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Complexity_C_Integer 2019-03-21 04.38 pair #429988852
details
property
value
status
complete
benchmark
gcd.c
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n082.star.cs.uiowa.edu
space
C4B_examples
run statistics
property
value
solver
AProVE
configuration
c_complexity
runtime (wallclock)
1.85642 seconds
cpu usage
2.54051
user time
2.30371
system time
0.236806
max virtual memory
1.8273644E7
max residence set size
181856.0
stage attributes
key
value
starexec-result
WORST_CASE(?, O(n^1))
output
2.18/1.50 WORST_CASE(?, O(n^1)) 2.18/1.51 proof of /export/starexec/sandbox/output/output_files/bench.koat 2.18/1.51 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 2.18/1.51 2.18/1.51 2.18/1.51 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^1). 2.18/1.51 2.18/1.51 (0) CpxIntTrs 2.18/1.51 (1) Koat Proof [FINISHED, 278 ms] 2.18/1.51 (2) BOUNDS(1, n^1) 2.18/1.51 2.18/1.51 2.18/1.51 ---------------------------------------- 2.18/1.51 2.18/1.51 (0) 2.18/1.51 Obligation: 2.18/1.51 Complexity Int TRS consisting of the following rules: 2.18/1.51 eval_gcd_start(v_.0, v_.01, v_x, v_y) -> Com_1(eval_gcd_bb0_in(v_.0, v_.01, v_x, v_y)) :|: TRUE 2.18/1.51 eval_gcd_bb0_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_gcd_bb1_in(v_x, v_y, v_x, v_y)) :|: TRUE 2.18/1.51 eval_gcd_bb1_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_gcd_bb2_in(v_.0, v_.01, v_x, v_y)) :|: v_.0 > 0 && v_.01 > 0 2.18/1.51 eval_gcd_bb1_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_gcd_bb3_in(v_.0, v_.01, v_x, v_y)) :|: v_.0 <= 0 2.18/1.51 eval_gcd_bb1_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_gcd_bb3_in(v_.0, v_.01, v_x, v_y)) :|: v_.01 <= 0 2.18/1.51 eval_gcd_bb2_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_gcd_bb1_in(v_.0 - v_.01, v_.01, v_x, v_y)) :|: v_.0 > v_.01 2.18/1.51 eval_gcd_bb2_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_gcd_bb1_in(v_.0, v_.01, v_x, v_y)) :|: v_.0 > v_.01 && v_.0 <= v_.01 2.18/1.51 eval_gcd_bb2_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_gcd_bb1_in(v_.0 - v_.01, v_.01 - v_.0, v_x, v_y)) :|: v_.0 <= v_.01 && v_.0 > v_.01 2.18/1.51 eval_gcd_bb2_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_gcd_bb1_in(v_.0, v_.01 - v_.0, v_x, v_y)) :|: v_.0 <= v_.01 2.18/1.51 eval_gcd_bb3_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_gcd_stop(v_.0, v_.01, v_x, v_y)) :|: TRUE 2.18/1.51 2.18/1.51 The start-symbols are:[eval_gcd_start_4] 2.18/1.51 2.18/1.51 2.18/1.51 ---------------------------------------- 2.18/1.51 2.18/1.51 (1) Koat Proof (FINISHED) 2.18/1.51 YES(?, 6*ar_1 + 6*ar_3 + 8) 2.18/1.51 2.18/1.51 2.18/1.51 2.18/1.51 Initial complexity problem: 2.18/1.51 2.18/1.51 1: T: 2.18/1.51 2.18/1.51 (Comp: ?, Cost: 1) evalgcdstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalgcdbb0in(ar_0, ar_1, ar_2, ar_3)) 2.18/1.51 2.18/1.51 (Comp: ?, Cost: 1) evalgcdbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalgcdbb1in(ar_1, ar_1, ar_3, ar_3)) 2.18/1.51 2.18/1.51 (Comp: ?, Cost: 1) evalgcdbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalgcdbb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 1 /\ ar_2 >= 1 ] 2.18/1.51 2.18/1.51 (Comp: ?, Cost: 1) evalgcdbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalgcdbb3in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ] 2.18/1.51 2.18/1.51 (Comp: ?, Cost: 1) evalgcdbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalgcdbb3in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 ] 2.18/1.51 2.18/1.51 (Comp: ?, Cost: 1) evalgcdbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalgcdbb1in(ar_0 - ar_2, ar_1, ar_2, ar_3)) [ ar_0 >= ar_2 + 1 ] 2.18/1.51 2.18/1.51 (Comp: ?, Cost: 1) evalgcdbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalgcdbb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_2 + 1 /\ ar_2 >= ar_0 ] 2.18/1.51 2.18/1.51 (Comp: ?, Cost: 1) evalgcdbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalgcdbb1in(ar_0 - ar_2, ar_1, ar_2 - ar_0, ar_3)) [ ar_2 >= ar_0 /\ ar_0 >= ar_2 + 1 ] 2.18/1.51 2.18/1.51 (Comp: ?, Cost: 1) evalgcdbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalgcdbb1in(ar_0, ar_1, ar_2 - ar_0, ar_3)) [ ar_2 >= ar_0 ] 2.18/1.51 2.18/1.51 (Comp: ?, Cost: 1) evalgcdbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalgcdstop(ar_0, ar_1, ar_2, ar_3)) 2.18/1.51 2.18/1.51 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalgcdstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ] 2.18/1.51 2.18/1.51 start location: koat_start 2.18/1.51 2.18/1.51 leaf cost: 0 2.18/1.51 2.18/1.51 2.18/1.51 2.18/1.51 Testing for reachability in the complexity graph removes the following transitions from problem 1: 2.18/1.51 2.18/1.51 evalgcdbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalgcdbb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_2 + 1 /\ ar_2 >= ar_0 ] 2.18/1.51 2.18/1.51 evalgcdbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalgcdbb1in(ar_0 - ar_2, ar_1, ar_2 - ar_0, ar_3)) [ ar_2 >= ar_0 /\ ar_0 >= ar_2 + 1 ] 2.18/1.51 2.18/1.51 We thus obtain the following problem: 2.18/1.51 2.18/1.51 2: T: 2.18/1.51 2.18/1.51 (Comp: ?, Cost: 1) evalgcdbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalgcdstop(ar_0, ar_1, ar_2, ar_3)) 2.18/1.51 2.18/1.51 (Comp: ?, Cost: 1) evalgcdbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalgcdbb1in(ar_0, ar_1, ar_2 - ar_0, ar_3)) [ ar_2 >= ar_0 ] 2.18/1.51 2.18/1.51 (Comp: ?, Cost: 1) evalgcdbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalgcdbb1in(ar_0 - ar_2, ar_1, ar_2, ar_3)) [ ar_0 >= ar_2 + 1 ] 2.18/1.51 2.18/1.51 (Comp: ?, Cost: 1) evalgcdbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalgcdbb3in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 ] 2.18/1.51 2.18/1.51 (Comp: ?, Cost: 1) evalgcdbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalgcdbb3in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ] 2.18/1.51 2.18/1.51 (Comp: ?, Cost: 1) evalgcdbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalgcdbb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 1 /\ ar_2 >= 1 ] 2.18/1.51 2.18/1.51 (Comp: ?, Cost: 1) evalgcdbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalgcdbb1in(ar_1, ar_1, ar_3, ar_3)) 2.18/1.51 2.18/1.51 (Comp: ?, Cost: 1) evalgcdstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalgcdbb0in(ar_0, ar_1, ar_2, ar_3)) 2.18/1.51 2.18/1.51 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalgcdstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ] 2.18/1.51 2.18/1.51 start location: koat_start 2.18/1.51
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