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Compl Integ Trans Syste 26843 pair #381744613
details
property
value
status
complete
benchmark
speedSimpleMultiple.c.koat
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n088.star.cs.uiowa.edu
space
Flores-Montoya_16
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
2.3968770504 seconds
cpu usage
5.316767015
max memory
3.17247488E8
stage attributes
key
value
output-size
34332
starexec-result
WORST_CASE(Omega(n^1), O(n^1))
output
/export/starexec/sandbox/solver/bin/starexec_run_complexity /export/starexec/sandbox/benchmark/theBenchmark.koat /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- WORST_CASE(Omega(n^1), O(n^1)) proof of /export/starexec/sandbox/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, n^1). (0) CpxIntTrs (1) Koat Proof [FINISHED, 216 ms] (2) BOUNDS(1, n^1) (3) Loat Proof [FINISHED, 732 ms] (4) BOUNDS(n^1, INF) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: eval_speedSimpleMultiple_start(v_m, v_n, v_x_0, v_y_0) -> Com_1(eval_speedSimpleMultiple_bb0_in(v_m, v_n, v_x_0, v_y_0)) :|: TRUE eval_speedSimpleMultiple_bb0_in(v_m, v_n, v_x_0, v_y_0) -> Com_1(eval_speedSimpleMultiple_0(v_m, v_n, v_x_0, v_y_0)) :|: TRUE eval_speedSimpleMultiple_0(v_m, v_n, v_x_0, v_y_0) -> Com_1(eval_speedSimpleMultiple_1(v_m, v_n, v_x_0, v_y_0)) :|: TRUE eval_speedSimpleMultiple_1(v_m, v_n, v_x_0, v_y_0) -> Com_1(eval_speedSimpleMultiple_2(v_m, v_n, v_x_0, v_y_0)) :|: TRUE eval_speedSimpleMultiple_2(v_m, v_n, v_x_0, v_y_0) -> Com_1(eval_speedSimpleMultiple_3(v_m, v_n, v_x_0, v_y_0)) :|: TRUE eval_speedSimpleMultiple_3(v_m, v_n, v_x_0, v_y_0) -> Com_1(eval_speedSimpleMultiple_4(v_m, v_n, v_x_0, v_y_0)) :|: TRUE eval_speedSimpleMultiple_4(v_m, v_n, v_x_0, v_y_0) -> Com_1(eval_speedSimpleMultiple_5(v_m, v_n, v_x_0, v_y_0)) :|: TRUE eval_speedSimpleMultiple_5(v_m, v_n, v_x_0, v_y_0) -> Com_1(eval_speedSimpleMultiple_6(v_m, v_n, v_x_0, v_y_0)) :|: TRUE eval_speedSimpleMultiple_6(v_m, v_n, v_x_0, v_y_0) -> Com_1(eval_speedSimpleMultiple_bb1_in(v_m, v_n, 0, 0)) :|: TRUE eval_speedSimpleMultiple_bb1_in(v_m, v_n, v_x_0, v_y_0) -> Com_1(eval_speedSimpleMultiple_bb2_in(v_m, v_n, v_x_0, v_y_0)) :|: v_x_0 < v_n eval_speedSimpleMultiple_bb1_in(v_m, v_n, v_x_0, v_y_0) -> Com_1(eval_speedSimpleMultiple_bb3_in(v_m, v_n, v_x_0, v_y_0)) :|: v_x_0 >= v_n eval_speedSimpleMultiple_bb2_in(v_m, v_n, v_x_0, v_y_0) -> Com_1(eval_speedSimpleMultiple_bb1_in(v_m, v_n, v_x_0, v_y_0 + 1)) :|: v_y_0 < v_m eval_speedSimpleMultiple_bb2_in(v_m, v_n, v_x_0, v_y_0) -> Com_1(eval_speedSimpleMultiple_bb1_in(v_m, v_n, v_x_0 + 1, v_y_0 + 1)) :|: v_y_0 < v_m && v_y_0 >= v_m eval_speedSimpleMultiple_bb2_in(v_m, v_n, v_x_0, v_y_0) -> Com_1(eval_speedSimpleMultiple_bb1_in(v_m, v_n, v_x_0, v_y_0)) :|: v_y_0 >= v_m && v_y_0 < v_m eval_speedSimpleMultiple_bb2_in(v_m, v_n, v_x_0, v_y_0) -> Com_1(eval_speedSimpleMultiple_bb1_in(v_m, v_n, v_x_0 + 1, v_y_0)) :|: v_y_0 >= v_m eval_speedSimpleMultiple_bb3_in(v_m, v_n, v_x_0, v_y_0) -> Com_1(eval_speedSimpleMultiple_stop(v_m, v_n, v_x_0, v_y_0)) :|: TRUE The start-symbols are:[eval_speedSimpleMultiple_start_4] ---------------------------------------- (1) Koat Proof (FINISHED) YES(?, 2*ar_2 + 2*ar_3 + 14) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) evalspeedSimpleMultiplestart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultiplebb0in(ar_0, ar_1, ar_2, ar_3)) (Comp: ?, Cost: 1) evalspeedSimpleMultiplebb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultiple0(ar_0, ar_1, ar_2, ar_3)) (Comp: ?, Cost: 1) evalspeedSimpleMultiple0(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultiple1(ar_0, ar_1, ar_2, ar_3)) (Comp: ?, Cost: 1) evalspeedSimpleMultiple1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultiple2(ar_0, ar_1, ar_2, ar_3)) (Comp: ?, Cost: 1) evalspeedSimpleMultiple2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultiple3(ar_0, ar_1, ar_2, ar_3)) (Comp: ?, Cost: 1) evalspeedSimpleMultiple3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultiple4(ar_0, ar_1, ar_2, ar_3)) (Comp: ?, Cost: 1) evalspeedSimpleMultiple4(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultiple5(ar_0, ar_1, ar_2, ar_3)) (Comp: ?, Cost: 1) evalspeedSimpleMultiple5(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultiple6(ar_0, ar_1, ar_2, ar_3)) (Comp: ?, Cost: 1) evalspeedSimpleMultiple6(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultiplebb1in(0, 0, ar_2, ar_3)) (Comp: ?, Cost: 1) evalspeedSimpleMultiplebb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultiplebb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 + 1 ] (Comp: ?, Cost: 1) evalspeedSimpleMultiplebb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultiplebb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_2 ] (Comp: ?, Cost: 1) evalspeedSimpleMultiplebb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultiplebb1in(ar_0, ar_1 + 1, ar_2, ar_3)) [ ar_3 >= ar_1 + 1 ] (Comp: ?, Cost: 1) evalspeedSimpleMultiplebb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultiplebb1in(ar_0 + 1, ar_1 + 1, ar_2, ar_3)) [ ar_3 >= ar_1 + 1 /\ ar_1 >= ar_3 ] (Comp: ?, Cost: 1) evalspeedSimpleMultiplebb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultiplebb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_3 /\ ar_3 >= ar_1 + 1 ] (Comp: ?, Cost: 1) evalspeedSimpleMultiplebb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultiplebb1in(ar_0 + 1, ar_1, ar_2, ar_3)) [ ar_1 >= ar_3 ] (Comp: ?, Cost: 1) evalspeedSimpleMultiplebb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultiplestop(ar_0, ar_1, ar_2, ar_3)) (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultiplestart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Testing for reachability in the complexity graph removes the following transitions from problem 1: evalspeedSimpleMultiplebb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultiplebb1in(ar_0 + 1, ar_1 + 1, ar_2, ar_3)) [ ar_3 >= ar_1 + 1 /\ ar_1 >= ar_3 ]
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