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Complexity_C_Integer 2019-03-21 04.38 pair #429989364
details
property
value
status
complete
benchmark
Masse-VMCAI2014-Ex6_true-termination.c
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n167.star.cs.uiowa.edu
space
Adapted_from_Stroeder_15
run statistics
property
value
solver
AProVE
configuration
c_complexity
runtime (wallclock)
1.57809 seconds
cpu usage
2.54946
user time
2.31545
system time
0.234009
max virtual memory
1.8273644E7
max residence set size
182368.0
stage attributes
key
value
starexec-result
WORST_CASE(?, O(n^3))
output
2.48/1.55 WORST_CASE(?, O(n^3)) 2.48/1.56 proof of /export/starexec/sandbox/output/output_files/bench.koat 2.48/1.56 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 2.48/1.56 2.48/1.56 2.48/1.56 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^3). 2.48/1.56 2.48/1.56 (0) CpxIntTrs 2.48/1.56 (1) Koat Proof [FINISHED, 274 ms] 2.48/1.56 (2) BOUNDS(1, n^3) 2.48/1.56 2.48/1.56 2.48/1.56 ---------------------------------------- 2.48/1.56 2.48/1.56 (0) 2.48/1.56 Obligation: 2.48/1.56 Complexity Int TRS consisting of the following rules: 2.48/1.56 eval_foo_start(v_.0, v_.01, v_x, v_y) -> Com_1(eval_foo_bb0_in(v_.0, v_.01, v_x, v_y)) :|: TRUE 2.48/1.56 eval_foo_bb0_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_foo_bb1_in(v_x, v_y, v_x, v_y)) :|: TRUE 2.48/1.56 eval_foo_bb1_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_foo_bb2_in(v_.0, v_.01, v_x, v_y)) :|: v_.0 >= 0 2.48/1.56 eval_foo_bb1_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_foo_bb3_in(v_.0, v_.01, v_x, v_y)) :|: v_.0 < 0 2.48/1.56 eval_foo_bb2_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_foo_bb1_in(v_.0 + v_.01, v_.01 - 1, v_x, v_y)) :|: v_.01 >= 0 2.48/1.56 eval_foo_bb2_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_foo_bb1_in(v_.0 + v_.01, v_.01, v_x, v_y)) :|: v_.01 < 0 2.48/1.56 eval_foo_bb3_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_foo_stop(v_.0, v_.01, v_x, v_y)) :|: TRUE 2.48/1.56 2.48/1.56 The start-symbols are:[eval_foo_start_4] 2.48/1.56 2.48/1.56 2.48/1.56 ---------------------------------------- 2.48/1.56 2.48/1.56 (1) Koat Proof (FINISHED) 2.48/1.56 YES(?, 8*ar_1 + 4*ar_1*ar_3 + 16*ar_3^2 + 4*ar_3^3 + 25*ar_3 + 23) 2.48/1.56 2.48/1.56 2.48/1.56 2.48/1.56 Initial complexity problem: 2.48/1.56 2.48/1.56 1: T: 2.48/1.56 2.48/1.56 (Comp: ?, Cost: 1) evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3)) 2.48/1.56 2.48/1.56 (Comp: ?, Cost: 1) evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3)) 2.48/1.56 2.48/1.56 (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 ] 2.48/1.56 2.48/1.56 (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 ] 2.48/1.56 2.48/1.56 (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 ] 2.48/1.56 2.48/1.56 (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 ] 2.48/1.56 2.48/1.56 (Comp: ?, Cost: 1) evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3)) 2.48/1.56 2.48/1.56 (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 ] 2.48/1.56 2.48/1.56 start location: koat_start 2.48/1.56 2.48/1.56 leaf cost: 0 2.48/1.56 2.48/1.56 2.48/1.56 2.48/1.56 Repeatedly propagating knowledge in problem 1 produces the following problem: 2.48/1.56 2.48/1.56 2: T: 2.48/1.56 2.48/1.56 (Comp: 1, Cost: 1) evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3)) 2.48/1.56 2.48/1.56 (Comp: 1, Cost: 1) evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3)) 2.48/1.56 2.48/1.56 (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 ] 2.48/1.56 2.48/1.56 (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 ] 2.48/1.56 2.48/1.56 (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 ] 2.48/1.56 2.48/1.56 (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 ] 2.48/1.56 2.48/1.56 (Comp: ?, Cost: 1) evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3)) 2.48/1.56 2.48/1.56 (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 ] 2.48/1.56 2.48/1.56 start location: koat_start 2.48/1.56 2.48/1.56 leaf cost: 0 2.48/1.56 2.48/1.56 2.48/1.56 2.48/1.56 A polynomial rank function with 2.48/1.56 2.48/1.56 Pol(evalfoostart) = 2 2.48/1.56 2.48/1.56 Pol(evalfoobb0in) = 2 2.48/1.56 2.48/1.56 Pol(evalfoobb1in) = 2 2.48/1.56 2.48/1.56 Pol(evalfoobb2in) = 2 2.48/1.56 2.48/1.56 Pol(evalfoobb3in) = 1 2.48/1.56 2.48/1.56 Pol(evalfoostop) = 0
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