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<=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):|:Arg_2<2
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_1+Arg_0
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<0
5:eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_foo_bb1_in(Arg_0+1,Arg_1-Arg_0,Arg_2,Arg_3)
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 && 0<=Arg_0+Arg_3 && Arg_2<=Arg_0 && 2<=Arg_2 && 4<=Arg_0+Arg_2 && 0<=Arg_0+Arg_1 && 2<=Arg_0 for location eval_foo_bb2_in

Found invariant Arg_1<=Arg_3 && Arg_2<=Arg_0 && 2<=Arg_2 && 4<=Arg_0+Arg_2 && 2<=Arg_0 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<=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):|:Arg_2<2
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):|:Arg_1<=Arg_3 && Arg_2<=Arg_0 && 2<=Arg_2 && 4<=Arg_0+Arg_2 && 2<=Arg_0 && 0<=Arg_1+Arg_0
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_3 && Arg_2<=Arg_0 && 2<=Arg_2 && 4<=Arg_0+Arg_2 && 2<=Arg_0 && Arg_1+Arg_0<0
5:eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_foo_bb1_in(Arg_0+1,Arg_1-Arg_0,Arg_2,Arg_3):|:Arg_1<=Arg_3 && 0<=Arg_0+Arg_3 && Arg_2<=Arg_0 && 2<=Arg_2 && 4<=Arg_0+Arg_2 && 0<=Arg_0+Arg_1 && 2<=Arg_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)

MPRF for transition 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):|:Arg_1<=Arg_3 && Arg_2<=Arg_0 && 2<=Arg_2 && 4<=Arg_0+Arg_2 && 2<=Arg_0 && 0<=Arg_1+Arg_0 of depth 1:

new bound:

Arg_2+Arg_3+1 {O(n)}

MPRF:

eval_foo_bb2_in [Arg_0+Arg_1 ]
eval_foo_bb1_in [Arg_0+Arg_1+1 ]

MPRF for transition 5:eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_foo_bb1_in(Arg_0+1,Arg_1-Arg_0,Arg_2,Arg_3):|:Arg_1<=Arg_3 && 0<=Arg_0+Arg_3 && Arg_2<=Arg_0 && 2<=Arg_2 && 4<=Arg_0+Arg_2 && 0<=Arg_0+Arg_1 && 2<=Arg_0 of depth 1:

new bound:

2*Arg_2+Arg_3+1 {O(n)}

MPRF:

eval_foo_bb2_in [Arg_0+Arg_1+1 ]
eval_foo_bb1_in [Arg_0+Arg_1+Arg_2-1 ]

All Bounds

Timebounds

Overall timebound:2*Arg_3+3*Arg_2+7 {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)}
3: eval_foo_bb1_in->eval_foo_bb2_in: Arg_2+Arg_3+1 {O(n)}
4: eval_foo_bb1_in->eval_foo_bb3_in: 1 {O(1)}
5: eval_foo_bb2_in->eval_foo_bb1_in: 2*Arg_2+Arg_3+1 {O(n)}
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+3*Arg_2+7 {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)}
3: eval_foo_bb1_in->eval_foo_bb2_in: Arg_2+Arg_3+1 {O(n)}
4: eval_foo_bb1_in->eval_foo_bb3_in: 1 {O(1)}
5: eval_foo_bb2_in->eval_foo_bb1_in: 2*Arg_2+Arg_3+1 {O(n)}
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_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)}
3: eval_foo_bb1_in->eval_foo_bb2_in, Arg_0: 3*Arg_2+Arg_3+1 {O(n)}
3: eval_foo_bb1_in->eval_foo_bb2_in, Arg_1: 5*Arg_2*Arg_3+6*Arg_2*Arg_2+Arg_3*Arg_3+4*Arg_3+8*Arg_2+2 {O(n^2)}
3: eval_foo_bb1_in->eval_foo_bb2_in, Arg_2: Arg_2 {O(n)}
3: eval_foo_bb1_in->eval_foo_bb2_in, Arg_3: Arg_3 {O(n)}
4: eval_foo_bb1_in->eval_foo_bb3_in, Arg_0: 4*Arg_2+Arg_3+1 {O(n)}
4: eval_foo_bb1_in->eval_foo_bb3_in, Arg_1: 5*Arg_2*Arg_3+6*Arg_2*Arg_2+Arg_3*Arg_3+5*Arg_3+8*Arg_2+2 {O(n^2)}
4: eval_foo_bb1_in->eval_foo_bb3_in, Arg_2: 2*Arg_2 {O(n)}
4: eval_foo_bb1_in->eval_foo_bb3_in, Arg_3: 2*Arg_3 {O(n)}
5: eval_foo_bb2_in->eval_foo_bb1_in, Arg_0: 3*Arg_2+Arg_3+1 {O(n)}
5: eval_foo_bb2_in->eval_foo_bb1_in, Arg_1: 5*Arg_2*Arg_3+6*Arg_2*Arg_2+Arg_3*Arg_3+4*Arg_3+8*Arg_2+2 {O(n^2)}
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: 4*Arg_2+Arg_0+Arg_3+1 {O(n)}
6: eval_foo_bb3_in->eval_foo_stop, Arg_1: 5*Arg_2*Arg_3+6*Arg_2*Arg_2+Arg_3*Arg_3+5*Arg_3+8*Arg_2+Arg_1+2 {O(n^2)}
6: eval_foo_bb3_in->eval_foo_stop, Arg_2: 3*Arg_2 {O(n)}
6: eval_foo_bb3_in->eval_foo_stop, Arg_3: 3*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)}