Initial Problem

Start: eval_foo_start
Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3, Arg_4, Arg_5, Arg_6, Arg_7
Temp_Vars: nondef.0
Locations: eval_foo_.critedge_in, eval_foo_2, eval_foo_3, eval_foo_bb0_in, eval_foo_bb1_in, eval_foo_bb2_in, eval_foo_start, eval_foo_stop
Transitions:
10:eval_foo_.critedge_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7) -> eval_foo_stop(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7)
8:eval_foo_2(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7) -> eval_foo_3(Arg_0,Arg_1,Arg_2,nondef.0,Arg_4,Arg_5,Arg_6,Arg_7)
9:eval_foo_3(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7) -> eval_foo_bb1_in(Arg_3,Arg_7,Arg_0,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7)
1:eval_foo_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7) -> eval_foo_bb1_in(Arg_5,Arg_6,Arg_4,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7)
3:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7) -> eval_foo_.critedge_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7):|:Arg_0<=0
4:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7) -> eval_foo_.critedge_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7):|:Arg_1<=Arg_0
5:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7) -> eval_foo_.critedge_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7):|:Arg_0<=2*Arg_2
2:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7) -> eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7):|:0<Arg_0 && Arg_0<Arg_1 && 2*Arg_2<Arg_0
6:eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7) -> eval_foo_2(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7)
0:eval_foo_start(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7) -> eval_foo_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7)

Preprocessing

Found invariant 2<=Arg_1 && 3<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 1<=Arg_0 for location eval_foo_2

Found invariant 2<=Arg_1 && 3<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 1<=Arg_0 for location eval_foo_3

Found invariant 2<=Arg_1 && 3<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 1<=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, Arg_4, Arg_5, Arg_6, Arg_7
Temp_Vars: nondef.0
Locations: eval_foo_.critedge_in, eval_foo_2, eval_foo_3, eval_foo_bb0_in, eval_foo_bb1_in, eval_foo_bb2_in, eval_foo_start, eval_foo_stop
Transitions:
10:eval_foo_.critedge_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7) -> eval_foo_stop(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7)
8:eval_foo_2(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7) -> eval_foo_3(Arg_0,Arg_1,Arg_2,nondef.0,Arg_4,Arg_5,Arg_6,Arg_7):|:2<=Arg_1 && 3<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 1<=Arg_0
9:eval_foo_3(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7) -> eval_foo_bb1_in(Arg_3,Arg_7,Arg_0,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7):|:2<=Arg_1 && 3<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 1<=Arg_0
1:eval_foo_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7) -> eval_foo_bb1_in(Arg_5,Arg_6,Arg_4,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7)
3:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7) -> eval_foo_.critedge_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7):|:Arg_0<=0
4:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7) -> eval_foo_.critedge_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7):|:Arg_1<=Arg_0
5:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7) -> eval_foo_.critedge_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7):|:Arg_0<=2*Arg_2
2:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7) -> eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7):|:0<Arg_0 && Arg_0<Arg_1 && 2*Arg_2<Arg_0
6:eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7) -> eval_foo_2(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7):|:2<=Arg_1 && 3<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 1<=Arg_0
0:eval_foo_start(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7) -> eval_foo_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7)

MPRF for transition 8:eval_foo_2(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7) -> eval_foo_3(Arg_0,Arg_1,Arg_2,nondef.0,Arg_4,Arg_5,Arg_6,Arg_7):|:2<=Arg_1 && 3<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 1<=Arg_0 of depth 2:

new bound:

48*Arg_4+8*Arg_6+8*Arg_7+41 {O(n)}

MPRF:

eval_foo_3 [Arg_7-2*Arg_0-5 ; Arg_7-2*Arg_0-2 ]
eval_foo_bb1_in [Arg_7-4*Arg_2-3 ; Arg_1-2*Arg_2-2 ]
eval_foo_bb2_in [Arg_7-2*Arg_0-1 ; 0 ]
eval_foo_2 [Arg_7-2*Arg_0-1 ; 0 ]

MPRF for transition 9:eval_foo_3(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7) -> eval_foo_bb1_in(Arg_3,Arg_7,Arg_0,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7):|:2<=Arg_1 && 3<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 1<=Arg_0 of depth 2:

new bound:

48*Arg_4+8*Arg_6+8*Arg_7+41 {O(n)}

MPRF:

eval_foo_3 [Arg_7-2*Arg_0-1 ; 0 ]
eval_foo_bb1_in [Arg_7-4*Arg_2-3 ; Arg_1-2*Arg_2-2 ]
eval_foo_bb2_in [Arg_7-2*Arg_0-1 ; Arg_1-Arg_0-1 ]
eval_foo_2 [Arg_7-2*Arg_0-1 ; 0 ]

MPRF for transition 2:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7) -> eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7):|:0<Arg_0 && Arg_0<Arg_1 && 2*Arg_2<Arg_0 of depth 2:

new bound:

48*Arg_4+8*Arg_6+8*Arg_7+25 {O(n)}

MPRF:

eval_foo_3 [Arg_7-4*Arg_0-3 ; Arg_7-2*Arg_0 ]
eval_foo_bb1_in [Arg_7-4*Arg_2-3 ; Arg_1-2*Arg_2 ]
eval_foo_bb2_in [Arg_7-2*Arg_0-5 ; Arg_1+Arg_7-3*Arg_0-1 ]
eval_foo_2 [Arg_7-4*Arg_0-3 ; Arg_7-2*Arg_0 ]

MPRF for transition 6:eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7) -> eval_foo_2(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7):|:2<=Arg_1 && 3<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 1<=Arg_0 of depth 2:

new bound:

16*Arg_4+8*Arg_6+8*Arg_7+9 {O(n)}

MPRF:

eval_foo_3 [Arg_7-2*Arg_0-1 ; Arg_7 ]
eval_foo_bb1_in [Arg_7-2*Arg_2-1 ; Arg_1 ]
eval_foo_bb2_in [Arg_7-Arg_0 ; Arg_1 ]
eval_foo_2 [Arg_7-2*Arg_0-1 ; Arg_1+Arg_7-Arg_0-1 ]

All Bounds

Timebounds

Overall timebound:160*Arg_4+32*Arg_6+32*Arg_7+122 {O(n)}
10: eval_foo_.critedge_in->eval_foo_stop: 1 {O(1)}
8: eval_foo_2->eval_foo_3: 48*Arg_4+8*Arg_6+8*Arg_7+41 {O(n)}
9: eval_foo_3->eval_foo_bb1_in: 48*Arg_4+8*Arg_6+8*Arg_7+41 {O(n)}
1: eval_foo_bb0_in->eval_foo_bb1_in: 1 {O(1)}
2: eval_foo_bb1_in->eval_foo_bb2_in: 48*Arg_4+8*Arg_6+8*Arg_7+25 {O(n)}
3: eval_foo_bb1_in->eval_foo_.critedge_in: 1 {O(1)}
4: eval_foo_bb1_in->eval_foo_.critedge_in: 1 {O(1)}
5: eval_foo_bb1_in->eval_foo_.critedge_in: 1 {O(1)}
6: eval_foo_bb2_in->eval_foo_2: 16*Arg_4+8*Arg_6+8*Arg_7+9 {O(n)}
0: eval_foo_start->eval_foo_bb0_in: 1 {O(1)}

Costbounds

Overall costbound: 160*Arg_4+32*Arg_6+32*Arg_7+122 {O(n)}
10: eval_foo_.critedge_in->eval_foo_stop: 1 {O(1)}
8: eval_foo_2->eval_foo_3: 48*Arg_4+8*Arg_6+8*Arg_7+41 {O(n)}
9: eval_foo_3->eval_foo_bb1_in: 48*Arg_4+8*Arg_6+8*Arg_7+41 {O(n)}
1: eval_foo_bb0_in->eval_foo_bb1_in: 1 {O(1)}
2: eval_foo_bb1_in->eval_foo_bb2_in: 48*Arg_4+8*Arg_6+8*Arg_7+25 {O(n)}
3: eval_foo_bb1_in->eval_foo_.critedge_in: 1 {O(1)}
4: eval_foo_bb1_in->eval_foo_.critedge_in: 1 {O(1)}
5: eval_foo_bb1_in->eval_foo_.critedge_in: 1 {O(1)}
6: eval_foo_bb2_in->eval_foo_2: 16*Arg_4+8*Arg_6+8*Arg_7+9 {O(n)}
0: eval_foo_start->eval_foo_bb0_in: 1 {O(1)}

Sizebounds

10: eval_foo_.critedge_in->eval_foo_stop, Arg_1: 3*Arg_6+3*Arg_7 {O(n)}
10: eval_foo_.critedge_in->eval_foo_stop, Arg_4: 6*Arg_4 {O(n)}
10: eval_foo_.critedge_in->eval_foo_stop, Arg_5: 6*Arg_5 {O(n)}
10: eval_foo_.critedge_in->eval_foo_stop, Arg_6: 6*Arg_6 {O(n)}
10: eval_foo_.critedge_in->eval_foo_stop, Arg_7: 6*Arg_7 {O(n)}
8: eval_foo_2->eval_foo_3, Arg_1: Arg_6+Arg_7 {O(n)}
8: eval_foo_2->eval_foo_3, Arg_4: Arg_4 {O(n)}
8: eval_foo_2->eval_foo_3, Arg_5: Arg_5 {O(n)}
8: eval_foo_2->eval_foo_3, Arg_6: Arg_6 {O(n)}
8: eval_foo_2->eval_foo_3, Arg_7: Arg_7 {O(n)}
9: eval_foo_3->eval_foo_bb1_in, Arg_1: Arg_7 {O(n)}
9: eval_foo_3->eval_foo_bb1_in, Arg_4: Arg_4 {O(n)}
9: eval_foo_3->eval_foo_bb1_in, Arg_5: Arg_5 {O(n)}
9: eval_foo_3->eval_foo_bb1_in, Arg_6: Arg_6 {O(n)}
9: eval_foo_3->eval_foo_bb1_in, Arg_7: Arg_7 {O(n)}
1: eval_foo_bb0_in->eval_foo_bb1_in, Arg_0: Arg_5 {O(n)}
1: eval_foo_bb0_in->eval_foo_bb1_in, Arg_1: Arg_6 {O(n)}
1: eval_foo_bb0_in->eval_foo_bb1_in, Arg_2: Arg_4 {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)}
1: eval_foo_bb0_in->eval_foo_bb1_in, Arg_5: Arg_5 {O(n)}
1: eval_foo_bb0_in->eval_foo_bb1_in, Arg_6: Arg_6 {O(n)}
1: eval_foo_bb0_in->eval_foo_bb1_in, Arg_7: Arg_7 {O(n)}
2: eval_foo_bb1_in->eval_foo_bb2_in, Arg_1: Arg_6+Arg_7 {O(n)}
2: eval_foo_bb1_in->eval_foo_bb2_in, Arg_4: Arg_4 {O(n)}
2: eval_foo_bb1_in->eval_foo_bb2_in, Arg_5: Arg_5 {O(n)}
2: eval_foo_bb1_in->eval_foo_bb2_in, Arg_6: Arg_6 {O(n)}
2: eval_foo_bb1_in->eval_foo_bb2_in, Arg_7: Arg_7 {O(n)}
3: eval_foo_bb1_in->eval_foo_.critedge_in, Arg_1: Arg_6+Arg_7 {O(n)}
3: eval_foo_bb1_in->eval_foo_.critedge_in, Arg_4: 2*Arg_4 {O(n)}
3: eval_foo_bb1_in->eval_foo_.critedge_in, Arg_5: 2*Arg_5 {O(n)}
3: eval_foo_bb1_in->eval_foo_.critedge_in, Arg_6: 2*Arg_6 {O(n)}
3: eval_foo_bb1_in->eval_foo_.critedge_in, Arg_7: 2*Arg_7 {O(n)}
4: eval_foo_bb1_in->eval_foo_.critedge_in, Arg_1: Arg_6+Arg_7 {O(n)}
4: eval_foo_bb1_in->eval_foo_.critedge_in, Arg_4: 2*Arg_4 {O(n)}
4: eval_foo_bb1_in->eval_foo_.critedge_in, Arg_5: 2*Arg_5 {O(n)}
4: eval_foo_bb1_in->eval_foo_.critedge_in, Arg_6: 2*Arg_6 {O(n)}
4: eval_foo_bb1_in->eval_foo_.critedge_in, Arg_7: 2*Arg_7 {O(n)}
5: eval_foo_bb1_in->eval_foo_.critedge_in, Arg_1: Arg_6+Arg_7 {O(n)}
5: eval_foo_bb1_in->eval_foo_.critedge_in, Arg_4: 2*Arg_4 {O(n)}
5: eval_foo_bb1_in->eval_foo_.critedge_in, Arg_5: 2*Arg_5 {O(n)}
5: eval_foo_bb1_in->eval_foo_.critedge_in, Arg_6: 2*Arg_6 {O(n)}
5: eval_foo_bb1_in->eval_foo_.critedge_in, Arg_7: 2*Arg_7 {O(n)}
6: eval_foo_bb2_in->eval_foo_2, Arg_1: Arg_6+Arg_7 {O(n)}
6: eval_foo_bb2_in->eval_foo_2, Arg_4: Arg_4 {O(n)}
6: eval_foo_bb2_in->eval_foo_2, Arg_5: Arg_5 {O(n)}
6: eval_foo_bb2_in->eval_foo_2, Arg_6: Arg_6 {O(n)}
6: eval_foo_bb2_in->eval_foo_2, Arg_7: Arg_7 {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)}
0: eval_foo_start->eval_foo_bb0_in, Arg_5: Arg_5 {O(n)}
0: eval_foo_start->eval_foo_bb0_in, Arg_6: Arg_6 {O(n)}
0: eval_foo_start->eval_foo_bb0_in, Arg_7: Arg_7 {O(n)}