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Complexity_C_Integer 2019-03-21 04.38 pair #429989208
details
property
value
status
complete
benchmark
AliasDarteFeautrierGonnord-SAS2010-speedpldi4_true-termination.c
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n132.star.cs.uiowa.edu
space
Adapted_from_Stroeder_15
run statistics
property
value
solver
AProVE
configuration
c_complexity
runtime (wallclock)
1.47904 seconds
cpu usage
2.552
user time
2.32499
system time
0.227006
max virtual memory
1.833918E7
max residence set size
185512.0
stage attributes
key
value
starexec-result
WORST_CASE(?, O(n^1))
output
2.48/1.44 WORST_CASE(?, O(n^1)) 2.48/1.45 proof of /export/starexec/sandbox2/output/output_files/bench.koat 2.48/1.45 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 2.48/1.45 2.48/1.45 2.48/1.45 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^1). 2.48/1.45 2.48/1.45 (0) CpxIntTrs 2.48/1.45 (1) Koat Proof [FINISHED, 276 ms] 2.48/1.45 (2) BOUNDS(1, n^1) 2.48/1.45 2.48/1.45 2.48/1.45 ---------------------------------------- 2.48/1.45 2.48/1.45 (0) 2.48/1.45 Obligation: 2.48/1.45 Complexity Int TRS consisting of the following rules: 2.48/1.45 eval_foo_start(v_.0, v_i, v_m, v_n) -> Com_1(eval_foo_bb0_in(v_.0, v_i, v_m, v_n)) :|: TRUE 2.48/1.45 eval_foo_bb0_in(v_.0, v_i, v_m, v_n) -> Com_1(eval_foo_bb1_in(v_n, v_i, v_m, v_n)) :|: v_m > 0 && v_n > v_m 2.48/1.45 eval_foo_bb0_in(v_.0, v_i, v_m, v_n) -> Com_1(eval_foo_bb3_in(v_.0, v_i, v_m, v_n)) :|: v_m <= 0 2.48/1.45 eval_foo_bb0_in(v_.0, v_i, v_m, v_n) -> Com_1(eval_foo_bb3_in(v_.0, v_i, v_m, v_n)) :|: v_n <= v_m 2.48/1.45 eval_foo_bb1_in(v_.0, v_i, v_m, v_n) -> Com_1(eval_foo_bb2_in(v_.0, v_i, v_m, v_n)) :|: v_.0 > 0 2.48/1.45 eval_foo_bb1_in(v_.0, v_i, v_m, v_n) -> Com_1(eval_foo_bb3_in(v_.0, v_i, v_m, v_n)) :|: v_.0 <= 0 2.48/1.45 eval_foo_bb2_in(v_.0, v_i, v_m, v_n) -> Com_1(eval_foo_bb1_in(v_.0 - 1, v_i, v_m, v_n)) :|: v_.0 < v_m 2.48/1.45 eval_foo_bb2_in(v_.0, v_i, v_m, v_n) -> Com_1(eval_foo_bb1_in(v_.0 - v_m, v_i, v_m, v_n)) :|: v_.0 >= v_m 2.48/1.45 eval_foo_bb3_in(v_.0, v_i, v_m, v_n) -> Com_1(eval_foo_stop(v_.0, v_i, v_m, v_n)) :|: TRUE 2.48/1.45 2.48/1.45 The start-symbols are:[eval_foo_start_4] 2.48/1.45 2.48/1.45 2.48/1.45 ---------------------------------------- 2.48/1.45 2.48/1.45 (1) Koat Proof (FINISHED) 2.48/1.45 YES(?, 6*ar_1 + 8) 2.48/1.45 2.48/1.45 2.48/1.45 2.48/1.45 Initial complexity problem: 2.48/1.45 2.48/1.45 1: T: 2.48/1.45 2.48/1.45 (Comp: ?, Cost: 1) evalfoostart(ar_0, ar_1, ar_2) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2)) 2.48/1.45 2.48/1.45 (Comp: ?, Cost: 1) evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_1)) [ ar_0 >= 1 /\ ar_1 >= ar_0 + 1 ] 2.48/1.45 2.48/1.45 (Comp: ?, Cost: 1) evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ 0 >= ar_0 ] 2.48/1.45 2.48/1.45 (Comp: ?, Cost: 1) evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ ar_0 >= ar_1 ] 2.48/1.45 2.48/1.45 (Comp: ?, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2)) [ ar_2 >= 1 ] 2.48/1.45 2.48/1.45 (Comp: ?, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ 0 >= ar_2 ] 2.48/1.45 2.48/1.45 (Comp: ?, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 - 1)) [ ar_0 >= ar_2 + 1 ] 2.48/1.45 2.48/1.45 (Comp: ?, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 - ar_0)) [ ar_2 >= ar_0 ] 2.48/1.45 2.48/1.45 (Comp: ?, Cost: 1) evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2)) 2.48/1.45 2.48/1.45 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfoostart(ar_0, ar_1, ar_2)) [ 0 <= 0 ] 2.48/1.45 2.48/1.45 start location: koat_start 2.48/1.45 2.48/1.45 leaf cost: 0 2.48/1.45 2.48/1.45 2.48/1.45 2.48/1.45 Repeatedly propagating knowledge in problem 1 produces the following problem: 2.48/1.45 2.48/1.45 2: T: 2.48/1.45 2.48/1.45 (Comp: 1, Cost: 1) evalfoostart(ar_0, ar_1, ar_2) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2)) 2.48/1.45 2.48/1.45 (Comp: 1, Cost: 1) evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_1)) [ ar_0 >= 1 /\ ar_1 >= ar_0 + 1 ] 2.48/1.45 2.48/1.45 (Comp: 1, Cost: 1) evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ 0 >= ar_0 ] 2.48/1.45 2.48/1.45 (Comp: 1, Cost: 1) evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ ar_0 >= ar_1 ] 2.48/1.45 2.48/1.45 (Comp: ?, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2)) [ ar_2 >= 1 ] 2.48/1.45 2.48/1.45 (Comp: ?, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ 0 >= ar_2 ] 2.48/1.45 2.48/1.45 (Comp: ?, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 - 1)) [ ar_0 >= ar_2 + 1 ] 2.48/1.45 2.48/1.45 (Comp: ?, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 - ar_0)) [ ar_2 >= ar_0 ] 2.48/1.45 2.48/1.45 (Comp: ?, Cost: 1) evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2)) 2.48/1.45 2.48/1.45 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfoostart(ar_0, ar_1, ar_2)) [ 0 <= 0 ] 2.48/1.45 2.48/1.45 start location: koat_start 2.48/1.45 2.48/1.45 leaf cost: 0 2.48/1.45 2.48/1.45 2.48/1.45 2.48/1.45 A polynomial rank function with 2.48/1.45 2.48/1.45 Pol(evalfoostart) = 2
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