Initial Problem

Start: eval_start_start
Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3, Arg_4
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,Arg_3,Arg_4) -> eval_start_1(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4)
3:eval_start_1(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_start_2(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4)
4:eval_start_2(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_start_3(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4)
5:eval_start_3(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_start_4(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4)
6:eval_start_4(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_start_5(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4)
7:eval_start_5(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_start_bb1_in(Arg_3,Arg_4,Arg_2,Arg_3,Arg_4)
1:eval_start_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_start_0(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4)
8:eval_start_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_start_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:Arg_0<Arg_2
9:eval_start_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_start_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:Arg_2<=Arg_0
10:eval_start_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_start_bb1_in(Arg_0+1,Arg_1,Arg_2,Arg_3,Arg_4):|:Arg_0<Arg_1 && Arg_0<Arg_1
11:eval_start_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_start_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:Arg_0<Arg_1 && Arg_1<=Arg_0
12:eval_start_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_start_bb1_in(Arg_0+1,Arg_1+1,Arg_2,Arg_3,Arg_4):|:Arg_1<=Arg_0 && Arg_0<Arg_1
13:eval_start_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_start_bb1_in(Arg_0,Arg_1+1,Arg_2,Arg_3,Arg_4):|:Arg_1<=Arg_0 && Arg_1<=Arg_0
14:eval_start_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_start_stop(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4)
0:eval_start_start(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_start_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4)

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_4<=Arg_1 && Arg_3<=Arg_0 for location eval_start_bb1_in

Found invariant Arg_4<=Arg_1 && Arg_3<=Arg_0 && Arg_2<=Arg_0 for location eval_start_stop

Found invariant Arg_4<=Arg_1 && 1+Arg_3<=Arg_2 && Arg_3<=Arg_0 && 1+Arg_0<=Arg_2 for location eval_start_bb2_in

Found invariant Arg_4<=Arg_1 && Arg_3<=Arg_0 && Arg_2<=Arg_0 for location eval_start_bb3_in

Problem after Preprocessing

Start: eval_start_start
Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3, Arg_4
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,Arg_3,Arg_4) -> eval_start_1(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4)
3:eval_start_1(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_start_2(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4)
4:eval_start_2(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_start_3(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4)
5:eval_start_3(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_start_4(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4)
6:eval_start_4(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_start_5(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4)
7:eval_start_5(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_start_bb1_in(Arg_3,Arg_4,Arg_2,Arg_3,Arg_4)
1:eval_start_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_start_0(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4)
8:eval_start_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_start_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:Arg_4<=Arg_1 && Arg_3<=Arg_0 && Arg_0<Arg_2
9:eval_start_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_start_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:Arg_4<=Arg_1 && Arg_3<=Arg_0 && Arg_2<=Arg_0
10:eval_start_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_start_bb1_in(Arg_0+1,Arg_1,Arg_2,Arg_3,Arg_4):|:Arg_4<=Arg_1 && 1+Arg_3<=Arg_2 && Arg_3<=Arg_0 && 1+Arg_0<=Arg_2 && Arg_0<Arg_1 && Arg_0<Arg_1
13:eval_start_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_start_bb1_in(Arg_0,Arg_1+1,Arg_2,Arg_3,Arg_4):|:Arg_4<=Arg_1 && 1+Arg_3<=Arg_2 && Arg_3<=Arg_0 && 1+Arg_0<=Arg_2 && Arg_1<=Arg_0 && Arg_1<=Arg_0
14:eval_start_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_start_stop(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:Arg_4<=Arg_1 && Arg_3<=Arg_0 && Arg_2<=Arg_0
0:eval_start_start(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_start_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4)

MPRF for transition 10:eval_start_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_start_bb1_in(Arg_0+1,Arg_1,Arg_2,Arg_3,Arg_4):|:Arg_4<=Arg_1 && 1+Arg_3<=Arg_2 && Arg_3<=Arg_0 && 1+Arg_0<=Arg_2 && Arg_0<Arg_1 && Arg_0<Arg_1 of depth 1:

new bound:

Arg_2+Arg_3 {O(n)}

MPRF:

eval_start_bb2_in [Arg_2-Arg_0 ]
eval_start_bb1_in [Arg_2-Arg_0 ]

MPRF for transition 13:eval_start_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_start_bb1_in(Arg_0,Arg_1+1,Arg_2,Arg_3,Arg_4):|:Arg_4<=Arg_1 && 1+Arg_3<=Arg_2 && Arg_3<=Arg_0 && 1+Arg_0<=Arg_2 && Arg_1<=Arg_0 && Arg_1<=Arg_0 of depth 1:

new bound:

Arg_2+Arg_4 {O(n)}

MPRF:

eval_start_bb2_in [Arg_2-Arg_1 ]
eval_start_bb1_in [Arg_2-Arg_1 ]

knowledge_propagation leads to new time bound 2*Arg_2+Arg_3+Arg_4+1 {O(n)} for transition 8:eval_start_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_start_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:Arg_4<=Arg_1 && Arg_3<=Arg_0 && Arg_0<Arg_2

All Bounds

Timebounds

Overall timebound:2*Arg_3+2*Arg_4+4*Arg_2+11 {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: 2*Arg_2+Arg_3+Arg_4+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+Arg_3 {O(n)}
13: eval_start_bb2_in->eval_start_bb1_in: Arg_2+Arg_4 {O(n)}
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_3+2*Arg_4+4*Arg_2+11 {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: 2*Arg_2+Arg_3+Arg_4+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+Arg_3 {O(n)}
13: eval_start_bb2_in->eval_start_bb1_in: Arg_2+Arg_4 {O(n)}
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)}
2: eval_start_0->eval_start_1, Arg_3: Arg_3 {O(n)}
2: eval_start_0->eval_start_1, Arg_4: Arg_4 {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)}
3: eval_start_1->eval_start_2, Arg_4: Arg_4 {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)}
4: eval_start_2->eval_start_3, Arg_4: Arg_4 {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)}
5: eval_start_3->eval_start_4, Arg_4: Arg_4 {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)}
6: eval_start_4->eval_start_5, Arg_3: Arg_3 {O(n)}
6: eval_start_4->eval_start_5, Arg_4: Arg_4 {O(n)}
7: eval_start_5->eval_start_bb1_in, Arg_0: Arg_3 {O(n)}
7: eval_start_5->eval_start_bb1_in, Arg_1: Arg_4 {O(n)}
7: eval_start_5->eval_start_bb1_in, Arg_2: Arg_2 {O(n)}
7: eval_start_5->eval_start_bb1_in, Arg_3: Arg_3 {O(n)}
7: eval_start_5->eval_start_bb1_in, Arg_4: Arg_4 {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)}
1: eval_start_bb0_in->eval_start_0, Arg_4: Arg_4 {O(n)}
8: eval_start_bb1_in->eval_start_bb2_in, Arg_0: 2*Arg_3+Arg_2 {O(n)}
8: eval_start_bb1_in->eval_start_bb2_in, Arg_1: 2*Arg_4+Arg_2 {O(n)}
8: eval_start_bb1_in->eval_start_bb2_in, Arg_2: Arg_2 {O(n)}
8: eval_start_bb1_in->eval_start_bb2_in, Arg_3: Arg_3 {O(n)}
8: eval_start_bb1_in->eval_start_bb2_in, Arg_4: Arg_4 {O(n)}
9: eval_start_bb1_in->eval_start_bb3_in, Arg_0: 3*Arg_3+Arg_2 {O(n)}
9: eval_start_bb1_in->eval_start_bb3_in, Arg_1: 3*Arg_4+Arg_2 {O(n)}
9: eval_start_bb1_in->eval_start_bb3_in, Arg_2: 2*Arg_2 {O(n)}
9: eval_start_bb1_in->eval_start_bb3_in, Arg_3: 2*Arg_3 {O(n)}
9: eval_start_bb1_in->eval_start_bb3_in, Arg_4: 2*Arg_4 {O(n)}
10: eval_start_bb2_in->eval_start_bb1_in, Arg_0: 2*Arg_3+Arg_2 {O(n)}
10: eval_start_bb2_in->eval_start_bb1_in, Arg_1: 2*Arg_4+Arg_2 {O(n)}
10: eval_start_bb2_in->eval_start_bb1_in, Arg_2: Arg_2 {O(n)}
10: eval_start_bb2_in->eval_start_bb1_in, Arg_3: Arg_3 {O(n)}
10: eval_start_bb2_in->eval_start_bb1_in, Arg_4: Arg_4 {O(n)}
13: eval_start_bb2_in->eval_start_bb1_in, Arg_0: 2*Arg_3+Arg_2 {O(n)}
13: eval_start_bb2_in->eval_start_bb1_in, Arg_1: 2*Arg_4+Arg_2 {O(n)}
13: eval_start_bb2_in->eval_start_bb1_in, Arg_2: Arg_2 {O(n)}
13: eval_start_bb2_in->eval_start_bb1_in, Arg_3: Arg_3 {O(n)}
13: eval_start_bb2_in->eval_start_bb1_in, Arg_4: Arg_4 {O(n)}
14: eval_start_bb3_in->eval_start_stop, Arg_0: 3*Arg_3+Arg_2 {O(n)}
14: eval_start_bb3_in->eval_start_stop, Arg_1: 3*Arg_4+Arg_2 {O(n)}
14: eval_start_bb3_in->eval_start_stop, Arg_2: 2*Arg_2 {O(n)}
14: eval_start_bb3_in->eval_start_stop, Arg_3: 2*Arg_3 {O(n)}
14: eval_start_bb3_in->eval_start_stop, Arg_4: 2*Arg_4 {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)}
0: eval_start_start->eval_start_bb0_in, Arg_4: Arg_4 {O(n)}