Initial Problem
Start: eval_speed_pldi09_fig1_start
Program_Vars: Arg_0, Arg_1, Arg_2
Temp_Vars:
Locations: eval_speed_pldi09_fig1_bb0_in, eval_speed_pldi09_fig1_bb1_in, eval_speed_pldi09_fig1_bb2_in, eval_speed_pldi09_fig1_bb3_in, eval_speed_pldi09_fig1_bb4_in, eval_speed_pldi09_fig1_bb5_in, eval_speed_pldi09_fig1_start, eval_speed_pldi09_fig1_stop
Transitions:
1:eval_speed_pldi09_fig1_bb0_in(Arg_0,Arg_1,Arg_2) -> eval_speed_pldi09_fig1_bb1_in(Arg_0,0,0)
2:eval_speed_pldi09_fig1_bb1_in(Arg_0,Arg_1,Arg_2) -> eval_speed_pldi09_fig1_bb2_in(Arg_0,Arg_1,Arg_2):|:Arg_1<Arg_0
3:eval_speed_pldi09_fig1_bb1_in(Arg_0,Arg_1,Arg_2) -> eval_speed_pldi09_fig1_bb3_in(Arg_0,Arg_1,Arg_2):|:Arg_0<=Arg_1
4:eval_speed_pldi09_fig1_bb2_in(Arg_0,Arg_1,Arg_2) -> eval_speed_pldi09_fig1_bb1_in(Arg_0,Arg_1+1,Arg_2+1)
5:eval_speed_pldi09_fig1_bb3_in(Arg_0,Arg_1,Arg_2) -> eval_speed_pldi09_fig1_bb4_in(Arg_0,Arg_1,Arg_2):|:0<Arg_2
6:eval_speed_pldi09_fig1_bb3_in(Arg_0,Arg_1,Arg_2) -> eval_speed_pldi09_fig1_bb5_in(Arg_0,Arg_1,Arg_2):|:Arg_2<=0
7:eval_speed_pldi09_fig1_bb4_in(Arg_0,Arg_1,Arg_2) -> eval_speed_pldi09_fig1_bb1_in(Arg_0,Arg_1,Arg_2-1)
8:eval_speed_pldi09_fig1_bb5_in(Arg_0,Arg_1,Arg_2) -> eval_speed_pldi09_fig1_stop(Arg_0,Arg_1,Arg_2)
0:eval_speed_pldi09_fig1_start(Arg_0,Arg_1,Arg_2) -> eval_speed_pldi09_fig1_bb0_in(Arg_0,Arg_1,Arg_2)
Preprocessing
Found invariant Arg_2<=Arg_1 && 1+Arg_2<=Arg_0 && 0<=Arg_2 && 0<=Arg_1+Arg_2 && 1<=Arg_0+Arg_2 && 1+Arg_1<=Arg_0 && 0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 for location eval_speed_pldi09_fig1_bb2_in
Found invariant Arg_2<=Arg_1 && 0<=Arg_2 && 0<=Arg_1+Arg_2 && 0<=Arg_1 for location eval_speed_pldi09_fig1_bb1_in
Found invariant Arg_2<=0 && Arg_2<=Arg_1 && 0<=Arg_2 && 0<=Arg_1+Arg_2 && 0<=Arg_1 && Arg_0<=Arg_1 for location eval_speed_pldi09_fig1_bb5_in
Found invariant Arg_2<=0 && Arg_2<=Arg_1 && 0<=Arg_2 && 0<=Arg_1+Arg_2 && 0<=Arg_1 && Arg_0<=Arg_1 for location eval_speed_pldi09_fig1_stop
Found invariant Arg_2<=Arg_1 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && 1<=Arg_1 && Arg_0<=Arg_1 for location eval_speed_pldi09_fig1_bb4_in
Found invariant Arg_2<=Arg_1 && 0<=Arg_2 && 0<=Arg_1+Arg_2 && 0<=Arg_1 && Arg_0<=Arg_1 for location eval_speed_pldi09_fig1_bb3_in
Problem after Preprocessing
Start: eval_speed_pldi09_fig1_start
Program_Vars: Arg_0, Arg_1, Arg_2
Temp_Vars:
Locations: eval_speed_pldi09_fig1_bb0_in, eval_speed_pldi09_fig1_bb1_in, eval_speed_pldi09_fig1_bb2_in, eval_speed_pldi09_fig1_bb3_in, eval_speed_pldi09_fig1_bb4_in, eval_speed_pldi09_fig1_bb5_in, eval_speed_pldi09_fig1_start, eval_speed_pldi09_fig1_stop
Transitions:
1:eval_speed_pldi09_fig1_bb0_in(Arg_0,Arg_1,Arg_2) -> eval_speed_pldi09_fig1_bb1_in(Arg_0,0,0)
2:eval_speed_pldi09_fig1_bb1_in(Arg_0,Arg_1,Arg_2) -> eval_speed_pldi09_fig1_bb2_in(Arg_0,Arg_1,Arg_2):|:Arg_2<=Arg_1 && 0<=Arg_2 && 0<=Arg_1+Arg_2 && 0<=Arg_1 && Arg_1<Arg_0
3:eval_speed_pldi09_fig1_bb1_in(Arg_0,Arg_1,Arg_2) -> eval_speed_pldi09_fig1_bb3_in(Arg_0,Arg_1,Arg_2):|:Arg_2<=Arg_1 && 0<=Arg_2 && 0<=Arg_1+Arg_2 && 0<=Arg_1 && Arg_0<=Arg_1
4:eval_speed_pldi09_fig1_bb2_in(Arg_0,Arg_1,Arg_2) -> eval_speed_pldi09_fig1_bb1_in(Arg_0,Arg_1+1,Arg_2+1):|:Arg_2<=Arg_1 && 1+Arg_2<=Arg_0 && 0<=Arg_2 && 0<=Arg_1+Arg_2 && 1<=Arg_0+Arg_2 && 1+Arg_1<=Arg_0 && 0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0
5:eval_speed_pldi09_fig1_bb3_in(Arg_0,Arg_1,Arg_2) -> eval_speed_pldi09_fig1_bb4_in(Arg_0,Arg_1,Arg_2):|:Arg_2<=Arg_1 && 0<=Arg_2 && 0<=Arg_1+Arg_2 && 0<=Arg_1 && Arg_0<=Arg_1 && 0<Arg_2
6:eval_speed_pldi09_fig1_bb3_in(Arg_0,Arg_1,Arg_2) -> eval_speed_pldi09_fig1_bb5_in(Arg_0,Arg_1,Arg_2):|:Arg_2<=Arg_1 && 0<=Arg_2 && 0<=Arg_1+Arg_2 && 0<=Arg_1 && Arg_0<=Arg_1 && Arg_2<=0
7:eval_speed_pldi09_fig1_bb4_in(Arg_0,Arg_1,Arg_2) -> eval_speed_pldi09_fig1_bb1_in(Arg_0,Arg_1,Arg_2-1):|:Arg_2<=Arg_1 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && 1<=Arg_1 && Arg_0<=Arg_1
8:eval_speed_pldi09_fig1_bb5_in(Arg_0,Arg_1,Arg_2) -> eval_speed_pldi09_fig1_stop(Arg_0,Arg_1,Arg_2):|:Arg_2<=0 && Arg_2<=Arg_1 && 0<=Arg_2 && 0<=Arg_1+Arg_2 && 0<=Arg_1 && Arg_0<=Arg_1
0:eval_speed_pldi09_fig1_start(Arg_0,Arg_1,Arg_2) -> eval_speed_pldi09_fig1_bb0_in(Arg_0,Arg_1,Arg_2)
MPRF for transition 2:eval_speed_pldi09_fig1_bb1_in(Arg_0,Arg_1,Arg_2) -> eval_speed_pldi09_fig1_bb2_in(Arg_0,Arg_1,Arg_2):|:Arg_2<=Arg_1 && 0<=Arg_2 && 0<=Arg_1+Arg_2 && 0<=Arg_1 && Arg_1<Arg_0 of depth 1:
new bound:
Arg_0 {O(n)}
MPRF:
eval_speed_pldi09_fig1_bb2_in [Arg_0-Arg_1-1 ]
eval_speed_pldi09_fig1_bb3_in [Arg_0-Arg_1 ]
eval_speed_pldi09_fig1_bb4_in [Arg_0-Arg_1 ]
eval_speed_pldi09_fig1_bb1_in [Arg_0-Arg_1 ]
MPRF for transition 4:eval_speed_pldi09_fig1_bb2_in(Arg_0,Arg_1,Arg_2) -> eval_speed_pldi09_fig1_bb1_in(Arg_0,Arg_1+1,Arg_2+1):|:Arg_2<=Arg_1 && 1+Arg_2<=Arg_0 && 0<=Arg_2 && 0<=Arg_1+Arg_2 && 1<=Arg_0+Arg_2 && 1+Arg_1<=Arg_0 && 0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 of depth 1:
new bound:
Arg_0 {O(n)}
MPRF:
eval_speed_pldi09_fig1_bb2_in [Arg_0-Arg_1 ]
eval_speed_pldi09_fig1_bb3_in [Arg_0-Arg_1 ]
eval_speed_pldi09_fig1_bb4_in [Arg_0-Arg_1 ]
eval_speed_pldi09_fig1_bb1_in [Arg_0-Arg_1 ]
MPRF for transition 3:eval_speed_pldi09_fig1_bb1_in(Arg_0,Arg_1,Arg_2) -> eval_speed_pldi09_fig1_bb3_in(Arg_0,Arg_1,Arg_2):|:Arg_2<=Arg_1 && 0<=Arg_2 && 0<=Arg_1+Arg_2 && 0<=Arg_1 && Arg_0<=Arg_1 of depth 1:
new bound:
Arg_0*Arg_0+Arg_0+1 {O(n^2)}
MPRF:
eval_speed_pldi09_fig1_bb2_in [Arg_2+1 ]
eval_speed_pldi09_fig1_bb3_in [Arg_2 ]
eval_speed_pldi09_fig1_bb4_in [Arg_2 ]
eval_speed_pldi09_fig1_bb1_in [Arg_2+1 ]
MPRF for transition 5:eval_speed_pldi09_fig1_bb3_in(Arg_0,Arg_1,Arg_2) -> eval_speed_pldi09_fig1_bb4_in(Arg_0,Arg_1,Arg_2):|:Arg_2<=Arg_1 && 0<=Arg_2 && 0<=Arg_1+Arg_2 && 0<=Arg_1 && Arg_0<=Arg_1 && 0<Arg_2 of depth 1:
new bound:
Arg_0*Arg_0+Arg_0+1 {O(n^2)}
MPRF:
eval_speed_pldi09_fig1_bb2_in [Arg_2+1-2*Arg_1 ]
eval_speed_pldi09_fig1_bb3_in [Arg_2+1 ]
eval_speed_pldi09_fig1_bb4_in [Arg_2 ]
eval_speed_pldi09_fig1_bb1_in [Arg_2+1 ]
MPRF for transition 7:eval_speed_pldi09_fig1_bb4_in(Arg_0,Arg_1,Arg_2) -> eval_speed_pldi09_fig1_bb1_in(Arg_0,Arg_1,Arg_2-1):|:Arg_2<=Arg_1 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && 1<=Arg_1 && Arg_0<=Arg_1 of depth 1:
new bound:
Arg_0*Arg_0 {O(n^2)}
MPRF:
eval_speed_pldi09_fig1_bb2_in [Arg_2 ]
eval_speed_pldi09_fig1_bb3_in [Arg_2 ]
eval_speed_pldi09_fig1_bb4_in [Arg_2 ]
eval_speed_pldi09_fig1_bb1_in [Arg_2 ]
Analysing control-flow refined program
Cut unsatisfiable transition 93: n_eval_speed_pldi09_fig1_bb3_in___5->eval_speed_pldi09_fig1_bb5_in
Found invariant 1+Arg_2<=Arg_1 && 1+Arg_2<=Arg_0 && 0<=Arg_2 && 1<=Arg_1+Arg_2 && 1<=Arg_0+Arg_2 && Arg_1<=Arg_0 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 1<=Arg_0 for location n_eval_speed_pldi09_fig1_bb1_in___3
Found invariant Arg_2<=Arg_1 && 1+Arg_2<=Arg_0 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 3<=Arg_0+Arg_2 && 1+Arg_1<=Arg_0 && 1<=Arg_1 && 3<=Arg_0+Arg_1 && 2<=Arg_0 for location n_eval_speed_pldi09_fig1_bb2_in___6
Found invariant Arg_2<=Arg_1 && Arg_2<=Arg_0 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 2<=Arg_0+Arg_2 && Arg_1<=Arg_0 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 for location n_eval_speed_pldi09_fig1_bb1_in___7
Found invariant Arg_2<=0 && Arg_2<=Arg_1 && Arg_1+Arg_2<=0 && 0<=Arg_2 && 0<=Arg_1+Arg_2 && Arg_1<=Arg_2 && Arg_1<=0 && 0<=Arg_1 for location eval_speed_pldi09_fig1_bb1_in
Found invariant Arg_2<=0 && Arg_2<=Arg_1 && Arg_1+Arg_2<=0 && 1+Arg_2<=Arg_0 && 0<=Arg_2 && 0<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 1<=Arg_0+Arg_2 && Arg_1<=0 && 1+Arg_1<=Arg_0 && 0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 for location n_eval_speed_pldi09_fig1_bb2_in___9
Found invariant 1+Arg_2<=Arg_1 && 1+Arg_2<=Arg_0 && 1<=Arg_2 && 3<=Arg_1+Arg_2 && 3<=Arg_0+Arg_2 && Arg_1<=Arg_0 && 2<=Arg_1 && 4<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 2<=Arg_0 for location n_eval_speed_pldi09_fig1_bb4_in___1
Found invariant Arg_2<=0 && Arg_2<=Arg_1 && 0<=Arg_2 && 0<=Arg_1+Arg_2 && 0<=Arg_1 && Arg_0<=Arg_1 for location eval_speed_pldi09_fig1_bb5_in
Found invariant Arg_2<=Arg_1 && Arg_2<=Arg_0 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 2<=Arg_0+Arg_2 && Arg_0<=Arg_2 && Arg_1<=Arg_0 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 1<=Arg_0 for location n_eval_speed_pldi09_fig1_bb3_in___5
Found invariant Arg_2<=0 && Arg_2<=Arg_1 && 0<=Arg_2 && 0<=Arg_1+Arg_2 && 0<=Arg_1 && Arg_0<=Arg_1 for location eval_speed_pldi09_fig1_stop
Found invariant 1+Arg_2<=Arg_1 && 1+Arg_2<=Arg_0 && 0<=Arg_2 && 1<=Arg_1+Arg_2 && 1<=Arg_0+Arg_2 && Arg_1<=Arg_0 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 1<=Arg_0 for location n_eval_speed_pldi09_fig1_bb3_in___2
Found invariant Arg_2<=0 && Arg_2<=Arg_1 && Arg_1+Arg_2<=0 && Arg_0+Arg_2<=0 && 0<=Arg_2 && 0<=Arg_1+Arg_2 && Arg_1<=Arg_2 && Arg_0<=Arg_2 && Arg_1<=0 && Arg_0+Arg_1<=0 && 0<=Arg_1 && Arg_0<=Arg_1 && Arg_0<=0 for location n_eval_speed_pldi09_fig1_bb3_in___8
Found invariant Arg_2<=Arg_1 && Arg_2<=Arg_0 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 2<=Arg_0+Arg_2 && Arg_0<=Arg_2 && Arg_1<=Arg_0 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 1<=Arg_0 for location n_eval_speed_pldi09_fig1_bb4_in___4
MPRF for transition 75:n_eval_speed_pldi09_fig1_bb1_in___7(Arg_0,Arg_1,Arg_2) -> n_eval_speed_pldi09_fig1_bb2_in___6(Arg_0,Arg_1,Arg_2):|:Arg_2<=Arg_1 && Arg_2<=Arg_0 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 2<=Arg_0+Arg_2 && Arg_1<=Arg_0 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 && Arg_2<=Arg_1 && 0<=Arg_2 && 0<Arg_2 && 1<=Arg_2 && 1<=Arg_2 && Arg_2<=Arg_1 && Arg_1<=Arg_0 && Arg_1<Arg_0 && Arg_2<=Arg_1 && 0<=Arg_2 of depth 1:
new bound:
Arg_0+2 {O(n)}
MPRF:
n_eval_speed_pldi09_fig1_bb2_in___6 [Arg_0-Arg_1 ]
n_eval_speed_pldi09_fig1_bb1_in___7 [Arg_0+1-Arg_1 ]
MPRF for transition 77:n_eval_speed_pldi09_fig1_bb2_in___6(Arg_0,Arg_1,Arg_2) -> n_eval_speed_pldi09_fig1_bb1_in___7(Arg_0,Arg_1+1,Arg_2+1):|:Arg_2<=Arg_1 && 1+Arg_2<=Arg_0 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 3<=Arg_0+Arg_2 && 1+Arg_1<=Arg_0 && 1<=Arg_1 && 3<=Arg_0+Arg_1 && 2<=Arg_0 && Arg_1<Arg_0 && Arg_2<=Arg_1 && 1<=Arg_2 && 1+Arg_1<=Arg_0 && Arg_2<=Arg_1 && 0<=Arg_2 of depth 1:
new bound:
Arg_0+1 {O(n)}
MPRF:
n_eval_speed_pldi09_fig1_bb2_in___6 [Arg_0-Arg_2 ]
n_eval_speed_pldi09_fig1_bb1_in___7 [Arg_0-Arg_1 ]
MPRF for transition 74:n_eval_speed_pldi09_fig1_bb1_in___3(Arg_0,Arg_1,Arg_2) -> n_eval_speed_pldi09_fig1_bb3_in___2(Arg_0,Arg_1,Arg_2):|:1+Arg_2<=Arg_1 && 1+Arg_2<=Arg_0 && 0<=Arg_2 && 1<=Arg_1+Arg_2 && 1<=Arg_0+Arg_2 && Arg_1<=Arg_0 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 1<=Arg_0 && Arg_2<=Arg_1 && 0<=Arg_2 && Arg_0<=Arg_1 && 0<=Arg_2 && Arg_2<=Arg_1 && Arg_0<=Arg_1 && 0<=Arg_2 && 1+Arg_2<=Arg_1 && Arg_0<=Arg_1 && Arg_2<=Arg_1 && 0<=Arg_2 && Arg_0<=Arg_1 of depth 1:
new bound:
Arg_0+4 {O(n)}
MPRF:
n_eval_speed_pldi09_fig1_bb3_in___2 [Arg_2 ]
n_eval_speed_pldi09_fig1_bb4_in___1 [Arg_2 ]
n_eval_speed_pldi09_fig1_bb1_in___3 [Arg_2+1 ]
MPRF for transition 79:n_eval_speed_pldi09_fig1_bb3_in___2(Arg_0,Arg_1,Arg_2) -> n_eval_speed_pldi09_fig1_bb4_in___1(Arg_0,Arg_1,Arg_2):|:1+Arg_2<=Arg_1 && 1+Arg_2<=Arg_0 && 0<=Arg_2 && 1<=Arg_1+Arg_2 && 1<=Arg_0+Arg_2 && Arg_1<=Arg_0 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 1<=Arg_0 && Arg_0<=Arg_1 && 1+Arg_2<=Arg_1 && 0<=Arg_2 && Arg_2<=Arg_1 && 0<Arg_2 && Arg_0<=Arg_1 of depth 1:
new bound:
Arg_0+4 {O(n)}
MPRF:
n_eval_speed_pldi09_fig1_bb3_in___2 [Arg_2+1 ]
n_eval_speed_pldi09_fig1_bb4_in___1 [Arg_2 ]
n_eval_speed_pldi09_fig1_bb1_in___3 [Arg_2+1 ]
MPRF for transition 81:n_eval_speed_pldi09_fig1_bb4_in___1(Arg_0,Arg_1,Arg_2) -> n_eval_speed_pldi09_fig1_bb1_in___3(Arg_0,Arg_1,Arg_2-1):|:1+Arg_2<=Arg_1 && 1+Arg_2<=Arg_0 && 1<=Arg_2 && 3<=Arg_1+Arg_2 && 3<=Arg_0+Arg_2 && Arg_1<=Arg_0 && 2<=Arg_1 && 4<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 2<=Arg_0 && Arg_0<=Arg_1 && 1+Arg_2<=Arg_1 && 0<Arg_2 && Arg_2<=Arg_1 && 1<=Arg_2 && Arg_0<=Arg_1 of depth 1:
new bound:
Arg_0+3 {O(n)}
MPRF:
n_eval_speed_pldi09_fig1_bb3_in___2 [Arg_2 ]
n_eval_speed_pldi09_fig1_bb4_in___1 [Arg_2 ]
n_eval_speed_pldi09_fig1_bb1_in___3 [Arg_2 ]
CFR: Improvement to new bound with the following program:
new bound:
5*Arg_0+14 {O(n)}
cfr-program:
Start: eval_speed_pldi09_fig1_start
Program_Vars: Arg_0, Arg_1, Arg_2
Temp_Vars:
Locations: eval_speed_pldi09_fig1_bb0_in, eval_speed_pldi09_fig1_bb1_in, eval_speed_pldi09_fig1_bb5_in, eval_speed_pldi09_fig1_start, eval_speed_pldi09_fig1_stop, n_eval_speed_pldi09_fig1_bb1_in___3, n_eval_speed_pldi09_fig1_bb1_in___7, n_eval_speed_pldi09_fig1_bb2_in___6, n_eval_speed_pldi09_fig1_bb2_in___9, n_eval_speed_pldi09_fig1_bb3_in___2, n_eval_speed_pldi09_fig1_bb3_in___5, n_eval_speed_pldi09_fig1_bb3_in___8, n_eval_speed_pldi09_fig1_bb4_in___1, n_eval_speed_pldi09_fig1_bb4_in___4
Transitions:
1:eval_speed_pldi09_fig1_bb0_in(Arg_0,Arg_1,Arg_2) -> eval_speed_pldi09_fig1_bb1_in(Arg_0,0,0)
72:eval_speed_pldi09_fig1_bb1_in(Arg_0,Arg_1,Arg_2) -> n_eval_speed_pldi09_fig1_bb2_in___9(Arg_0,Arg_1,Arg_2):|:Arg_2<=0 && Arg_2<=Arg_1 && Arg_1+Arg_2<=0 && 0<=Arg_2 && 0<=Arg_1+Arg_2 && Arg_1<=Arg_2 && Arg_1<=0 && 0<=Arg_1 && Arg_2<=Arg_1 && 0<=Arg_2 && Arg_1<=0 && 0<=Arg_1 && Arg_2<=0 && 0<=Arg_2 && Arg_1<Arg_0 && Arg_2<=Arg_1 && 0<=Arg_2
73:eval_speed_pldi09_fig1_bb1_in(Arg_0,Arg_1,Arg_2) -> n_eval_speed_pldi09_fig1_bb3_in___8(Arg_0,Arg_1,Arg_2):|:Arg_2<=0 && Arg_2<=Arg_1 && Arg_1+Arg_2<=0 && 0<=Arg_2 && 0<=Arg_1+Arg_2 && Arg_1<=Arg_2 && Arg_1<=0 && 0<=Arg_1 && Arg_2<=Arg_1 && 0<=Arg_2 && Arg_1<=0 && 0<=Arg_1 && Arg_2<=0 && 0<=Arg_2 && Arg_2<=Arg_1 && 0<=Arg_2 && Arg_0<=Arg_1
8:eval_speed_pldi09_fig1_bb5_in(Arg_0,Arg_1,Arg_2) -> eval_speed_pldi09_fig1_stop(Arg_0,Arg_1,Arg_2):|:Arg_2<=0 && Arg_2<=Arg_1 && 0<=Arg_2 && 0<=Arg_1+Arg_2 && 0<=Arg_1 && Arg_0<=Arg_1 && Arg_2<=0 && Arg_2<=Arg_1 && 0<=Arg_2 && 0<=Arg_1+Arg_2 && 0<=Arg_1 && Arg_0<=Arg_1
0:eval_speed_pldi09_fig1_start(Arg_0,Arg_1,Arg_2) -> eval_speed_pldi09_fig1_bb0_in(Arg_0,Arg_1,Arg_2)
74:n_eval_speed_pldi09_fig1_bb1_in___3(Arg_0,Arg_1,Arg_2) -> n_eval_speed_pldi09_fig1_bb3_in___2(Arg_0,Arg_1,Arg_2):|:1+Arg_2<=Arg_1 && 1+Arg_2<=Arg_0 && 0<=Arg_2 && 1<=Arg_1+Arg_2 && 1<=Arg_0+Arg_2 && Arg_1<=Arg_0 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 1<=Arg_0 && Arg_2<=Arg_1 && 0<=Arg_2 && Arg_0<=Arg_1 && 0<=Arg_2 && Arg_2<=Arg_1 && Arg_0<=Arg_1 && 0<=Arg_2 && 1+Arg_2<=Arg_1 && Arg_0<=Arg_1 && Arg_2<=Arg_1 && 0<=Arg_2 && Arg_0<=Arg_1
75:n_eval_speed_pldi09_fig1_bb1_in___7(Arg_0,Arg_1,Arg_2) -> n_eval_speed_pldi09_fig1_bb2_in___6(Arg_0,Arg_1,Arg_2):|:Arg_2<=Arg_1 && Arg_2<=Arg_0 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 2<=Arg_0+Arg_2 && Arg_1<=Arg_0 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 && Arg_2<=Arg_1 && 0<=Arg_2 && 0<Arg_2 && 1<=Arg_2 && 1<=Arg_2 && Arg_2<=Arg_1 && Arg_1<=Arg_0 && Arg_1<Arg_0 && Arg_2<=Arg_1 && 0<=Arg_2
76:n_eval_speed_pldi09_fig1_bb1_in___7(Arg_0,Arg_1,Arg_2) -> n_eval_speed_pldi09_fig1_bb3_in___5(Arg_0,Arg_1,Arg_2):|:Arg_2<=Arg_1 && Arg_2<=Arg_0 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 2<=Arg_0+Arg_2 && Arg_1<=Arg_0 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 && Arg_2<=Arg_1 && 0<=Arg_2 && 0<Arg_2 && 1<=Arg_2 && 1<=Arg_2 && Arg_2<=Arg_1 && Arg_1<=Arg_0 && Arg_2<=Arg_1 && 0<=Arg_2 && Arg_0<=Arg_1
77:n_eval_speed_pldi09_fig1_bb2_in___6(Arg_0,Arg_1,Arg_2) -> n_eval_speed_pldi09_fig1_bb1_in___7(Arg_0,Arg_1+1,Arg_2+1):|:Arg_2<=Arg_1 && 1+Arg_2<=Arg_0 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 3<=Arg_0+Arg_2 && 1+Arg_1<=Arg_0 && 1<=Arg_1 && 3<=Arg_0+Arg_1 && 2<=Arg_0 && Arg_1<Arg_0 && Arg_2<=Arg_1 && 1<=Arg_2 && 1+Arg_1<=Arg_0 && Arg_2<=Arg_1 && 0<=Arg_2
78:n_eval_speed_pldi09_fig1_bb2_in___9(Arg_0,Arg_1,Arg_2) -> n_eval_speed_pldi09_fig1_bb1_in___7(Arg_0,Arg_1+1,Arg_2+1):|:Arg_2<=0 && Arg_2<=Arg_1 && Arg_1+Arg_2<=0 && 1+Arg_2<=Arg_0 && 0<=Arg_2 && 0<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 1<=Arg_0+Arg_2 && Arg_1<=0 && 1+Arg_1<=Arg_0 && 0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 && 0<Arg_0 && Arg_2<=0 && 0<=Arg_2 && Arg_1<=0 && 0<=Arg_1 && 1+Arg_1<=Arg_0 && Arg_2<=Arg_1 && 0<=Arg_2
92:n_eval_speed_pldi09_fig1_bb3_in___2(Arg_0,Arg_1,Arg_2) -> eval_speed_pldi09_fig1_bb5_in(Arg_0,Arg_1,Arg_2):|:1+Arg_2<=Arg_1 && 1+Arg_2<=Arg_0 && 0<=Arg_2 && 1<=Arg_1+Arg_2 && 1<=Arg_0+Arg_2 && Arg_1<=Arg_0 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 1<=Arg_0 && Arg_2<=Arg_1 && 0<=Arg_2 && 0<=Arg_1+Arg_2 && 0<=Arg_1 && Arg_0<=Arg_1 && Arg_2<=0
79:n_eval_speed_pldi09_fig1_bb3_in___2(Arg_0,Arg_1,Arg_2) -> n_eval_speed_pldi09_fig1_bb4_in___1(Arg_0,Arg_1,Arg_2):|:1+Arg_2<=Arg_1 && 1+Arg_2<=Arg_0 && 0<=Arg_2 && 1<=Arg_1+Arg_2 && 1<=Arg_0+Arg_2 && Arg_1<=Arg_0 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 1<=Arg_0 && Arg_0<=Arg_1 && 1+Arg_2<=Arg_1 && 0<=Arg_2 && Arg_2<=Arg_1 && 0<Arg_2 && Arg_0<=Arg_1
80:n_eval_speed_pldi09_fig1_bb3_in___5(Arg_0,Arg_1,Arg_2) -> n_eval_speed_pldi09_fig1_bb4_in___4(Arg_0,Arg_1,Arg_2):|:Arg_2<=Arg_1 && Arg_2<=Arg_0 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 2<=Arg_0+Arg_2 && Arg_0<=Arg_2 && Arg_1<=Arg_0 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 1<=Arg_0 && Arg_2<=Arg_0 && 1<=Arg_2 && Arg_0<=Arg_1 && Arg_1<=Arg_0 && Arg_2<=Arg_1 && 0<Arg_2 && Arg_0<=Arg_1
94:n_eval_speed_pldi09_fig1_bb3_in___8(Arg_0,Arg_1,Arg_2) -> eval_speed_pldi09_fig1_bb5_in(Arg_0,Arg_1,Arg_2):|:Arg_2<=0 && Arg_2<=Arg_1 && Arg_1+Arg_2<=0 && Arg_0+Arg_2<=0 && 0<=Arg_2 && 0<=Arg_1+Arg_2 && Arg_1<=Arg_2 && Arg_0<=Arg_2 && Arg_1<=0 && Arg_0+Arg_1<=0 && 0<=Arg_1 && Arg_0<=Arg_1 && Arg_0<=0 && Arg_2<=Arg_1 && 0<=Arg_2 && 0<=Arg_1+Arg_2 && 0<=Arg_1 && Arg_0<=Arg_1 && Arg_2<=0
81:n_eval_speed_pldi09_fig1_bb4_in___1(Arg_0,Arg_1,Arg_2) -> n_eval_speed_pldi09_fig1_bb1_in___3(Arg_0,Arg_1,Arg_2-1):|:1+Arg_2<=Arg_1 && 1+Arg_2<=Arg_0 && 1<=Arg_2 && 3<=Arg_1+Arg_2 && 3<=Arg_0+Arg_2 && Arg_1<=Arg_0 && 2<=Arg_1 && 4<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 2<=Arg_0 && Arg_0<=Arg_1 && 1+Arg_2<=Arg_1 && 0<Arg_2 && Arg_2<=Arg_1 && 1<=Arg_2 && Arg_0<=Arg_1
82:n_eval_speed_pldi09_fig1_bb4_in___4(Arg_0,Arg_1,Arg_2) -> n_eval_speed_pldi09_fig1_bb1_in___3(Arg_0,Arg_1,Arg_2-1):|:Arg_2<=Arg_1 && Arg_2<=Arg_0 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 2<=Arg_0+Arg_2 && Arg_0<=Arg_2 && Arg_1<=Arg_0 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 1<=Arg_0 && Arg_2<=Arg_0 && 1<=Arg_2 && Arg_0<=Arg_1 && Arg_1<=Arg_0 && Arg_2<=Arg_1 && 1<=Arg_2 && Arg_0<=Arg_1
All Bounds
Timebounds
Overall timebound:5*Arg_0+25 {O(n)}
1: eval_speed_pldi09_fig1_bb0_in->eval_speed_pldi09_fig1_bb1_in: 1 {O(1)}
72: eval_speed_pldi09_fig1_bb1_in->n_eval_speed_pldi09_fig1_bb2_in___9: 1 {O(1)}
73: eval_speed_pldi09_fig1_bb1_in->n_eval_speed_pldi09_fig1_bb3_in___8: 1 {O(1)}
8: eval_speed_pldi09_fig1_bb5_in->eval_speed_pldi09_fig1_stop: 1 {O(1)}
0: eval_speed_pldi09_fig1_start->eval_speed_pldi09_fig1_bb0_in: 1 {O(1)}
74: n_eval_speed_pldi09_fig1_bb1_in___3->n_eval_speed_pldi09_fig1_bb3_in___2: Arg_0+4 {O(n)}
75: n_eval_speed_pldi09_fig1_bb1_in___7->n_eval_speed_pldi09_fig1_bb2_in___6: Arg_0+2 {O(n)}
76: n_eval_speed_pldi09_fig1_bb1_in___7->n_eval_speed_pldi09_fig1_bb3_in___5: 1 {O(1)}
77: n_eval_speed_pldi09_fig1_bb2_in___6->n_eval_speed_pldi09_fig1_bb1_in___7: Arg_0+1 {O(n)}
78: n_eval_speed_pldi09_fig1_bb2_in___9->n_eval_speed_pldi09_fig1_bb1_in___7: 1 {O(1)}
79: n_eval_speed_pldi09_fig1_bb3_in___2->n_eval_speed_pldi09_fig1_bb4_in___1: Arg_0+4 {O(n)}
92: n_eval_speed_pldi09_fig1_bb3_in___2->eval_speed_pldi09_fig1_bb5_in: 1 {O(1)}
80: n_eval_speed_pldi09_fig1_bb3_in___5->n_eval_speed_pldi09_fig1_bb4_in___4: 1 {O(1)}
94: n_eval_speed_pldi09_fig1_bb3_in___8->eval_speed_pldi09_fig1_bb5_in: 1 {O(1)}
81: n_eval_speed_pldi09_fig1_bb4_in___1->n_eval_speed_pldi09_fig1_bb1_in___3: Arg_0+3 {O(n)}
82: n_eval_speed_pldi09_fig1_bb4_in___4->n_eval_speed_pldi09_fig1_bb1_in___3: 1 {O(1)}
Costbounds
Overall costbound: 5*Arg_0+25 {O(n)}
1: eval_speed_pldi09_fig1_bb0_in->eval_speed_pldi09_fig1_bb1_in: 1 {O(1)}
72: eval_speed_pldi09_fig1_bb1_in->n_eval_speed_pldi09_fig1_bb2_in___9: 1 {O(1)}
73: eval_speed_pldi09_fig1_bb1_in->n_eval_speed_pldi09_fig1_bb3_in___8: 1 {O(1)}
8: eval_speed_pldi09_fig1_bb5_in->eval_speed_pldi09_fig1_stop: 1 {O(1)}
0: eval_speed_pldi09_fig1_start->eval_speed_pldi09_fig1_bb0_in: 1 {O(1)}
74: n_eval_speed_pldi09_fig1_bb1_in___3->n_eval_speed_pldi09_fig1_bb3_in___2: Arg_0+4 {O(n)}
75: n_eval_speed_pldi09_fig1_bb1_in___7->n_eval_speed_pldi09_fig1_bb2_in___6: Arg_0+2 {O(n)}
76: n_eval_speed_pldi09_fig1_bb1_in___7->n_eval_speed_pldi09_fig1_bb3_in___5: 1 {O(1)}
77: n_eval_speed_pldi09_fig1_bb2_in___6->n_eval_speed_pldi09_fig1_bb1_in___7: Arg_0+1 {O(n)}
78: n_eval_speed_pldi09_fig1_bb2_in___9->n_eval_speed_pldi09_fig1_bb1_in___7: 1 {O(1)}
79: n_eval_speed_pldi09_fig1_bb3_in___2->n_eval_speed_pldi09_fig1_bb4_in___1: Arg_0+4 {O(n)}
92: n_eval_speed_pldi09_fig1_bb3_in___2->eval_speed_pldi09_fig1_bb5_in: 1 {O(1)}
80: n_eval_speed_pldi09_fig1_bb3_in___5->n_eval_speed_pldi09_fig1_bb4_in___4: 1 {O(1)}
94: n_eval_speed_pldi09_fig1_bb3_in___8->eval_speed_pldi09_fig1_bb5_in: 1 {O(1)}
81: n_eval_speed_pldi09_fig1_bb4_in___1->n_eval_speed_pldi09_fig1_bb1_in___3: Arg_0+3 {O(n)}
82: n_eval_speed_pldi09_fig1_bb4_in___4->n_eval_speed_pldi09_fig1_bb1_in___3: 1 {O(1)}
Sizebounds
1: eval_speed_pldi09_fig1_bb0_in->eval_speed_pldi09_fig1_bb1_in, Arg_0: Arg_0 {O(n)}
1: eval_speed_pldi09_fig1_bb0_in->eval_speed_pldi09_fig1_bb1_in, Arg_1: 0 {O(1)}
1: eval_speed_pldi09_fig1_bb0_in->eval_speed_pldi09_fig1_bb1_in, Arg_2: 0 {O(1)}
72: eval_speed_pldi09_fig1_bb1_in->n_eval_speed_pldi09_fig1_bb2_in___9, Arg_0: Arg_0 {O(n)}
72: eval_speed_pldi09_fig1_bb1_in->n_eval_speed_pldi09_fig1_bb2_in___9, Arg_1: 0 {O(1)}
72: eval_speed_pldi09_fig1_bb1_in->n_eval_speed_pldi09_fig1_bb2_in___9, Arg_2: 0 {O(1)}
73: eval_speed_pldi09_fig1_bb1_in->n_eval_speed_pldi09_fig1_bb3_in___8, Arg_0: Arg_0 {O(n)}
73: eval_speed_pldi09_fig1_bb1_in->n_eval_speed_pldi09_fig1_bb3_in___8, Arg_1: 0 {O(1)}
73: eval_speed_pldi09_fig1_bb1_in->n_eval_speed_pldi09_fig1_bb3_in___8, Arg_2: 0 {O(1)}
8: eval_speed_pldi09_fig1_bb5_in->eval_speed_pldi09_fig1_stop, Arg_0: 3*Arg_0 {O(n)}
8: eval_speed_pldi09_fig1_bb5_in->eval_speed_pldi09_fig1_stop, Arg_1: Arg_0 {O(n)}
8: eval_speed_pldi09_fig1_bb5_in->eval_speed_pldi09_fig1_stop, Arg_2: 0 {O(1)}
0: eval_speed_pldi09_fig1_start->eval_speed_pldi09_fig1_bb0_in, Arg_0: Arg_0 {O(n)}
0: eval_speed_pldi09_fig1_start->eval_speed_pldi09_fig1_bb0_in, Arg_1: Arg_1 {O(n)}
0: eval_speed_pldi09_fig1_start->eval_speed_pldi09_fig1_bb0_in, Arg_2: Arg_2 {O(n)}
74: n_eval_speed_pldi09_fig1_bb1_in___3->n_eval_speed_pldi09_fig1_bb3_in___2, Arg_0: 2*Arg_0 {O(n)}
74: n_eval_speed_pldi09_fig1_bb1_in___3->n_eval_speed_pldi09_fig1_bb3_in___2, Arg_1: Arg_0+3 {O(n)}
74: n_eval_speed_pldi09_fig1_bb1_in___3->n_eval_speed_pldi09_fig1_bb3_in___2, Arg_2: Arg_0+3 {O(n)}
75: n_eval_speed_pldi09_fig1_bb1_in___7->n_eval_speed_pldi09_fig1_bb2_in___6, Arg_0: Arg_0 {O(n)}
75: n_eval_speed_pldi09_fig1_bb1_in___7->n_eval_speed_pldi09_fig1_bb2_in___6, Arg_1: Arg_0+2 {O(n)}
75: n_eval_speed_pldi09_fig1_bb1_in___7->n_eval_speed_pldi09_fig1_bb2_in___6, Arg_2: Arg_0+2 {O(n)}
76: n_eval_speed_pldi09_fig1_bb1_in___7->n_eval_speed_pldi09_fig1_bb3_in___5, Arg_0: 2*Arg_0 {O(n)}
76: n_eval_speed_pldi09_fig1_bb1_in___7->n_eval_speed_pldi09_fig1_bb3_in___5, Arg_1: Arg_0+3 {O(n)}
76: n_eval_speed_pldi09_fig1_bb1_in___7->n_eval_speed_pldi09_fig1_bb3_in___5, Arg_2: Arg_0+3 {O(n)}
77: n_eval_speed_pldi09_fig1_bb2_in___6->n_eval_speed_pldi09_fig1_bb1_in___7, Arg_0: Arg_0 {O(n)}
77: n_eval_speed_pldi09_fig1_bb2_in___6->n_eval_speed_pldi09_fig1_bb1_in___7, Arg_1: Arg_0+2 {O(n)}
77: n_eval_speed_pldi09_fig1_bb2_in___6->n_eval_speed_pldi09_fig1_bb1_in___7, Arg_2: Arg_0+2 {O(n)}
78: n_eval_speed_pldi09_fig1_bb2_in___9->n_eval_speed_pldi09_fig1_bb1_in___7, Arg_0: Arg_0 {O(n)}
78: n_eval_speed_pldi09_fig1_bb2_in___9->n_eval_speed_pldi09_fig1_bb1_in___7, Arg_1: 1 {O(1)}
78: n_eval_speed_pldi09_fig1_bb2_in___9->n_eval_speed_pldi09_fig1_bb1_in___7, Arg_2: 1 {O(1)}
79: n_eval_speed_pldi09_fig1_bb3_in___2->n_eval_speed_pldi09_fig1_bb4_in___1, Arg_0: 2*Arg_0 {O(n)}
79: n_eval_speed_pldi09_fig1_bb3_in___2->n_eval_speed_pldi09_fig1_bb4_in___1, Arg_1: Arg_0+3 {O(n)}
79: n_eval_speed_pldi09_fig1_bb3_in___2->n_eval_speed_pldi09_fig1_bb4_in___1, Arg_2: Arg_0+3 {O(n)}
92: n_eval_speed_pldi09_fig1_bb3_in___2->eval_speed_pldi09_fig1_bb5_in, Arg_0: 2*Arg_0 {O(n)}
92: n_eval_speed_pldi09_fig1_bb3_in___2->eval_speed_pldi09_fig1_bb5_in, Arg_1: Arg_0+3 {O(n)}
92: n_eval_speed_pldi09_fig1_bb3_in___2->eval_speed_pldi09_fig1_bb5_in, Arg_2: 0 {O(1)}
80: n_eval_speed_pldi09_fig1_bb3_in___5->n_eval_speed_pldi09_fig1_bb4_in___4, Arg_0: 2*Arg_0 {O(n)}
80: n_eval_speed_pldi09_fig1_bb3_in___5->n_eval_speed_pldi09_fig1_bb4_in___4, Arg_1: Arg_0+3 {O(n)}
80: n_eval_speed_pldi09_fig1_bb3_in___5->n_eval_speed_pldi09_fig1_bb4_in___4, Arg_2: Arg_0+3 {O(n)}
94: n_eval_speed_pldi09_fig1_bb3_in___8->eval_speed_pldi09_fig1_bb5_in, Arg_0: Arg_0 {O(n)}
94: n_eval_speed_pldi09_fig1_bb3_in___8->eval_speed_pldi09_fig1_bb5_in, Arg_1: 0 {O(1)}
94: n_eval_speed_pldi09_fig1_bb3_in___8->eval_speed_pldi09_fig1_bb5_in, Arg_2: 0 {O(1)}
81: n_eval_speed_pldi09_fig1_bb4_in___1->n_eval_speed_pldi09_fig1_bb1_in___3, Arg_0: 2*Arg_0 {O(n)}
81: n_eval_speed_pldi09_fig1_bb4_in___1->n_eval_speed_pldi09_fig1_bb1_in___3, Arg_1: Arg_0+3 {O(n)}
81: n_eval_speed_pldi09_fig1_bb4_in___1->n_eval_speed_pldi09_fig1_bb1_in___3, Arg_2: Arg_0+3 {O(n)}
82: n_eval_speed_pldi09_fig1_bb4_in___4->n_eval_speed_pldi09_fig1_bb1_in___3, Arg_0: 2*Arg_0 {O(n)}
82: n_eval_speed_pldi09_fig1_bb4_in___4->n_eval_speed_pldi09_fig1_bb1_in___3, Arg_1: Arg_0+3 {O(n)}
82: n_eval_speed_pldi09_fig1_bb4_in___4->n_eval_speed_pldi09_fig1_bb1_in___3, Arg_2: Arg_0+3 {O(n)}