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Complexity_C_Integer 2019-03-21 04.38 pair #429988898
details
property
value
status
complete
benchmark
Bangalore_true-termination.c
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n120.star.cs.uiowa.edu
space
Adapted_from_Stroeder_15
run statistics
property
value
solver
AProVE
configuration
c_complexity
runtime (wallclock)
1.51121 seconds
cpu usage
4.41136
user time
4.02857
system time
0.382788
max virtual memory
1.833918E7
max residence set size
181640.0
stage attributes
key
value
starexec-result
WORST_CASE(?, O(n^1))
output
1.96/1.47 WORST_CASE(?, O(n^1)) 2.18/1.48 proof of /export/starexec/sandbox/output/output_files/bench.koat 2.18/1.48 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 2.18/1.48 2.18/1.48 2.18/1.48 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^1). 2.18/1.48 2.18/1.48 (0) CpxIntTrs 2.18/1.48 (1) Koat Proof [FINISHED, 183 ms] 2.18/1.48 (2) BOUNDS(1, n^1) 2.18/1.48 2.18/1.48 2.18/1.48 ---------------------------------------- 2.18/1.48 2.18/1.48 (0) 2.18/1.48 Obligation: 2.18/1.48 Complexity Int TRS consisting of the following rules: 2.18/1.48 eval_foo_start(v_.0, v_x, v_y) -> Com_1(eval_foo_bb0_in(v_.0, v_x, v_y)) :|: TRUE 2.18/1.48 eval_foo_bb0_in(v_.0, v_x, v_y) -> Com_1(eval_foo_bb1_in(v_x, v_x, v_y)) :|: v_y >= 1 2.18/1.48 eval_foo_bb0_in(v_.0, v_x, v_y) -> Com_1(eval_foo_bb3_in(v_.0, v_x, v_y)) :|: v_y < 1 2.18/1.48 eval_foo_bb1_in(v_.0, v_x, v_y) -> Com_1(eval_foo_bb2_in(v_.0, v_x, v_y)) :|: v_.0 >= 0 2.18/1.48 eval_foo_bb1_in(v_.0, v_x, v_y) -> Com_1(eval_foo_bb3_in(v_.0, v_x, v_y)) :|: v_.0 < 0 2.18/1.48 eval_foo_bb2_in(v_.0, v_x, v_y) -> Com_1(eval_foo_bb1_in(v_.0 - v_y, v_x, v_y)) :|: TRUE 2.18/1.48 eval_foo_bb3_in(v_.0, v_x, v_y) -> Com_1(eval_foo_stop(v_.0, v_x, v_y)) :|: TRUE 2.18/1.48 2.18/1.48 The start-symbols are:[eval_foo_start_3] 2.18/1.48 2.18/1.48 2.18/1.48 ---------------------------------------- 2.18/1.48 2.18/1.48 (1) Koat Proof (FINISHED) 2.18/1.48 YES(?, 4*ar_2 + 11) 2.18/1.48 2.18/1.48 2.18/1.48 2.18/1.48 Initial complexity problem: 2.18/1.48 2.18/1.48 1: T: 2.18/1.48 2.18/1.48 (Comp: ?, Cost: 1) evalfoostart(ar_0, ar_1, ar_2) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2)) 2.18/1.48 2.18/1.48 (Comp: ?, Cost: 1) evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0, ar_2, ar_2)) [ ar_0 >= 1 ] 2.18/1.48 2.18/1.48 (Comp: ?, Cost: 1) evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ 0 >= ar_0 ] 2.18/1.48 2.18/1.48 (Comp: ?, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2)) [ ar_1 >= 0 ] 2.18/1.48 2.18/1.48 (Comp: ?, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ 0 >= ar_1 + 1 ] 2.18/1.48 2.18/1.48 (Comp: ?, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0, ar_1 - ar_0, ar_2)) 2.18/1.48 2.18/1.48 (Comp: ?, Cost: 1) evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2)) 2.18/1.48 2.18/1.48 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfoostart(ar_0, ar_1, ar_2)) [ 0 <= 0 ] 2.18/1.48 2.18/1.48 start location: koat_start 2.18/1.48 2.18/1.48 leaf cost: 0 2.18/1.48 2.18/1.48 2.18/1.48 2.18/1.48 Repeatedly propagating knowledge in problem 1 produces the following problem: 2.18/1.48 2.18/1.48 2: T: 2.18/1.48 2.18/1.48 (Comp: 1, Cost: 1) evalfoostart(ar_0, ar_1, ar_2) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2)) 2.18/1.48 2.18/1.48 (Comp: 1, Cost: 1) evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0, ar_2, ar_2)) [ ar_0 >= 1 ] 2.18/1.48 2.18/1.48 (Comp: 1, Cost: 1) evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ 0 >= ar_0 ] 2.18/1.48 2.18/1.48 (Comp: ?, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2)) [ ar_1 >= 0 ] 2.18/1.48 2.18/1.48 (Comp: ?, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ 0 >= ar_1 + 1 ] 2.18/1.48 2.18/1.48 (Comp: ?, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0, ar_1 - ar_0, ar_2)) 2.18/1.48 2.18/1.48 (Comp: ?, Cost: 1) evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2)) 2.18/1.48 2.18/1.48 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfoostart(ar_0, ar_1, ar_2)) [ 0 <= 0 ] 2.18/1.48 2.18/1.48 start location: koat_start 2.18/1.48 2.18/1.48 leaf cost: 0 2.18/1.48 2.18/1.48 2.18/1.48 2.18/1.48 A polynomial rank function with 2.18/1.48 2.18/1.48 Pol(evalfoostart) = 2 2.18/1.48 2.18/1.48 Pol(evalfoobb0in) = 2 2.18/1.48 2.18/1.48 Pol(evalfoobb1in) = 2 2.18/1.48 2.18/1.48 Pol(evalfoobb3in) = 1 2.18/1.48 2.18/1.48 Pol(evalfoobb2in) = 2 2.18/1.48 2.18/1.48 Pol(evalfoostop) = 0
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