Initial Problem

Start: eval_speed_popl10_simple_single_2_start
Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3
Temp_Vars:
Locations: eval_speed_popl10_simple_single_2_bb0_in, eval_speed_popl10_simple_single_2_bb1_in, eval_speed_popl10_simple_single_2_bb2_in, eval_speed_popl10_simple_single_2_bb3_in, eval_speed_popl10_simple_single_2_bb4_in, eval_speed_popl10_simple_single_2_bb5_in, eval_speed_popl10_simple_single_2_start, eval_speed_popl10_simple_single_2_stop
Transitions:
1:eval_speed_popl10_simple_single_2_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_speed_popl10_simple_single_2_bb1_in(Arg_0,Arg_1,0,0)
2:eval_speed_popl10_simple_single_2_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_speed_popl10_simple_single_2_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_2<Arg_1
3:eval_speed_popl10_simple_single_2_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_speed_popl10_simple_single_2_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_1<=Arg_2
4:eval_speed_popl10_simple_single_2_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_speed_popl10_simple_single_2_bb1_in(Arg_0,Arg_1,Arg_2+1,Arg_3+1)
5:eval_speed_popl10_simple_single_2_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_speed_popl10_simple_single_2_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_3<Arg_0
6:eval_speed_popl10_simple_single_2_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_speed_popl10_simple_single_2_bb5_in(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_0<=Arg_3
7:eval_speed_popl10_simple_single_2_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_speed_popl10_simple_single_2_bb1_in(Arg_0,Arg_1,Arg_2+1,Arg_3+1)
8:eval_speed_popl10_simple_single_2_bb5_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_speed_popl10_simple_single_2_stop(Arg_0,Arg_1,Arg_2,Arg_3)
0:eval_speed_popl10_simple_single_2_start(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_speed_popl10_simple_single_2_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3)

Preprocessing

Found invariant Arg_3<=Arg_2 && 0<=Arg_3 && 0<=Arg_2+Arg_3 && Arg_2<=Arg_3 && Arg_1<=Arg_3 && 0<=Arg_2 && Arg_1<=Arg_2 for location eval_speed_popl10_simple_single_2_bb3_in

Found invariant Arg_3<=Arg_2 && 0<=Arg_3 && 0<=Arg_2+Arg_3 && Arg_2<=Arg_3 && Arg_1<=Arg_3 && Arg_0<=Arg_3 && 0<=Arg_2 && Arg_1<=Arg_2 && Arg_0<=Arg_2 for location eval_speed_popl10_simple_single_2_bb5_in

Found invariant Arg_3<=Arg_2 && 0<=Arg_3 && 0<=Arg_2+Arg_3 && Arg_2<=Arg_3 && 0<=Arg_2 for location eval_speed_popl10_simple_single_2_bb1_in

Found invariant Arg_3<=Arg_2 && 1+Arg_3<=Arg_1 && 0<=Arg_3 && 0<=Arg_2+Arg_3 && Arg_2<=Arg_3 && 1<=Arg_1+Arg_3 && 1+Arg_2<=Arg_1 && 0<=Arg_2 && 1<=Arg_1+Arg_2 && 1<=Arg_1 for location eval_speed_popl10_simple_single_2_bb2_in

Found invariant Arg_3<=Arg_2 && 1+Arg_3<=Arg_0 && 0<=Arg_3 && 0<=Arg_2+Arg_3 && Arg_2<=Arg_3 && Arg_1<=Arg_3 && 1<=Arg_0+Arg_3 && 1+Arg_2<=Arg_0 && 0<=Arg_2 && Arg_1<=Arg_2 && 1<=Arg_0+Arg_2 && 1+Arg_1<=Arg_0 && 1<=Arg_0 for location eval_speed_popl10_simple_single_2_bb4_in

Found invariant Arg_3<=Arg_2 && 0<=Arg_3 && 0<=Arg_2+Arg_3 && Arg_2<=Arg_3 && Arg_1<=Arg_3 && Arg_0<=Arg_3 && 0<=Arg_2 && Arg_1<=Arg_2 && Arg_0<=Arg_2 for location eval_speed_popl10_simple_single_2_stop

Problem after Preprocessing

Start: eval_speed_popl10_simple_single_2_start
Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3
Temp_Vars:
Locations: eval_speed_popl10_simple_single_2_bb0_in, eval_speed_popl10_simple_single_2_bb1_in, eval_speed_popl10_simple_single_2_bb2_in, eval_speed_popl10_simple_single_2_bb3_in, eval_speed_popl10_simple_single_2_bb4_in, eval_speed_popl10_simple_single_2_bb5_in, eval_speed_popl10_simple_single_2_start, eval_speed_popl10_simple_single_2_stop
Transitions:
1:eval_speed_popl10_simple_single_2_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_speed_popl10_simple_single_2_bb1_in(Arg_0,Arg_1,0,0)
2:eval_speed_popl10_simple_single_2_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_speed_popl10_simple_single_2_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_3<=Arg_2 && 0<=Arg_3 && 0<=Arg_2+Arg_3 && Arg_2<=Arg_3 && 0<=Arg_2 && Arg_2<Arg_1
3:eval_speed_popl10_simple_single_2_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_speed_popl10_simple_single_2_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_3<=Arg_2 && 0<=Arg_3 && 0<=Arg_2+Arg_3 && Arg_2<=Arg_3 && 0<=Arg_2 && Arg_1<=Arg_2
4:eval_speed_popl10_simple_single_2_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_speed_popl10_simple_single_2_bb1_in(Arg_0,Arg_1,Arg_2+1,Arg_3+1):|:Arg_3<=Arg_2 && 1+Arg_3<=Arg_1 && 0<=Arg_3 && 0<=Arg_2+Arg_3 && Arg_2<=Arg_3 && 1<=Arg_1+Arg_3 && 1+Arg_2<=Arg_1 && 0<=Arg_2 && 1<=Arg_1+Arg_2 && 1<=Arg_1
5:eval_speed_popl10_simple_single_2_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_speed_popl10_simple_single_2_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_3<=Arg_2 && 0<=Arg_3 && 0<=Arg_2+Arg_3 && Arg_2<=Arg_3 && Arg_1<=Arg_3 && 0<=Arg_2 && Arg_1<=Arg_2 && Arg_3<Arg_0
6:eval_speed_popl10_simple_single_2_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_speed_popl10_simple_single_2_bb5_in(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_3<=Arg_2 && 0<=Arg_3 && 0<=Arg_2+Arg_3 && Arg_2<=Arg_3 && Arg_1<=Arg_3 && 0<=Arg_2 && Arg_1<=Arg_2 && Arg_0<=Arg_3
7:eval_speed_popl10_simple_single_2_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_speed_popl10_simple_single_2_bb1_in(Arg_0,Arg_1,Arg_2+1,Arg_3+1):|:Arg_3<=Arg_2 && 1+Arg_3<=Arg_0 && 0<=Arg_3 && 0<=Arg_2+Arg_3 && Arg_2<=Arg_3 && Arg_1<=Arg_3 && 1<=Arg_0+Arg_3 && 1+Arg_2<=Arg_0 && 0<=Arg_2 && Arg_1<=Arg_2 && 1<=Arg_0+Arg_2 && 1+Arg_1<=Arg_0 && 1<=Arg_0
8:eval_speed_popl10_simple_single_2_bb5_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_speed_popl10_simple_single_2_stop(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_3<=Arg_2 && 0<=Arg_3 && 0<=Arg_2+Arg_3 && Arg_2<=Arg_3 && Arg_1<=Arg_3 && Arg_0<=Arg_3 && 0<=Arg_2 && Arg_1<=Arg_2 && Arg_0<=Arg_2
0:eval_speed_popl10_simple_single_2_start(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_speed_popl10_simple_single_2_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3)

MPRF for transition 2:eval_speed_popl10_simple_single_2_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_speed_popl10_simple_single_2_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_3<=Arg_2 && 0<=Arg_3 && 0<=Arg_2+Arg_3 && Arg_2<=Arg_3 && 0<=Arg_2 && Arg_2<Arg_1 of depth 1:

new bound:

Arg_1 {O(n)}

MPRF:

eval_speed_popl10_simple_single_2_bb2_in [Arg_1-Arg_3-1 ]
eval_speed_popl10_simple_single_2_bb3_in [Arg_1-Arg_2 ]
eval_speed_popl10_simple_single_2_bb4_in [Arg_1-Arg_2 ]
eval_speed_popl10_simple_single_2_bb1_in [Arg_1-Arg_2 ]

MPRF for transition 4:eval_speed_popl10_simple_single_2_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_speed_popl10_simple_single_2_bb1_in(Arg_0,Arg_1,Arg_2+1,Arg_3+1):|:Arg_3<=Arg_2 && 1+Arg_3<=Arg_1 && 0<=Arg_3 && 0<=Arg_2+Arg_3 && Arg_2<=Arg_3 && 1<=Arg_1+Arg_3 && 1+Arg_2<=Arg_1 && 0<=Arg_2 && 1<=Arg_1+Arg_2 && 1<=Arg_1 of depth 1:

new bound:

Arg_1 {O(n)}

MPRF:

eval_speed_popl10_simple_single_2_bb2_in [Arg_1-Arg_2 ]
eval_speed_popl10_simple_single_2_bb3_in [Arg_1-Arg_3 ]
eval_speed_popl10_simple_single_2_bb4_in [Arg_1-Arg_3 ]
eval_speed_popl10_simple_single_2_bb1_in [Arg_1-Arg_3 ]

MPRF for transition 5:eval_speed_popl10_simple_single_2_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_speed_popl10_simple_single_2_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_3<=Arg_2 && 0<=Arg_3 && 0<=Arg_2+Arg_3 && Arg_2<=Arg_3 && Arg_1<=Arg_3 && 0<=Arg_2 && Arg_1<=Arg_2 && Arg_3<Arg_0 of depth 1:

new bound:

Arg_0+1 {O(n)}

MPRF:

eval_speed_popl10_simple_single_2_bb2_in [Arg_0+1-Arg_3 ]
eval_speed_popl10_simple_single_2_bb3_in [Arg_0+1-Arg_2 ]
eval_speed_popl10_simple_single_2_bb4_in [Arg_0-Arg_2 ]
eval_speed_popl10_simple_single_2_bb1_in [Arg_0+1-Arg_3 ]

MPRF for transition 7:eval_speed_popl10_simple_single_2_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_speed_popl10_simple_single_2_bb1_in(Arg_0,Arg_1,Arg_2+1,Arg_3+1):|:Arg_3<=Arg_2 && 1+Arg_3<=Arg_0 && 0<=Arg_3 && 0<=Arg_2+Arg_3 && Arg_2<=Arg_3 && Arg_1<=Arg_3 && 1<=Arg_0+Arg_3 && 1+Arg_2<=Arg_0 && 0<=Arg_2 && Arg_1<=Arg_2 && 1<=Arg_0+Arg_2 && 1+Arg_1<=Arg_0 && 1<=Arg_0 of depth 1:

new bound:

Arg_0 {O(n)}

MPRF:

eval_speed_popl10_simple_single_2_bb2_in [Arg_0-Arg_3 ]
eval_speed_popl10_simple_single_2_bb3_in [Arg_0-Arg_3 ]
eval_speed_popl10_simple_single_2_bb4_in [Arg_0-Arg_2 ]
eval_speed_popl10_simple_single_2_bb1_in [Arg_0-Arg_2 ]

knowledge_propagation leads to new time bound Arg_0+Arg_1+1 {O(n)} for transition 3:eval_speed_popl10_simple_single_2_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_speed_popl10_simple_single_2_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_3<=Arg_2 && 0<=Arg_3 && 0<=Arg_2+Arg_3 && Arg_2<=Arg_3 && 0<=Arg_2 && Arg_1<=Arg_2

All Bounds

Timebounds

Overall timebound:3*Arg_0+3*Arg_1+6 {O(n)}
1: eval_speed_popl10_simple_single_2_bb0_in->eval_speed_popl10_simple_single_2_bb1_in: 1 {O(1)}
2: eval_speed_popl10_simple_single_2_bb1_in->eval_speed_popl10_simple_single_2_bb2_in: Arg_1 {O(n)}
3: eval_speed_popl10_simple_single_2_bb1_in->eval_speed_popl10_simple_single_2_bb3_in: Arg_0+Arg_1+1 {O(n)}
4: eval_speed_popl10_simple_single_2_bb2_in->eval_speed_popl10_simple_single_2_bb1_in: Arg_1 {O(n)}
5: eval_speed_popl10_simple_single_2_bb3_in->eval_speed_popl10_simple_single_2_bb4_in: Arg_0+1 {O(n)}
6: eval_speed_popl10_simple_single_2_bb3_in->eval_speed_popl10_simple_single_2_bb5_in: 1 {O(1)}
7: eval_speed_popl10_simple_single_2_bb4_in->eval_speed_popl10_simple_single_2_bb1_in: Arg_0 {O(n)}
8: eval_speed_popl10_simple_single_2_bb5_in->eval_speed_popl10_simple_single_2_stop: 1 {O(1)}
0: eval_speed_popl10_simple_single_2_start->eval_speed_popl10_simple_single_2_bb0_in: 1 {O(1)}

Costbounds

Overall costbound: 3*Arg_0+3*Arg_1+6 {O(n)}
1: eval_speed_popl10_simple_single_2_bb0_in->eval_speed_popl10_simple_single_2_bb1_in: 1 {O(1)}
2: eval_speed_popl10_simple_single_2_bb1_in->eval_speed_popl10_simple_single_2_bb2_in: Arg_1 {O(n)}
3: eval_speed_popl10_simple_single_2_bb1_in->eval_speed_popl10_simple_single_2_bb3_in: Arg_0+Arg_1+1 {O(n)}
4: eval_speed_popl10_simple_single_2_bb2_in->eval_speed_popl10_simple_single_2_bb1_in: Arg_1 {O(n)}
5: eval_speed_popl10_simple_single_2_bb3_in->eval_speed_popl10_simple_single_2_bb4_in: Arg_0+1 {O(n)}
6: eval_speed_popl10_simple_single_2_bb3_in->eval_speed_popl10_simple_single_2_bb5_in: 1 {O(1)}
7: eval_speed_popl10_simple_single_2_bb4_in->eval_speed_popl10_simple_single_2_bb1_in: Arg_0 {O(n)}
8: eval_speed_popl10_simple_single_2_bb5_in->eval_speed_popl10_simple_single_2_stop: 1 {O(1)}
0: eval_speed_popl10_simple_single_2_start->eval_speed_popl10_simple_single_2_bb0_in: 1 {O(1)}

Sizebounds

1: eval_speed_popl10_simple_single_2_bb0_in->eval_speed_popl10_simple_single_2_bb1_in, Arg_0: Arg_0 {O(n)}
1: eval_speed_popl10_simple_single_2_bb0_in->eval_speed_popl10_simple_single_2_bb1_in, Arg_1: Arg_1 {O(n)}
1: eval_speed_popl10_simple_single_2_bb0_in->eval_speed_popl10_simple_single_2_bb1_in, Arg_2: 0 {O(1)}
1: eval_speed_popl10_simple_single_2_bb0_in->eval_speed_popl10_simple_single_2_bb1_in, Arg_3: 0 {O(1)}
2: eval_speed_popl10_simple_single_2_bb1_in->eval_speed_popl10_simple_single_2_bb2_in, Arg_0: Arg_0 {O(n)}
2: eval_speed_popl10_simple_single_2_bb1_in->eval_speed_popl10_simple_single_2_bb2_in, Arg_1: Arg_1 {O(n)}
2: eval_speed_popl10_simple_single_2_bb1_in->eval_speed_popl10_simple_single_2_bb2_in, Arg_2: Arg_1 {O(n)}
2: eval_speed_popl10_simple_single_2_bb1_in->eval_speed_popl10_simple_single_2_bb2_in, Arg_3: Arg_1 {O(n)}
3: eval_speed_popl10_simple_single_2_bb1_in->eval_speed_popl10_simple_single_2_bb3_in, Arg_0: 2*Arg_0 {O(n)}
3: eval_speed_popl10_simple_single_2_bb1_in->eval_speed_popl10_simple_single_2_bb3_in, Arg_1: 2*Arg_1 {O(n)}
3: eval_speed_popl10_simple_single_2_bb1_in->eval_speed_popl10_simple_single_2_bb3_in, Arg_2: Arg_0+Arg_1 {O(n)}
3: eval_speed_popl10_simple_single_2_bb1_in->eval_speed_popl10_simple_single_2_bb3_in, Arg_3: Arg_0+Arg_1 {O(n)}
4: eval_speed_popl10_simple_single_2_bb2_in->eval_speed_popl10_simple_single_2_bb1_in, Arg_0: Arg_0 {O(n)}
4: eval_speed_popl10_simple_single_2_bb2_in->eval_speed_popl10_simple_single_2_bb1_in, Arg_1: Arg_1 {O(n)}
4: eval_speed_popl10_simple_single_2_bb2_in->eval_speed_popl10_simple_single_2_bb1_in, Arg_2: Arg_1 {O(n)}
4: eval_speed_popl10_simple_single_2_bb2_in->eval_speed_popl10_simple_single_2_bb1_in, Arg_3: Arg_1 {O(n)}
5: eval_speed_popl10_simple_single_2_bb3_in->eval_speed_popl10_simple_single_2_bb4_in, Arg_0: 2*Arg_0 {O(n)}
5: eval_speed_popl10_simple_single_2_bb3_in->eval_speed_popl10_simple_single_2_bb4_in, Arg_1: 2*Arg_1 {O(n)}
5: eval_speed_popl10_simple_single_2_bb3_in->eval_speed_popl10_simple_single_2_bb4_in, Arg_2: Arg_0+Arg_1 {O(n)}
5: eval_speed_popl10_simple_single_2_bb3_in->eval_speed_popl10_simple_single_2_bb4_in, Arg_3: Arg_0+Arg_1 {O(n)}
6: eval_speed_popl10_simple_single_2_bb3_in->eval_speed_popl10_simple_single_2_bb5_in, Arg_0: 2*Arg_0 {O(n)}
6: eval_speed_popl10_simple_single_2_bb3_in->eval_speed_popl10_simple_single_2_bb5_in, Arg_1: 2*Arg_1 {O(n)}
6: eval_speed_popl10_simple_single_2_bb3_in->eval_speed_popl10_simple_single_2_bb5_in, Arg_2: Arg_0+Arg_1 {O(n)}
6: eval_speed_popl10_simple_single_2_bb3_in->eval_speed_popl10_simple_single_2_bb5_in, Arg_3: Arg_0+Arg_1 {O(n)}
7: eval_speed_popl10_simple_single_2_bb4_in->eval_speed_popl10_simple_single_2_bb1_in, Arg_0: 2*Arg_0 {O(n)}
7: eval_speed_popl10_simple_single_2_bb4_in->eval_speed_popl10_simple_single_2_bb1_in, Arg_1: 2*Arg_1 {O(n)}
7: eval_speed_popl10_simple_single_2_bb4_in->eval_speed_popl10_simple_single_2_bb1_in, Arg_2: Arg_0+Arg_1 {O(n)}
7: eval_speed_popl10_simple_single_2_bb4_in->eval_speed_popl10_simple_single_2_bb1_in, Arg_3: Arg_0+Arg_1 {O(n)}
8: eval_speed_popl10_simple_single_2_bb5_in->eval_speed_popl10_simple_single_2_stop, Arg_0: 2*Arg_0 {O(n)}
8: eval_speed_popl10_simple_single_2_bb5_in->eval_speed_popl10_simple_single_2_stop, Arg_1: 2*Arg_1 {O(n)}
8: eval_speed_popl10_simple_single_2_bb5_in->eval_speed_popl10_simple_single_2_stop, Arg_2: Arg_0+Arg_1 {O(n)}
8: eval_speed_popl10_simple_single_2_bb5_in->eval_speed_popl10_simple_single_2_stop, Arg_3: Arg_0+Arg_1 {O(n)}
0: eval_speed_popl10_simple_single_2_start->eval_speed_popl10_simple_single_2_bb0_in, Arg_0: Arg_0 {O(n)}
0: eval_speed_popl10_simple_single_2_start->eval_speed_popl10_simple_single_2_bb0_in, Arg_1: Arg_1 {O(n)}
0: eval_speed_popl10_simple_single_2_start->eval_speed_popl10_simple_single_2_bb0_in, Arg_2: Arg_2 {O(n)}
0: eval_speed_popl10_simple_single_2_start->eval_speed_popl10_simple_single_2_bb0_in, Arg_3: Arg_3 {O(n)}