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Complexity_C_Integer 2019-03-21 04.38 pair #429988820
details
property
value
status
complete
benchmark
speed_popl10_simple_multiple.c
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n016.star.cs.uiowa.edu
space
C4B_examples
run statistics
property
value
solver
AProVE
configuration
c_complexity
runtime (wallclock)
1.50414 seconds
cpu usage
2.56761
user time
2.34948
system time
0.218131
max virtual memory
1.8273644E7
max residence set size
182100.0
stage attributes
key
value
starexec-result
WORST_CASE(?, O(n^1))
output
2.26/1.47 WORST_CASE(?, O(n^1)) 2.52/1.48 proof of /export/starexec/sandbox/output/output_files/bench.koat 2.52/1.48 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 2.52/1.48 2.52/1.48 2.52/1.48 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^1). 2.52/1.48 2.52/1.48 (0) CpxIntTrs 2.52/1.48 (1) Koat Proof [FINISHED, 185 ms] 2.52/1.48 (2) BOUNDS(1, n^1) 2.52/1.48 2.52/1.48 2.52/1.48 ---------------------------------------- 2.52/1.48 2.52/1.48 (0) 2.52/1.48 Obligation: 2.52/1.48 Complexity Int TRS consisting of the following rules: 2.52/1.48 eval_speed_popl10_simple_multiple_start(v_m, v_n, v_x.0, v_y.0) -> Com_1(eval_speed_popl10_simple_multiple_bb0_in(v_m, v_n, v_x.0, v_y.0)) :|: TRUE 2.52/1.48 eval_speed_popl10_simple_multiple_bb0_in(v_m, v_n, v_x.0, v_y.0) -> Com_1(eval_speed_popl10_simple_multiple_bb1_in(v_m, v_n, 0, 0)) :|: TRUE 2.52/1.48 eval_speed_popl10_simple_multiple_bb1_in(v_m, v_n, v_x.0, v_y.0) -> Com_1(eval_speed_popl10_simple_multiple_bb2_in(v_m, v_n, v_x.0, v_y.0)) :|: v_x.0 < v_n 2.52/1.48 eval_speed_popl10_simple_multiple_bb1_in(v_m, v_n, v_x.0, v_y.0) -> Com_1(eval_speed_popl10_simple_multiple_bb3_in(v_m, v_n, v_x.0, v_y.0)) :|: v_x.0 >= v_n 2.52/1.48 eval_speed_popl10_simple_multiple_bb2_in(v_m, v_n, v_x.0, v_y.0) -> Com_1(eval_speed_popl10_simple_multiple_bb1_in(v_m, v_n, v_x.0, v_y.0 + 1)) :|: v_y.0 < v_m 2.52/1.48 eval_speed_popl10_simple_multiple_bb2_in(v_m, v_n, v_x.0, v_y.0) -> Com_1(eval_speed_popl10_simple_multiple_bb1_in(v_m, v_n, v_x.0 + 1, v_y.0 + 1)) :|: v_y.0 < v_m && v_y.0 >= v_m 2.52/1.48 eval_speed_popl10_simple_multiple_bb2_in(v_m, v_n, v_x.0, v_y.0) -> Com_1(eval_speed_popl10_simple_multiple_bb1_in(v_m, v_n, v_x.0, v_y.0)) :|: v_y.0 >= v_m && v_y.0 < v_m 2.52/1.48 eval_speed_popl10_simple_multiple_bb2_in(v_m, v_n, v_x.0, v_y.0) -> Com_1(eval_speed_popl10_simple_multiple_bb1_in(v_m, v_n, v_x.0 + 1, v_y.0)) :|: v_y.0 >= v_m 2.52/1.48 eval_speed_popl10_simple_multiple_bb3_in(v_m, v_n, v_x.0, v_y.0) -> Com_1(eval_speed_popl10_simple_multiple_stop(v_m, v_n, v_x.0, v_y.0)) :|: TRUE 2.52/1.48 2.52/1.48 The start-symbols are:[eval_speed_popl10_simple_multiple_start_4] 2.52/1.48 2.52/1.48 2.52/1.48 ---------------------------------------- 2.52/1.48 2.52/1.48 (1) Koat Proof (FINISHED) 2.52/1.48 YES(?, 2*ar_2 + 2*ar_3 + 7) 2.52/1.48 2.52/1.48 2.52/1.48 2.52/1.48 Initial complexity problem: 2.52/1.48 2.52/1.48 1: T: 2.52/1.48 2.52/1.48 (Comp: ?, Cost: 1) evalspeedpopl10simplemultiplestart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplemultiplebb0in(ar_0, ar_1, ar_2, ar_3)) 2.52/1.48 2.52/1.48 (Comp: ?, Cost: 1) evalspeedpopl10simplemultiplebb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplemultiplebb1in(0, 0, ar_2, ar_3)) 2.52/1.48 2.52/1.48 (Comp: ?, Cost: 1) evalspeedpopl10simplemultiplebb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplemultiplebb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 + 1 ] 2.52/1.48 2.52/1.48 (Comp: ?, Cost: 1) evalspeedpopl10simplemultiplebb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplemultiplebb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_2 ] 2.52/1.48 2.52/1.48 (Comp: ?, Cost: 1) evalspeedpopl10simplemultiplebb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplemultiplebb1in(ar_0, ar_1 + 1, ar_2, ar_3)) [ ar_3 >= ar_1 + 1 ] 2.52/1.48 2.52/1.48 (Comp: ?, Cost: 1) evalspeedpopl10simplemultiplebb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplemultiplebb1in(ar_0 + 1, ar_1 + 1, ar_2, ar_3)) [ ar_3 >= ar_1 + 1 /\ ar_1 >= ar_3 ] 2.52/1.48 2.52/1.48 (Comp: ?, Cost: 1) evalspeedpopl10simplemultiplebb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplemultiplebb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_3 /\ ar_3 >= ar_1 + 1 ] 2.52/1.48 2.52/1.48 (Comp: ?, Cost: 1) evalspeedpopl10simplemultiplebb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplemultiplebb1in(ar_0 + 1, ar_1, ar_2, ar_3)) [ ar_1 >= ar_3 ] 2.52/1.48 2.52/1.48 (Comp: ?, Cost: 1) evalspeedpopl10simplemultiplebb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplemultiplestop(ar_0, ar_1, ar_2, ar_3)) 2.52/1.48 2.52/1.48 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplemultiplestart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ] 2.52/1.48 2.52/1.48 start location: koat_start 2.52/1.48 2.52/1.48 leaf cost: 0 2.52/1.48 2.52/1.48 2.52/1.48 2.52/1.48 Testing for reachability in the complexity graph removes the following transitions from problem 1: 2.52/1.48 2.52/1.48 evalspeedpopl10simplemultiplebb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplemultiplebb1in(ar_0 + 1, ar_1 + 1, ar_2, ar_3)) [ ar_3 >= ar_1 + 1 /\ ar_1 >= ar_3 ] 2.52/1.48 2.52/1.48 evalspeedpopl10simplemultiplebb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplemultiplebb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_3 /\ ar_3 >= ar_1 + 1 ] 2.52/1.48 2.52/1.48 We thus obtain the following problem: 2.52/1.48 2.52/1.48 2: T: 2.52/1.48 2.52/1.48 (Comp: ?, Cost: 1) evalspeedpopl10simplemultiplebb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplemultiplestop(ar_0, ar_1, ar_2, ar_3)) 2.52/1.48 2.52/1.48 (Comp: ?, Cost: 1) evalspeedpopl10simplemultiplebb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplemultiplebb1in(ar_0 + 1, ar_1, ar_2, ar_3)) [ ar_1 >= ar_3 ] 2.52/1.48 2.52/1.48 (Comp: ?, Cost: 1) evalspeedpopl10simplemultiplebb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplemultiplebb1in(ar_0, ar_1 + 1, ar_2, ar_3)) [ ar_3 >= ar_1 + 1 ] 2.52/1.48 2.52/1.48 (Comp: ?, Cost: 1) evalspeedpopl10simplemultiplebb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplemultiplebb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_2 ] 2.52/1.48 2.52/1.48 (Comp: ?, Cost: 1) evalspeedpopl10simplemultiplebb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplemultiplebb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 + 1 ] 2.52/1.48 2.52/1.48 (Comp: ?, Cost: 1) evalspeedpopl10simplemultiplebb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplemultiplebb1in(0, 0, ar_2, ar_3)) 2.52/1.48 2.52/1.48 (Comp: ?, Cost: 1) evalspeedpopl10simplemultiplestart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplemultiplebb0in(ar_0, ar_1, ar_2, ar_3)) 2.52/1.48 2.52/1.48 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplemultiplestart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ] 2.52/1.48 2.52/1.48 start location: koat_start 2.52/1.48 2.52/1.48 leaf cost: 0 2.52/1.48 2.52/1.48 2.52/1.48 2.52/1.48 Repeatedly propagating knowledge in problem 2 produces the following problem:
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