Initial Problem

Start: eval_foo_start
Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3, Arg_4
Temp_Vars: nondef.0
Locations: eval_foo_0, eval_foo_1, eval_foo_bb0_in, eval_foo_bb1_in, eval_foo_bb2_in, eval_foo_bb3_in, eval_foo_bb4_in, eval_foo_bb5_in, eval_foo_start, eval_foo_stop
Transitions:
8:eval_foo_0(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_foo_1(Arg_0,Arg_1,nondef.0,Arg_3,Arg_4)
9:eval_foo_1(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_foo_bb1_in(Arg_2,0,Arg_2,Arg_3,Arg_4)
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):|:0<Arg_0
3:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_foo_bb5_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:Arg_0<=0
4:eval_foo_bb2_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):|:0<Arg_1
5:eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_foo_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:Arg_1<=0
6:eval_foo_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_foo_0(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4)
10:eval_foo_bb4_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)
11:eval_foo_bb5_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_1<=Arg_4 && Arg_0<=0 for location eval_foo_bb5_in

Found invariant 1<=Arg_4 && 2<=Arg_1+Arg_4 && Arg_1<=Arg_4 && 2<=Arg_0+Arg_4 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 for location eval_foo_0

Found invariant Arg_1<=Arg_4 && Arg_0<=0 for location eval_foo_stop

Found invariant 1<=Arg_4 && 2<=Arg_1+Arg_4 && Arg_1<=Arg_4 && 2<=Arg_0+Arg_4 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 for location eval_foo_bb3_in

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

Found invariant 1<=Arg_4 && 2<=Arg_1+Arg_4 && Arg_1<=Arg_4 && 2<=Arg_0+Arg_4 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 for location eval_foo_1

Found invariant Arg_1<=Arg_4 for location eval_foo_bb1_in

Found invariant Arg_1<=Arg_4 && Arg_1<=0 && 1+Arg_1<=Arg_0 && 1<=Arg_0 for location eval_foo_bb4_in

Problem after Preprocessing

Start: eval_foo_start
Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3, Arg_4
Temp_Vars: nondef.0
Locations: eval_foo_0, eval_foo_1, eval_foo_bb0_in, eval_foo_bb1_in, eval_foo_bb2_in, eval_foo_bb3_in, eval_foo_bb4_in, eval_foo_bb5_in, eval_foo_start, eval_foo_stop
Transitions:
8:eval_foo_0(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_foo_1(Arg_0,Arg_1,nondef.0,Arg_3,Arg_4):|:1<=Arg_4 && 2<=Arg_1+Arg_4 && Arg_1<=Arg_4 && 2<=Arg_0+Arg_4 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0
9:eval_foo_1(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_foo_bb1_in(Arg_2,0,Arg_2,Arg_3,Arg_4):|:1<=Arg_4 && 2<=Arg_1+Arg_4 && Arg_1<=Arg_4 && 2<=Arg_0+Arg_4 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0
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_1<=Arg_4 && 0<Arg_0
3:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_foo_bb5_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:Arg_1<=Arg_4 && Arg_0<=0
4:eval_foo_bb2_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_1<=Arg_4 && 1<=Arg_0 && 0<Arg_1
5:eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_foo_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:Arg_1<=Arg_4 && 1<=Arg_0 && Arg_1<=0
6:eval_foo_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_foo_0(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:1<=Arg_4 && 2<=Arg_1+Arg_4 && Arg_1<=Arg_4 && 2<=Arg_0+Arg_4 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0
10:eval_foo_bb4_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):|:Arg_1<=Arg_4 && Arg_1<=0 && 1+Arg_1<=Arg_0 && 1<=Arg_0
11:eval_foo_bb5_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_1<=Arg_4 && Arg_0<=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 8:eval_foo_0(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_foo_1(Arg_0,Arg_1,nondef.0,Arg_3,Arg_4):|:1<=Arg_4 && 2<=Arg_1+Arg_4 && Arg_1<=Arg_4 && 2<=Arg_0+Arg_4 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 of depth 1:

new bound:

Arg_4 {O(n)}

MPRF:

eval_foo_1 [0 ]
eval_foo_bb2_in [Arg_1 ]
eval_foo_bb3_in [Arg_1 ]
eval_foo_0 [1 ]
eval_foo_bb4_in [Arg_1 ]
eval_foo_bb1_in [Arg_1 ]

MPRF for transition 9:eval_foo_1(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_foo_bb1_in(Arg_2,0,Arg_2,Arg_3,Arg_4):|:1<=Arg_4 && 2<=Arg_1+Arg_4 && Arg_1<=Arg_4 && 2<=Arg_0+Arg_4 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 of depth 1:

new bound:

Arg_4 {O(n)}

MPRF:

eval_foo_1 [1 ]
eval_foo_bb2_in [Arg_1 ]
eval_foo_bb3_in [Arg_1 ]
eval_foo_0 [1 ]
eval_foo_bb4_in [Arg_1 ]
eval_foo_bb1_in [Arg_1 ]

MPRF for transition 4:eval_foo_bb2_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_1<=Arg_4 && 1<=Arg_0 && 0<Arg_1 of depth 1:

new bound:

Arg_4 {O(n)}

MPRF:

eval_foo_1 [0 ]
eval_foo_bb2_in [Arg_1 ]
eval_foo_bb3_in [0 ]
eval_foo_0 [0 ]
eval_foo_bb4_in [Arg_1 ]
eval_foo_bb1_in [Arg_1 ]

MPRF for transition 6:eval_foo_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_foo_0(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:1<=Arg_4 && 2<=Arg_1+Arg_4 && Arg_1<=Arg_4 && 2<=Arg_0+Arg_4 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 of depth 1:

new bound:

Arg_4 {O(n)}

MPRF:

eval_foo_1 [0 ]
eval_foo_bb2_in [Arg_1 ]
eval_foo_bb3_in [1 ]
eval_foo_0 [0 ]
eval_foo_bb4_in [Arg_1 ]
eval_foo_bb1_in [Arg_1 ]

All Bounds

Timebounds

Overall timebound:inf {Infinity}
8: eval_foo_0->eval_foo_1: Arg_4 {O(n)}
9: eval_foo_1->eval_foo_bb1_in: Arg_4 {O(n)}
1: eval_foo_bb0_in->eval_foo_bb1_in: 1 {O(1)}
2: eval_foo_bb1_in->eval_foo_bb2_in: inf {Infinity}
3: eval_foo_bb1_in->eval_foo_bb5_in: 1 {O(1)}
4: eval_foo_bb2_in->eval_foo_bb3_in: Arg_4 {O(n)}
5: eval_foo_bb2_in->eval_foo_bb4_in: inf {Infinity}
6: eval_foo_bb3_in->eval_foo_0: Arg_4 {O(n)}
10: eval_foo_bb4_in->eval_foo_bb1_in: inf {Infinity}
11: eval_foo_bb5_in->eval_foo_stop: 1 {O(1)}
0: eval_foo_start->eval_foo_bb0_in: 1 {O(1)}

Costbounds

Overall costbound: inf {Infinity}
8: eval_foo_0->eval_foo_1: Arg_4 {O(n)}
9: eval_foo_1->eval_foo_bb1_in: Arg_4 {O(n)}
1: eval_foo_bb0_in->eval_foo_bb1_in: 1 {O(1)}
2: eval_foo_bb1_in->eval_foo_bb2_in: inf {Infinity}
3: eval_foo_bb1_in->eval_foo_bb5_in: 1 {O(1)}
4: eval_foo_bb2_in->eval_foo_bb3_in: Arg_4 {O(n)}
5: eval_foo_bb2_in->eval_foo_bb4_in: inf {Infinity}
6: eval_foo_bb3_in->eval_foo_0: Arg_4 {O(n)}
10: eval_foo_bb4_in->eval_foo_bb1_in: inf {Infinity}
11: eval_foo_bb5_in->eval_foo_stop: 1 {O(1)}
0: eval_foo_start->eval_foo_bb0_in: 1 {O(1)}

Sizebounds

8: eval_foo_0->eval_foo_1, Arg_3: Arg_3 {O(n)}
8: eval_foo_0->eval_foo_1, Arg_4: Arg_4 {O(n)}
9: eval_foo_1->eval_foo_bb1_in, Arg_1: 0 {O(1)}
9: eval_foo_1->eval_foo_bb1_in, Arg_3: Arg_3 {O(n)}
9: eval_foo_1->eval_foo_bb1_in, Arg_4: Arg_4 {O(n)}
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_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_bb5_in, Arg_3: 3*Arg_3 {O(n)}
3: eval_foo_bb1_in->eval_foo_bb5_in, Arg_4: 3*Arg_4 {O(n)}
4: eval_foo_bb2_in->eval_foo_bb3_in, Arg_3: Arg_3 {O(n)}
4: eval_foo_bb2_in->eval_foo_bb3_in, Arg_4: Arg_4 {O(n)}
5: eval_foo_bb2_in->eval_foo_bb4_in, Arg_3: Arg_3 {O(n)}
5: eval_foo_bb2_in->eval_foo_bb4_in, Arg_4: Arg_4 {O(n)}
6: eval_foo_bb3_in->eval_foo_0, Arg_3: Arg_3 {O(n)}
6: eval_foo_bb3_in->eval_foo_0, Arg_4: Arg_4 {O(n)}
10: eval_foo_bb4_in->eval_foo_bb1_in, Arg_3: Arg_3 {O(n)}
10: eval_foo_bb4_in->eval_foo_bb1_in, Arg_4: Arg_4 {O(n)}
11: eval_foo_bb5_in->eval_foo_stop, Arg_3: 3*Arg_3 {O(n)}
11: eval_foo_bb5_in->eval_foo_stop, Arg_4: 3*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)}