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Complexity_C_Integer 2019-03-21 04.38 pair #429988968
details
property
value
status
complete
benchmark
GCD4.c
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n086.star.cs.uiowa.edu
space
Adapted_from_Stroeder_15
run statistics
property
value
solver
AProVE
configuration
c_complexity
runtime (wallclock)
1.41523 seconds
cpu usage
2.36838
user time
2.19616
system time
0.172224
max virtual memory
1.8273644E7
max residence set size
181660.0
stage attributes
key
value
starexec-result
WORST_CASE(?, ?)
output
2.09/1.38 WORST_CASE(?, ?) 2.09/1.39 proof of /export/starexec/sandbox/output/output_files/bench.koat 2.09/1.39 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 2.09/1.39 2.09/1.39 2.09/1.39 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, EXP). 2.09/1.39 2.09/1.39 (0) CpxIntTrs 2.09/1.39 (1) Koat Proof [FINISHED, 178 ms] 2.09/1.39 (2) BOUNDS(1, EXP) 2.09/1.39 2.09/1.39 2.09/1.39 ---------------------------------------- 2.09/1.39 2.09/1.39 (0) 2.09/1.39 Obligation: 2.09/1.39 Complexity Int TRS consisting of the following rules: 2.09/1.39 eval_foo_start(v_.0, v_.01, v_.02, v_tmp, v_x, v_xtmp, v_y) -> Com_1(eval_foo_bb0_in(v_.0, v_.01, v_.02, v_tmp, v_x, v_xtmp, v_y)) :|: TRUE 2.09/1.39 eval_foo_bb0_in(v_.0, v_.01, v_.02, v_tmp, v_x, v_xtmp, v_y) -> Com_1(eval_foo_bb1_in(v_x, v_y, v_.02, v_tmp, v_x, v_xtmp, v_y)) :|: TRUE 2.09/1.39 eval_foo_bb1_in(v_.0, v_.01, v_.02, v_tmp, v_x, v_xtmp, v_y) -> Com_1(eval_foo_bb2_in(v_.0, v_.01, v_.0, v_tmp, v_x, v_xtmp, v_y)) :|: v_.01 > 0 && v_.0 > 0 2.09/1.39 eval_foo_bb1_in(v_.0, v_.01, v_.02, v_tmp, v_x, v_xtmp, v_y) -> Com_1(eval_foo_bb4_in(v_.0, v_.01, v_.02, v_tmp, v_x, v_xtmp, v_y)) :|: v_.01 <= 0 2.09/1.39 eval_foo_bb1_in(v_.0, v_.01, v_.02, v_tmp, v_x, v_xtmp, v_y) -> Com_1(eval_foo_bb4_in(v_.0, v_.01, v_.02, v_tmp, v_x, v_xtmp, v_y)) :|: v_.0 <= 0 2.09/1.39 eval_foo_bb2_in(v_.0, v_.01, v_.02, v_tmp, v_x, v_xtmp, v_y) -> Com_1(eval_foo_bb3_in(v_.0, v_.01, v_.02, v_tmp, v_x, v_xtmp, v_y)) :|: v_.02 >= v_.01 && v_.01 > 0 2.09/1.39 eval_foo_bb2_in(v_.0, v_.01, v_.02, v_tmp, v_x, v_xtmp, v_y) -> Com_1(eval_foo_bb1_in(v_.01, v_.02, v_.02, v_tmp, v_x, v_xtmp, v_y)) :|: v_.02 < v_.01 2.09/1.39 eval_foo_bb2_in(v_.0, v_.01, v_.02, v_tmp, v_x, v_xtmp, v_y) -> Com_1(eval_foo_bb1_in(v_.01, v_.02, v_.02, v_tmp, v_x, v_xtmp, v_y)) :|: v_.01 <= 0 2.09/1.39 eval_foo_bb3_in(v_.0, v_.01, v_.02, v_tmp, v_x, v_xtmp, v_y) -> Com_1(eval_foo_bb2_in(v_.0, v_.01, v_.02 - v_.01, v_tmp, v_x, v_xtmp, v_y)) :|: TRUE 2.09/1.39 eval_foo_bb4_in(v_.0, v_.01, v_.02, v_tmp, v_x, v_xtmp, v_y) -> Com_1(eval_foo_stop(v_.0, v_.01, v_.02, v_tmp, v_x, v_xtmp, v_y)) :|: TRUE 2.09/1.39 2.09/1.39 The start-symbols are:[eval_foo_start_7] 2.09/1.39 2.09/1.39 2.09/1.39 ---------------------------------------- 2.09/1.39 2.09/1.39 (1) Koat Proof (FINISHED) 2.09/1.39 YES(?, 4 * pow(2, ar_1 + ar_3) * (ar_1^2 + 2*ar_1*ar_3 + ar_3^2) + 5*ar_1 + 5*ar_3 + 11) 2.09/1.39 2.09/1.39 2.09/1.39 2.09/1.39 Initial complexity problem: 2.09/1.39 2.09/1.39 1: T: 2.09/1.39 2.09/1.39 (Comp: ?, Cost: 1) evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4)) 2.09/1.39 2.09/1.39 (Comp: ?, Cost: 1) evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3, ar_4)) 2.09/1.39 2.09/1.39 (Comp: ?, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_0)) [ ar_2 >= 1 /\ ar_0 >= 1 ] 2.09/1.39 2.09/1.39 (Comp: ?, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_2 ] 2.09/1.39 2.09/1.39 (Comp: ?, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_0 ] 2.09/1.39 2.09/1.39 (Comp: ?, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_2 /\ ar_2 >= 1 ] 2.09/1.39 2.09/1.39 (Comp: ?, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_2, ar_1, ar_4, ar_3, ar_4)) [ ar_2 >= ar_4 + 1 ] 2.09/1.39 2.09/1.39 (Comp: ?, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_2, ar_1, ar_4, ar_3, ar_4)) [ 0 >= ar_2 ] 2.09/1.39 2.09/1.39 (Comp: ?, Cost: 1) evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4 - ar_2)) 2.09/1.39 2.09/1.39 (Comp: ?, Cost: 1) evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_4)) 2.09/1.39 2.09/1.39 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ] 2.09/1.39 2.09/1.39 start location: koat_start 2.09/1.39 2.09/1.39 leaf cost: 0 2.09/1.39 2.09/1.39 2.09/1.39 2.09/1.39 Repeatedly propagating knowledge in problem 1 produces the following problem: 2.09/1.39 2.09/1.39 2: T: 2.09/1.39 2.09/1.39 (Comp: 1, Cost: 1) evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4)) 2.09/1.39 2.09/1.39 (Comp: 1, Cost: 1) evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3, ar_4)) 2.09/1.39 2.09/1.39 (Comp: ?, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_0)) [ ar_2 >= 1 /\ ar_0 >= 1 ] 2.09/1.39 2.09/1.39 (Comp: ?, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_2 ] 2.09/1.39 2.09/1.39 (Comp: ?, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_0 ] 2.09/1.39 2.09/1.39 (Comp: ?, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_2 /\ ar_2 >= 1 ] 2.09/1.39 2.09/1.39 (Comp: ?, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_2, ar_1, ar_4, ar_3, ar_4)) [ ar_2 >= ar_4 + 1 ] 2.09/1.39 2.09/1.39 (Comp: ?, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_2, ar_1, ar_4, ar_3, ar_4)) [ 0 >= ar_2 ] 2.09/1.39 2.09/1.39 (Comp: ?, Cost: 1) evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4 - ar_2)) 2.09/1.39 2.09/1.39 (Comp: ?, Cost: 1) evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_4)) 2.09/1.39 2.09/1.39 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ] 2.09/1.39 2.09/1.39 start location: koat_start 2.09/1.39 2.09/1.39 leaf cost: 0 2.09/1.39
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