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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307619
details
property
value
status
timeout (wallclock)
benchmark
id_inc.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
space
AProVE_08
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
300.103 seconds
cpu usage
369.44
user time
363.65
system time
5.79
max virtual memory
1.8279384E7
max residence set size
1452.0
stage attributes
unavailable
output
335.63/291.49 WORST_CASE(Omega(n^1), ?) 335.63/291.50 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 335.63/291.50 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 335.63/291.50 335.63/291.50 335.63/291.50 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 335.63/291.50 335.63/291.50 (0) CpxTRS 335.63/291.50 (1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 335.63/291.50 (2) CpxTRS 335.63/291.50 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 335.63/291.50 (4) typed CpxTrs 335.63/291.50 (5) OrderProof [LOWER BOUND(ID), 0 ms] 335.63/291.50 (6) typed CpxTrs 335.63/291.50 (7) RewriteLemmaProof [LOWER BOUND(ID), 276 ms] 335.63/291.50 (8) BEST 335.63/291.50 (9) proven lower bound 335.63/291.50 (10) LowerBoundPropagationProof [FINISHED, 0 ms] 335.63/291.50 (11) BOUNDS(n^1, INF) 335.63/291.50 (12) typed CpxTrs 335.63/291.50 335.63/291.50 335.63/291.50 ---------------------------------------- 335.63/291.50 335.63/291.50 (0) 335.63/291.50 Obligation: 335.63/291.50 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 335.63/291.50 335.63/291.50 335.63/291.50 The TRS R consists of the following rules: 335.63/291.50 335.63/291.50 f(s(x)) -> f(id_inc(c(x, x))) 335.63/291.50 f(c(s(x), y)) -> g(c(x, y)) 335.63/291.50 g(c(s(x), y)) -> g(c(y, x)) 335.63/291.50 g(c(x, s(y))) -> g(c(y, x)) 335.63/291.50 g(c(x, x)) -> f(x) 335.63/291.50 id_inc(c(x, y)) -> c(id_inc(x), id_inc(y)) 335.63/291.50 id_inc(s(x)) -> s(id_inc(x)) 335.63/291.50 id_inc(0) -> 0 335.63/291.50 id_inc(0) -> s(0) 335.63/291.50 335.63/291.50 S is empty. 335.63/291.50 Rewrite Strategy: FULL 335.63/291.50 ---------------------------------------- 335.63/291.50 335.63/291.50 (1) RenamingProof (BOTH BOUNDS(ID, ID)) 335.63/291.50 Renamed function symbols to avoid clashes with predefined symbol. 335.63/291.50 ---------------------------------------- 335.63/291.50 335.63/291.50 (2) 335.63/291.50 Obligation: 335.63/291.50 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 335.63/291.50 335.63/291.50 335.63/291.50 The TRS R consists of the following rules: 335.63/291.50 335.63/291.50 f(s(x)) -> f(id_inc(c(x, x))) 335.63/291.50 f(c(s(x), y)) -> g(c(x, y)) 335.63/291.50 g(c(s(x), y)) -> g(c(y, x)) 335.63/291.50 g(c(x, s(y))) -> g(c(y, x)) 335.63/291.50 g(c(x, x)) -> f(x) 335.63/291.50 id_inc(c(x, y)) -> c(id_inc(x), id_inc(y)) 335.63/291.50 id_inc(s(x)) -> s(id_inc(x)) 335.63/291.50 id_inc(0') -> 0' 335.63/291.50 id_inc(0') -> s(0') 335.63/291.50 335.63/291.50 S is empty. 335.63/291.50 Rewrite Strategy: FULL 335.63/291.50 ---------------------------------------- 335.63/291.50 335.63/291.50 (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) 335.63/291.50 Infered types. 335.63/291.50 ---------------------------------------- 335.63/291.50 335.63/291.50 (4) 335.63/291.50 Obligation: 335.63/291.50 TRS: 335.63/291.50 Rules: 335.63/291.50 f(s(x)) -> f(id_inc(c(x, x))) 335.63/291.50 f(c(s(x), y)) -> g(c(x, y)) 335.63/291.50 g(c(s(x), y)) -> g(c(y, x)) 335.63/291.50 g(c(x, s(y))) -> g(c(y, x)) 335.63/291.50 g(c(x, x)) -> f(x) 335.63/291.50 id_inc(c(x, y)) -> c(id_inc(x), id_inc(y)) 335.63/291.50 id_inc(s(x)) -> s(id_inc(x)) 335.63/291.50 id_inc(0') -> 0' 335.63/291.50 id_inc(0') -> s(0') 335.63/291.50 335.63/291.50 Types: 335.63/291.50 f :: s:c:0' -> f:g 335.63/291.50 s :: s:c:0' -> s:c:0' 335.63/291.50 id_inc :: s:c:0' -> s:c:0' 335.63/291.50 c :: s:c:0' -> s:c:0' -> s:c:0' 335.63/291.50 g :: s:c:0' -> f:g 335.63/291.50 0' :: s:c:0' 335.63/291.50 hole_f:g1_0 :: f:g 335.63/291.50 hole_s:c:0'2_0 :: s:c:0' 335.63/291.50 gen_s:c:0'3_0 :: Nat -> s:c:0' 335.63/291.50 335.63/291.50 ----------------------------------------
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