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_3,1,Arg_2,Arg_3)
2:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3):|:0<Arg_1
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):|:Arg_1<=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):|:100<Arg_0
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<=100
6:eval_foo_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_foo_bb1_in(Arg_0-10,Arg_1-1,Arg_2,Arg_3)
7:eval_foo_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_foo_bb1_in(Arg_0+11,Arg_1+1,Arg_2,Arg_3)
8: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_2} that do not contribute to the problem

Found invariant Arg_1<=0 && 0<=Arg_1 for location eval_foo_bb5_in

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

Found invariant 1<=Arg_1 && 102<=Arg_0+Arg_1 && 101<=Arg_0 for location eval_foo_bb3_in

Found invariant 1<=Arg_1 for location eval_foo_bb2_in

Found invariant 0<=Arg_1 for location eval_foo_bb1_in

Found invariant 1<=Arg_1 && Arg_0<=99+Arg_1 && Arg_0<=100 for location eval_foo_bb4_in

Problem after Preprocessing

Start: eval_foo_start
Program_Vars: Arg_0, Arg_1, 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:
18:eval_foo_bb0_in(Arg_0,Arg_1,Arg_3) -> eval_foo_bb1_in(Arg_3,1,Arg_3)
19:eval_foo_bb1_in(Arg_0,Arg_1,Arg_3) -> eval_foo_bb2_in(Arg_0,Arg_1,Arg_3):|:0<=Arg_1 && 0<Arg_1
20:eval_foo_bb1_in(Arg_0,Arg_1,Arg_3) -> eval_foo_bb5_in(Arg_0,Arg_1,Arg_3):|:0<=Arg_1 && Arg_1<=0
21:eval_foo_bb2_in(Arg_0,Arg_1,Arg_3) -> eval_foo_bb3_in(Arg_0,Arg_1,Arg_3):|:1<=Arg_1 && 100<Arg_0
22:eval_foo_bb2_in(Arg_0,Arg_1,Arg_3) -> eval_foo_bb4_in(Arg_0,Arg_1,Arg_3):|:1<=Arg_1 && Arg_0<=100
23:eval_foo_bb3_in(Arg_0,Arg_1,Arg_3) -> eval_foo_bb1_in(Arg_0-10,Arg_1-1,Arg_3):|:1<=Arg_1 && 102<=Arg_0+Arg_1 && 101<=Arg_0
24:eval_foo_bb4_in(Arg_0,Arg_1,Arg_3) -> eval_foo_bb1_in(Arg_0+11,Arg_1+1,Arg_3):|:1<=Arg_1 && Arg_0<=99+Arg_1 && Arg_0<=100
25:eval_foo_bb5_in(Arg_0,Arg_1,Arg_3) -> eval_foo_stop(Arg_0,Arg_1,Arg_3):|:Arg_1<=0 && 0<=Arg_1
26:eval_foo_start(Arg_0,Arg_1,Arg_3) -> eval_foo_bb0_in(Arg_0,Arg_1,Arg_3)

MPRF for transition 22:eval_foo_bb2_in(Arg_0,Arg_1,Arg_3) -> eval_foo_bb4_in(Arg_0,Arg_1,Arg_3):|:1<=Arg_1 && Arg_0<=100 of depth 1:

new bound:

Arg_3+101 {O(n)}

MPRF:

eval_foo_bb2_in [10*Arg_1+91-Arg_0 ]
eval_foo_bb3_in [10*Arg_1+91-Arg_0 ]
eval_foo_bb4_in [10*Arg_1+90-Arg_0 ]
eval_foo_bb1_in [10*Arg_1+91-Arg_0 ]

MPRF for transition 24:eval_foo_bb4_in(Arg_0,Arg_1,Arg_3) -> eval_foo_bb1_in(Arg_0+11,Arg_1+1,Arg_3):|:1<=Arg_1 && Arg_0<=99+Arg_1 && Arg_0<=100 of depth 1:

new bound:

Arg_3+101 {O(n)}

MPRF:

eval_foo_bb2_in [10*Arg_1+91-Arg_0 ]
eval_foo_bb3_in [10*Arg_1+91-Arg_0 ]
eval_foo_bb4_in [10*Arg_1+91-Arg_0 ]
eval_foo_bb1_in [10*Arg_1+91-Arg_0 ]

MPRF for transition 19:eval_foo_bb1_in(Arg_0,Arg_1,Arg_3) -> eval_foo_bb2_in(Arg_0,Arg_1,Arg_3):|:0<=Arg_1 && 0<Arg_1 of depth 1:

new bound:

Arg_3*Arg_3+204*Arg_3+10405 {O(n^2)}

MPRF:

eval_foo_bb2_in [Arg_1 ]
eval_foo_bb4_in [Arg_1 ]
eval_foo_bb3_in [Arg_1 ]
eval_foo_bb1_in [Arg_1+1 ]

MPRF for transition 21:eval_foo_bb2_in(Arg_0,Arg_1,Arg_3) -> eval_foo_bb3_in(Arg_0,Arg_1,Arg_3):|:1<=Arg_1 && 100<Arg_0 of depth 1:

new bound:

Arg_3*Arg_3+385*Arg_3+28867 {O(n^2)}

MPRF:

eval_foo_bb2_in [Arg_1+182 ]
eval_foo_bb4_in [Arg_1+182 ]
eval_foo_bb3_in [Arg_1+181 ]
eval_foo_bb1_in [Arg_1+182 ]

MPRF for transition 23:eval_foo_bb3_in(Arg_0,Arg_1,Arg_3) -> eval_foo_bb1_in(Arg_0-10,Arg_1-1,Arg_3):|:1<=Arg_1 && 102<=Arg_0+Arg_1 && 101<=Arg_0 of depth 1:

new bound:

Arg_3*Arg_3+294*Arg_3+19585 {O(n^2)}

MPRF:

eval_foo_bb2_in [Arg_1+91 ]
eval_foo_bb4_in [Arg_1+91 ]
eval_foo_bb3_in [Arg_1+91 ]
eval_foo_bb1_in [Arg_1+91 ]

All Bounds

Timebounds

Overall timebound:3*Arg_3*Arg_3+885*Arg_3+59063 {O(n^2)}
18: eval_foo_bb0_in->eval_foo_bb1_in: 1 {O(1)}
19: eval_foo_bb1_in->eval_foo_bb2_in: Arg_3*Arg_3+204*Arg_3+10405 {O(n^2)}
20: eval_foo_bb1_in->eval_foo_bb5_in: 1 {O(1)}
21: eval_foo_bb2_in->eval_foo_bb3_in: Arg_3*Arg_3+385*Arg_3+28867 {O(n^2)}
22: eval_foo_bb2_in->eval_foo_bb4_in: Arg_3+101 {O(n)}
23: eval_foo_bb3_in->eval_foo_bb1_in: Arg_3*Arg_3+294*Arg_3+19585 {O(n^2)}
24: eval_foo_bb4_in->eval_foo_bb1_in: Arg_3+101 {O(n)}
25: eval_foo_bb5_in->eval_foo_stop: 1 {O(1)}
26: eval_foo_start->eval_foo_bb0_in: 1 {O(1)}

Costbounds

Overall costbound: 3*Arg_3*Arg_3+885*Arg_3+59063 {O(n^2)}
18: eval_foo_bb0_in->eval_foo_bb1_in: 1 {O(1)}
19: eval_foo_bb1_in->eval_foo_bb2_in: Arg_3*Arg_3+204*Arg_3+10405 {O(n^2)}
20: eval_foo_bb1_in->eval_foo_bb5_in: 1 {O(1)}
21: eval_foo_bb2_in->eval_foo_bb3_in: Arg_3*Arg_3+385*Arg_3+28867 {O(n^2)}
22: eval_foo_bb2_in->eval_foo_bb4_in: Arg_3+101 {O(n)}
23: eval_foo_bb3_in->eval_foo_bb1_in: Arg_3*Arg_3+294*Arg_3+19585 {O(n^2)}
24: eval_foo_bb4_in->eval_foo_bb1_in: Arg_3+101 {O(n)}
25: eval_foo_bb5_in->eval_foo_stop: 1 {O(1)}
26: eval_foo_start->eval_foo_bb0_in: 1 {O(1)}

Sizebounds

18: eval_foo_bb0_in->eval_foo_bb1_in, Arg_0: Arg_3 {O(n)}
18: eval_foo_bb0_in->eval_foo_bb1_in, Arg_1: 1 {O(1)}
18: eval_foo_bb0_in->eval_foo_bb1_in, Arg_3: Arg_3 {O(n)}
19: eval_foo_bb1_in->eval_foo_bb2_in, Arg_0: 12*Arg_3+1111 {O(n)}
19: eval_foo_bb1_in->eval_foo_bb2_in, Arg_1: Arg_3+102 {O(n)}
19: eval_foo_bb1_in->eval_foo_bb2_in, Arg_3: Arg_3 {O(n)}
20: eval_foo_bb1_in->eval_foo_bb5_in, Arg_0: 12*Arg_3+1111 {O(n)}
20: eval_foo_bb1_in->eval_foo_bb5_in, Arg_1: 0 {O(1)}
20: eval_foo_bb1_in->eval_foo_bb5_in, Arg_3: Arg_3 {O(n)}
21: eval_foo_bb2_in->eval_foo_bb3_in, Arg_0: 12*Arg_3+1111 {O(n)}
21: eval_foo_bb2_in->eval_foo_bb3_in, Arg_1: Arg_3+102 {O(n)}
21: eval_foo_bb2_in->eval_foo_bb3_in, Arg_3: Arg_3 {O(n)}
22: eval_foo_bb2_in->eval_foo_bb4_in, Arg_0: 12*Arg_3+1111 {O(n)}
22: eval_foo_bb2_in->eval_foo_bb4_in, Arg_1: Arg_3+102 {O(n)}
22: eval_foo_bb2_in->eval_foo_bb4_in, Arg_3: Arg_3 {O(n)}
23: eval_foo_bb3_in->eval_foo_bb1_in, Arg_0: 12*Arg_3+1111 {O(n)}
23: eval_foo_bb3_in->eval_foo_bb1_in, Arg_1: Arg_3+102 {O(n)}
23: eval_foo_bb3_in->eval_foo_bb1_in, Arg_3: Arg_3 {O(n)}
24: eval_foo_bb4_in->eval_foo_bb1_in, Arg_0: 12*Arg_3+1111 {O(n)}
24: eval_foo_bb4_in->eval_foo_bb1_in, Arg_1: Arg_3+102 {O(n)}
24: eval_foo_bb4_in->eval_foo_bb1_in, Arg_3: Arg_3 {O(n)}
25: eval_foo_bb5_in->eval_foo_stop, Arg_0: 12*Arg_3+1111 {O(n)}
25: eval_foo_bb5_in->eval_foo_stop, Arg_1: 0 {O(1)}
25: eval_foo_bb5_in->eval_foo_stop, Arg_3: Arg_3 {O(n)}
26: eval_foo_start->eval_foo_bb0_in, Arg_0: Arg_0 {O(n)}
26: eval_foo_start->eval_foo_bb0_in, Arg_1: Arg_1 {O(n)}
26: eval_foo_start->eval_foo_bb0_in, Arg_3: Arg_3 {O(n)}