Initial Problem

Start: eval_speedpldi2_start
Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3
Temp_Vars:
Locations: eval_speedpldi2_bb0_in, eval_speedpldi2_bb1_in, eval_speedpldi2_bb2_in, eval_speedpldi2_bb3_in, eval_speedpldi2_bb4_in, eval_speedpldi2_start, eval_speedpldi2_stop
Transitions:
1:eval_speedpldi2_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_speedpldi2_bb1_in(Arg_0,Arg_1,Arg_1,0):|:0<=Arg_1 && 0<Arg_0
2:eval_speedpldi2_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_speedpldi2_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_1<0
3:eval_speedpldi2_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_speedpldi2_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_0<=0
4:eval_speedpldi2_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_speedpldi2_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3):|:0<Arg_2
5:eval_speedpldi2_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_speedpldi2_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_2<=0
7:eval_speedpldi2_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_speedpldi2_bb1_in(Arg_0,Arg_1,Arg_2,0):|:Arg_0<=Arg_3
6:eval_speedpldi2_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_speedpldi2_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_3<Arg_0
8:eval_speedpldi2_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_speedpldi2_bb1_in(Arg_0,Arg_1,Arg_2-1,Arg_3+1)
9:eval_speedpldi2_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_speedpldi2_stop(Arg_0,Arg_1,Arg_2,Arg_3)
0:eval_speedpldi2_start(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_speedpldi2_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3)

Preprocessing

Found invariant Arg_3<=Arg_0 && 0<=Arg_3 && 0<=Arg_2+Arg_3 && 0<=Arg_1+Arg_3 && 1<=Arg_0+Arg_3 && Arg_2<=Arg_1 && 0<=Arg_2 && 0<=Arg_1+Arg_2 && 1<=Arg_0+Arg_2 && 0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 for location eval_speedpldi2_bb1_in

Found invariant Arg_3<=Arg_0 && 0<=Arg_3 && 1<=Arg_2+Arg_3 && 1<=Arg_1+Arg_3 && 1<=Arg_0+Arg_3 && Arg_2<=Arg_1 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && 2<=Arg_0+Arg_2 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 for location eval_speedpldi2_bb2_in

Found invariant 1+Arg_3<=Arg_0 && 0<=Arg_3 && 1<=Arg_2+Arg_3 && 1<=Arg_1+Arg_3 && 1<=Arg_0+Arg_3 && Arg_2<=Arg_1 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && 2<=Arg_0+Arg_2 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 for location eval_speedpldi2_bb3_in

Problem after Preprocessing

Start: eval_speedpldi2_start
Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3
Temp_Vars:
Locations: eval_speedpldi2_bb0_in, eval_speedpldi2_bb1_in, eval_speedpldi2_bb2_in, eval_speedpldi2_bb3_in, eval_speedpldi2_bb4_in, eval_speedpldi2_start, eval_speedpldi2_stop
Transitions:
1:eval_speedpldi2_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_speedpldi2_bb1_in(Arg_0,Arg_1,Arg_1,0):|:0<=Arg_1 && 0<Arg_0
2:eval_speedpldi2_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_speedpldi2_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_1<0
3:eval_speedpldi2_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_speedpldi2_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_0<=0
4:eval_speedpldi2_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_speedpldi2_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_3<=Arg_0 && 0<=Arg_3 && 0<=Arg_2+Arg_3 && 0<=Arg_1+Arg_3 && 1<=Arg_0+Arg_3 && Arg_2<=Arg_1 && 0<=Arg_2 && 0<=Arg_1+Arg_2 && 1<=Arg_0+Arg_2 && 0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 && 0<Arg_2
5:eval_speedpldi2_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_speedpldi2_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_3<=Arg_0 && 0<=Arg_3 && 0<=Arg_2+Arg_3 && 0<=Arg_1+Arg_3 && 1<=Arg_0+Arg_3 && Arg_2<=Arg_1 && 0<=Arg_2 && 0<=Arg_1+Arg_2 && 1<=Arg_0+Arg_2 && 0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 && Arg_2<=0
7:eval_speedpldi2_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_speedpldi2_bb1_in(Arg_0,Arg_1,Arg_2,0):|:Arg_3<=Arg_0 && 0<=Arg_3 && 1<=Arg_2+Arg_3 && 1<=Arg_1+Arg_3 && 1<=Arg_0+Arg_3 && Arg_2<=Arg_1 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && 2<=Arg_0+Arg_2 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 && Arg_0<=Arg_3
6:eval_speedpldi2_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_speedpldi2_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_3<=Arg_0 && 0<=Arg_3 && 1<=Arg_2+Arg_3 && 1<=Arg_1+Arg_3 && 1<=Arg_0+Arg_3 && Arg_2<=Arg_1 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && 2<=Arg_0+Arg_2 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 && Arg_3<Arg_0
8:eval_speedpldi2_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_speedpldi2_bb1_in(Arg_0,Arg_1,Arg_2-1,Arg_3+1):|:1+Arg_3<=Arg_0 && 0<=Arg_3 && 1<=Arg_2+Arg_3 && 1<=Arg_1+Arg_3 && 1<=Arg_0+Arg_3 && Arg_2<=Arg_1 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && 2<=Arg_0+Arg_2 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0
9:eval_speedpldi2_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_speedpldi2_stop(Arg_0,Arg_1,Arg_2,Arg_3)
0:eval_speedpldi2_start(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_speedpldi2_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3)

MPRF for transition 4:eval_speedpldi2_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_speedpldi2_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_3<=Arg_0 && 0<=Arg_3 && 0<=Arg_2+Arg_3 && 0<=Arg_1+Arg_3 && 1<=Arg_0+Arg_3 && Arg_2<=Arg_1 && 0<=Arg_2 && 0<=Arg_1+Arg_2 && 1<=Arg_0+Arg_2 && 0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 && 0<Arg_2 of depth 1:

new bound:

2*Arg_1+1 {O(n)}

MPRF:

eval_speedpldi2_bb2_in [2*Arg_2+Arg_3 ]
eval_speedpldi2_bb3_in [2*Arg_2+Arg_3 ]
eval_speedpldi2_bb1_in [2*Arg_2+Arg_3+1 ]

MPRF for transition 6:eval_speedpldi2_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_speedpldi2_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_3<=Arg_0 && 0<=Arg_3 && 1<=Arg_2+Arg_3 && 1<=Arg_1+Arg_3 && 1<=Arg_0+Arg_3 && Arg_2<=Arg_1 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && 2<=Arg_0+Arg_2 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 && Arg_3<Arg_0 of depth 1:

new bound:

Arg_1 {O(n)}

MPRF:

eval_speedpldi2_bb2_in [Arg_2 ]
eval_speedpldi2_bb3_in [Arg_2-1 ]
eval_speedpldi2_bb1_in [Arg_2 ]

MPRF for transition 7:eval_speedpldi2_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_speedpldi2_bb1_in(Arg_0,Arg_1,Arg_2,0):|:Arg_3<=Arg_0 && 0<=Arg_3 && 1<=Arg_2+Arg_3 && 1<=Arg_1+Arg_3 && 1<=Arg_0+Arg_3 && Arg_2<=Arg_1 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && 2<=Arg_0+Arg_2 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 && Arg_0<=Arg_3 of depth 1:

new bound:

Arg_1 {O(n)}

MPRF:

eval_speedpldi2_bb2_in [Arg_2+Arg_3 ]
eval_speedpldi2_bb3_in [Arg_2+Arg_3 ]
eval_speedpldi2_bb1_in [Arg_2+Arg_3 ]

MPRF for transition 8:eval_speedpldi2_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_speedpldi2_bb1_in(Arg_0,Arg_1,Arg_2-1,Arg_3+1):|:1+Arg_3<=Arg_0 && 0<=Arg_3 && 1<=Arg_2+Arg_3 && 1<=Arg_1+Arg_3 && 1<=Arg_0+Arg_3 && Arg_2<=Arg_1 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && 2<=Arg_0+Arg_2 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 of depth 1:

new bound:

Arg_1 {O(n)}

MPRF:

eval_speedpldi2_bb2_in [Arg_2 ]
eval_speedpldi2_bb3_in [Arg_2 ]
eval_speedpldi2_bb1_in [Arg_2 ]

All Bounds

Timebounds

Overall timebound:5*Arg_1+7 {O(n)}
1: eval_speedpldi2_bb0_in->eval_speedpldi2_bb1_in: 1 {O(1)}
2: eval_speedpldi2_bb0_in->eval_speedpldi2_bb4_in: 1 {O(1)}
3: eval_speedpldi2_bb0_in->eval_speedpldi2_bb4_in: 1 {O(1)}
4: eval_speedpldi2_bb1_in->eval_speedpldi2_bb2_in: 2*Arg_1+1 {O(n)}
5: eval_speedpldi2_bb1_in->eval_speedpldi2_bb4_in: 1 {O(1)}
6: eval_speedpldi2_bb2_in->eval_speedpldi2_bb3_in: Arg_1 {O(n)}
7: eval_speedpldi2_bb2_in->eval_speedpldi2_bb1_in: Arg_1 {O(n)}
8: eval_speedpldi2_bb3_in->eval_speedpldi2_bb1_in: Arg_1 {O(n)}
9: eval_speedpldi2_bb4_in->eval_speedpldi2_stop: 1 {O(1)}
0: eval_speedpldi2_start->eval_speedpldi2_bb0_in: 1 {O(1)}

Costbounds

Overall costbound: 5*Arg_1+7 {O(n)}
1: eval_speedpldi2_bb0_in->eval_speedpldi2_bb1_in: 1 {O(1)}
2: eval_speedpldi2_bb0_in->eval_speedpldi2_bb4_in: 1 {O(1)}
3: eval_speedpldi2_bb0_in->eval_speedpldi2_bb4_in: 1 {O(1)}
4: eval_speedpldi2_bb1_in->eval_speedpldi2_bb2_in: 2*Arg_1+1 {O(n)}
5: eval_speedpldi2_bb1_in->eval_speedpldi2_bb4_in: 1 {O(1)}
6: eval_speedpldi2_bb2_in->eval_speedpldi2_bb3_in: Arg_1 {O(n)}
7: eval_speedpldi2_bb2_in->eval_speedpldi2_bb1_in: Arg_1 {O(n)}
8: eval_speedpldi2_bb3_in->eval_speedpldi2_bb1_in: Arg_1 {O(n)}
9: eval_speedpldi2_bb4_in->eval_speedpldi2_stop: 1 {O(1)}
0: eval_speedpldi2_start->eval_speedpldi2_bb0_in: 1 {O(1)}

Sizebounds

1: eval_speedpldi2_bb0_in->eval_speedpldi2_bb1_in, Arg_0: Arg_0 {O(n)}
1: eval_speedpldi2_bb0_in->eval_speedpldi2_bb1_in, Arg_1: Arg_1 {O(n)}
1: eval_speedpldi2_bb0_in->eval_speedpldi2_bb1_in, Arg_2: Arg_1 {O(n)}
1: eval_speedpldi2_bb0_in->eval_speedpldi2_bb1_in, Arg_3: 0 {O(1)}
2: eval_speedpldi2_bb0_in->eval_speedpldi2_bb4_in, Arg_0: Arg_0 {O(n)}
2: eval_speedpldi2_bb0_in->eval_speedpldi2_bb4_in, Arg_1: Arg_1 {O(n)}
2: eval_speedpldi2_bb0_in->eval_speedpldi2_bb4_in, Arg_2: Arg_2 {O(n)}
2: eval_speedpldi2_bb0_in->eval_speedpldi2_bb4_in, Arg_3: Arg_3 {O(n)}
3: eval_speedpldi2_bb0_in->eval_speedpldi2_bb4_in, Arg_0: Arg_0 {O(n)}
3: eval_speedpldi2_bb0_in->eval_speedpldi2_bb4_in, Arg_1: Arg_1 {O(n)}
3: eval_speedpldi2_bb0_in->eval_speedpldi2_bb4_in, Arg_2: Arg_2 {O(n)}
3: eval_speedpldi2_bb0_in->eval_speedpldi2_bb4_in, Arg_3: Arg_3 {O(n)}
4: eval_speedpldi2_bb1_in->eval_speedpldi2_bb2_in, Arg_0: Arg_0 {O(n)}
4: eval_speedpldi2_bb1_in->eval_speedpldi2_bb2_in, Arg_1: Arg_1 {O(n)}
4: eval_speedpldi2_bb1_in->eval_speedpldi2_bb2_in, Arg_2: Arg_1 {O(n)}
4: eval_speedpldi2_bb1_in->eval_speedpldi2_bb2_in, Arg_3: Arg_1 {O(n)}
5: eval_speedpldi2_bb1_in->eval_speedpldi2_bb4_in, Arg_0: 2*Arg_0 {O(n)}
5: eval_speedpldi2_bb1_in->eval_speedpldi2_bb4_in, Arg_1: 2*Arg_1 {O(n)}
5: eval_speedpldi2_bb1_in->eval_speedpldi2_bb4_in, Arg_2: 0 {O(1)}
5: eval_speedpldi2_bb1_in->eval_speedpldi2_bb4_in, Arg_3: Arg_1 {O(n)}
6: eval_speedpldi2_bb2_in->eval_speedpldi2_bb3_in, Arg_0: Arg_0 {O(n)}
6: eval_speedpldi2_bb2_in->eval_speedpldi2_bb3_in, Arg_1: Arg_1 {O(n)}
6: eval_speedpldi2_bb2_in->eval_speedpldi2_bb3_in, Arg_2: Arg_1 {O(n)}
6: eval_speedpldi2_bb2_in->eval_speedpldi2_bb3_in, Arg_3: Arg_1 {O(n)}
7: eval_speedpldi2_bb2_in->eval_speedpldi2_bb1_in, Arg_0: Arg_0 {O(n)}
7: eval_speedpldi2_bb2_in->eval_speedpldi2_bb1_in, Arg_1: Arg_1 {O(n)}
7: eval_speedpldi2_bb2_in->eval_speedpldi2_bb1_in, Arg_2: Arg_1 {O(n)}
7: eval_speedpldi2_bb2_in->eval_speedpldi2_bb1_in, Arg_3: 0 {O(1)}
8: eval_speedpldi2_bb3_in->eval_speedpldi2_bb1_in, Arg_0: Arg_0 {O(n)}
8: eval_speedpldi2_bb3_in->eval_speedpldi2_bb1_in, Arg_1: Arg_1 {O(n)}
8: eval_speedpldi2_bb3_in->eval_speedpldi2_bb1_in, Arg_2: Arg_1 {O(n)}
8: eval_speedpldi2_bb3_in->eval_speedpldi2_bb1_in, Arg_3: Arg_1 {O(n)}
9: eval_speedpldi2_bb4_in->eval_speedpldi2_stop, Arg_0: 4*Arg_0 {O(n)}
9: eval_speedpldi2_bb4_in->eval_speedpldi2_stop, Arg_1: 4*Arg_1 {O(n)}
9: eval_speedpldi2_bb4_in->eval_speedpldi2_stop, Arg_2: 2*Arg_2 {O(n)}
9: eval_speedpldi2_bb4_in->eval_speedpldi2_stop, Arg_3: 2*Arg_3+Arg_1 {O(n)}
0: eval_speedpldi2_start->eval_speedpldi2_bb0_in, Arg_0: Arg_0 {O(n)}
0: eval_speedpldi2_start->eval_speedpldi2_bb0_in, Arg_1: Arg_1 {O(n)}
0: eval_speedpldi2_start->eval_speedpldi2_bb0_in, Arg_2: Arg_2 {O(n)}
0: eval_speedpldi2_start->eval_speedpldi2_bb0_in, Arg_3: Arg_3 {O(n)}