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Complexity_C_Integer 2019-03-21 04.38 pair #429989316
details
property
value
status
complete
benchmark
AliasDarteFeautrierGonnord-SAS2010-cousot9_true-termination.c
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n081.star.cs.uiowa.edu
space
Adapted_from_Stroeder_15
run statistics
property
value
solver
AProVE
configuration
c_complexity
runtime (wallclock)
1.45823 seconds
cpu usage
2.43719
user time
2.23346
system time
0.203733
max virtual memory
1.8273644E7
max residence set size
180644.0
stage attributes
key
value
starexec-result
WORST_CASE(?, O(n^2))
output
2.12/1.43 WORST_CASE(?, O(n^2)) 2.39/1.44 proof of /export/starexec/sandbox/output/output_files/bench.koat 2.39/1.44 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 2.39/1.44 2.39/1.44 2.39/1.44 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^2). 2.39/1.44 2.39/1.44 (0) CpxIntTrs 2.39/1.44 (1) Koat Proof [FINISHED, 269 ms] 2.39/1.44 (2) BOUNDS(1, n^2) 2.39/1.44 2.39/1.44 2.39/1.44 ---------------------------------------- 2.39/1.44 2.39/1.44 (0) 2.39/1.44 Obligation: 2.39/1.44 Complexity Int TRS consisting of the following rules: 2.39/1.44 eval_foo_start(v_.0, v_.01, v_N, v_i, v_j) -> Com_1(eval_foo_bb0_in(v_.0, v_.01, v_N, v_i, v_j)) :|: TRUE 2.39/1.44 eval_foo_bb0_in(v_.0, v_.01, v_N, v_i, v_j) -> Com_1(eval_foo_bb1_in(v_N, v_j, v_N, v_i, v_j)) :|: TRUE 2.39/1.44 eval_foo_bb1_in(v_.0, v_.01, v_N, v_i, v_j) -> Com_1(eval_foo_bb2_in(v_.0, v_.01, v_N, v_i, v_j)) :|: v_.0 > 0 2.39/1.44 eval_foo_bb1_in(v_.0, v_.01, v_N, v_i, v_j) -> Com_1(eval_foo_bb3_in(v_.0, v_.01, v_N, v_i, v_j)) :|: v_.0 <= 0 2.39/1.44 eval_foo_bb2_in(v_.0, v_.01, v_N, v_i, v_j) -> Com_1(eval_foo_bb1_in(v_.0, v_.01 - 1, v_N, v_i, v_j)) :|: v_.01 > 0 2.39/1.44 eval_foo_bb2_in(v_.0, v_.01, v_N, v_i, v_j) -> Com_1(eval_foo_bb1_in(v_.0 - 1, v_.01 - 1, v_N, v_i, v_j)) :|: v_.01 > 0 && v_.01 <= 0 2.39/1.44 eval_foo_bb2_in(v_.0, v_.01, v_N, v_i, v_j) -> Com_1(eval_foo_bb1_in(v_.0, v_N, v_N, v_i, v_j)) :|: v_.01 <= 0 && v_.01 > 0 2.39/1.44 eval_foo_bb2_in(v_.0, v_.01, v_N, v_i, v_j) -> Com_1(eval_foo_bb1_in(v_.0 - 1, v_N, v_N, v_i, v_j)) :|: v_.01 <= 0 2.39/1.44 eval_foo_bb3_in(v_.0, v_.01, v_N, v_i, v_j) -> Com_1(eval_foo_stop(v_.0, v_.01, v_N, v_i, v_j)) :|: TRUE 2.39/1.44 2.39/1.44 The start-symbols are:[eval_foo_start_5] 2.39/1.44 2.39/1.44 2.39/1.44 ---------------------------------------- 2.39/1.44 2.39/1.44 (1) Koat Proof (FINISHED) 2.39/1.44 YES(?, 2*ar_1 + 2*ar_1^2 + 2*ar_3 + 7) 2.39/1.44 2.39/1.44 2.39/1.44 2.39/1.44 Initial complexity problem: 2.39/1.44 2.39/1.44 1: T: 2.39/1.44 2.39/1.44 (Comp: ?, Cost: 1) evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3)) 2.39/1.44 2.39/1.44 (Comp: ?, Cost: 1) evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3)) 2.39/1.44 2.39/1.44 (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 >= 1 ] 2.39/1.44 2.39/1.44 (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 ] 2.39/1.44 2.39/1.44 (Comp: ?, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_2 >= 1 ] 2.39/1.44 2.39/1.44 (Comp: ?, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_2 - 1, ar_3)) [ ar_2 >= 1 /\ 0 >= ar_2 ] 2.39/1.44 2.39/1.44 (Comp: ?, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_1, ar_3)) [ 0 >= ar_2 /\ ar_2 >= 1 ] 2.39/1.44 2.39/1.44 (Comp: ?, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_1, ar_3)) [ 0 >= ar_2 ] 2.39/1.44 2.39/1.44 (Comp: ?, Cost: 1) evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3)) 2.39/1.44 2.39/1.44 (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 ] 2.39/1.44 2.39/1.44 start location: koat_start 2.39/1.44 2.39/1.44 leaf cost: 0 2.39/1.44 2.39/1.44 2.39/1.44 2.39/1.44 Testing for reachability in the complexity graph removes the following transitions from problem 1: 2.39/1.44 2.39/1.44 evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_2 - 1, ar_3)) [ ar_2 >= 1 /\ 0 >= ar_2 ] 2.39/1.44 2.39/1.44 evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_1, ar_3)) [ 0 >= ar_2 /\ ar_2 >= 1 ] 2.39/1.44 2.39/1.44 We thus obtain the following problem: 2.39/1.44 2.39/1.44 2: T: 2.39/1.44 2.39/1.44 (Comp: ?, Cost: 1) evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3)) 2.39/1.44 2.39/1.44 (Comp: ?, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_1, ar_3)) [ 0 >= ar_2 ] 2.39/1.44 2.39/1.44 (Comp: ?, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_2 >= 1 ] 2.39/1.44 2.39/1.44 (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 ] 2.39/1.44 2.39/1.44 (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 >= 1 ] 2.39/1.44 2.39/1.44 (Comp: ?, Cost: 1) evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3)) 2.39/1.44 2.39/1.44 (Comp: ?, Cost: 1) evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3)) 2.39/1.44 2.39/1.44 (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 ] 2.39/1.44 2.39/1.44 start location: koat_start 2.39/1.44 2.39/1.44 leaf cost: 0 2.39/1.44 2.39/1.44 2.39/1.44 2.39/1.44 Repeatedly propagating knowledge in problem 2 produces the following problem:
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return to Complexity_C_Integer 2019-03-21 04.38