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 ]
All Bounds
Timebounds
Overall timebound:3*Arg_0*Arg_0+4*Arg_0+6 {O(n^2)}
1: eval_speed_pldi09_fig1_bb0_in->eval_speed_pldi09_fig1_bb1_in: 1 {O(1)}
2: eval_speed_pldi09_fig1_bb1_in->eval_speed_pldi09_fig1_bb2_in: Arg_0 {O(n)}
3: eval_speed_pldi09_fig1_bb1_in->eval_speed_pldi09_fig1_bb3_in: Arg_0*Arg_0+Arg_0+1 {O(n^2)}
4: eval_speed_pldi09_fig1_bb2_in->eval_speed_pldi09_fig1_bb1_in: Arg_0 {O(n)}
5: eval_speed_pldi09_fig1_bb3_in->eval_speed_pldi09_fig1_bb4_in: Arg_0*Arg_0+Arg_0+1 {O(n^2)}
6: eval_speed_pldi09_fig1_bb3_in->eval_speed_pldi09_fig1_bb5_in: 1 {O(1)}
7: eval_speed_pldi09_fig1_bb4_in->eval_speed_pldi09_fig1_bb1_in: Arg_0*Arg_0 {O(n^2)}
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)}
Costbounds
Overall costbound: 3*Arg_0*Arg_0+4*Arg_0+6 {O(n^2)}
1: eval_speed_pldi09_fig1_bb0_in->eval_speed_pldi09_fig1_bb1_in: 1 {O(1)}
2: eval_speed_pldi09_fig1_bb1_in->eval_speed_pldi09_fig1_bb2_in: Arg_0 {O(n)}
3: eval_speed_pldi09_fig1_bb1_in->eval_speed_pldi09_fig1_bb3_in: Arg_0*Arg_0+Arg_0+1 {O(n^2)}
4: eval_speed_pldi09_fig1_bb2_in->eval_speed_pldi09_fig1_bb1_in: Arg_0 {O(n)}
5: eval_speed_pldi09_fig1_bb3_in->eval_speed_pldi09_fig1_bb4_in: Arg_0*Arg_0+Arg_0+1 {O(n^2)}
6: eval_speed_pldi09_fig1_bb3_in->eval_speed_pldi09_fig1_bb5_in: 1 {O(1)}
7: eval_speed_pldi09_fig1_bb4_in->eval_speed_pldi09_fig1_bb1_in: Arg_0*Arg_0 {O(n^2)}
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)}
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)}
2: eval_speed_pldi09_fig1_bb1_in->eval_speed_pldi09_fig1_bb2_in, Arg_0: Arg_0 {O(n)}
2: eval_speed_pldi09_fig1_bb1_in->eval_speed_pldi09_fig1_bb2_in, Arg_1: Arg_0 {O(n)}
2: eval_speed_pldi09_fig1_bb1_in->eval_speed_pldi09_fig1_bb2_in, Arg_2: Arg_0 {O(n)}
3: eval_speed_pldi09_fig1_bb1_in->eval_speed_pldi09_fig1_bb3_in, Arg_0: 2*Arg_0 {O(n)}
3: eval_speed_pldi09_fig1_bb1_in->eval_speed_pldi09_fig1_bb3_in, Arg_1: Arg_0 {O(n)}
3: eval_speed_pldi09_fig1_bb1_in->eval_speed_pldi09_fig1_bb3_in, Arg_2: Arg_0 {O(n)}
4: eval_speed_pldi09_fig1_bb2_in->eval_speed_pldi09_fig1_bb1_in, Arg_0: Arg_0 {O(n)}
4: eval_speed_pldi09_fig1_bb2_in->eval_speed_pldi09_fig1_bb1_in, Arg_1: Arg_0 {O(n)}
4: eval_speed_pldi09_fig1_bb2_in->eval_speed_pldi09_fig1_bb1_in, Arg_2: Arg_0 {O(n)}
5: eval_speed_pldi09_fig1_bb3_in->eval_speed_pldi09_fig1_bb4_in, Arg_0: 2*Arg_0 {O(n)}
5: eval_speed_pldi09_fig1_bb3_in->eval_speed_pldi09_fig1_bb4_in, Arg_1: Arg_0 {O(n)}
5: eval_speed_pldi09_fig1_bb3_in->eval_speed_pldi09_fig1_bb4_in, Arg_2: Arg_0 {O(n)}
6: eval_speed_pldi09_fig1_bb3_in->eval_speed_pldi09_fig1_bb5_in, Arg_0: 2*Arg_0 {O(n)}
6: eval_speed_pldi09_fig1_bb3_in->eval_speed_pldi09_fig1_bb5_in, Arg_1: Arg_0 {O(n)}
6: eval_speed_pldi09_fig1_bb3_in->eval_speed_pldi09_fig1_bb5_in, Arg_2: 0 {O(1)}
7: eval_speed_pldi09_fig1_bb4_in->eval_speed_pldi09_fig1_bb1_in, Arg_0: 2*Arg_0 {O(n)}
7: eval_speed_pldi09_fig1_bb4_in->eval_speed_pldi09_fig1_bb1_in, Arg_1: Arg_0 {O(n)}
7: eval_speed_pldi09_fig1_bb4_in->eval_speed_pldi09_fig1_bb1_in, Arg_2: Arg_0 {O(n)}
8: eval_speed_pldi09_fig1_bb5_in->eval_speed_pldi09_fig1_stop, Arg_0: 2*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)}