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(10000,1,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):|:1+Arg_1<=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<Arg_1+1
4:eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_foo_bb1_in(Arg_0-1,Arg_1+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_2,Arg_3} that do not contribute to the problem

Found invariant Arg_0+Arg_1<=10001 && 5001<=Arg_1 && 10001<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && Arg_0<=5000 for location eval_foo_stop

Found invariant Arg_0+Arg_1<=10001 && 5001<=Arg_1 && 10001<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && Arg_0<=5000 for location eval_foo_bb3_in

Found invariant Arg_1<=5000 && 1+Arg_1<=Arg_0 && Arg_0+Arg_1<=10001 && 1<=Arg_1 && 10001<=Arg_0+Arg_1 && Arg_0<=9999+Arg_1 && Arg_0<=10000 && 5001<=Arg_0 for location eval_foo_bb2_in

Found invariant Arg_0+Arg_1<=10001 && 1<=Arg_1 && 10001<=Arg_0+Arg_1 && Arg_0<=9999+Arg_1 && Arg_0<=10000 for location eval_foo_bb1_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:
12:eval_foo_bb0_in(Arg_0,Arg_1) -> eval_foo_bb1_in(10000,1)
13:eval_foo_bb1_in(Arg_0,Arg_1) -> eval_foo_bb2_in(Arg_0,Arg_1):|:Arg_0+Arg_1<=10001 && 1<=Arg_1 && 10001<=Arg_0+Arg_1 && Arg_0<=9999+Arg_1 && Arg_0<=10000 && 1+Arg_1<=Arg_0
14:eval_foo_bb1_in(Arg_0,Arg_1) -> eval_foo_bb3_in(Arg_0,Arg_1):|:Arg_0+Arg_1<=10001 && 1<=Arg_1 && 10001<=Arg_0+Arg_1 && Arg_0<=9999+Arg_1 && Arg_0<=10000 && Arg_0<Arg_1+1
15:eval_foo_bb2_in(Arg_0,Arg_1) -> eval_foo_bb1_in(Arg_0-1,Arg_1+1):|:Arg_1<=5000 && 1+Arg_1<=Arg_0 && Arg_0+Arg_1<=10001 && 1<=Arg_1 && 10001<=Arg_0+Arg_1 && Arg_0<=9999+Arg_1 && Arg_0<=10000 && 5001<=Arg_0
16:eval_foo_bb3_in(Arg_0,Arg_1) -> eval_foo_stop(Arg_0,Arg_1):|:Arg_0+Arg_1<=10001 && 5001<=Arg_1 && 10001<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && Arg_0<=5000
17:eval_foo_start(Arg_0,Arg_1) -> eval_foo_bb0_in(Arg_0,Arg_1)

MPRF for transition 13:eval_foo_bb1_in(Arg_0,Arg_1) -> eval_foo_bb2_in(Arg_0,Arg_1):|:Arg_0+Arg_1<=10001 && 1<=Arg_1 && 10001<=Arg_0+Arg_1 && Arg_0<=9999+Arg_1 && Arg_0<=10000 && 1+Arg_1<=Arg_0 of depth 1:

new bound:

30001 {O(1)}

MPRF:

eval_foo_bb2_in [2*Arg_0-10003 ]
eval_foo_bb1_in [2*Arg_0-10001 ]

MPRF for transition 15:eval_foo_bb2_in(Arg_0,Arg_1) -> eval_foo_bb1_in(Arg_0-1,Arg_1+1):|:Arg_1<=5000 && 1+Arg_1<=Arg_0 && Arg_0+Arg_1<=10001 && 1<=Arg_1 && 10001<=Arg_0+Arg_1 && Arg_0<=9999+Arg_1 && Arg_0<=10000 && 5001<=Arg_0 of depth 1:

new bound:

5002 {O(1)}

MPRF:

eval_foo_bb2_in [5001-Arg_1 ]
eval_foo_bb1_in [5001-Arg_1 ]

All Bounds

Timebounds

Overall timebound:35007 {O(1)}
12: eval_foo_bb0_in->eval_foo_bb1_in: 1 {O(1)}
13: eval_foo_bb1_in->eval_foo_bb2_in: 30001 {O(1)}
14: eval_foo_bb1_in->eval_foo_bb3_in: 1 {O(1)}
15: eval_foo_bb2_in->eval_foo_bb1_in: 5002 {O(1)}
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: 35007 {O(1)}
12: eval_foo_bb0_in->eval_foo_bb1_in: 1 {O(1)}
13: eval_foo_bb1_in->eval_foo_bb2_in: 30001 {O(1)}
14: eval_foo_bb1_in->eval_foo_bb3_in: 1 {O(1)}
15: eval_foo_bb2_in->eval_foo_bb1_in: 5002 {O(1)}
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: 10000 {O(1)}
12: eval_foo_bb0_in->eval_foo_bb1_in, Arg_1: 1 {O(1)}
13: eval_foo_bb1_in->eval_foo_bb2_in, Arg_0: 10000 {O(1)}
13: eval_foo_bb1_in->eval_foo_bb2_in, Arg_1: 5003 {O(1)}
14: eval_foo_bb1_in->eval_foo_bb3_in, Arg_0: 10000 {O(1)}
14: eval_foo_bb1_in->eval_foo_bb3_in, Arg_1: 5003 {O(1)}
15: eval_foo_bb2_in->eval_foo_bb1_in, Arg_0: 10000 {O(1)}
15: eval_foo_bb2_in->eval_foo_bb1_in, Arg_1: 5003 {O(1)}
16: eval_foo_bb3_in->eval_foo_stop, Arg_0: 10000 {O(1)}
16: eval_foo_bb3_in->eval_foo_stop, Arg_1: 5003 {O(1)}
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)}