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Complexity_C_Integer 2019-03-21 04.38 pair #429989554
details
property
value
status
complete
benchmark
Loopus2011_ex3.c
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n106.star.cs.uiowa.edu
space
Loopus
run statistics
property
value
solver
AProVE
configuration
c_complexity
runtime (wallclock)
1.86437 seconds
cpu usage
2.94145
user time
2.67002
system time
0.27143
max virtual memory
1.8486264E7
max residence set size
184528.0
stage attributes
key
value
starexec-result
WORST_CASE(?, O(n^1))
output
2.81/1.83 WORST_CASE(?, O(n^1)) 2.81/1.84 proof of /export/starexec/sandbox/output/output_files/bench.koat 2.81/1.84 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 2.81/1.84 2.81/1.84 2.81/1.84 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^1). 2.81/1.84 2.81/1.84 (0) CpxIntTrs 2.81/1.84 (1) Koat Proof [FINISHED, 578 ms] 2.81/1.84 (2) BOUNDS(1, n^1) 2.81/1.84 2.81/1.84 2.81/1.84 ---------------------------------------- 2.81/1.84 2.81/1.84 (0) 2.81/1.84 Obligation: 2.81/1.84 Complexity Int TRS consisting of the following rules: 2.81/1.84 eval_Loopus2011_ex3_start(v_.0, v_b, v_x) -> Com_1(eval_Loopus2011_ex3_bb0_in(v_.0, v_b, v_x)) :|: TRUE 2.81/1.84 eval_Loopus2011_ex3_bb0_in(v_.0, v_b, v_x) -> Com_1(eval_Loopus2011_ex3_bb1_in(v_x, v_b, v_x)) :|: TRUE 2.81/1.84 eval_Loopus2011_ex3_bb1_in(v_.0, v_b, v_x) -> Com_1(eval_Loopus2011_ex3_bb2_in(v_.0, v_b, v_x)) :|: 0 < v_.0 && v_.0 < 255 2.81/1.84 eval_Loopus2011_ex3_bb1_in(v_.0, v_b, v_x) -> Com_1(eval_Loopus2011_ex3_bb3_in(v_.0, v_b, v_x)) :|: 0 >= v_.0 2.81/1.84 eval_Loopus2011_ex3_bb1_in(v_.0, v_b, v_x) -> Com_1(eval_Loopus2011_ex3_bb3_in(v_.0, v_b, v_x)) :|: v_.0 >= 255 2.81/1.84 eval_Loopus2011_ex3_bb2_in(v_.0, v_b, v_x) -> Com_1(eval_Loopus2011_ex3_bb1_in(v_.0 + 1, v_b, v_x)) :|: v_b < 0 2.81/1.84 eval_Loopus2011_ex3_bb2_in(v_.0, v_b, v_x) -> Com_1(eval_Loopus2011_ex3_bb1_in(v_.0 + 1, v_b, v_x)) :|: v_b > 0 2.81/1.84 eval_Loopus2011_ex3_bb2_in(v_.0, v_b, v_x) -> Com_1(eval_Loopus2011_ex3_bb1_in(v_.0 - 1, v_b, v_x)) :|: v_b >= 0 && v_b <= 0 2.81/1.84 eval_Loopus2011_ex3_bb3_in(v_.0, v_b, v_x) -> Com_1(eval_Loopus2011_ex3_stop(v_.0, v_b, v_x)) :|: TRUE 2.81/1.84 2.81/1.84 The start-symbols are:[eval_Loopus2011_ex3_start_3] 2.81/1.84 2.81/1.84 2.81/1.84 ---------------------------------------- 2.81/1.84 2.81/1.84 (1) Koat Proof (FINISHED) 2.81/1.84 YES(?, 4076*ar_1 + 16) 2.81/1.84 2.81/1.84 2.81/1.84 2.81/1.84 Initial complexity problem: 2.81/1.84 2.81/1.84 1: T: 2.81/1.84 2.81/1.84 (Comp: ?, Cost: 1) evalLoopus2011ex3start(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb0in(ar_0, ar_1, ar_2)) 2.81/1.84 2.81/1.84 (Comp: ?, Cost: 1) evalLoopus2011ex3bb0in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb1in(ar_1, ar_1, ar_2)) 2.81/1.84 2.81/1.84 (Comp: ?, Cost: 1) evalLoopus2011ex3bb1in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb2in(ar_0, ar_1, ar_2)) [ ar_0 >= 1 /\ 254 >= ar_0 ] 2.81/1.84 2.81/1.84 (Comp: ?, Cost: 1) evalLoopus2011ex3bb1in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb3in(ar_0, ar_1, ar_2)) [ 0 >= ar_0 ] 2.81/1.84 2.81/1.84 (Comp: ?, Cost: 1) evalLoopus2011ex3bb1in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb3in(ar_0, ar_1, ar_2)) [ ar_0 >= 255 ] 2.81/1.84 2.81/1.84 (Comp: ?, Cost: 1) evalLoopus2011ex3bb2in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb1in(ar_0 + 1, ar_1, ar_2)) [ 0 >= ar_2 + 1 ] 2.81/1.84 2.81/1.84 (Comp: ?, Cost: 1) evalLoopus2011ex3bb2in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb1in(ar_0 + 1, ar_1, ar_2)) [ ar_2 >= 1 ] 2.81/1.84 2.81/1.84 (Comp: ?, Cost: 1) evalLoopus2011ex3bb2in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb1in(ar_0 - 1, ar_1, ar_2)) [ ar_2 = 0 ] 2.81/1.84 2.81/1.84 (Comp: ?, Cost: 1) evalLoopus2011ex3bb3in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3stop(ar_0, ar_1, ar_2)) 2.81/1.84 2.81/1.84 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3start(ar_0, ar_1, ar_2)) [ 0 <= 0 ] 2.81/1.84 2.81/1.84 start location: koat_start 2.81/1.84 2.81/1.84 leaf cost: 0 2.81/1.84 2.81/1.84 2.81/1.84 2.81/1.84 Repeatedly propagating knowledge in problem 1 produces the following problem: 2.81/1.84 2.81/1.84 2: T: 2.81/1.84 2.81/1.84 (Comp: 1, Cost: 1) evalLoopus2011ex3start(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb0in(ar_0, ar_1, ar_2)) 2.81/1.84 2.81/1.84 (Comp: 1, Cost: 1) evalLoopus2011ex3bb0in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb1in(ar_1, ar_1, ar_2)) 2.81/1.84 2.81/1.84 (Comp: ?, Cost: 1) evalLoopus2011ex3bb1in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb2in(ar_0, ar_1, ar_2)) [ ar_0 >= 1 /\ 254 >= ar_0 ] 2.81/1.84 2.81/1.84 (Comp: ?, Cost: 1) evalLoopus2011ex3bb1in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb3in(ar_0, ar_1, ar_2)) [ 0 >= ar_0 ] 2.81/1.84 2.81/1.84 (Comp: ?, Cost: 1) evalLoopus2011ex3bb1in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb3in(ar_0, ar_1, ar_2)) [ ar_0 >= 255 ] 2.81/1.84 2.81/1.84 (Comp: ?, Cost: 1) evalLoopus2011ex3bb2in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb1in(ar_0 + 1, ar_1, ar_2)) [ 0 >= ar_2 + 1 ] 2.81/1.84 2.81/1.84 (Comp: ?, Cost: 1) evalLoopus2011ex3bb2in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb1in(ar_0 + 1, ar_1, ar_2)) [ ar_2 >= 1 ] 2.81/1.84 2.81/1.84 (Comp: ?, Cost: 1) evalLoopus2011ex3bb2in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb1in(ar_0 - 1, ar_1, ar_2)) [ ar_2 = 0 ] 2.81/1.84 2.81/1.84 (Comp: ?, Cost: 1) evalLoopus2011ex3bb3in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3stop(ar_0, ar_1, ar_2)) 2.81/1.84 2.81/1.84 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3start(ar_0, ar_1, ar_2)) [ 0 <= 0 ] 2.81/1.84 2.81/1.84 start location: koat_start 2.81/1.84 2.81/1.84 leaf cost: 0 2.81/1.84 2.81/1.84 2.81/1.84 2.81/1.84 A polynomial rank function with 2.81/1.84 2.81/1.84 Pol(evalLoopus2011ex3start) = 2
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