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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307761
details
property
value
status
complete
benchmark
kabasci02.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n118.star.cs.uiowa.edu
space
AProVE_07
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.604 seconds
cpu usage
346.329
user time
343.57
system time
2.75929
max virtual memory
1.8282024E7
max residence set size
6128760.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^3), ?)
output
346.23/291.55 WORST_CASE(Omega(n^3), ?) 346.23/291.56 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 346.23/291.56 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 346.23/291.56 346.23/291.56 346.23/291.56 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^3, INF). 346.23/291.56 346.23/291.56 (0) CpxTRS 346.23/291.56 (1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 346.23/291.56 (2) CpxTRS 346.23/291.56 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 346.23/291.56 (4) typed CpxTrs 346.23/291.56 (5) OrderProof [LOWER BOUND(ID), 0 ms] 346.23/291.56 (6) typed CpxTrs 346.23/291.56 (7) RewriteLemmaProof [LOWER BOUND(ID), 222 ms] 346.23/291.56 (8) BEST 346.23/291.56 (9) proven lower bound 346.23/291.56 (10) LowerBoundPropagationProof [FINISHED, 0 ms] 346.23/291.56 (11) BOUNDS(n^1, INF) 346.23/291.56 (12) typed CpxTrs 346.23/291.56 (13) RewriteLemmaProof [LOWER BOUND(ID), 101 ms] 346.23/291.56 (14) BEST 346.23/291.56 (15) proven lower bound 346.23/291.56 (16) LowerBoundPropagationProof [FINISHED, 0 ms] 346.23/291.56 (17) BOUNDS(n^3, INF) 346.23/291.56 (18) typed CpxTrs 346.23/291.56 (19) RewriteLemmaProof [LOWER BOUND(ID), 77 ms] 346.23/291.56 (20) typed CpxTrs 346.23/291.56 (21) RewriteLemmaProof [LOWER BOUND(ID), 83 ms] 346.23/291.56 (22) typed CpxTrs 346.23/291.56 346.23/291.56 346.23/291.56 ---------------------------------------- 346.23/291.56 346.23/291.56 (0) 346.23/291.56 Obligation: 346.23/291.56 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^3, INF). 346.23/291.56 346.23/291.56 346.23/291.56 The TRS R consists of the following rules: 346.23/291.56 346.23/291.56 p(0) -> 0 346.23/291.56 p(s(x)) -> x 346.23/291.56 plus(x, 0) -> x 346.23/291.56 plus(0, y) -> y 346.23/291.56 plus(s(x), y) -> s(plus(x, y)) 346.23/291.56 plus(s(x), y) -> s(plus(p(s(x)), y)) 346.23/291.56 plus(x, s(y)) -> s(plus(x, p(s(y)))) 346.23/291.56 times(0, y) -> 0 346.23/291.56 times(s(0), y) -> y 346.23/291.56 times(s(x), y) -> plus(y, times(x, y)) 346.23/291.56 div(0, y) -> 0 346.23/291.56 div(x, y) -> quot(x, y, y) 346.23/291.56 quot(zero(y), s(y), z) -> 0 346.23/291.56 quot(s(x), s(y), z) -> quot(x, y, z) 346.23/291.56 quot(x, 0, s(z)) -> s(div(x, s(z))) 346.23/291.56 div(div(x, y), z) -> div(x, times(zero(y), z)) 346.23/291.56 eq(0, 0) -> true 346.23/291.56 eq(s(x), 0) -> false 346.23/291.56 eq(0, s(y)) -> false 346.23/291.56 eq(s(x), s(y)) -> eq(x, y) 346.23/291.56 divides(y, x) -> eq(x, times(div(x, y), y)) 346.23/291.56 prime(s(s(x))) -> pr(s(s(x)), s(x)) 346.23/291.56 pr(x, s(0)) -> true 346.23/291.56 pr(x, s(s(y))) -> if(divides(s(s(y)), x), x, s(y)) 346.23/291.56 if(true, x, y) -> false 346.23/291.56 if(false, x, y) -> pr(x, y) 346.23/291.56 zero(div(x, x)) -> x 346.23/291.56 zero(divides(x, x)) -> x 346.23/291.56 zero(times(x, x)) -> x 346.23/291.56 zero(quot(x, x, x)) -> x 346.23/291.56 zero(s(x)) -> if(eq(x, s(0)), plus(zero(0), 0), s(plus(0, zero(0)))) 346.23/291.56 346.23/291.56 S is empty. 346.23/291.56 Rewrite Strategy: FULL 346.23/291.56 ---------------------------------------- 346.23/291.56 346.23/291.56 (1) RenamingProof (BOTH BOUNDS(ID, ID)) 346.23/291.56 Renamed function symbols to avoid clashes with predefined symbol. 346.23/291.56 ---------------------------------------- 346.23/291.56 346.23/291.56 (2) 346.23/291.56 Obligation: 346.23/291.56 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^3, INF). 346.23/291.56 346.23/291.56 346.23/291.56 The TRS R consists of the following rules: 346.23/291.56 346.23/291.56 p(0') -> 0' 346.23/291.56 p(s(x)) -> x 346.23/291.56 plus(x, 0') -> x 346.23/291.56 plus(0', y) -> y 346.23/291.56 plus(s(x), y) -> s(plus(x, y)) 346.23/291.56 plus(s(x), y) -> s(plus(p(s(x)), y)) 346.23/291.56 plus(x, s(y)) -> s(plus(x, p(s(y)))) 346.23/291.56 times(0', y) -> 0' 346.23/291.56 times(s(0'), y) -> y 346.23/291.56 times(s(x), y) -> plus(y, times(x, y)) 346.23/291.56 div(0', y) -> 0' 346.23/291.56 div(x, y) -> quot(x, y, y)
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