Initial Problem

Start: eval_start_start
Program_Vars: Arg_0, Arg_1
Temp_Vars:
Locations: eval_start_0, eval_start_1, eval_start_2, eval_start_3, eval_start_4, eval_start_5, eval_start_6, eval_start_bb0_in, eval_start_bb1_in, eval_start_bb2_in, eval_start_bb3_in, eval_start_start, eval_start_stop
Transitions:
2:eval_start_0(Arg_0,Arg_1) -> eval_start_1(Arg_0,Arg_1)
3:eval_start_1(Arg_0,Arg_1) -> eval_start_2(Arg_0,Arg_1)
4:eval_start_2(Arg_0,Arg_1) -> eval_start_3(Arg_0,Arg_1)
5:eval_start_3(Arg_0,Arg_1) -> eval_start_4(Arg_0,Arg_1)
6:eval_start_4(Arg_0,Arg_1) -> eval_start_bb1_in(Arg_0,0)
10:eval_start_5(Arg_0,Arg_1) -> eval_start_6(Arg_0,Arg_1)
11:eval_start_6(Arg_0,Arg_1) -> eval_start_bb1_in(Arg_0,Arg_1+1)
1:eval_start_bb0_in(Arg_0,Arg_1) -> eval_start_0(Arg_0,Arg_1)
7:eval_start_bb1_in(Arg_0,Arg_1) -> eval_start_bb2_in(Arg_0,Arg_1):|:Arg_1<Arg_0
8:eval_start_bb1_in(Arg_0,Arg_1) -> eval_start_bb3_in(Arg_0,Arg_1):|:Arg_0<=Arg_1
9:eval_start_bb2_in(Arg_0,Arg_1) -> eval_start_5(Arg_0,Arg_1)
12:eval_start_bb3_in(Arg_0,Arg_1) -> eval_start_stop(Arg_0,Arg_1)
0:eval_start_start(Arg_0,Arg_1) -> eval_start_bb0_in(Arg_0,Arg_1)

Preprocessing

Found invariant 0<=Arg_1 for location eval_start_bb1_in

Found invariant 1+Arg_1<=Arg_0 && 0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 for location eval_start_5

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

Found invariant 1+Arg_1<=Arg_0 && 0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 for location eval_start_6

Found invariant 1+Arg_1<=Arg_0 && 0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 for location eval_start_bb2_in

Found invariant 0<=Arg_1 && Arg_0<=Arg_1 for location eval_start_bb3_in

Problem after Preprocessing

Start: eval_start_start
Program_Vars: Arg_0, Arg_1
Temp_Vars:
Locations: eval_start_0, eval_start_1, eval_start_2, eval_start_3, eval_start_4, eval_start_5, eval_start_6, eval_start_bb0_in, eval_start_bb1_in, eval_start_bb2_in, eval_start_bb3_in, eval_start_start, eval_start_stop
Transitions:
2:eval_start_0(Arg_0,Arg_1) -> eval_start_1(Arg_0,Arg_1)
3:eval_start_1(Arg_0,Arg_1) -> eval_start_2(Arg_0,Arg_1)
4:eval_start_2(Arg_0,Arg_1) -> eval_start_3(Arg_0,Arg_1)
5:eval_start_3(Arg_0,Arg_1) -> eval_start_4(Arg_0,Arg_1)
6:eval_start_4(Arg_0,Arg_1) -> eval_start_bb1_in(Arg_0,0)
10:eval_start_5(Arg_0,Arg_1) -> eval_start_6(Arg_0,Arg_1):|:1+Arg_1<=Arg_0 && 0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0
11:eval_start_6(Arg_0,Arg_1) -> eval_start_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_start_bb0_in(Arg_0,Arg_1) -> eval_start_0(Arg_0,Arg_1)
7:eval_start_bb1_in(Arg_0,Arg_1) -> eval_start_bb2_in(Arg_0,Arg_1):|:0<=Arg_1 && Arg_1<Arg_0
8:eval_start_bb1_in(Arg_0,Arg_1) -> eval_start_bb3_in(Arg_0,Arg_1):|:0<=Arg_1 && Arg_0<=Arg_1
9:eval_start_bb2_in(Arg_0,Arg_1) -> eval_start_5(Arg_0,Arg_1):|:1+Arg_1<=Arg_0 && 0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0
12:eval_start_bb3_in(Arg_0,Arg_1) -> eval_start_stop(Arg_0,Arg_1):|:0<=Arg_1 && Arg_0<=Arg_1
0:eval_start_start(Arg_0,Arg_1) -> eval_start_bb0_in(Arg_0,Arg_1)

MPRF for transition 10:eval_start_5(Arg_0,Arg_1) -> eval_start_6(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_start_6 [Arg_0-Arg_1-1 ]
eval_start_bb1_in [Arg_0-Arg_1 ]
eval_start_bb2_in [Arg_0-Arg_1 ]
eval_start_5 [Arg_0-Arg_1 ]

MPRF for transition 11:eval_start_6(Arg_0,Arg_1) -> eval_start_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_start_6 [Arg_0-Arg_1 ]
eval_start_bb1_in [Arg_0-Arg_1 ]
eval_start_bb2_in [Arg_0-Arg_1 ]
eval_start_5 [Arg_0-Arg_1 ]

MPRF for transition 7:eval_start_bb1_in(Arg_0,Arg_1) -> eval_start_bb2_in(Arg_0,Arg_1):|:0<=Arg_1 && Arg_1<Arg_0 of depth 1:

new bound:

Arg_0 {O(n)}

MPRF:

eval_start_6 [Arg_0-Arg_1-1 ]
eval_start_bb1_in [Arg_0-Arg_1 ]
eval_start_bb2_in [Arg_0-Arg_1-1 ]
eval_start_5 [Arg_0-Arg_1-1 ]

MPRF for transition 9:eval_start_bb2_in(Arg_0,Arg_1) -> eval_start_5(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_start_6 [Arg_0-Arg_1-1 ]
eval_start_bb1_in [Arg_0-Arg_1 ]
eval_start_bb2_in [Arg_0-Arg_1 ]
eval_start_5 [Arg_0-Arg_1-1 ]

All Bounds

Timebounds

Overall timebound:4*Arg_0+9 {O(n)}
2: eval_start_0->eval_start_1: 1 {O(1)}
3: eval_start_1->eval_start_2: 1 {O(1)}
4: eval_start_2->eval_start_3: 1 {O(1)}
5: eval_start_3->eval_start_4: 1 {O(1)}
6: eval_start_4->eval_start_bb1_in: 1 {O(1)}
10: eval_start_5->eval_start_6: Arg_0 {O(n)}
11: eval_start_6->eval_start_bb1_in: Arg_0 {O(n)}
1: eval_start_bb0_in->eval_start_0: 1 {O(1)}
7: eval_start_bb1_in->eval_start_bb2_in: Arg_0 {O(n)}
8: eval_start_bb1_in->eval_start_bb3_in: 1 {O(1)}
9: eval_start_bb2_in->eval_start_5: Arg_0 {O(n)}
12: eval_start_bb3_in->eval_start_stop: 1 {O(1)}
0: eval_start_start->eval_start_bb0_in: 1 {O(1)}

Costbounds

Overall costbound: 4*Arg_0+9 {O(n)}
2: eval_start_0->eval_start_1: 1 {O(1)}
3: eval_start_1->eval_start_2: 1 {O(1)}
4: eval_start_2->eval_start_3: 1 {O(1)}
5: eval_start_3->eval_start_4: 1 {O(1)}
6: eval_start_4->eval_start_bb1_in: 1 {O(1)}
10: eval_start_5->eval_start_6: Arg_0 {O(n)}
11: eval_start_6->eval_start_bb1_in: Arg_0 {O(n)}
1: eval_start_bb0_in->eval_start_0: 1 {O(1)}
7: eval_start_bb1_in->eval_start_bb2_in: Arg_0 {O(n)}
8: eval_start_bb1_in->eval_start_bb3_in: 1 {O(1)}
9: eval_start_bb2_in->eval_start_5: Arg_0 {O(n)}
12: eval_start_bb3_in->eval_start_stop: 1 {O(1)}
0: eval_start_start->eval_start_bb0_in: 1 {O(1)}

Sizebounds

2: eval_start_0->eval_start_1, Arg_0: Arg_0 {O(n)}
2: eval_start_0->eval_start_1, Arg_1: Arg_1 {O(n)}
3: eval_start_1->eval_start_2, Arg_0: Arg_0 {O(n)}
3: eval_start_1->eval_start_2, Arg_1: Arg_1 {O(n)}
4: eval_start_2->eval_start_3, Arg_0: Arg_0 {O(n)}
4: eval_start_2->eval_start_3, Arg_1: Arg_1 {O(n)}
5: eval_start_3->eval_start_4, Arg_0: Arg_0 {O(n)}
5: eval_start_3->eval_start_4, Arg_1: Arg_1 {O(n)}
6: eval_start_4->eval_start_bb1_in, Arg_0: Arg_0 {O(n)}
6: eval_start_4->eval_start_bb1_in, Arg_1: 0 {O(1)}
10: eval_start_5->eval_start_6, Arg_0: Arg_0 {O(n)}
10: eval_start_5->eval_start_6, Arg_1: Arg_0 {O(n)}
11: eval_start_6->eval_start_bb1_in, Arg_0: Arg_0 {O(n)}
11: eval_start_6->eval_start_bb1_in, Arg_1: Arg_0 {O(n)}
1: eval_start_bb0_in->eval_start_0, Arg_0: Arg_0 {O(n)}
1: eval_start_bb0_in->eval_start_0, Arg_1: Arg_1 {O(n)}
7: eval_start_bb1_in->eval_start_bb2_in, Arg_0: Arg_0 {O(n)}
7: eval_start_bb1_in->eval_start_bb2_in, Arg_1: Arg_0 {O(n)}
8: eval_start_bb1_in->eval_start_bb3_in, Arg_0: 2*Arg_0 {O(n)}
8: eval_start_bb1_in->eval_start_bb3_in, Arg_1: Arg_0 {O(n)}
9: eval_start_bb2_in->eval_start_5, Arg_0: Arg_0 {O(n)}
9: eval_start_bb2_in->eval_start_5, Arg_1: Arg_0 {O(n)}
12: eval_start_bb3_in->eval_start_stop, Arg_0: 2*Arg_0 {O(n)}
12: eval_start_bb3_in->eval_start_stop, Arg_1: Arg_0 {O(n)}
0: eval_start_start->eval_start_bb0_in, Arg_0: Arg_0 {O(n)}
0: eval_start_start->eval_start_bb0_in, Arg_1: Arg_1 {O(n)}