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Compl Integ Trans Syste 26843 pair #381744396
details
property
value
status
complete
benchmark
realselect.koat
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n079.star.cs.uiowa.edu
space
WTC
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
2.04581594467 seconds
cpu usage
4.433022944
max memory
2.909184E8
stage attributes
key
value
output-size
32868
starexec-result
WORST_CASE(Omega(n^2), O(n^2))
output
/export/starexec/sandbox2/solver/bin/starexec_run_complexity /export/starexec/sandbox2/benchmark/theBenchmark.koat /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- WORST_CASE(Omega(n^2), O(n^2)) proof of /export/starexec/sandbox2/benchmark/theBenchmark.koat # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^2, n^2). (0) CpxIntTrs (1) Koat Proof [FINISHED, 141 ms] (2) BOUNDS(1, n^2) (3) Loat Proof [FINISHED, 422 ms] (4) BOUNDS(n^2, INF) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: evalrealselectstart(A, B, C) -> Com_1(evalrealselectentryin(A, B, C)) :|: TRUE evalrealselectentryin(A, B, C) -> Com_1(evalrealselectbb6in(0, B, C)) :|: TRUE evalrealselectbb6in(A, B, C) -> Com_1(evalrealselectbbin(A, B, C)) :|: B >= 2 + A evalrealselectbb6in(A, B, C) -> Com_1(evalrealselectreturnin(A, B, C)) :|: A + 1 >= B evalrealselectbbin(A, B, C) -> Com_1(evalrealselectbb4in(A, B, A + 1)) :|: TRUE evalrealselectbb4in(A, B, C) -> Com_1(evalrealselectbb1in(A, B, C)) :|: B >= C + 1 evalrealselectbb4in(A, B, C) -> Com_1(evalrealselectbb5in(A, B, C)) :|: C >= B evalrealselectbb1in(A, B, C) -> Com_1(evalrealselectbb4in(A, B, C + 1)) :|: D >= E + 1 evalrealselectbb1in(A, B, C) -> Com_1(evalrealselectbb4in(A, B, C + 1)) :|: E >= D evalrealselectbb5in(A, B, C) -> Com_1(evalrealselectbb6in(A + 1, B, C)) :|: TRUE evalrealselectreturnin(A, B, C) -> Com_1(evalrealselectstop(A, B, C)) :|: TRUE The start-symbols are:[evalrealselectstart_3] ---------------------------------------- (1) Koat Proof (FINISHED) YES(?, 72*ar_1 + 9*ar_1^2 + 69) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) evalrealselectstart(ar_0, ar_1, ar_2) -> Com_1(evalrealselectentryin(ar_0, ar_1, ar_2)) (Comp: ?, Cost: 1) evalrealselectentryin(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbb6in(0, ar_1, ar_2)) (Comp: ?, Cost: 1) evalrealselectbb6in(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbbin(ar_0, ar_1, ar_2)) [ ar_1 >= ar_0 + 2 ] (Comp: ?, Cost: 1) evalrealselectbb6in(ar_0, ar_1, ar_2) -> Com_1(evalrealselectreturnin(ar_0, ar_1, ar_2)) [ ar_0 + 1 >= ar_1 ] (Comp: ?, Cost: 1) evalrealselectbbin(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbb4in(ar_0, ar_1, ar_0 + 1)) (Comp: ?, Cost: 1) evalrealselectbb4in(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbb1in(ar_0, ar_1, ar_2)) [ ar_1 >= ar_2 + 1 ] (Comp: ?, Cost: 1) evalrealselectbb4in(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbb5in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_1 ] (Comp: ?, Cost: 1) evalrealselectbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbb4in(ar_0, ar_1, ar_2 + 1)) [ d >= e + 1 ] (Comp: ?, Cost: 1) evalrealselectbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbb4in(ar_0, ar_1, ar_2 + 1)) [ d >= e ] (Comp: ?, Cost: 1) evalrealselectbb5in(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbb6in(ar_0 + 1, ar_1, ar_2)) (Comp: ?, Cost: 1) evalrealselectreturnin(ar_0, ar_1, ar_2) -> Com_1(evalrealselectstop(ar_0, ar_1, ar_2)) (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2) -> Com_1(evalrealselectstart(ar_0, ar_1, ar_2)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Repeatedly propagating knowledge in problem 1 produces the following problem: 2: T: (Comp: 1, Cost: 1) evalrealselectstart(ar_0, ar_1, ar_2) -> Com_1(evalrealselectentryin(ar_0, ar_1, ar_2)) (Comp: 1, Cost: 1) evalrealselectentryin(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbb6in(0, ar_1, ar_2)) (Comp: ?, Cost: 1) evalrealselectbb6in(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbbin(ar_0, ar_1, ar_2)) [ ar_1 >= ar_0 + 2 ] (Comp: ?, Cost: 1) evalrealselectbb6in(ar_0, ar_1, ar_2) -> Com_1(evalrealselectreturnin(ar_0, ar_1, ar_2)) [ ar_0 + 1 >= ar_1 ] (Comp: ?, Cost: 1) evalrealselectbbin(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbb4in(ar_0, ar_1, ar_0 + 1)) (Comp: ?, Cost: 1) evalrealselectbb4in(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbb1in(ar_0, ar_1, ar_2)) [ ar_1 >= ar_2 + 1 ] (Comp: ?, Cost: 1) evalrealselectbb4in(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbb5in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_1 ] (Comp: ?, Cost: 1) evalrealselectbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbb4in(ar_0, ar_1, ar_2 + 1)) [ d >= e + 1 ]
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