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Complexity_C_Integer 2019-03-21 04.38 pair #429989136
details
property
value
status
complete
benchmark
svcomp_a.10.c
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n110.star.cs.uiowa.edu
space
Adapted_from_Stroeder_15
run statistics
property
value
solver
AProVE
configuration
c_complexity
runtime (wallclock)
1.42899 seconds
cpu usage
2.38725
user time
2.20658
system time
0.180673
max virtual memory
1.8273644E7
max residence set size
182552.0
stage attributes
key
value
starexec-result
WORST_CASE(?, O(n^2))
output
2.17/1.40 WORST_CASE(?, O(n^2)) 2.17/1.41 proof of /export/starexec/sandbox/output/output_files/bench.koat 2.17/1.41 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 2.17/1.41 2.17/1.41 2.17/1.41 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^2). 2.17/1.41 2.17/1.41 (0) CpxIntTrs 2.17/1.41 (1) Koat Proof [FINISHED, 88 ms] 2.17/1.41 (2) BOUNDS(1, n^2) 2.17/1.41 2.17/1.41 2.17/1.41 ---------------------------------------- 2.17/1.41 2.17/1.41 (0) 2.17/1.41 Obligation: 2.17/1.41 Complexity Int TRS consisting of the following rules: 2.17/1.41 eval_foo_start(v_.01, v_.02, v_c, v_x, v_y) -> Com_1(eval_foo_bb0_in(v_.01, v_.02, v_c, v_x, v_y)) :|: TRUE 2.17/1.41 eval_foo_bb0_in(v_.01, v_.02, v_c, v_x, v_y) -> Com_1(eval_foo_bb1_in(v_x, v_y, v_c, v_x, v_y)) :|: TRUE 2.17/1.41 eval_foo_bb1_in(v_.01, v_.02, v_c, v_x, v_y) -> Com_1(eval_foo_bb2_in(v_.01, v_.02, v_c, v_x, v_y)) :|: v_.01 < v_.02 2.17/1.41 eval_foo_bb1_in(v_.01, v_.02, v_c, v_x, v_y) -> Com_1(eval_foo_bb2_in(v_.01, v_.02, v_c, v_x, v_y)) :|: v_.01 > v_.02 2.17/1.41 eval_foo_bb1_in(v_.01, v_.02, v_c, v_x, v_y) -> Com_1(eval_foo_bb3_in(v_.01, v_.02, v_c, v_x, v_y)) :|: v_.01 >= v_.02 && v_.01 <= v_.02 2.17/1.41 eval_foo_bb2_in(v_.01, v_.02, v_c, v_x, v_y) -> Com_1(eval_foo_bb1_in(v_.01, v_.02 + 1, v_c, v_x, v_y)) :|: v_.01 > v_.02 2.17/1.41 eval_foo_bb2_in(v_.01, v_.02, v_c, v_x, v_y) -> Com_1(eval_foo_bb1_in(v_.01 + 1, v_.02 + 1, v_c, v_x, v_y)) :|: v_.01 > v_.02 && v_.01 <= v_.02 2.17/1.41 eval_foo_bb2_in(v_.01, v_.02, v_c, v_x, v_y) -> Com_1(eval_foo_bb1_in(v_.01, v_.02, v_c, v_x, v_y)) :|: v_.01 <= v_.02 && v_.01 > v_.02 2.17/1.41 eval_foo_bb2_in(v_.01, v_.02, v_c, v_x, v_y) -> Com_1(eval_foo_bb1_in(v_.01 + 1, v_.02, v_c, v_x, v_y)) :|: v_.01 <= v_.02 2.17/1.41 eval_foo_bb3_in(v_.01, v_.02, v_c, v_x, v_y) -> Com_1(eval_foo_stop(v_.01, v_.02, v_c, v_x, v_y)) :|: TRUE 2.17/1.41 2.17/1.41 The start-symbols are:[eval_foo_start_5] 2.17/1.41 2.17/1.41 2.17/1.41 ---------------------------------------- 2.17/1.41 2.17/1.41 (1) Koat Proof (FINISHED) 2.17/1.41 YES(?, 24*ar_1^2 + 56*ar_1*ar_3 + 32*ar_3^2 + 176*ar_1 + 184*ar_3 + 154) 2.17/1.41 2.17/1.41 2.17/1.41 2.17/1.41 Initial complexity problem: 2.17/1.41 2.17/1.41 1: T: 2.17/1.41 2.17/1.41 (Comp: ?, Cost: 1) evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3)) 2.17/1.41 2.17/1.41 (Comp: ?, Cost: 1) evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3)) 2.17/1.41 2.17/1.41 (Comp: ?, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 + 1 ] 2.17/1.41 2.17/1.41 (Comp: ?, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_2 + 1 ] 2.17/1.41 2.17/1.41 (Comp: ?, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 = ar_2 ] 2.17/1.41 2.17/1.41 (Comp: ?, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_0 >= ar_2 + 1 ] 2.17/1.41 2.17/1.41 (Comp: ?, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 + 1, ar_1, ar_2 + 1, ar_3)) [ ar_0 >= ar_2 + 1 /\ ar_2 >= ar_0 ] 2.17/1.41 2.17/1.41 (Comp: ?, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 /\ ar_0 >= ar_2 + 1 ] 2.17/1.41 2.17/1.41 (Comp: ?, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 + 1, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 ] 2.17/1.41 2.17/1.41 (Comp: ?, Cost: 1) evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3)) 2.17/1.41 2.17/1.41 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ] 2.17/1.41 2.17/1.41 start location: koat_start 2.17/1.41 2.17/1.41 leaf cost: 0 2.17/1.41 2.17/1.41 2.17/1.41 2.17/1.41 Testing for reachability in the complexity graph removes the following transitions from problem 1: 2.17/1.41 2.17/1.41 evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 + 1, ar_1, ar_2 + 1, ar_3)) [ ar_0 >= ar_2 + 1 /\ ar_2 >= ar_0 ] 2.17/1.41 2.17/1.41 evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 /\ ar_0 >= ar_2 + 1 ] 2.17/1.41 2.17/1.41 We thus obtain the following problem: 2.17/1.41 2.17/1.41 2: T: 2.17/1.41 2.17/1.41 (Comp: ?, Cost: 1) evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3)) 2.17/1.41 2.17/1.41 (Comp: ?, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_0 >= ar_2 + 1 ] 2.17/1.41 2.17/1.41 (Comp: ?, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 + 1, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 ] 2.17/1.41 2.17/1.41 (Comp: ?, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 = ar_2 ] 2.17/1.41 2.17/1.41 (Comp: ?, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_2 + 1 ] 2.17/1.41 2.17/1.41 (Comp: ?, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 + 1 ] 2.17/1.41 2.17/1.41 (Comp: ?, Cost: 1) evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3)) 2.17/1.41 2.17/1.41 (Comp: ?, Cost: 1) evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3)) 2.17/1.41 2.17/1.41 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ] 2.17/1.41 2.17/1.41 start location: koat_start 2.17/1.41
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