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_5, eval_start_6, eval_start_7, 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) -> 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_5(Arg_0,Arg_1,Arg_2,Arg_3)
7:eval_start_5(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_start_6(Arg_0,Arg_1,Arg_2,Arg_3)
8:eval_start_6(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_start_7(Arg_0,Arg_1,Arg_2,Arg_3)
9:eval_start_7(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_start_bb1_in(Arg_2,Arg_3,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)
10: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_0
11:eval_start_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_start_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_0<=0
12:eval_start_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_start_bb1_in(Arg_1,Arg_0-1,Arg_2,Arg_3)
13:eval_start_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_start_stop(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_0<=0 for location eval_start_stop

Found invariant 1<=Arg_0 for location eval_start_bb2_in

Found invariant Arg_0<=0 for location eval_start_bb3_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_5, eval_start_6, eval_start_7, 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) -> 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_5(Arg_0,Arg_1,Arg_2,Arg_3)
7:eval_start_5(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_start_6(Arg_0,Arg_1,Arg_2,Arg_3)
8:eval_start_6(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_start_7(Arg_0,Arg_1,Arg_2,Arg_3)
9:eval_start_7(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_start_bb1_in(Arg_2,Arg_3,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)
10: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_0
11:eval_start_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_start_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_0<=0
12:eval_start_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_start_bb1_in(Arg_1,Arg_0-1,Arg_2,Arg_3):|:1<=Arg_0
13:eval_start_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_start_stop(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)

Analysing control-flow refined program

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

Found invariant 1<=Arg_2 && 1<=Arg_1+Arg_2 && 0<=Arg_1 for location n_eval_start_bb1_in___2

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

Found invariant 1<=Arg_2 && 1<=Arg_1+Arg_2 && 2<=Arg_0+Arg_2 && 0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 for location n_eval_start_bb2_in___1

Found invariant Arg_3<=Arg_1 && Arg_1<=Arg_3 && Arg_2<=Arg_0 && 1<=Arg_2 && 2<=Arg_0+Arg_2 && Arg_0<=Arg_2 && 1<=Arg_0 for location n_eval_start_bb2_in___3

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

MPRF for transition 77:n_eval_start_bb1_in___2(Arg_0,Arg_1,Arg_2,Arg_3) -> n_eval_start_bb2_in___1(Arg_0,Arg_1,Arg_2,Arg_3):|:1<=Arg_2 && 1<=Arg_1+Arg_2 && 0<=Arg_1 && 0<=Arg_1 && 0<Arg_0 of depth 1:

new bound:

Arg_2+Arg_3 {O(n)}

MPRF:

n_eval_start_bb2_in___1 [Arg_0+Arg_1-1 ]
n_eval_start_bb1_in___2 [Arg_0+Arg_1 ]

MPRF for transition 79:n_eval_start_bb2_in___1(Arg_0,Arg_1,Arg_2,Arg_3) -> n_eval_start_bb1_in___2(Arg_1,Arg_0-1,Arg_2,Arg_3):|:1<=Arg_2 && 1<=Arg_1+Arg_2 && 2<=Arg_0+Arg_2 && 0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 && 0<=Arg_1 && 0<Arg_0 && 1<=Arg_0 of depth 1:

new bound:

Arg_2+Arg_3 {O(n)}

MPRF:

n_eval_start_bb2_in___1 [Arg_0+Arg_1 ]
n_eval_start_bb1_in___2 [Arg_0+Arg_1 ]

CFR: Improvement to new bound with the following program:

new bound:

2*Arg_2+2*Arg_3 {O(n)}

cfr-program:

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_5, eval_start_6, eval_start_7, eval_start_bb0_in, eval_start_bb1_in, eval_start_bb3_in, eval_start_start, eval_start_stop, n_eval_start_bb1_in___2, n_eval_start_bb2_in___1, n_eval_start_bb2_in___3
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_5(Arg_0,Arg_1,Arg_2,Arg_3)
7:eval_start_5(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_start_6(Arg_0,Arg_1,Arg_2,Arg_3)
8:eval_start_6(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_start_7(Arg_0,Arg_1,Arg_2,Arg_3)
9:eval_start_7(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_start_bb1_in(Arg_2,Arg_3,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)
11:eval_start_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_start_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_3<=Arg_1 && Arg_1<=Arg_3 && Arg_2<=Arg_0 && Arg_0<=Arg_2 && Arg_0<=0
78:eval_start_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3) -> n_eval_start_bb2_in___3(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_3<=Arg_1 && Arg_1<=Arg_3 && Arg_2<=Arg_0 && Arg_0<=Arg_2 && Arg_1<=Arg_3 && Arg_3<=Arg_1 && Arg_0<=Arg_2 && Arg_2<=Arg_0 && 0<Arg_0
13:eval_start_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_start_stop(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_0<=Arg_2 && Arg_0<=0 && 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)
85:n_eval_start_bb1_in___2(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_start_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3):|:1<=Arg_2 && 1<=Arg_1+Arg_2 && 0<=Arg_1 && Arg_0<=0
77:n_eval_start_bb1_in___2(Arg_0,Arg_1,Arg_2,Arg_3) -> n_eval_start_bb2_in___1(Arg_0,Arg_1,Arg_2,Arg_3):|:1<=Arg_2 && 1<=Arg_1+Arg_2 && 0<=Arg_1 && 0<=Arg_1 && 0<Arg_0
79:n_eval_start_bb2_in___1(Arg_0,Arg_1,Arg_2,Arg_3) -> n_eval_start_bb1_in___2(Arg_1,Arg_0-1,Arg_2,Arg_3):|:1<=Arg_2 && 1<=Arg_1+Arg_2 && 2<=Arg_0+Arg_2 && 0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 && 0<=Arg_1 && 0<Arg_0 && 1<=Arg_0
80:n_eval_start_bb2_in___3(Arg_0,Arg_1,Arg_2,Arg_3) -> n_eval_start_bb1_in___2(Arg_1,Arg_0-1,Arg_2,Arg_3):|:Arg_3<=Arg_1 && Arg_1<=Arg_3 && Arg_2<=Arg_0 && 1<=Arg_2 && 2<=Arg_0+Arg_2 && Arg_0<=Arg_2 && 1<=Arg_0 && 0<Arg_0 && Arg_0<=Arg_2 && Arg_2<=Arg_0 && Arg_1<=Arg_3 && Arg_3<=Arg_1 && 1<=Arg_0

All Bounds

Timebounds

Overall timebound:2*Arg_2+2*Arg_3+15 {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_6: 1 {O(1)}
8: eval_start_6->eval_start_7: 1 {O(1)}
9: eval_start_7->eval_start_bb1_in: 1 {O(1)}
1: eval_start_bb0_in->eval_start_0: 1 {O(1)}
11: eval_start_bb1_in->eval_start_bb3_in: 1 {O(1)}
78: eval_start_bb1_in->n_eval_start_bb2_in___3: 1 {O(1)}
13: eval_start_bb3_in->eval_start_stop: 1 {O(1)}
0: eval_start_start->eval_start_bb0_in: 1 {O(1)}
77: n_eval_start_bb1_in___2->n_eval_start_bb2_in___1: Arg_2+Arg_3 {O(n)}
85: n_eval_start_bb1_in___2->eval_start_bb3_in: 1 {O(1)}
79: n_eval_start_bb2_in___1->n_eval_start_bb1_in___2: Arg_2+Arg_3 {O(n)}
80: n_eval_start_bb2_in___3->n_eval_start_bb1_in___2: 1 {O(1)}

Costbounds

Overall costbound: 2*Arg_2+2*Arg_3+15 {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_6: 1 {O(1)}
8: eval_start_6->eval_start_7: 1 {O(1)}
9: eval_start_7->eval_start_bb1_in: 1 {O(1)}
1: eval_start_bb0_in->eval_start_0: 1 {O(1)}
11: eval_start_bb1_in->eval_start_bb3_in: 1 {O(1)}
78: eval_start_bb1_in->n_eval_start_bb2_in___3: 1 {O(1)}
13: eval_start_bb3_in->eval_start_stop: 1 {O(1)}
0: eval_start_start->eval_start_bb0_in: 1 {O(1)}
77: n_eval_start_bb1_in___2->n_eval_start_bb2_in___1: Arg_2+Arg_3 {O(n)}
85: n_eval_start_bb1_in___2->eval_start_bb3_in: 1 {O(1)}
79: n_eval_start_bb2_in___1->n_eval_start_bb1_in___2: Arg_2+Arg_3 {O(n)}
80: n_eval_start_bb2_in___3->n_eval_start_bb1_in___2: 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_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)}
7: eval_start_5->eval_start_6, Arg_0: Arg_0 {O(n)}
7: eval_start_5->eval_start_6, Arg_1: Arg_1 {O(n)}
7: eval_start_5->eval_start_6, Arg_2: Arg_2 {O(n)}
7: eval_start_5->eval_start_6, Arg_3: Arg_3 {O(n)}
8: eval_start_6->eval_start_7, Arg_0: Arg_0 {O(n)}
8: eval_start_6->eval_start_7, Arg_1: Arg_1 {O(n)}
8: eval_start_6->eval_start_7, Arg_2: Arg_2 {O(n)}
8: eval_start_6->eval_start_7, Arg_3: Arg_3 {O(n)}
9: eval_start_7->eval_start_bb1_in, Arg_0: Arg_2 {O(n)}
9: eval_start_7->eval_start_bb1_in, Arg_1: Arg_3 {O(n)}
9: eval_start_7->eval_start_bb1_in, Arg_2: Arg_2 {O(n)}
9: eval_start_7->eval_start_bb1_in, 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)}
11: eval_start_bb1_in->eval_start_bb3_in, Arg_0: Arg_2 {O(n)}
11: eval_start_bb1_in->eval_start_bb3_in, Arg_1: Arg_3 {O(n)}
11: eval_start_bb1_in->eval_start_bb3_in, Arg_2: Arg_2 {O(n)}
11: eval_start_bb1_in->eval_start_bb3_in, Arg_3: Arg_3 {O(n)}
78: eval_start_bb1_in->n_eval_start_bb2_in___3, Arg_0: Arg_2 {O(n)}
78: eval_start_bb1_in->n_eval_start_bb2_in___3, Arg_1: Arg_3 {O(n)}
78: eval_start_bb1_in->n_eval_start_bb2_in___3, Arg_2: Arg_2 {O(n)}
78: eval_start_bb1_in->n_eval_start_bb2_in___3, Arg_3: Arg_3 {O(n)}
13: eval_start_bb3_in->eval_start_stop, Arg_0: 2*Arg_2+Arg_3 {O(n)}
13: eval_start_bb3_in->eval_start_stop, Arg_1: 2*Arg_3+Arg_2 {O(n)}
13: eval_start_bb3_in->eval_start_stop, Arg_2: 3*Arg_2 {O(n)}
13: eval_start_bb3_in->eval_start_stop, Arg_3: 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)}
77: n_eval_start_bb1_in___2->n_eval_start_bb2_in___1, Arg_0: Arg_2+Arg_3 {O(n)}
77: n_eval_start_bb1_in___2->n_eval_start_bb2_in___1, Arg_1: Arg_2+Arg_3 {O(n)}
77: n_eval_start_bb1_in___2->n_eval_start_bb2_in___1, Arg_2: Arg_2 {O(n)}
77: n_eval_start_bb1_in___2->n_eval_start_bb2_in___1, Arg_3: Arg_3 {O(n)}
85: n_eval_start_bb1_in___2->eval_start_bb3_in, Arg_0: 2*Arg_3+Arg_2 {O(n)}
85: n_eval_start_bb1_in___2->eval_start_bb3_in, Arg_1: 2*Arg_2+Arg_3 {O(n)}
85: n_eval_start_bb1_in___2->eval_start_bb3_in, Arg_2: 2*Arg_2 {O(n)}
85: n_eval_start_bb1_in___2->eval_start_bb3_in, Arg_3: 2*Arg_3 {O(n)}
79: n_eval_start_bb2_in___1->n_eval_start_bb1_in___2, Arg_0: Arg_2+Arg_3 {O(n)}
79: n_eval_start_bb2_in___1->n_eval_start_bb1_in___2, Arg_1: Arg_2+Arg_3 {O(n)}
79: n_eval_start_bb2_in___1->n_eval_start_bb1_in___2, Arg_2: Arg_2 {O(n)}
79: n_eval_start_bb2_in___1->n_eval_start_bb1_in___2, Arg_3: Arg_3 {O(n)}
80: n_eval_start_bb2_in___3->n_eval_start_bb1_in___2, Arg_0: Arg_3 {O(n)}
80: n_eval_start_bb2_in___3->n_eval_start_bb1_in___2, Arg_1: Arg_2 {O(n)}
80: n_eval_start_bb2_in___3->n_eval_start_bb1_in___2, Arg_2: Arg_2 {O(n)}
80: n_eval_start_bb2_in___3->n_eval_start_bb1_in___2, Arg_3: Arg_3 {O(n)}