Initial Problem

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

Preprocessing

Eliminate variables {Arg_1,Arg_2} that do not contribute to the problem

Found invariant Arg_0<=Arg_3 && Arg_0<=0 for location eval_foo_stop

Found invariant Arg_0<=Arg_3 && Arg_0<=0 for location eval_foo_bb3_in

Found invariant 1<=Arg_3 && 2<=Arg_0+Arg_3 && Arg_0<=Arg_3 && 1<=Arg_0 for location eval_foo_bb2_in

Found invariant Arg_0<=Arg_3 for location eval_foo_bb1_in

Problem after Preprocessing

Start: eval_foo_start
Program_Vars: Arg_0, Arg_3
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_3) -> eval_foo_bb1_in(Arg_3,Arg_3)
13:eval_foo_bb1_in(Arg_0,Arg_3) -> eval_foo_bb2_in(Arg_0,Arg_3):|:Arg_0<=Arg_3 && 0<Arg_0
14:eval_foo_bb1_in(Arg_0,Arg_3) -> eval_foo_bb3_in(Arg_0,Arg_3):|:Arg_0<=Arg_3 && Arg_0<=0
15:eval_foo_bb2_in(Arg_0,Arg_3) -> eval_foo_bb1_in(Arg_0-1,Arg_3):|:1<=Arg_3 && 2<=Arg_0+Arg_3 && Arg_0<=Arg_3 && 1<=Arg_0
16:eval_foo_bb3_in(Arg_0,Arg_3) -> eval_foo_stop(Arg_0,Arg_3):|:Arg_0<=Arg_3 && Arg_0<=0
17:eval_foo_start(Arg_0,Arg_3) -> eval_foo_bb0_in(Arg_0,Arg_3)

MPRF for transition 13:eval_foo_bb1_in(Arg_0,Arg_3) -> eval_foo_bb2_in(Arg_0,Arg_3):|:Arg_0<=Arg_3 && 0<Arg_0 of depth 1:

new bound:

Arg_3 {O(n)}

MPRF:

eval_foo_bb2_in [Arg_0-1 ]
eval_foo_bb1_in [Arg_0 ]

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

new bound:

Arg_3 {O(n)}

MPRF:

eval_foo_bb2_in [Arg_0 ]
eval_foo_bb1_in [Arg_0 ]

All Bounds

Timebounds

Overall timebound:2*Arg_3+4 {O(n)}
12: eval_foo_bb0_in->eval_foo_bb1_in: 1 {O(1)}
13: eval_foo_bb1_in->eval_foo_bb2_in: Arg_3 {O(n)}
14: eval_foo_bb1_in->eval_foo_bb3_in: 1 {O(1)}
15: eval_foo_bb2_in->eval_foo_bb1_in: Arg_3 {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: 2*Arg_3+4 {O(n)}
12: eval_foo_bb0_in->eval_foo_bb1_in: 1 {O(1)}
13: eval_foo_bb1_in->eval_foo_bb2_in: Arg_3 {O(n)}
14: eval_foo_bb1_in->eval_foo_bb3_in: 1 {O(1)}
15: eval_foo_bb2_in->eval_foo_bb1_in: Arg_3 {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_3: Arg_3 {O(n)}
13: eval_foo_bb1_in->eval_foo_bb2_in, Arg_0: Arg_3 {O(n)}
13: eval_foo_bb1_in->eval_foo_bb2_in, Arg_3: Arg_3 {O(n)}
14: eval_foo_bb1_in->eval_foo_bb3_in, Arg_0: 2*Arg_3 {O(n)}
14: eval_foo_bb1_in->eval_foo_bb3_in, Arg_3: 2*Arg_3 {O(n)}
15: eval_foo_bb2_in->eval_foo_bb1_in, Arg_0: Arg_3 {O(n)}
15: eval_foo_bb2_in->eval_foo_bb1_in, Arg_3: Arg_3 {O(n)}
16: eval_foo_bb3_in->eval_foo_stop, Arg_0: 2*Arg_3 {O(n)}
16: eval_foo_bb3_in->eval_foo_stop, Arg_3: 2*Arg_3 {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_3: Arg_3 {O(n)}