Initial Problem

Start: eval_foo_start
Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3, 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_start, eval_foo_stop
Transitions:
1:eval_foo_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_foo_bb1_in(Arg_3,Arg_1,Arg_2,Arg_3,Arg_4)
2:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_foo_bb2_in(Arg_0,1,Arg_2,Arg_3,Arg_4):|:0<=Arg_0
3:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_foo_bb5_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:Arg_0<0
4:eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_foo_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:Arg_1<Arg_0
5:eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_foo_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:Arg_0<=Arg_1
6:eval_foo_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_foo_bb2_in(Arg_0,2*Arg_1,Arg_2,Arg_3,Arg_4)
7:eval_foo_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_foo_bb1_in(Arg_0-1,Arg_1,Arg_2,Arg_3,Arg_4)
8:eval_foo_bb5_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_foo_stop(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4)
0:eval_foo_start(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_foo_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4)

Preprocessing

Eliminate variables {Arg_2,Arg_4} that do not contribute to the problem

Found invariant Arg_0<=Arg_3 && 1+Arg_0<=0 for location eval_foo_bb5_in

Found invariant Arg_0<=Arg_3 && 1+Arg_0<=0 for location eval_foo_stop

Found invariant 2<=Arg_3 && 3<=Arg_1+Arg_3 && 1+Arg_1<=Arg_3 && 4<=Arg_0+Arg_3 && Arg_0<=Arg_3 && 1+Arg_1<=Arg_0 && 1<=Arg_1 && 3<=Arg_0+Arg_1 && 2<=Arg_0 for location eval_foo_bb3_in

Found invariant 0<=Arg_3 && 1<=Arg_1+Arg_3 && 0<=Arg_0+Arg_3 && Arg_0<=Arg_3 && 1<=Arg_1 && 1<=Arg_0+Arg_1 && 0<=Arg_0 for location eval_foo_bb2_in

Found invariant Arg_0<=Arg_3 for location eval_foo_bb1_in

Found invariant 0<=Arg_3 && 1<=Arg_1+Arg_3 && 0<=Arg_0+Arg_3 && Arg_0<=Arg_3 && 1<=Arg_1 && 1<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 0<=Arg_0 for location eval_foo_bb4_in

Problem after Preprocessing

Start: eval_foo_start
Program_Vars: Arg_0, Arg_1, 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:
18:eval_foo_bb0_in(Arg_0,Arg_1,Arg_3) -> eval_foo_bb1_in(Arg_3,Arg_1,Arg_3)
19:eval_foo_bb1_in(Arg_0,Arg_1,Arg_3) -> eval_foo_bb2_in(Arg_0,1,Arg_3):|:Arg_0<=Arg_3 && 0<=Arg_0
20:eval_foo_bb1_in(Arg_0,Arg_1,Arg_3) -> eval_foo_bb5_in(Arg_0,Arg_1,Arg_3):|:Arg_0<=Arg_3 && Arg_0<0
21:eval_foo_bb2_in(Arg_0,Arg_1,Arg_3) -> eval_foo_bb3_in(Arg_0,Arg_1,Arg_3):|:0<=Arg_3 && 1<=Arg_1+Arg_3 && 0<=Arg_0+Arg_3 && Arg_0<=Arg_3 && 1<=Arg_1 && 1<=Arg_0+Arg_1 && 0<=Arg_0 && Arg_1<Arg_0
22:eval_foo_bb2_in(Arg_0,Arg_1,Arg_3) -> eval_foo_bb4_in(Arg_0,Arg_1,Arg_3):|:0<=Arg_3 && 1<=Arg_1+Arg_3 && 0<=Arg_0+Arg_3 && Arg_0<=Arg_3 && 1<=Arg_1 && 1<=Arg_0+Arg_1 && 0<=Arg_0 && Arg_0<=Arg_1
23:eval_foo_bb3_in(Arg_0,Arg_1,Arg_3) -> eval_foo_bb2_in(Arg_0,2*Arg_1,Arg_3):|:2<=Arg_3 && 3<=Arg_1+Arg_3 && 1+Arg_1<=Arg_3 && 4<=Arg_0+Arg_3 && Arg_0<=Arg_3 && 1+Arg_1<=Arg_0 && 1<=Arg_1 && 3<=Arg_0+Arg_1 && 2<=Arg_0
24:eval_foo_bb4_in(Arg_0,Arg_1,Arg_3) -> eval_foo_bb1_in(Arg_0-1,Arg_1,Arg_3):|:0<=Arg_3 && 1<=Arg_1+Arg_3 && 0<=Arg_0+Arg_3 && Arg_0<=Arg_3 && 1<=Arg_1 && 1<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 0<=Arg_0
25:eval_foo_bb5_in(Arg_0,Arg_1,Arg_3) -> eval_foo_stop(Arg_0,Arg_1,Arg_3):|:Arg_0<=Arg_3 && 1+Arg_0<=0
26:eval_foo_start(Arg_0,Arg_1,Arg_3) -> eval_foo_bb0_in(Arg_0,Arg_1,Arg_3)

MPRF for transition 19:eval_foo_bb1_in(Arg_0,Arg_1,Arg_3) -> eval_foo_bb2_in(Arg_0,1,Arg_3):|:Arg_0<=Arg_3 && 0<=Arg_0 of depth 1:

new bound:

Arg_3+1 {O(n)}

MPRF:

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

MPRF for transition 22:eval_foo_bb2_in(Arg_0,Arg_1,Arg_3) -> eval_foo_bb4_in(Arg_0,Arg_1,Arg_3):|:0<=Arg_3 && 1<=Arg_1+Arg_3 && 0<=Arg_0+Arg_3 && Arg_0<=Arg_3 && 1<=Arg_1 && 1<=Arg_0+Arg_1 && 0<=Arg_0 && Arg_0<=Arg_1 of depth 1:

new bound:

Arg_3+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_3) -> eval_foo_bb1_in(Arg_0-1,Arg_1,Arg_3):|:0<=Arg_3 && 1<=Arg_1+Arg_3 && 0<=Arg_0+Arg_3 && Arg_0<=Arg_3 && 1<=Arg_1 && 1<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 0<=Arg_0 of depth 1:

new bound:

Arg_3+1 {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+1 ]

MPRF for transition 21:eval_foo_bb2_in(Arg_0,Arg_1,Arg_3) -> eval_foo_bb3_in(Arg_0,Arg_1,Arg_3):|:0<=Arg_3 && 1<=Arg_1+Arg_3 && 0<=Arg_0+Arg_3 && Arg_0<=Arg_3 && 1<=Arg_1 && 1<=Arg_0+Arg_1 && 0<=Arg_0 && Arg_1<Arg_0 of depth 1:

new bound:

Arg_3*Arg_3+2*Arg_3 {O(n^2)}

MPRF:

eval_foo_bb1_in [Arg_3 ]
eval_foo_bb4_in [-Arg_1 ]
eval_foo_bb3_in [Arg_3-Arg_1-1 ]
eval_foo_bb2_in [Arg_3-Arg_1 ]

MPRF for transition 23:eval_foo_bb3_in(Arg_0,Arg_1,Arg_3) -> eval_foo_bb2_in(Arg_0,2*Arg_1,Arg_3):|:2<=Arg_3 && 3<=Arg_1+Arg_3 && 1+Arg_1<=Arg_3 && 4<=Arg_0+Arg_3 && Arg_0<=Arg_3 && 1+Arg_1<=Arg_0 && 1<=Arg_1 && 3<=Arg_0+Arg_1 && 2<=Arg_0 of depth 1:

new bound:

Arg_3*Arg_3+3*Arg_3+1 {O(n^2)}

MPRF:

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

Analysing control-flow refined program

Cut unsatisfiable transition 91: n_eval_foo_bb1_in___3->eval_foo_bb5_in

Found invariant Arg_0<=Arg_3 && 1+Arg_0<=0 for location eval_foo_bb5_in

Found invariant 0<=Arg_3 && 1<=Arg_1+Arg_3 && Arg_1<=1+Arg_3 && 0<=Arg_0+Arg_3 && Arg_0<=Arg_3 && Arg_1<=1 && Arg_1<=1+Arg_0 && Arg_0+Arg_1<=2 && 1<=Arg_1 && 1<=Arg_0+Arg_1 && Arg_0<=Arg_1 && Arg_0<=1 && 0<=Arg_0 for location n_eval_foo_bb4_in___7

Found invariant Arg_0<=Arg_3 && 1+Arg_0<=0 for location eval_foo_stop

Found invariant 2<=Arg_3 && 4<=Arg_1+Arg_3 && 3<=Arg_0+Arg_3 && 1+Arg_0<=Arg_3 && 2<=Arg_1 && 3<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 1<=Arg_0 for location n_eval_foo_bb1_in___3

Found invariant 3<=Arg_3 && 5<=Arg_1+Arg_3 && 1+Arg_1<=Arg_3 && 6<=Arg_0+Arg_3 && Arg_0<=Arg_3 && 1+Arg_1<=Arg_0 && 2<=Arg_1 && 5<=Arg_0+Arg_1 && 3<=Arg_0 for location n_eval_foo_bb3_in___5

Found invariant 0<=Arg_3 && 1<=Arg_1+Arg_3 && Arg_1<=1+Arg_3 && 0<=1+Arg_0+Arg_3 && 1+Arg_0<=Arg_3 && Arg_1<=1 && Arg_1<=2+Arg_0 && Arg_0+Arg_1<=1 && 1<=Arg_1 && 0<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && Arg_0<=0 && 0<=1+Arg_0 for location n_eval_foo_bb1_in___2

Found invariant 2<=Arg_3 && 3<=Arg_1+Arg_3 && 1+Arg_1<=Arg_3 && 4<=Arg_0+Arg_3 && Arg_0<=Arg_3 && Arg_1<=1 && 1+Arg_1<=Arg_0 && 1<=Arg_1 && 3<=Arg_0+Arg_1 && 2<=Arg_0 for location n_eval_foo_bb3_in___8

Found invariant 1<=Arg_3 && 2<=Arg_1+Arg_3 && Arg_1<=Arg_3 && 1<=Arg_0+Arg_3 && 1+Arg_0<=Arg_3 && Arg_1<=1 && Arg_1<=1+Arg_0 && Arg_0+Arg_1<=1 && 1<=Arg_1 && 1<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && Arg_0<=0 && 0<=Arg_0 for location n_eval_foo_bb2_in___1

Found invariant Arg_3<=Arg_0 && Arg_0<=Arg_3 for location eval_foo_bb1_in

Found invariant 2<=Arg_3 && 4<=Arg_1+Arg_3 && 4<=Arg_0+Arg_3 && Arg_0<=Arg_3 && 2<=Arg_1 && 4<=Arg_0+Arg_1 && 2<=Arg_0 for location n_eval_foo_bb2_in___6

Found invariant 0<=Arg_3 && 1<=Arg_1+Arg_3 && Arg_1<=1+Arg_3 && 0<=Arg_0+Arg_3 && Arg_0<=Arg_3 && Arg_1<=1 && Arg_1<=1+Arg_0 && 1<=Arg_1 && 1<=Arg_0+Arg_1 && 0<=Arg_0 for location n_eval_foo_bb2_in___9

Found invariant 2<=Arg_3 && 4<=Arg_1+Arg_3 && 4<=Arg_0+Arg_3 && Arg_0<=Arg_3 && 2<=Arg_1 && 4<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 2<=Arg_0 for location n_eval_foo_bb4_in___4

MPRF for transition 71:n_eval_foo_bb1_in___3(Arg_0,Arg_1,Arg_3) -> n_eval_foo_bb2_in___9(Arg_0,1,Arg_3):|:2<=Arg_3 && 4<=Arg_1+Arg_3 && 3<=Arg_0+Arg_3 && 1+Arg_0<=Arg_3 && 2<=Arg_1 && 3<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 1<=Arg_0 && Arg_0<=Arg_3 && 0<=Arg_0 && 0<=Arg_0 && Arg_0<=Arg_3 && 1+Arg_0<=Arg_3 && 1<=Arg_1 && 0<=1+Arg_0 && 1+Arg_0<=Arg_1 && 0<=Arg_0 && Arg_0<=Arg_3 of depth 1:

new bound:

Arg_3 {O(n)}

MPRF:

n_eval_foo_bb2_in___9 [Arg_0 ]
n_eval_foo_bb3_in___5 [Arg_0 ]
n_eval_foo_bb3_in___8 [Arg_0 ]
n_eval_foo_bb2_in___6 [Arg_0 ]
n_eval_foo_bb4_in___4 [Arg_0 ]
n_eval_foo_bb1_in___3 [Arg_0+1 ]

MPRF for transition 74:n_eval_foo_bb2_in___6(Arg_0,Arg_1,Arg_3) -> n_eval_foo_bb4_in___4(Arg_0,Arg_1,Arg_3):|:2<=Arg_3 && 4<=Arg_1+Arg_3 && 4<=Arg_0+Arg_3 && Arg_0<=Arg_3 && 2<=Arg_1 && 4<=Arg_0+Arg_1 && 2<=Arg_0 && Arg_0<=Arg_3 && 1<=Arg_1 && 0<=Arg_0 && 2<=Arg_1 && 2+Arg_1<=2*Arg_0 && Arg_0<=Arg_3 && 1<=Arg_1 && 0<=Arg_0 && Arg_0<=Arg_1 && Arg_0<=Arg_3 of depth 1:

new bound:

Arg_3+2 {O(n)}

MPRF:

n_eval_foo_bb2_in___9 [Arg_0+2 ]
n_eval_foo_bb3_in___5 [Arg_0+2 ]
n_eval_foo_bb3_in___8 [Arg_0+2*Arg_1 ]
n_eval_foo_bb2_in___6 [Arg_0+2 ]
n_eval_foo_bb4_in___4 [Arg_0+1 ]
n_eval_foo_bb1_in___3 [Arg_0+2 ]

MPRF for transition 75:n_eval_foo_bb2_in___9(Arg_0,Arg_1,Arg_3) -> n_eval_foo_bb3_in___8(Arg_0,Arg_1,Arg_3):|:0<=Arg_3 && 1<=Arg_1+Arg_3 && Arg_1<=1+Arg_3 && 0<=Arg_0+Arg_3 && Arg_0<=Arg_3 && Arg_1<=1 && Arg_1<=1+Arg_0 && 1<=Arg_1 && 1<=Arg_0+Arg_1 && 0<=Arg_0 && Arg_0<=Arg_3 && 1<=Arg_1 && 0<=Arg_0 && Arg_1<=1 && 1<=Arg_1 && 0<=Arg_0 && Arg_0<=Arg_3 && 1<=Arg_1 && Arg_1<Arg_0 && Arg_0<=Arg_3 of depth 1:

new bound:

Arg_3+1 {O(n)}

MPRF:

n_eval_foo_bb2_in___9 [Arg_0+1 ]
n_eval_foo_bb3_in___5 [Arg_0 ]
n_eval_foo_bb3_in___8 [Arg_0 ]
n_eval_foo_bb2_in___6 [Arg_0 ]
n_eval_foo_bb4_in___4 [Arg_0 ]
n_eval_foo_bb1_in___3 [Arg_0+1 ]

MPRF for transition 78:n_eval_foo_bb3_in___8(Arg_0,Arg_1,Arg_3) -> n_eval_foo_bb2_in___6(Arg_0,2*Arg_1,Arg_3):|:2<=Arg_3 && 3<=Arg_1+Arg_3 && 1+Arg_1<=Arg_3 && 4<=Arg_0+Arg_3 && Arg_0<=Arg_3 && Arg_1<=1 && 1+Arg_1<=Arg_0 && 1<=Arg_1 && 3<=Arg_0+Arg_1 && 2<=Arg_0 && Arg_0<=Arg_3 && 1<Arg_0 && Arg_1<=1 && 1<=Arg_1 && 1<=Arg_1 && 1+Arg_1<=Arg_0 && Arg_0<=Arg_3 of depth 1:

new bound:

Arg_3+1 {O(n)}

MPRF:

n_eval_foo_bb2_in___9 [Arg_0-Arg_1 ]
n_eval_foo_bb3_in___5 [Arg_0-2 ]
n_eval_foo_bb3_in___8 [Arg_0-1 ]
n_eval_foo_bb2_in___6 [Arg_0-2 ]
n_eval_foo_bb4_in___4 [Arg_0-2 ]
n_eval_foo_bb1_in___3 [Arg_0-1 ]

MPRF for transition 79:n_eval_foo_bb4_in___4(Arg_0,Arg_1,Arg_3) -> n_eval_foo_bb1_in___3(Arg_0-1,Arg_1,Arg_3):|:2<=Arg_3 && 4<=Arg_1+Arg_3 && 4<=Arg_0+Arg_3 && Arg_0<=Arg_3 && 2<=Arg_1 && 4<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 2<=Arg_0 && Arg_0<=Arg_3 && 2+Arg_1<=2*Arg_0 && Arg_0<=Arg_1 && 1<=Arg_1 && 0<=Arg_0 && Arg_0<=Arg_1 && Arg_0<=Arg_3 of depth 1:

new bound:

Arg_3 {O(n)}

MPRF:

n_eval_foo_bb2_in___9 [Arg_0 ]
n_eval_foo_bb3_in___5 [Arg_0 ]
n_eval_foo_bb3_in___8 [Arg_0 ]
n_eval_foo_bb2_in___6 [Arg_0 ]
n_eval_foo_bb4_in___4 [Arg_0 ]
n_eval_foo_bb1_in___3 [Arg_0 ]

MPRF for transition 73:n_eval_foo_bb2_in___6(Arg_0,Arg_1,Arg_3) -> n_eval_foo_bb3_in___5(Arg_0,Arg_1,Arg_3):|:2<=Arg_3 && 4<=Arg_1+Arg_3 && 4<=Arg_0+Arg_3 && Arg_0<=Arg_3 && 2<=Arg_1 && 4<=Arg_0+Arg_1 && 2<=Arg_0 && Arg_0<=Arg_3 && 1<=Arg_1 && 0<=Arg_0 && 2<=Arg_1 && 2+Arg_1<=2*Arg_0 && Arg_0<=Arg_3 && 1<=Arg_1 && Arg_1<Arg_0 && Arg_0<=Arg_3 of depth 1:

new bound:

2*Arg_3*Arg_3+2*Arg_3 {O(n^2)}

MPRF:

n_eval_foo_bb1_in___3 [2*Arg_0 ]
n_eval_foo_bb4_in___4 [2*Arg_0-Arg_1 ]
n_eval_foo_bb2_in___9 [2*Arg_0 ]
n_eval_foo_bb3_in___5 [2*Arg_0-2*Arg_1 ]
n_eval_foo_bb3_in___8 [2*Arg_0-2*Arg_1 ]
n_eval_foo_bb2_in___6 [2*Arg_0-Arg_1 ]

MPRF for transition 77:n_eval_foo_bb3_in___5(Arg_0,Arg_1,Arg_3) -> n_eval_foo_bb2_in___6(Arg_0,2*Arg_1,Arg_3):|:3<=Arg_3 && 5<=Arg_1+Arg_3 && 1+Arg_1<=Arg_3 && 6<=Arg_0+Arg_3 && Arg_0<=Arg_3 && 1+Arg_1<=Arg_0 && 2<=Arg_1 && 5<=Arg_0+Arg_1 && 3<=Arg_0 && Arg_0<=Arg_3 && Arg_1<Arg_0 && 2<=Arg_1 && 1<=Arg_1 && 1+Arg_1<=Arg_0 && Arg_0<=Arg_3 of depth 1:

new bound:

2*Arg_3*Arg_3+2*Arg_3 {O(n^2)}

MPRF:

n_eval_foo_bb1_in___3 [2*Arg_0 ]
n_eval_foo_bb4_in___4 [2*Arg_0-Arg_1-3 ]
n_eval_foo_bb2_in___9 [2*Arg_0 ]
n_eval_foo_bb3_in___5 [2*Arg_0-2*Arg_1-1 ]
n_eval_foo_bb3_in___8 [2*Arg_0 ]
n_eval_foo_bb2_in___6 [2*Arg_0-Arg_1-3 ]

MPRF for transition 70:n_eval_foo_bb1_in___2(Arg_0,Arg_1,Arg_3) -> n_eval_foo_bb2_in___1(Arg_0,1,Arg_3):|:0<=Arg_3 && 1<=Arg_1+Arg_3 && Arg_1<=1+Arg_3 && 0<=1+Arg_0+Arg_3 && 1+Arg_0<=Arg_3 && Arg_1<=1 && Arg_1<=2+Arg_0 && Arg_0+Arg_1<=1 && 1<=Arg_1 && 0<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && Arg_0<=0 && 0<=1+Arg_0 && Arg_0<=Arg_3 && Arg_0<=1 && 1+Arg_0<=Arg_3 && 1<=Arg_1 && 0<=1+Arg_0 && 1+Arg_0<=Arg_1 && 0<=Arg_0 && Arg_0<=Arg_3 of depth 1:

new bound:

1 {O(1)}

MPRF:

n_eval_foo_bb2_in___1 [0 ]
n_eval_foo_bb4_in___7 [Arg_0 ]
n_eval_foo_bb1_in___2 [Arg_0+1 ]

MPRF for transition 72:n_eval_foo_bb2_in___1(Arg_0,Arg_1,Arg_3) -> n_eval_foo_bb4_in___7(Arg_0,Arg_1,Arg_3):|:1<=Arg_3 && 2<=Arg_1+Arg_3 && Arg_1<=Arg_3 && 1<=Arg_0+Arg_3 && 1+Arg_0<=Arg_3 && Arg_1<=1 && Arg_1<=1+Arg_0 && Arg_0+Arg_1<=1 && 1<=Arg_1 && 1<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && Arg_0<=0 && 0<=Arg_0 && Arg_0<=Arg_3 && 1<=Arg_1 && Arg_0<=Arg_1 && 0<=Arg_0 && Arg_1<=1 && 1<=Arg_1 && 0<=Arg_0 && Arg_0<=Arg_3 && Arg_0<=Arg_3 && 0<=Arg_0 && 1<=Arg_1 && Arg_0<=Arg_1 && 1<=Arg_1 && 0<=Arg_0 && Arg_0<=Arg_1 && Arg_0<=Arg_3 of depth 1:

new bound:

1 {O(1)}

MPRF:

n_eval_foo_bb2_in___1 [1 ]
n_eval_foo_bb4_in___7 [Arg_0 ]
n_eval_foo_bb1_in___2 [Arg_0+1 ]

MPRF for transition 80:n_eval_foo_bb4_in___7(Arg_0,Arg_1,Arg_3) -> n_eval_foo_bb1_in___2(Arg_0-1,Arg_1,Arg_3):|:0<=Arg_3 && 1<=Arg_1+Arg_3 && Arg_1<=1+Arg_3 && 0<=Arg_0+Arg_3 && Arg_0<=Arg_3 && Arg_1<=1 && Arg_1<=1+Arg_0 && Arg_0+Arg_1<=2 && 1<=Arg_1 && 1<=Arg_0+Arg_1 && Arg_0<=Arg_1 && Arg_0<=1 && 0<=Arg_0 && Arg_0<=1 && 0<=Arg_0 && Arg_0<=Arg_3 && Arg_1<=1 && 1<=Arg_1 && 1<=Arg_1 && 0<=Arg_0 && Arg_0<=Arg_1 && Arg_0<=Arg_3 of depth 1:

new bound:

2 {O(1)}

MPRF:

n_eval_foo_bb2_in___1 [1 ]
n_eval_foo_bb4_in___7 [Arg_0+1 ]
n_eval_foo_bb1_in___2 [Arg_0+1 ]

CFR did not improve the program. Rolling back

All Bounds

Timebounds

Overall timebound:2*Arg_3*Arg_3+8*Arg_3+8 {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_3+1 {O(n)}
20: eval_foo_bb1_in->eval_foo_bb5_in: 1 {O(1)}
21: eval_foo_bb2_in->eval_foo_bb3_in: Arg_3*Arg_3+2*Arg_3 {O(n^2)}
22: eval_foo_bb2_in->eval_foo_bb4_in: Arg_3+1 {O(n)}
23: eval_foo_bb3_in->eval_foo_bb2_in: Arg_3*Arg_3+3*Arg_3+1 {O(n^2)}
24: eval_foo_bb4_in->eval_foo_bb1_in: Arg_3+1 {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_3*Arg_3+8*Arg_3+8 {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_3+1 {O(n)}
20: eval_foo_bb1_in->eval_foo_bb5_in: 1 {O(1)}
21: eval_foo_bb2_in->eval_foo_bb3_in: Arg_3*Arg_3+2*Arg_3 {O(n^2)}
22: eval_foo_bb2_in->eval_foo_bb4_in: Arg_3+1 {O(n)}
23: eval_foo_bb3_in->eval_foo_bb2_in: Arg_3*Arg_3+3*Arg_3+1 {O(n^2)}
24: eval_foo_bb4_in->eval_foo_bb1_in: Arg_3+1 {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_3 {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_3: Arg_3 {O(n)}
19: eval_foo_bb1_in->eval_foo_bb2_in, Arg_0: Arg_3+1 {O(n)}
19: eval_foo_bb1_in->eval_foo_bb2_in, Arg_1: 1 {O(1)}
19: eval_foo_bb1_in->eval_foo_bb2_in, Arg_3: Arg_3 {O(n)}
20: eval_foo_bb1_in->eval_foo_bb5_in, Arg_0: 2*Arg_3+1 {O(n)}
20: eval_foo_bb1_in->eval_foo_bb5_in, Arg_1: 2^(Arg_3*Arg_3+3*Arg_3+1)+Arg_1+1 {O(EXP)}
20: eval_foo_bb1_in->eval_foo_bb5_in, Arg_3: 2*Arg_3 {O(n)}
21: eval_foo_bb2_in->eval_foo_bb3_in, Arg_0: Arg_3+1 {O(n)}
21: eval_foo_bb2_in->eval_foo_bb3_in, Arg_1: 2^(Arg_3*Arg_3+3*Arg_3+1) {O(EXP)}
21: eval_foo_bb2_in->eval_foo_bb3_in, Arg_3: Arg_3 {O(n)}
22: eval_foo_bb2_in->eval_foo_bb4_in, Arg_0: Arg_3+1 {O(n)}
22: eval_foo_bb2_in->eval_foo_bb4_in, Arg_1: 2^(Arg_3*Arg_3+3*Arg_3+1)+1 {O(EXP)}
22: eval_foo_bb2_in->eval_foo_bb4_in, Arg_3: Arg_3 {O(n)}
23: eval_foo_bb3_in->eval_foo_bb2_in, Arg_0: Arg_3+1 {O(n)}
23: eval_foo_bb3_in->eval_foo_bb2_in, Arg_1: 2^(Arg_3*Arg_3+3*Arg_3+1) {O(EXP)}
23: eval_foo_bb3_in->eval_foo_bb2_in, Arg_3: Arg_3 {O(n)}
24: eval_foo_bb4_in->eval_foo_bb1_in, Arg_0: Arg_3+1 {O(n)}
24: eval_foo_bb4_in->eval_foo_bb1_in, Arg_1: 2^(Arg_3*Arg_3+3*Arg_3+1)+1 {O(EXP)}
24: eval_foo_bb4_in->eval_foo_bb1_in, Arg_3: Arg_3 {O(n)}
25: eval_foo_bb5_in->eval_foo_stop, Arg_0: 2*Arg_3+1 {O(n)}
25: eval_foo_bb5_in->eval_foo_stop, Arg_1: 2^(Arg_3*Arg_3+3*Arg_3+1)+Arg_1+1 {O(EXP)}
25: eval_foo_bb5_in->eval_foo_stop, Arg_3: 2*Arg_3 {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_3: Arg_3 {O(n)}