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_8, eval_start_9, eval_start_bb0_in, eval_start_bb1_in, eval_start_bb2_in, eval_start_bb3_in, eval_start_bb4_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_bb1_in(Arg_2,Arg_1,Arg_2):|:0<Arg_1
6:eval_start_3(Arg_0,Arg_1,Arg_2) -> eval_start_bb4_in(Arg_0,Arg_1,Arg_2):|:Arg_1<=0
13:eval_start_8(Arg_0,Arg_1,Arg_2) -> eval_start_9(Arg_0,Arg_1,Arg_2)
14:eval_start_9(Arg_0,Arg_1,Arg_2) -> eval_start_stop(Arg_0,Arg_1,Arg_2)
1:eval_start_bb0_in(Arg_0,Arg_1,Arg_2) -> eval_start_0(Arg_0,Arg_1,Arg_2)
7:eval_start_bb1_in(Arg_0,Arg_1,Arg_2) -> eval_start_bb2_in(Arg_0,Arg_1,Arg_2):|:0<Arg_0
8:eval_start_bb1_in(Arg_0,Arg_1,Arg_2) -> eval_start_bb3_in(Arg_0,Arg_1,Arg_2):|:Arg_0<=0
9:eval_start_bb2_in(Arg_0,Arg_1,Arg_2) -> eval_start_bb1_in(Arg_0-1,Arg_1,Arg_2):|:Arg_0<Arg_1
10:eval_start_bb2_in(Arg_0,Arg_1,Arg_2) -> eval_start_bb1_in(Arg_0-Arg_1,Arg_1,Arg_2):|:Arg_1<=Arg_0
11:eval_start_bb3_in(Arg_0,Arg_1,Arg_2) -> eval_start_stop(Arg_0,Arg_1,Arg_2)
12:eval_start_bb4_in(Arg_0,Arg_1,Arg_2) -> eval_start_8(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

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

Found invariant Arg_1<=0 for location eval_start_9

Found invariant Arg_1<=0 for location eval_start_8

Found invariant 1<=Arg_2 && 2<=Arg_1+Arg_2 && 2<=Arg_0+Arg_2 && Arg_0<=Arg_2 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 for location eval_start_bb2_in

Found invariant Arg_0<=Arg_2 && 1<=Arg_1 && 1+Arg_0<=Arg_1 && Arg_0<=0 for location eval_start_bb3_in

Found invariant Arg_1<=0 for location eval_start_bb4_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_8, eval_start_9, eval_start_bb0_in, eval_start_bb1_in, eval_start_bb2_in, eval_start_bb3_in, eval_start_bb4_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_bb1_in(Arg_2,Arg_1,Arg_2):|:0<Arg_1
6:eval_start_3(Arg_0,Arg_1,Arg_2) -> eval_start_bb4_in(Arg_0,Arg_1,Arg_2):|:Arg_1<=0
13:eval_start_8(Arg_0,Arg_1,Arg_2) -> eval_start_9(Arg_0,Arg_1,Arg_2):|:Arg_1<=0
14:eval_start_9(Arg_0,Arg_1,Arg_2) -> eval_start_stop(Arg_0,Arg_1,Arg_2):|:Arg_1<=0
1:eval_start_bb0_in(Arg_0,Arg_1,Arg_2) -> eval_start_0(Arg_0,Arg_1,Arg_2)
7:eval_start_bb1_in(Arg_0,Arg_1,Arg_2) -> eval_start_bb2_in(Arg_0,Arg_1,Arg_2):|:Arg_0<=Arg_2 && 1<=Arg_1 && 0<Arg_0
8:eval_start_bb1_in(Arg_0,Arg_1,Arg_2) -> eval_start_bb3_in(Arg_0,Arg_1,Arg_2):|:Arg_0<=Arg_2 && 1<=Arg_1 && Arg_0<=0
9:eval_start_bb2_in(Arg_0,Arg_1,Arg_2) -> eval_start_bb1_in(Arg_0-1,Arg_1,Arg_2):|:1<=Arg_2 && 2<=Arg_1+Arg_2 && 2<=Arg_0+Arg_2 && Arg_0<=Arg_2 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 && Arg_0<Arg_1
10:eval_start_bb2_in(Arg_0,Arg_1,Arg_2) -> eval_start_bb1_in(Arg_0-Arg_1,Arg_1,Arg_2):|:1<=Arg_2 && 2<=Arg_1+Arg_2 && 2<=Arg_0+Arg_2 && Arg_0<=Arg_2 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 && Arg_1<=Arg_0
11:eval_start_bb3_in(Arg_0,Arg_1,Arg_2) -> eval_start_stop(Arg_0,Arg_1,Arg_2):|:Arg_0<=Arg_2 && 1<=Arg_1 && 1+Arg_0<=Arg_1 && Arg_0<=0
12:eval_start_bb4_in(Arg_0,Arg_1,Arg_2) -> eval_start_8(Arg_0,Arg_1,Arg_2):|:Arg_1<=0
0:eval_start_start(Arg_0,Arg_1,Arg_2) -> eval_start_bb0_in(Arg_0,Arg_1,Arg_2)

MPRF for transition 7:eval_start_bb1_in(Arg_0,Arg_1,Arg_2) -> eval_start_bb2_in(Arg_0,Arg_1,Arg_2):|:Arg_0<=Arg_2 && 1<=Arg_1 && 0<Arg_0 of depth 1:

new bound:

Arg_2 {O(n)}

MPRF:

eval_start_bb2_in [Arg_0-1 ]
eval_start_bb1_in [Arg_0 ]

MPRF for transition 9:eval_start_bb2_in(Arg_0,Arg_1,Arg_2) -> eval_start_bb1_in(Arg_0-1,Arg_1,Arg_2):|:1<=Arg_2 && 2<=Arg_1+Arg_2 && 2<=Arg_0+Arg_2 && Arg_0<=Arg_2 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 && Arg_0<Arg_1 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 10:eval_start_bb2_in(Arg_0,Arg_1,Arg_2) -> eval_start_bb1_in(Arg_0-Arg_1,Arg_1,Arg_2):|:1<=Arg_2 && 2<=Arg_1+Arg_2 && 2<=Arg_0+Arg_2 && Arg_0<=Arg_2 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 && Arg_1<=Arg_0 of depth 1:

new bound:

Arg_2 {O(n)}

MPRF:

eval_start_bb2_in [Arg_0 ]
eval_start_bb1_in [Arg_0 ]

All Bounds

Timebounds

Overall timebound:3*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_bb1_in: 1 {O(1)}
6: eval_start_3->eval_start_bb4_in: 1 {O(1)}
13: eval_start_8->eval_start_9: 1 {O(1)}
14: eval_start_9->eval_start_stop: 1 {O(1)}
1: eval_start_bb0_in->eval_start_0: 1 {O(1)}
7: eval_start_bb1_in->eval_start_bb2_in: Arg_2 {O(n)}
8: eval_start_bb1_in->eval_start_bb3_in: 1 {O(1)}
9: eval_start_bb2_in->eval_start_bb1_in: Arg_2 {O(n)}
10: eval_start_bb2_in->eval_start_bb1_in: Arg_2 {O(n)}
11: eval_start_bb3_in->eval_start_stop: 1 {O(1)}
12: eval_start_bb4_in->eval_start_8: 1 {O(1)}
0: eval_start_start->eval_start_bb0_in: 1 {O(1)}

Costbounds

Overall costbound: 3*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_bb1_in: 1 {O(1)}
6: eval_start_3->eval_start_bb4_in: 1 {O(1)}
13: eval_start_8->eval_start_9: 1 {O(1)}
14: eval_start_9->eval_start_stop: 1 {O(1)}
1: eval_start_bb0_in->eval_start_0: 1 {O(1)}
7: eval_start_bb1_in->eval_start_bb2_in: Arg_2 {O(n)}
8: eval_start_bb1_in->eval_start_bb3_in: 1 {O(1)}
9: eval_start_bb2_in->eval_start_bb1_in: Arg_2 {O(n)}
10: eval_start_bb2_in->eval_start_bb1_in: Arg_2 {O(n)}
11: eval_start_bb3_in->eval_start_stop: 1 {O(1)}
12: eval_start_bb4_in->eval_start_8: 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_bb1_in, Arg_0: Arg_2 {O(n)}
5: eval_start_3->eval_start_bb1_in, Arg_1: Arg_1 {O(n)}
5: eval_start_3->eval_start_bb1_in, Arg_2: Arg_2 {O(n)}
6: eval_start_3->eval_start_bb4_in, Arg_0: Arg_0 {O(n)}
6: eval_start_3->eval_start_bb4_in, Arg_1: Arg_1 {O(n)}
6: eval_start_3->eval_start_bb4_in, Arg_2: Arg_2 {O(n)}
13: eval_start_8->eval_start_9, Arg_0: Arg_0 {O(n)}
13: eval_start_8->eval_start_9, Arg_1: Arg_1 {O(n)}
13: eval_start_8->eval_start_9, Arg_2: Arg_2 {O(n)}
14: eval_start_9->eval_start_stop, Arg_0: Arg_0 {O(n)}
14: eval_start_9->eval_start_stop, Arg_1: Arg_1 {O(n)}
14: eval_start_9->eval_start_stop, 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)}
7: eval_start_bb1_in->eval_start_bb2_in, Arg_0: Arg_2 {O(n)}
7: eval_start_bb1_in->eval_start_bb2_in, Arg_1: Arg_1 {O(n)}
7: eval_start_bb1_in->eval_start_bb2_in, Arg_2: Arg_2 {O(n)}
8: eval_start_bb1_in->eval_start_bb3_in, Arg_0: 3*Arg_2 {O(n)}
8: eval_start_bb1_in->eval_start_bb3_in, Arg_1: 3*Arg_1 {O(n)}
8: eval_start_bb1_in->eval_start_bb3_in, Arg_2: 3*Arg_2 {O(n)}
9: eval_start_bb2_in->eval_start_bb1_in, Arg_0: Arg_2 {O(n)}
9: eval_start_bb2_in->eval_start_bb1_in, Arg_1: Arg_1 {O(n)}
9: eval_start_bb2_in->eval_start_bb1_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: Arg_1 {O(n)}
10: eval_start_bb2_in->eval_start_bb1_in, Arg_2: Arg_2 {O(n)}
11: eval_start_bb3_in->eval_start_stop, Arg_0: 3*Arg_2 {O(n)}
11: eval_start_bb3_in->eval_start_stop, Arg_1: 3*Arg_1 {O(n)}
11: eval_start_bb3_in->eval_start_stop, Arg_2: 3*Arg_2 {O(n)}
12: eval_start_bb4_in->eval_start_8, Arg_0: Arg_0 {O(n)}
12: eval_start_bb4_in->eval_start_8, Arg_1: Arg_1 {O(n)}
12: eval_start_bb4_in->eval_start_8, 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)}