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Complexity_C_Integer 2019-03-21 04.38 pair #429989104
details
property
value
status
complete
benchmark
PastaC2.c
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n049.star.cs.uiowa.edu
space
Adapted_from_Stroeder_15
run statistics
property
value
solver
AProVE
configuration
c_complexity
runtime (wallclock)
1.77243 seconds
cpu usage
2.30245
user time
2.12026
system time
0.182189
max virtual memory
1.8273644E7
max residence set size
181252.0
stage attributes
key
value
starexec-result
WORST_CASE(?, O(n^2))
output
2.24/1.74 WORST_CASE(?, O(n^2)) 2.24/1.75 proof of /export/starexec/sandbox/output/output_files/bench.koat 2.24/1.75 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 2.24/1.75 2.24/1.75 2.24/1.75 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^2). 2.24/1.75 2.24/1.75 (0) CpxIntTrs 2.24/1.75 (1) Koat Proof [FINISHED, 85 ms] 2.24/1.75 (2) BOUNDS(1, n^2) 2.24/1.75 2.24/1.75 2.24/1.75 ---------------------------------------- 2.24/1.75 2.24/1.75 (0) 2.24/1.75 Obligation: 2.24/1.75 Complexity Int TRS consisting of the following rules: 2.24/1.75 eval_foo_start(v_.0, v_.01, v_1, v_x, v_y) -> Com_1(eval_foo_bb0_in(v_.0, v_.01, v_1, v_x, v_y)) :|: TRUE 2.24/1.75 eval_foo_bb0_in(v_.0, v_.01, v_1, v_x, v_y) -> Com_1(eval_foo_bb1_in(v_x, v_.01, v_1, v_x, v_y)) :|: TRUE 2.24/1.75 eval_foo_bb1_in(v_.0, v_.01, v_1, v_x, v_y) -> Com_1(eval_foo_bb2_in(v_.0, v_.01, v_1, v_x, v_y)) :|: v_.0 >= 0 2.24/1.75 eval_foo_bb1_in(v_.0, v_.01, v_1, v_x, v_y) -> Com_1(eval_foo_bb6_in(v_.0, v_.01, v_1, v_x, v_y)) :|: v_.0 < 0 2.24/1.75 eval_foo_bb2_in(v_.0, v_.01, v_1, v_x, v_y) -> Com_1(eval_foo_bb3_in(v_.0, 1, v_.0 + 1, v_x, v_y)) :|: TRUE 2.24/1.75 eval_foo_bb3_in(v_.0, v_.01, v_1, v_x, v_y) -> Com_1(eval_foo_bb4_in(v_.0, v_.01, v_1, v_x, v_y)) :|: v_1 >= v_.01 2.24/1.75 eval_foo_bb3_in(v_.0, v_.01, v_1, v_x, v_y) -> Com_1(eval_foo_bb5_in(v_.0, v_.01, v_1, v_x, v_y)) :|: v_1 < v_.01 2.24/1.75 eval_foo_bb4_in(v_.0, v_.01, v_1, v_x, v_y) -> Com_1(eval_foo_bb3_in(v_.0, v_.01 + 1, v_1, v_x, v_y)) :|: TRUE 2.24/1.75 eval_foo_bb5_in(v_.0, v_.01, v_1, v_x, v_y) -> Com_1(eval_foo_bb1_in(v_1 - 2, v_.01, v_1, v_x, v_y)) :|: TRUE 2.24/1.75 eval_foo_bb6_in(v_.0, v_.01, v_1, v_x, v_y) -> Com_1(eval_foo_stop(v_.0, v_.01, v_1, v_x, v_y)) :|: TRUE 2.24/1.75 2.24/1.75 The start-symbols are:[eval_foo_start_5] 2.24/1.75 2.24/1.75 2.24/1.75 ---------------------------------------- 2.24/1.75 2.24/1.75 (1) Koat Proof (FINISHED) 2.24/1.75 YES(?, 754*ar_1 + 12*ar_1^2 + 1466) 2.24/1.75 2.24/1.75 2.24/1.75 2.24/1.75 Initial complexity problem: 2.24/1.75 2.24/1.75 1: T: 2.24/1.75 2.24/1.75 (Comp: ?, Cost: 1) evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3)) 2.24/1.75 2.24/1.75 (Comp: ?, Cost: 1) evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_2, ar_3)) 2.24/1.75 2.24/1.75 (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 ] 2.24/1.75 2.24/1.75 (Comp: ?, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb6in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 + 1 ] 2.24/1.75 2.24/1.75 (Comp: ?, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, 1, ar_0 + 1)) 2.24/1.75 2.24/1.75 (Comp: ?, Cost: 1) evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_2 ] 2.24/1.75 2.24/1.75 (Comp: ?, Cost: 1) evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_3 + 1 ] 2.24/1.75 2.24/1.75 (Comp: ?, Cost: 1) evalfoobb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2 + 1, ar_3)) 2.24/1.75 2.24/1.75 (Comp: ?, Cost: 1) evalfoobb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_3 - 2, ar_1, ar_2, ar_3)) 2.24/1.75 2.24/1.75 (Comp: ?, Cost: 1) evalfoobb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3)) 2.24/1.75 2.24/1.75 (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 ] 2.24/1.75 2.24/1.75 start location: koat_start 2.24/1.75 2.24/1.75 leaf cost: 0 2.24/1.75 2.24/1.75 2.24/1.75 2.24/1.75 Repeatedly propagating knowledge in problem 1 produces the following problem: 2.24/1.75 2.24/1.75 2: T: 2.24/1.75 2.24/1.75 (Comp: 1, Cost: 1) evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3)) 2.24/1.75 2.24/1.75 (Comp: 1, Cost: 1) evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_2, ar_3)) 2.24/1.75 2.24/1.75 (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 ] 2.24/1.75 2.24/1.75 (Comp: ?, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb6in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 + 1 ] 2.24/1.75 2.24/1.75 (Comp: ?, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, 1, ar_0 + 1)) 2.24/1.75 2.24/1.75 (Comp: ?, Cost: 1) evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_2 ] 2.24/1.75 2.24/1.75 (Comp: ?, Cost: 1) evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_3 + 1 ] 2.24/1.75 2.24/1.75 (Comp: ?, Cost: 1) evalfoobb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2 + 1, ar_3)) 2.24/1.75 2.24/1.75 (Comp: ?, Cost: 1) evalfoobb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_3 - 2, ar_1, ar_2, ar_3)) 2.24/1.75 2.24/1.75 (Comp: ?, Cost: 1) evalfoobb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3)) 2.24/1.75 2.24/1.75 (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 ] 2.24/1.75 2.24/1.75 start location: koat_start 2.24/1.75 2.24/1.75 leaf cost: 0 2.24/1.75
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