Initial Problem

Start: eval_foo_start
Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3, Arg_4, Arg_5
Temp_Vars: nondef.0
Locations: eval_foo_.critedge_in, eval_foo_1, eval_foo_2, 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) -> eval_foo_stop(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5)
8:eval_foo_1(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_foo_2(Arg_0,Arg_1,Arg_2,nondef.0,Arg_4,Arg_5)
9:eval_foo_2(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_foo_bb1_in(Arg_2,Arg_3,Arg_2,Arg_3,Arg_4,Arg_5)
1:eval_foo_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_foo_bb1_in(Arg_4,Arg_5,Arg_2,Arg_3,Arg_4,Arg_5)
3:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_foo_.critedge_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5):|:Arg_0<=Arg_1
4:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_foo_.critedge_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5):|:Arg_1<1
5:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_foo_.critedge_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5):|:2<Arg_1
2:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5):|:Arg_1<Arg_0 && 1<=Arg_1 && Arg_1<=2
6:eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_foo_1(Arg_0,Arg_1,Arg_0-Arg_1,Arg_3,Arg_4,Arg_5)
0:eval_foo_start(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_foo_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5)

Preprocessing

Found invariant 2<=Arg_4 && 3<=Arg_2+Arg_4 && 1+Arg_2<=Arg_4 && 3<=Arg_1+Arg_4 && 1+Arg_1<=Arg_4 && 4<=Arg_0+Arg_4 && Arg_0<=Arg_4 && 1+Arg_2<=Arg_0 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && Arg_1<=1+Arg_2 && 3<=Arg_0+Arg_2 && Arg_0<=2+Arg_2 && Arg_1<=2 && 1+Arg_1<=Arg_0 && 1<=Arg_1 && 3<=Arg_0+Arg_1 && 2<=Arg_0 for location eval_foo_2

Found invariant Arg_0<=Arg_4 for location eval_foo_stop

Found invariant 2<=Arg_4 && 3<=Arg_1+Arg_4 && 1+Arg_1<=Arg_4 && 4<=Arg_0+Arg_4 && Arg_0<=Arg_4 && Arg_1<=2 && 1+Arg_1<=Arg_0 && 1<=Arg_1 && 3<=Arg_0+Arg_1 && 2<=Arg_0 for location eval_foo_bb2_in

Found invariant 2<=Arg_4 && 3<=Arg_2+Arg_4 && 1+Arg_2<=Arg_4 && 3<=Arg_1+Arg_4 && 1+Arg_1<=Arg_4 && 4<=Arg_0+Arg_4 && Arg_0<=Arg_4 && 1+Arg_2<=Arg_0 && 0<=Arg_2 && 2<=Arg_1+Arg_2 && Arg_1<=1+Arg_2 && 3<=Arg_0+Arg_2 && Arg_0<=2+Arg_2 && Arg_1<=2 && 1+Arg_1<=Arg_0 && 1<=Arg_1 && 3<=Arg_0+Arg_1 && 2<=Arg_0 for location eval_foo_1

Found invariant Arg_0<=Arg_4 for location eval_foo_bb1_in

Found invariant Arg_0<=Arg_4 for location eval_foo_.critedge_in

Problem after Preprocessing

Start: eval_foo_start
Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3, Arg_4, Arg_5
Temp_Vars: nondef.0
Locations: eval_foo_.critedge_in, eval_foo_1, eval_foo_2, 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) -> eval_foo_stop(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5):|:Arg_0<=Arg_4
8:eval_foo_1(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_foo_2(Arg_0,Arg_1,Arg_2,nondef.0,Arg_4,Arg_5):|:2<=Arg_4 && 3<=Arg_2+Arg_4 && 1+Arg_2<=Arg_4 && 3<=Arg_1+Arg_4 && 1+Arg_1<=Arg_4 && 4<=Arg_0+Arg_4 && Arg_0<=Arg_4 && 1+Arg_2<=Arg_0 && 0<=Arg_2 && 2<=Arg_1+Arg_2 && Arg_1<=1+Arg_2 && 3<=Arg_0+Arg_2 && Arg_0<=2+Arg_2 && Arg_1<=2 && 1+Arg_1<=Arg_0 && 1<=Arg_1 && 3<=Arg_0+Arg_1 && 2<=Arg_0
9:eval_foo_2(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_foo_bb1_in(Arg_2,Arg_3,Arg_2,Arg_3,Arg_4,Arg_5):|:2<=Arg_4 && 3<=Arg_2+Arg_4 && 1+Arg_2<=Arg_4 && 3<=Arg_1+Arg_4 && 1+Arg_1<=Arg_4 && 4<=Arg_0+Arg_4 && Arg_0<=Arg_4 && 1+Arg_2<=Arg_0 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && Arg_1<=1+Arg_2 && 3<=Arg_0+Arg_2 && Arg_0<=2+Arg_2 && Arg_1<=2 && 1+Arg_1<=Arg_0 && 1<=Arg_1 && 3<=Arg_0+Arg_1 && 2<=Arg_0
1:eval_foo_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_foo_bb1_in(Arg_4,Arg_5,Arg_2,Arg_3,Arg_4,Arg_5)
3:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_foo_.critedge_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5):|:Arg_0<=Arg_4 && Arg_0<=Arg_1
4:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_foo_.critedge_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5):|:Arg_0<=Arg_4 && Arg_1<1
5:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_foo_.critedge_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5):|:Arg_0<=Arg_4 && 2<Arg_1
2:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5):|:Arg_0<=Arg_4 && Arg_1<Arg_0 && 1<=Arg_1 && Arg_1<=2
6:eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_foo_1(Arg_0,Arg_1,Arg_0-Arg_1,Arg_3,Arg_4,Arg_5):|:2<=Arg_4 && 3<=Arg_1+Arg_4 && 1+Arg_1<=Arg_4 && 4<=Arg_0+Arg_4 && Arg_0<=Arg_4 && Arg_1<=2 && 1+Arg_1<=Arg_0 && 1<=Arg_1 && 3<=Arg_0+Arg_1 && 2<=Arg_0
0:eval_foo_start(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_foo_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5)

MPRF for transition 8:eval_foo_1(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_foo_2(Arg_0,Arg_1,Arg_2,nondef.0,Arg_4,Arg_5):|:2<=Arg_4 && 3<=Arg_2+Arg_4 && 1+Arg_2<=Arg_4 && 3<=Arg_1+Arg_4 && 1+Arg_1<=Arg_4 && 4<=Arg_0+Arg_4 && Arg_0<=Arg_4 && 1+Arg_2<=Arg_0 && 0<=Arg_2 && 2<=Arg_1+Arg_2 && Arg_1<=1+Arg_2 && 3<=Arg_0+Arg_2 && Arg_0<=2+Arg_2 && Arg_1<=2 && 1+Arg_1<=Arg_0 && 1<=Arg_1 && 3<=Arg_0+Arg_1 && 2<=Arg_0 of depth 1:

new bound:

Arg_4 {O(n)}

MPRF:

eval_foo_2 [Arg_2 ]
eval_foo_bb1_in [Arg_0 ]
eval_foo_bb2_in [Arg_0 ]
eval_foo_1 [Arg_2+1 ]

MPRF for transition 9:eval_foo_2(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_foo_bb1_in(Arg_2,Arg_3,Arg_2,Arg_3,Arg_4,Arg_5):|:2<=Arg_4 && 3<=Arg_2+Arg_4 && 1+Arg_2<=Arg_4 && 3<=Arg_1+Arg_4 && 1+Arg_1<=Arg_4 && 4<=Arg_0+Arg_4 && Arg_0<=Arg_4 && 1+Arg_2<=Arg_0 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && Arg_1<=1+Arg_2 && 3<=Arg_0+Arg_2 && Arg_0<=2+Arg_2 && Arg_1<=2 && 1+Arg_1<=Arg_0 && 1<=Arg_1 && 3<=Arg_0+Arg_1 && 2<=Arg_0 of depth 1:

new bound:

Arg_4+1 {O(n)}

MPRF:

eval_foo_2 [Arg_2 ]
eval_foo_bb1_in [Arg_0-1 ]
eval_foo_bb2_in [Arg_0-1 ]
eval_foo_1 [Arg_2 ]

MPRF for transition 2:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5):|:Arg_0<=Arg_4 && Arg_1<Arg_0 && 1<=Arg_1 && Arg_1<=2 of depth 1:

new bound:

Arg_4+1 {O(n)}

MPRF:

eval_foo_2 [Arg_2-1 ]
eval_foo_bb1_in [Arg_0-1 ]
eval_foo_bb2_in [Arg_0-Arg_1-1 ]
eval_foo_1 [Arg_2-1 ]

MPRF for transition 6:eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_foo_1(Arg_0,Arg_1,Arg_0-Arg_1,Arg_3,Arg_4,Arg_5):|:2<=Arg_4 && 3<=Arg_1+Arg_4 && 1+Arg_1<=Arg_4 && 4<=Arg_0+Arg_4 && Arg_0<=Arg_4 && Arg_1<=2 && 1+Arg_1<=Arg_0 && 1<=Arg_1 && 3<=Arg_0+Arg_1 && 2<=Arg_0 of depth 1:

new bound:

Arg_4+1 {O(n)}

MPRF:

eval_foo_2 [Arg_2-1 ]
eval_foo_bb1_in [Arg_0-1 ]
eval_foo_bb2_in [Arg_0-1 ]
eval_foo_1 [Arg_0-2 ]

All Bounds

Timebounds

Overall timebound:4*Arg_4+9 {O(n)}
10: eval_foo_.critedge_in->eval_foo_stop: 1 {O(1)}
8: eval_foo_1->eval_foo_2: Arg_4 {O(n)}
9: eval_foo_2->eval_foo_bb1_in: Arg_4+1 {O(n)}
1: eval_foo_bb0_in->eval_foo_bb1_in: 1 {O(1)}
2: eval_foo_bb1_in->eval_foo_bb2_in: Arg_4+1 {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_1: Arg_4+1 {O(n)}
0: eval_foo_start->eval_foo_bb0_in: 1 {O(1)}

Costbounds

Overall costbound: 4*Arg_4+9 {O(n)}
10: eval_foo_.critedge_in->eval_foo_stop: 1 {O(1)}
8: eval_foo_1->eval_foo_2: Arg_4 {O(n)}
9: eval_foo_2->eval_foo_bb1_in: Arg_4+1 {O(n)}
1: eval_foo_bb0_in->eval_foo_bb1_in: 1 {O(1)}
2: eval_foo_bb1_in->eval_foo_bb2_in: Arg_4+1 {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_1: Arg_4+1 {O(n)}
0: eval_foo_start->eval_foo_bb0_in: 1 {O(1)}

Sizebounds

10: eval_foo_.critedge_in->eval_foo_stop, Arg_0: 6*Arg_4 {O(n)}
10: eval_foo_.critedge_in->eval_foo_stop, Arg_2: 3*Arg_2+3*Arg_4 {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)}
8: eval_foo_1->eval_foo_2, Arg_0: Arg_4 {O(n)}
8: eval_foo_1->eval_foo_2, Arg_1: 2 {O(1)}
8: eval_foo_1->eval_foo_2, Arg_2: Arg_4 {O(n)}
8: eval_foo_1->eval_foo_2, Arg_4: Arg_4 {O(n)}
8: eval_foo_1->eval_foo_2, Arg_5: Arg_5 {O(n)}
9: eval_foo_2->eval_foo_bb1_in, Arg_0: Arg_4 {O(n)}
9: eval_foo_2->eval_foo_bb1_in, Arg_2: Arg_4 {O(n)}
9: eval_foo_2->eval_foo_bb1_in, Arg_4: Arg_4 {O(n)}
9: eval_foo_2->eval_foo_bb1_in, Arg_5: Arg_5 {O(n)}
1: eval_foo_bb0_in->eval_foo_bb1_in, Arg_0: Arg_4 {O(n)}
1: eval_foo_bb0_in->eval_foo_bb1_in, Arg_1: Arg_5 {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)}
1: eval_foo_bb0_in->eval_foo_bb1_in, Arg_5: Arg_5 {O(n)}
2: eval_foo_bb1_in->eval_foo_bb2_in, Arg_0: Arg_4 {O(n)}
2: eval_foo_bb1_in->eval_foo_bb2_in, Arg_1: 2 {O(1)}
2: eval_foo_bb1_in->eval_foo_bb2_in, Arg_2: Arg_2+Arg_4 {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)}
3: eval_foo_bb1_in->eval_foo_.critedge_in, Arg_0: 2*Arg_4 {O(n)}
3: eval_foo_bb1_in->eval_foo_.critedge_in, Arg_2: Arg_2+Arg_4 {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)}
4: eval_foo_bb1_in->eval_foo_.critedge_in, Arg_0: 2*Arg_4 {O(n)}
4: eval_foo_bb1_in->eval_foo_.critedge_in, Arg_2: Arg_2+Arg_4 {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)}
5: eval_foo_bb1_in->eval_foo_.critedge_in, Arg_0: 2*Arg_4 {O(n)}
5: eval_foo_bb1_in->eval_foo_.critedge_in, Arg_2: Arg_2+Arg_4 {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)}
6: eval_foo_bb2_in->eval_foo_1, Arg_0: Arg_4 {O(n)}
6: eval_foo_bb2_in->eval_foo_1, Arg_1: 2 {O(1)}
6: eval_foo_bb2_in->eval_foo_1, Arg_2: Arg_4 {O(n)}
6: eval_foo_bb2_in->eval_foo_1, Arg_4: Arg_4 {O(n)}
6: eval_foo_bb2_in->eval_foo_1, Arg_5: Arg_5 {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)}