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Complexity_C_Integer 2019-03-21 04.38 pair #429989478
details
property
value
status
complete
benchmark
Gothenburg_true-termination.c
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n093.star.cs.uiowa.edu
space
Adapted_from_Stroeder_15
run statistics
property
value
solver
AProVE
configuration
c_complexity
runtime (wallclock)
1.75062 seconds
cpu usage
2.84796
user time
2.58665
system time
0.261309
max virtual memory
1.8534916E7
max residence set size
180988.0
stage attributes
key
value
starexec-result
WORST_CASE(?, O(n^2))
output
2.70/1.71 WORST_CASE(?, O(n^2)) 2.70/1.72 proof of /export/starexec/sandbox/output/output_files/bench.koat 2.70/1.72 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 2.70/1.72 2.70/1.72 2.70/1.72 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^2). 2.70/1.72 2.70/1.72 (0) CpxIntTrs 2.70/1.72 (1) Koat Proof [FINISHED, 578 ms] 2.70/1.72 (2) BOUNDS(1, n^2) 2.70/1.72 2.70/1.72 2.70/1.72 ---------------------------------------- 2.70/1.72 2.70/1.72 (0) 2.70/1.72 Obligation: 2.70/1.72 Complexity Int TRS consisting of the following rules: 2.70/1.72 eval_foo_start(v_.0, v_.01, v_a, v_b, v_x, v_y) -> Com_1(eval_foo_bb0_in(v_.0, v_.01, v_a, v_b, v_x, v_y)) :|: TRUE 2.70/1.72 eval_foo_bb0_in(v_.0, v_.01, v_a, v_b, v_x, v_y) -> Com_1(eval_foo_bb1_in(v_x, v_y, v_a, v_b, v_x, v_y)) :|: v_a >= v_b && v_a <= v_b 2.70/1.72 eval_foo_bb0_in(v_.0, v_.01, v_a, v_b, v_x, v_y) -> Com_1(eval_foo_bb3_in(v_.0, v_.01, v_a, v_b, v_x, v_y)) :|: v_a < v_b 2.70/1.72 eval_foo_bb0_in(v_.0, v_.01, v_a, v_b, v_x, v_y) -> Com_1(eval_foo_bb3_in(v_.0, v_.01, v_a, v_b, v_x, v_y)) :|: v_a > v_b 2.70/1.72 eval_foo_bb1_in(v_.0, v_.01, v_a, v_b, v_x, v_y) -> Com_1(eval_foo_bb2_in(v_.0, v_.01, v_a, v_b, v_x, v_y)) :|: v_.0 >= 0 2.70/1.72 eval_foo_bb1_in(v_.0, v_.01, v_a, v_b, v_x, v_y) -> Com_1(eval_foo_bb2_in(v_.0, v_.01, v_a, v_b, v_x, v_y)) :|: v_.01 >= 0 2.70/1.72 eval_foo_bb1_in(v_.0, v_.01, v_a, v_b, v_x, v_y) -> Com_1(eval_foo_bb3_in(v_.0, v_.01, v_a, v_b, v_x, v_y)) :|: v_.0 < 0 && v_.01 < 0 2.70/1.72 eval_foo_bb2_in(v_.0, v_.01, v_a, v_b, v_x, v_y) -> Com_1(eval_foo_bb1_in(v_.0 + v_a - v_b - 1, v_.01 + v_b - v_a - 1, v_a, v_b, v_x, v_y)) :|: TRUE 2.70/1.72 eval_foo_bb3_in(v_.0, v_.01, v_a, v_b, v_x, v_y) -> Com_1(eval_foo_stop(v_.0, v_.01, v_a, v_b, v_x, v_y)) :|: TRUE 2.70/1.72 2.70/1.72 The start-symbols are:[eval_foo_start_6] 2.70/1.72 2.70/1.72 2.70/1.72 ---------------------------------------- 2.70/1.72 2.70/1.72 (1) Koat Proof (FINISHED) 2.70/1.72 YES(?, 4*ar_3 + 2*ar_3*ar_5 + 2*ar_5^2 + 10*ar_5 + 18) 2.70/1.72 2.70/1.72 2.70/1.72 2.70/1.72 Initial complexity problem: 2.70/1.72 2.70/1.72 1: T: 2.70/1.72 2.70/1.72 (Comp: ?, Cost: 1) evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 2.70/1.72 2.70/1.72 (Comp: ?, Cost: 1) evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_3, ar_3, ar_5, ar_5)) [ ar_0 = ar_1 ] 2.70/1.72 2.70/1.72 (Comp: ?, Cost: 1) evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_1 >= ar_0 + 1 ] 2.70/1.72 2.70/1.72 (Comp: ?, Cost: 1) evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= ar_1 + 1 ] 2.70/1.72 2.70/1.72 (Comp: ?, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 >= 0 ] 2.70/1.72 2.70/1.72 (Comp: ?, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_4 >= 0 ] 2.70/1.72 2.70/1.72 (Comp: ?, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 >= ar_2 + 1 /\ 0 >= ar_4 + 1 ] 2.70/1.72 2.70/1.72 (Comp: ?, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 + ar_0 - ar_1 - 1, ar_3, ar_4 + ar_1 - ar_0 - 1, ar_5)) 2.70/1.72 2.70/1.72 (Comp: ?, Cost: 1) evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 2.70/1.72 2.70/1.72 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ] 2.70/1.72 2.70/1.72 start location: koat_start 2.70/1.72 2.70/1.72 leaf cost: 0 2.70/1.72 2.70/1.72 2.70/1.72 2.70/1.72 Repeatedly propagating knowledge in problem 1 produces the following problem: 2.70/1.72 2.70/1.72 2: T: 2.70/1.72 2.70/1.72 (Comp: 1, Cost: 1) evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 2.70/1.72 2.70/1.72 (Comp: 1, Cost: 1) evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_3, ar_3, ar_5, ar_5)) [ ar_0 = ar_1 ] 2.70/1.72 2.70/1.72 (Comp: 1, Cost: 1) evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_1 >= ar_0 + 1 ] 2.70/1.72 2.70/1.72 (Comp: 1, Cost: 1) evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= ar_1 + 1 ] 2.70/1.72 2.70/1.72 (Comp: ?, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 >= 0 ] 2.70/1.72 2.70/1.72 (Comp: ?, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_4 >= 0 ] 2.70/1.72 2.70/1.72 (Comp: ?, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 >= ar_2 + 1 /\ 0 >= ar_4 + 1 ] 2.70/1.72 2.70/1.72 (Comp: ?, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 + ar_0 - ar_1 - 1, ar_3, ar_4 + ar_1 - ar_0 - 1, ar_5)) 2.70/1.72 2.70/1.72 (Comp: ?, Cost: 1) evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 2.70/1.72 2.70/1.72 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ] 2.70/1.72 2.70/1.72 start location: koat_start 2.70/1.72 2.70/1.72 leaf cost: 0 2.70/1.72 2.70/1.72 2.70/1.72 2.70/1.72 A polynomial rank function with 2.70/1.72 2.70/1.72 Pol(evalfoostart) = 2
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