Initial Problem

Start: eval_speed_popl10_simple_single_start
Program_Vars: Arg_0, Arg_1
Temp_Vars:
Locations: eval_speed_popl10_simple_single_0, eval_speed_popl10_simple_single_1, eval_speed_popl10_simple_single_bb0_in, eval_speed_popl10_simple_single_bb1_in, eval_speed_popl10_simple_single_bb2_in, eval_speed_popl10_simple_single_bb3_in, eval_speed_popl10_simple_single_start, eval_speed_popl10_simple_single_stop
Transitions:
6:eval_speed_popl10_simple_single_0(Arg_0,Arg_1) -> eval_speed_popl10_simple_single_1(Arg_0,Arg_1)
7:eval_speed_popl10_simple_single_1(Arg_0,Arg_1) -> eval_speed_popl10_simple_single_bb1_in(Arg_0,Arg_1+1)
1:eval_speed_popl10_simple_single_bb0_in(Arg_0,Arg_1) -> eval_speed_popl10_simple_single_bb1_in(Arg_0,0)
2:eval_speed_popl10_simple_single_bb1_in(Arg_0,Arg_1) -> eval_speed_popl10_simple_single_bb2_in(Arg_0,Arg_1):|:Arg_1<Arg_0
3:eval_speed_popl10_simple_single_bb1_in(Arg_0,Arg_1) -> eval_speed_popl10_simple_single_bb3_in(Arg_0,Arg_1):|:Arg_0<=Arg_1
4:eval_speed_popl10_simple_single_bb2_in(Arg_0,Arg_1) -> eval_speed_popl10_simple_single_0(Arg_0,Arg_1)
8:eval_speed_popl10_simple_single_bb3_in(Arg_0,Arg_1) -> eval_speed_popl10_simple_single_stop(Arg_0,Arg_1)
0:eval_speed_popl10_simple_single_start(Arg_0,Arg_1) -> eval_speed_popl10_simple_single_bb0_in(Arg_0,Arg_1)

Preprocessing

Found invariant 1+Arg_1<=Arg_0 && 0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 for location eval_speed_popl10_simple_single_0

Found invariant 0<=Arg_1 && Arg_0<=Arg_1 for location eval_speed_popl10_simple_single_bb3_in

Found invariant 1+Arg_1<=Arg_0 && 0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 for location eval_speed_popl10_simple_single_bb2_in

Found invariant 0<=Arg_1 for location eval_speed_popl10_simple_single_bb1_in

Found invariant 1+Arg_1<=Arg_0 && 0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 for location eval_speed_popl10_simple_single_1

Found invariant 0<=Arg_1 && Arg_0<=Arg_1 for location eval_speed_popl10_simple_single_stop

Problem after Preprocessing

Start: eval_speed_popl10_simple_single_start
Program_Vars: Arg_0, Arg_1
Temp_Vars:
Locations: eval_speed_popl10_simple_single_0, eval_speed_popl10_simple_single_1, eval_speed_popl10_simple_single_bb0_in, eval_speed_popl10_simple_single_bb1_in, eval_speed_popl10_simple_single_bb2_in, eval_speed_popl10_simple_single_bb3_in, eval_speed_popl10_simple_single_start, eval_speed_popl10_simple_single_stop
Transitions:
6:eval_speed_popl10_simple_single_0(Arg_0,Arg_1) -> eval_speed_popl10_simple_single_1(Arg_0,Arg_1):|:1+Arg_1<=Arg_0 && 0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0
7:eval_speed_popl10_simple_single_1(Arg_0,Arg_1) -> eval_speed_popl10_simple_single_bb1_in(Arg_0,Arg_1+1):|:1+Arg_1<=Arg_0 && 0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0
1:eval_speed_popl10_simple_single_bb0_in(Arg_0,Arg_1) -> eval_speed_popl10_simple_single_bb1_in(Arg_0,0)
2:eval_speed_popl10_simple_single_bb1_in(Arg_0,Arg_1) -> eval_speed_popl10_simple_single_bb2_in(Arg_0,Arg_1):|:0<=Arg_1 && Arg_1<Arg_0
3:eval_speed_popl10_simple_single_bb1_in(Arg_0,Arg_1) -> eval_speed_popl10_simple_single_bb3_in(Arg_0,Arg_1):|:0<=Arg_1 && Arg_0<=Arg_1
4:eval_speed_popl10_simple_single_bb2_in(Arg_0,Arg_1) -> eval_speed_popl10_simple_single_0(Arg_0,Arg_1):|:1+Arg_1<=Arg_0 && 0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0
8:eval_speed_popl10_simple_single_bb3_in(Arg_0,Arg_1) -> eval_speed_popl10_simple_single_stop(Arg_0,Arg_1):|:0<=Arg_1 && Arg_0<=Arg_1
0:eval_speed_popl10_simple_single_start(Arg_0,Arg_1) -> eval_speed_popl10_simple_single_bb0_in(Arg_0,Arg_1)

MPRF for transition 6:eval_speed_popl10_simple_single_0(Arg_0,Arg_1) -> eval_speed_popl10_simple_single_1(Arg_0,Arg_1):|:1+Arg_1<=Arg_0 && 0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 of depth 1:

new bound:

Arg_0 {O(n)}

MPRF:

eval_speed_popl10_simple_single_1 [Arg_0-Arg_1-1 ]
eval_speed_popl10_simple_single_bb1_in [Arg_0-Arg_1 ]
eval_speed_popl10_simple_single_bb2_in [Arg_0-Arg_1 ]
eval_speed_popl10_simple_single_0 [Arg_0-Arg_1 ]

MPRF for transition 7:eval_speed_popl10_simple_single_1(Arg_0,Arg_1) -> eval_speed_popl10_simple_single_bb1_in(Arg_0,Arg_1+1):|:1+Arg_1<=Arg_0 && 0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 of depth 1:

new bound:

Arg_0 {O(n)}

MPRF:

eval_speed_popl10_simple_single_1 [Arg_0-Arg_1 ]
eval_speed_popl10_simple_single_bb1_in [Arg_0-Arg_1 ]
eval_speed_popl10_simple_single_bb2_in [Arg_0-Arg_1 ]
eval_speed_popl10_simple_single_0 [Arg_0-Arg_1 ]

MPRF for transition 2:eval_speed_popl10_simple_single_bb1_in(Arg_0,Arg_1) -> eval_speed_popl10_simple_single_bb2_in(Arg_0,Arg_1):|:0<=Arg_1 && Arg_1<Arg_0 of depth 1:

new bound:

Arg_0 {O(n)}

MPRF:

eval_speed_popl10_simple_single_1 [Arg_0-Arg_1-1 ]
eval_speed_popl10_simple_single_bb1_in [Arg_0-Arg_1 ]
eval_speed_popl10_simple_single_bb2_in [Arg_0-Arg_1-1 ]
eval_speed_popl10_simple_single_0 [Arg_0-Arg_1-1 ]

MPRF for transition 4:eval_speed_popl10_simple_single_bb2_in(Arg_0,Arg_1) -> eval_speed_popl10_simple_single_0(Arg_0,Arg_1):|:1+Arg_1<=Arg_0 && 0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 of depth 1:

new bound:

Arg_0 {O(n)}

MPRF:

eval_speed_popl10_simple_single_1 [Arg_0-Arg_1-1 ]
eval_speed_popl10_simple_single_bb1_in [Arg_0-Arg_1 ]
eval_speed_popl10_simple_single_bb2_in [Arg_0-Arg_1 ]
eval_speed_popl10_simple_single_0 [Arg_0-Arg_1-1 ]

All Bounds

Timebounds

Overall timebound:4*Arg_0+4 {O(n)}
6: eval_speed_popl10_simple_single_0->eval_speed_popl10_simple_single_1: Arg_0 {O(n)}
7: eval_speed_popl10_simple_single_1->eval_speed_popl10_simple_single_bb1_in: Arg_0 {O(n)}
1: eval_speed_popl10_simple_single_bb0_in->eval_speed_popl10_simple_single_bb1_in: 1 {O(1)}
2: eval_speed_popl10_simple_single_bb1_in->eval_speed_popl10_simple_single_bb2_in: Arg_0 {O(n)}
3: eval_speed_popl10_simple_single_bb1_in->eval_speed_popl10_simple_single_bb3_in: 1 {O(1)}
4: eval_speed_popl10_simple_single_bb2_in->eval_speed_popl10_simple_single_0: Arg_0 {O(n)}
8: eval_speed_popl10_simple_single_bb3_in->eval_speed_popl10_simple_single_stop: 1 {O(1)}
0: eval_speed_popl10_simple_single_start->eval_speed_popl10_simple_single_bb0_in: 1 {O(1)}

Costbounds

Overall costbound: 4*Arg_0+4 {O(n)}
6: eval_speed_popl10_simple_single_0->eval_speed_popl10_simple_single_1: Arg_0 {O(n)}
7: eval_speed_popl10_simple_single_1->eval_speed_popl10_simple_single_bb1_in: Arg_0 {O(n)}
1: eval_speed_popl10_simple_single_bb0_in->eval_speed_popl10_simple_single_bb1_in: 1 {O(1)}
2: eval_speed_popl10_simple_single_bb1_in->eval_speed_popl10_simple_single_bb2_in: Arg_0 {O(n)}
3: eval_speed_popl10_simple_single_bb1_in->eval_speed_popl10_simple_single_bb3_in: 1 {O(1)}
4: eval_speed_popl10_simple_single_bb2_in->eval_speed_popl10_simple_single_0: Arg_0 {O(n)}
8: eval_speed_popl10_simple_single_bb3_in->eval_speed_popl10_simple_single_stop: 1 {O(1)}
0: eval_speed_popl10_simple_single_start->eval_speed_popl10_simple_single_bb0_in: 1 {O(1)}

Sizebounds

6: eval_speed_popl10_simple_single_0->eval_speed_popl10_simple_single_1, Arg_0: Arg_0 {O(n)}
6: eval_speed_popl10_simple_single_0->eval_speed_popl10_simple_single_1, Arg_1: Arg_0 {O(n)}
7: eval_speed_popl10_simple_single_1->eval_speed_popl10_simple_single_bb1_in, Arg_0: Arg_0 {O(n)}
7: eval_speed_popl10_simple_single_1->eval_speed_popl10_simple_single_bb1_in, Arg_1: Arg_0 {O(n)}
1: eval_speed_popl10_simple_single_bb0_in->eval_speed_popl10_simple_single_bb1_in, Arg_0: Arg_0 {O(n)}
1: eval_speed_popl10_simple_single_bb0_in->eval_speed_popl10_simple_single_bb1_in, Arg_1: 0 {O(1)}
2: eval_speed_popl10_simple_single_bb1_in->eval_speed_popl10_simple_single_bb2_in, Arg_0: Arg_0 {O(n)}
2: eval_speed_popl10_simple_single_bb1_in->eval_speed_popl10_simple_single_bb2_in, Arg_1: Arg_0 {O(n)}
3: eval_speed_popl10_simple_single_bb1_in->eval_speed_popl10_simple_single_bb3_in, Arg_0: 2*Arg_0 {O(n)}
3: eval_speed_popl10_simple_single_bb1_in->eval_speed_popl10_simple_single_bb3_in, Arg_1: Arg_0 {O(n)}
4: eval_speed_popl10_simple_single_bb2_in->eval_speed_popl10_simple_single_0, Arg_0: Arg_0 {O(n)}
4: eval_speed_popl10_simple_single_bb2_in->eval_speed_popl10_simple_single_0, Arg_1: Arg_0 {O(n)}
8: eval_speed_popl10_simple_single_bb3_in->eval_speed_popl10_simple_single_stop, Arg_0: 2*Arg_0 {O(n)}
8: eval_speed_popl10_simple_single_bb3_in->eval_speed_popl10_simple_single_stop, Arg_1: Arg_0 {O(n)}
0: eval_speed_popl10_simple_single_start->eval_speed_popl10_simple_single_bb0_in, Arg_0: Arg_0 {O(n)}
0: eval_speed_popl10_simple_single_start->eval_speed_popl10_simple_single_bb0_in, Arg_1: Arg_1 {O(n)}