Initial Problem

Start: eval_foo_start
Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3, Arg_4, Arg_5
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,Arg_3,Arg_4,Arg_5) -> eval_foo_bb1_in(Arg_3,Arg_4,Arg_2,Arg_3,Arg_4,Arg_5)
2:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5):|:0<Arg_1
3:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_foo_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5):|:Arg_1<=0
4:eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_foo_bb1_in(Arg_1-1,Arg_0,Arg_2,Arg_3,Arg_4,Arg_5)
5:eval_foo_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_foo_stop(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5)
0:eval_foo_start(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_foo_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5)

Preprocessing

Eliminate variables {Arg_2,Arg_5} that do not contribute to the problem

Found invariant Arg_1<=0 for location eval_foo_stop

Found invariant Arg_1<=0 for location eval_foo_bb3_in

Found invariant 1<=Arg_1 for location eval_foo_bb2_in

Problem after Preprocessing

Start: eval_foo_start
Program_Vars: Arg_0, Arg_1, Arg_3, Arg_4
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:
12:eval_foo_bb0_in(Arg_0,Arg_1,Arg_3,Arg_4) -> eval_foo_bb1_in(Arg_3,Arg_4,Arg_3,Arg_4)
13:eval_foo_bb1_in(Arg_0,Arg_1,Arg_3,Arg_4) -> eval_foo_bb2_in(Arg_0,Arg_1,Arg_3,Arg_4):|:0<Arg_1
14:eval_foo_bb1_in(Arg_0,Arg_1,Arg_3,Arg_4) -> eval_foo_bb3_in(Arg_0,Arg_1,Arg_3,Arg_4):|:Arg_1<=0
15:eval_foo_bb2_in(Arg_0,Arg_1,Arg_3,Arg_4) -> eval_foo_bb1_in(Arg_1-1,Arg_0,Arg_3,Arg_4):|:1<=Arg_1
16:eval_foo_bb3_in(Arg_0,Arg_1,Arg_3,Arg_4) -> eval_foo_stop(Arg_0,Arg_1,Arg_3,Arg_4):|:Arg_1<=0
17:eval_foo_start(Arg_0,Arg_1,Arg_3,Arg_4) -> eval_foo_bb0_in(Arg_0,Arg_1,Arg_3,Arg_4)

MPRF for transition 13:eval_foo_bb1_in(Arg_0,Arg_1,Arg_3,Arg_4) -> eval_foo_bb2_in(Arg_0,Arg_1,Arg_3,Arg_4):|:0<Arg_1 of depth 2:

new bound:

16*Arg_4+8*Arg_3+9 {O(n)}

MPRF:

eval_foo_bb2_in [Arg_0+Arg_1-2 ; Arg_0 ]
eval_foo_bb1_in [Arg_0+Arg_1-1 ; Arg_1 ]

MPRF for transition 15:eval_foo_bb2_in(Arg_0,Arg_1,Arg_3,Arg_4) -> eval_foo_bb1_in(Arg_1-1,Arg_0,Arg_3,Arg_4):|:1<=Arg_1 of depth 2:

new bound:

16*Arg_4+8*Arg_3+17 {O(n)}

MPRF:

eval_foo_bb2_in [Arg_0+Arg_1-1 ; 0 ]
eval_foo_bb1_in [Arg_0+Arg_1-1 ; Arg_1-1 ]

All Bounds

Timebounds

Overall timebound:16*Arg_3+32*Arg_4+30 {O(n)}
12: eval_foo_bb0_in->eval_foo_bb1_in: 1 {O(1)}
13: eval_foo_bb1_in->eval_foo_bb2_in: 16*Arg_4+8*Arg_3+9 {O(n)}
14: eval_foo_bb1_in->eval_foo_bb3_in: 1 {O(1)}
15: eval_foo_bb2_in->eval_foo_bb1_in: 16*Arg_4+8*Arg_3+17 {O(n)}
16: eval_foo_bb3_in->eval_foo_stop: 1 {O(1)}
17: eval_foo_start->eval_foo_bb0_in: 1 {O(1)}

Costbounds

Overall costbound: 16*Arg_3+32*Arg_4+30 {O(n)}
12: eval_foo_bb0_in->eval_foo_bb1_in: 1 {O(1)}
13: eval_foo_bb1_in->eval_foo_bb2_in: 16*Arg_4+8*Arg_3+9 {O(n)}
14: eval_foo_bb1_in->eval_foo_bb3_in: 1 {O(1)}
15: eval_foo_bb2_in->eval_foo_bb1_in: 16*Arg_4+8*Arg_3+17 {O(n)}
16: eval_foo_bb3_in->eval_foo_stop: 1 {O(1)}
17: eval_foo_start->eval_foo_bb0_in: 1 {O(1)}

Sizebounds

12: eval_foo_bb0_in->eval_foo_bb1_in, Arg_0: Arg_3 {O(n)}
12: eval_foo_bb0_in->eval_foo_bb1_in, Arg_1: Arg_4 {O(n)}
12: eval_foo_bb0_in->eval_foo_bb1_in, Arg_3: Arg_3 {O(n)}
12: eval_foo_bb0_in->eval_foo_bb1_in, Arg_4: Arg_4 {O(n)}
13: eval_foo_bb1_in->eval_foo_bb2_in, Arg_0: Arg_3+Arg_4 {O(n)}
13: eval_foo_bb1_in->eval_foo_bb2_in, Arg_1: Arg_3+Arg_4 {O(n)}
13: eval_foo_bb1_in->eval_foo_bb2_in, Arg_3: Arg_3 {O(n)}
13: eval_foo_bb1_in->eval_foo_bb2_in, Arg_4: Arg_4 {O(n)}
14: eval_foo_bb1_in->eval_foo_bb3_in, Arg_0: 2*Arg_3+Arg_4 {O(n)}
14: eval_foo_bb1_in->eval_foo_bb3_in, Arg_1: 2*Arg_4+Arg_3 {O(n)}
14: eval_foo_bb1_in->eval_foo_bb3_in, Arg_3: 2*Arg_3 {O(n)}
14: eval_foo_bb1_in->eval_foo_bb3_in, Arg_4: 2*Arg_4 {O(n)}
15: eval_foo_bb2_in->eval_foo_bb1_in, Arg_0: Arg_3+Arg_4 {O(n)}
15: eval_foo_bb2_in->eval_foo_bb1_in, Arg_1: Arg_3+Arg_4 {O(n)}
15: eval_foo_bb2_in->eval_foo_bb1_in, Arg_3: Arg_3 {O(n)}
15: eval_foo_bb2_in->eval_foo_bb1_in, Arg_4: Arg_4 {O(n)}
16: eval_foo_bb3_in->eval_foo_stop, Arg_0: 2*Arg_3+Arg_4 {O(n)}
16: eval_foo_bb3_in->eval_foo_stop, Arg_1: 2*Arg_4+Arg_3 {O(n)}
16: eval_foo_bb3_in->eval_foo_stop, Arg_3: 2*Arg_3 {O(n)}
16: eval_foo_bb3_in->eval_foo_stop, Arg_4: 2*Arg_4 {O(n)}
17: eval_foo_start->eval_foo_bb0_in, Arg_0: Arg_0 {O(n)}
17: eval_foo_start->eval_foo_bb0_in, Arg_1: Arg_1 {O(n)}
17: eval_foo_start->eval_foo_bb0_in, Arg_3: Arg_3 {O(n)}
17: eval_foo_start->eval_foo_bb0_in, Arg_4: Arg_4 {O(n)}