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Complexity_C_Integer 2019-03-21 04.38 pair #429988848
details
property
value
status
complete
benchmark
t07.c
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n166.star.cs.uiowa.edu
space
C4B_examples
run statistics
property
value
solver
AProVE
configuration
c_complexity
runtime (wallclock)
1.527 seconds
cpu usage
2.5463
user time
2.36466
system time
0.181643
max virtual memory
1.8273644E7
max residence set size
184956.0
stage attributes
key
value
starexec-result
WORST_CASE(?, O(n^1))
output
2.29/1.49 WORST_CASE(?, O(n^1)) 2.29/1.50 proof of /export/starexec/sandbox2/output/output_files/bench.koat 2.29/1.50 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 2.29/1.50 2.29/1.50 2.29/1.50 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^1). 2.29/1.50 2.29/1.50 (0) CpxIntTrs 2.29/1.50 (1) Koat Proof [FINISHED, 178 ms] 2.29/1.50 (2) BOUNDS(1, n^1) 2.29/1.50 2.29/1.50 2.29/1.50 ---------------------------------------- 2.29/1.50 2.29/1.50 (0) 2.29/1.50 Obligation: 2.29/1.50 Complexity Int TRS consisting of the following rules: 2.29/1.50 eval_t07_start(v_.0, v_.01, v_.1, v_.2, v_x, v_y) -> Com_1(eval_t07_bb0_in(v_.0, v_.01, v_.1, v_.2, v_x, v_y)) :|: TRUE 2.29/1.50 eval_t07_bb0_in(v_.0, v_.01, v_.1, v_.2, v_x, v_y) -> Com_1(eval_t07_bb1_in(v_x, v_y, v_.1, v_.2, v_x, v_y)) :|: TRUE 2.29/1.50 eval_t07_bb1_in(v_.0, v_.01, v_.1, v_.2, v_x, v_y) -> Com_1(eval_t07_bb2_in(v_.0, v_.01, v_.1, v_.2, v_x, v_y)) :|: v_.0 > 0 2.29/1.50 eval_t07_bb1_in(v_.0, v_.01, v_.1, v_.2, v_x, v_y) -> Com_1(eval_t07_bb3_in(v_.0, v_.01, v_.01, v_.2, v_x, v_y)) :|: v_.0 <= 0 2.29/1.50 eval_t07_bb2_in(v_.0, v_.01, v_.1, v_.2, v_x, v_y) -> Com_1(eval_t07_bb1_in(v_.0 - 1, v_.01 + 2, v_.1, v_.2, v_x, v_y)) :|: TRUE 2.29/1.50 eval_t07_bb3_in(v_.0, v_.01, v_.1, v_.2, v_x, v_y) -> Com_1(eval_t07_bb4_in(v_.0, v_.01, v_.1, v_.2, v_x, v_y)) :|: v_.1 > 0 2.29/1.50 eval_t07_bb3_in(v_.0, v_.01, v_.1, v_.2, v_x, v_y) -> Com_1(eval_t07_bb5_in(v_.0, v_.01, v_.1, v_.1, v_x, v_y)) :|: v_.1 <= 0 2.29/1.50 eval_t07_bb4_in(v_.0, v_.01, v_.1, v_.2, v_x, v_y) -> Com_1(eval_t07_bb3_in(v_.0, v_.01, v_.1 - 1, v_.2, v_x, v_y)) :|: TRUE 2.29/1.50 eval_t07_bb5_in(v_.0, v_.01, v_.1, v_.2, v_x, v_y) -> Com_1(eval_t07_bb6_in(v_.0, v_.01, v_.1, v_.2, v_x, v_y)) :|: v_.2 > 0 2.29/1.50 eval_t07_bb5_in(v_.0, v_.01, v_.1, v_.2, v_x, v_y) -> Com_1(eval_t07_bb7_in(v_.0, v_.01, v_.1, v_.2, v_x, v_y)) :|: v_.2 <= 0 2.29/1.50 eval_t07_bb6_in(v_.0, v_.01, v_.1, v_.2, v_x, v_y) -> Com_1(eval_t07_bb5_in(v_.0, v_.01, v_.1, v_.2 - 1, v_x, v_y)) :|: TRUE 2.29/1.50 eval_t07_bb7_in(v_.0, v_.01, v_.1, v_.2, v_x, v_y) -> Com_1(eval_t07_stop(v_.0, v_.01, v_.1, v_.2, v_x, v_y)) :|: TRUE 2.29/1.50 2.29/1.50 The start-symbols are:[eval_t07_start_6] 2.29/1.50 2.29/1.50 2.29/1.50 ---------------------------------------- 2.29/1.50 2.29/1.50 (1) Koat Proof (FINISHED) 2.29/1.50 YES(?, 26*ar_1 + 24*ar_3 + 18) 2.29/1.50 2.29/1.50 2.29/1.50 2.29/1.50 Initial complexity problem: 2.29/1.50 2.29/1.50 1: T: 2.29/1.50 2.29/1.50 (Comp: ?, Cost: 1) evalt07start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 2.29/1.50 2.29/1.50 (Comp: ?, Cost: 1) evalt07bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb1in(ar_1, ar_1, ar_3, ar_3, ar_4, ar_5)) 2.29/1.50 2.29/1.50 (Comp: ?, Cost: 1) evalt07bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= 1 ] 2.29/1.50 2.29/1.50 (Comp: ?, Cost: 1) evalt07bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb3in(ar_0, ar_1, ar_2, ar_3, ar_2, ar_5)) [ 0 >= ar_0 ] 2.29/1.50 2.29/1.50 (Comp: ?, Cost: 1) evalt07bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb1in(ar_0 - 1, ar_1, ar_2 + 2, ar_3, ar_4, ar_5)) 2.29/1.50 2.29/1.50 (Comp: ?, Cost: 1) evalt07bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_4 >= 1 ] 2.29/1.50 2.29/1.50 (Comp: ?, Cost: 1) evalt07bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_4)) [ 0 >= ar_4 ] 2.29/1.50 2.29/1.50 (Comp: ?, Cost: 1) evalt07bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb3in(ar_0, ar_1, ar_2, ar_3, ar_4 - 1, ar_5)) 2.29/1.50 2.29/1.50 (Comp: ?, Cost: 1) evalt07bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_5 >= 1 ] 2.29/1.50 2.29/1.50 (Comp: ?, Cost: 1) evalt07bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 >= ar_5 ] 2.29/1.50 2.29/1.50 (Comp: ?, Cost: 1) evalt07bb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5 - 1)) 2.29/1.50 2.29/1.50 (Comp: ?, Cost: 1) evalt07bb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 2.29/1.50 2.29/1.50 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ] 2.29/1.50 2.29/1.50 start location: koat_start 2.29/1.50 2.29/1.50 leaf cost: 0 2.29/1.50 2.29/1.50 2.29/1.50 2.29/1.50 Testing for reachability in the complexity graph removes the following transitions from problem 1: 2.29/1.50 2.29/1.50 evalt07bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_5 >= 1 ] 2.29/1.50 2.29/1.50 evalt07bb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5 - 1)) 2.29/1.50 2.29/1.50 We thus obtain the following problem: 2.29/1.50 2.29/1.50 2: T: 2.29/1.50 2.29/1.50 (Comp: ?, Cost: 1) evalt07bb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 2.29/1.50 2.29/1.50 (Comp: ?, Cost: 1) evalt07bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 >= ar_5 ] 2.29/1.50 2.29/1.50 (Comp: ?, Cost: 1) evalt07bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb3in(ar_0, ar_1, ar_2, ar_3, ar_4 - 1, ar_5)) 2.29/1.50 2.29/1.50 (Comp: ?, Cost: 1) evalt07bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_4)) [ 0 >= ar_4 ] 2.29/1.50 2.29/1.50 (Comp: ?, Cost: 1) evalt07bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_4 >= 1 ] 2.29/1.50 2.29/1.50 (Comp: ?, Cost: 1) evalt07bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb1in(ar_0 - 1, ar_1, ar_2 + 2, ar_3, ar_4, ar_5)) 2.29/1.50 2.29/1.50 (Comp: ?, Cost: 1) evalt07bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb3in(ar_0, ar_1, ar_2, ar_3, ar_2, ar_5)) [ 0 >= ar_0 ] 2.29/1.50
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