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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313487
details
property
value
status
complete
benchmark
ExIntrod_GM99_GM.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n128.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
292.833 seconds
cpu usage
1124.85
user time
1111.68
system time
13.1693
max virtual memory
3.7281308E7
max residence set size
1.5232376E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
1119.61/291.54 WORST_CASE(Omega(n^1), ?) 1124.53/292.76 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 1124.53/292.76 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1124.53/292.76 1124.53/292.76 1124.53/292.76 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1124.53/292.76 1124.53/292.76 (0) CpxTRS 1124.53/292.76 (1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 1124.53/292.76 (2) CpxTRS 1124.53/292.76 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 1124.53/292.76 (4) typed CpxTrs 1124.53/292.76 (5) OrderProof [LOWER BOUND(ID), 0 ms] 1124.53/292.76 (6) typed CpxTrs 1124.53/292.76 (7) RewriteLemmaProof [LOWER BOUND(ID), 2566 ms] 1124.53/292.76 (8) BEST 1124.53/292.76 (9) proven lower bound 1124.53/292.76 (10) LowerBoundPropagationProof [FINISHED, 0 ms] 1124.53/292.76 (11) BOUNDS(n^1, INF) 1124.53/292.76 (12) typed CpxTrs 1124.53/292.76 1124.53/292.76 1124.53/292.76 ---------------------------------------- 1124.53/292.76 1124.53/292.76 (0) 1124.53/292.76 Obligation: 1124.53/292.76 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1124.53/292.76 1124.53/292.76 1124.53/292.76 The TRS R consists of the following rules: 1124.53/292.76 1124.53/292.76 a__primes -> a__sieve(a__from(s(s(0)))) 1124.53/292.76 a__from(X) -> cons(mark(X), from(s(X))) 1124.53/292.76 a__head(cons(X, Y)) -> mark(X) 1124.53/292.76 a__tail(cons(X, Y)) -> mark(Y) 1124.53/292.76 a__if(true, X, Y) -> mark(X) 1124.53/292.76 a__if(false, X, Y) -> mark(Y) 1124.53/292.76 a__filter(s(s(X)), cons(Y, Z)) -> a__if(divides(s(s(mark(X))), mark(Y)), filter(s(s(X)), Z), cons(Y, filter(X, sieve(Y)))) 1124.53/292.76 a__sieve(cons(X, Y)) -> cons(mark(X), filter(X, sieve(Y))) 1124.53/292.76 mark(primes) -> a__primes 1124.53/292.76 mark(sieve(X)) -> a__sieve(mark(X)) 1124.53/292.76 mark(from(X)) -> a__from(mark(X)) 1124.53/292.76 mark(head(X)) -> a__head(mark(X)) 1124.53/292.76 mark(tail(X)) -> a__tail(mark(X)) 1124.53/292.76 mark(if(X1, X2, X3)) -> a__if(mark(X1), X2, X3) 1124.53/292.76 mark(filter(X1, X2)) -> a__filter(mark(X1), mark(X2)) 1124.53/292.76 mark(s(X)) -> s(mark(X)) 1124.53/292.76 mark(0) -> 0 1124.53/292.76 mark(cons(X1, X2)) -> cons(mark(X1), X2) 1124.53/292.76 mark(true) -> true 1124.53/292.76 mark(false) -> false 1124.53/292.76 mark(divides(X1, X2)) -> divides(mark(X1), mark(X2)) 1124.53/292.76 a__primes -> primes 1124.53/292.76 a__sieve(X) -> sieve(X) 1124.53/292.76 a__from(X) -> from(X) 1124.53/292.76 a__head(X) -> head(X) 1124.53/292.76 a__tail(X) -> tail(X) 1124.53/292.76 a__if(X1, X2, X3) -> if(X1, X2, X3) 1124.53/292.76 a__filter(X1, X2) -> filter(X1, X2) 1124.53/292.76 1124.53/292.76 S is empty. 1124.53/292.76 Rewrite Strategy: INNERMOST 1124.53/292.76 ---------------------------------------- 1124.53/292.76 1124.53/292.76 (1) RenamingProof (BOTH BOUNDS(ID, ID)) 1124.53/292.76 Renamed function symbols to avoid clashes with predefined symbol. 1124.53/292.76 ---------------------------------------- 1124.53/292.76 1124.53/292.76 (2) 1124.53/292.76 Obligation: 1124.53/292.76 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1124.53/292.76 1124.53/292.76 1124.53/292.76 The TRS R consists of the following rules: 1124.53/292.76 1124.53/292.76 a__primes -> a__sieve(a__from(s(s(0')))) 1124.53/292.76 a__from(X) -> cons(mark(X), from(s(X))) 1124.53/292.76 a__head(cons(X, Y)) -> mark(X) 1124.53/292.76 a__tail(cons(X, Y)) -> mark(Y) 1124.53/292.76 a__if(true, X, Y) -> mark(X) 1124.53/292.76 a__if(false, X, Y) -> mark(Y) 1124.53/292.76 a__filter(s(s(X)), cons(Y, Z)) -> a__if(divides(s(s(mark(X))), mark(Y)), filter(s(s(X)), Z), cons(Y, filter(X, sieve(Y)))) 1124.53/292.76 a__sieve(cons(X, Y)) -> cons(mark(X), filter(X, sieve(Y))) 1124.53/292.76 mark(primes) -> a__primes 1124.53/292.76 mark(sieve(X)) -> a__sieve(mark(X)) 1124.53/292.76 mark(from(X)) -> a__from(mark(X)) 1124.53/292.76 mark(head(X)) -> a__head(mark(X)) 1124.53/292.76 mark(tail(X)) -> a__tail(mark(X)) 1124.53/292.76 mark(if(X1, X2, X3)) -> a__if(mark(X1), X2, X3) 1124.53/292.76 mark(filter(X1, X2)) -> a__filter(mark(X1), mark(X2)) 1124.53/292.76 mark(s(X)) -> s(mark(X)) 1124.53/292.76 mark(0') -> 0' 1124.53/292.76 mark(cons(X1, X2)) -> cons(mark(X1), X2) 1124.53/292.76 mark(true) -> true 1124.53/292.76 mark(false) -> false 1124.53/292.76 mark(divides(X1, X2)) -> divides(mark(X1), mark(X2)) 1124.53/292.76 a__primes -> primes 1124.53/292.76 a__sieve(X) -> sieve(X) 1124.53/292.76 a__from(X) -> from(X) 1124.53/292.76 a__head(X) -> head(X)
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