Initial Problem

Start: eval_speed_pldi10_ex4_start
Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3, Arg_4
Temp_Vars:
Locations: eval_speed_pldi10_ex4_bb0_in, eval_speed_pldi10_ex4_bb1_in, eval_speed_pldi10_ex4_bb2_in, eval_speed_pldi10_ex4_bb3_in, eval_speed_pldi10_ex4_bb4_in, eval_speed_pldi10_ex4_start, eval_speed_pldi10_ex4_stop
Transitions:
1:eval_speed_pldi10_ex4_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_speed_pldi10_ex4_bb1_in(Arg_4,Arg_1,1,Arg_3,Arg_4)
2:eval_speed_pldi10_ex4_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_speed_pldi10_ex4_bb2_in(Arg_0,Arg_0,Arg_2,0,Arg_4):|:0<Arg_2
3:eval_speed_pldi10_ex4_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_speed_pldi10_ex4_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:Arg_2<=0
5:eval_speed_pldi10_ex4_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_speed_pldi10_ex4_bb1_in(Arg_1,Arg_1,Arg_3,Arg_3,Arg_4):|:Arg_1<=0
4:eval_speed_pldi10_ex4_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_speed_pldi10_ex4_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:0<Arg_1
6:eval_speed_pldi10_ex4_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_speed_pldi10_ex4_bb2_in(Arg_0,Arg_1-1,Arg_2,1,Arg_4)
7:eval_speed_pldi10_ex4_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_speed_pldi10_ex4_stop(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4)
0:eval_speed_pldi10_ex4_start(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_speed_pldi10_ex4_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4)

Preprocessing

Found invariant Arg_0<=Arg_4 && Arg_2<=0 && 0<=Arg_2 for location eval_speed_pldi10_ex4_stop

Found invariant 1<=Arg_4 && 1<=Arg_3+Arg_4 && Arg_3<=Arg_4 && 2<=Arg_2+Arg_4 && Arg_2<=Arg_4 && 2<=Arg_1+Arg_4 && Arg_1<=Arg_4 && 2<=Arg_0+Arg_4 && Arg_0<=Arg_4 && Arg_3<=1 && Arg_3<=Arg_2 && Arg_2+Arg_3<=2 && Arg_3<=Arg_1 && Arg_3<=Arg_0 && 0<=Arg_3 && 1<=Arg_2+Arg_3 && Arg_2<=1+Arg_3 && 1<=Arg_1+Arg_3 && 1<=Arg_0+Arg_3 && Arg_2<=1 && Arg_2<=Arg_1 && Arg_2<=Arg_0 && 1<=Arg_2 && 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 eval_speed_pldi10_ex4_bb3_in

Found invariant Arg_0<=Arg_4 && Arg_2<=1 && 0<=Arg_2 for location eval_speed_pldi10_ex4_bb1_in

Found invariant Arg_1<=Arg_4 && Arg_0<=Arg_4 && Arg_3<=1 && Arg_3<=Arg_2 && Arg_2+Arg_3<=2 && 0<=Arg_3 && 1<=Arg_2+Arg_3 && Arg_2<=1+Arg_3 && Arg_2<=1 && 1<=Arg_2 && Arg_1<=Arg_0 for location eval_speed_pldi10_ex4_bb2_in

Found invariant Arg_0<=Arg_4 && Arg_2<=0 && 0<=Arg_2 for location eval_speed_pldi10_ex4_bb4_in

Problem after Preprocessing

Start: eval_speed_pldi10_ex4_start
Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3, Arg_4
Temp_Vars:
Locations: eval_speed_pldi10_ex4_bb0_in, eval_speed_pldi10_ex4_bb1_in, eval_speed_pldi10_ex4_bb2_in, eval_speed_pldi10_ex4_bb3_in, eval_speed_pldi10_ex4_bb4_in, eval_speed_pldi10_ex4_start, eval_speed_pldi10_ex4_stop
Transitions:
1:eval_speed_pldi10_ex4_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_speed_pldi10_ex4_bb1_in(Arg_4,Arg_1,1,Arg_3,Arg_4)
2:eval_speed_pldi10_ex4_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_speed_pldi10_ex4_bb2_in(Arg_0,Arg_0,Arg_2,0,Arg_4):|:Arg_0<=Arg_4 && Arg_2<=1 && 0<=Arg_2 && 0<Arg_2
3:eval_speed_pldi10_ex4_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_speed_pldi10_ex4_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:Arg_0<=Arg_4 && Arg_2<=1 && 0<=Arg_2 && Arg_2<=0
5:eval_speed_pldi10_ex4_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_speed_pldi10_ex4_bb1_in(Arg_1,Arg_1,Arg_3,Arg_3,Arg_4):|:Arg_1<=Arg_4 && Arg_0<=Arg_4 && Arg_3<=1 && Arg_3<=Arg_2 && Arg_2+Arg_3<=2 && 0<=Arg_3 && 1<=Arg_2+Arg_3 && Arg_2<=1+Arg_3 && Arg_2<=1 && 1<=Arg_2 && Arg_1<=Arg_0 && Arg_1<=0
4:eval_speed_pldi10_ex4_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_speed_pldi10_ex4_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:Arg_1<=Arg_4 && Arg_0<=Arg_4 && Arg_3<=1 && Arg_3<=Arg_2 && Arg_2+Arg_3<=2 && 0<=Arg_3 && 1<=Arg_2+Arg_3 && Arg_2<=1+Arg_3 && Arg_2<=1 && 1<=Arg_2 && Arg_1<=Arg_0 && 0<Arg_1
6:eval_speed_pldi10_ex4_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_speed_pldi10_ex4_bb2_in(Arg_0,Arg_1-1,Arg_2,1,Arg_4):|:1<=Arg_4 && 1<=Arg_3+Arg_4 && Arg_3<=Arg_4 && 2<=Arg_2+Arg_4 && Arg_2<=Arg_4 && 2<=Arg_1+Arg_4 && Arg_1<=Arg_4 && 2<=Arg_0+Arg_4 && Arg_0<=Arg_4 && Arg_3<=1 && Arg_3<=Arg_2 && Arg_2+Arg_3<=2 && Arg_3<=Arg_1 && Arg_3<=Arg_0 && 0<=Arg_3 && 1<=Arg_2+Arg_3 && Arg_2<=1+Arg_3 && 1<=Arg_1+Arg_3 && 1<=Arg_0+Arg_3 && Arg_2<=1 && Arg_2<=Arg_1 && Arg_2<=Arg_0 && 1<=Arg_2 && 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
7:eval_speed_pldi10_ex4_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_speed_pldi10_ex4_stop(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:Arg_0<=Arg_4 && Arg_2<=0 && 0<=Arg_2
0:eval_speed_pldi10_ex4_start(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_speed_pldi10_ex4_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4)

MPRF for transition 4:eval_speed_pldi10_ex4_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_speed_pldi10_ex4_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:Arg_1<=Arg_4 && Arg_0<=Arg_4 && Arg_3<=1 && Arg_3<=Arg_2 && Arg_2+Arg_3<=2 && 0<=Arg_3 && 1<=Arg_2+Arg_3 && Arg_2<=1+Arg_3 && Arg_2<=1 && 1<=Arg_2 && Arg_1<=Arg_0 && 0<Arg_1 of depth 1:

new bound:

Arg_4 {O(n)}

MPRF:

eval_speed_pldi10_ex4_bb1_in [Arg_0 ]
eval_speed_pldi10_ex4_bb3_in [Arg_1-1 ]
eval_speed_pldi10_ex4_bb2_in [Arg_1 ]

MPRF for transition 6:eval_speed_pldi10_ex4_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_speed_pldi10_ex4_bb2_in(Arg_0,Arg_1-1,Arg_2,1,Arg_4):|:1<=Arg_4 && 1<=Arg_3+Arg_4 && Arg_3<=Arg_4 && 2<=Arg_2+Arg_4 && Arg_2<=Arg_4 && 2<=Arg_1+Arg_4 && Arg_1<=Arg_4 && 2<=Arg_0+Arg_4 && Arg_0<=Arg_4 && Arg_3<=1 && Arg_3<=Arg_2 && Arg_2+Arg_3<=2 && Arg_3<=Arg_1 && Arg_3<=Arg_0 && 0<=Arg_3 && 1<=Arg_2+Arg_3 && Arg_2<=1+Arg_3 && 1<=Arg_1+Arg_3 && 1<=Arg_0+Arg_3 && Arg_2<=1 && Arg_2<=Arg_1 && Arg_2<=Arg_0 && 1<=Arg_2 && 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 of depth 1:

new bound:

Arg_4 {O(n)}

MPRF:

eval_speed_pldi10_ex4_bb1_in [Arg_0 ]
eval_speed_pldi10_ex4_bb3_in [Arg_1 ]
eval_speed_pldi10_ex4_bb2_in [Arg_1 ]

MPRF for transition 2:eval_speed_pldi10_ex4_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_speed_pldi10_ex4_bb2_in(Arg_0,Arg_0,Arg_2,0,Arg_4):|:Arg_0<=Arg_4 && Arg_2<=1 && 0<=Arg_2 && 0<Arg_2 of depth 1:

new bound:

2*Arg_4+2 {O(n)}

MPRF:

eval_speed_pldi10_ex4_bb3_in [Arg_2 ]
eval_speed_pldi10_ex4_bb2_in [Arg_2+Arg_3 ]
eval_speed_pldi10_ex4_bb1_in [Arg_2+1 ]

MPRF for transition 5:eval_speed_pldi10_ex4_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_speed_pldi10_ex4_bb1_in(Arg_1,Arg_1,Arg_3,Arg_3,Arg_4):|:Arg_1<=Arg_4 && Arg_0<=Arg_4 && Arg_3<=1 && Arg_3<=Arg_2 && Arg_2+Arg_3<=2 && 0<=Arg_3 && 1<=Arg_2+Arg_3 && Arg_2<=1+Arg_3 && Arg_2<=1 && 1<=Arg_2 && Arg_1<=Arg_0 && Arg_1<=0 of depth 1:

new bound:

2*Arg_4+1 {O(n)}

MPRF:

eval_speed_pldi10_ex4_bb3_in [Arg_3+1 ]
eval_speed_pldi10_ex4_bb2_in [Arg_3+1 ]
eval_speed_pldi10_ex4_bb1_in [Arg_2 ]

All Bounds

Timebounds

Overall timebound:6*Arg_4+7 {O(n)}
1: eval_speed_pldi10_ex4_bb0_in->eval_speed_pldi10_ex4_bb1_in: 1 {O(1)}
2: eval_speed_pldi10_ex4_bb1_in->eval_speed_pldi10_ex4_bb2_in: 2*Arg_4+2 {O(n)}
3: eval_speed_pldi10_ex4_bb1_in->eval_speed_pldi10_ex4_bb4_in: 1 {O(1)}
4: eval_speed_pldi10_ex4_bb2_in->eval_speed_pldi10_ex4_bb3_in: Arg_4 {O(n)}
5: eval_speed_pldi10_ex4_bb2_in->eval_speed_pldi10_ex4_bb1_in: 2*Arg_4+1 {O(n)}
6: eval_speed_pldi10_ex4_bb3_in->eval_speed_pldi10_ex4_bb2_in: Arg_4 {O(n)}
7: eval_speed_pldi10_ex4_bb4_in->eval_speed_pldi10_ex4_stop: 1 {O(1)}
0: eval_speed_pldi10_ex4_start->eval_speed_pldi10_ex4_bb0_in: 1 {O(1)}

Costbounds

Overall costbound: 6*Arg_4+7 {O(n)}
1: eval_speed_pldi10_ex4_bb0_in->eval_speed_pldi10_ex4_bb1_in: 1 {O(1)}
2: eval_speed_pldi10_ex4_bb1_in->eval_speed_pldi10_ex4_bb2_in: 2*Arg_4+2 {O(n)}
3: eval_speed_pldi10_ex4_bb1_in->eval_speed_pldi10_ex4_bb4_in: 1 {O(1)}
4: eval_speed_pldi10_ex4_bb2_in->eval_speed_pldi10_ex4_bb3_in: Arg_4 {O(n)}
5: eval_speed_pldi10_ex4_bb2_in->eval_speed_pldi10_ex4_bb1_in: 2*Arg_4+1 {O(n)}
6: eval_speed_pldi10_ex4_bb3_in->eval_speed_pldi10_ex4_bb2_in: Arg_4 {O(n)}
7: eval_speed_pldi10_ex4_bb4_in->eval_speed_pldi10_ex4_stop: 1 {O(1)}
0: eval_speed_pldi10_ex4_start->eval_speed_pldi10_ex4_bb0_in: 1 {O(1)}

Sizebounds

1: eval_speed_pldi10_ex4_bb0_in->eval_speed_pldi10_ex4_bb1_in, Arg_0: Arg_4 {O(n)}
1: eval_speed_pldi10_ex4_bb0_in->eval_speed_pldi10_ex4_bb1_in, Arg_1: Arg_1 {O(n)}
1: eval_speed_pldi10_ex4_bb0_in->eval_speed_pldi10_ex4_bb1_in, Arg_2: 1 {O(1)}
1: eval_speed_pldi10_ex4_bb0_in->eval_speed_pldi10_ex4_bb1_in, Arg_3: Arg_3 {O(n)}
1: eval_speed_pldi10_ex4_bb0_in->eval_speed_pldi10_ex4_bb1_in, Arg_4: Arg_4 {O(n)}
2: eval_speed_pldi10_ex4_bb1_in->eval_speed_pldi10_ex4_bb2_in, Arg_0: 2*Arg_4 {O(n)}
2: eval_speed_pldi10_ex4_bb1_in->eval_speed_pldi10_ex4_bb2_in, Arg_1: Arg_4 {O(n)}
2: eval_speed_pldi10_ex4_bb1_in->eval_speed_pldi10_ex4_bb2_in, Arg_2: 1 {O(1)}
2: eval_speed_pldi10_ex4_bb1_in->eval_speed_pldi10_ex4_bb2_in, Arg_3: 0 {O(1)}
2: eval_speed_pldi10_ex4_bb1_in->eval_speed_pldi10_ex4_bb2_in, Arg_4: Arg_4 {O(n)}
3: eval_speed_pldi10_ex4_bb1_in->eval_speed_pldi10_ex4_bb4_in, Arg_0: Arg_4 {O(n)}
3: eval_speed_pldi10_ex4_bb1_in->eval_speed_pldi10_ex4_bb4_in, Arg_1: 2*Arg_4 {O(n)}
3: eval_speed_pldi10_ex4_bb1_in->eval_speed_pldi10_ex4_bb4_in, Arg_2: 0 {O(1)}
3: eval_speed_pldi10_ex4_bb1_in->eval_speed_pldi10_ex4_bb4_in, Arg_3: 1 {O(1)}
3: eval_speed_pldi10_ex4_bb1_in->eval_speed_pldi10_ex4_bb4_in, Arg_4: Arg_4 {O(n)}
4: eval_speed_pldi10_ex4_bb2_in->eval_speed_pldi10_ex4_bb3_in, Arg_0: 2*Arg_4 {O(n)}
4: eval_speed_pldi10_ex4_bb2_in->eval_speed_pldi10_ex4_bb3_in, Arg_1: Arg_4 {O(n)}
4: eval_speed_pldi10_ex4_bb2_in->eval_speed_pldi10_ex4_bb3_in, Arg_2: 1 {O(1)}
4: eval_speed_pldi10_ex4_bb2_in->eval_speed_pldi10_ex4_bb3_in, Arg_3: 1 {O(1)}
4: eval_speed_pldi10_ex4_bb2_in->eval_speed_pldi10_ex4_bb3_in, Arg_4: Arg_4 {O(n)}
5: eval_speed_pldi10_ex4_bb2_in->eval_speed_pldi10_ex4_bb1_in, Arg_0: Arg_4 {O(n)}
5: eval_speed_pldi10_ex4_bb2_in->eval_speed_pldi10_ex4_bb1_in, Arg_1: 2*Arg_4 {O(n)}
5: eval_speed_pldi10_ex4_bb2_in->eval_speed_pldi10_ex4_bb1_in, Arg_2: 1 {O(1)}
5: eval_speed_pldi10_ex4_bb2_in->eval_speed_pldi10_ex4_bb1_in, Arg_3: 1 {O(1)}
5: eval_speed_pldi10_ex4_bb2_in->eval_speed_pldi10_ex4_bb1_in, Arg_4: Arg_4 {O(n)}
6: eval_speed_pldi10_ex4_bb3_in->eval_speed_pldi10_ex4_bb2_in, Arg_0: 2*Arg_4 {O(n)}
6: eval_speed_pldi10_ex4_bb3_in->eval_speed_pldi10_ex4_bb2_in, Arg_1: Arg_4 {O(n)}
6: eval_speed_pldi10_ex4_bb3_in->eval_speed_pldi10_ex4_bb2_in, Arg_2: 1 {O(1)}
6: eval_speed_pldi10_ex4_bb3_in->eval_speed_pldi10_ex4_bb2_in, Arg_3: 1 {O(1)}
6: eval_speed_pldi10_ex4_bb3_in->eval_speed_pldi10_ex4_bb2_in, Arg_4: Arg_4 {O(n)}
7: eval_speed_pldi10_ex4_bb4_in->eval_speed_pldi10_ex4_stop, Arg_0: Arg_4 {O(n)}
7: eval_speed_pldi10_ex4_bb4_in->eval_speed_pldi10_ex4_stop, Arg_1: 2*Arg_4 {O(n)}
7: eval_speed_pldi10_ex4_bb4_in->eval_speed_pldi10_ex4_stop, Arg_2: 0 {O(1)}
7: eval_speed_pldi10_ex4_bb4_in->eval_speed_pldi10_ex4_stop, Arg_3: 1 {O(1)}
7: eval_speed_pldi10_ex4_bb4_in->eval_speed_pldi10_ex4_stop, Arg_4: Arg_4 {O(n)}
0: eval_speed_pldi10_ex4_start->eval_speed_pldi10_ex4_bb0_in, Arg_0: Arg_0 {O(n)}
0: eval_speed_pldi10_ex4_start->eval_speed_pldi10_ex4_bb0_in, Arg_1: Arg_1 {O(n)}
0: eval_speed_pldi10_ex4_start->eval_speed_pldi10_ex4_bb0_in, Arg_2: Arg_2 {O(n)}
0: eval_speed_pldi10_ex4_start->eval_speed_pldi10_ex4_bb0_in, Arg_3: Arg_3 {O(n)}
0: eval_speed_pldi10_ex4_start->eval_speed_pldi10_ex4_bb0_in, Arg_4: Arg_4 {O(n)}