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_1,Arg_1,Arg_2,Arg_3):|:Arg_3<=2*Arg_2
2:eval_foo_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_foo_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3):|:2*Arg_2<Arg_3
3: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 && Arg_3<=1 && 1<=Arg_3
4: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
5: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_3<1
6:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_foo_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3):|:1<Arg_3
7:eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_foo_bb1_in(Arg_0+1-2*Arg_2,Arg_1,Arg_2,Arg_3)
8: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_3<=1 && Arg_3<=1+Arg_0 && 1<=Arg_3 && 1<=Arg_0+Arg_3 && 0<=Arg_0 for location eval_foo_bb2_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_1,Arg_1,Arg_2,Arg_3):|:Arg_3<=2*Arg_2
2:eval_foo_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_foo_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3):|:2*Arg_2<Arg_3
3: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 && Arg_3<=1 && 1<=Arg_3
4: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
5: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_3<1
6:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_foo_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3):|:1<Arg_3
7:eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_foo_bb1_in(Arg_0+1-2*Arg_2,Arg_1,Arg_2,Arg_3):|:Arg_3<=1 && Arg_3<=1+Arg_0 && 1<=Arg_3 && 1<=Arg_0+Arg_3 && 0<=Arg_0
8: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)

Analysing control-flow refined program

Found invariant Arg_3<=1 && Arg_3<=Arg_2 && Arg_3<=1+Arg_1 && 1<=Arg_3 && 2<=Arg_2+Arg_3 && 1<=Arg_1+Arg_3 && 1<=Arg_2 && 1<=Arg_1+Arg_2 && 0<=Arg_1 && 1+Arg_0<=Arg_1 for location n_eval_foo_bb1_in___2

Found invariant Arg_3<=1 && Arg_3<=Arg_2 && Arg_3<=Arg_1 && Arg_3<=1+Arg_0 && 1<=Arg_3 && 2<=Arg_2+Arg_3 && 2<=Arg_1+Arg_3 && 1<=Arg_0+Arg_3 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && 1<=Arg_0+Arg_2 && 1<=Arg_1 && 1<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 0<=Arg_0 for location n_eval_foo_bb2_in___1

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

Found invariant Arg_3<=1 && Arg_3<=Arg_2 && Arg_3<=1+Arg_1 && Arg_3<=1+Arg_0 && 1<=Arg_3 && 2<=Arg_2+Arg_3 && 1<=Arg_1+Arg_3 && 1<=Arg_0+Arg_3 && 1<=Arg_2 && 1<=Arg_1+Arg_2 && 1<=Arg_0+Arg_2 && Arg_1<=Arg_0 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 0<=Arg_0 for location n_eval_foo_bb2_in___3

MPRF for transition 59:n_eval_foo_bb1_in___2(Arg_0,Arg_1,Arg_2,Arg_3) -> n_eval_foo_bb2_in___1(Arg_0,Arg_1,Arg_2,1):|:Arg_3<=1 && Arg_3<=Arg_2 && Arg_3<=1+Arg_1 && 1<=Arg_3 && 2<=Arg_2+Arg_3 && 1<=Arg_1+Arg_3 && 1<=Arg_2 && 1<=Arg_1+Arg_2 && 0<=Arg_1 && 1+Arg_0<=Arg_1 && Arg_3<=1 && 1<=Arg_3 && Arg_3<=1 && 1<=Arg_3 && 1<=Arg_0+2*Arg_2 && 0<=Arg_0 && Arg_3<=1 && 1<=Arg_3 of depth 1:

new bound:

2*Arg_1+2*Arg_2+1 {O(n)}

MPRF:

n_eval_foo_bb2_in___1 [Arg_0+2-2*Arg_3 ]
n_eval_foo_bb1_in___2 [Arg_0+1 ]

MPRF for transition 61:n_eval_foo_bb2_in___1(Arg_0,Arg_1,Arg_2,Arg_3) -> n_eval_foo_bb1_in___2(Arg_0+1-2*Arg_2,Arg_1,Arg_2,1):|:Arg_3<=1 && Arg_3<=Arg_2 && Arg_3<=Arg_1 && Arg_3<=1+Arg_0 && 1<=Arg_3 && 2<=Arg_2+Arg_3 && 2<=Arg_1+Arg_3 && 1<=Arg_0+Arg_3 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && 1<=Arg_0+Arg_2 && 1<=Arg_1 && 1<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 0<=Arg_0 && 1<=Arg_0+2*Arg_2 && 0<=Arg_0 && Arg_3<=1 && 1<=Arg_3 && 0<=Arg_0 && Arg_3<=1 && 1<=Arg_3 of depth 1:

new bound:

2*Arg_1+2*Arg_2+1 {O(n)}

MPRF:

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

CFR: Improvement to new bound with the following program:

new bound:

4*Arg_1+4*Arg_2+2 {O(n)}

cfr-program:

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_bb3_in, eval_foo_start, eval_foo_stop, n_eval_foo_bb1_in___2, n_eval_foo_bb2_in___1, n_eval_foo_bb2_in___3
Transitions:
1:eval_foo_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_foo_bb1_in(Arg_1,Arg_1,Arg_2,Arg_3):|:Arg_3<=2*Arg_2
2:eval_foo_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_foo_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3):|:2*Arg_2<Arg_3
4: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_0 && Arg_0<=Arg_1 && Arg_0<0
5: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_0 && Arg_0<=Arg_1 && Arg_3<1
6: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_0 && Arg_0<=Arg_1 && 1<Arg_3
60:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3) -> n_eval_foo_bb2_in___3(Arg_0,Arg_1,Arg_2,1):|:Arg_1<=Arg_0 && Arg_0<=Arg_1 && Arg_0<=Arg_1 && Arg_1<=Arg_0 && Arg_3<=2*Arg_2 && 0<=Arg_0 && Arg_3<=1 && 1<=Arg_3
8: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)
69:n_eval_foo_bb1_in___2(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_foo_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_3<=1 && Arg_3<=Arg_2 && Arg_3<=1+Arg_1 && 1<=Arg_3 && 2<=Arg_2+Arg_3 && 1<=Arg_1+Arg_3 && 1<=Arg_2 && 1<=Arg_1+Arg_2 && 0<=Arg_1 && 1+Arg_0<=Arg_1 && Arg_0<0
59:n_eval_foo_bb1_in___2(Arg_0,Arg_1,Arg_2,Arg_3) -> n_eval_foo_bb2_in___1(Arg_0,Arg_1,Arg_2,1):|:Arg_3<=1 && Arg_3<=Arg_2 && Arg_3<=1+Arg_1 && 1<=Arg_3 && 2<=Arg_2+Arg_3 && 1<=Arg_1+Arg_3 && 1<=Arg_2 && 1<=Arg_1+Arg_2 && 0<=Arg_1 && 1+Arg_0<=Arg_1 && Arg_3<=1 && 1<=Arg_3 && Arg_3<=1 && 1<=Arg_3 && 1<=Arg_0+2*Arg_2 && 0<=Arg_0 && Arg_3<=1 && 1<=Arg_3
61:n_eval_foo_bb2_in___1(Arg_0,Arg_1,Arg_2,Arg_3) -> n_eval_foo_bb1_in___2(Arg_0+1-2*Arg_2,Arg_1,Arg_2,1):|:Arg_3<=1 && Arg_3<=Arg_2 && Arg_3<=Arg_1 && Arg_3<=1+Arg_0 && 1<=Arg_3 && 2<=Arg_2+Arg_3 && 2<=Arg_1+Arg_3 && 1<=Arg_0+Arg_3 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && 1<=Arg_0+Arg_2 && 1<=Arg_1 && 1<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 0<=Arg_0 && 1<=Arg_0+2*Arg_2 && 0<=Arg_0 && Arg_3<=1 && 1<=Arg_3 && 0<=Arg_0 && Arg_3<=1 && 1<=Arg_3
62:n_eval_foo_bb2_in___3(Arg_0,Arg_1,Arg_2,Arg_3) -> n_eval_foo_bb1_in___2(Arg_0+1-2*Arg_2,Arg_1,Arg_2,1):|:Arg_3<=1 && Arg_3<=Arg_2 && Arg_3<=1+Arg_1 && Arg_3<=1+Arg_0 && 1<=Arg_3 && 2<=Arg_2+Arg_3 && 1<=Arg_1+Arg_3 && 1<=Arg_0+Arg_3 && 1<=Arg_2 && 1<=Arg_1+Arg_2 && 1<=Arg_0+Arg_2 && Arg_1<=Arg_0 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 0<=Arg_0 && 1<=2*Arg_2 && 0<=Arg_0 && Arg_0<=Arg_1 && Arg_1<=Arg_0 && Arg_3<=1 && 1<=Arg_3 && 0<=Arg_0 && Arg_3<=1 && 1<=Arg_3

All Bounds

Timebounds

Overall timebound:4*Arg_1+4*Arg_2+12 {O(n)}
1: eval_foo_bb0_in->eval_foo_bb1_in: 1 {O(1)}
2: eval_foo_bb0_in->eval_foo_bb3_in: 1 {O(1)}
4: eval_foo_bb1_in->eval_foo_bb3_in: 1 {O(1)}
5: eval_foo_bb1_in->eval_foo_bb3_in: 1 {O(1)}
6: eval_foo_bb1_in->eval_foo_bb3_in: 1 {O(1)}
60: eval_foo_bb1_in->n_eval_foo_bb2_in___3: 1 {O(1)}
8: eval_foo_bb3_in->eval_foo_stop: 1 {O(1)}
0: eval_foo_start->eval_foo_bb0_in: 1 {O(1)}
59: n_eval_foo_bb1_in___2->n_eval_foo_bb2_in___1: 2*Arg_1+2*Arg_2+1 {O(n)}
69: n_eval_foo_bb1_in___2->eval_foo_bb3_in: 1 {O(1)}
61: n_eval_foo_bb2_in___1->n_eval_foo_bb1_in___2: 2*Arg_1+2*Arg_2+1 {O(n)}
62: n_eval_foo_bb2_in___3->n_eval_foo_bb1_in___2: 1 {O(1)}

Costbounds

Overall costbound: 4*Arg_1+4*Arg_2+12 {O(n)}
1: eval_foo_bb0_in->eval_foo_bb1_in: 1 {O(1)}
2: eval_foo_bb0_in->eval_foo_bb3_in: 1 {O(1)}
4: eval_foo_bb1_in->eval_foo_bb3_in: 1 {O(1)}
5: eval_foo_bb1_in->eval_foo_bb3_in: 1 {O(1)}
6: eval_foo_bb1_in->eval_foo_bb3_in: 1 {O(1)}
60: eval_foo_bb1_in->n_eval_foo_bb2_in___3: 1 {O(1)}
8: eval_foo_bb3_in->eval_foo_stop: 1 {O(1)}
0: eval_foo_start->eval_foo_bb0_in: 1 {O(1)}
59: n_eval_foo_bb1_in___2->n_eval_foo_bb2_in___1: 2*Arg_1+2*Arg_2+1 {O(n)}
69: n_eval_foo_bb1_in___2->eval_foo_bb3_in: 1 {O(1)}
61: n_eval_foo_bb2_in___1->n_eval_foo_bb1_in___2: 2*Arg_1+2*Arg_2+1 {O(n)}
62: n_eval_foo_bb2_in___3->n_eval_foo_bb1_in___2: 1 {O(1)}

Sizebounds

1: eval_foo_bb0_in->eval_foo_bb1_in, Arg_0: Arg_1 {O(n)}
1: eval_foo_bb0_in->eval_foo_bb1_in, Arg_1: Arg_1 {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_bb0_in->eval_foo_bb3_in, Arg_0: Arg_0 {O(n)}
2: eval_foo_bb0_in->eval_foo_bb3_in, Arg_1: Arg_1 {O(n)}
2: eval_foo_bb0_in->eval_foo_bb3_in, Arg_2: Arg_2 {O(n)}
2: eval_foo_bb0_in->eval_foo_bb3_in, Arg_3: Arg_3 {O(n)}
4: eval_foo_bb1_in->eval_foo_bb3_in, Arg_0: Arg_1 {O(n)}
4: eval_foo_bb1_in->eval_foo_bb3_in, Arg_1: Arg_1 {O(n)}
4: eval_foo_bb1_in->eval_foo_bb3_in, Arg_2: Arg_2 {O(n)}
4: eval_foo_bb1_in->eval_foo_bb3_in, Arg_3: Arg_3 {O(n)}
5: eval_foo_bb1_in->eval_foo_bb3_in, Arg_0: Arg_1 {O(n)}
5: eval_foo_bb1_in->eval_foo_bb3_in, Arg_1: Arg_1 {O(n)}
5: eval_foo_bb1_in->eval_foo_bb3_in, Arg_2: Arg_2 {O(n)}
5: eval_foo_bb1_in->eval_foo_bb3_in, Arg_3: Arg_3 {O(n)}
6: eval_foo_bb1_in->eval_foo_bb3_in, Arg_0: Arg_1 {O(n)}
6: eval_foo_bb1_in->eval_foo_bb3_in, Arg_1: Arg_1 {O(n)}
6: eval_foo_bb1_in->eval_foo_bb3_in, Arg_2: Arg_2 {O(n)}
6: eval_foo_bb1_in->eval_foo_bb3_in, Arg_3: Arg_3 {O(n)}
60: eval_foo_bb1_in->n_eval_foo_bb2_in___3, Arg_0: Arg_1 {O(n)}
60: eval_foo_bb1_in->n_eval_foo_bb2_in___3, Arg_1: Arg_1 {O(n)}
60: eval_foo_bb1_in->n_eval_foo_bb2_in___3, Arg_2: Arg_2 {O(n)}
60: eval_foo_bb1_in->n_eval_foo_bb2_in___3, Arg_3: 1 {O(1)}
8: eval_foo_bb3_in->eval_foo_stop, Arg_0: 2*2^(2*Arg_1+2*Arg_2+1)*Arg_1+2*2^(2*Arg_1+2*Arg_2+1)*Arg_1*Arg_2+2*2^(2*Arg_1+2*Arg_2+1)*Arg_2*Arg_2+2^(2*Arg_1+2*Arg_2+1)*4*Arg_2+2*Arg_2+5*Arg_1+Arg_0 {O(EXP)}
8: eval_foo_bb3_in->eval_foo_stop, Arg_1: 6*Arg_1 {O(n)}
8: eval_foo_bb3_in->eval_foo_stop, Arg_2: 6*Arg_2 {O(n)}
8: eval_foo_bb3_in->eval_foo_stop, Arg_3: 4*Arg_3+1 {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)}
59: n_eval_foo_bb1_in___2->n_eval_foo_bb2_in___1, Arg_0: 2*2^(2*Arg_1+2*Arg_2+1)*Arg_1+2*2^(2*Arg_1+2*Arg_2+1)*Arg_1*Arg_2+2*2^(2*Arg_1+2*Arg_2+1)*Arg_2*Arg_2+2^(2*Arg_1+2*Arg_2+1)*4*Arg_2 {O(EXP)}
59: n_eval_foo_bb1_in___2->n_eval_foo_bb2_in___1, Arg_1: Arg_1 {O(n)}
59: n_eval_foo_bb1_in___2->n_eval_foo_bb2_in___1, Arg_2: Arg_2 {O(n)}
59: n_eval_foo_bb1_in___2->n_eval_foo_bb2_in___1, Arg_3: 1 {O(1)}
69: n_eval_foo_bb1_in___2->eval_foo_bb3_in, Arg_0: 2*2^(2*Arg_1+2*Arg_2+1)*Arg_1+2*2^(2*Arg_1+2*Arg_2+1)*Arg_1*Arg_2+2*2^(2*Arg_1+2*Arg_2+1)*Arg_2*Arg_2+2^(2*Arg_1+2*Arg_2+1)*4*Arg_2+2*Arg_1+2*Arg_2 {O(EXP)}
69: n_eval_foo_bb1_in___2->eval_foo_bb3_in, Arg_1: 2*Arg_1 {O(n)}
69: n_eval_foo_bb1_in___2->eval_foo_bb3_in, Arg_2: 2*Arg_2 {O(n)}
69: n_eval_foo_bb1_in___2->eval_foo_bb3_in, Arg_3: 1 {O(1)}
61: n_eval_foo_bb2_in___1->n_eval_foo_bb1_in___2, Arg_0: 2*2^(2*Arg_1+2*Arg_2+1)*Arg_1+2*2^(2*Arg_1+2*Arg_2+1)*Arg_1*Arg_2+2*2^(2*Arg_1+2*Arg_2+1)*Arg_2*Arg_2+2^(2*Arg_1+2*Arg_2+1)*4*Arg_2 {O(EXP)}
61: n_eval_foo_bb2_in___1->n_eval_foo_bb1_in___2, Arg_1: Arg_1 {O(n)}
61: n_eval_foo_bb2_in___1->n_eval_foo_bb1_in___2, Arg_2: Arg_2 {O(n)}
61: n_eval_foo_bb2_in___1->n_eval_foo_bb1_in___2, Arg_3: 1 {O(1)}
62: n_eval_foo_bb2_in___3->n_eval_foo_bb1_in___2, Arg_0: 2*Arg_1+2*Arg_2 {O(n)}
62: n_eval_foo_bb2_in___3->n_eval_foo_bb1_in___2, Arg_1: Arg_1 {O(n)}
62: n_eval_foo_bb2_in___3->n_eval_foo_bb1_in___2, Arg_2: Arg_2 {O(n)}
62: n_eval_foo_bb2_in___3->n_eval_foo_bb1_in___2, Arg_3: 1 {O(1)}