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_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_4,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):|:Arg_0<Arg_2 && Arg_1<Arg_2
3:eval_foo_bb1_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_2<=Arg_0
4:eval_foo_bb1_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_2<=Arg_1
5:eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_foo_bb1_in(Arg_0+1,Arg_1+1,Arg_2,Arg_3,Arg_4)
6:eval_foo_bb3_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

Found invariant Arg_4<=Arg_1 && Arg_3<=Arg_0 for location eval_foo_stop

Found invariant Arg_4<=Arg_1 && Arg_3<=Arg_0 for location eval_foo_bb3_in

Found invariant 1+Arg_4<=Arg_2 && Arg_4<=Arg_1 && 1+Arg_3<=Arg_2 && Arg_3<=Arg_0 && 1+Arg_1<=Arg_2 && 1+Arg_0<=Arg_2 for location eval_foo_bb2_in

Found invariant Arg_4<=Arg_1 && Arg_3<=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, Arg_4
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,Arg_4) -> eval_foo_bb1_in(Arg_3,Arg_4,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):|:Arg_4<=Arg_1 && Arg_3<=Arg_0 && Arg_0<Arg_2 && Arg_1<Arg_2
3:eval_foo_bb1_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_4<=Arg_1 && Arg_3<=Arg_0 && Arg_2<=Arg_0
4:eval_foo_bb1_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_4<=Arg_1 && Arg_3<=Arg_0 && Arg_2<=Arg_1
5:eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_foo_bb1_in(Arg_0+1,Arg_1+1,Arg_2,Arg_3,Arg_4):|:1+Arg_4<=Arg_2 && Arg_4<=Arg_1 && 1+Arg_3<=Arg_2 && Arg_3<=Arg_0 && 1+Arg_1<=Arg_2 && 1+Arg_0<=Arg_2
6:eval_foo_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_foo_stop(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:Arg_4<=Arg_1 && Arg_3<=Arg_0
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)

MPRF for transition 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):|:Arg_4<=Arg_1 && Arg_3<=Arg_0 && Arg_0<Arg_2 && Arg_1<Arg_2 of depth 1:

new bound:

Arg_2+Arg_4 {O(n)}

MPRF:

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

MPRF for transition 5:eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_foo_bb1_in(Arg_0+1,Arg_1+1,Arg_2,Arg_3,Arg_4):|:1+Arg_4<=Arg_2 && Arg_4<=Arg_1 && 1+Arg_3<=Arg_2 && Arg_3<=Arg_0 && 1+Arg_1<=Arg_2 && 1+Arg_0<=Arg_2 of depth 1:

new bound:

Arg_2+Arg_3 {O(n)}

MPRF:

eval_foo_bb2_in [Arg_2-Arg_0 ]
eval_foo_bb1_in [Arg_2-Arg_0 ]

All Bounds

Timebounds

Overall timebound:2*Arg_2+Arg_3+Arg_4+5 {O(n)}
1: eval_foo_bb0_in->eval_foo_bb1_in: 1 {O(1)}
2: eval_foo_bb1_in->eval_foo_bb2_in: Arg_2+Arg_4 {O(n)}
3: eval_foo_bb1_in->eval_foo_bb3_in: 1 {O(1)}
4: eval_foo_bb1_in->eval_foo_bb3_in: 1 {O(1)}
5: eval_foo_bb2_in->eval_foo_bb1_in: Arg_2+Arg_3 {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_2+Arg_3+Arg_4+5 {O(n)}
1: eval_foo_bb0_in->eval_foo_bb1_in: 1 {O(1)}
2: eval_foo_bb1_in->eval_foo_bb2_in: Arg_2+Arg_4 {O(n)}
3: eval_foo_bb1_in->eval_foo_bb3_in: 1 {O(1)}
4: eval_foo_bb1_in->eval_foo_bb3_in: 1 {O(1)}
5: eval_foo_bb2_in->eval_foo_bb1_in: Arg_2+Arg_3 {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_3 {O(n)}
1: eval_foo_bb0_in->eval_foo_bb1_in, Arg_1: Arg_4 {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)}
1: eval_foo_bb0_in->eval_foo_bb1_in, Arg_4: Arg_4 {O(n)}
2: eval_foo_bb1_in->eval_foo_bb2_in, Arg_0: 2*Arg_3+Arg_2 {O(n)}
2: eval_foo_bb1_in->eval_foo_bb2_in, Arg_1: Arg_2+Arg_3+Arg_4 {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)}
2: eval_foo_bb1_in->eval_foo_bb2_in, Arg_4: Arg_4 {O(n)}
3: eval_foo_bb1_in->eval_foo_bb3_in, Arg_0: 3*Arg_3+Arg_2 {O(n)}
3: eval_foo_bb1_in->eval_foo_bb3_in, Arg_1: 2*Arg_4+Arg_2+Arg_3 {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)}
3: eval_foo_bb1_in->eval_foo_bb3_in, Arg_4: 2*Arg_4 {O(n)}
4: eval_foo_bb1_in->eval_foo_bb3_in, Arg_0: 3*Arg_3+Arg_2 {O(n)}
4: eval_foo_bb1_in->eval_foo_bb3_in, Arg_1: 2*Arg_4+Arg_2+Arg_3 {O(n)}
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)}
4: eval_foo_bb1_in->eval_foo_bb3_in, Arg_4: 2*Arg_4 {O(n)}
5: eval_foo_bb2_in->eval_foo_bb1_in, Arg_0: 2*Arg_3+Arg_2 {O(n)}
5: eval_foo_bb2_in->eval_foo_bb1_in, Arg_1: Arg_2+Arg_3+Arg_4 {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)}
5: eval_foo_bb2_in->eval_foo_bb1_in, Arg_4: Arg_4 {O(n)}
6: eval_foo_bb3_in->eval_foo_stop, Arg_0: 2*Arg_2+6*Arg_3 {O(n)}
6: eval_foo_bb3_in->eval_foo_stop, Arg_1: 2*Arg_2+2*Arg_3+4*Arg_4 {O(n)}
6: eval_foo_bb3_in->eval_foo_stop, Arg_2: 4*Arg_2 {O(n)}
6: eval_foo_bb3_in->eval_foo_stop, Arg_3: 4*Arg_3 {O(n)}
6: eval_foo_bb3_in->eval_foo_stop, Arg_4: 4*Arg_4 {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)}
0: eval_foo_start->eval_foo_bb0_in, Arg_4: Arg_4 {O(n)}