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_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_3,Arg_2,Arg_3)
2:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3):|:0<=Arg_0
3:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_foo_bb3_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_bb1_in(Arg_0+Arg_1,Arg_1-1,Arg_2,Arg_3):|:0<=Arg_1
5:eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_foo_bb1_in(Arg_0+Arg_1,Arg_1,Arg_2,Arg_3):|:Arg_1<0
6:eval_foo_bb3_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

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

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

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

Found invariant Arg_1<=Arg_3 for location eval_foo_bb1_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_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_3,Arg_2,Arg_3)
2: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_1<=Arg_3 && 0<=Arg_0
3:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_foo_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_1<=Arg_3 && Arg_0<0
4:eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_foo_bb1_in(Arg_0+Arg_1,Arg_1-1,Arg_2,Arg_3):|:Arg_1<=Arg_3 && 0<=Arg_0 && 0<=Arg_1
5:eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_foo_bb1_in(Arg_0+Arg_1,Arg_1,Arg_2,Arg_3):|:Arg_1<=Arg_3 && 0<=Arg_0 && Arg_1<0
6:eval_foo_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_foo_stop(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_1<=Arg_3 && 1+Arg_0<=0
0: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 4:eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_foo_bb1_in(Arg_0+Arg_1,Arg_1-1,Arg_2,Arg_3):|:Arg_1<=Arg_3 && 0<=Arg_0 && 0<=Arg_1 of depth 1:

new bound:

Arg_3+1 {O(n)}

MPRF:

eval_foo_bb2_in [Arg_1+1 ]
eval_foo_bb1_in [Arg_1+1 ]

MPRF for transition 2: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_1<=Arg_3 && 0<=Arg_0 of depth 1:

new bound:

Arg_3*Arg_3*Arg_3+5*Arg_3*Arg_3+Arg_2*Arg_3+2*Arg_2+9*Arg_3+7 {O(n^3)}

MPRF:

eval_foo_bb2_in [Arg_0+1 ]
eval_foo_bb1_in [Arg_0+2 ]

MPRF for transition 5:eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_foo_bb1_in(Arg_0+Arg_1,Arg_1,Arg_2,Arg_3):|:Arg_1<=Arg_3 && 0<=Arg_0 && Arg_1<0 of depth 1:

new bound:

Arg_3*Arg_3*Arg_3+5*Arg_3*Arg_3+Arg_2*Arg_3+2*Arg_2+8*Arg_3+5 {O(n^3)}

MPRF:

eval_foo_bb2_in [Arg_0+1 ]
eval_foo_bb1_in [Arg_0+1 ]

Analysing control-flow refined program

Cut unsatisfiable transition 67: n_eval_foo_bb1_in___4->eval_foo_bb3_in

Found invariant Arg_3<=Arg_0 && 0<=Arg_3 && 0<=Arg_2+Arg_3 && 0<=1+Arg_1+Arg_3 && 1+Arg_1<=Arg_3 && 0<=Arg_0+Arg_3 && Arg_2<=Arg_0 && 0<=Arg_2 && 0<=1+Arg_1+Arg_2 && 0<=Arg_0+Arg_2 && 1+Arg_1<=Arg_0 && 0<=1+Arg_1 && 0<=1+Arg_0+Arg_1 && 0<=Arg_0 for location n_eval_foo_bb2_in___2

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

Found invariant Arg_1<=Arg_3 && 0<=Arg_2 && 1+Arg_1<=Arg_2 && 1+Arg_1<=0 && Arg_1<=Arg_0 for location n_eval_foo_bb1_in___3

Found invariant Arg_3<=Arg_0 && 0<=Arg_3 && 0<=Arg_2+Arg_3 && 0<=1+Arg_1+Arg_3 && 1+Arg_1<=Arg_3 && 0<=Arg_0+Arg_3 && Arg_2<=Arg_0 && 0<=Arg_2 && 0<=1+Arg_1+Arg_2 && 0<=Arg_0+Arg_2 && 1+Arg_1<=Arg_0 && 0<=1+Arg_1 && 0<=1+Arg_0+Arg_1 && 0<=Arg_0 for location n_eval_foo_bb1_in___4

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

Found invariant Arg_3<=Arg_1 && Arg_1<=Arg_3 && Arg_2<=Arg_0 && 0<=Arg_2 && 0<=Arg_0+Arg_2 && Arg_0<=Arg_2 && 0<=Arg_0 for location n_eval_foo_bb2_in___5

Found invariant Arg_1<=Arg_3 && 0<=Arg_2 && 1+Arg_1<=Arg_2 && 0<=Arg_0+Arg_2 && 1+Arg_1<=0 && 1+Arg_1<=Arg_0 && 0<=Arg_0 for location n_eval_foo_bb2_in___1

Found invariant Arg_3<=Arg_1 && Arg_1<=Arg_3 && Arg_2<=Arg_0 && Arg_0<=Arg_2 for location eval_foo_bb1_in

MPRF for transition 52:n_eval_foo_bb1_in___4(Arg_0,Arg_1,Arg_2,Arg_3) -> n_eval_foo_bb2_in___2(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_3<=Arg_0 && 0<=Arg_3 && 0<=Arg_2+Arg_3 && 0<=1+Arg_1+Arg_3 && 1+Arg_1<=Arg_3 && 0<=Arg_0+Arg_3 && Arg_2<=Arg_0 && 0<=Arg_2 && 0<=1+Arg_1+Arg_2 && 0<=Arg_0+Arg_2 && 1+Arg_1<=Arg_0 && 0<=1+Arg_1 && 0<=1+Arg_0+Arg_1 && 0<=Arg_0 && Arg_1<=Arg_3 && 0<=Arg_0 && 0<=Arg_0 && Arg_1<=Arg_3 && 0<=1+Arg_1 && 1+Arg_1<=Arg_0 && 1+Arg_1<=Arg_3 && 0<=Arg_0 && Arg_1<=Arg_3 of depth 1:

new bound:

Arg_3+3 {O(n)}

MPRF:

n_eval_foo_bb2_in___2 [Arg_1+1 ]
n_eval_foo_bb1_in___4 [Arg_1+2 ]

MPRF for transition 56:n_eval_foo_bb2_in___2(Arg_0,Arg_1,Arg_2,Arg_3) -> n_eval_foo_bb1_in___4(Arg_0+Arg_1,Arg_1-1,Arg_2,Arg_3):|:Arg_3<=Arg_0 && 0<=Arg_3 && 0<=Arg_2+Arg_3 && 0<=1+Arg_1+Arg_3 && 1+Arg_1<=Arg_3 && 0<=Arg_0+Arg_3 && Arg_2<=Arg_0 && 0<=Arg_2 && 0<=1+Arg_1+Arg_2 && 0<=Arg_0+Arg_2 && 1+Arg_1<=Arg_0 && 0<=1+Arg_1 && 0<=1+Arg_0+Arg_1 && 0<=Arg_0 && 1+Arg_1<=Arg_3 && 1+Arg_1<=Arg_0 && 0<=1+Arg_1 && 0<=Arg_0 && 0<=Arg_1 && Arg_1<=Arg_3 of depth 1:

new bound:

Arg_3+2 {O(n)}

MPRF:

n_eval_foo_bb2_in___2 [Arg_1+1 ]
n_eval_foo_bb1_in___4 [Arg_1+1 ]

MPRF for transition 51:n_eval_foo_bb1_in___3(Arg_0,Arg_1,Arg_2,Arg_3) -> n_eval_foo_bb2_in___1(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_1<=Arg_3 && 0<=Arg_2 && 1+Arg_1<=Arg_2 && 1+Arg_1<=0 && Arg_1<=Arg_0 && Arg_1<=Arg_3 && Arg_1<0 && 0<=Arg_0 && Arg_1<=Arg_3 of depth 1:

new bound:

2^(Arg_3+2)*Arg_2+2^(Arg_3+2)*Arg_3+Arg_2+Arg_3+3 {O(EXP)}

MPRF:

n_eval_foo_bb2_in___1 [Arg_0 ]
n_eval_foo_bb1_in___3 [Arg_0+1 ]

MPRF for transition 54:n_eval_foo_bb2_in___1(Arg_0,Arg_1,Arg_2,Arg_3) -> n_eval_foo_bb1_in___3(Arg_0+Arg_1,Arg_1,Arg_2,Arg_3):|:Arg_1<=Arg_3 && 0<=Arg_2 && 1+Arg_1<=Arg_2 && 0<=Arg_0+Arg_2 && 1+Arg_1<=0 && 1+Arg_1<=Arg_0 && 0<=Arg_0 && Arg_1<0 && Arg_1<=Arg_3 && 0<=Arg_0 && 0<=Arg_0 && Arg_1<=Arg_3 && Arg_1<0 of depth 1:

new bound:

2^(Arg_3+2)*Arg_2+2^(Arg_3+2)*Arg_3+2*Arg_3+Arg_2+2 {O(EXP)}

MPRF:

n_eval_foo_bb2_in___1 [Arg_0+1 ]
n_eval_foo_bb1_in___3 [Arg_0-Arg_1 ]

CFR did not improve the program. Rolling back

All Bounds

Timebounds

Overall timebound:2*Arg_3*Arg_3*Arg_3+10*Arg_3*Arg_3+2*Arg_2*Arg_3+18*Arg_3+4*Arg_2+17 {O(n^3)}
1: eval_foo_bb0_in->eval_foo_bb1_in: 1 {O(1)}
2: eval_foo_bb1_in->eval_foo_bb2_in: Arg_3*Arg_3*Arg_3+5*Arg_3*Arg_3+Arg_2*Arg_3+2*Arg_2+9*Arg_3+7 {O(n^3)}
3: eval_foo_bb1_in->eval_foo_bb3_in: 1 {O(1)}
4: eval_foo_bb2_in->eval_foo_bb1_in: Arg_3+1 {O(n)}
5: eval_foo_bb2_in->eval_foo_bb1_in: Arg_3*Arg_3*Arg_3+5*Arg_3*Arg_3+Arg_2*Arg_3+2*Arg_2+8*Arg_3+5 {O(n^3)}
6: eval_foo_bb3_in->eval_foo_stop: 1 {O(1)}
0: eval_foo_start->eval_foo_bb0_in: 1 {O(1)}

Costbounds

Overall costbound: 2*Arg_3*Arg_3*Arg_3+10*Arg_3*Arg_3+2*Arg_2*Arg_3+18*Arg_3+4*Arg_2+17 {O(n^3)}
1: eval_foo_bb0_in->eval_foo_bb1_in: 1 {O(1)}
2: eval_foo_bb1_in->eval_foo_bb2_in: Arg_3*Arg_3*Arg_3+5*Arg_3*Arg_3+Arg_2*Arg_3+2*Arg_2+9*Arg_3+7 {O(n^3)}
3: eval_foo_bb1_in->eval_foo_bb3_in: 1 {O(1)}
4: eval_foo_bb2_in->eval_foo_bb1_in: Arg_3+1 {O(n)}
5: eval_foo_bb2_in->eval_foo_bb1_in: Arg_3*Arg_3*Arg_3+5*Arg_3*Arg_3+Arg_2*Arg_3+2*Arg_2+8*Arg_3+5 {O(n^3)}
6: eval_foo_bb3_in->eval_foo_stop: 1 {O(1)}
0: eval_foo_start->eval_foo_bb0_in: 1 {O(1)}

Sizebounds

1: eval_foo_bb0_in->eval_foo_bb1_in, Arg_0: Arg_2 {O(n)}
1: eval_foo_bb0_in->eval_foo_bb1_in, Arg_1: Arg_3 {O(n)}
1: eval_foo_bb0_in->eval_foo_bb1_in, Arg_2: Arg_2 {O(n)}
1: eval_foo_bb0_in->eval_foo_bb1_in, Arg_3: Arg_3 {O(n)}
2: eval_foo_bb1_in->eval_foo_bb2_in, Arg_0: Arg_3*Arg_3+4*Arg_3+Arg_2+3 {O(n^2)}
2: eval_foo_bb1_in->eval_foo_bb2_in, Arg_1: Arg_3+1 {O(n)}
2: eval_foo_bb1_in->eval_foo_bb2_in, Arg_2: Arg_2 {O(n)}
2: eval_foo_bb1_in->eval_foo_bb2_in, Arg_3: Arg_3 {O(n)}
3: eval_foo_bb1_in->eval_foo_bb3_in, Arg_0: Arg_3*Arg_3+2*Arg_2+4*Arg_3+3 {O(n^2)}
3: eval_foo_bb1_in->eval_foo_bb3_in, Arg_1: 2*Arg_3+1 {O(n)}
3: eval_foo_bb1_in->eval_foo_bb3_in, Arg_2: 2*Arg_2 {O(n)}
3: eval_foo_bb1_in->eval_foo_bb3_in, Arg_3: 2*Arg_3 {O(n)}
4: eval_foo_bb2_in->eval_foo_bb1_in, Arg_0: Arg_3*Arg_3+4*Arg_3+Arg_2+3 {O(n^2)}
4: eval_foo_bb2_in->eval_foo_bb1_in, Arg_1: Arg_3+1 {O(n)}
4: eval_foo_bb2_in->eval_foo_bb1_in, Arg_2: Arg_2 {O(n)}
4: eval_foo_bb2_in->eval_foo_bb1_in, Arg_3: Arg_3 {O(n)}
5: eval_foo_bb2_in->eval_foo_bb1_in, Arg_0: Arg_3*Arg_3+4*Arg_3+Arg_2+3 {O(n^2)}
5: eval_foo_bb2_in->eval_foo_bb1_in, Arg_1: Arg_3+1 {O(n)}
5: eval_foo_bb2_in->eval_foo_bb1_in, Arg_2: Arg_2 {O(n)}
5: eval_foo_bb2_in->eval_foo_bb1_in, Arg_3: Arg_3 {O(n)}
6: eval_foo_bb3_in->eval_foo_stop, Arg_0: Arg_3*Arg_3+2*Arg_2+4*Arg_3+3 {O(n^2)}
6: eval_foo_bb3_in->eval_foo_stop, Arg_1: 2*Arg_3+1 {O(n)}
6: eval_foo_bb3_in->eval_foo_stop, Arg_2: 2*Arg_2 {O(n)}
6: eval_foo_bb3_in->eval_foo_stop, Arg_3: 2*Arg_3 {O(n)}
0: eval_foo_start->eval_foo_bb0_in, Arg_0: Arg_0 {O(n)}
0: eval_foo_start->eval_foo_bb0_in, Arg_1: Arg_1 {O(n)}
0: eval_foo_start->eval_foo_bb0_in, Arg_2: Arg_2 {O(n)}
0: eval_foo_start->eval_foo_bb0_in, Arg_3: Arg_3 {O(n)}