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Complexity_C_Integer 2019-03-21 04.38 pair #429988874
details
property
value
status
complete
benchmark
t16.c
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n080.star.cs.uiowa.edu
space
C4B_examples
run statistics
property
value
solver
AProVE
configuration
c_complexity
runtime (wallclock)
1.79602 seconds
cpu usage
2.69355
user time
2.46646
system time
0.227093
max virtual memory
1.8443624E7
max residence set size
180260.0
stage attributes
key
value
starexec-result
WORST_CASE(?, O(n^2))
output
2.62/1.75 WORST_CASE(?, O(n^2)) 2.63/1.76 proof of /export/starexec/sandbox/output/output_files/bench.koat 2.63/1.76 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 2.63/1.76 2.63/1.76 2.63/1.76 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^2). 2.63/1.76 2.63/1.76 (0) CpxIntTrs 2.63/1.76 (1) Koat Proof [FINISHED, 478 ms] 2.63/1.76 (2) BOUNDS(1, n^2) 2.63/1.76 2.63/1.76 2.63/1.76 ---------------------------------------- 2.63/1.76 2.63/1.76 (0) 2.63/1.76 Obligation: 2.63/1.76 Complexity Int TRS consisting of the following rules: 2.63/1.76 eval_t16_start(v_.0, v_3, v_x, v_y, v_z.0) -> Com_1(eval_t16_bb0_in(v_.0, v_3, v_x, v_y, v_z.0)) :|: TRUE 2.63/1.76 eval_t16_bb0_in(v_.0, v_3, v_x, v_y, v_z.0) -> Com_1(eval_t16_bb5_in(v_.0, v_3, v_x, v_y, v_z.0)) :|: v_y < 0 2.63/1.76 eval_t16_bb0_in(v_.0, v_3, v_x, v_y, v_z.0) -> Com_1(eval_t16_bb1_in(v_x, v_3, v_x, v_y, v_z.0)) :|: v_y >= 0 2.63/1.76 eval_t16_bb1_in(v_.0, v_3, v_x, v_y, v_z.0) -> Com_1(eval_t16_bb2_in(v_.0, v_3, v_x, v_y, v_z.0)) :|: v_.0 > v_y 2.63/1.76 eval_t16_bb1_in(v_.0, v_3, v_x, v_y, v_z.0) -> Com_1(eval_t16_bb5_in(v_.0, v_3, v_x, v_y, v_z.0)) :|: v_.0 <= v_y 2.63/1.76 eval_t16_bb2_in(v_.0, v_3, v_x, v_y, v_z.0) -> Com_1(eval_t16_bb3_in(v_.0, v_.0 - v_y - 1, v_x, v_y, 2 * v_y + 100)) :|: TRUE 2.63/1.77 eval_t16_bb3_in(v_.0, v_3, v_x, v_y, v_z.0) -> Com_1(eval_t16_bb4_in(v_.0, v_3, v_x, v_y, v_z.0)) :|: v_z.0 > 0 2.63/1.77 eval_t16_bb3_in(v_.0, v_3, v_x, v_y, v_z.0) -> Com_1(eval_t16_bb1_in(v_3, v_3, v_x, v_y, v_z.0)) :|: v_z.0 <= 0 2.63/1.77 eval_t16_bb4_in(v_.0, v_3, v_x, v_y, v_z.0) -> Com_1(eval_t16_bb3_in(v_.0, v_3, v_x, v_y, v_z.0 - 1)) :|: TRUE 2.63/1.77 eval_t16_bb5_in(v_.0, v_3, v_x, v_y, v_z.0) -> Com_1(eval_t16_stop(v_.0, v_3, v_x, v_y, v_z.0)) :|: TRUE 2.63/1.77 2.63/1.77 The start-symbols are:[eval_t16_start_5] 2.63/1.77 2.63/1.77 2.63/1.77 ---------------------------------------- 2.63/1.77 2.63/1.77 (1) Koat Proof (FINISHED) 2.63/1.77 YES(?, 24*ar_2^2 + 2377*ar_2 + 1581) 2.63/1.77 2.63/1.77 2.63/1.77 2.63/1.77 Initial complexity problem: 2.63/1.77 2.63/1.77 1: T: 2.63/1.77 2.63/1.77 (Comp: ?, Cost: 1) evalt16start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalt16bb0in(ar_0, ar_1, ar_2, ar_3, ar_4)) 2.63/1.77 2.63/1.77 (Comp: ?, Cost: 1) evalt16bb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalt16bb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_0 + 1 ] 2.63/1.77 2.63/1.77 (Comp: ?, Cost: 1) evalt16bb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalt16bb1in(ar_0, ar_2, ar_2, ar_3, ar_4)) [ ar_0 >= 0 ] 2.63/1.77 2.63/1.77 (Comp: ?, Cost: 1) evalt16bb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalt16bb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 + 1 ] 2.63/1.77 2.63/1.77 (Comp: ?, Cost: 1) evalt16bb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalt16bb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_1 ] 2.63/1.77 2.63/1.77 (Comp: ?, Cost: 1) evalt16bb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalt16bb3in(ar_0, ar_1, ar_2, ar_1 - ar_0 - 1, 2*ar_0 + 100)) 2.63/1.77 2.63/1.77 (Comp: ?, Cost: 1) evalt16bb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalt16bb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= 1 ] 2.63/1.77 2.63/1.77 (Comp: ?, Cost: 1) evalt16bb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalt16bb1in(ar_0, ar_3, ar_2, ar_3, ar_4)) [ 0 >= ar_4 ] 2.63/1.77 2.63/1.77 (Comp: ?, Cost: 1) evalt16bb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalt16bb3in(ar_0, ar_1, ar_2, ar_3, ar_4 - 1)) 2.63/1.77 2.63/1.77 (Comp: ?, Cost: 1) evalt16bb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalt16stop(ar_0, ar_1, ar_2, ar_3, ar_4)) 2.63/1.77 2.63/1.77 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalt16start(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ] 2.63/1.77 2.63/1.77 start location: koat_start 2.63/1.77 2.63/1.77 leaf cost: 0 2.63/1.77 2.63/1.77 2.63/1.77 2.63/1.77 Repeatedly propagating knowledge in problem 1 produces the following problem: 2.63/1.77 2.63/1.77 2: T: 2.63/1.77 2.63/1.77 (Comp: 1, Cost: 1) evalt16start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalt16bb0in(ar_0, ar_1, ar_2, ar_3, ar_4)) 2.63/1.77 2.63/1.77 (Comp: 1, Cost: 1) evalt16bb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalt16bb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_0 + 1 ] 2.63/1.77 2.63/1.77 (Comp: 1, Cost: 1) evalt16bb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalt16bb1in(ar_0, ar_2, ar_2, ar_3, ar_4)) [ ar_0 >= 0 ] 2.63/1.77 2.63/1.77 (Comp: ?, Cost: 1) evalt16bb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalt16bb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 + 1 ] 2.63/1.77 2.63/1.77 (Comp: ?, Cost: 1) evalt16bb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalt16bb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_1 ] 2.63/1.77 2.63/1.77 (Comp: ?, Cost: 1) evalt16bb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalt16bb3in(ar_0, ar_1, ar_2, ar_1 - ar_0 - 1, 2*ar_0 + 100)) 2.63/1.77 2.63/1.77 (Comp: ?, Cost: 1) evalt16bb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalt16bb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= 1 ] 2.63/1.77 2.63/1.77 (Comp: ?, Cost: 1) evalt16bb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalt16bb1in(ar_0, ar_3, ar_2, ar_3, ar_4)) [ 0 >= ar_4 ] 2.63/1.77 2.63/1.77 (Comp: ?, Cost: 1) evalt16bb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalt16bb3in(ar_0, ar_1, ar_2, ar_3, ar_4 - 1)) 2.63/1.77 2.63/1.77 (Comp: ?, Cost: 1) evalt16bb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalt16stop(ar_0, ar_1, ar_2, ar_3, ar_4)) 2.63/1.77 2.63/1.77 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalt16start(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ] 2.63/1.77 2.63/1.77 start location: koat_start 2.63/1.77 2.63/1.77 leaf cost: 0 2.63/1.77
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