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_bb4_in, eval_foo_bb5_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_2,Arg_1,Arg_2,Arg_3)
2:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_foo_bb2_in(Arg_0,0,Arg_2,Arg_3):|:0<Arg_0
3:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_foo_bb5_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_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_1<Arg_0
5:eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_foo_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_0<=Arg_1
6:eval_foo_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_foo_bb2_in(Arg_0,Arg_1+1,Arg_2,Arg_3)
7:eval_foo_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_foo_bb1_in(Arg_0-1,Arg_1,Arg_2,Arg_3)
8:eval_foo_bb5_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_3} that do not contribute to the problem

Found invariant Arg_0<=Arg_2 && Arg_0<=0 for location eval_foo_bb5_in

Found invariant Arg_0<=Arg_2 && Arg_0<=0 for location eval_foo_stop

Found invariant 1<=Arg_2 && 1<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 2<=Arg_0+Arg_2 && Arg_0<=Arg_2 && 1+Arg_1<=Arg_0 && 0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 for location eval_foo_bb3_in

Found invariant 1<=Arg_2 && 1<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 2<=Arg_0+Arg_2 && Arg_0<=Arg_2 && Arg_1<=Arg_0 && 0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 for location eval_foo_bb2_in

Found invariant Arg_0<=Arg_2 for location eval_foo_bb1_in

Found invariant 1<=Arg_2 && 2<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 2<=Arg_0+Arg_2 && Arg_0<=Arg_2 && Arg_1<=Arg_0 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 1<=Arg_0 for location eval_foo_bb4_in

Problem after Preprocessing

Start: eval_foo_start
Program_Vars: Arg_0, Arg_1, Arg_2
Temp_Vars:
Locations: eval_foo_bb0_in, eval_foo_bb1_in, eval_foo_bb2_in, eval_foo_bb3_in, eval_foo_bb4_in, eval_foo_bb5_in, eval_foo_start, eval_foo_stop
Transitions:
18:eval_foo_bb0_in(Arg_0,Arg_1,Arg_2) -> eval_foo_bb1_in(Arg_2,Arg_1,Arg_2)
19:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2) -> eval_foo_bb2_in(Arg_0,0,Arg_2):|:Arg_0<=Arg_2 && 0<Arg_0
20:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2) -> eval_foo_bb5_in(Arg_0,Arg_1,Arg_2):|:Arg_0<=Arg_2 && Arg_0<=0
21:eval_foo_bb2_in(Arg_0,Arg_1,Arg_2) -> eval_foo_bb3_in(Arg_0,Arg_1,Arg_2):|:1<=Arg_2 && 1<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 2<=Arg_0+Arg_2 && Arg_0<=Arg_2 && Arg_1<=Arg_0 && 0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 && Arg_1<Arg_0
22:eval_foo_bb2_in(Arg_0,Arg_1,Arg_2) -> eval_foo_bb4_in(Arg_0,Arg_1,Arg_2):|:1<=Arg_2 && 1<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 2<=Arg_0+Arg_2 && Arg_0<=Arg_2 && Arg_1<=Arg_0 && 0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 && Arg_0<=Arg_1
23:eval_foo_bb3_in(Arg_0,Arg_1,Arg_2) -> eval_foo_bb2_in(Arg_0,Arg_1+1,Arg_2):|:1<=Arg_2 && 1<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 2<=Arg_0+Arg_2 && Arg_0<=Arg_2 && 1+Arg_1<=Arg_0 && 0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0
24:eval_foo_bb4_in(Arg_0,Arg_1,Arg_2) -> eval_foo_bb1_in(Arg_0-1,Arg_1,Arg_2):|:1<=Arg_2 && 2<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 2<=Arg_0+Arg_2 && Arg_0<=Arg_2 && Arg_1<=Arg_0 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 1<=Arg_0
25:eval_foo_bb5_in(Arg_0,Arg_1,Arg_2) -> eval_foo_stop(Arg_0,Arg_1,Arg_2):|:Arg_0<=Arg_2 && Arg_0<=0
26:eval_foo_start(Arg_0,Arg_1,Arg_2) -> eval_foo_bb0_in(Arg_0,Arg_1,Arg_2)

MPRF for transition 19:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2) -> eval_foo_bb2_in(Arg_0,0,Arg_2):|:Arg_0<=Arg_2 && 0<Arg_0 of depth 1:

new bound:

Arg_2 {O(n)}

MPRF:

eval_foo_bb3_in [Arg_0-1 ]
eval_foo_bb2_in [Arg_0-1 ]
eval_foo_bb4_in [Arg_0-1 ]
eval_foo_bb1_in [Arg_0 ]

MPRF for transition 22:eval_foo_bb2_in(Arg_0,Arg_1,Arg_2) -> eval_foo_bb4_in(Arg_0,Arg_1,Arg_2):|:1<=Arg_2 && 1<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 2<=Arg_0+Arg_2 && Arg_0<=Arg_2 && Arg_1<=Arg_0 && 0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 && Arg_0<=Arg_1 of depth 1:

new bound:

Arg_2+1 {O(n)}

MPRF:

eval_foo_bb3_in [Arg_0+1 ]
eval_foo_bb2_in [Arg_0+1 ]
eval_foo_bb4_in [Arg_0 ]
eval_foo_bb1_in [Arg_0+1 ]

MPRF for transition 24:eval_foo_bb4_in(Arg_0,Arg_1,Arg_2) -> eval_foo_bb1_in(Arg_0-1,Arg_1,Arg_2):|:1<=Arg_2 && 2<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 2<=Arg_0+Arg_2 && Arg_0<=Arg_2 && Arg_1<=Arg_0 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 1<=Arg_0 of depth 1:

new bound:

Arg_2 {O(n)}

MPRF:

eval_foo_bb3_in [Arg_0 ]
eval_foo_bb2_in [Arg_0 ]
eval_foo_bb4_in [Arg_1 ]
eval_foo_bb1_in [Arg_0 ]

MPRF for transition 21:eval_foo_bb2_in(Arg_0,Arg_1,Arg_2) -> eval_foo_bb3_in(Arg_0,Arg_1,Arg_2):|:1<=Arg_2 && 1<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 2<=Arg_0+Arg_2 && Arg_0<=Arg_2 && Arg_1<=Arg_0 && 0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 && Arg_1<Arg_0 of depth 1:

new bound:

Arg_2*Arg_2+2*Arg_2+1 {O(n^2)}

MPRF:

eval_foo_bb1_in [Arg_0+1 ]
eval_foo_bb4_in [0 ]
eval_foo_bb3_in [Arg_0-Arg_1 ]
eval_foo_bb2_in [Arg_0+1-Arg_1 ]

MPRF for transition 23:eval_foo_bb3_in(Arg_0,Arg_1,Arg_2) -> eval_foo_bb2_in(Arg_0,Arg_1+1,Arg_2):|:1<=Arg_2 && 1<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 2<=Arg_0+Arg_2 && Arg_0<=Arg_2 && 1+Arg_1<=Arg_0 && 0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 of depth 1:

new bound:

Arg_2*Arg_2+Arg_2 {O(n^2)}

MPRF:

eval_foo_bb1_in [Arg_0 ]
eval_foo_bb4_in [0 ]
eval_foo_bb3_in [Arg_0-Arg_1 ]
eval_foo_bb2_in [Arg_0-Arg_1 ]

Analysing control-flow refined program

Cut unsatisfiable transition 22: eval_foo_bb2_in->eval_foo_bb4_in

Found invariant Arg_0<=Arg_2 && Arg_0<=0 for location eval_foo_bb5_in

Found invariant 1<=Arg_2 && 2<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 2<=Arg_0+Arg_2 && Arg_0<=Arg_2 && Arg_1<=Arg_0 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 for location n_eval_foo_bb2_in___2

Found invariant 2<=Arg_2 && 3<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 4<=Arg_0+Arg_2 && Arg_0<=Arg_2 && 1+Arg_1<=Arg_0 && 1<=Arg_1 && 3<=Arg_0+Arg_1 && 2<=Arg_0 for location n_eval_foo_bb3_in___1

Found invariant Arg_0<=Arg_2 && Arg_0<=0 for location eval_foo_stop

Found invariant 1<=Arg_2 && 1<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 2<=Arg_0+Arg_2 && Arg_0<=Arg_2 && Arg_1<=0 && 1+Arg_1<=Arg_0 && 0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 for location n_eval_foo_bb3_in___3

Found invariant 1<=Arg_2 && 1<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 2<=Arg_0+Arg_2 && Arg_0<=Arg_2 && Arg_1<=0 && 1+Arg_1<=Arg_0 && 0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 for location eval_foo_bb2_in

Found invariant Arg_0<=Arg_2 for location eval_foo_bb1_in

Found invariant 1<=Arg_2 && 2<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 2<=Arg_0+Arg_2 && Arg_0<=Arg_2 && Arg_1<=Arg_0 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 1<=Arg_0 for location eval_foo_bb4_in

knowledge_propagation leads to new time bound Arg_2 {O(n)} for transition 60:eval_foo_bb2_in(Arg_0,Arg_1,Arg_2) -> n_eval_foo_bb3_in___3(Arg_0,Arg_1,Arg_2):|:1<=Arg_2 && 1<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 2<=Arg_0+Arg_2 && Arg_0<=Arg_2 && Arg_1<=0 && 1+Arg_1<=Arg_0 && 0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 && Arg_1<Arg_0 && 0<=Arg_1 && Arg_0<=Arg_2 && 0<=Arg_1 && Arg_1<Arg_0 && 1<=Arg_0 && Arg_0<=Arg_2

knowledge_propagation leads to new time bound Arg_2 {O(n)} for transition 62:n_eval_foo_bb3_in___3(Arg_0,Arg_1,Arg_2) -> n_eval_foo_bb2_in___2(Arg_0,Arg_1+1,Arg_2):|:1<=Arg_2 && 1<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 2<=Arg_0+Arg_2 && Arg_0<=Arg_2 && Arg_1<=0 && 1+Arg_1<=Arg_0 && 0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 && Arg_1<Arg_0 && 1<=Arg_0 && 0<=Arg_1 && Arg_0<=Arg_2 && 0<=Arg_1 && 1+Arg_1<=Arg_0 && Arg_0<=Arg_2

MPRF for transition 59:n_eval_foo_bb2_in___2(Arg_0,Arg_1,Arg_2) -> n_eval_foo_bb3_in___1(Arg_0,Arg_1,Arg_2):|:1<=Arg_2 && 2<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 2<=Arg_0+Arg_2 && Arg_0<=Arg_2 && Arg_1<=Arg_0 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 && 1<=Arg_0 && 0<=Arg_1 && Arg_0<=Arg_2 && 1<=Arg_1 && Arg_1<=Arg_0 && Arg_0<=Arg_2 && 0<=Arg_1 && Arg_1<Arg_0 && 1<=Arg_0 && Arg_0<=Arg_2 of depth 1:

new bound:

Arg_2*Arg_2+2*Arg_2 {O(n^2)}

MPRF:

eval_foo_bb2_in [0 ]
n_eval_foo_bb3_in___3 [0 ]
eval_foo_bb1_in [0 ]
eval_foo_bb4_in [Arg_0-Arg_1 ]
n_eval_foo_bb3_in___1 [Arg_0-Arg_1 ]
n_eval_foo_bb2_in___2 [Arg_0+1-Arg_1 ]

MPRF for transition 67:n_eval_foo_bb2_in___2(Arg_0,Arg_1,Arg_2) -> eval_foo_bb4_in(Arg_0,Arg_1,Arg_2):|:1<=Arg_2 && 2<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 2<=Arg_0+Arg_2 && Arg_0<=Arg_2 && Arg_1<=Arg_0 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 && 1<=Arg_2 && 1<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 2<=Arg_0+Arg_2 && Arg_0<=Arg_2 && Arg_1<=Arg_0 && 0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 && Arg_0<=Arg_1 of depth 1:

new bound:

Arg_2+1 {O(n)}

MPRF:

eval_foo_bb2_in [Arg_0+1 ]
eval_foo_bb1_in [Arg_0+1 ]
eval_foo_bb4_in [Arg_1 ]
n_eval_foo_bb3_in___1 [Arg_0+1 ]
n_eval_foo_bb3_in___3 [Arg_0+1 ]
n_eval_foo_bb2_in___2 [Arg_0+1 ]

MPRF for transition 61:n_eval_foo_bb3_in___1(Arg_0,Arg_1,Arg_2) -> n_eval_foo_bb2_in___2(Arg_0,Arg_1+1,Arg_2):|:2<=Arg_2 && 3<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 4<=Arg_0+Arg_2 && Arg_0<=Arg_2 && 1+Arg_1<=Arg_0 && 1<=Arg_1 && 3<=Arg_0+Arg_1 && 2<=Arg_0 && Arg_0<=Arg_2 && Arg_1<Arg_0 && 1<=Arg_1 && 0<=Arg_1 && 1+Arg_1<=Arg_0 && Arg_0<=Arg_2 of depth 1:

new bound:

Arg_2*Arg_2+Arg_2 {O(n^2)}

MPRF:

eval_foo_bb2_in [0 ]
n_eval_foo_bb3_in___3 [0 ]
eval_foo_bb1_in [0 ]
eval_foo_bb4_in [0 ]
n_eval_foo_bb3_in___1 [Arg_0-Arg_1 ]
n_eval_foo_bb2_in___2 [Arg_0-Arg_1 ]

CFR did not improve the program. Rolling back

All Bounds

Timebounds

Overall timebound:2*Arg_2*Arg_2+6*Arg_2+6 {O(n^2)}
18: eval_foo_bb0_in->eval_foo_bb1_in: 1 {O(1)}
19: eval_foo_bb1_in->eval_foo_bb2_in: Arg_2 {O(n)}
20: eval_foo_bb1_in->eval_foo_bb5_in: 1 {O(1)}
21: eval_foo_bb2_in->eval_foo_bb3_in: Arg_2*Arg_2+2*Arg_2+1 {O(n^2)}
22: eval_foo_bb2_in->eval_foo_bb4_in: Arg_2+1 {O(n)}
23: eval_foo_bb3_in->eval_foo_bb2_in: Arg_2*Arg_2+Arg_2 {O(n^2)}
24: eval_foo_bb4_in->eval_foo_bb1_in: Arg_2 {O(n)}
25: eval_foo_bb5_in->eval_foo_stop: 1 {O(1)}
26: eval_foo_start->eval_foo_bb0_in: 1 {O(1)}

Costbounds

Overall costbound: 2*Arg_2*Arg_2+6*Arg_2+6 {O(n^2)}
18: eval_foo_bb0_in->eval_foo_bb1_in: 1 {O(1)}
19: eval_foo_bb1_in->eval_foo_bb2_in: Arg_2 {O(n)}
20: eval_foo_bb1_in->eval_foo_bb5_in: 1 {O(1)}
21: eval_foo_bb2_in->eval_foo_bb3_in: Arg_2*Arg_2+2*Arg_2+1 {O(n^2)}
22: eval_foo_bb2_in->eval_foo_bb4_in: Arg_2+1 {O(n)}
23: eval_foo_bb3_in->eval_foo_bb2_in: Arg_2*Arg_2+Arg_2 {O(n^2)}
24: eval_foo_bb4_in->eval_foo_bb1_in: Arg_2 {O(n)}
25: eval_foo_bb5_in->eval_foo_stop: 1 {O(1)}
26: eval_foo_start->eval_foo_bb0_in: 1 {O(1)}

Sizebounds

18: eval_foo_bb0_in->eval_foo_bb1_in, Arg_0: Arg_2 {O(n)}
18: eval_foo_bb0_in->eval_foo_bb1_in, Arg_1: Arg_1 {O(n)}
18: eval_foo_bb0_in->eval_foo_bb1_in, Arg_2: Arg_2 {O(n)}
19: eval_foo_bb1_in->eval_foo_bb2_in, Arg_0: Arg_2 {O(n)}
19: eval_foo_bb1_in->eval_foo_bb2_in, Arg_1: 0 {O(1)}
19: eval_foo_bb1_in->eval_foo_bb2_in, Arg_2: Arg_2 {O(n)}
20: eval_foo_bb1_in->eval_foo_bb5_in, Arg_0: 2*Arg_2 {O(n)}
20: eval_foo_bb1_in->eval_foo_bb5_in, Arg_1: Arg_2*Arg_2+Arg_1+Arg_2 {O(n^2)}
20: eval_foo_bb1_in->eval_foo_bb5_in, Arg_2: 2*Arg_2 {O(n)}
21: eval_foo_bb2_in->eval_foo_bb3_in, Arg_0: Arg_2 {O(n)}
21: eval_foo_bb2_in->eval_foo_bb3_in, Arg_1: Arg_2*Arg_2+Arg_2 {O(n^2)}
21: eval_foo_bb2_in->eval_foo_bb3_in, Arg_2: Arg_2 {O(n)}
22: eval_foo_bb2_in->eval_foo_bb4_in, Arg_0: Arg_2 {O(n)}
22: eval_foo_bb2_in->eval_foo_bb4_in, Arg_1: Arg_2*Arg_2+Arg_2 {O(n^2)}
22: eval_foo_bb2_in->eval_foo_bb4_in, Arg_2: Arg_2 {O(n)}
23: eval_foo_bb3_in->eval_foo_bb2_in, Arg_0: Arg_2 {O(n)}
23: eval_foo_bb3_in->eval_foo_bb2_in, Arg_1: Arg_2*Arg_2+Arg_2 {O(n^2)}
23: eval_foo_bb3_in->eval_foo_bb2_in, Arg_2: Arg_2 {O(n)}
24: eval_foo_bb4_in->eval_foo_bb1_in, Arg_0: Arg_2 {O(n)}
24: eval_foo_bb4_in->eval_foo_bb1_in, Arg_1: Arg_2*Arg_2+Arg_2 {O(n^2)}
24: eval_foo_bb4_in->eval_foo_bb1_in, Arg_2: Arg_2 {O(n)}
25: eval_foo_bb5_in->eval_foo_stop, Arg_0: 2*Arg_2 {O(n)}
25: eval_foo_bb5_in->eval_foo_stop, Arg_1: Arg_2*Arg_2+Arg_1+Arg_2 {O(n^2)}
25: eval_foo_bb5_in->eval_foo_stop, Arg_2: 2*Arg_2 {O(n)}
26: eval_foo_start->eval_foo_bb0_in, Arg_0: Arg_0 {O(n)}
26: eval_foo_start->eval_foo_bb0_in, Arg_1: Arg_1 {O(n)}
26: eval_foo_start->eval_foo_bb0_in, Arg_2: Arg_2 {O(n)}