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_bb4_in, eval_foo_bb5_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_1,Arg_2,Arg_3)
2:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_foo_bb2_in(Arg_0,0,Arg_2,Arg_3):|:Arg_0<5
3:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_foo_bb5_in(Arg_0,Arg_1,Arg_2,Arg_3):|:5<=Arg_0
4:eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_foo_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3):|:2<Arg_0 && Arg_1<=9
5:eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_foo_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_0<=2
6:eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_foo_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3):|:9<Arg_1
7:eval_foo_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_foo_bb2_in(Arg_0,Arg_1+1,Arg_2,Arg_3)
8:eval_foo_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_foo_bb1_in(Arg_0+1,Arg_1,Arg_2,Arg_3)
9:eval_foo_bb5_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

Eliminate variables {Arg_3} that do not contribute to the problem

Found invariant Arg_2<=Arg_0 && 5<=Arg_0 for location eval_foo_bb5_in

Found invariant Arg_2<=Arg_0 && 5<=Arg_0 for location eval_foo_stop

Found invariant Arg_2<=4 && Arg_2<=4+Arg_1 && Arg_1+Arg_2<=13 && Arg_2<=Arg_0 && Arg_0+Arg_2<=8 && Arg_1<=9 && Arg_1<=6+Arg_0 && Arg_0+Arg_1<=13 && 0<=Arg_1 && 3<=Arg_0+Arg_1 && Arg_0<=4+Arg_1 && Arg_0<=4 && 3<=Arg_0 for location eval_foo_bb3_in

Found invariant Arg_2<=4 && Arg_2<=4+Arg_1 && Arg_2<=Arg_0 && Arg_0+Arg_2<=8 && 0<=Arg_1 && Arg_0<=4+Arg_1 && Arg_0<=4 for location eval_foo_bb2_in

Found invariant Arg_2<=Arg_0 for location eval_foo_bb1_in

Found invariant Arg_2<=4 && Arg_2<=2+Arg_1 && Arg_2<=Arg_0 && Arg_0+Arg_2<=8 && 0<=Arg_1 && Arg_0<=2+Arg_1 && Arg_0<=4 for location eval_foo_bb4_in

Problem after Preprocessing

Start: eval_foo_start
Program_Vars: Arg_0, Arg_1, Arg_2
Temp_Vars:
Locations: 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:
20:eval_foo_bb0_in(Arg_0,Arg_1,Arg_2) -> eval_foo_bb1_in(Arg_2,Arg_1,Arg_2)
21:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2) -> eval_foo_bb2_in(Arg_0,0,Arg_2):|:Arg_2<=Arg_0 && Arg_0<5
22:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2) -> eval_foo_bb5_in(Arg_0,Arg_1,Arg_2):|:Arg_2<=Arg_0 && 5<=Arg_0
23:eval_foo_bb2_in(Arg_0,Arg_1,Arg_2) -> eval_foo_bb3_in(Arg_0,Arg_1,Arg_2):|:Arg_2<=4 && Arg_2<=4+Arg_1 && Arg_2<=Arg_0 && Arg_0+Arg_2<=8 && 0<=Arg_1 && Arg_0<=4+Arg_1 && Arg_0<=4 && 2<Arg_0 && Arg_1<=9
24:eval_foo_bb2_in(Arg_0,Arg_1,Arg_2) -> eval_foo_bb4_in(Arg_0,Arg_1,Arg_2):|:Arg_2<=4 && Arg_2<=4+Arg_1 && Arg_2<=Arg_0 && Arg_0+Arg_2<=8 && 0<=Arg_1 && Arg_0<=4+Arg_1 && Arg_0<=4 && Arg_0<=2
25:eval_foo_bb2_in(Arg_0,Arg_1,Arg_2) -> eval_foo_bb4_in(Arg_0,Arg_1,Arg_2):|:Arg_2<=4 && Arg_2<=4+Arg_1 && Arg_2<=Arg_0 && Arg_0+Arg_2<=8 && 0<=Arg_1 && Arg_0<=4+Arg_1 && Arg_0<=4 && 9<Arg_1
26:eval_foo_bb3_in(Arg_0,Arg_1,Arg_2) -> eval_foo_bb2_in(Arg_0,Arg_1+1,Arg_2):|:Arg_2<=4 && Arg_2<=4+Arg_1 && Arg_1+Arg_2<=13 && Arg_2<=Arg_0 && Arg_0+Arg_2<=8 && Arg_1<=9 && Arg_1<=6+Arg_0 && Arg_0+Arg_1<=13 && 0<=Arg_1 && 3<=Arg_0+Arg_1 && Arg_0<=4+Arg_1 && Arg_0<=4 && 3<=Arg_0
27:eval_foo_bb4_in(Arg_0,Arg_1,Arg_2) -> eval_foo_bb1_in(Arg_0+1,Arg_1,Arg_2):|:Arg_2<=4 && Arg_2<=2+Arg_1 && Arg_2<=Arg_0 && Arg_0+Arg_2<=8 && 0<=Arg_1 && Arg_0<=2+Arg_1 && Arg_0<=4
28:eval_foo_bb5_in(Arg_0,Arg_1,Arg_2) -> eval_foo_stop(Arg_0,Arg_1,Arg_2):|:Arg_2<=Arg_0 && 5<=Arg_0
29:eval_foo_start(Arg_0,Arg_1,Arg_2) -> eval_foo_bb0_in(Arg_0,Arg_1,Arg_2)

MPRF for transition 21:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2) -> eval_foo_bb2_in(Arg_0,0,Arg_2):|:Arg_2<=Arg_0 && Arg_0<5 of depth 1:

new bound:

Arg_2+5 {O(n)}

MPRF:

eval_foo_bb3_in [4-Arg_0 ]
eval_foo_bb2_in [4-Arg_0 ]
eval_foo_bb4_in [4-Arg_0 ]
eval_foo_bb1_in [5-Arg_0 ]

MPRF for transition 24:eval_foo_bb2_in(Arg_0,Arg_1,Arg_2) -> eval_foo_bb4_in(Arg_0,Arg_1,Arg_2):|:Arg_2<=4 && Arg_2<=4+Arg_1 && Arg_2<=Arg_0 && Arg_0+Arg_2<=8 && 0<=Arg_1 && Arg_0<=4+Arg_1 && Arg_0<=4 && Arg_0<=2 of depth 1:

new bound:

Arg_2+5 {O(n)}

MPRF:

eval_foo_bb3_in [5-Arg_0 ]
eval_foo_bb2_in [5-Arg_0 ]
eval_foo_bb4_in [4-Arg_0 ]
eval_foo_bb1_in [5-Arg_0 ]

MPRF for transition 25:eval_foo_bb2_in(Arg_0,Arg_1,Arg_2) -> eval_foo_bb4_in(Arg_0,Arg_1,Arg_2):|:Arg_2<=4 && Arg_2<=4+Arg_1 && Arg_2<=Arg_0 && Arg_0+Arg_2<=8 && 0<=Arg_1 && Arg_0<=4+Arg_1 && Arg_0<=4 && 9<Arg_1 of depth 1:

new bound:

Arg_2+5 {O(n)}

MPRF:

eval_foo_bb3_in [5-Arg_0 ]
eval_foo_bb2_in [5-Arg_0 ]
eval_foo_bb4_in [4-Arg_0 ]
eval_foo_bb1_in [5-Arg_0 ]

MPRF for transition 27:eval_foo_bb4_in(Arg_0,Arg_1,Arg_2) -> eval_foo_bb1_in(Arg_0+1,Arg_1,Arg_2):|:Arg_2<=4 && Arg_2<=2+Arg_1 && Arg_2<=Arg_0 && Arg_0+Arg_2<=8 && 0<=Arg_1 && Arg_0<=2+Arg_1 && Arg_0<=4 of depth 1:

new bound:

Arg_2+5 {O(n)}

MPRF:

eval_foo_bb3_in [5-Arg_0 ]
eval_foo_bb2_in [5-Arg_0 ]
eval_foo_bb4_in [5-Arg_0 ]
eval_foo_bb1_in [5-Arg_0 ]

MPRF for transition 23:eval_foo_bb2_in(Arg_0,Arg_1,Arg_2) -> eval_foo_bb3_in(Arg_0,Arg_1,Arg_2):|:Arg_2<=4 && Arg_2<=4+Arg_1 && Arg_2<=Arg_0 && Arg_0+Arg_2<=8 && 0<=Arg_1 && Arg_0<=4+Arg_1 && Arg_0<=4 && 2<Arg_0 && Arg_1<=9 of depth 1:

new bound:

10*Arg_2+60 {O(n)}

MPRF:

eval_foo_bb1_in [10 ]
eval_foo_bb4_in [-Arg_1 ]
eval_foo_bb3_in [9-Arg_1 ]
eval_foo_bb2_in [10-Arg_1 ]

MPRF for transition 26:eval_foo_bb3_in(Arg_0,Arg_1,Arg_2) -> eval_foo_bb2_in(Arg_0,Arg_1+1,Arg_2):|:Arg_2<=4 && Arg_2<=4+Arg_1 && Arg_1+Arg_2<=13 && Arg_2<=Arg_0 && Arg_0+Arg_2<=8 && Arg_1<=9 && Arg_1<=6+Arg_0 && Arg_0+Arg_1<=13 && 0<=Arg_1 && 3<=Arg_0+Arg_1 && Arg_0<=4+Arg_1 && Arg_0<=4 && 3<=Arg_0 of depth 1:

new bound:

10*Arg_2+60 {O(n)}

MPRF:

eval_foo_bb1_in [10 ]
eval_foo_bb4_in [-Arg_1 ]
eval_foo_bb3_in [10-Arg_1 ]
eval_foo_bb2_in [10-Arg_1 ]

All Bounds

Timebounds

Overall timebound:24*Arg_2+144 {O(n)}
20: eval_foo_bb0_in->eval_foo_bb1_in: 1 {O(1)}
21: eval_foo_bb1_in->eval_foo_bb2_in: Arg_2+5 {O(n)}
22: eval_foo_bb1_in->eval_foo_bb5_in: 1 {O(1)}
23: eval_foo_bb2_in->eval_foo_bb3_in: 10*Arg_2+60 {O(n)}
24: eval_foo_bb2_in->eval_foo_bb4_in: Arg_2+5 {O(n)}
25: eval_foo_bb2_in->eval_foo_bb4_in: Arg_2+5 {O(n)}
26: eval_foo_bb3_in->eval_foo_bb2_in: 10*Arg_2+60 {O(n)}
27: eval_foo_bb4_in->eval_foo_bb1_in: Arg_2+5 {O(n)}
28: eval_foo_bb5_in->eval_foo_stop: 1 {O(1)}
29: eval_foo_start->eval_foo_bb0_in: 1 {O(1)}

Costbounds

Overall costbound: 24*Arg_2+144 {O(n)}
20: eval_foo_bb0_in->eval_foo_bb1_in: 1 {O(1)}
21: eval_foo_bb1_in->eval_foo_bb2_in: Arg_2+5 {O(n)}
22: eval_foo_bb1_in->eval_foo_bb5_in: 1 {O(1)}
23: eval_foo_bb2_in->eval_foo_bb3_in: 10*Arg_2+60 {O(n)}
24: eval_foo_bb2_in->eval_foo_bb4_in: Arg_2+5 {O(n)}
25: eval_foo_bb2_in->eval_foo_bb4_in: Arg_2+5 {O(n)}
26: eval_foo_bb3_in->eval_foo_bb2_in: 10*Arg_2+60 {O(n)}
27: eval_foo_bb4_in->eval_foo_bb1_in: Arg_2+5 {O(n)}
28: eval_foo_bb5_in->eval_foo_stop: 1 {O(1)}
29: eval_foo_start->eval_foo_bb0_in: 1 {O(1)}

Sizebounds

20: eval_foo_bb0_in->eval_foo_bb1_in, Arg_0: Arg_2 {O(n)}
20: eval_foo_bb0_in->eval_foo_bb1_in, Arg_1: Arg_1 {O(n)}
20: eval_foo_bb0_in->eval_foo_bb1_in, Arg_2: Arg_2 {O(n)}
21: eval_foo_bb1_in->eval_foo_bb2_in, Arg_0: 2*Arg_2+9 {O(n)}
21: eval_foo_bb1_in->eval_foo_bb2_in, Arg_1: 0 {O(1)}
21: eval_foo_bb1_in->eval_foo_bb2_in, Arg_2: Arg_2 {O(n)}
22: eval_foo_bb1_in->eval_foo_bb5_in, Arg_0: 3*Arg_2+9 {O(n)}
22: eval_foo_bb1_in->eval_foo_bb5_in, Arg_1: Arg_1+10 {O(n)}
22: eval_foo_bb1_in->eval_foo_bb5_in, Arg_2: 2*Arg_2 {O(n)}
23: eval_foo_bb2_in->eval_foo_bb3_in, Arg_0: 4 {O(1)}
23: eval_foo_bb2_in->eval_foo_bb3_in, Arg_1: 9 {O(1)}
23: eval_foo_bb2_in->eval_foo_bb3_in, Arg_2: Arg_2 {O(n)}
24: eval_foo_bb2_in->eval_foo_bb4_in, Arg_0: 2*Arg_2+9 {O(n)}
24: eval_foo_bb2_in->eval_foo_bb4_in, Arg_1: 0 {O(1)}
24: eval_foo_bb2_in->eval_foo_bb4_in, Arg_2: Arg_2 {O(n)}
25: eval_foo_bb2_in->eval_foo_bb4_in, Arg_0: 4 {O(1)}
25: eval_foo_bb2_in->eval_foo_bb4_in, Arg_1: 10 {O(1)}
25: eval_foo_bb2_in->eval_foo_bb4_in, Arg_2: Arg_2 {O(n)}
26: eval_foo_bb3_in->eval_foo_bb2_in, Arg_0: 4 {O(1)}
26: eval_foo_bb3_in->eval_foo_bb2_in, Arg_1: 10 {O(1)}
26: eval_foo_bb3_in->eval_foo_bb2_in, Arg_2: Arg_2 {O(n)}
27: eval_foo_bb4_in->eval_foo_bb1_in, Arg_0: 2*Arg_2+9 {O(n)}
27: eval_foo_bb4_in->eval_foo_bb1_in, Arg_1: 10 {O(1)}
27: eval_foo_bb4_in->eval_foo_bb1_in, Arg_2: Arg_2 {O(n)}
28: eval_foo_bb5_in->eval_foo_stop, Arg_0: 3*Arg_2+9 {O(n)}
28: eval_foo_bb5_in->eval_foo_stop, Arg_1: Arg_1+10 {O(n)}
28: eval_foo_bb5_in->eval_foo_stop, Arg_2: 2*Arg_2 {O(n)}
29: eval_foo_start->eval_foo_bb0_in, Arg_0: Arg_0 {O(n)}
29: eval_foo_start->eval_foo_bb0_in, Arg_1: Arg_1 {O(n)}
29: eval_foo_start->eval_foo_bb0_in, Arg_2: Arg_2 {O(n)}