Initial Problem

Start: eval_start_start
Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3
Temp_Vars:
Locations: eval_start_0, eval_start_1, eval_start_2, eval_start_3, eval_start_4, 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_bb5_in, eval_start_start, eval_start_stop
Transitions:
2:eval_start_0(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_start_1(Arg_0,Arg_1,Arg_2,Arg_3)
3:eval_start_1(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_start_2(Arg_0,Arg_1,Arg_2,Arg_3)
4:eval_start_2(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_start_3(Arg_0,Arg_1,Arg_2,Arg_3)
5:eval_start_3(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_start_4(Arg_0,Arg_1,Arg_2,Arg_3)
6:eval_start_4(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_start_bb1_in(Arg_0,Arg_1,Arg_1,0):|:0<Arg_0
7:eval_start_4(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_start_bb5_in(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_0<=0
15:eval_start_8(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_start_9(Arg_0,Arg_1,Arg_2,Arg_3)
16:eval_start_9(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_start_stop(Arg_0,Arg_1,Arg_2,Arg_3)
1:eval_start_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_start_0(Arg_0,Arg_1,Arg_2,Arg_3)
8:eval_start_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_start_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3):|:0<Arg_2
9:eval_start_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_start_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_2<=0
11:eval_start_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_start_bb1_in(Arg_0,Arg_1,Arg_2,0):|:Arg_0<=Arg_3
10:eval_start_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_start_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_3<Arg_0
12:eval_start_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_start_bb1_in(Arg_0,Arg_1,Arg_2-1,Arg_3+1)
13:eval_start_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_start_stop(Arg_0,Arg_1,Arg_2,Arg_3)
14:eval_start_bb5_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_start_8(Arg_0,Arg_1,Arg_2,Arg_3)
0:eval_start_start(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_start_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3)

Preprocessing

Found invariant Arg_3<=Arg_0 && 0<=Arg_3 && 1<=Arg_0+Arg_3 && Arg_2<=Arg_1 && 1<=Arg_0 for location eval_start_bb1_in

Found invariant Arg_0<=0 for location eval_start_9

Found invariant Arg_0<=0 for location eval_start_bb5_in

Found invariant Arg_0<=0 for location eval_start_8

Found invariant Arg_3<=Arg_0 && 0<=Arg_3 && 1<=Arg_2+Arg_3 && 1<=Arg_1+Arg_3 && 1<=Arg_0+Arg_3 && Arg_2<=Arg_1 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && 2<=Arg_0+Arg_2 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 for location eval_start_bb2_in

Found invariant 1+Arg_3<=Arg_0 && 0<=Arg_3 && 1<=Arg_2+Arg_3 && 1<=Arg_1+Arg_3 && 1<=Arg_0+Arg_3 && Arg_2<=Arg_1 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && 2<=Arg_0+Arg_2 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 for location eval_start_bb3_in

Found invariant Arg_3<=Arg_0 && 0<=Arg_3 && Arg_2<=Arg_3 && 1<=Arg_0+Arg_3 && Arg_2<=0 && Arg_2<=Arg_1 && 1+Arg_2<=Arg_0 && 1<=Arg_0 for location eval_start_bb4_in

Problem after Preprocessing

Start: eval_start_start
Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3
Temp_Vars:
Locations: eval_start_0, eval_start_1, eval_start_2, eval_start_3, eval_start_4, 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_bb5_in, eval_start_start, eval_start_stop
Transitions:
2:eval_start_0(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_start_1(Arg_0,Arg_1,Arg_2,Arg_3)
3:eval_start_1(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_start_2(Arg_0,Arg_1,Arg_2,Arg_3)
4:eval_start_2(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_start_3(Arg_0,Arg_1,Arg_2,Arg_3)
5:eval_start_3(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_start_4(Arg_0,Arg_1,Arg_2,Arg_3)
6:eval_start_4(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_start_bb1_in(Arg_0,Arg_1,Arg_1,0):|:0<Arg_0
7:eval_start_4(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_start_bb5_in(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_0<=0
15:eval_start_8(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_start_9(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_0<=0
16:eval_start_9(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_start_stop(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_0<=0
1:eval_start_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_start_0(Arg_0,Arg_1,Arg_2,Arg_3)
8:eval_start_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_start_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_3<=Arg_0 && 0<=Arg_3 && 1<=Arg_0+Arg_3 && Arg_2<=Arg_1 && 1<=Arg_0 && 0<Arg_2
9:eval_start_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_start_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_3<=Arg_0 && 0<=Arg_3 && 1<=Arg_0+Arg_3 && Arg_2<=Arg_1 && 1<=Arg_0 && Arg_2<=0
11:eval_start_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_start_bb1_in(Arg_0,Arg_1,Arg_2,0):|:Arg_3<=Arg_0 && 0<=Arg_3 && 1<=Arg_2+Arg_3 && 1<=Arg_1+Arg_3 && 1<=Arg_0+Arg_3 && Arg_2<=Arg_1 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && 2<=Arg_0+Arg_2 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 && Arg_0<=Arg_3
10:eval_start_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_start_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_3<=Arg_0 && 0<=Arg_3 && 1<=Arg_2+Arg_3 && 1<=Arg_1+Arg_3 && 1<=Arg_0+Arg_3 && Arg_2<=Arg_1 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && 2<=Arg_0+Arg_2 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 && Arg_3<Arg_0
12:eval_start_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_start_bb1_in(Arg_0,Arg_1,Arg_2-1,Arg_3+1):|:1+Arg_3<=Arg_0 && 0<=Arg_3 && 1<=Arg_2+Arg_3 && 1<=Arg_1+Arg_3 && 1<=Arg_0+Arg_3 && Arg_2<=Arg_1 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && 2<=Arg_0+Arg_2 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0
13:eval_start_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_start_stop(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_3<=Arg_0 && 0<=Arg_3 && Arg_2<=Arg_3 && 1<=Arg_0+Arg_3 && Arg_2<=0 && Arg_2<=Arg_1 && 1+Arg_2<=Arg_0 && 1<=Arg_0
14:eval_start_bb5_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_start_8(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_0<=0
0:eval_start_start(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_start_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3)

MPRF for transition 8:eval_start_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_start_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_3<=Arg_0 && 0<=Arg_3 && 1<=Arg_0+Arg_3 && Arg_2<=Arg_1 && 1<=Arg_0 && 0<Arg_2 of depth 1:

new bound:

2*Arg_1+1 {O(n)}

MPRF:

eval_start_bb2_in [2*Arg_2+Arg_3-2 ]
eval_start_bb3_in [2*Arg_2+Arg_3-2 ]
eval_start_bb1_in [2*Arg_2+Arg_3-1 ]

MPRF for transition 10:eval_start_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_start_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_3<=Arg_0 && 0<=Arg_3 && 1<=Arg_2+Arg_3 && 1<=Arg_1+Arg_3 && 1<=Arg_0+Arg_3 && Arg_2<=Arg_1 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && 2<=Arg_0+Arg_2 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 && Arg_3<Arg_0 of depth 1:

new bound:

Arg_1 {O(n)}

MPRF:

eval_start_bb2_in [Arg_2 ]
eval_start_bb3_in [Arg_2-1 ]
eval_start_bb1_in [Arg_2 ]

MPRF for transition 11:eval_start_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_start_bb1_in(Arg_0,Arg_1,Arg_2,0):|:Arg_3<=Arg_0 && 0<=Arg_3 && 1<=Arg_2+Arg_3 && 1<=Arg_1+Arg_3 && 1<=Arg_0+Arg_3 && Arg_2<=Arg_1 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && 2<=Arg_0+Arg_2 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 && Arg_0<=Arg_3 of depth 1:

new bound:

Arg_1 {O(n)}

MPRF:

eval_start_bb2_in [Arg_2+Arg_3 ]
eval_start_bb3_in [Arg_2+Arg_3 ]
eval_start_bb1_in [Arg_2+Arg_3 ]

MPRF for transition 12:eval_start_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_start_bb1_in(Arg_0,Arg_1,Arg_2-1,Arg_3+1):|:1+Arg_3<=Arg_0 && 0<=Arg_3 && 1<=Arg_2+Arg_3 && 1<=Arg_1+Arg_3 && 1<=Arg_0+Arg_3 && Arg_2<=Arg_1 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && 2<=Arg_0+Arg_2 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 of depth 1:

new bound:

Arg_1 {O(n)}

MPRF:

eval_start_bb2_in [Arg_2 ]
eval_start_bb3_in [Arg_2 ]
eval_start_bb1_in [Arg_2 ]

All Bounds

Timebounds

Overall timebound:5*Arg_1+14 {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)}
7: eval_start_4->eval_start_bb5_in: 1 {O(1)}
15: eval_start_8->eval_start_9: 1 {O(1)}
16: eval_start_9->eval_start_stop: 1 {O(1)}
1: eval_start_bb0_in->eval_start_0: 1 {O(1)}
8: eval_start_bb1_in->eval_start_bb2_in: 2*Arg_1+1 {O(n)}
9: eval_start_bb1_in->eval_start_bb4_in: 1 {O(1)}
10: eval_start_bb2_in->eval_start_bb3_in: Arg_1 {O(n)}
11: eval_start_bb2_in->eval_start_bb1_in: Arg_1 {O(n)}
12: eval_start_bb3_in->eval_start_bb1_in: Arg_1 {O(n)}
13: eval_start_bb4_in->eval_start_stop: 1 {O(1)}
14: eval_start_bb5_in->eval_start_8: 1 {O(1)}
0: eval_start_start->eval_start_bb0_in: 1 {O(1)}

Costbounds

Overall costbound: 5*Arg_1+14 {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)}
7: eval_start_4->eval_start_bb5_in: 1 {O(1)}
15: eval_start_8->eval_start_9: 1 {O(1)}
16: eval_start_9->eval_start_stop: 1 {O(1)}
1: eval_start_bb0_in->eval_start_0: 1 {O(1)}
8: eval_start_bb1_in->eval_start_bb2_in: 2*Arg_1+1 {O(n)}
9: eval_start_bb1_in->eval_start_bb4_in: 1 {O(1)}
10: eval_start_bb2_in->eval_start_bb3_in: Arg_1 {O(n)}
11: eval_start_bb2_in->eval_start_bb1_in: Arg_1 {O(n)}
12: eval_start_bb3_in->eval_start_bb1_in: Arg_1 {O(n)}
13: eval_start_bb4_in->eval_start_stop: 1 {O(1)}
14: eval_start_bb5_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)}
2: eval_start_0->eval_start_1, Arg_3: Arg_3 {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)}
3: eval_start_1->eval_start_2, Arg_3: Arg_3 {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)}
4: eval_start_2->eval_start_3, Arg_3: Arg_3 {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)}
5: eval_start_3->eval_start_4, Arg_3: Arg_3 {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: Arg_1 {O(n)}
6: eval_start_4->eval_start_bb1_in, Arg_2: Arg_1 {O(n)}
6: eval_start_4->eval_start_bb1_in, Arg_3: 0 {O(1)}
7: eval_start_4->eval_start_bb5_in, Arg_0: Arg_0 {O(n)}
7: eval_start_4->eval_start_bb5_in, Arg_1: Arg_1 {O(n)}
7: eval_start_4->eval_start_bb5_in, Arg_2: Arg_2 {O(n)}
7: eval_start_4->eval_start_bb5_in, Arg_3: Arg_3 {O(n)}
15: eval_start_8->eval_start_9, Arg_0: Arg_0 {O(n)}
15: eval_start_8->eval_start_9, Arg_1: Arg_1 {O(n)}
15: eval_start_8->eval_start_9, Arg_2: Arg_2 {O(n)}
15: eval_start_8->eval_start_9, Arg_3: Arg_3 {O(n)}
16: eval_start_9->eval_start_stop, Arg_0: Arg_0 {O(n)}
16: eval_start_9->eval_start_stop, Arg_1: Arg_1 {O(n)}
16: eval_start_9->eval_start_stop, Arg_2: Arg_2 {O(n)}
16: eval_start_9->eval_start_stop, Arg_3: Arg_3 {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)}
1: eval_start_bb0_in->eval_start_0, Arg_3: Arg_3 {O(n)}
8: eval_start_bb1_in->eval_start_bb2_in, Arg_0: Arg_0 {O(n)}
8: eval_start_bb1_in->eval_start_bb2_in, Arg_1: Arg_1 {O(n)}
8: eval_start_bb1_in->eval_start_bb2_in, Arg_2: Arg_1 {O(n)}
8: eval_start_bb1_in->eval_start_bb2_in, Arg_3: Arg_1 {O(n)}
9: eval_start_bb1_in->eval_start_bb4_in, Arg_0: 2*Arg_0 {O(n)}
9: eval_start_bb1_in->eval_start_bb4_in, Arg_1: 2*Arg_1 {O(n)}
9: eval_start_bb1_in->eval_start_bb4_in, Arg_2: 2*Arg_1 {O(n)}
9: eval_start_bb1_in->eval_start_bb4_in, Arg_3: Arg_1 {O(n)}
10: eval_start_bb2_in->eval_start_bb3_in, Arg_0: Arg_0 {O(n)}
10: eval_start_bb2_in->eval_start_bb3_in, Arg_1: Arg_1 {O(n)}
10: eval_start_bb2_in->eval_start_bb3_in, Arg_2: Arg_1 {O(n)}
10: eval_start_bb2_in->eval_start_bb3_in, Arg_3: Arg_1 {O(n)}
11: eval_start_bb2_in->eval_start_bb1_in, Arg_0: Arg_0 {O(n)}
11: eval_start_bb2_in->eval_start_bb1_in, Arg_1: Arg_1 {O(n)}
11: eval_start_bb2_in->eval_start_bb1_in, Arg_2: Arg_1 {O(n)}
11: eval_start_bb2_in->eval_start_bb1_in, Arg_3: 0 {O(1)}
12: eval_start_bb3_in->eval_start_bb1_in, Arg_0: Arg_0 {O(n)}
12: eval_start_bb3_in->eval_start_bb1_in, Arg_1: Arg_1 {O(n)}
12: eval_start_bb3_in->eval_start_bb1_in, Arg_2: Arg_1 {O(n)}
12: eval_start_bb3_in->eval_start_bb1_in, Arg_3: Arg_1 {O(n)}
13: eval_start_bb4_in->eval_start_stop, Arg_0: 2*Arg_0 {O(n)}
13: eval_start_bb4_in->eval_start_stop, Arg_1: 2*Arg_1 {O(n)}
13: eval_start_bb4_in->eval_start_stop, Arg_2: 2*Arg_1 {O(n)}
13: eval_start_bb4_in->eval_start_stop, Arg_3: Arg_1 {O(n)}
14: eval_start_bb5_in->eval_start_8, Arg_0: Arg_0 {O(n)}
14: eval_start_bb5_in->eval_start_8, Arg_1: Arg_1 {O(n)}
14: eval_start_bb5_in->eval_start_8, Arg_2: Arg_2 {O(n)}
14: eval_start_bb5_in->eval_start_8, Arg_3: Arg_3 {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)}
0: eval_start_start->eval_start_bb0_in, Arg_3: Arg_3 {O(n)}