Initial Problem

Start: eval_start_start
Program_Vars: Arg_0, Arg_1, Arg_2
Temp_Vars:
Locations: eval_start_0, eval_start_1, eval_start_2, eval_start_3, eval_start_4, eval_start_5, 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,Arg_2) -> eval_start_1(Arg_0,Arg_1,Arg_2)
3:eval_start_1(Arg_0,Arg_1,Arg_2) -> eval_start_2(Arg_0,Arg_1,Arg_2)
4:eval_start_2(Arg_0,Arg_1,Arg_2) -> eval_start_3(Arg_0,Arg_1,Arg_2)
5:eval_start_3(Arg_0,Arg_1,Arg_2) -> eval_start_4(Arg_0,Arg_1,Arg_2)
6:eval_start_4(Arg_0,Arg_1,Arg_2) -> eval_start_5(Arg_0,Arg_1,Arg_2)
7:eval_start_5(Arg_0,Arg_1,Arg_2) -> eval_start_bb1_in(Arg_2,1,Arg_2)
1:eval_start_bb0_in(Arg_0,Arg_1,Arg_2) -> eval_start_0(Arg_0,Arg_1,Arg_2)
8:eval_start_bb1_in(Arg_0,Arg_1,Arg_2) -> eval_start_bb2_in(Arg_0,Arg_1,Arg_2):|:0<Arg_1
9:eval_start_bb1_in(Arg_0,Arg_1,Arg_2) -> eval_start_bb3_in(Arg_0,Arg_1,Arg_2):|:Arg_1<=0
10:eval_start_bb2_in(Arg_0,Arg_1,Arg_2) -> eval_start_bb1_in(Arg_0-1,1,Arg_2):|:0<Arg_0 && 0<Arg_0
11:eval_start_bb2_in(Arg_0,Arg_1,Arg_2) -> eval_start_bb1_in(Arg_0,1,Arg_2):|:0<Arg_0 && Arg_0<=0
12:eval_start_bb2_in(Arg_0,Arg_1,Arg_2) -> eval_start_bb1_in(Arg_0-1,0,Arg_2):|:Arg_0<=0 && 0<Arg_0
13:eval_start_bb2_in(Arg_0,Arg_1,Arg_2) -> eval_start_bb1_in(Arg_0,0,Arg_2):|:Arg_0<=0 && Arg_0<=0
14:eval_start_bb3_in(Arg_0,Arg_1,Arg_2) -> eval_start_stop(Arg_0,Arg_1,Arg_2)
0:eval_start_start(Arg_0,Arg_1,Arg_2) -> eval_start_bb0_in(Arg_0,Arg_1,Arg_2)

Preprocessing

Cut unsatisfiable transition 11: eval_start_bb2_in->eval_start_bb1_in

Cut unsatisfiable transition 12: eval_start_bb2_in->eval_start_bb1_in

Found invariant Arg_0<=Arg_2 && Arg_1<=1 && 0<=Arg_1 for location eval_start_bb1_in

Found invariant Arg_0<=Arg_2 && Arg_1<=0 && 0<=Arg_1 for location eval_start_stop

Found invariant Arg_0<=Arg_2 && Arg_1<=1 && 1<=Arg_1 for location eval_start_bb2_in

Found invariant Arg_0<=Arg_2 && Arg_1<=0 && 0<=Arg_1 for location eval_start_bb3_in

Problem after Preprocessing

Start: eval_start_start
Program_Vars: Arg_0, Arg_1, Arg_2
Temp_Vars:
Locations: eval_start_0, eval_start_1, eval_start_2, eval_start_3, eval_start_4, eval_start_5, 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,Arg_2) -> eval_start_1(Arg_0,Arg_1,Arg_2)
3:eval_start_1(Arg_0,Arg_1,Arg_2) -> eval_start_2(Arg_0,Arg_1,Arg_2)
4:eval_start_2(Arg_0,Arg_1,Arg_2) -> eval_start_3(Arg_0,Arg_1,Arg_2)
5:eval_start_3(Arg_0,Arg_1,Arg_2) -> eval_start_4(Arg_0,Arg_1,Arg_2)
6:eval_start_4(Arg_0,Arg_1,Arg_2) -> eval_start_5(Arg_0,Arg_1,Arg_2)
7:eval_start_5(Arg_0,Arg_1,Arg_2) -> eval_start_bb1_in(Arg_2,1,Arg_2)
1:eval_start_bb0_in(Arg_0,Arg_1,Arg_2) -> eval_start_0(Arg_0,Arg_1,Arg_2)
8:eval_start_bb1_in(Arg_0,Arg_1,Arg_2) -> eval_start_bb2_in(Arg_0,Arg_1,Arg_2):|:Arg_0<=Arg_2 && Arg_1<=1 && 0<=Arg_1 && 0<Arg_1
9:eval_start_bb1_in(Arg_0,Arg_1,Arg_2) -> eval_start_bb3_in(Arg_0,Arg_1,Arg_2):|:Arg_0<=Arg_2 && Arg_1<=1 && 0<=Arg_1 && Arg_1<=0
10:eval_start_bb2_in(Arg_0,Arg_1,Arg_2) -> eval_start_bb1_in(Arg_0-1,1,Arg_2):|:Arg_0<=Arg_2 && Arg_1<=1 && 1<=Arg_1 && 0<Arg_0 && 0<Arg_0
13:eval_start_bb2_in(Arg_0,Arg_1,Arg_2) -> eval_start_bb1_in(Arg_0,0,Arg_2):|:Arg_0<=Arg_2 && Arg_1<=1 && 1<=Arg_1 && Arg_0<=0 && Arg_0<=0
14:eval_start_bb3_in(Arg_0,Arg_1,Arg_2) -> eval_start_stop(Arg_0,Arg_1,Arg_2):|:Arg_0<=Arg_2 && Arg_1<=0 && 0<=Arg_1
0:eval_start_start(Arg_0,Arg_1,Arg_2) -> eval_start_bb0_in(Arg_0,Arg_1,Arg_2)

MPRF for transition 10:eval_start_bb2_in(Arg_0,Arg_1,Arg_2) -> eval_start_bb1_in(Arg_0-1,1,Arg_2):|:Arg_0<=Arg_2 && Arg_1<=1 && 1<=Arg_1 && 0<Arg_0 && 0<Arg_0 of depth 1:

new bound:

Arg_2 {O(n)}

MPRF:

eval_start_bb2_in [Arg_0 ]
eval_start_bb1_in [Arg_0 ]

MPRF for transition 13:eval_start_bb2_in(Arg_0,Arg_1,Arg_2) -> eval_start_bb1_in(Arg_0,0,Arg_2):|:Arg_0<=Arg_2 && Arg_1<=1 && 1<=Arg_1 && Arg_0<=0 && Arg_0<=0 of depth 1:

new bound:

1 {O(1)}

MPRF:

eval_start_bb2_in [1 ]
eval_start_bb1_in [Arg_1 ]

knowledge_propagation leads to new time bound Arg_2+1 {O(n)} for transition 8:eval_start_bb1_in(Arg_0,Arg_1,Arg_2) -> eval_start_bb2_in(Arg_0,Arg_1,Arg_2):|:Arg_0<=Arg_2 && Arg_1<=1 && 0<=Arg_1 && 0<Arg_1

All Bounds

Timebounds

Overall timebound:2*Arg_2+12 {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_5: 1 {O(1)}
7: eval_start_5->eval_start_bb1_in: 1 {O(1)}
1: eval_start_bb0_in->eval_start_0: 1 {O(1)}
8: eval_start_bb1_in->eval_start_bb2_in: Arg_2+1 {O(n)}
9: eval_start_bb1_in->eval_start_bb3_in: 1 {O(1)}
10: eval_start_bb2_in->eval_start_bb1_in: Arg_2 {O(n)}
13: eval_start_bb2_in->eval_start_bb1_in: 1 {O(1)}
14: eval_start_bb3_in->eval_start_stop: 1 {O(1)}
0: eval_start_start->eval_start_bb0_in: 1 {O(1)}

Costbounds

Overall costbound: 2*Arg_2+12 {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_5: 1 {O(1)}
7: eval_start_5->eval_start_bb1_in: 1 {O(1)}
1: eval_start_bb0_in->eval_start_0: 1 {O(1)}
8: eval_start_bb1_in->eval_start_bb2_in: Arg_2+1 {O(n)}
9: eval_start_bb1_in->eval_start_bb3_in: 1 {O(1)}
10: eval_start_bb2_in->eval_start_bb1_in: Arg_2 {O(n)}
13: eval_start_bb2_in->eval_start_bb1_in: 1 {O(1)}
14: 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)}
2: eval_start_0->eval_start_1, Arg_2: Arg_2 {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)}
3: eval_start_1->eval_start_2, Arg_2: Arg_2 {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)}
4: eval_start_2->eval_start_3, Arg_2: Arg_2 {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)}
5: eval_start_3->eval_start_4, Arg_2: Arg_2 {O(n)}
6: eval_start_4->eval_start_5, Arg_0: Arg_0 {O(n)}
6: eval_start_4->eval_start_5, Arg_1: Arg_1 {O(n)}
6: eval_start_4->eval_start_5, Arg_2: Arg_2 {O(n)}
7: eval_start_5->eval_start_bb1_in, Arg_0: Arg_2 {O(n)}
7: eval_start_5->eval_start_bb1_in, Arg_1: 1 {O(1)}
7: eval_start_5->eval_start_bb1_in, Arg_2: Arg_2 {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)}
1: eval_start_bb0_in->eval_start_0, Arg_2: Arg_2 {O(n)}
8: eval_start_bb1_in->eval_start_bb2_in, Arg_0: Arg_2 {O(n)}
8: eval_start_bb1_in->eval_start_bb2_in, Arg_1: 1 {O(1)}
8: eval_start_bb1_in->eval_start_bb2_in, Arg_2: Arg_2 {O(n)}
9: eval_start_bb1_in->eval_start_bb3_in, Arg_0: Arg_2 {O(n)}
9: eval_start_bb1_in->eval_start_bb3_in, Arg_1: 0 {O(1)}
9: eval_start_bb1_in->eval_start_bb3_in, Arg_2: Arg_2 {O(n)}
10: eval_start_bb2_in->eval_start_bb1_in, Arg_0: Arg_2 {O(n)}
10: eval_start_bb2_in->eval_start_bb1_in, Arg_1: 1 {O(1)}
10: eval_start_bb2_in->eval_start_bb1_in, Arg_2: Arg_2 {O(n)}
13: eval_start_bb2_in->eval_start_bb1_in, Arg_0: Arg_2 {O(n)}
13: eval_start_bb2_in->eval_start_bb1_in, Arg_1: 0 {O(1)}
13: eval_start_bb2_in->eval_start_bb1_in, Arg_2: Arg_2 {O(n)}
14: eval_start_bb3_in->eval_start_stop, Arg_0: Arg_2 {O(n)}
14: eval_start_bb3_in->eval_start_stop, Arg_1: 0 {O(1)}
14: eval_start_bb3_in->eval_start_stop, Arg_2: Arg_2 {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)}
0: eval_start_start->eval_start_bb0_in, Arg_2: Arg_2 {O(n)}