Initial Problem

Start: eval_foo_start
Program_Vars: Arg_0, Arg_1, Arg_2
Temp_Vars:
Locations: eval_foo_bb0_in, eval_foo_bb1_in, eval_foo_bb2_in, eval_foo_bb3_in, eval_foo_start, eval_foo_stop
Transitions:
1:eval_foo_bb0_in(Arg_0,Arg_1,Arg_2) -> eval_foo_bb1_in(Arg_2,Arg_1,Arg_2):|:0<Arg_1
2:eval_foo_bb0_in(Arg_0,Arg_1,Arg_2) -> eval_foo_bb3_in(Arg_0,Arg_1,Arg_2):|:Arg_1<=0
3:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2) -> eval_foo_bb2_in(Arg_0,Arg_1,Arg_2):|:Arg_0<Arg_1
4:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2) -> eval_foo_bb2_in(Arg_0,Arg_1,Arg_2):|:Arg_1<Arg_0
5:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2) -> eval_foo_bb3_in(Arg_0,Arg_1,Arg_2):|:Arg_0<=Arg_1 && Arg_1<=Arg_0
6:eval_foo_bb2_in(Arg_0,Arg_1,Arg_2) -> eval_foo_bb1_in(0,Arg_1,Arg_2):|:Arg_1<Arg_0
7:eval_foo_bb2_in(Arg_0,Arg_1,Arg_2) -> eval_foo_bb1_in(Arg_0+1,Arg_1,Arg_2):|:Arg_0<=Arg_1
8:eval_foo_bb3_in(Arg_0,Arg_1,Arg_2) -> eval_foo_stop(Arg_0,Arg_1,Arg_2)
0:eval_foo_start(Arg_0,Arg_1,Arg_2) -> eval_foo_bb0_in(Arg_0,Arg_1,Arg_2)

Preprocessing

Found invariant 1<=Arg_1 for location eval_foo_bb2_in

Found invariant 1<=Arg_1 for location eval_foo_bb1_in

Problem after Preprocessing

Start: eval_foo_start
Program_Vars: Arg_0, Arg_1, Arg_2
Temp_Vars:
Locations: eval_foo_bb0_in, eval_foo_bb1_in, eval_foo_bb2_in, eval_foo_bb3_in, eval_foo_start, eval_foo_stop
Transitions:
1:eval_foo_bb0_in(Arg_0,Arg_1,Arg_2) -> eval_foo_bb1_in(Arg_2,Arg_1,Arg_2):|:0<Arg_1
2:eval_foo_bb0_in(Arg_0,Arg_1,Arg_2) -> eval_foo_bb3_in(Arg_0,Arg_1,Arg_2):|:Arg_1<=0
3:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2) -> eval_foo_bb2_in(Arg_0,Arg_1,Arg_2):|:1<=Arg_1 && Arg_0<Arg_1
4:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2) -> eval_foo_bb2_in(Arg_0,Arg_1,Arg_2):|:1<=Arg_1 && Arg_1<Arg_0
5:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2) -> eval_foo_bb3_in(Arg_0,Arg_1,Arg_2):|:1<=Arg_1 && Arg_0<=Arg_1 && Arg_1<=Arg_0
6:eval_foo_bb2_in(Arg_0,Arg_1,Arg_2) -> eval_foo_bb1_in(0,Arg_1,Arg_2):|:1<=Arg_1 && Arg_1<Arg_0
7:eval_foo_bb2_in(Arg_0,Arg_1,Arg_2) -> eval_foo_bb1_in(Arg_0+1,Arg_1,Arg_2):|:1<=Arg_1 && Arg_0<=Arg_1
8:eval_foo_bb3_in(Arg_0,Arg_1,Arg_2) -> eval_foo_stop(Arg_0,Arg_1,Arg_2)
0:eval_foo_start(Arg_0,Arg_1,Arg_2) -> eval_foo_bb0_in(Arg_0,Arg_1,Arg_2)

Analysing control-flow refined program

Cut unsatisfiable transition 95: n_eval_foo_bb1_in___2->eval_foo_bb3_in

Cut unsatisfiable transition 76: n_eval_foo_bb1_in___4->n_eval_foo_bb2_in___3

Cut unreachable locations [n_eval_foo_bb2_in___3] from the program graph

Found invariant 1<=Arg_1 && Arg_0<=Arg_1 for location n_eval_foo_bb1_in___4

Found invariant 2<=Arg_2 && 3<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 2<=Arg_0+Arg_2 && 2+Arg_0<=Arg_2 && 1<=Arg_1 && 1<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && Arg_0<=0 && 0<=Arg_0 for location n_eval_foo_bb1_in___2

Found invariant Arg_2<=Arg_0 && 2<=Arg_2 && 3<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 4<=Arg_0+Arg_2 && Arg_0<=Arg_2 && 1+Arg_1<=Arg_0 && 1<=Arg_1 && 3<=Arg_0+Arg_1 && 2<=Arg_0 for location n_eval_foo_bb2_in___5

Found invariant 2<=Arg_2 && 3<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 2<=Arg_0+Arg_2 && 2+Arg_0<=Arg_2 && 1<=Arg_1 && 1<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && Arg_0<=0 && 0<=Arg_0 for location n_eval_foo_bb2_in___1

Found invariant Arg_2<=Arg_0 && Arg_0<=Arg_2 && 1<=Arg_1 for location eval_foo_bb1_in

Found invariant 1<=Arg_1 && 1+Arg_0<=Arg_1 for location n_eval_foo_bb2_in___6

MPRF for transition 77:n_eval_foo_bb1_in___4(Arg_0,Arg_1,Arg_2) -> n_eval_foo_bb2_in___6(Arg_0,Arg_1,Arg_2):|:1<=Arg_1 && Arg_0<=Arg_1 && 1<=Arg_1 && 1<=Arg_1 && Arg_0<=1+Arg_1 && 1<=Arg_1 && Arg_0<Arg_1 of depth 1:

new bound:

2*Arg_1+Arg_2+2 {O(n)}

MPRF:

n_eval_foo_bb2_in___6 [Arg_1-Arg_0 ]
n_eval_foo_bb1_in___4 [Arg_1+1-Arg_0 ]

MPRF for transition 83:n_eval_foo_bb2_in___6(Arg_0,Arg_1,Arg_2) -> n_eval_foo_bb1_in___4(Arg_0+1,Arg_1,Arg_2):|:1<=Arg_1 && 1+Arg_0<=Arg_1 && Arg_0<Arg_1 && 1<=Arg_1 && 1<=Arg_1 && Arg_0<=Arg_1 of depth 1:

new bound:

2*Arg_1+Arg_2+3 {O(n)}

MPRF:

n_eval_foo_bb2_in___6 [Arg_1+1-Arg_0 ]
n_eval_foo_bb1_in___4 [Arg_1+1-Arg_0 ]

CFR: Improvement to new bound with the following program:

new bound:

2*Arg_2+4*Arg_1+5 {O(n)}

cfr-program:

Start: eval_foo_start
Program_Vars: Arg_0, Arg_1, Arg_2
Temp_Vars:
Locations: eval_foo_bb0_in, eval_foo_bb1_in, eval_foo_bb3_in, eval_foo_start, eval_foo_stop, n_eval_foo_bb1_in___2, n_eval_foo_bb1_in___4, n_eval_foo_bb2_in___1, n_eval_foo_bb2_in___5, n_eval_foo_bb2_in___6
Transitions:
1:eval_foo_bb0_in(Arg_0,Arg_1,Arg_2) -> eval_foo_bb1_in(Arg_2,Arg_1,Arg_2):|:0<Arg_1
2:eval_foo_bb0_in(Arg_0,Arg_1,Arg_2) -> eval_foo_bb3_in(Arg_0,Arg_1,Arg_2):|:Arg_1<=0
5:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2) -> eval_foo_bb3_in(Arg_0,Arg_1,Arg_2):|:Arg_2<=Arg_0 && Arg_0<=Arg_2 && 1<=Arg_1 && 1<=Arg_1 && Arg_0<=Arg_1 && Arg_1<=Arg_0
78:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2) -> n_eval_foo_bb2_in___5(Arg_0,Arg_1,Arg_2):|:Arg_2<=Arg_0 && Arg_0<=Arg_2 && 1<=Arg_1 && Arg_1<Arg_0 && 1<=Arg_1
79:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2) -> n_eval_foo_bb2_in___6(Arg_0,Arg_1,Arg_2):|:Arg_2<=Arg_0 && Arg_0<=Arg_2 && 1<=Arg_1 && 1<=Arg_1 && Arg_0<Arg_1
8:eval_foo_bb3_in(Arg_0,Arg_1,Arg_2) -> eval_foo_stop(Arg_0,Arg_1,Arg_2)
0:eval_foo_start(Arg_0,Arg_1,Arg_2) -> eval_foo_bb0_in(Arg_0,Arg_1,Arg_2)
75:n_eval_foo_bb1_in___2(Arg_0,Arg_1,Arg_2) -> n_eval_foo_bb2_in___1(Arg_0,Arg_1,Arg_2):|:2<=Arg_2 && 3<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 2<=Arg_0+Arg_2 && 2+Arg_0<=Arg_2 && 1<=Arg_1 && 1<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && Arg_0<=0 && 0<=Arg_0 && Arg_0<Arg_1 && 1<=Arg_1 && 1<=Arg_1 && 1+Arg_0<=Arg_1 && Arg_0<=0 && 0<=Arg_0 && 1<=Arg_1 && 1<=Arg_1 && Arg_0<=1+Arg_1 && 1<=Arg_1 && Arg_0<Arg_1
96:n_eval_foo_bb1_in___4(Arg_0,Arg_1,Arg_2) -> eval_foo_bb3_in(Arg_0,Arg_1,Arg_2):|:1<=Arg_1 && Arg_0<=Arg_1 && 1<=Arg_1 && Arg_0<=Arg_1 && Arg_1<=Arg_0
77:n_eval_foo_bb1_in___4(Arg_0,Arg_1,Arg_2) -> n_eval_foo_bb2_in___6(Arg_0,Arg_1,Arg_2):|:1<=Arg_1 && Arg_0<=Arg_1 && 1<=Arg_1 && 1<=Arg_1 && Arg_0<=1+Arg_1 && 1<=Arg_1 && Arg_0<Arg_1
80:n_eval_foo_bb2_in___1(Arg_0,Arg_1,Arg_2) -> n_eval_foo_bb1_in___4(Arg_0+1,Arg_1,Arg_2):|:2<=Arg_2 && 3<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 2<=Arg_0+Arg_2 && 2+Arg_0<=Arg_2 && 1<=Arg_1 && 1<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && Arg_0<=0 && 0<=Arg_0 && 1<=Arg_1 && Arg_0<=0 && 0<=Arg_0 && 1<=Arg_1 && Arg_0<=Arg_1
82:n_eval_foo_bb2_in___5(Arg_0,Arg_1,Arg_2) -> n_eval_foo_bb1_in___2(0,Arg_1,Arg_2):|:Arg_2<=Arg_0 && 2<=Arg_2 && 3<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 4<=Arg_0+Arg_2 && Arg_0<=Arg_2 && 1+Arg_1<=Arg_0 && 1<=Arg_1 && 3<=Arg_0+Arg_1 && 2<=Arg_0 && Arg_1<Arg_0 && 1<=Arg_1 && Arg_1<Arg_0 && 1<=Arg_1
83:n_eval_foo_bb2_in___6(Arg_0,Arg_1,Arg_2) -> n_eval_foo_bb1_in___4(Arg_0+1,Arg_1,Arg_2):|:1<=Arg_1 && 1+Arg_0<=Arg_1 && Arg_0<Arg_1 && 1<=Arg_1 && 1<=Arg_1 && Arg_0<=Arg_1

All Bounds

Timebounds

Overall timebound:2*Arg_2+4*Arg_1+16 {O(n)}
1: eval_foo_bb0_in->eval_foo_bb1_in: 1 {O(1)}
2: eval_foo_bb0_in->eval_foo_bb3_in: 1 {O(1)}
5: eval_foo_bb1_in->eval_foo_bb3_in: 1 {O(1)}
78: eval_foo_bb1_in->n_eval_foo_bb2_in___5: 1 {O(1)}
79: eval_foo_bb1_in->n_eval_foo_bb2_in___6: 1 {O(1)}
8: eval_foo_bb3_in->eval_foo_stop: 1 {O(1)}
0: eval_foo_start->eval_foo_bb0_in: 1 {O(1)}
75: n_eval_foo_bb1_in___2->n_eval_foo_bb2_in___1: 1 {O(1)}
77: n_eval_foo_bb1_in___4->n_eval_foo_bb2_in___6: 2*Arg_1+Arg_2+2 {O(n)}
96: n_eval_foo_bb1_in___4->eval_foo_bb3_in: 1 {O(1)}
80: n_eval_foo_bb2_in___1->n_eval_foo_bb1_in___4: 1 {O(1)}
82: n_eval_foo_bb2_in___5->n_eval_foo_bb1_in___2: 1 {O(1)}
83: n_eval_foo_bb2_in___6->n_eval_foo_bb1_in___4: 2*Arg_1+Arg_2+3 {O(n)}

Costbounds

Overall costbound: 2*Arg_2+4*Arg_1+16 {O(n)}
1: eval_foo_bb0_in->eval_foo_bb1_in: 1 {O(1)}
2: eval_foo_bb0_in->eval_foo_bb3_in: 1 {O(1)}
5: eval_foo_bb1_in->eval_foo_bb3_in: 1 {O(1)}
78: eval_foo_bb1_in->n_eval_foo_bb2_in___5: 1 {O(1)}
79: eval_foo_bb1_in->n_eval_foo_bb2_in___6: 1 {O(1)}
8: eval_foo_bb3_in->eval_foo_stop: 1 {O(1)}
0: eval_foo_start->eval_foo_bb0_in: 1 {O(1)}
75: n_eval_foo_bb1_in___2->n_eval_foo_bb2_in___1: 1 {O(1)}
77: n_eval_foo_bb1_in___4->n_eval_foo_bb2_in___6: 2*Arg_1+Arg_2+2 {O(n)}
96: n_eval_foo_bb1_in___4->eval_foo_bb3_in: 1 {O(1)}
80: n_eval_foo_bb2_in___1->n_eval_foo_bb1_in___4: 1 {O(1)}
82: n_eval_foo_bb2_in___5->n_eval_foo_bb1_in___2: 1 {O(1)}
83: n_eval_foo_bb2_in___6->n_eval_foo_bb1_in___4: 2*Arg_1+Arg_2+3 {O(n)}

Sizebounds

1: eval_foo_bb0_in->eval_foo_bb1_in, Arg_0: Arg_2 {O(n)}
1: eval_foo_bb0_in->eval_foo_bb1_in, Arg_1: Arg_1 {O(n)}
1: eval_foo_bb0_in->eval_foo_bb1_in, Arg_2: Arg_2 {O(n)}
2: eval_foo_bb0_in->eval_foo_bb3_in, Arg_0: Arg_0 {O(n)}
2: eval_foo_bb0_in->eval_foo_bb3_in, Arg_1: Arg_1 {O(n)}
2: eval_foo_bb0_in->eval_foo_bb3_in, Arg_2: Arg_2 {O(n)}
5: eval_foo_bb1_in->eval_foo_bb3_in, Arg_0: Arg_2 {O(n)}
5: eval_foo_bb1_in->eval_foo_bb3_in, Arg_1: Arg_1 {O(n)}
5: eval_foo_bb1_in->eval_foo_bb3_in, Arg_2: Arg_2 {O(n)}
78: eval_foo_bb1_in->n_eval_foo_bb2_in___5, Arg_0: Arg_2 {O(n)}
78: eval_foo_bb1_in->n_eval_foo_bb2_in___5, Arg_1: Arg_1 {O(n)}
78: eval_foo_bb1_in->n_eval_foo_bb2_in___5, Arg_2: Arg_2 {O(n)}
79: eval_foo_bb1_in->n_eval_foo_bb2_in___6, Arg_0: Arg_2 {O(n)}
79: eval_foo_bb1_in->n_eval_foo_bb2_in___6, Arg_1: Arg_1 {O(n)}
79: eval_foo_bb1_in->n_eval_foo_bb2_in___6, Arg_2: Arg_2 {O(n)}
8: eval_foo_bb3_in->eval_foo_stop, Arg_0: 2*Arg_1+3*Arg_2+Arg_0+5 {O(n)}
8: eval_foo_bb3_in->eval_foo_stop, Arg_1: 5*Arg_1 {O(n)}
8: eval_foo_bb3_in->eval_foo_stop, Arg_2: 5*Arg_2 {O(n)}
0: eval_foo_start->eval_foo_bb0_in, Arg_0: Arg_0 {O(n)}
0: eval_foo_start->eval_foo_bb0_in, Arg_1: Arg_1 {O(n)}
0: eval_foo_start->eval_foo_bb0_in, Arg_2: Arg_2 {O(n)}
75: n_eval_foo_bb1_in___2->n_eval_foo_bb2_in___1, Arg_0: 0 {O(1)}
75: n_eval_foo_bb1_in___2->n_eval_foo_bb2_in___1, Arg_1: Arg_1 {O(n)}
75: n_eval_foo_bb1_in___2->n_eval_foo_bb2_in___1, Arg_2: Arg_2 {O(n)}
77: n_eval_foo_bb1_in___4->n_eval_foo_bb2_in___6, Arg_0: 2*Arg_1+2*Arg_2+4 {O(n)}
77: n_eval_foo_bb1_in___4->n_eval_foo_bb2_in___6, Arg_1: 2*Arg_1 {O(n)}
77: n_eval_foo_bb1_in___4->n_eval_foo_bb2_in___6, Arg_2: 2*Arg_2 {O(n)}
96: n_eval_foo_bb1_in___4->eval_foo_bb3_in, Arg_0: 2*Arg_1+2*Arg_2+5 {O(n)}
96: n_eval_foo_bb1_in___4->eval_foo_bb3_in, Arg_1: 3*Arg_1 {O(n)}
96: n_eval_foo_bb1_in___4->eval_foo_bb3_in, Arg_2: 3*Arg_2 {O(n)}
80: n_eval_foo_bb2_in___1->n_eval_foo_bb1_in___4, Arg_0: 1 {O(1)}
80: n_eval_foo_bb2_in___1->n_eval_foo_bb1_in___4, Arg_1: Arg_1 {O(n)}
80: n_eval_foo_bb2_in___1->n_eval_foo_bb1_in___4, Arg_2: Arg_2 {O(n)}
82: n_eval_foo_bb2_in___5->n_eval_foo_bb1_in___2, Arg_0: 0 {O(1)}
82: n_eval_foo_bb2_in___5->n_eval_foo_bb1_in___2, Arg_1: Arg_1 {O(n)}
82: n_eval_foo_bb2_in___5->n_eval_foo_bb1_in___2, Arg_2: Arg_2 {O(n)}
83: n_eval_foo_bb2_in___6->n_eval_foo_bb1_in___4, Arg_0: 2*Arg_1+2*Arg_2+4 {O(n)}
83: n_eval_foo_bb2_in___6->n_eval_foo_bb1_in___4, Arg_1: 2*Arg_1 {O(n)}
83: n_eval_foo_bb2_in___6->n_eval_foo_bb1_in___4, Arg_2: 2*Arg_2 {O(n)}