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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313843
details
property
value
status
complete
benchmark
cade13t.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n171.star.cs.uiowa.edu
space
GTSSK07
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.559 seconds
cpu usage
1054.88
user time
1049.92
system time
4.96067
max virtual memory
1.9325424E7
max residence set size
5706832.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
1054.58/291.50 WORST_CASE(Omega(n^1), ?) 1054.58/291.51 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 1054.58/291.51 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1054.58/291.51 1054.58/291.51 1054.58/291.51 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1054.58/291.51 1054.58/291.51 (0) CpxTRS 1054.58/291.51 (1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 1054.58/291.51 (2) CpxTRS 1054.58/291.51 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 1054.58/291.51 (4) typed CpxTrs 1054.58/291.51 (5) OrderProof [LOWER BOUND(ID), 0 ms] 1054.58/291.51 (6) typed CpxTrs 1054.58/291.51 (7) RewriteLemmaProof [LOWER BOUND(ID), 301 ms] 1054.58/291.51 (8) BEST 1054.58/291.51 (9) proven lower bound 1054.58/291.51 (10) LowerBoundPropagationProof [FINISHED, 0 ms] 1054.58/291.51 (11) BOUNDS(n^1, INF) 1054.58/291.51 (12) typed CpxTrs 1054.58/291.51 (13) RewriteLemmaProof [LOWER BOUND(ID), 59 ms] 1054.58/291.51 (14) typed CpxTrs 1054.58/291.51 1054.58/291.51 1054.58/291.51 ---------------------------------------- 1054.58/291.51 1054.58/291.51 (0) 1054.58/291.51 Obligation: 1054.58/291.51 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1054.58/291.51 1054.58/291.51 1054.58/291.51 The TRS R consists of the following rules: 1054.58/291.51 1054.58/291.51 div(x, s(y)) -> d(x, s(y), 0) 1054.58/291.51 d(x, s(y), z) -> cond(ge(x, z), x, y, z) 1054.58/291.51 cond(true, x, y, z) -> s(d(x, s(y), plus(s(y), z))) 1054.58/291.51 cond(false, x, y, z) -> 0 1054.58/291.51 ge(u, 0) -> true 1054.58/291.51 ge(0, s(v)) -> false 1054.58/291.51 ge(s(u), s(v)) -> ge(u, v) 1054.58/291.51 plus(n, 0) -> n 1054.58/291.51 plus(n, s(m)) -> s(plus(n, m)) 1054.58/291.51 1054.58/291.51 S is empty. 1054.58/291.51 Rewrite Strategy: INNERMOST 1054.58/291.51 ---------------------------------------- 1054.58/291.51 1054.58/291.51 (1) RenamingProof (BOTH BOUNDS(ID, ID)) 1054.58/291.51 Renamed function symbols to avoid clashes with predefined symbol. 1054.58/291.51 ---------------------------------------- 1054.58/291.51 1054.58/291.51 (2) 1054.58/291.51 Obligation: 1054.58/291.51 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1054.58/291.51 1054.58/291.51 1054.58/291.51 The TRS R consists of the following rules: 1054.58/291.51 1054.58/291.51 div(x, s(y)) -> d(x, s(y), 0') 1054.58/291.51 d(x, s(y), z) -> cond(ge(x, z), x, y, z) 1054.58/291.51 cond(true, x, y, z) -> s(d(x, s(y), plus(s(y), z))) 1054.58/291.51 cond(false, x, y, z) -> 0' 1054.58/291.51 ge(u, 0') -> true 1054.58/291.51 ge(0', s(v)) -> false 1054.58/291.51 ge(s(u), s(v)) -> ge(u, v) 1054.58/291.51 plus(n, 0') -> n 1054.58/291.51 plus(n, s(m)) -> s(plus(n, m)) 1054.58/291.51 1054.58/291.51 S is empty. 1054.58/291.51 Rewrite Strategy: INNERMOST 1054.58/291.51 ---------------------------------------- 1054.58/291.51 1054.58/291.51 (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) 1054.58/291.51 Infered types. 1054.58/291.51 ---------------------------------------- 1054.58/291.51 1054.58/291.51 (4) 1054.58/291.51 Obligation: 1054.58/291.51 Innermost TRS: 1054.58/291.51 Rules: 1054.58/291.51 div(x, s(y)) -> d(x, s(y), 0') 1054.58/291.51 d(x, s(y), z) -> cond(ge(x, z), x, y, z) 1054.58/291.51 cond(true, x, y, z) -> s(d(x, s(y), plus(s(y), z))) 1054.58/291.51 cond(false, x, y, z) -> 0' 1054.58/291.51 ge(u, 0') -> true 1054.58/291.51 ge(0', s(v)) -> false 1054.58/291.51 ge(s(u), s(v)) -> ge(u, v) 1054.58/291.51 plus(n, 0') -> n 1054.58/291.51 plus(n, s(m)) -> s(plus(n, m)) 1054.58/291.51 1054.58/291.51 Types: 1054.58/291.51 div :: s:0' -> s:0' -> s:0' 1054.58/291.51 s :: s:0' -> s:0' 1054.58/291.51 d :: s:0' -> s:0' -> s:0' -> s:0' 1054.58/291.51 0' :: s:0' 1054.58/291.51 cond :: true:false -> s:0' -> s:0' -> s:0' -> s:0' 1054.58/291.51 ge :: s:0' -> s:0' -> true:false 1054.58/291.51 true :: true:false 1054.58/291.51 plus :: s:0' -> s:0' -> s:0' 1054.58/291.51 false :: true:false
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