Initial Problem

Start: eval_speed_popl10_fig2_1_start
Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3, Arg_4, Arg_5
Temp_Vars:
Locations: eval_speed_popl10_fig2_1_bb0_in, eval_speed_popl10_fig2_1_bb1_in, eval_speed_popl10_fig2_1_bb2_in, eval_speed_popl10_fig2_1_bb3_in, eval_speed_popl10_fig2_1_start, eval_speed_popl10_fig2_1_stop
Transitions:
1:eval_speed_popl10_fig2_1_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_speed_popl10_fig2_1_bb1_in(Arg_4,Arg_5,Arg_2,Arg_3,Arg_4,Arg_5)
2:eval_speed_popl10_fig2_1_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_speed_popl10_fig2_1_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5):|:Arg_0<Arg_3
3:eval_speed_popl10_fig2_1_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_speed_popl10_fig2_1_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5):|:Arg_3<=Arg_0
4:eval_speed_popl10_fig2_1_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_speed_popl10_fig2_1_bb1_in(Arg_0,Arg_1+1,Arg_2,Arg_3,Arg_4,Arg_5):|:Arg_1<Arg_2 && Arg_1<Arg_2
5:eval_speed_popl10_fig2_1_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_speed_popl10_fig2_1_bb1_in(Arg_0+1,Arg_1+1,Arg_2,Arg_3,Arg_4,Arg_5):|:Arg_1<Arg_2 && Arg_2<=Arg_1
6:eval_speed_popl10_fig2_1_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_speed_popl10_fig2_1_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5):|:Arg_2<=Arg_1 && Arg_1<Arg_2
7:eval_speed_popl10_fig2_1_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_speed_popl10_fig2_1_bb1_in(Arg_0+1,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5):|:Arg_2<=Arg_1 && Arg_2<=Arg_1
8:eval_speed_popl10_fig2_1_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_speed_popl10_fig2_1_stop(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5)
0:eval_speed_popl10_fig2_1_start(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_speed_popl10_fig2_1_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5)

Preprocessing

Cut unsatisfiable transition 5: eval_speed_popl10_fig2_1_bb2_in->eval_speed_popl10_fig2_1_bb1_in

Cut unsatisfiable transition 6: eval_speed_popl10_fig2_1_bb2_in->eval_speed_popl10_fig2_1_bb1_in

Found invariant Arg_5<=Arg_1 && 1+Arg_4<=Arg_3 && Arg_4<=Arg_0 && 1+Arg_0<=Arg_3 for location eval_speed_popl10_fig2_1_bb2_in

Found invariant Arg_5<=Arg_1 && Arg_4<=Arg_0 && Arg_3<=Arg_0 for location eval_speed_popl10_fig2_1_bb3_in

Found invariant Arg_5<=Arg_1 && Arg_4<=Arg_0 for location eval_speed_popl10_fig2_1_bb1_in

Found invariant Arg_5<=Arg_1 && Arg_4<=Arg_0 && Arg_3<=Arg_0 for location eval_speed_popl10_fig2_1_stop

Problem after Preprocessing

Start: eval_speed_popl10_fig2_1_start
Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3, Arg_4, Arg_5
Temp_Vars:
Locations: eval_speed_popl10_fig2_1_bb0_in, eval_speed_popl10_fig2_1_bb1_in, eval_speed_popl10_fig2_1_bb2_in, eval_speed_popl10_fig2_1_bb3_in, eval_speed_popl10_fig2_1_start, eval_speed_popl10_fig2_1_stop
Transitions:
1:eval_speed_popl10_fig2_1_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_speed_popl10_fig2_1_bb1_in(Arg_4,Arg_5,Arg_2,Arg_3,Arg_4,Arg_5)
2:eval_speed_popl10_fig2_1_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_speed_popl10_fig2_1_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5):|:Arg_5<=Arg_1 && Arg_4<=Arg_0 && Arg_0<Arg_3
3:eval_speed_popl10_fig2_1_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_speed_popl10_fig2_1_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5):|:Arg_5<=Arg_1 && Arg_4<=Arg_0 && Arg_3<=Arg_0
4:eval_speed_popl10_fig2_1_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_speed_popl10_fig2_1_bb1_in(Arg_0,Arg_1+1,Arg_2,Arg_3,Arg_4,Arg_5):|:Arg_5<=Arg_1 && 1+Arg_4<=Arg_3 && Arg_4<=Arg_0 && 1+Arg_0<=Arg_3 && Arg_1<Arg_2 && Arg_1<Arg_2
7:eval_speed_popl10_fig2_1_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_speed_popl10_fig2_1_bb1_in(Arg_0+1,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5):|:Arg_5<=Arg_1 && 1+Arg_4<=Arg_3 && Arg_4<=Arg_0 && 1+Arg_0<=Arg_3 && Arg_2<=Arg_1 && Arg_2<=Arg_1
8:eval_speed_popl10_fig2_1_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_speed_popl10_fig2_1_stop(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5):|:Arg_5<=Arg_1 && Arg_4<=Arg_0 && Arg_3<=Arg_0
0:eval_speed_popl10_fig2_1_start(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_speed_popl10_fig2_1_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5)

MPRF for transition 4:eval_speed_popl10_fig2_1_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_speed_popl10_fig2_1_bb1_in(Arg_0,Arg_1+1,Arg_2,Arg_3,Arg_4,Arg_5):|:Arg_5<=Arg_1 && 1+Arg_4<=Arg_3 && Arg_4<=Arg_0 && 1+Arg_0<=Arg_3 && Arg_1<Arg_2 && Arg_1<Arg_2 of depth 1:

new bound:

Arg_2+Arg_5 {O(n)}

MPRF:

eval_speed_popl10_fig2_1_bb2_in [Arg_2-Arg_1 ]
eval_speed_popl10_fig2_1_bb1_in [Arg_2-Arg_1 ]

MPRF for transition 7:eval_speed_popl10_fig2_1_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_speed_popl10_fig2_1_bb1_in(Arg_0+1,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5):|:Arg_5<=Arg_1 && 1+Arg_4<=Arg_3 && Arg_4<=Arg_0 && 1+Arg_0<=Arg_3 && Arg_2<=Arg_1 && Arg_2<=Arg_1 of depth 1:

new bound:

Arg_3+Arg_4 {O(n)}

MPRF:

eval_speed_popl10_fig2_1_bb2_in [Arg_3-Arg_0 ]
eval_speed_popl10_fig2_1_bb1_in [Arg_3-Arg_0 ]

knowledge_propagation leads to new time bound Arg_2+Arg_3+Arg_4+Arg_5+1 {O(n)} for transition 2:eval_speed_popl10_fig2_1_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_speed_popl10_fig2_1_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5):|:Arg_5<=Arg_1 && Arg_4<=Arg_0 && Arg_0<Arg_3

All Bounds

Timebounds

Overall timebound:2*Arg_2+2*Arg_3+2*Arg_4+2*Arg_5+5 {O(n)}
1: eval_speed_popl10_fig2_1_bb0_in->eval_speed_popl10_fig2_1_bb1_in: 1 {O(1)}
2: eval_speed_popl10_fig2_1_bb1_in->eval_speed_popl10_fig2_1_bb2_in: Arg_2+Arg_3+Arg_4+Arg_5+1 {O(n)}
3: eval_speed_popl10_fig2_1_bb1_in->eval_speed_popl10_fig2_1_bb3_in: 1 {O(1)}
4: eval_speed_popl10_fig2_1_bb2_in->eval_speed_popl10_fig2_1_bb1_in: Arg_2+Arg_5 {O(n)}
7: eval_speed_popl10_fig2_1_bb2_in->eval_speed_popl10_fig2_1_bb1_in: Arg_3+Arg_4 {O(n)}
8: eval_speed_popl10_fig2_1_bb3_in->eval_speed_popl10_fig2_1_stop: 1 {O(1)}
0: eval_speed_popl10_fig2_1_start->eval_speed_popl10_fig2_1_bb0_in: 1 {O(1)}

Costbounds

Overall costbound: 2*Arg_2+2*Arg_3+2*Arg_4+2*Arg_5+5 {O(n)}
1: eval_speed_popl10_fig2_1_bb0_in->eval_speed_popl10_fig2_1_bb1_in: 1 {O(1)}
2: eval_speed_popl10_fig2_1_bb1_in->eval_speed_popl10_fig2_1_bb2_in: Arg_2+Arg_3+Arg_4+Arg_5+1 {O(n)}
3: eval_speed_popl10_fig2_1_bb1_in->eval_speed_popl10_fig2_1_bb3_in: 1 {O(1)}
4: eval_speed_popl10_fig2_1_bb2_in->eval_speed_popl10_fig2_1_bb1_in: Arg_2+Arg_5 {O(n)}
7: eval_speed_popl10_fig2_1_bb2_in->eval_speed_popl10_fig2_1_bb1_in: Arg_3+Arg_4 {O(n)}
8: eval_speed_popl10_fig2_1_bb3_in->eval_speed_popl10_fig2_1_stop: 1 {O(1)}
0: eval_speed_popl10_fig2_1_start->eval_speed_popl10_fig2_1_bb0_in: 1 {O(1)}

Sizebounds

1: eval_speed_popl10_fig2_1_bb0_in->eval_speed_popl10_fig2_1_bb1_in, Arg_0: Arg_4 {O(n)}
1: eval_speed_popl10_fig2_1_bb0_in->eval_speed_popl10_fig2_1_bb1_in, Arg_1: Arg_5 {O(n)}
1: eval_speed_popl10_fig2_1_bb0_in->eval_speed_popl10_fig2_1_bb1_in, Arg_2: Arg_2 {O(n)}
1: eval_speed_popl10_fig2_1_bb0_in->eval_speed_popl10_fig2_1_bb1_in, Arg_3: Arg_3 {O(n)}
1: eval_speed_popl10_fig2_1_bb0_in->eval_speed_popl10_fig2_1_bb1_in, Arg_4: Arg_4 {O(n)}
1: eval_speed_popl10_fig2_1_bb0_in->eval_speed_popl10_fig2_1_bb1_in, Arg_5: Arg_5 {O(n)}
2: eval_speed_popl10_fig2_1_bb1_in->eval_speed_popl10_fig2_1_bb2_in, Arg_0: 2*Arg_4+Arg_3 {O(n)}
2: eval_speed_popl10_fig2_1_bb1_in->eval_speed_popl10_fig2_1_bb2_in, Arg_1: 2*Arg_5+Arg_2 {O(n)}
2: eval_speed_popl10_fig2_1_bb1_in->eval_speed_popl10_fig2_1_bb2_in, Arg_2: Arg_2 {O(n)}
2: eval_speed_popl10_fig2_1_bb1_in->eval_speed_popl10_fig2_1_bb2_in, Arg_3: Arg_3 {O(n)}
2: eval_speed_popl10_fig2_1_bb1_in->eval_speed_popl10_fig2_1_bb2_in, Arg_4: Arg_4 {O(n)}
2: eval_speed_popl10_fig2_1_bb1_in->eval_speed_popl10_fig2_1_bb2_in, Arg_5: Arg_5 {O(n)}
3: eval_speed_popl10_fig2_1_bb1_in->eval_speed_popl10_fig2_1_bb3_in, Arg_0: 3*Arg_4+Arg_3 {O(n)}
3: eval_speed_popl10_fig2_1_bb1_in->eval_speed_popl10_fig2_1_bb3_in, Arg_1: 3*Arg_5+Arg_2 {O(n)}
3: eval_speed_popl10_fig2_1_bb1_in->eval_speed_popl10_fig2_1_bb3_in, Arg_2: 2*Arg_2 {O(n)}
3: eval_speed_popl10_fig2_1_bb1_in->eval_speed_popl10_fig2_1_bb3_in, Arg_3: 2*Arg_3 {O(n)}
3: eval_speed_popl10_fig2_1_bb1_in->eval_speed_popl10_fig2_1_bb3_in, Arg_4: 2*Arg_4 {O(n)}
3: eval_speed_popl10_fig2_1_bb1_in->eval_speed_popl10_fig2_1_bb3_in, Arg_5: 2*Arg_5 {O(n)}
4: eval_speed_popl10_fig2_1_bb2_in->eval_speed_popl10_fig2_1_bb1_in, Arg_0: 2*Arg_4+Arg_3 {O(n)}
4: eval_speed_popl10_fig2_1_bb2_in->eval_speed_popl10_fig2_1_bb1_in, Arg_1: 2*Arg_5+Arg_2 {O(n)}
4: eval_speed_popl10_fig2_1_bb2_in->eval_speed_popl10_fig2_1_bb1_in, Arg_2: Arg_2 {O(n)}
4: eval_speed_popl10_fig2_1_bb2_in->eval_speed_popl10_fig2_1_bb1_in, Arg_3: Arg_3 {O(n)}
4: eval_speed_popl10_fig2_1_bb2_in->eval_speed_popl10_fig2_1_bb1_in, Arg_4: Arg_4 {O(n)}
4: eval_speed_popl10_fig2_1_bb2_in->eval_speed_popl10_fig2_1_bb1_in, Arg_5: Arg_5 {O(n)}
7: eval_speed_popl10_fig2_1_bb2_in->eval_speed_popl10_fig2_1_bb1_in, Arg_0: 2*Arg_4+Arg_3 {O(n)}
7: eval_speed_popl10_fig2_1_bb2_in->eval_speed_popl10_fig2_1_bb1_in, Arg_1: 2*Arg_5+Arg_2 {O(n)}
7: eval_speed_popl10_fig2_1_bb2_in->eval_speed_popl10_fig2_1_bb1_in, Arg_2: Arg_2 {O(n)}
7: eval_speed_popl10_fig2_1_bb2_in->eval_speed_popl10_fig2_1_bb1_in, Arg_3: Arg_3 {O(n)}
7: eval_speed_popl10_fig2_1_bb2_in->eval_speed_popl10_fig2_1_bb1_in, Arg_4: Arg_4 {O(n)}
7: eval_speed_popl10_fig2_1_bb2_in->eval_speed_popl10_fig2_1_bb1_in, Arg_5: Arg_5 {O(n)}
8: eval_speed_popl10_fig2_1_bb3_in->eval_speed_popl10_fig2_1_stop, Arg_0: 3*Arg_4+Arg_3 {O(n)}
8: eval_speed_popl10_fig2_1_bb3_in->eval_speed_popl10_fig2_1_stop, Arg_1: 3*Arg_5+Arg_2 {O(n)}
8: eval_speed_popl10_fig2_1_bb3_in->eval_speed_popl10_fig2_1_stop, Arg_2: 2*Arg_2 {O(n)}
8: eval_speed_popl10_fig2_1_bb3_in->eval_speed_popl10_fig2_1_stop, Arg_3: 2*Arg_3 {O(n)}
8: eval_speed_popl10_fig2_1_bb3_in->eval_speed_popl10_fig2_1_stop, Arg_4: 2*Arg_4 {O(n)}
8: eval_speed_popl10_fig2_1_bb3_in->eval_speed_popl10_fig2_1_stop, Arg_5: 2*Arg_5 {O(n)}
0: eval_speed_popl10_fig2_1_start->eval_speed_popl10_fig2_1_bb0_in, Arg_0: Arg_0 {O(n)}
0: eval_speed_popl10_fig2_1_start->eval_speed_popl10_fig2_1_bb0_in, Arg_1: Arg_1 {O(n)}
0: eval_speed_popl10_fig2_1_start->eval_speed_popl10_fig2_1_bb0_in, Arg_2: Arg_2 {O(n)}
0: eval_speed_popl10_fig2_1_start->eval_speed_popl10_fig2_1_bb0_in, Arg_3: Arg_3 {O(n)}
0: eval_speed_popl10_fig2_1_start->eval_speed_popl10_fig2_1_bb0_in, Arg_4: Arg_4 {O(n)}
0: eval_speed_popl10_fig2_1_start->eval_speed_popl10_fig2_1_bb0_in, Arg_5: Arg_5 {O(n)}