Initial Problem

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

Preprocessing

Found invariant Arg_0<=0 && 0<=Arg_0 for location eval_foo_stop

Found invariant Arg_0<=0 && 0<=Arg_0 for location eval_foo_bb3_in

Problem after Preprocessing

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

MPRF for transition 2:eval_foo_bb1_in(Arg_0,Arg_1) -> eval_foo_bb2_in(Arg_0,Arg_1):|:Arg_0<0 of depth 1:

new bound:

Arg_1 {O(n)}

MPRF:

eval_foo_bb2_in [-Arg_0-1 ]
eval_foo_bb1_in [-Arg_0 ]

MPRF for transition 6:eval_foo_bb2_in(Arg_0,Arg_1) -> eval_foo_bb1_in(Arg_0+1,Arg_1):|:Arg_0<=0 of depth 1:

new bound:

Arg_1+1 {O(n)}

MPRF:

eval_foo_bb2_in [1-Arg_0 ]
eval_foo_bb1_in [1-Arg_0 ]

MPRF for transition 3:eval_foo_bb1_in(Arg_0,Arg_1) -> eval_foo_bb2_in(Arg_0,Arg_1):|:0<Arg_0 of depth 1:

new bound:

Arg_1*Arg_1+5*Arg_1+5 {O(n^2)}

MPRF:

eval_foo_bb2_in [Arg_0+1 ]
eval_foo_bb1_in [Arg_0+2 ]

MPRF for transition 5:eval_foo_bb2_in(Arg_0,Arg_1) -> eval_foo_bb1_in(Arg_0-1,Arg_1):|:0<Arg_0 of depth 1:

new bound:

Arg_1*Arg_1+4*Arg_1+3 {O(n^2)}

MPRF:

eval_foo_bb2_in [Arg_0+1 ]
eval_foo_bb1_in [Arg_0+1 ]

Analysing control-flow refined program

Cut unsatisfiable transition 74: n_eval_foo_bb1_in___2->n_eval_foo_bb2_in___4

Cut unsatisfiable transition 75: n_eval_foo_bb1_in___5->n_eval_foo_bb2_in___3

Cut unreachable locations [n_eval_foo_bb2_in___3] from the program graph

Found invariant 2+Arg_1<=0 && 1+Arg_1<=Arg_0 && 3+Arg_0+Arg_1<=0 && 1+Arg_0<=0 for location n_eval_foo_bb2_in___4

Found invariant 1+Arg_1<=0 && Arg_1<=Arg_0 && 2+Arg_0+Arg_1<=0 && Arg_0<=Arg_1 && 1+Arg_0<=0 for location n_eval_foo_bb2_in___7

Found invariant Arg_0<=0 && 0<=Arg_0 for location eval_foo_stop

Found invariant Arg_0<=0 && 0<=Arg_0 for location eval_foo_bb3_in

Found invariant 1+Arg_1<=0 && 1+Arg_1<=Arg_0 && 1+Arg_0+Arg_1<=0 && Arg_0<=0 for location n_eval_foo_bb1_in___5

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

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

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

Found invariant Arg_1<=Arg_0 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 1<=Arg_0 for location n_eval_foo_bb2_in___6

MPRF for transition 73:n_eval_foo_bb1_in___2(Arg_0,Arg_1) -> n_eval_foo_bb2_in___1(Arg_0,Arg_1):|:1<=Arg_1 && 1<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 0<=Arg_0 && 0<Arg_0 of depth 1:

new bound:

Arg_1+1 {O(n)}

MPRF:

n_eval_foo_bb2_in___1 [Arg_0 ]
n_eval_foo_bb1_in___2 [Arg_0+1 ]

MPRF for transition 79:n_eval_foo_bb2_in___1(Arg_0,Arg_1) -> n_eval_foo_bb1_in___2(Arg_0-1,Arg_1):|:2<=Arg_1 && 3<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 1<=Arg_0 && 0<Arg_0 && 0<Arg_0 of depth 1:

new bound:

Arg_1 {O(n)}

MPRF:

n_eval_foo_bb2_in___1 [Arg_0 ]
n_eval_foo_bb1_in___2 [Arg_0 ]

MPRF for transition 76:n_eval_foo_bb1_in___5(Arg_0,Arg_1) -> n_eval_foo_bb2_in___4(Arg_0,Arg_1):|:1+Arg_1<=0 && 1+Arg_1<=Arg_0 && 1+Arg_0+Arg_1<=0 && Arg_0<=0 && Arg_0<=1 && Arg_0<0 of depth 1:

new bound:

Arg_1+1 {O(n)}

MPRF:

n_eval_foo_bb2_in___4 [-Arg_0 ]
n_eval_foo_bb1_in___5 [1-Arg_0 ]

MPRF for transition 81:n_eval_foo_bb2_in___4(Arg_0,Arg_1) -> n_eval_foo_bb1_in___5(Arg_0+1,Arg_1):|:2+Arg_1<=0 && 1+Arg_1<=Arg_0 && 3+Arg_0+Arg_1<=0 && 1+Arg_0<=0 && Arg_0<0 && Arg_0<=0 of depth 1:

new bound:

Arg_1+1 {O(n)}

MPRF:

n_eval_foo_bb2_in___4 [1-Arg_0 ]
n_eval_foo_bb1_in___5 [1-Arg_0 ]

CFR: Improvement to new bound with the following program:

new bound:

4*Arg_1+3 {O(n)}

cfr-program:

Start: eval_foo_start
Program_Vars: Arg_0, Arg_1
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___5, n_eval_foo_bb2_in___1, n_eval_foo_bb2_in___4, n_eval_foo_bb2_in___6, n_eval_foo_bb2_in___7
Transitions:
1:eval_foo_bb0_in(Arg_0,Arg_1) -> eval_foo_bb1_in(Arg_1,Arg_1)
4:eval_foo_bb1_in(Arg_0,Arg_1) -> eval_foo_bb3_in(Arg_0,Arg_1):|:Arg_1<=Arg_0 && Arg_0<=Arg_1 && Arg_0<=0 && 0<=Arg_0
77:eval_foo_bb1_in(Arg_0,Arg_1) -> n_eval_foo_bb2_in___6(Arg_0,Arg_1):|:Arg_1<=Arg_0 && Arg_0<=Arg_1 && Arg_0<=Arg_1 && Arg_1<=Arg_0 && 0<Arg_0
78:eval_foo_bb1_in(Arg_0,Arg_1) -> n_eval_foo_bb2_in___7(Arg_0,Arg_1):|:Arg_1<=Arg_0 && Arg_0<=Arg_1 && Arg_0<=Arg_1 && Arg_1<=Arg_0 && Arg_0<0
7:eval_foo_bb3_in(Arg_0,Arg_1) -> eval_foo_stop(Arg_0,Arg_1):|:Arg_0<=0 && 0<=Arg_0 && Arg_0<=0 && 0<=Arg_0
0:eval_foo_start(Arg_0,Arg_1) -> eval_foo_bb0_in(Arg_0,Arg_1)
95:n_eval_foo_bb1_in___2(Arg_0,Arg_1) -> eval_foo_bb3_in(Arg_0,Arg_1):|:1<=Arg_1 && 1<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 0<=Arg_0 && Arg_0<=0 && 0<=Arg_0
73:n_eval_foo_bb1_in___2(Arg_0,Arg_1) -> n_eval_foo_bb2_in___1(Arg_0,Arg_1):|:1<=Arg_1 && 1<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 0<=Arg_0 && 0<Arg_0
96:n_eval_foo_bb1_in___5(Arg_0,Arg_1) -> eval_foo_bb3_in(Arg_0,Arg_1):|:1+Arg_1<=0 && 1+Arg_1<=Arg_0 && 1+Arg_0+Arg_1<=0 && Arg_0<=0 && Arg_0<=0 && 0<=Arg_0
76:n_eval_foo_bb1_in___5(Arg_0,Arg_1) -> n_eval_foo_bb2_in___4(Arg_0,Arg_1):|:1+Arg_1<=0 && 1+Arg_1<=Arg_0 && 1+Arg_0+Arg_1<=0 && Arg_0<=0 && Arg_0<=1 && Arg_0<0
79:n_eval_foo_bb2_in___1(Arg_0,Arg_1) -> n_eval_foo_bb1_in___2(Arg_0-1,Arg_1):|:2<=Arg_1 && 3<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 1<=Arg_0 && 0<Arg_0 && 0<Arg_0
81:n_eval_foo_bb2_in___4(Arg_0,Arg_1) -> n_eval_foo_bb1_in___5(Arg_0+1,Arg_1):|:2+Arg_1<=0 && 1+Arg_1<=Arg_0 && 3+Arg_0+Arg_1<=0 && 1+Arg_0<=0 && Arg_0<0 && Arg_0<=0
82:n_eval_foo_bb2_in___6(Arg_0,Arg_1) -> n_eval_foo_bb1_in___2(Arg_0-1,Arg_1):|:Arg_1<=Arg_0 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 1<=Arg_0 && 0<Arg_0 && Arg_0<=Arg_1 && Arg_1<=Arg_0 && 0<Arg_0
83:n_eval_foo_bb2_in___7(Arg_0,Arg_1) -> n_eval_foo_bb1_in___5(Arg_0+1,Arg_1):|:1+Arg_1<=0 && Arg_1<=Arg_0 && 2+Arg_0+Arg_1<=0 && Arg_0<=Arg_1 && 1+Arg_0<=0 && Arg_0<0 && Arg_0<=Arg_1 && Arg_1<=Arg_0 && Arg_0<=0

All Bounds

Timebounds

Overall timebound:4*Arg_1+13 {O(n)}
1: eval_foo_bb0_in->eval_foo_bb1_in: 1 {O(1)}
4: eval_foo_bb1_in->eval_foo_bb3_in: 1 {O(1)}
77: eval_foo_bb1_in->n_eval_foo_bb2_in___6: 1 {O(1)}
78: eval_foo_bb1_in->n_eval_foo_bb2_in___7: 1 {O(1)}
7: eval_foo_bb3_in->eval_foo_stop: 1 {O(1)}
0: eval_foo_start->eval_foo_bb0_in: 1 {O(1)}
73: n_eval_foo_bb1_in___2->n_eval_foo_bb2_in___1: Arg_1+1 {O(n)}
95: n_eval_foo_bb1_in___2->eval_foo_bb3_in: 1 {O(1)}
76: n_eval_foo_bb1_in___5->n_eval_foo_bb2_in___4: Arg_1+1 {O(n)}
96: n_eval_foo_bb1_in___5->eval_foo_bb3_in: 1 {O(1)}
79: n_eval_foo_bb2_in___1->n_eval_foo_bb1_in___2: Arg_1 {O(n)}
81: n_eval_foo_bb2_in___4->n_eval_foo_bb1_in___5: Arg_1+1 {O(n)}
82: n_eval_foo_bb2_in___6->n_eval_foo_bb1_in___2: 1 {O(1)}
83: n_eval_foo_bb2_in___7->n_eval_foo_bb1_in___5: 1 {O(1)}

Costbounds

Overall costbound: 4*Arg_1+13 {O(n)}
1: eval_foo_bb0_in->eval_foo_bb1_in: 1 {O(1)}
4: eval_foo_bb1_in->eval_foo_bb3_in: 1 {O(1)}
77: eval_foo_bb1_in->n_eval_foo_bb2_in___6: 1 {O(1)}
78: eval_foo_bb1_in->n_eval_foo_bb2_in___7: 1 {O(1)}
7: eval_foo_bb3_in->eval_foo_stop: 1 {O(1)}
0: eval_foo_start->eval_foo_bb0_in: 1 {O(1)}
73: n_eval_foo_bb1_in___2->n_eval_foo_bb2_in___1: Arg_1+1 {O(n)}
95: n_eval_foo_bb1_in___2->eval_foo_bb3_in: 1 {O(1)}
76: n_eval_foo_bb1_in___5->n_eval_foo_bb2_in___4: Arg_1+1 {O(n)}
96: n_eval_foo_bb1_in___5->eval_foo_bb3_in: 1 {O(1)}
79: n_eval_foo_bb2_in___1->n_eval_foo_bb1_in___2: Arg_1 {O(n)}
81: n_eval_foo_bb2_in___4->n_eval_foo_bb1_in___5: Arg_1+1 {O(n)}
82: n_eval_foo_bb2_in___6->n_eval_foo_bb1_in___2: 1 {O(1)}
83: n_eval_foo_bb2_in___7->n_eval_foo_bb1_in___5: 1 {O(1)}

Sizebounds

1: eval_foo_bb0_in->eval_foo_bb1_in, Arg_0: Arg_1 {O(n)}
1: eval_foo_bb0_in->eval_foo_bb1_in, Arg_1: Arg_1 {O(n)}
4: eval_foo_bb1_in->eval_foo_bb3_in, Arg_0: 0 {O(1)}
4: eval_foo_bb1_in->eval_foo_bb3_in, Arg_1: Arg_1 {O(n)}
77: eval_foo_bb1_in->n_eval_foo_bb2_in___6, Arg_0: Arg_1 {O(n)}
77: eval_foo_bb1_in->n_eval_foo_bb2_in___6, Arg_1: Arg_1 {O(n)}
78: eval_foo_bb1_in->n_eval_foo_bb2_in___7, Arg_0: Arg_1 {O(n)}
78: eval_foo_bb1_in->n_eval_foo_bb2_in___7, Arg_1: Arg_1 {O(n)}
7: eval_foo_bb3_in->eval_foo_stop, Arg_0: 0 {O(1)}
7: eval_foo_bb3_in->eval_foo_stop, Arg_1: 5*Arg_1 {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)}
73: n_eval_foo_bb1_in___2->n_eval_foo_bb2_in___1, Arg_0: Arg_1 {O(n)}
73: n_eval_foo_bb1_in___2->n_eval_foo_bb2_in___1, Arg_1: Arg_1 {O(n)}
95: n_eval_foo_bb1_in___2->eval_foo_bb3_in, Arg_0: 0 {O(1)}
95: n_eval_foo_bb1_in___2->eval_foo_bb3_in, Arg_1: 2*Arg_1 {O(n)}
76: n_eval_foo_bb1_in___5->n_eval_foo_bb2_in___4, Arg_0: Arg_1 {O(n)}
76: n_eval_foo_bb1_in___5->n_eval_foo_bb2_in___4, Arg_1: Arg_1 {O(n)}
96: n_eval_foo_bb1_in___5->eval_foo_bb3_in, Arg_0: 0 {O(1)}
96: n_eval_foo_bb1_in___5->eval_foo_bb3_in, Arg_1: 2*Arg_1 {O(n)}
79: n_eval_foo_bb2_in___1->n_eval_foo_bb1_in___2, Arg_0: Arg_1 {O(n)}
79: n_eval_foo_bb2_in___1->n_eval_foo_bb1_in___2, Arg_1: Arg_1 {O(n)}
81: n_eval_foo_bb2_in___4->n_eval_foo_bb1_in___5, Arg_0: Arg_1 {O(n)}
81: n_eval_foo_bb2_in___4->n_eval_foo_bb1_in___5, Arg_1: Arg_1 {O(n)}
82: n_eval_foo_bb2_in___6->n_eval_foo_bb1_in___2, Arg_0: Arg_1 {O(n)}
82: n_eval_foo_bb2_in___6->n_eval_foo_bb1_in___2, Arg_1: Arg_1 {O(n)}
83: n_eval_foo_bb2_in___7->n_eval_foo_bb1_in___5, Arg_0: Arg_1 {O(n)}
83: n_eval_foo_bb2_in___7->n_eval_foo_bb1_in___5, Arg_1: Arg_1 {O(n)}