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Complexity_C_Integer 2019-03-21 04.38 pair #429988940
details
property
value
status
complete
benchmark
Masse-VMCAI2014-Fig1a_true-termination.c
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n053.star.cs.uiowa.edu
space
Adapted_from_Stroeder_15
run statistics
property
value
solver
AProVE
configuration
c_complexity
runtime (wallclock)
1.56744 seconds
cpu usage
2.53151
user time
2.24984
system time
0.281663
max virtual memory
1.8273644E7
max residence set size
181080.0
stage attributes
key
value
starexec-result
WORST_CASE(?, O(n^3))
output
2.12/1.52 WORST_CASE(?, O(n^3)) 2.12/1.53 proof of /export/starexec/sandbox/output/output_files/bench.koat 2.12/1.53 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 2.12/1.53 2.12/1.53 2.12/1.53 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^3). 2.12/1.53 2.12/1.53 (0) CpxIntTrs 2.12/1.53 (1) Koat Proof [FINISHED, 284 ms] 2.12/1.53 (2) BOUNDS(1, n^3) 2.12/1.53 2.12/1.53 2.12/1.53 ---------------------------------------- 2.12/1.53 2.12/1.53 (0) 2.12/1.53 Obligation: 2.12/1.53 Complexity Int TRS consisting of the following rules: 2.12/1.53 eval_foo_start(v_.0, v_.01, v_a, v_b) -> Com_1(eval_foo_bb0_in(v_.0, v_.01, v_a, v_b)) :|: TRUE 2.12/1.53 eval_foo_bb0_in(v_.0, v_.01, v_a, v_b) -> Com_1(eval_foo_bb1_in(v_a, v_b, v_a, v_b)) :|: TRUE 2.12/1.53 eval_foo_bb1_in(v_.0, v_.01, v_a, v_b) -> Com_1(eval_foo_bb2_in(v_.0, v_.01, v_a, v_b)) :|: v_.0 >= 0 2.12/1.53 eval_foo_bb1_in(v_.0, v_.01, v_a, v_b) -> Com_1(eval_foo_bb3_in(v_.0, v_.01, v_a, v_b)) :|: v_.0 < 0 2.12/1.53 eval_foo_bb2_in(v_.0, v_.01, v_a, v_b) -> Com_1(eval_foo_bb1_in(v_.0 + v_.01, -(v_.01) - 1, v_a, v_b)) :|: v_.01 >= 0 2.12/1.53 eval_foo_bb2_in(v_.0, v_.01, v_a, v_b) -> Com_1(eval_foo_bb1_in(v_.0 + v_.01, -(v_.01), v_a, v_b)) :|: v_.01 < 0 2.12/1.53 eval_foo_bb3_in(v_.0, v_.01, v_a, v_b) -> Com_1(eval_foo_stop(v_.0, v_.01, v_a, v_b)) :|: TRUE 2.12/1.53 2.12/1.53 The start-symbols are:[eval_foo_start_4] 2.12/1.53 2.12/1.53 2.12/1.53 ---------------------------------------- 2.12/1.53 2.12/1.53 (1) Koat Proof (FINISHED) 2.12/1.53 YES(?, 198*ar_1 + 200*ar_1^2 + 228*ar_1*ar_3 + 64*ar_3^2 + 48*ar_1^3 + 96*ar_1^2*ar_3 + 60*ar_1*ar_3^2 + 12*ar_3^3 + 105*ar_3 + 63) 2.12/1.53 2.12/1.53 2.12/1.53 2.12/1.53 Initial complexity problem: 2.12/1.53 2.12/1.53 1: T: 2.12/1.53 2.12/1.53 (Comp: ?, Cost: 1) evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3)) 2.12/1.53 2.12/1.53 (Comp: ?, Cost: 1) evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3)) 2.12/1.53 2.12/1.53 (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 >= 0 ] 2.12/1.53 2.12/1.53 (Comp: ?, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 + 1 ] 2.12/1.53 2.12/1.53 (Comp: ?, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 + ar_2, ar_1, -ar_2 - 1, ar_3)) [ ar_2 >= 0 ] 2.12/1.53 2.12/1.53 (Comp: ?, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 + ar_2, ar_1, -ar_2, ar_3)) [ 0 >= ar_2 + 1 ] 2.12/1.54 2.12/1.54 (Comp: ?, Cost: 1) evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3)) 2.12/1.54 2.12/1.54 (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 ] 2.12/1.54 2.12/1.54 start location: koat_start 2.12/1.54 2.12/1.54 leaf cost: 0 2.12/1.54 2.12/1.54 2.12/1.54 2.12/1.54 Repeatedly propagating knowledge in problem 1 produces the following problem: 2.12/1.54 2.12/1.54 2: T: 2.12/1.54 2.12/1.54 (Comp: 1, Cost: 1) evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3)) 2.12/1.54 2.12/1.54 (Comp: 1, Cost: 1) evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3)) 2.12/1.54 2.12/1.54 (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 >= 0 ] 2.12/1.54 2.12/1.54 (Comp: ?, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 + 1 ] 2.12/1.54 2.12/1.54 (Comp: ?, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 + ar_2, ar_1, -ar_2 - 1, ar_3)) [ ar_2 >= 0 ] 2.12/1.54 2.12/1.54 (Comp: ?, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 + ar_2, ar_1, -ar_2, ar_3)) [ 0 >= ar_2 + 1 ] 2.12/1.54 2.12/1.54 (Comp: ?, Cost: 1) evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3)) 2.12/1.54 2.12/1.54 (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 ] 2.12/1.54 2.12/1.54 start location: koat_start 2.12/1.54 2.12/1.54 leaf cost: 0 2.12/1.54 2.12/1.54 2.12/1.54 2.12/1.54 A polynomial rank function with 2.12/1.54 2.12/1.54 Pol(evalfoostart) = 2 2.12/1.54 2.12/1.54 Pol(evalfoobb0in) = 2 2.12/1.54 2.12/1.54 Pol(evalfoobb1in) = 2 2.12/1.54 2.12/1.54 Pol(evalfoobb2in) = 2 2.12/1.54 2.12/1.54 Pol(evalfoobb3in) = 1 2.12/1.54 2.12/1.54 Pol(evalfoostop) = 0
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