------------------------- 1140.50/291.53 1140.50/291.53 (1) RenamingProof (BOTH BOUNDS(ID, ID)) 1140.50/291.53 Renamed function symbols to avoid clashes with predefined symbol. 1140.50/291.53 ---------------------------------------- 1140.50/291.53 1140.50/291.53 (2) 1140.50/291.53 Obligation: 1140.50/291.53 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1140.50/291.53 1140.50/291.53 1140.50/291.53 The TRS R consists of the following rules: 1140.50/291.53 1140.50/291.53 ge(x, 0') -> true 1140.50/291.53 ge(0', s(y)) -> false 1140.50/291.53 ge(s(x), s(y)) -> ge(x, y) 1140.50/291.53 rev(x) -> if(x, eq(0', length(x)), nil, 0', length(x)) 1140.50/291.53 if(x, true, z, c, l) -> z 1140.50/291.53 if(x, false, z, c, l) -> help(s(c), l, x, z) 1140.50/291.53 help(c, l, cons(x, y), z) -> if(append(y, cons(x, nil)), ge(c, l), cons(x, z), c, l) 1140.50/291.53 append(nil, y) -> y 1140.50/291.53 append(cons(x, y), z) -> cons(x, append(y, z)) 1140.50/291.53 length(nil) -> 0' 1140.50/291.53 length(cons(x, y)) -> s(length(y)) 1140.50/291.53 1140.50/291.53 S is empty. 1140.50/291.53 Rewrite Strategy: INNERMOST 1140.50/291.53 ---------------------------------------- 1140.50/291.53 1140.50/291.53 (3) SlicingProof (LOWER BOUND(ID)) 1140.50/291.53 Sliced the following arguments: 1140.50/291.53 eq/0 1140.50/291.53 cons/0 1140.50/291.53 1140.50/291.53 ---------------------------------------- 1140.50/291.53 1140.50/291.53 (4) 1140.50/291.53 Obligation: 1140.50/291.53 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1140.50/291.53 1140.50/291.53 1140.50/291.53 The TRS R consists of the following rules: 1140.50/291.53 1140.50/291.53 ge(x, 0') -> true 1140.50/291.53 ge(0', s(y)) -> false 1140.50/291.53 ge(s(x), s(y)) -> ge(x, y) 1140.50/291.53 rev(x) -> if(x, eq(length(x)), nil, 0', length(x)) 1140.50/291.53 if(x, true, z, c, l) -> z 1140.50/291.53 if(x, false, z, c, l) -> help(s(c), l, x, z)
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