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Compl Integ Trans Syste 26843 pair #381744270
details
property
value
status
complete
benchmark
ax.koat
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n075.star.cs.uiowa.edu
space
WTC
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
2.08676195145 seconds
cpu usage
4.58136917
max memory
2.8430336E8
stage attributes
key
value
output-size
26144
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^2, n^2).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, 26 ms] (2) BOUNDS(1, n^2) (3) Loat Proof [FINISHED, 490 ms] (4) BOUNDS(n^2, INF) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: evalaxstart(A, B, C) -> Com_1(evalaxentryin(A, B, C)) :|: TRUE evalaxentryin(A, B, C) -> Com_1(evalaxbbin(0, B, C)) :|: TRUE evalaxbbin(A, B, C) -> Com_1(evalaxbb2in(A, 0, C)) :|: TRUE evalaxbb2in(A, B, C) -> Com_1(evalaxbb1in(A, B, C)) :|: C >= 2 + B evalaxbb2in(A, B, C) -> Com_1(evalaxbb3in(A, B, C)) :|: B + 1 >= C evalaxbb1in(A, B, C) -> Com_1(evalaxbb2in(A, B + 1, C)) :|: TRUE evalaxbb3in(A, B, C) -> Com_1(evalaxbbin(A + 1, B, C)) :|: B + 1 >= C && C >= 3 + A evalaxbb3in(A, B, C) -> Com_1(evalaxreturnin(A, B, C)) :|: C >= 2 + B evalaxbb3in(A, B, C) -> Com_1(evalaxreturnin(A, B, C)) :|: A + 2 >= C evalaxreturnin(A, B, C) -> Com_1(evalaxstop(A, B, C)) :|: TRUE The start-symbols are:[evalaxstart_3] ---------------------------------------- (1) Koat Proof (FINISHED) YES(?, 5*ar_2 + 2*ar_2^2 + 8) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) evalaxstart(ar_0, ar_1, ar_2) -> Com_1(evalaxentryin(ar_0, ar_1, ar_2)) (Comp: ?, Cost: 1) evalaxentryin(ar_0, ar_1, ar_2) -> Com_1(evalaxbbin(0, ar_1, ar_2)) (Comp: ?, Cost: 1) evalaxbbin(ar_0, ar_1, ar_2) -> Com_1(evalaxbb2in(ar_0, 0, ar_2)) (Comp: ?, Cost: 1) evalaxbb2in(ar_0, ar_1, ar_2) -> Com_1(evalaxbb1in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_1 + 2 ] (Comp: ?, Cost: 1) evalaxbb2in(ar_0, ar_1, ar_2) -> Com_1(evalaxbb3in(ar_0, ar_1, ar_2)) [ ar_1 + 1 >= ar_2 ] (Comp: ?, Cost: 1) evalaxbb1in(ar_0, ar_1, ar_2) -> Com_1(evalaxbb2in(ar_0, ar_1 + 1, ar_2)) (Comp: ?, Cost: 1) evalaxbb3in(ar_0, ar_1, ar_2) -> Com_1(evalaxbbin(ar_0 + 1, ar_1, ar_2)) [ ar_1 + 1 >= ar_2 /\ ar_2 >= ar_0 + 3 ] (Comp: ?, Cost: 1) evalaxbb3in(ar_0, ar_1, ar_2) -> Com_1(evalaxreturnin(ar_0, ar_1, ar_2)) [ ar_2 >= ar_1 + 2 ] (Comp: ?, Cost: 1) evalaxbb3in(ar_0, ar_1, ar_2) -> Com_1(evalaxreturnin(ar_0, ar_1, ar_2)) [ ar_0 + 2 >= ar_2 ] (Comp: ?, Cost: 1) evalaxreturnin(ar_0, ar_1, ar_2) -> Com_1(evalaxstop(ar_0, ar_1, ar_2)) (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2) -> Com_1(evalaxstart(ar_0, ar_1, ar_2)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Testing for reachability in the complexity graph removes the following transition from problem 1: evalaxbb3in(ar_0, ar_1, ar_2) -> Com_1(evalaxreturnin(ar_0, ar_1, ar_2)) [ ar_2 >= ar_1 + 2 ] We thus obtain the following problem: 2: T: (Comp: ?, Cost: 1) evalaxreturnin(ar_0, ar_1, ar_2) -> Com_1(evalaxstop(ar_0, ar_1, ar_2)) (Comp: ?, Cost: 1) evalaxbb3in(ar_0, ar_1, ar_2) -> Com_1(evalaxreturnin(ar_0, ar_1, ar_2)) [ ar_0 + 2 >= ar_2 ] (Comp: ?, Cost: 1) evalaxbb3in(ar_0, ar_1, ar_2) -> Com_1(evalaxbbin(ar_0 + 1, ar_1, ar_2)) [ ar_1 + 1 >= ar_2 /\ ar_2 >= ar_0 + 3 ] (Comp: ?, Cost: 1) evalaxbb1in(ar_0, ar_1, ar_2) -> Com_1(evalaxbb2in(ar_0, ar_1 + 1, ar_2)) (Comp: ?, Cost: 1) evalaxbb2in(ar_0, ar_1, ar_2) -> Com_1(evalaxbb3in(ar_0, ar_1, ar_2)) [ ar_1 + 1 >= ar_2 ] (Comp: ?, Cost: 1) evalaxbb2in(ar_0, ar_1, ar_2) -> Com_1(evalaxbb1in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_1 + 2 ] (Comp: ?, Cost: 1) evalaxbbin(ar_0, ar_1, ar_2) -> Com_1(evalaxbb2in(ar_0, 0, ar_2))
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