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_bb6_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,Arg_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_bb6_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_0,1,Arg_0+1,Arg_3,Arg_4)
5:eval_foo_bb3_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_1<=Arg_2
6:eval_foo_bb3_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_2<Arg_1
7:eval_foo_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_foo_bb3_in(Arg_0,Arg_1+1,Arg_2,Arg_3,Arg_4)
8:eval_foo_bb5_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_foo_bb1_in(Arg_2-2,Arg_1,Arg_2,Arg_3,Arg_4)
9:eval_foo_bb6_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_4} that do not contribute to the problem

Found invariant 0<=Arg_3 && 1<=Arg_2+Arg_3 && Arg_2<=1+Arg_3 && 2<=Arg_1+Arg_3 && Arg_1<=2+Arg_3 && 0<=Arg_0+Arg_3 && Arg_0<=Arg_3 && 1+Arg_2<=Arg_1 && Arg_2<=1+Arg_0 && 1<=Arg_2 && 3<=Arg_1+Arg_2 && Arg_1<=1+Arg_2 && 1<=Arg_0+Arg_2 && 1+Arg_0<=Arg_2 && Arg_1<=2+Arg_0 && 2<=Arg_1 && 2<=Arg_0+Arg_1 && 2+Arg_0<=Arg_1 && 0<=Arg_0 for location eval_foo_bb5_in

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

Found invariant 0<=Arg_3 && 1<=Arg_2+Arg_3 && Arg_2<=1+Arg_3 && 1<=Arg_1+Arg_3 && Arg_1<=2+Arg_3 && 0<=Arg_0+Arg_3 && Arg_0<=Arg_3 && Arg_2<=1+Arg_0 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && Arg_1<=1+Arg_2 && 1<=Arg_0+Arg_2 && 1+Arg_0<=Arg_2 && Arg_1<=2+Arg_0 && 1<=Arg_1 && 1<=Arg_0+Arg_1 && 0<=Arg_0 for location eval_foo_bb3_in

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

Found invariant Arg_0<=Arg_3 for location eval_foo_bb1_in

Found invariant Arg_0<=Arg_3 && 1+Arg_0<=0 for location eval_foo_bb6_in

Found invariant 0<=Arg_3 && 1<=Arg_2+Arg_3 && Arg_2<=1+Arg_3 && 1<=Arg_1+Arg_3 && Arg_1<=1+Arg_3 && 0<=Arg_0+Arg_3 && Arg_0<=Arg_3 && 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_bb4_in

Problem after Preprocessing

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_bb6_in, eval_foo_start, eval_foo_stop
Transitions:
20:eval_foo_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_foo_bb1_in(Arg_3,Arg_1,Arg_2,Arg_3)
21:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_0<=Arg_3 && 0<=Arg_0
22:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_foo_bb6_in(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_0<=Arg_3 && Arg_0<0
23:eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_foo_bb3_in(Arg_0,1,Arg_0+1,Arg_3):|:0<=Arg_3 && 0<=Arg_0+Arg_3 && Arg_0<=Arg_3 && 0<=Arg_0
24:eval_foo_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_foo_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3):|:0<=Arg_3 && 1<=Arg_2+Arg_3 && Arg_2<=1+Arg_3 && 1<=Arg_1+Arg_3 && Arg_1<=2+Arg_3 && 0<=Arg_0+Arg_3 && Arg_0<=Arg_3 && Arg_2<=1+Arg_0 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && Arg_1<=1+Arg_2 && 1<=Arg_0+Arg_2 && 1+Arg_0<=Arg_2 && Arg_1<=2+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_3) -> eval_foo_bb5_in(Arg_0,Arg_1,Arg_2,Arg_3):|:0<=Arg_3 && 1<=Arg_2+Arg_3 && Arg_2<=1+Arg_3 && 1<=Arg_1+Arg_3 && Arg_1<=2+Arg_3 && 0<=Arg_0+Arg_3 && Arg_0<=Arg_3 && Arg_2<=1+Arg_0 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && Arg_1<=1+Arg_2 && 1<=Arg_0+Arg_2 && 1+Arg_0<=Arg_2 && Arg_1<=2+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_3) -> eval_foo_bb3_in(Arg_0,Arg_1+1,Arg_2,Arg_3):|:0<=Arg_3 && 1<=Arg_2+Arg_3 && Arg_2<=1+Arg_3 && 1<=Arg_1+Arg_3 && Arg_1<=1+Arg_3 && 0<=Arg_0+Arg_3 && Arg_0<=Arg_3 && 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
27:eval_foo_bb5_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_foo_bb1_in(Arg_2-2,Arg_1,Arg_2,Arg_3):|:0<=Arg_3 && 1<=Arg_2+Arg_3 && Arg_2<=1+Arg_3 && 2<=Arg_1+Arg_3 && Arg_1<=2+Arg_3 && 0<=Arg_0+Arg_3 && Arg_0<=Arg_3 && 1+Arg_2<=Arg_1 && Arg_2<=1+Arg_0 && 1<=Arg_2 && 3<=Arg_1+Arg_2 && Arg_1<=1+Arg_2 && 1<=Arg_0+Arg_2 && 1+Arg_0<=Arg_2 && Arg_1<=2+Arg_0 && 2<=Arg_1 && 2<=Arg_0+Arg_1 && 2+Arg_0<=Arg_1 && 0<=Arg_0
28:eval_foo_bb6_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_foo_stop(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_0<=Arg_3 && 1+Arg_0<=0
29:eval_foo_start(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_foo_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3)

MPRF for transition 21:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_0<=Arg_3 && 0<=Arg_0 of depth 1:

new bound:

Arg_3+2 {O(n)}

MPRF:

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

MPRF for transition 23:eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_foo_bb3_in(Arg_0,1,Arg_0+1,Arg_3):|:0<=Arg_3 && 0<=Arg_0+Arg_3 && Arg_0<=Arg_3 && 0<=Arg_0 of depth 1:

new bound:

Arg_3+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 ]
eval_foo_bb1_in [Arg_0+1 ]

MPRF for transition 25:eval_foo_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_foo_bb5_in(Arg_0,Arg_1,Arg_2,Arg_3):|:0<=Arg_3 && 1<=Arg_2+Arg_3 && Arg_2<=1+Arg_3 && 1<=Arg_1+Arg_3 && Arg_1<=2+Arg_3 && 0<=Arg_0+Arg_3 && Arg_0<=Arg_3 && Arg_2<=1+Arg_0 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && Arg_1<=1+Arg_2 && 1<=Arg_0+Arg_2 && 1+Arg_0<=Arg_2 && Arg_1<=2+Arg_0 && 1<=Arg_1 && 1<=Arg_0+Arg_1 && 0<=Arg_0 && Arg_2<Arg_1 of depth 1:

new bound:

Arg_3+1 {O(n)}

MPRF:

eval_foo_bb2_in [Arg_0+1 ]
eval_foo_bb4_in [Arg_0+1 ]
eval_foo_bb3_in [Arg_0+1 ]
eval_foo_bb5_in [Arg_1-2 ]
eval_foo_bb1_in [Arg_0+1 ]

MPRF for transition 27:eval_foo_bb5_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_foo_bb1_in(Arg_2-2,Arg_1,Arg_2,Arg_3):|:0<=Arg_3 && 1<=Arg_2+Arg_3 && Arg_2<=1+Arg_3 && 2<=Arg_1+Arg_3 && Arg_1<=2+Arg_3 && 0<=Arg_0+Arg_3 && Arg_0<=Arg_3 && 1+Arg_2<=Arg_1 && Arg_2<=1+Arg_0 && 1<=Arg_2 && 3<=Arg_1+Arg_2 && Arg_1<=1+Arg_2 && 1<=Arg_0+Arg_2 && 1+Arg_0<=Arg_2 && Arg_1<=2+Arg_0 && 2<=Arg_1 && 2<=Arg_0+Arg_1 && 2+Arg_0<=Arg_1 && 0<=Arg_0 of depth 1:

new bound:

Arg_3+1 {O(n)}

MPRF:

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

MPRF for transition 24:eval_foo_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_foo_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3):|:0<=Arg_3 && 1<=Arg_2+Arg_3 && Arg_2<=1+Arg_3 && 1<=Arg_1+Arg_3 && Arg_1<=2+Arg_3 && 0<=Arg_0+Arg_3 && Arg_0<=Arg_3 && Arg_2<=1+Arg_0 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && Arg_1<=1+Arg_2 && 1<=Arg_0+Arg_2 && 1+Arg_0<=Arg_2 && Arg_1<=2+Arg_0 && 1<=Arg_1 && 1<=Arg_0+Arg_1 && 0<=Arg_0 && Arg_1<=Arg_2 of depth 1:

new bound:

Arg_3*Arg_3+4*Arg_3+3 {O(n^2)}

MPRF:

eval_foo_bb1_in [Arg_0+1 ]
eval_foo_bb2_in [Arg_0+1 ]
eval_foo_bb5_in [Arg_2-Arg_1 ]
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_3) -> eval_foo_bb3_in(Arg_0,Arg_1+1,Arg_2,Arg_3):|:0<=Arg_3 && 1<=Arg_2+Arg_3 && Arg_2<=1+Arg_3 && 1<=Arg_1+Arg_3 && Arg_1<=1+Arg_3 && 0<=Arg_0+Arg_3 && Arg_0<=Arg_3 && 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 of depth 1:

new bound:

Arg_3*Arg_3+4*Arg_3+3 {O(n^2)}

MPRF:

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

Analysing control-flow refined program

Cut unsatisfiable transition 25: eval_foo_bb3_in->eval_foo_bb5_in

Found invariant 0<=Arg_3 && 1<=Arg_2+Arg_3 && Arg_2<=1+Arg_3 && 2<=Arg_1+Arg_3 && Arg_1<=2+Arg_3 && 0<=Arg_0+Arg_3 && Arg_0<=Arg_3 && 1+Arg_2<=Arg_1 && Arg_2<=1+Arg_0 && 1<=Arg_2 && 3<=Arg_1+Arg_2 && Arg_1<=1+Arg_2 && 1<=Arg_0+Arg_2 && 1+Arg_0<=Arg_2 && Arg_1<=2+Arg_0 && 2<=Arg_1 && 2<=Arg_0+Arg_1 && 2+Arg_0<=Arg_1 && 0<=Arg_0 for location eval_foo_bb5_in

Found invariant 0<=Arg_3 && 1<=Arg_2+Arg_3 && Arg_2<=1+Arg_3 && 2<=Arg_1+Arg_3 && Arg_1<=2+Arg_3 && 0<=Arg_0+Arg_3 && Arg_0<=Arg_3 && Arg_2<=1+Arg_0 && 1<=Arg_2 && 3<=Arg_1+Arg_2 && Arg_1<=1+Arg_2 && 1<=Arg_0+Arg_2 && 1+Arg_0<=Arg_2 && Arg_1<=2+Arg_0 && 2<=Arg_1 && 2<=Arg_0+Arg_1 && 0<=Arg_0 for location n_eval_foo_bb3_in___2

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

Found invariant 1<=Arg_3 && 3<=Arg_2+Arg_3 && Arg_2<=1+Arg_3 && 3<=Arg_1+Arg_3 && Arg_1<=1+Arg_3 && 2<=Arg_0+Arg_3 && Arg_0<=Arg_3 && 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_bb4_in___1

Found invariant 0<=Arg_3 && 1<=Arg_2+Arg_3 && Arg_2<=1+Arg_3 && 1<=Arg_1+Arg_3 && Arg_1<=1+Arg_3 && 0<=Arg_0+Arg_3 && Arg_0<=Arg_3 && 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 0<=Arg_3 && 1<=Arg_2+Arg_3 && Arg_2<=1+Arg_3 && 1<=Arg_1+Arg_3 && Arg_1<=1+Arg_3 && 0<=Arg_0+Arg_3 && Arg_0<=Arg_3 && 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 n_eval_foo_bb4_in___3

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

Found invariant Arg_0<=Arg_3 for location eval_foo_bb1_in

Found invariant Arg_0<=Arg_3 && 1+Arg_0<=0 for location eval_foo_bb6_in

knowledge_propagation leads to new time bound Arg_3+1 {O(n)} for transition 66:eval_foo_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3) -> n_eval_foo_bb4_in___3(Arg_0,Arg_1,Arg_0+1,Arg_3):|:0<=Arg_3 && 1<=Arg_2+Arg_3 && Arg_2<=1+Arg_3 && 1<=Arg_1+Arg_3 && Arg_1<=1+Arg_3 && 0<=Arg_0+Arg_3 && Arg_0<=Arg_3 && 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_2<=1+Arg_3 && Arg_1<=Arg_2 && 1<=Arg_1 && Arg_0+1<=Arg_2 && Arg_2<=1+Arg_0 && 1+Arg_0<=Arg_2 && Arg_2<=1+Arg_0 && 1<=Arg_1 && Arg_1<=Arg_2 && Arg_2<=1+Arg_3 && Arg_1<=1 && 1<=Arg_1 && 1+Arg_0<=Arg_2 && Arg_2<=1+Arg_0 && 1<=Arg_2 && Arg_2<=1+Arg_3 && Arg_1<=1+Arg_0 && 1<=Arg_1 && Arg_0<=Arg_3 && Arg_0+1<=Arg_2 && Arg_2<=1+Arg_0

knowledge_propagation leads to new time bound Arg_3+1 {O(n)} for transition 68:n_eval_foo_bb4_in___3(Arg_0,Arg_1,Arg_2,Arg_3) -> n_eval_foo_bb3_in___2(Arg_0,Arg_1+1,Arg_0+1,Arg_3):|:0<=Arg_3 && 1<=Arg_2+Arg_3 && Arg_2<=1+Arg_3 && 1<=Arg_1+Arg_3 && Arg_1<=1+Arg_3 && 0<=Arg_0+Arg_3 && Arg_0<=Arg_3 && 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_2<=1+Arg_3 && 1<=Arg_2 && Arg_0+1<=Arg_2 && Arg_2<=1+Arg_0 && Arg_1<=1 && 1<=Arg_1 && 1<=Arg_1 && Arg_1<=1+Arg_0 && Arg_0<=Arg_3 && 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_3) -> n_eval_foo_bb4_in___1(Arg_0,Arg_1,Arg_0+1,Arg_3):|:0<=Arg_3 && 1<=Arg_2+Arg_3 && Arg_2<=1+Arg_3 && 2<=Arg_1+Arg_3 && Arg_1<=2+Arg_3 && 0<=Arg_0+Arg_3 && Arg_0<=Arg_3 && Arg_2<=1+Arg_0 && 1<=Arg_2 && 3<=Arg_1+Arg_2 && Arg_1<=1+Arg_2 && 1<=Arg_0+Arg_2 && 1+Arg_0<=Arg_2 && Arg_1<=2+Arg_0 && 2<=Arg_1 && 2<=Arg_0+Arg_1 && 0<=Arg_0 && Arg_2<=1+Arg_3 && 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_2 && Arg_2<=1+Arg_3 && Arg_1<=1+Arg_0 && 1<=Arg_1 && Arg_0<=Arg_3 && Arg_0+1<=Arg_2 && Arg_2<=1+Arg_0 of depth 1:

new bound:

Arg_3*Arg_3+8*Arg_3+7 {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 [Arg_2+1-Arg_1 ]
n_eval_foo_bb4_in___1 [Arg_0+3-Arg_1 ]
n_eval_foo_bb3_in___2 [Arg_2+3-Arg_1 ]

MPRF for transition 73:n_eval_foo_bb3_in___2(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_foo_bb5_in(Arg_0,Arg_1,Arg_2,Arg_3):|:0<=Arg_3 && 1<=Arg_2+Arg_3 && Arg_2<=1+Arg_3 && 2<=Arg_1+Arg_3 && Arg_1<=2+Arg_3 && 0<=Arg_0+Arg_3 && Arg_0<=Arg_3 && Arg_2<=1+Arg_0 && 1<=Arg_2 && 3<=Arg_1+Arg_2 && Arg_1<=1+Arg_2 && 1<=Arg_0+Arg_2 && 1+Arg_0<=Arg_2 && Arg_1<=2+Arg_0 && 2<=Arg_1 && 2<=Arg_0+Arg_1 && 0<=Arg_0 && 0<=Arg_3 && 1<=Arg_2+Arg_3 && Arg_2<=1+Arg_3 && 1<=Arg_1+Arg_3 && Arg_1<=2+Arg_3 && 0<=Arg_0+Arg_3 && Arg_0<=Arg_3 && Arg_2<=1+Arg_0 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && Arg_1<=1+Arg_2 && 1<=Arg_0+Arg_2 && 1+Arg_0<=Arg_2 && Arg_1<=2+Arg_0 && 1<=Arg_1 && 1<=Arg_0+Arg_1 && 0<=Arg_0 && Arg_2<Arg_1 of depth 1:

new bound:

Arg_3+1 {O(n)}

MPRF:

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

MPRF for transition 67:n_eval_foo_bb4_in___1(Arg_0,Arg_1,Arg_2,Arg_3) -> n_eval_foo_bb3_in___2(Arg_0,Arg_1+1,Arg_0+1,Arg_3):|:1<=Arg_3 && 3<=Arg_2+Arg_3 && Arg_2<=1+Arg_3 && 3<=Arg_1+Arg_3 && Arg_1<=1+Arg_3 && 2<=Arg_0+Arg_3 && Arg_0<=Arg_3 && 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_3 && Arg_1<=1+Arg_0 && 2<=Arg_1 && Arg_0+1<=Arg_2 && Arg_2<=1+Arg_0 && 1<=Arg_1 && Arg_1<=1+Arg_0 && Arg_0<=Arg_3 && Arg_0+1<=Arg_2 && Arg_2<=1+Arg_0 of depth 1:

new bound:

Arg_3*Arg_3+6*Arg_3+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 [2*Arg_0+4-2*Arg_1 ]
n_eval_foo_bb4_in___1 [Arg_0+2-Arg_1 ]
n_eval_foo_bb3_in___2 [Arg_2+1-Arg_1 ]

CFR did not improve the program. Rolling back

All Bounds

Timebounds

Overall timebound:2*Arg_3*Arg_3+12*Arg_3+15 {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_3+2 {O(n)}
22: eval_foo_bb1_in->eval_foo_bb6_in: 1 {O(1)}
23: eval_foo_bb2_in->eval_foo_bb3_in: Arg_3+1 {O(n)}
24: eval_foo_bb3_in->eval_foo_bb4_in: Arg_3*Arg_3+4*Arg_3+3 {O(n^2)}
25: eval_foo_bb3_in->eval_foo_bb5_in: Arg_3+1 {O(n)}
26: eval_foo_bb4_in->eval_foo_bb3_in: Arg_3*Arg_3+4*Arg_3+3 {O(n^2)}
27: eval_foo_bb5_in->eval_foo_bb1_in: Arg_3+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: 2*Arg_3*Arg_3+12*Arg_3+15 {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_3+2 {O(n)}
22: eval_foo_bb1_in->eval_foo_bb6_in: 1 {O(1)}
23: eval_foo_bb2_in->eval_foo_bb3_in: Arg_3+1 {O(n)}
24: eval_foo_bb3_in->eval_foo_bb4_in: Arg_3*Arg_3+4*Arg_3+3 {O(n^2)}
25: eval_foo_bb3_in->eval_foo_bb5_in: Arg_3+1 {O(n)}
26: eval_foo_bb4_in->eval_foo_bb3_in: Arg_3*Arg_3+4*Arg_3+3 {O(n^2)}
27: eval_foo_bb5_in->eval_foo_bb1_in: Arg_3+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_3 {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_3: Arg_3 {O(n)}
21: eval_foo_bb1_in->eval_foo_bb2_in, Arg_0: Arg_3+1 {O(n)}
21: eval_foo_bb1_in->eval_foo_bb2_in, Arg_1: Arg_3*Arg_3+4*Arg_3+Arg_1+4 {O(n^2)}
21: eval_foo_bb1_in->eval_foo_bb2_in, Arg_2: Arg_2+Arg_3+2 {O(n)}
21: eval_foo_bb1_in->eval_foo_bb2_in, Arg_3: Arg_3 {O(n)}
22: eval_foo_bb1_in->eval_foo_bb6_in, Arg_0: 2*Arg_3+1 {O(n)}
22: eval_foo_bb1_in->eval_foo_bb6_in, Arg_1: Arg_3*Arg_3+4*Arg_3+Arg_1+4 {O(n^2)}
22: eval_foo_bb1_in->eval_foo_bb6_in, Arg_2: Arg_2+Arg_3+2 {O(n)}
22: eval_foo_bb1_in->eval_foo_bb6_in, Arg_3: 2*Arg_3 {O(n)}
23: eval_foo_bb2_in->eval_foo_bb3_in, Arg_0: Arg_3+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_3+2 {O(n)}
23: eval_foo_bb2_in->eval_foo_bb3_in, Arg_3: Arg_3 {O(n)}
24: eval_foo_bb3_in->eval_foo_bb4_in, Arg_0: Arg_3+1 {O(n)}
24: eval_foo_bb3_in->eval_foo_bb4_in, Arg_1: Arg_3*Arg_3+4*Arg_3+4 {O(n^2)}
24: eval_foo_bb3_in->eval_foo_bb4_in, Arg_2: Arg_3+2 {O(n)}
24: eval_foo_bb3_in->eval_foo_bb4_in, Arg_3: Arg_3 {O(n)}
25: eval_foo_bb3_in->eval_foo_bb5_in, Arg_0: Arg_3+1 {O(n)}
25: eval_foo_bb3_in->eval_foo_bb5_in, Arg_1: Arg_3*Arg_3+4*Arg_3+4 {O(n^2)}
25: eval_foo_bb3_in->eval_foo_bb5_in, Arg_2: Arg_3+2 {O(n)}
25: eval_foo_bb3_in->eval_foo_bb5_in, Arg_3: Arg_3 {O(n)}
26: eval_foo_bb4_in->eval_foo_bb3_in, Arg_0: Arg_3+1 {O(n)}
26: eval_foo_bb4_in->eval_foo_bb3_in, Arg_1: Arg_3*Arg_3+4*Arg_3+4 {O(n^2)}
26: eval_foo_bb4_in->eval_foo_bb3_in, Arg_2: Arg_3+2 {O(n)}
26: eval_foo_bb4_in->eval_foo_bb3_in, Arg_3: Arg_3 {O(n)}
27: eval_foo_bb5_in->eval_foo_bb1_in, Arg_0: Arg_3+1 {O(n)}
27: eval_foo_bb5_in->eval_foo_bb1_in, Arg_1: Arg_3*Arg_3+4*Arg_3+4 {O(n^2)}
27: eval_foo_bb5_in->eval_foo_bb1_in, Arg_2: Arg_3+2 {O(n)}
27: eval_foo_bb5_in->eval_foo_bb1_in, Arg_3: Arg_3 {O(n)}
28: eval_foo_bb6_in->eval_foo_stop, Arg_0: 2*Arg_3+1 {O(n)}
28: eval_foo_bb6_in->eval_foo_stop, Arg_1: Arg_3*Arg_3+4*Arg_3+Arg_1+4 {O(n^2)}
28: eval_foo_bb6_in->eval_foo_stop, Arg_2: Arg_2+Arg_3+2 {O(n)}
28: eval_foo_bb6_in->eval_foo_stop, Arg_3: 2*Arg_3 {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_3: Arg_3 {O(n)}