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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307677
details
property
value
status
complete
benchmark
IJCAR_26.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n008.star.cs.uiowa.edu
space
AProVE_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.602 seconds
cpu usage
1113.11
user time
1099.87
system time
13.2385
max virtual memory
5.6602936E7
max residence set size
1.5047084E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^3), ?)
output
1112.70/291.49 WORST_CASE(Omega(n^3), ?) 1112.91/291.53 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 1112.91/291.53 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1112.91/291.53 1112.91/291.53 1112.91/291.53 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^3, INF). 1112.91/291.53 1112.91/291.53 (0) CpxTRS 1112.91/291.53 (1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 1112.91/291.53 (2) CpxTRS 1112.91/291.53 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 1112.91/291.53 (4) typed CpxTrs 1112.91/291.53 (5) OrderProof [LOWER BOUND(ID), 0 ms] 1112.91/291.53 (6) typed CpxTrs 1112.91/291.53 (7) RewriteLemmaProof [LOWER BOUND(ID), 250 ms] 1112.91/291.53 (8) BEST 1112.91/291.53 (9) proven lower bound 1112.91/291.53 (10) LowerBoundPropagationProof [FINISHED, 0 ms] 1112.91/291.53 (11) BOUNDS(n^1, INF) 1112.91/291.53 (12) typed CpxTrs 1112.91/291.53 (13) RewriteLemmaProof [LOWER BOUND(ID), 46 ms] 1112.91/291.53 (14) BEST 1112.91/291.53 (15) proven lower bound 1112.91/291.53 (16) LowerBoundPropagationProof [FINISHED, 0 ms] 1112.91/291.53 (17) BOUNDS(n^3, INF) 1112.91/291.53 (18) typed CpxTrs 1112.91/291.53 (19) RewriteLemmaProof [LOWER BOUND(ID), 74 ms] 1112.91/291.53 (20) typed CpxTrs 1112.91/291.53 (21) RewriteLemmaProof [LOWER BOUND(ID), 45 ms] 1112.91/291.53 (22) typed CpxTrs 1112.91/291.53 1112.91/291.53 1112.91/291.53 ---------------------------------------- 1112.91/291.53 1112.91/291.53 (0) 1112.91/291.53 Obligation: 1112.91/291.53 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^3, INF). 1112.91/291.53 1112.91/291.53 1112.91/291.53 The TRS R consists of the following rules: 1112.91/291.53 1112.91/291.53 p(s(x)) -> x 1112.91/291.53 plus(x, 0) -> x 1112.91/291.53 plus(0, y) -> y 1112.91/291.53 plus(s(x), y) -> s(plus(x, y)) 1112.91/291.53 plus(s(x), y) -> s(plus(p(s(x)), y)) 1112.91/291.53 plus(x, s(y)) -> s(plus(x, p(s(y)))) 1112.91/291.53 times(0, y) -> 0 1112.91/291.53 times(s(0), y) -> y 1112.91/291.53 times(s(x), y) -> plus(y, times(x, y)) 1112.91/291.53 div(0, y) -> 0 1112.91/291.53 div(x, y) -> quot(x, y, y) 1112.91/291.53 quot(0, s(y), z) -> 0 1112.91/291.53 quot(s(x), s(y), z) -> quot(x, y, z) 1112.91/291.53 quot(x, 0, s(z)) -> s(div(x, s(z))) 1112.91/291.53 div(div(x, y), z) -> div(x, times(y, z)) 1112.91/291.53 eq(0, 0) -> true 1112.91/291.53 eq(s(x), 0) -> false 1112.91/291.53 eq(0, s(y)) -> false 1112.91/291.53 eq(s(x), s(y)) -> eq(x, y) 1112.91/291.53 divides(y, x) -> eq(x, times(div(x, y), y)) 1112.91/291.53 prime(s(s(x))) -> pr(s(s(x)), s(x)) 1112.91/291.53 pr(x, s(0)) -> true 1112.91/291.53 pr(x, s(s(y))) -> if(divides(s(s(y)), x), x, s(y)) 1112.91/291.53 if(true, x, y) -> false 1112.91/291.53 if(false, x, y) -> pr(x, y) 1112.91/291.53 1112.91/291.53 S is empty. 1112.91/291.53 Rewrite Strategy: FULL 1112.91/291.53 ---------------------------------------- 1112.91/291.53 1112.91/291.53 (1) RenamingProof (BOTH BOUNDS(ID, ID)) 1112.91/291.53 Renamed function symbols to avoid clashes with predefined symbol. 1112.91/291.53 ---------------------------------------- 1112.91/291.53 1112.91/291.53 (2) 1112.91/291.53 Obligation: 1112.91/291.53 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^3, INF). 1112.91/291.53 1112.91/291.53 1112.91/291.53 The TRS R consists of the following rules: 1112.91/291.53 1112.91/291.53 p(s(x)) -> x 1112.91/291.53 plus(x, 0') -> x 1112.91/291.53 plus(0', y) -> y 1112.91/291.53 plus(s(x), y) -> s(plus(x, y)) 1112.91/291.53 plus(s(x), y) -> s(plus(p(s(x)), y)) 1112.91/291.53 plus(x, s(y)) -> s(plus(x, p(s(y)))) 1112.91/291.53 times(0', y) -> 0' 1112.91/291.53 times(s(0'), y) -> y 1112.91/291.53 times(s(x), y) -> plus(y, times(x, y)) 1112.91/291.53 div(0', y) -> 0' 1112.91/291.53 div(x, y) -> quot(x, y, y) 1112.91/291.53 quot(0', s(y), z) -> 0' 1112.91/291.53 quot(s(x), s(y), z) -> quot(x, y, z) 1112.91/291.53 quot(x, 0', s(z)) -> s(div(x, s(z))) 1112.91/291.53 div(div(x, y), z) -> div(x, times(y, z)) 1112.91/291.53 eq(0', 0') -> true 1112.91/291.53 eq(s(x), 0') -> false 1112.91/291.53 eq(0', s(y)) -> false
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