Initial Problem

Start: eval_speedpldi3_start
Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3
Temp_Vars:
Locations: eval_speedpldi3_bb0_in, eval_speedpldi3_bb1_in, eval_speedpldi3_bb2_in, eval_speedpldi3_bb3_in, eval_speedpldi3_start, eval_speedpldi3_stop
Transitions:
3:eval_speedpldi3_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_speedpldi3_bb1_in(0,0,Arg_2,Arg_3):|:0<Arg_2 && Arg_2<Arg_3
1:eval_speedpldi3_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_speedpldi3_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_2<=0
2:eval_speedpldi3_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_speedpldi3_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_3<=Arg_2
4:eval_speedpldi3_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_speedpldi3_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_0<Arg_3
5:eval_speedpldi3_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_speedpldi3_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_3<=Arg_0
6:eval_speedpldi3_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_speedpldi3_bb1_in(Arg_0,Arg_1+1,Arg_2,Arg_3):|:Arg_1<Arg_2 && Arg_1<Arg_2
7:eval_speedpldi3_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_speedpldi3_bb1_in(Arg_0+1,Arg_1+1,Arg_2,Arg_3):|:Arg_1<Arg_2 && Arg_2<=Arg_1
8:eval_speedpldi3_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_speedpldi3_bb1_in(Arg_0,0,Arg_2,Arg_3):|:Arg_2<=Arg_1 && Arg_1<Arg_2
9:eval_speedpldi3_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_speedpldi3_bb1_in(Arg_0+1,0,Arg_2,Arg_3):|:Arg_2<=Arg_1 && Arg_2<=Arg_1
10:eval_speedpldi3_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_speedpldi3_stop(Arg_0,Arg_1,Arg_2,Arg_3)
0:eval_speedpldi3_start(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_speedpldi3_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3)

Preprocessing

Cut unsatisfiable transition 7: eval_speedpldi3_bb2_in->eval_speedpldi3_bb1_in

Cut unsatisfiable transition 8: eval_speedpldi3_bb2_in->eval_speedpldi3_bb1_in

Found invariant 2<=Arg_3 && 3<=Arg_2+Arg_3 && 1+Arg_2<=Arg_3 && 2<=Arg_1+Arg_3 && 1+Arg_1<=Arg_3 && 2<=Arg_0+Arg_3 && 1+Arg_0<=Arg_3 && 1<=Arg_2 && 1<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 1<=Arg_0+Arg_2 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=Arg_0 for location eval_speedpldi3_bb2_in

Found invariant 2<=Arg_3 && 3<=Arg_2+Arg_3 && 1+Arg_2<=Arg_3 && 2<=Arg_1+Arg_3 && 1+Arg_1<=Arg_3 && 2<=Arg_0+Arg_3 && Arg_0<=Arg_3 && 1<=Arg_2 && 1<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 1<=Arg_0+Arg_2 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=Arg_0 for location eval_speedpldi3_bb1_in

Problem after Preprocessing

Start: eval_speedpldi3_start
Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3
Temp_Vars:
Locations: eval_speedpldi3_bb0_in, eval_speedpldi3_bb1_in, eval_speedpldi3_bb2_in, eval_speedpldi3_bb3_in, eval_speedpldi3_start, eval_speedpldi3_stop
Transitions:
3:eval_speedpldi3_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_speedpldi3_bb1_in(0,0,Arg_2,Arg_3):|:0<Arg_2 && Arg_2<Arg_3
1:eval_speedpldi3_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_speedpldi3_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_2<=0
2:eval_speedpldi3_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_speedpldi3_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_3<=Arg_2
4:eval_speedpldi3_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_speedpldi3_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3):|:2<=Arg_3 && 3<=Arg_2+Arg_3 && 1+Arg_2<=Arg_3 && 2<=Arg_1+Arg_3 && 1+Arg_1<=Arg_3 && 2<=Arg_0+Arg_3 && Arg_0<=Arg_3 && 1<=Arg_2 && 1<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 1<=Arg_0+Arg_2 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=Arg_0 && Arg_0<Arg_3
5:eval_speedpldi3_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_speedpldi3_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3):|:2<=Arg_3 && 3<=Arg_2+Arg_3 && 1+Arg_2<=Arg_3 && 2<=Arg_1+Arg_3 && 1+Arg_1<=Arg_3 && 2<=Arg_0+Arg_3 && Arg_0<=Arg_3 && 1<=Arg_2 && 1<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 1<=Arg_0+Arg_2 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=Arg_0 && Arg_3<=Arg_0
6:eval_speedpldi3_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_speedpldi3_bb1_in(Arg_0,Arg_1+1,Arg_2,Arg_3):|:2<=Arg_3 && 3<=Arg_2+Arg_3 && 1+Arg_2<=Arg_3 && 2<=Arg_1+Arg_3 && 1+Arg_1<=Arg_3 && 2<=Arg_0+Arg_3 && 1+Arg_0<=Arg_3 && 1<=Arg_2 && 1<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 1<=Arg_0+Arg_2 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=Arg_0 && Arg_1<Arg_2 && Arg_1<Arg_2
9:eval_speedpldi3_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_speedpldi3_bb1_in(Arg_0+1,0,Arg_2,Arg_3):|:2<=Arg_3 && 3<=Arg_2+Arg_3 && 1+Arg_2<=Arg_3 && 2<=Arg_1+Arg_3 && 1+Arg_1<=Arg_3 && 2<=Arg_0+Arg_3 && 1+Arg_0<=Arg_3 && 1<=Arg_2 && 1<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 1<=Arg_0+Arg_2 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=Arg_0 && Arg_2<=Arg_1 && Arg_2<=Arg_1
10:eval_speedpldi3_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_speedpldi3_stop(Arg_0,Arg_1,Arg_2,Arg_3)
0:eval_speedpldi3_start(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_speedpldi3_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3)

MPRF for transition 9:eval_speedpldi3_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_speedpldi3_bb1_in(Arg_0+1,0,Arg_2,Arg_3):|:2<=Arg_3 && 3<=Arg_2+Arg_3 && 1+Arg_2<=Arg_3 && 2<=Arg_1+Arg_3 && 1+Arg_1<=Arg_3 && 2<=Arg_0+Arg_3 && 1+Arg_0<=Arg_3 && 1<=Arg_2 && 1<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 1<=Arg_0+Arg_2 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=Arg_0 && Arg_2<=Arg_1 && Arg_2<=Arg_1 of depth 1:

new bound:

Arg_3 {O(n)}

MPRF:

eval_speedpldi3_bb2_in [Arg_3-Arg_0 ]
eval_speedpldi3_bb1_in [Arg_3-Arg_0 ]

MPRF for transition 4:eval_speedpldi3_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_speedpldi3_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3):|:2<=Arg_3 && 3<=Arg_2+Arg_3 && 1+Arg_2<=Arg_3 && 2<=Arg_1+Arg_3 && 1+Arg_1<=Arg_3 && 2<=Arg_0+Arg_3 && Arg_0<=Arg_3 && 1<=Arg_2 && 1<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 1<=Arg_0+Arg_2 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=Arg_0 && Arg_0<Arg_3 of depth 1:

new bound:

Arg_3*Arg_3+Arg_3 {O(n^2)}

MPRF:

eval_speedpldi3_bb2_in [Arg_3-Arg_1-1 ]
eval_speedpldi3_bb1_in [Arg_3-Arg_1 ]

MPRF for transition 6:eval_speedpldi3_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_speedpldi3_bb1_in(Arg_0,Arg_1+1,Arg_2,Arg_3):|:2<=Arg_3 && 3<=Arg_2+Arg_3 && 1+Arg_2<=Arg_3 && 2<=Arg_1+Arg_3 && 1+Arg_1<=Arg_3 && 2<=Arg_0+Arg_3 && 1+Arg_0<=Arg_3 && 1<=Arg_2 && 1<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 1<=Arg_0+Arg_2 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=Arg_0 && Arg_1<Arg_2 && Arg_1<Arg_2 of depth 1:

new bound:

Arg_2*Arg_3+Arg_2+Arg_3+1 {O(n^2)}

MPRF:

eval_speedpldi3_bb2_in [Arg_2+1-Arg_1 ]
eval_speedpldi3_bb1_in [Arg_2+1-Arg_1 ]

All Bounds

Timebounds

Overall timebound:Arg_2*Arg_3+Arg_3*Arg_3+3*Arg_3+Arg_2+7 {O(n^2)}
1: eval_speedpldi3_bb0_in->eval_speedpldi3_bb3_in: 1 {O(1)}
2: eval_speedpldi3_bb0_in->eval_speedpldi3_bb3_in: 1 {O(1)}
3: eval_speedpldi3_bb0_in->eval_speedpldi3_bb1_in: 1 {O(1)}
4: eval_speedpldi3_bb1_in->eval_speedpldi3_bb2_in: Arg_3*Arg_3+Arg_3 {O(n^2)}
5: eval_speedpldi3_bb1_in->eval_speedpldi3_bb3_in: 1 {O(1)}
6: eval_speedpldi3_bb2_in->eval_speedpldi3_bb1_in: Arg_2*Arg_3+Arg_2+Arg_3+1 {O(n^2)}
9: eval_speedpldi3_bb2_in->eval_speedpldi3_bb1_in: Arg_3 {O(n)}
10: eval_speedpldi3_bb3_in->eval_speedpldi3_stop: 1 {O(1)}
0: eval_speedpldi3_start->eval_speedpldi3_bb0_in: 1 {O(1)}

Costbounds

Overall costbound: Arg_2*Arg_3+Arg_3*Arg_3+3*Arg_3+Arg_2+7 {O(n^2)}
1: eval_speedpldi3_bb0_in->eval_speedpldi3_bb3_in: 1 {O(1)}
2: eval_speedpldi3_bb0_in->eval_speedpldi3_bb3_in: 1 {O(1)}
3: eval_speedpldi3_bb0_in->eval_speedpldi3_bb1_in: 1 {O(1)}
4: eval_speedpldi3_bb1_in->eval_speedpldi3_bb2_in: Arg_3*Arg_3+Arg_3 {O(n^2)}
5: eval_speedpldi3_bb1_in->eval_speedpldi3_bb3_in: 1 {O(1)}
6: eval_speedpldi3_bb2_in->eval_speedpldi3_bb1_in: Arg_2*Arg_3+Arg_2+Arg_3+1 {O(n^2)}
9: eval_speedpldi3_bb2_in->eval_speedpldi3_bb1_in: Arg_3 {O(n)}
10: eval_speedpldi3_bb3_in->eval_speedpldi3_stop: 1 {O(1)}
0: eval_speedpldi3_start->eval_speedpldi3_bb0_in: 1 {O(1)}

Sizebounds

1: eval_speedpldi3_bb0_in->eval_speedpldi3_bb3_in, Arg_0: Arg_0 {O(n)}
1: eval_speedpldi3_bb0_in->eval_speedpldi3_bb3_in, Arg_1: Arg_1 {O(n)}
1: eval_speedpldi3_bb0_in->eval_speedpldi3_bb3_in, Arg_2: Arg_2 {O(n)}
1: eval_speedpldi3_bb0_in->eval_speedpldi3_bb3_in, Arg_3: Arg_3 {O(n)}
2: eval_speedpldi3_bb0_in->eval_speedpldi3_bb3_in, Arg_0: Arg_0 {O(n)}
2: eval_speedpldi3_bb0_in->eval_speedpldi3_bb3_in, Arg_1: Arg_1 {O(n)}
2: eval_speedpldi3_bb0_in->eval_speedpldi3_bb3_in, Arg_2: Arg_2 {O(n)}
2: eval_speedpldi3_bb0_in->eval_speedpldi3_bb3_in, Arg_3: Arg_3 {O(n)}
3: eval_speedpldi3_bb0_in->eval_speedpldi3_bb1_in, Arg_0: 0 {O(1)}
3: eval_speedpldi3_bb0_in->eval_speedpldi3_bb1_in, Arg_1: 0 {O(1)}
3: eval_speedpldi3_bb0_in->eval_speedpldi3_bb1_in, Arg_2: Arg_2 {O(n)}
3: eval_speedpldi3_bb0_in->eval_speedpldi3_bb1_in, Arg_3: Arg_3 {O(n)}
4: eval_speedpldi3_bb1_in->eval_speedpldi3_bb2_in, Arg_0: Arg_3 {O(n)}
4: eval_speedpldi3_bb1_in->eval_speedpldi3_bb2_in, Arg_1: Arg_2*Arg_3+Arg_2+Arg_3+1 {O(n^2)}
4: eval_speedpldi3_bb1_in->eval_speedpldi3_bb2_in, Arg_2: Arg_2 {O(n)}
4: eval_speedpldi3_bb1_in->eval_speedpldi3_bb2_in, Arg_3: Arg_3 {O(n)}
5: eval_speedpldi3_bb1_in->eval_speedpldi3_bb3_in, Arg_0: Arg_3 {O(n)}
5: eval_speedpldi3_bb1_in->eval_speedpldi3_bb3_in, Arg_1: 0 {O(1)}
5: eval_speedpldi3_bb1_in->eval_speedpldi3_bb3_in, Arg_2: Arg_2 {O(n)}
5: eval_speedpldi3_bb1_in->eval_speedpldi3_bb3_in, Arg_3: Arg_3 {O(n)}
6: eval_speedpldi3_bb2_in->eval_speedpldi3_bb1_in, Arg_0: Arg_3 {O(n)}
6: eval_speedpldi3_bb2_in->eval_speedpldi3_bb1_in, Arg_1: Arg_2*Arg_3+Arg_2+Arg_3+1 {O(n^2)}
6: eval_speedpldi3_bb2_in->eval_speedpldi3_bb1_in, Arg_2: Arg_2 {O(n)}
6: eval_speedpldi3_bb2_in->eval_speedpldi3_bb1_in, Arg_3: Arg_3 {O(n)}
9: eval_speedpldi3_bb2_in->eval_speedpldi3_bb1_in, Arg_0: Arg_3 {O(n)}
9: eval_speedpldi3_bb2_in->eval_speedpldi3_bb1_in, Arg_1: 0 {O(1)}
9: eval_speedpldi3_bb2_in->eval_speedpldi3_bb1_in, Arg_2: Arg_2 {O(n)}
9: eval_speedpldi3_bb2_in->eval_speedpldi3_bb1_in, Arg_3: Arg_3 {O(n)}
10: eval_speedpldi3_bb3_in->eval_speedpldi3_stop, Arg_0: 2*Arg_0+Arg_3 {O(n)}
10: eval_speedpldi3_bb3_in->eval_speedpldi3_stop, Arg_1: 2*Arg_1 {O(n)}
10: eval_speedpldi3_bb3_in->eval_speedpldi3_stop, Arg_2: 3*Arg_2 {O(n)}
10: eval_speedpldi3_bb3_in->eval_speedpldi3_stop, Arg_3: 3*Arg_3 {O(n)}
0: eval_speedpldi3_start->eval_speedpldi3_bb0_in, Arg_0: Arg_0 {O(n)}
0: eval_speedpldi3_start->eval_speedpldi3_bb0_in, Arg_1: Arg_1 {O(n)}
0: eval_speedpldi3_start->eval_speedpldi3_bb0_in, Arg_2: Arg_2 {O(n)}
0: eval_speedpldi3_start->eval_speedpldi3_bb0_in, Arg_3: Arg_3 {O(n)}