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Compl Integ Trans Syste 26843 pair #381744416
details
property
value
status
complete
benchmark
speedpldi4.koat
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n004.star.cs.uiowa.edu
space
WTC
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
2.27354693413 seconds
cpu usage
4.788983402
max memory
3.4148352E8
stage attributes
key
value
output-size
23426
starexec-result
WORST_CASE(?, O(n^1))
output
/export/starexec/sandbox2/solver/bin/starexec_run_complexity /export/starexec/sandbox2/benchmark/theBenchmark.koat /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- WORST_CASE(?, O(n^1)) 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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, max(5, 1 + 2 * Arg_1) * max(4, 4 * Arg_0) + max(5, 1 + 2 * Arg_1) * max(5, 5 * Arg_0) + max(5, 1 + 2 * Arg_1) * max(3, 3 * Arg_0) + nat(Arg_1) + max(7 + 2 * Arg_1, 11)). (0) CpxIntTrs (1) Koat Proof [FINISHED, 136 ms] (2) BOUNDS(1, n^1) (3) Loat Proof [FINISHED, 411 ms] (4) BOUNDS(1, INF) (5) Koat2 Proof [FINISHED, 632 ms] (6) BOUNDS(1, max(5, 1 + 2 * Arg_1) * max(4, 4 * Arg_0) + max(5, 1 + 2 * Arg_1) * max(5, 5 * Arg_0) + max(5, 1 + 2 * Arg_1) * max(3, 3 * Arg_0) + nat(Arg_1) + max(7 + 2 * Arg_1, 11)) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: evalspeedpldi4start(A, B) -> Com_1(evalspeedpldi4entryin(A, B)) :|: TRUE evalspeedpldi4entryin(A, B) -> Com_1(evalspeedpldi4returnin(A, B)) :|: 0 >= A evalspeedpldi4entryin(A, B) -> Com_1(evalspeedpldi4returnin(A, B)) :|: A >= B evalspeedpldi4entryin(A, B) -> Com_1(evalspeedpldi4bb5in(A, B)) :|: A >= 1 && B >= A + 1 evalspeedpldi4bb5in(A, B) -> Com_1(evalspeedpldi4bb2in(A, B)) :|: B >= 1 evalspeedpldi4bb5in(A, B) -> Com_1(evalspeedpldi4returnin(A, B)) :|: 0 >= B evalspeedpldi4bb2in(A, B) -> Com_1(evalspeedpldi4bb3in(A, B)) :|: A >= B + 1 evalspeedpldi4bb2in(A, B) -> Com_1(evalspeedpldi4bb4in(A, B)) :|: B >= A evalspeedpldi4bb3in(A, B) -> Com_1(evalspeedpldi4bb5in(A, B - 1)) :|: TRUE evalspeedpldi4bb4in(A, B) -> Com_1(evalspeedpldi4bb5in(A, B - A)) :|: TRUE evalspeedpldi4returnin(A, B) -> Com_1(evalspeedpldi4stop(A, B)) :|: TRUE The start-symbols are:[evalspeedpldi4start_2] ---------------------------------------- (1) Koat Proof (FINISHED) YES(?, 15*ar_0 + 15*ar_1 + 8) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) evalspeedpldi4start(ar_0, ar_1) -> Com_1(evalspeedpldi4entryin(ar_0, ar_1)) (Comp: ?, Cost: 1) evalspeedpldi4entryin(ar_0, ar_1) -> Com_1(evalspeedpldi4returnin(ar_0, ar_1)) [ 0 >= ar_0 ] (Comp: ?, Cost: 1) evalspeedpldi4entryin(ar_0, ar_1) -> Com_1(evalspeedpldi4returnin(ar_0, ar_1)) [ ar_0 >= ar_1 ] (Comp: ?, Cost: 1) evalspeedpldi4entryin(ar_0, ar_1) -> Com_1(evalspeedpldi4bb5in(ar_0, ar_1)) [ ar_0 >= 1 /\ ar_1 >= ar_0 + 1 ] (Comp: ?, Cost: 1) evalspeedpldi4bb5in(ar_0, ar_1) -> Com_1(evalspeedpldi4bb2in(ar_0, ar_1)) [ ar_1 >= 1 ] (Comp: ?, Cost: 1) evalspeedpldi4bb5in(ar_0, ar_1) -> Com_1(evalspeedpldi4returnin(ar_0, ar_1)) [ 0 >= ar_1 ] (Comp: ?, Cost: 1) evalspeedpldi4bb2in(ar_0, ar_1) -> Com_1(evalspeedpldi4bb3in(ar_0, ar_1)) [ ar_0 >= ar_1 + 1 ] (Comp: ?, Cost: 1) evalspeedpldi4bb2in(ar_0, ar_1) -> Com_1(evalspeedpldi4bb4in(ar_0, ar_1)) [ ar_1 >= ar_0 ] (Comp: ?, Cost: 1) evalspeedpldi4bb3in(ar_0, ar_1) -> Com_1(evalspeedpldi4bb5in(ar_0, ar_1 - 1)) (Comp: ?, Cost: 1) evalspeedpldi4bb4in(ar_0, ar_1) -> Com_1(evalspeedpldi4bb5in(ar_0, ar_1 - ar_0)) (Comp: ?, Cost: 1) evalspeedpldi4returnin(ar_0, ar_1) -> Com_1(evalspeedpldi4stop(ar_0, ar_1)) (Comp: 1, Cost: 0) koat_start(ar_0, ar_1) -> Com_1(evalspeedpldi4start(ar_0, ar_1)) [ 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) evalspeedpldi4start(ar_0, ar_1) -> Com_1(evalspeedpldi4entryin(ar_0, ar_1)) (Comp: 1, Cost: 1) evalspeedpldi4entryin(ar_0, ar_1) -> Com_1(evalspeedpldi4returnin(ar_0, ar_1)) [ 0 >= ar_0 ] (Comp: 1, Cost: 1) evalspeedpldi4entryin(ar_0, ar_1) -> Com_1(evalspeedpldi4returnin(ar_0, ar_1)) [ ar_0 >= ar_1 ] (Comp: 1, Cost: 1) evalspeedpldi4entryin(ar_0, ar_1) -> Com_1(evalspeedpldi4bb5in(ar_0, ar_1)) [ ar_0 >= 1 /\ ar_1 >= ar_0 + 1 ] (Comp: ?, Cost: 1) evalspeedpldi4bb5in(ar_0, ar_1) -> Com_1(evalspeedpldi4bb2in(ar_0, ar_1)) [ ar_1 >= 1 ] (Comp: ?, Cost: 1) evalspeedpldi4bb5in(ar_0, ar_1) -> Com_1(evalspeedpldi4returnin(ar_0, ar_1)) [ 0 >= ar_1 ] (Comp: ?, Cost: 1) evalspeedpldi4bb2in(ar_0, ar_1) -> Com_1(evalspeedpldi4bb3in(ar_0, ar_1)) [ ar_0 >= ar_1 + 1 ]
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