Initial Problem

Start: eval_speedSimpleMultiple_start
Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3
Temp_Vars:
Locations: eval_speedSimpleMultiple_0, eval_speedSimpleMultiple_1, eval_speedSimpleMultiple_2, eval_speedSimpleMultiple_3, eval_speedSimpleMultiple_4, eval_speedSimpleMultiple_5, eval_speedSimpleMultiple_6, eval_speedSimpleMultiple_bb0_in, eval_speedSimpleMultiple_bb1_in, eval_speedSimpleMultiple_bb2_in, eval_speedSimpleMultiple_bb3_in, eval_speedSimpleMultiple_start, eval_speedSimpleMultiple_stop
Transitions:
2:eval_speedSimpleMultiple_0(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_speedSimpleMultiple_1(Arg_0,Arg_1,Arg_2,Arg_3)
3:eval_speedSimpleMultiple_1(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_speedSimpleMultiple_2(Arg_0,Arg_1,Arg_2,Arg_3)
4:eval_speedSimpleMultiple_2(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_speedSimpleMultiple_3(Arg_0,Arg_1,Arg_2,Arg_3)
5:eval_speedSimpleMultiple_3(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_speedSimpleMultiple_4(Arg_0,Arg_1,Arg_2,Arg_3)
6:eval_speedSimpleMultiple_4(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_speedSimpleMultiple_5(Arg_0,Arg_1,Arg_2,Arg_3)
7:eval_speedSimpleMultiple_5(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_speedSimpleMultiple_6(Arg_0,Arg_1,Arg_2,Arg_3)
8:eval_speedSimpleMultiple_6(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_speedSimpleMultiple_bb1_in(Arg_0,Arg_1,0,0)
1:eval_speedSimpleMultiple_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_speedSimpleMultiple_0(Arg_0,Arg_1,Arg_2,Arg_3)
9:eval_speedSimpleMultiple_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_speedSimpleMultiple_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_2<Arg_1
10:eval_speedSimpleMultiple_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_speedSimpleMultiple_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_1<=Arg_2
11:eval_speedSimpleMultiple_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_speedSimpleMultiple_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3+1):|:Arg_3<Arg_0 && Arg_3<Arg_0
12:eval_speedSimpleMultiple_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_speedSimpleMultiple_bb1_in(Arg_0,Arg_1,Arg_2+1,Arg_3+1):|:Arg_3<Arg_0 && Arg_0<=Arg_3
13:eval_speedSimpleMultiple_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_speedSimpleMultiple_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_0<=Arg_3 && Arg_3<Arg_0
14:eval_speedSimpleMultiple_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_speedSimpleMultiple_bb1_in(Arg_0,Arg_1,Arg_2+1,Arg_3):|:Arg_0<=Arg_3 && Arg_0<=Arg_3
15:eval_speedSimpleMultiple_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_speedSimpleMultiple_stop(Arg_0,Arg_1,Arg_2,Arg_3)
0:eval_speedSimpleMultiple_start(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_speedSimpleMultiple_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3)

Preprocessing

Cut unsatisfiable transition 12: eval_speedSimpleMultiple_bb2_in->eval_speedSimpleMultiple_bb1_in

Cut unsatisfiable transition 13: eval_speedSimpleMultiple_bb2_in->eval_speedSimpleMultiple_bb1_in

Found invariant 0<=Arg_3 && 0<=Arg_2+Arg_3 && 0<=Arg_2 && Arg_1<=Arg_2 for location eval_speedSimpleMultiple_bb3_in

Found invariant 0<=Arg_3 && 0<=Arg_2+Arg_3 && 0<=Arg_2 for location eval_speedSimpleMultiple_bb1_in

Found invariant 0<=Arg_3 && 0<=Arg_2+Arg_3 && 0<=Arg_2 && Arg_1<=Arg_2 for location eval_speedSimpleMultiple_stop

Found invariant 0<=Arg_3 && 0<=Arg_2+Arg_3 && 1<=Arg_1+Arg_3 && 1+Arg_2<=Arg_1 && 0<=Arg_2 && 1<=Arg_1+Arg_2 && 1<=Arg_1 for location eval_speedSimpleMultiple_bb2_in

Problem after Preprocessing

Start: eval_speedSimpleMultiple_start
Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3
Temp_Vars:
Locations: eval_speedSimpleMultiple_0, eval_speedSimpleMultiple_1, eval_speedSimpleMultiple_2, eval_speedSimpleMultiple_3, eval_speedSimpleMultiple_4, eval_speedSimpleMultiple_5, eval_speedSimpleMultiple_6, eval_speedSimpleMultiple_bb0_in, eval_speedSimpleMultiple_bb1_in, eval_speedSimpleMultiple_bb2_in, eval_speedSimpleMultiple_bb3_in, eval_speedSimpleMultiple_start, eval_speedSimpleMultiple_stop
Transitions:
2:eval_speedSimpleMultiple_0(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_speedSimpleMultiple_1(Arg_0,Arg_1,Arg_2,Arg_3)
3:eval_speedSimpleMultiple_1(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_speedSimpleMultiple_2(Arg_0,Arg_1,Arg_2,Arg_3)
4:eval_speedSimpleMultiple_2(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_speedSimpleMultiple_3(Arg_0,Arg_1,Arg_2,Arg_3)
5:eval_speedSimpleMultiple_3(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_speedSimpleMultiple_4(Arg_0,Arg_1,Arg_2,Arg_3)
6:eval_speedSimpleMultiple_4(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_speedSimpleMultiple_5(Arg_0,Arg_1,Arg_2,Arg_3)
7:eval_speedSimpleMultiple_5(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_speedSimpleMultiple_6(Arg_0,Arg_1,Arg_2,Arg_3)
8:eval_speedSimpleMultiple_6(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_speedSimpleMultiple_bb1_in(Arg_0,Arg_1,0,0)
1:eval_speedSimpleMultiple_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_speedSimpleMultiple_0(Arg_0,Arg_1,Arg_2,Arg_3)
9:eval_speedSimpleMultiple_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_speedSimpleMultiple_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3):|:0<=Arg_3 && 0<=Arg_2+Arg_3 && 0<=Arg_2 && Arg_2<Arg_1
10:eval_speedSimpleMultiple_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_speedSimpleMultiple_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3):|:0<=Arg_3 && 0<=Arg_2+Arg_3 && 0<=Arg_2 && Arg_1<=Arg_2
11:eval_speedSimpleMultiple_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_speedSimpleMultiple_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3+1):|:0<=Arg_3 && 0<=Arg_2+Arg_3 && 1<=Arg_1+Arg_3 && 1+Arg_2<=Arg_1 && 0<=Arg_2 && 1<=Arg_1+Arg_2 && 1<=Arg_1 && Arg_3<Arg_0 && Arg_3<Arg_0
14:eval_speedSimpleMultiple_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_speedSimpleMultiple_bb1_in(Arg_0,Arg_1,Arg_2+1,Arg_3):|:0<=Arg_3 && 0<=Arg_2+Arg_3 && 1<=Arg_1+Arg_3 && 1+Arg_2<=Arg_1 && 0<=Arg_2 && 1<=Arg_1+Arg_2 && 1<=Arg_1 && Arg_0<=Arg_3 && Arg_0<=Arg_3
15:eval_speedSimpleMultiple_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_speedSimpleMultiple_stop(Arg_0,Arg_1,Arg_2,Arg_3):|:0<=Arg_3 && 0<=Arg_2+Arg_3 && 0<=Arg_2 && Arg_1<=Arg_2
0:eval_speedSimpleMultiple_start(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_speedSimpleMultiple_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3)

MPRF for transition 11:eval_speedSimpleMultiple_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_speedSimpleMultiple_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3+1):|:0<=Arg_3 && 0<=Arg_2+Arg_3 && 1<=Arg_1+Arg_3 && 1+Arg_2<=Arg_1 && 0<=Arg_2 && 1<=Arg_1+Arg_2 && 1<=Arg_1 && Arg_3<Arg_0 && Arg_3<Arg_0 of depth 1:

new bound:

Arg_0 {O(n)}

MPRF:

eval_speedSimpleMultiple_bb2_in [Arg_0-Arg_3 ]
eval_speedSimpleMultiple_bb1_in [Arg_0-Arg_3 ]

MPRF for transition 14:eval_speedSimpleMultiple_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_speedSimpleMultiple_bb1_in(Arg_0,Arg_1,Arg_2+1,Arg_3):|:0<=Arg_3 && 0<=Arg_2+Arg_3 && 1<=Arg_1+Arg_3 && 1+Arg_2<=Arg_1 && 0<=Arg_2 && 1<=Arg_1+Arg_2 && 1<=Arg_1 && Arg_0<=Arg_3 && Arg_0<=Arg_3 of depth 1:

new bound:

Arg_1 {O(n)}

MPRF:

eval_speedSimpleMultiple_bb2_in [Arg_1-Arg_2 ]
eval_speedSimpleMultiple_bb1_in [Arg_1-Arg_2 ]

knowledge_propagation leads to new time bound Arg_0+Arg_1+1 {O(n)} for transition 9:eval_speedSimpleMultiple_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_speedSimpleMultiple_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3):|:0<=Arg_3 && 0<=Arg_2+Arg_3 && 0<=Arg_2 && Arg_2<Arg_1

All Bounds

Timebounds

Overall timebound:2*Arg_0+2*Arg_1+12 {O(n)}
2: eval_speedSimpleMultiple_0->eval_speedSimpleMultiple_1: 1 {O(1)}
3: eval_speedSimpleMultiple_1->eval_speedSimpleMultiple_2: 1 {O(1)}
4: eval_speedSimpleMultiple_2->eval_speedSimpleMultiple_3: 1 {O(1)}
5: eval_speedSimpleMultiple_3->eval_speedSimpleMultiple_4: 1 {O(1)}
6: eval_speedSimpleMultiple_4->eval_speedSimpleMultiple_5: 1 {O(1)}
7: eval_speedSimpleMultiple_5->eval_speedSimpleMultiple_6: 1 {O(1)}
8: eval_speedSimpleMultiple_6->eval_speedSimpleMultiple_bb1_in: 1 {O(1)}
1: eval_speedSimpleMultiple_bb0_in->eval_speedSimpleMultiple_0: 1 {O(1)}
9: eval_speedSimpleMultiple_bb1_in->eval_speedSimpleMultiple_bb2_in: Arg_0+Arg_1+1 {O(n)}
10: eval_speedSimpleMultiple_bb1_in->eval_speedSimpleMultiple_bb3_in: 1 {O(1)}
11: eval_speedSimpleMultiple_bb2_in->eval_speedSimpleMultiple_bb1_in: Arg_0 {O(n)}
14: eval_speedSimpleMultiple_bb2_in->eval_speedSimpleMultiple_bb1_in: Arg_1 {O(n)}
15: eval_speedSimpleMultiple_bb3_in->eval_speedSimpleMultiple_stop: 1 {O(1)}
0: eval_speedSimpleMultiple_start->eval_speedSimpleMultiple_bb0_in: 1 {O(1)}

Costbounds

Overall costbound: 2*Arg_0+2*Arg_1+12 {O(n)}
2: eval_speedSimpleMultiple_0->eval_speedSimpleMultiple_1: 1 {O(1)}
3: eval_speedSimpleMultiple_1->eval_speedSimpleMultiple_2: 1 {O(1)}
4: eval_speedSimpleMultiple_2->eval_speedSimpleMultiple_3: 1 {O(1)}
5: eval_speedSimpleMultiple_3->eval_speedSimpleMultiple_4: 1 {O(1)}
6: eval_speedSimpleMultiple_4->eval_speedSimpleMultiple_5: 1 {O(1)}
7: eval_speedSimpleMultiple_5->eval_speedSimpleMultiple_6: 1 {O(1)}
8: eval_speedSimpleMultiple_6->eval_speedSimpleMultiple_bb1_in: 1 {O(1)}
1: eval_speedSimpleMultiple_bb0_in->eval_speedSimpleMultiple_0: 1 {O(1)}
9: eval_speedSimpleMultiple_bb1_in->eval_speedSimpleMultiple_bb2_in: Arg_0+Arg_1+1 {O(n)}
10: eval_speedSimpleMultiple_bb1_in->eval_speedSimpleMultiple_bb3_in: 1 {O(1)}
11: eval_speedSimpleMultiple_bb2_in->eval_speedSimpleMultiple_bb1_in: Arg_0 {O(n)}
14: eval_speedSimpleMultiple_bb2_in->eval_speedSimpleMultiple_bb1_in: Arg_1 {O(n)}
15: eval_speedSimpleMultiple_bb3_in->eval_speedSimpleMultiple_stop: 1 {O(1)}
0: eval_speedSimpleMultiple_start->eval_speedSimpleMultiple_bb0_in: 1 {O(1)}

Sizebounds

2: eval_speedSimpleMultiple_0->eval_speedSimpleMultiple_1, Arg_0: Arg_0 {O(n)}
2: eval_speedSimpleMultiple_0->eval_speedSimpleMultiple_1, Arg_1: Arg_1 {O(n)}
2: eval_speedSimpleMultiple_0->eval_speedSimpleMultiple_1, Arg_2: Arg_2 {O(n)}
2: eval_speedSimpleMultiple_0->eval_speedSimpleMultiple_1, Arg_3: Arg_3 {O(n)}
3: eval_speedSimpleMultiple_1->eval_speedSimpleMultiple_2, Arg_0: Arg_0 {O(n)}
3: eval_speedSimpleMultiple_1->eval_speedSimpleMultiple_2, Arg_1: Arg_1 {O(n)}
3: eval_speedSimpleMultiple_1->eval_speedSimpleMultiple_2, Arg_2: Arg_2 {O(n)}
3: eval_speedSimpleMultiple_1->eval_speedSimpleMultiple_2, Arg_3: Arg_3 {O(n)}
4: eval_speedSimpleMultiple_2->eval_speedSimpleMultiple_3, Arg_0: Arg_0 {O(n)}
4: eval_speedSimpleMultiple_2->eval_speedSimpleMultiple_3, Arg_1: Arg_1 {O(n)}
4: eval_speedSimpleMultiple_2->eval_speedSimpleMultiple_3, Arg_2: Arg_2 {O(n)}
4: eval_speedSimpleMultiple_2->eval_speedSimpleMultiple_3, Arg_3: Arg_3 {O(n)}
5: eval_speedSimpleMultiple_3->eval_speedSimpleMultiple_4, Arg_0: Arg_0 {O(n)}
5: eval_speedSimpleMultiple_3->eval_speedSimpleMultiple_4, Arg_1: Arg_1 {O(n)}
5: eval_speedSimpleMultiple_3->eval_speedSimpleMultiple_4, Arg_2: Arg_2 {O(n)}
5: eval_speedSimpleMultiple_3->eval_speedSimpleMultiple_4, Arg_3: Arg_3 {O(n)}
6: eval_speedSimpleMultiple_4->eval_speedSimpleMultiple_5, Arg_0: Arg_0 {O(n)}
6: eval_speedSimpleMultiple_4->eval_speedSimpleMultiple_5, Arg_1: Arg_1 {O(n)}
6: eval_speedSimpleMultiple_4->eval_speedSimpleMultiple_5, Arg_2: Arg_2 {O(n)}
6: eval_speedSimpleMultiple_4->eval_speedSimpleMultiple_5, Arg_3: Arg_3 {O(n)}
7: eval_speedSimpleMultiple_5->eval_speedSimpleMultiple_6, Arg_0: Arg_0 {O(n)}
7: eval_speedSimpleMultiple_5->eval_speedSimpleMultiple_6, Arg_1: Arg_1 {O(n)}
7: eval_speedSimpleMultiple_5->eval_speedSimpleMultiple_6, Arg_2: Arg_2 {O(n)}
7: eval_speedSimpleMultiple_5->eval_speedSimpleMultiple_6, Arg_3: Arg_3 {O(n)}
8: eval_speedSimpleMultiple_6->eval_speedSimpleMultiple_bb1_in, Arg_0: Arg_0 {O(n)}
8: eval_speedSimpleMultiple_6->eval_speedSimpleMultiple_bb1_in, Arg_1: Arg_1 {O(n)}
8: eval_speedSimpleMultiple_6->eval_speedSimpleMultiple_bb1_in, Arg_2: 0 {O(1)}
8: eval_speedSimpleMultiple_6->eval_speedSimpleMultiple_bb1_in, Arg_3: 0 {O(1)}
1: eval_speedSimpleMultiple_bb0_in->eval_speedSimpleMultiple_0, Arg_0: Arg_0 {O(n)}
1: eval_speedSimpleMultiple_bb0_in->eval_speedSimpleMultiple_0, Arg_1: Arg_1 {O(n)}
1: eval_speedSimpleMultiple_bb0_in->eval_speedSimpleMultiple_0, Arg_2: Arg_2 {O(n)}
1: eval_speedSimpleMultiple_bb0_in->eval_speedSimpleMultiple_0, Arg_3: Arg_3 {O(n)}
9: eval_speedSimpleMultiple_bb1_in->eval_speedSimpleMultiple_bb2_in, Arg_0: Arg_0 {O(n)}
9: eval_speedSimpleMultiple_bb1_in->eval_speedSimpleMultiple_bb2_in, Arg_1: Arg_1 {O(n)}
9: eval_speedSimpleMultiple_bb1_in->eval_speedSimpleMultiple_bb2_in, Arg_2: Arg_1 {O(n)}
9: eval_speedSimpleMultiple_bb1_in->eval_speedSimpleMultiple_bb2_in, Arg_3: Arg_0 {O(n)}
10: eval_speedSimpleMultiple_bb1_in->eval_speedSimpleMultiple_bb3_in, Arg_0: 2*Arg_0 {O(n)}
10: eval_speedSimpleMultiple_bb1_in->eval_speedSimpleMultiple_bb3_in, Arg_1: 2*Arg_1 {O(n)}
10: eval_speedSimpleMultiple_bb1_in->eval_speedSimpleMultiple_bb3_in, Arg_2: Arg_1 {O(n)}
10: eval_speedSimpleMultiple_bb1_in->eval_speedSimpleMultiple_bb3_in, Arg_3: Arg_0 {O(n)}
11: eval_speedSimpleMultiple_bb2_in->eval_speedSimpleMultiple_bb1_in, Arg_0: Arg_0 {O(n)}
11: eval_speedSimpleMultiple_bb2_in->eval_speedSimpleMultiple_bb1_in, Arg_1: Arg_1 {O(n)}
11: eval_speedSimpleMultiple_bb2_in->eval_speedSimpleMultiple_bb1_in, Arg_2: Arg_1 {O(n)}
11: eval_speedSimpleMultiple_bb2_in->eval_speedSimpleMultiple_bb1_in, Arg_3: Arg_0 {O(n)}
14: eval_speedSimpleMultiple_bb2_in->eval_speedSimpleMultiple_bb1_in, Arg_0: Arg_0 {O(n)}
14: eval_speedSimpleMultiple_bb2_in->eval_speedSimpleMultiple_bb1_in, Arg_1: Arg_1 {O(n)}
14: eval_speedSimpleMultiple_bb2_in->eval_speedSimpleMultiple_bb1_in, Arg_2: Arg_1 {O(n)}
14: eval_speedSimpleMultiple_bb2_in->eval_speedSimpleMultiple_bb1_in, Arg_3: Arg_0 {O(n)}
15: eval_speedSimpleMultiple_bb3_in->eval_speedSimpleMultiple_stop, Arg_0: 2*Arg_0 {O(n)}
15: eval_speedSimpleMultiple_bb3_in->eval_speedSimpleMultiple_stop, Arg_1: 2*Arg_1 {O(n)}
15: eval_speedSimpleMultiple_bb3_in->eval_speedSimpleMultiple_stop, Arg_2: Arg_1 {O(n)}
15: eval_speedSimpleMultiple_bb3_in->eval_speedSimpleMultiple_stop, Arg_3: Arg_0 {O(n)}
0: eval_speedSimpleMultiple_start->eval_speedSimpleMultiple_bb0_in, Arg_0: Arg_0 {O(n)}
0: eval_speedSimpleMultiple_start->eval_speedSimpleMultiple_bb0_in, Arg_1: Arg_1 {O(n)}
0: eval_speedSimpleMultiple_start->eval_speedSimpleMultiple_bb0_in, Arg_2: Arg_2 {O(n)}
0: eval_speedSimpleMultiple_start->eval_speedSimpleMultiple_bb0_in, Arg_3: Arg_3 {O(n)}