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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433308056
details
property
value
status
complete
benchmark
ExIntrod_GM99_C.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n056.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.574 seconds
cpu usage
375.538
user time
370.261
system time
5.27757
max virtual memory
1.8281908E7
max residence set size
8577456.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
375.43/291.51 WORST_CASE(Omega(n^1), ?) 375.43/291.52 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 375.43/291.52 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 375.43/291.52 375.43/291.52 375.43/291.52 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 375.43/291.52 375.43/291.52 (0) CpxTRS 375.43/291.52 (1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 375.43/291.52 (2) TRS for Loop Detection 375.43/291.52 (3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 375.43/291.52 (4) BEST 375.43/291.52 (5) proven lower bound 375.43/291.52 (6) LowerBoundPropagationProof [FINISHED, 0 ms] 375.43/291.52 (7) BOUNDS(n^1, INF) 375.43/291.52 (8) TRS for Loop Detection 375.43/291.52 375.43/291.52 375.43/291.52 ---------------------------------------- 375.43/291.52 375.43/291.52 (0) 375.43/291.52 Obligation: 375.43/291.52 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 375.43/291.52 375.43/291.52 375.43/291.52 The TRS R consists of the following rules: 375.43/291.52 375.43/291.52 active(primes) -> mark(sieve(from(s(s(0))))) 375.43/291.52 active(from(X)) -> mark(cons(X, from(s(X)))) 375.43/291.52 active(head(cons(X, Y))) -> mark(X) 375.43/291.52 active(tail(cons(X, Y))) -> mark(Y) 375.43/291.52 active(if(true, X, Y)) -> mark(X) 375.43/291.52 active(if(false, X, Y)) -> mark(Y) 375.43/291.52 active(filter(s(s(X)), cons(Y, Z))) -> mark(if(divides(s(s(X)), Y), filter(s(s(X)), Z), cons(Y, filter(X, sieve(Y))))) 375.43/291.52 active(sieve(cons(X, Y))) -> mark(cons(X, filter(X, sieve(Y)))) 375.43/291.52 active(sieve(X)) -> sieve(active(X)) 375.43/291.52 active(from(X)) -> from(active(X)) 375.43/291.52 active(s(X)) -> s(active(X)) 375.43/291.52 active(cons(X1, X2)) -> cons(active(X1), X2) 375.43/291.52 active(head(X)) -> head(active(X)) 375.43/291.52 active(tail(X)) -> tail(active(X)) 375.43/291.52 active(if(X1, X2, X3)) -> if(active(X1), X2, X3) 375.43/291.52 active(filter(X1, X2)) -> filter(active(X1), X2) 375.43/291.52 active(filter(X1, X2)) -> filter(X1, active(X2)) 375.43/291.52 active(divides(X1, X2)) -> divides(active(X1), X2) 375.43/291.52 active(divides(X1, X2)) -> divides(X1, active(X2)) 375.43/291.52 sieve(mark(X)) -> mark(sieve(X)) 375.43/291.52 from(mark(X)) -> mark(from(X)) 375.43/291.52 s(mark(X)) -> mark(s(X)) 375.43/291.52 cons(mark(X1), X2) -> mark(cons(X1, X2)) 375.43/291.52 head(mark(X)) -> mark(head(X)) 375.43/291.52 tail(mark(X)) -> mark(tail(X)) 375.43/291.52 if(mark(X1), X2, X3) -> mark(if(X1, X2, X3)) 375.43/291.52 filter(mark(X1), X2) -> mark(filter(X1, X2)) 375.43/291.52 filter(X1, mark(X2)) -> mark(filter(X1, X2)) 375.43/291.52 divides(mark(X1), X2) -> mark(divides(X1, X2)) 375.43/291.52 divides(X1, mark(X2)) -> mark(divides(X1, X2)) 375.43/291.52 proper(primes) -> ok(primes) 375.43/291.52 proper(sieve(X)) -> sieve(proper(X)) 375.43/291.52 proper(from(X)) -> from(proper(X)) 375.43/291.52 proper(s(X)) -> s(proper(X)) 375.43/291.52 proper(0) -> ok(0) 375.43/291.52 proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)) 375.43/291.52 proper(head(X)) -> head(proper(X)) 375.43/291.52 proper(tail(X)) -> tail(proper(X)) 375.43/291.52 proper(if(X1, X2, X3)) -> if(proper(X1), proper(X2), proper(X3)) 375.43/291.52 proper(true) -> ok(true) 375.43/291.52 proper(false) -> ok(false) 375.43/291.52 proper(filter(X1, X2)) -> filter(proper(X1), proper(X2)) 375.43/291.52 proper(divides(X1, X2)) -> divides(proper(X1), proper(X2)) 375.43/291.52 sieve(ok(X)) -> ok(sieve(X)) 375.43/291.52 from(ok(X)) -> ok(from(X)) 375.43/291.52 s(ok(X)) -> ok(s(X)) 375.43/291.52 cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)) 375.43/291.52 head(ok(X)) -> ok(head(X)) 375.43/291.52 tail(ok(X)) -> ok(tail(X)) 375.43/291.52 if(ok(X1), ok(X2), ok(X3)) -> ok(if(X1, X2, X3)) 375.43/291.52 filter(ok(X1), ok(X2)) -> ok(filter(X1, X2)) 375.43/291.52 divides(ok(X1), ok(X2)) -> ok(divides(X1, X2)) 375.43/291.52 top(mark(X)) -> top(proper(X)) 375.43/291.52 top(ok(X)) -> top(active(X)) 375.43/291.52 375.43/291.52 S is empty. 375.43/291.52 Rewrite Strategy: FULL 375.43/291.52 ---------------------------------------- 375.43/291.52 375.43/291.52 (1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) 375.43/291.52 Transformed a relative TRS into a decreasing-loop problem. 375.43/291.52 ---------------------------------------- 375.43/291.52 375.43/291.52 (2) 375.43/291.52 Obligation: 375.43/291.52 Analyzing the following TRS for decreasing loops: 375.43/291.52 375.43/291.52 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 375.43/291.52 375.43/291.52 375.43/291.52 The TRS R consists of the following rules: 375.43/291.52 375.43/291.52 active(primes) -> mark(sieve(from(s(s(0)))))
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