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_bb4_in, eval_foo_bb5_in, eval_foo_bb6_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_4,Arg_1,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_0
3:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_foo_bb6_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5):|:Arg_0<0
4:eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_foo_bb3_in(Arg_0,1,Arg_0+1,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_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5):|:Arg_1<Arg_2
6:eval_foo_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_foo_bb5_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5):|:Arg_2<=Arg_1
7:eval_foo_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_foo_bb3_in(Arg_0,Arg_1+1,Arg_2,Arg_3,Arg_4,Arg_5)
8:eval_foo_bb5_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_foo_bb1_in(Arg_2-2,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5)
9:eval_foo_bb6_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_3,Arg_5} that do not contribute to the problem

Found invariant 0<=Arg_4 && 1<=Arg_2+Arg_4 && Arg_2<=1+Arg_4 && 1<=Arg_1+Arg_4 && Arg_1<=1+Arg_4 && 0<=Arg_0+Arg_4 && Arg_0<=Arg_4 && Arg_2<=Arg_1 && Arg_2<=1+Arg_0 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 1<=Arg_0+Arg_2 && 1+Arg_0<=Arg_2 && Arg_1<=1+Arg_0 && 1<=Arg_1 && 1<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 0<=Arg_0 for location eval_foo_bb5_in

Found invariant Arg_0<=Arg_4 && 1+Arg_0<=0 for location eval_foo_stop

Found invariant 0<=Arg_4 && 1<=Arg_2+Arg_4 && Arg_2<=1+Arg_4 && 1<=Arg_1+Arg_4 && Arg_1<=1+Arg_4 && 0<=Arg_0+Arg_4 && Arg_0<=Arg_4 && Arg_2<=1+Arg_0 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 1<=Arg_0+Arg_2 && 1+Arg_0<=Arg_2 && Arg_1<=1+Arg_0 && 1<=Arg_1 && 1<=Arg_0+Arg_1 && 0<=Arg_0 for location eval_foo_bb3_in

Found invariant 0<=Arg_4 && 0<=Arg_0+Arg_4 && Arg_0<=Arg_4 && 0<=Arg_0 for location eval_foo_bb2_in

Found invariant Arg_0<=Arg_4 for location eval_foo_bb1_in

Found invariant Arg_0<=Arg_4 && 1+Arg_0<=0 for location eval_foo_bb6_in

Found invariant 1<=Arg_4 && 3<=Arg_2+Arg_4 && Arg_2<=1+Arg_4 && 2<=Arg_1+Arg_4 && Arg_1<=Arg_4 && 2<=Arg_0+Arg_4 && Arg_0<=Arg_4 && Arg_2<=1+Arg_0 && 2<=Arg_2 && 3<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 3<=Arg_0+Arg_2 && 1+Arg_0<=Arg_2 && Arg_1<=Arg_0 && 1<=Arg_1 && 2<=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, Arg_4
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_bb6_in, eval_foo_start, eval_foo_stop
Transitions:
20:eval_foo_bb0_in(Arg_0,Arg_1,Arg_2,Arg_4) -> eval_foo_bb1_in(Arg_4,Arg_1,Arg_2,Arg_4)
21:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2,Arg_4) -> eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_4):|:Arg_0<=Arg_4 && 0<=Arg_0
22:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2,Arg_4) -> eval_foo_bb6_in(Arg_0,Arg_1,Arg_2,Arg_4):|:Arg_0<=Arg_4 && Arg_0<0
23:eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_4) -> eval_foo_bb3_in(Arg_0,1,Arg_0+1,Arg_4):|:0<=Arg_4 && 0<=Arg_0+Arg_4 && Arg_0<=Arg_4 && 0<=Arg_0
24:eval_foo_bb3_in(Arg_0,Arg_1,Arg_2,Arg_4) -> eval_foo_bb4_in(Arg_0,Arg_1,Arg_2,Arg_4):|:0<=Arg_4 && 1<=Arg_2+Arg_4 && Arg_2<=1+Arg_4 && 1<=Arg_1+Arg_4 && Arg_1<=1+Arg_4 && 0<=Arg_0+Arg_4 && Arg_0<=Arg_4 && Arg_2<=1+Arg_0 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 1<=Arg_0+Arg_2 && 1+Arg_0<=Arg_2 && Arg_1<=1+Arg_0 && 1<=Arg_1 && 1<=Arg_0+Arg_1 && 0<=Arg_0 && Arg_1<Arg_2
25:eval_foo_bb3_in(Arg_0,Arg_1,Arg_2,Arg_4) -> eval_foo_bb5_in(Arg_0,Arg_1,Arg_2,Arg_4):|:0<=Arg_4 && 1<=Arg_2+Arg_4 && Arg_2<=1+Arg_4 && 1<=Arg_1+Arg_4 && Arg_1<=1+Arg_4 && 0<=Arg_0+Arg_4 && Arg_0<=Arg_4 && Arg_2<=1+Arg_0 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 1<=Arg_0+Arg_2 && 1+Arg_0<=Arg_2 && Arg_1<=1+Arg_0 && 1<=Arg_1 && 1<=Arg_0+Arg_1 && 0<=Arg_0 && Arg_2<=Arg_1
26:eval_foo_bb4_in(Arg_0,Arg_1,Arg_2,Arg_4) -> eval_foo_bb3_in(Arg_0,Arg_1+1,Arg_2,Arg_4):|:1<=Arg_4 && 3<=Arg_2+Arg_4 && Arg_2<=1+Arg_4 && 2<=Arg_1+Arg_4 && Arg_1<=Arg_4 && 2<=Arg_0+Arg_4 && Arg_0<=Arg_4 && Arg_2<=1+Arg_0 && 2<=Arg_2 && 3<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 3<=Arg_0+Arg_2 && 1+Arg_0<=Arg_2 && Arg_1<=Arg_0 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0
27:eval_foo_bb5_in(Arg_0,Arg_1,Arg_2,Arg_4) -> eval_foo_bb1_in(Arg_2-2,Arg_1,Arg_2,Arg_4):|:0<=Arg_4 && 1<=Arg_2+Arg_4 && Arg_2<=1+Arg_4 && 1<=Arg_1+Arg_4 && Arg_1<=1+Arg_4 && 0<=Arg_0+Arg_4 && Arg_0<=Arg_4 && Arg_2<=Arg_1 && Arg_2<=1+Arg_0 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 1<=Arg_0+Arg_2 && 1+Arg_0<=Arg_2 && Arg_1<=1+Arg_0 && 1<=Arg_1 && 1<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 0<=Arg_0
28:eval_foo_bb6_in(Arg_0,Arg_1,Arg_2,Arg_4) -> eval_foo_stop(Arg_0,Arg_1,Arg_2,Arg_4):|:Arg_0<=Arg_4 && 1+Arg_0<=0
29:eval_foo_start(Arg_0,Arg_1,Arg_2,Arg_4) -> eval_foo_bb0_in(Arg_0,Arg_1,Arg_2,Arg_4)

MPRF for transition 21:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2,Arg_4) -> eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_4):|:Arg_0<=Arg_4 && 0<=Arg_0 of depth 1:

new bound:

Arg_4+1 {O(n)}

MPRF:

eval_foo_bb2_in [Arg_0 ]
eval_foo_bb4_in [Arg_2-1 ]
eval_foo_bb3_in [Arg_2-1 ]
eval_foo_bb5_in [Arg_0 ]
eval_foo_bb1_in [Arg_0+1 ]

MPRF for transition 23:eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_4) -> eval_foo_bb3_in(Arg_0,1,Arg_0+1,Arg_4):|:0<=Arg_4 && 0<=Arg_0+Arg_4 && Arg_0<=Arg_4 && 0<=Arg_0 of depth 1:

new bound:

Arg_4+1 {O(n)}

MPRF:

eval_foo_bb2_in [Arg_0+1 ]
eval_foo_bb4_in [Arg_0 ]
eval_foo_bb3_in [Arg_0 ]
eval_foo_bb5_in [Arg_0+Arg_2-Arg_1 ]
eval_foo_bb1_in [Arg_0+1 ]

MPRF for transition 25:eval_foo_bb3_in(Arg_0,Arg_1,Arg_2,Arg_4) -> eval_foo_bb5_in(Arg_0,Arg_1,Arg_2,Arg_4):|:0<=Arg_4 && 1<=Arg_2+Arg_4 && Arg_2<=1+Arg_4 && 1<=Arg_1+Arg_4 && Arg_1<=1+Arg_4 && 0<=Arg_0+Arg_4 && Arg_0<=Arg_4 && Arg_2<=1+Arg_0 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 1<=Arg_0+Arg_2 && 1+Arg_0<=Arg_2 && Arg_1<=1+Arg_0 && 1<=Arg_1 && 1<=Arg_0+Arg_1 && 0<=Arg_0 && Arg_2<=Arg_1 of depth 1:

new bound:

Arg_4+1 {O(n)}

MPRF:

eval_foo_bb2_in [Arg_0+1 ]
eval_foo_bb4_in [Arg_2 ]
eval_foo_bb3_in [Arg_0+1 ]
eval_foo_bb5_in [Arg_0 ]
eval_foo_bb1_in [Arg_0+1 ]

MPRF for transition 27:eval_foo_bb5_in(Arg_0,Arg_1,Arg_2,Arg_4) -> eval_foo_bb1_in(Arg_2-2,Arg_1,Arg_2,Arg_4):|:0<=Arg_4 && 1<=Arg_2+Arg_4 && Arg_2<=1+Arg_4 && 1<=Arg_1+Arg_4 && Arg_1<=1+Arg_4 && 0<=Arg_0+Arg_4 && Arg_0<=Arg_4 && Arg_2<=Arg_1 && Arg_2<=1+Arg_0 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 1<=Arg_0+Arg_2 && 1+Arg_0<=Arg_2 && Arg_1<=1+Arg_0 && 1<=Arg_1 && 1<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 0<=Arg_0 of depth 1:

new bound:

2*Arg_4+1 {O(n)}

MPRF:

eval_foo_bb2_in [2*Arg_0+1 ]
eval_foo_bb4_in [Arg_0+Arg_2 ]
eval_foo_bb3_in [Arg_0+Arg_2 ]
eval_foo_bb5_in [Arg_0+Arg_2 ]
eval_foo_bb1_in [2*Arg_0+1 ]

MPRF for transition 24:eval_foo_bb3_in(Arg_0,Arg_1,Arg_2,Arg_4) -> eval_foo_bb4_in(Arg_0,Arg_1,Arg_2,Arg_4):|:0<=Arg_4 && 1<=Arg_2+Arg_4 && Arg_2<=1+Arg_4 && 1<=Arg_1+Arg_4 && Arg_1<=1+Arg_4 && 0<=Arg_0+Arg_4 && Arg_0<=Arg_4 && Arg_2<=1+Arg_0 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 1<=Arg_0+Arg_2 && 1+Arg_0<=Arg_2 && Arg_1<=1+Arg_0 && 1<=Arg_1 && 1<=Arg_0+Arg_1 && 0<=Arg_0 && Arg_1<Arg_2 of depth 1:

new bound:

2*Arg_4*Arg_4+6*Arg_4+3 {O(n^2)}

MPRF:

eval_foo_bb1_in [Arg_0+1 ]
eval_foo_bb2_in [Arg_0+1 ]
eval_foo_bb5_in [0 ]
eval_foo_bb4_in [Arg_2-Arg_1 ]
eval_foo_bb3_in [Arg_2+1-Arg_1 ]

MPRF for transition 26:eval_foo_bb4_in(Arg_0,Arg_1,Arg_2,Arg_4) -> eval_foo_bb3_in(Arg_0,Arg_1+1,Arg_2,Arg_4):|:1<=Arg_4 && 3<=Arg_2+Arg_4 && Arg_2<=1+Arg_4 && 2<=Arg_1+Arg_4 && Arg_1<=Arg_4 && 2<=Arg_0+Arg_4 && Arg_0<=Arg_4 && Arg_2<=1+Arg_0 && 2<=Arg_2 && 3<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 3<=Arg_0+Arg_2 && 1+Arg_0<=Arg_2 && Arg_1<=Arg_0 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 of depth 1:

new bound:

2*Arg_4*Arg_4+2*Arg_4 {O(n^2)}

MPRF:

eval_foo_bb1_in [Arg_4 ]
eval_foo_bb2_in [Arg_0 ]
eval_foo_bb5_in [Arg_0-Arg_1 ]
eval_foo_bb4_in [Arg_0+1-Arg_1 ]
eval_foo_bb3_in [Arg_0+1-Arg_1 ]

Analysing control-flow refined program

Found invariant 0<=Arg_4 && 1<=Arg_2+Arg_4 && Arg_2<=1+Arg_4 && 1<=Arg_1+Arg_4 && Arg_1<=1+Arg_4 && 0<=Arg_0+Arg_4 && Arg_0<=Arg_4 && Arg_2<=Arg_1 && Arg_2<=1+Arg_0 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 1<=Arg_0+Arg_2 && 1+Arg_0<=Arg_2 && Arg_1<=1+Arg_0 && 1<=Arg_1 && 1<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 0<=Arg_0 for location eval_foo_bb5_in

Found invariant 1<=Arg_4 && 3<=Arg_2+Arg_4 && Arg_2<=1+Arg_4 && 3<=Arg_1+Arg_4 && Arg_1<=1+Arg_4 && 2<=Arg_0+Arg_4 && Arg_0<=Arg_4 && Arg_2<=1+Arg_0 && 2<=Arg_2 && 4<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 3<=Arg_0+Arg_2 && 1+Arg_0<=Arg_2 && Arg_1<=1+Arg_0 && 2<=Arg_1 && 3<=Arg_0+Arg_1 && 1<=Arg_0 for location n_eval_foo_bb3_in___2

Found invariant Arg_0<=Arg_4 && 1+Arg_0<=0 for location eval_foo_stop

Found invariant 2<=Arg_4 && 5<=Arg_2+Arg_4 && Arg_2<=1+Arg_4 && 4<=Arg_1+Arg_4 && Arg_1<=Arg_4 && 4<=Arg_0+Arg_4 && Arg_0<=Arg_4 && Arg_2<=1+Arg_0 && 3<=Arg_2 && 5<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 5<=Arg_0+Arg_2 && 1+Arg_0<=Arg_2 && Arg_1<=Arg_0 && 2<=Arg_1 && 4<=Arg_0+Arg_1 && 2<=Arg_0 for location n_eval_foo_bb4_in___1

Found invariant 0<=Arg_4 && 1<=Arg_2+Arg_4 && Arg_2<=1+Arg_4 && 1<=Arg_1+Arg_4 && Arg_1<=1+Arg_4 && 0<=Arg_0+Arg_4 && Arg_0<=Arg_4 && Arg_2<=1+Arg_0 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 1<=Arg_0+Arg_2 && 1+Arg_0<=Arg_2 && Arg_1<=1 && Arg_1<=1+Arg_0 && 1<=Arg_1 && 1<=Arg_0+Arg_1 && 0<=Arg_0 for location eval_foo_bb3_in

Found invariant 1<=Arg_4 && 3<=Arg_2+Arg_4 && Arg_2<=1+Arg_4 && 2<=Arg_1+Arg_4 && Arg_1<=Arg_4 && 2<=Arg_0+Arg_4 && Arg_0<=Arg_4 && Arg_2<=1+Arg_0 && 2<=Arg_2 && 3<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 3<=Arg_0+Arg_2 && 1+Arg_0<=Arg_2 && Arg_1<=1 && Arg_1<=Arg_0 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 for location n_eval_foo_bb4_in___3

Found invariant 0<=Arg_4 && 0<=Arg_0+Arg_4 && Arg_0<=Arg_4 && 0<=Arg_0 for location eval_foo_bb2_in

Found invariant Arg_0<=Arg_4 for location eval_foo_bb1_in

Found invariant Arg_0<=Arg_4 && 1+Arg_0<=0 for location eval_foo_bb6_in

knowledge_propagation leads to new time bound Arg_4+1 {O(n)} for transition 66:eval_foo_bb3_in(Arg_0,Arg_1,Arg_2,Arg_4) -> n_eval_foo_bb4_in___3(Arg_0,Arg_1,Arg_0+1,Arg_4):|:0<=Arg_4 && 1<=Arg_2+Arg_4 && Arg_2<=1+Arg_4 && 1<=Arg_1+Arg_4 && Arg_1<=1+Arg_4 && 0<=Arg_0+Arg_4 && Arg_0<=Arg_4 && Arg_2<=1+Arg_0 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 1<=Arg_0+Arg_2 && 1+Arg_0<=Arg_2 && Arg_1<=1 && Arg_1<=1+Arg_0 && 1<=Arg_1 && 1<=Arg_0+Arg_1 && 0<=Arg_0 && Arg_0<=Arg_4 && 1<=Arg_1 && Arg_0+1<=Arg_2 && Arg_2<=1+Arg_0 && Arg_1<=1 && 1<=Arg_1 && 1+Arg_0<=Arg_2 && Arg_2<=1+Arg_0 && 1<=Arg_2 && Arg_2<=1+Arg_4 && Arg_1<1+Arg_0 && 1<=Arg_1 && Arg_0<=Arg_4 && Arg_0+1<=Arg_2 && Arg_2<=1+Arg_0

knowledge_propagation leads to new time bound Arg_4+1 {O(n)} for transition 68:n_eval_foo_bb4_in___3(Arg_0,Arg_1,Arg_2,Arg_4) -> n_eval_foo_bb3_in___2(Arg_0,Arg_1+1,Arg_0+1,Arg_4):|:1<=Arg_4 && 3<=Arg_2+Arg_4 && Arg_2<=1+Arg_4 && 2<=Arg_1+Arg_4 && Arg_1<=Arg_4 && 2<=Arg_0+Arg_4 && Arg_0<=Arg_4 && Arg_2<=1+Arg_0 && 2<=Arg_2 && 3<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 3<=Arg_0+Arg_2 && 1+Arg_0<=Arg_2 && Arg_1<=1 && Arg_1<=Arg_0 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 && Arg_0<=Arg_4 && 0<Arg_0 && Arg_0+1<=Arg_2 && Arg_2<=1+Arg_0 && Arg_1<=1 && 1<=Arg_1 && 1<=Arg_1 && Arg_1<=Arg_0 && Arg_0<=Arg_4 && Arg_0+1<=Arg_2 && Arg_2<=1+Arg_0

MPRF for transition 65:n_eval_foo_bb3_in___2(Arg_0,Arg_1,Arg_2,Arg_4) -> n_eval_foo_bb4_in___1(Arg_0,Arg_1,Arg_0+1,Arg_4):|:1<=Arg_4 && 3<=Arg_2+Arg_4 && Arg_2<=1+Arg_4 && 3<=Arg_1+Arg_4 && Arg_1<=1+Arg_4 && 2<=Arg_0+Arg_4 && Arg_0<=Arg_4 && Arg_2<=1+Arg_0 && 2<=Arg_2 && 4<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 3<=Arg_0+Arg_2 && 1+Arg_0<=Arg_2 && Arg_1<=1+Arg_0 && 2<=Arg_1 && 3<=Arg_0+Arg_1 && 1<=Arg_0 && Arg_0<=Arg_4 && 1<=Arg_1 && Arg_0+1<=Arg_2 && Arg_2<=1+Arg_0 && 1+Arg_0<=Arg_2 && Arg_2<=1+Arg_0 && 2<=Arg_1 && Arg_1<=1+Arg_0 && Arg_0<=Arg_4 && Arg_1<1+Arg_0 && 1<=Arg_1 && Arg_0<=Arg_4 && Arg_0+1<=Arg_2 && Arg_2<=1+Arg_0 of depth 1:

new bound:

Arg_4*Arg_4+6*Arg_4+5 {O(n^2)}

MPRF:

eval_foo_bb2_in [0 ]
eval_foo_bb3_in [0 ]
n_eval_foo_bb4_in___3 [0 ]
eval_foo_bb1_in [0 ]
eval_foo_bb5_in [0 ]
n_eval_foo_bb4_in___1 [Arg_0+1-Arg_1 ]
n_eval_foo_bb3_in___2 [Arg_0+2-Arg_1 ]

MPRF for transition 73:n_eval_foo_bb3_in___2(Arg_0,Arg_1,Arg_2,Arg_4) -> eval_foo_bb5_in(Arg_0,Arg_1,Arg_2,Arg_4):|:1<=Arg_4 && 3<=Arg_2+Arg_4 && Arg_2<=1+Arg_4 && 3<=Arg_1+Arg_4 && Arg_1<=1+Arg_4 && 2<=Arg_0+Arg_4 && Arg_0<=Arg_4 && Arg_2<=1+Arg_0 && 2<=Arg_2 && 4<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 3<=Arg_0+Arg_2 && 1+Arg_0<=Arg_2 && Arg_1<=1+Arg_0 && 2<=Arg_1 && 3<=Arg_0+Arg_1 && 1<=Arg_0 && 0<=Arg_4 && 1<=Arg_2+Arg_4 && Arg_2<=1+Arg_4 && 1<=Arg_1+Arg_4 && Arg_1<=1+Arg_4 && 0<=Arg_0+Arg_4 && Arg_0<=Arg_4 && Arg_2<=1+Arg_0 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 1<=Arg_0+Arg_2 && 1+Arg_0<=Arg_2 && Arg_1<=1+Arg_0 && 1<=Arg_1 && 1<=Arg_0+Arg_1 && 0<=Arg_0 && Arg_2<=Arg_1 of depth 1:

new bound:

Arg_4+1 {O(n)}

MPRF:

eval_foo_bb2_in [Arg_0+1 ]
eval_foo_bb3_in [Arg_0+1 ]
eval_foo_bb1_in [Arg_0+1 ]
eval_foo_bb5_in [Arg_2-1 ]
n_eval_foo_bb4_in___1 [Arg_0+1 ]
n_eval_foo_bb4_in___3 [Arg_0+Arg_1 ]
n_eval_foo_bb3_in___2 [Arg_2 ]

MPRF for transition 67:n_eval_foo_bb4_in___1(Arg_0,Arg_1,Arg_2,Arg_4) -> n_eval_foo_bb3_in___2(Arg_0,Arg_1+1,Arg_0+1,Arg_4):|:2<=Arg_4 && 5<=Arg_2+Arg_4 && Arg_2<=1+Arg_4 && 4<=Arg_1+Arg_4 && Arg_1<=Arg_4 && 4<=Arg_0+Arg_4 && Arg_0<=Arg_4 && Arg_2<=1+Arg_0 && 3<=Arg_2 && 5<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 5<=Arg_0+Arg_2 && 1+Arg_0<=Arg_2 && Arg_1<=Arg_0 && 2<=Arg_1 && 4<=Arg_0+Arg_1 && 2<=Arg_0 && Arg_0<=Arg_4 && Arg_1<1+Arg_0 && 2<=Arg_1 && Arg_0+1<=Arg_2 && Arg_2<=1+Arg_0 && 1<=Arg_1 && Arg_1<=Arg_0 && Arg_0<=Arg_4 && Arg_0+1<=Arg_2 && Arg_2<=1+Arg_0 of depth 1:

new bound:

Arg_4*Arg_4+5*Arg_4+4 {O(n^2)}

MPRF:

eval_foo_bb2_in [0 ]
eval_foo_bb3_in [0 ]
n_eval_foo_bb4_in___3 [0 ]
eval_foo_bb1_in [0 ]
eval_foo_bb5_in [0 ]
n_eval_foo_bb4_in___1 [Arg_0+1-Arg_1 ]
n_eval_foo_bb3_in___2 [Arg_0+1-Arg_1 ]

CFR did not improve the program. Rolling back

All Bounds

Timebounds

Overall timebound:4*Arg_4*Arg_4+13*Arg_4+11 {O(n^2)}
20: eval_foo_bb0_in->eval_foo_bb1_in: 1 {O(1)}
21: eval_foo_bb1_in->eval_foo_bb2_in: Arg_4+1 {O(n)}
22: eval_foo_bb1_in->eval_foo_bb6_in: 1 {O(1)}
23: eval_foo_bb2_in->eval_foo_bb3_in: Arg_4+1 {O(n)}
24: eval_foo_bb3_in->eval_foo_bb4_in: 2*Arg_4*Arg_4+6*Arg_4+3 {O(n^2)}
25: eval_foo_bb3_in->eval_foo_bb5_in: Arg_4+1 {O(n)}
26: eval_foo_bb4_in->eval_foo_bb3_in: 2*Arg_4*Arg_4+2*Arg_4 {O(n^2)}
27: eval_foo_bb5_in->eval_foo_bb1_in: 2*Arg_4+1 {O(n)}
28: eval_foo_bb6_in->eval_foo_stop: 1 {O(1)}
29: eval_foo_start->eval_foo_bb0_in: 1 {O(1)}

Costbounds

Overall costbound: 4*Arg_4*Arg_4+13*Arg_4+11 {O(n^2)}
20: eval_foo_bb0_in->eval_foo_bb1_in: 1 {O(1)}
21: eval_foo_bb1_in->eval_foo_bb2_in: Arg_4+1 {O(n)}
22: eval_foo_bb1_in->eval_foo_bb6_in: 1 {O(1)}
23: eval_foo_bb2_in->eval_foo_bb3_in: Arg_4+1 {O(n)}
24: eval_foo_bb3_in->eval_foo_bb4_in: 2*Arg_4*Arg_4+6*Arg_4+3 {O(n^2)}
25: eval_foo_bb3_in->eval_foo_bb5_in: Arg_4+1 {O(n)}
26: eval_foo_bb4_in->eval_foo_bb3_in: 2*Arg_4*Arg_4+2*Arg_4 {O(n^2)}
27: eval_foo_bb5_in->eval_foo_bb1_in: 2*Arg_4+1 {O(n)}
28: eval_foo_bb6_in->eval_foo_stop: 1 {O(1)}
29: eval_foo_start->eval_foo_bb0_in: 1 {O(1)}

Sizebounds

20: eval_foo_bb0_in->eval_foo_bb1_in, Arg_0: Arg_4 {O(n)}
20: eval_foo_bb0_in->eval_foo_bb1_in, Arg_1: Arg_1 {O(n)}
20: eval_foo_bb0_in->eval_foo_bb1_in, Arg_2: Arg_2 {O(n)}
20: eval_foo_bb0_in->eval_foo_bb1_in, Arg_4: Arg_4 {O(n)}
21: eval_foo_bb1_in->eval_foo_bb2_in, Arg_0: Arg_4+1 {O(n)}
21: eval_foo_bb1_in->eval_foo_bb2_in, Arg_1: 2*Arg_4*Arg_4+2*Arg_4+Arg_1+2 {O(n^2)}
21: eval_foo_bb1_in->eval_foo_bb2_in, Arg_2: 2*Arg_4+Arg_2+4 {O(n)}
21: eval_foo_bb1_in->eval_foo_bb2_in, Arg_4: Arg_4 {O(n)}
22: eval_foo_bb1_in->eval_foo_bb6_in, Arg_0: 2*Arg_4+1 {O(n)}
22: eval_foo_bb1_in->eval_foo_bb6_in, Arg_1: 2*Arg_4*Arg_4+2*Arg_4+Arg_1+2 {O(n^2)}
22: eval_foo_bb1_in->eval_foo_bb6_in, Arg_2: 2*Arg_4+Arg_2+4 {O(n)}
22: eval_foo_bb1_in->eval_foo_bb6_in, Arg_4: 2*Arg_4 {O(n)}
23: eval_foo_bb2_in->eval_foo_bb3_in, Arg_0: Arg_4+1 {O(n)}
23: eval_foo_bb2_in->eval_foo_bb3_in, Arg_1: 1 {O(1)}
23: eval_foo_bb2_in->eval_foo_bb3_in, Arg_2: Arg_4+2 {O(n)}
23: eval_foo_bb2_in->eval_foo_bb3_in, Arg_4: Arg_4 {O(n)}
24: eval_foo_bb3_in->eval_foo_bb4_in, Arg_0: Arg_4+1 {O(n)}
24: eval_foo_bb3_in->eval_foo_bb4_in, Arg_1: 2*Arg_4*Arg_4+2*Arg_4+1 {O(n^2)}
24: eval_foo_bb3_in->eval_foo_bb4_in, Arg_2: Arg_4+2 {O(n)}
24: eval_foo_bb3_in->eval_foo_bb4_in, Arg_4: Arg_4 {O(n)}
25: eval_foo_bb3_in->eval_foo_bb5_in, Arg_0: Arg_4+1 {O(n)}
25: eval_foo_bb3_in->eval_foo_bb5_in, Arg_1: 2*Arg_4*Arg_4+2*Arg_4+2 {O(n^2)}
25: eval_foo_bb3_in->eval_foo_bb5_in, Arg_2: 2*Arg_4+4 {O(n)}
25: eval_foo_bb3_in->eval_foo_bb5_in, Arg_4: Arg_4 {O(n)}
26: eval_foo_bb4_in->eval_foo_bb3_in, Arg_0: Arg_4+1 {O(n)}
26: eval_foo_bb4_in->eval_foo_bb3_in, Arg_1: 2*Arg_4*Arg_4+2*Arg_4+1 {O(n^2)}
26: eval_foo_bb4_in->eval_foo_bb3_in, Arg_2: Arg_4+2 {O(n)}
26: eval_foo_bb4_in->eval_foo_bb3_in, Arg_4: Arg_4 {O(n)}
27: eval_foo_bb5_in->eval_foo_bb1_in, Arg_0: Arg_4+1 {O(n)}
27: eval_foo_bb5_in->eval_foo_bb1_in, Arg_1: 2*Arg_4*Arg_4+2*Arg_4+2 {O(n^2)}
27: eval_foo_bb5_in->eval_foo_bb1_in, Arg_2: 2*Arg_4+4 {O(n)}
27: eval_foo_bb5_in->eval_foo_bb1_in, Arg_4: Arg_4 {O(n)}
28: eval_foo_bb6_in->eval_foo_stop, Arg_0: 2*Arg_4+1 {O(n)}
28: eval_foo_bb6_in->eval_foo_stop, Arg_1: 2*Arg_4*Arg_4+2*Arg_4+Arg_1+2 {O(n^2)}
28: eval_foo_bb6_in->eval_foo_stop, Arg_2: 2*Arg_4+Arg_2+4 {O(n)}
28: eval_foo_bb6_in->eval_foo_stop, Arg_4: 2*Arg_4 {O(n)}
29: eval_foo_start->eval_foo_bb0_in, Arg_0: Arg_0 {O(n)}
29: eval_foo_start->eval_foo_bb0_in, Arg_1: Arg_1 {O(n)}
29: eval_foo_start->eval_foo_bb0_in, Arg_2: Arg_2 {O(n)}
29: eval_foo_start->eval_foo_bb0_in, Arg_4: Arg_4 {O(n)}