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Complexity_C_Integer 2019-03-21 04.38 pair #429989666
details
property
value
status
complete
benchmark
wise.c
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n092.star.cs.uiowa.edu
space
WTC_V2
run statistics
property
value
solver
AProVE
configuration
c_complexity
runtime (wallclock)
1.63281 seconds
cpu usage
2.31215
user time
2.112
system time
0.200151
max virtual memory
1.8273644E7
max residence set size
182744.0
stage attributes
key
value
starexec-result
WORST_CASE(?, O(n^1))
output
2.08/1.59 WORST_CASE(?, O(n^1)) 2.08/1.60 proof of /export/starexec/sandbox/output/output_files/bench.koat 2.08/1.60 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 2.08/1.60 2.08/1.60 2.08/1.60 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^1). 2.08/1.60 2.08/1.60 (0) CpxIntTrs 2.08/1.60 (1) Koat Proof [FINISHED, 132 ms] 2.08/1.60 (2) BOUNDS(1, n^1) 2.08/1.60 2.08/1.60 2.08/1.60 ---------------------------------------- 2.08/1.60 2.08/1.60 (0) 2.08/1.60 Obligation: 2.08/1.60 Complexity Int TRS consisting of the following rules: 2.08/1.60 eval_wise_start(v_.0, v_.01, v_x, v_y) -> Com_1(eval_wise_bb0_in(v_.0, v_.01, v_x, v_y)) :|: TRUE 2.08/1.60 eval_wise_bb0_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_wise_bb2_in(v_.0, v_.01, v_x, v_y)) :|: v_x < 0 2.08/1.60 eval_wise_bb0_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_wise_bb2_in(v_.0, v_.01, v_x, v_y)) :|: v_y < 0 2.08/1.60 eval_wise_bb0_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_wise_bb1_in(v_x, v_y, v_x, v_y)) :|: v_x >= 0 && v_y >= 0 2.08/1.60 eval_wise_bb1_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_wise_.critedge_in(v_.0, v_.01, v_x, v_y)) :|: v_.0 - v_.01 > 2 2.08/1.60 eval_wise_bb1_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_wise_.critedge_in(v_.0, v_.01, v_x, v_y)) :|: v_.01 - v_.0 > 2 2.08/1.60 eval_wise_bb1_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_wise_bb2_in(v_.0, v_.01, v_x, v_y)) :|: v_.0 - v_.01 <= 2 && v_.01 - v_.0 <= 2 2.08/1.60 eval_wise_.critedge_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_wise_bb1_in(v_.0 + 1, v_.01, v_x, v_y)) :|: v_.0 < v_.01 2.08/1.60 eval_wise_.critedge_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_wise_bb1_in(v_.0, v_.01, v_x, v_y)) :|: v_.0 < v_.01 && v_.0 >= v_.01 2.08/1.60 eval_wise_.critedge_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_wise_bb1_in(v_.0 + 1, v_.01 + 1, v_x, v_y)) :|: v_.0 >= v_.01 && v_.0 < v_.01 2.08/1.60 eval_wise_.critedge_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_wise_bb1_in(v_.0, v_.01 + 1, v_x, v_y)) :|: v_.0 >= v_.01 2.08/1.60 eval_wise_bb2_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_wise_stop(v_.0, v_.01, v_x, v_y)) :|: TRUE 2.08/1.60 2.08/1.60 The start-symbols are:[eval_wise_start_4] 2.08/1.60 2.08/1.60 2.08/1.60 ---------------------------------------- 2.08/1.60 2.08/1.60 (1) Koat Proof (FINISHED) 2.08/1.60 YES(?, 8*ar_0 + 8*ar_1 + 14) 2.08/1.60 2.08/1.60 2.08/1.60 2.08/1.60 Initial complexity problem: 2.08/1.60 2.08/1.60 1: T: 2.08/1.60 2.08/1.60 (Comp: ?, Cost: 1) evalwisestart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisebb0in(ar_0, ar_1, ar_2, ar_3)) 2.08/1.60 2.08/1.60 (Comp: ?, Cost: 1) evalwisebb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisebb2in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 + 1 ] 2.08/1.60 2.08/1.60 (Comp: ?, Cost: 1) evalwisebb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisebb2in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_1 + 1 ] 2.08/1.60 2.08/1.60 (Comp: ?, Cost: 1) evalwisebb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisebb1in(ar_0, ar_1, ar_0, ar_1)) [ ar_0 >= 0 /\ ar_1 >= 0 ] 2.08/1.60 2.08/1.60 (Comp: ?, Cost: 1) evalwisebb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisecritedgein(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_3 + 3 ] 2.08/1.60 2.08/1.60 (Comp: ?, Cost: 1) evalwisebb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisecritedgein(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_2 + 3 ] 2.08/1.60 2.08/1.60 (Comp: ?, Cost: 1) evalwisebb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisebb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 + 2 >= ar_2 /\ ar_2 + 2 >= ar_3 ] 2.08/1.60 2.08/1.60 (Comp: ?, Cost: 1) evalwisecritedgein(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisebb1in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_3 >= ar_2 + 1 ] 2.08/1.60 2.08/1.60 (Comp: ?, Cost: 1) evalwisecritedgein(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisebb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_2 + 1 /\ ar_2 >= ar_3 ] 2.08/1.60 2.08/1.60 (Comp: ?, Cost: 1) evalwisecritedgein(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisebb1in(ar_0, ar_1, ar_2 + 1, ar_3 + 1)) [ ar_2 >= ar_3 /\ ar_3 >= ar_2 + 1 ] 2.08/1.60 2.08/1.60 (Comp: ?, Cost: 1) evalwisecritedgein(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisebb1in(ar_0, ar_1, ar_2, ar_3 + 1)) [ ar_2 >= ar_3 ] 2.08/1.60 2.08/1.60 (Comp: ?, Cost: 1) evalwisebb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisestop(ar_0, ar_1, ar_2, ar_3)) 2.08/1.60 2.08/1.60 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisestart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ] 2.08/1.60 2.08/1.60 start location: koat_start 2.08/1.60 2.08/1.60 leaf cost: 0 2.08/1.60 2.08/1.60 2.08/1.60 2.08/1.60 Testing for reachability in the complexity graph removes the following transitions from problem 1: 2.08/1.60 2.08/1.60 evalwisecritedgein(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisebb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_2 + 1 /\ ar_2 >= ar_3 ] 2.08/1.60 2.08/1.60 evalwisecritedgein(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisebb1in(ar_0, ar_1, ar_2 + 1, ar_3 + 1)) [ ar_2 >= ar_3 /\ ar_3 >= ar_2 + 1 ] 2.08/1.60 2.08/1.60 We thus obtain the following problem: 2.08/1.60 2.08/1.60 2: T: 2.08/1.60 2.08/1.60 (Comp: ?, Cost: 1) evalwisecritedgein(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisebb1in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_3 >= ar_2 + 1 ] 2.08/1.60 2.08/1.60 (Comp: ?, Cost: 1) evalwisecritedgein(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisebb1in(ar_0, ar_1, ar_2, ar_3 + 1)) [ ar_2 >= ar_3 ] 2.08/1.60 2.08/1.60 (Comp: ?, Cost: 1) evalwisebb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisebb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 + 2 >= ar_2 /\ ar_2 + 2 >= ar_3 ] 2.08/1.60 2.08/1.60 (Comp: ?, Cost: 1) evalwisebb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisecritedgein(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_2 + 3 ] 2.08/1.60 2.08/1.60 (Comp: ?, Cost: 1) evalwisebb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisecritedgein(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_3 + 3 ] 2.08/1.60 2.08/1.60 (Comp: ?, Cost: 1) evalwisebb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisestop(ar_0, ar_1, ar_2, ar_3)) 2.08/1.60 2.08/1.60 (Comp: ?, Cost: 1) evalwisebb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisebb1in(ar_0, ar_1, ar_0, ar_1)) [ ar_0 >= 0 /\ ar_1 >= 0 ] 2.08/1.60
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