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(0,Arg_1)
2:eval_foo_bb1_in(Arg_0,Arg_1) -> eval_foo_bb2_in(Arg_0,Arg_1):|:Arg_0<100
3:eval_foo_bb1_in(Arg_0,Arg_1) -> eval_foo_bb3_in(Arg_0,Arg_1):|:100<=Arg_0
4:eval_foo_bb2_in(Arg_0,Arg_1) -> eval_foo_bb1_in(Arg_0+1,Arg_1):|:Arg_0<50
5:eval_foo_bb2_in(Arg_0,Arg_1) -> eval_foo_bb1_in(Arg_0-1,Arg_1):|:50<=Arg_0
6: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

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

Found invariant 100<=Arg_0 for location eval_foo_stop

Found invariant 100<=Arg_0 for location eval_foo_bb3_in

Found invariant Arg_0<=99 && 0<=Arg_0 for location eval_foo_bb2_in

Found invariant 0<=Arg_0 for location eval_foo_bb1_in

Cut unsatisfiable transition 16: eval_foo_bb1_in->eval_foo_bb3_in

Cut unreachable locations [eval_foo_bb3_in; eval_foo_stop] from the program graph

Problem after Preprocessing

Start: eval_foo_start
Program_Vars: Arg_0
Temp_Vars:
Locations: eval_foo_bb0_in, eval_foo_bb1_in, eval_foo_bb2_in, eval_foo_start
Transitions:
14:eval_foo_bb0_in(Arg_0) -> eval_foo_bb1_in(0)
15:eval_foo_bb1_in(Arg_0) -> eval_foo_bb2_in(Arg_0):|:0<=Arg_0 && Arg_0<100
17:eval_foo_bb2_in(Arg_0) -> eval_foo_bb1_in(Arg_0+1):|:Arg_0<=99 && 0<=Arg_0 && Arg_0<50
18:eval_foo_bb2_in(Arg_0) -> eval_foo_bb1_in(Arg_0-1):|:Arg_0<=99 && 0<=Arg_0 && 50<=Arg_0
20:eval_foo_start(Arg_0) -> eval_foo_bb0_in(Arg_0)

Analysing control-flow refined program

Found invariant Arg_0<=1 && 1<=Arg_0 for location n_eval_foo_bb2_in___7

Found invariant Arg_0<=98 && 49<=Arg_0 for location n_eval_foo_bb1_in___4

Found invariant Arg_0<=50 && 50<=Arg_0 for location n_eval_foo_bb1_in___2

Found invariant Arg_0<=99 && 2<=Arg_0 for location n_eval_foo_bb2_in___5

Found invariant Arg_0<=50 && 50<=Arg_0 for location n_eval_foo_bb2_in___1

Found invariant Arg_0<=0 && 0<=Arg_0 for location eval_foo_bb1_in

Found invariant Arg_0<=1 && 1<=Arg_0 for location n_eval_foo_bb1_in___8

Found invariant Arg_0<=98 && 49<=Arg_0 for location n_eval_foo_bb2_in___3

Found invariant Arg_0<=0 && 0<=Arg_0 for location n_eval_foo_bb2_in___9

Found invariant Arg_0<=50 && 2<=Arg_0 for location n_eval_foo_bb1_in___6

MPRF for transition 54:n_eval_foo_bb1_in___6(Arg_0) -> n_eval_foo_bb2_in___5(Arg_0):|:Arg_0<=50 && 2<=Arg_0 && 0<=Arg_0 && Arg_0<100 && Arg_0<=99 && 0<=Arg_0 && Arg_0<=99 && 0<=Arg_0 && Arg_0<100 of depth 1:

new bound:

102 {O(1)}

MPRF:

n_eval_foo_bb2_in___5 [99-Arg_0 ]
n_eval_foo_bb1_in___6 [100-Arg_0 ]

MPRF for transition 60:n_eval_foo_bb2_in___5(Arg_0) -> n_eval_foo_bb1_in___6(Arg_0+1):|:Arg_0<=99 && 2<=Arg_0 && Arg_0<=99 && 0<=Arg_0 && 0<=Arg_0 && Arg_0<50 of depth 1:

new bound:

52 {O(1)}

MPRF:

n_eval_foo_bb2_in___5 [50-Arg_0 ]
n_eval_foo_bb1_in___6 [50-Arg_0 ]

MPRF for transition 58:n_eval_foo_bb2_in___3(Arg_0) -> n_eval_foo_bb1_in___4(Arg_0-1):|:Arg_0<=98 && 49<=Arg_0 && Arg_0<=98 && 49<=Arg_0 && 50<=Arg_0 && Arg_0<=99 of depth 1:

new bound:

147 {O(1)}

MPRF:

n_eval_foo_bb2_in___1 [Arg_0-50 ]
n_eval_foo_bb1_in___2 [Arg_0-50 ]
n_eval_foo_bb2_in___3 [Arg_0-49 ]
n_eval_foo_bb1_in___4 [Arg_0-49 ]

CFR did not improve the program. Rolling back

All Bounds

Timebounds

Overall timebound:inf {Infinity}
14: eval_foo_bb0_in->eval_foo_bb1_in: 1 {O(1)}
15: eval_foo_bb1_in->eval_foo_bb2_in: inf {Infinity}
17: eval_foo_bb2_in->eval_foo_bb1_in: inf {Infinity}
18: eval_foo_bb2_in->eval_foo_bb1_in: inf {Infinity}
20: eval_foo_start->eval_foo_bb0_in: 1 {O(1)}

Costbounds

Overall costbound: inf {Infinity}
14: eval_foo_bb0_in->eval_foo_bb1_in: 1 {O(1)}
15: eval_foo_bb1_in->eval_foo_bb2_in: inf {Infinity}
17: eval_foo_bb2_in->eval_foo_bb1_in: inf {Infinity}
18: eval_foo_bb2_in->eval_foo_bb1_in: inf {Infinity}
20: eval_foo_start->eval_foo_bb0_in: 1 {O(1)}

Sizebounds

14: eval_foo_bb0_in->eval_foo_bb1_in, Arg_0: 0 {O(1)}
15: eval_foo_bb1_in->eval_foo_bb2_in, Arg_0: 99 {O(1)}
17: eval_foo_bb2_in->eval_foo_bb1_in, Arg_0: 50 {O(1)}
18: eval_foo_bb2_in->eval_foo_bb1_in, Arg_0: 98 {O(1)}
20: eval_foo_start->eval_foo_bb0_in, Arg_0: Arg_0 {O(n)}