Initial Problem

Start: eval_foo_start
Program_Vars: Arg_0, Arg_1, Arg_2
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_start, eval_foo_stop
Transitions:
3:eval_foo_0(Arg_0,Arg_1,Arg_2) -> eval_foo_1(Arg_0,nondef.0,Arg_2)
4:eval_foo_1(Arg_0,Arg_1,Arg_2) -> eval_foo_bb1_in(Arg_2,Arg_1,Arg_2):|:Arg_1<Arg_2
5:eval_foo_1(Arg_0,Arg_1,Arg_2) -> eval_foo_bb3_in(Arg_0,Arg_1,Arg_2):|:Arg_2<=Arg_1
1:eval_foo_bb0_in(Arg_0,Arg_1,Arg_2) -> eval_foo_0(Arg_0,Arg_1,Arg_2)
6:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2) -> eval_foo_bb2_in(Arg_0,Arg_1,Arg_2):|:Arg_0<0
7:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2) -> eval_foo_bb2_in(Arg_0,Arg_1,Arg_2):|:0<Arg_0
8:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2) -> eval_foo_bb3_in(Arg_0,Arg_1,Arg_2):|:Arg_0<=0 && 0<=Arg_0
9:eval_foo_bb2_in(Arg_0,Arg_1,Arg_2) -> eval_foo_bb1_in(Arg_0-1,Arg_1,Arg_2)
10:eval_foo_bb3_in(Arg_0,Arg_1,Arg_2) -> eval_foo_stop(Arg_0,Arg_1,Arg_2)
0:eval_foo_start(Arg_0,Arg_1,Arg_2) -> eval_foo_bb0_in(Arg_0,Arg_1,Arg_2)

Preprocessing

Found invariant 1+Arg_1<=Arg_2 && Arg_0<=Arg_2 for location eval_foo_bb2_in

Found invariant 1+Arg_1<=Arg_2 && Arg_0<=Arg_2 for location eval_foo_bb1_in

Problem after Preprocessing

Start: eval_foo_start
Program_Vars: Arg_0, Arg_1, Arg_2
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_start, eval_foo_stop
Transitions:
3:eval_foo_0(Arg_0,Arg_1,Arg_2) -> eval_foo_1(Arg_0,nondef.0,Arg_2)
4:eval_foo_1(Arg_0,Arg_1,Arg_2) -> eval_foo_bb1_in(Arg_2,Arg_1,Arg_2):|:Arg_1<Arg_2
5:eval_foo_1(Arg_0,Arg_1,Arg_2) -> eval_foo_bb3_in(Arg_0,Arg_1,Arg_2):|:Arg_2<=Arg_1
1:eval_foo_bb0_in(Arg_0,Arg_1,Arg_2) -> eval_foo_0(Arg_0,Arg_1,Arg_2)
6:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2) -> eval_foo_bb2_in(Arg_0,Arg_1,Arg_2):|:1+Arg_1<=Arg_2 && Arg_0<=Arg_2 && Arg_0<0
7:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2) -> eval_foo_bb2_in(Arg_0,Arg_1,Arg_2):|:1+Arg_1<=Arg_2 && Arg_0<=Arg_2 && 0<Arg_0
8:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2) -> eval_foo_bb3_in(Arg_0,Arg_1,Arg_2):|:1+Arg_1<=Arg_2 && Arg_0<=Arg_2 && Arg_0<=0 && 0<=Arg_0
9:eval_foo_bb2_in(Arg_0,Arg_1,Arg_2) -> eval_foo_bb1_in(Arg_0-1,Arg_1,Arg_2):|:1+Arg_1<=Arg_2 && Arg_0<=Arg_2
10:eval_foo_bb3_in(Arg_0,Arg_1,Arg_2) -> eval_foo_stop(Arg_0,Arg_1,Arg_2)
0:eval_foo_start(Arg_0,Arg_1,Arg_2) -> eval_foo_bb0_in(Arg_0,Arg_1,Arg_2)

MPRF for transition 7:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2) -> eval_foo_bb2_in(Arg_0,Arg_1,Arg_2):|:1+Arg_1<=Arg_2 && Arg_0<=Arg_2 && 0<Arg_0 of depth 1:

new bound:

Arg_2 {O(n)}

MPRF:

eval_foo_bb2_in [Arg_0-1 ]
eval_foo_bb1_in [Arg_0 ]

All Bounds

Timebounds

Overall timebound:inf {Infinity}
3: eval_foo_0->eval_foo_1: 1 {O(1)}
4: eval_foo_1->eval_foo_bb1_in: 1 {O(1)}
5: eval_foo_1->eval_foo_bb3_in: 1 {O(1)}
1: eval_foo_bb0_in->eval_foo_0: 1 {O(1)}
6: eval_foo_bb1_in->eval_foo_bb2_in: inf {Infinity}
7: eval_foo_bb1_in->eval_foo_bb2_in: Arg_2 {O(n)}
8: eval_foo_bb1_in->eval_foo_bb3_in: 1 {O(1)}
9: eval_foo_bb2_in->eval_foo_bb1_in: inf {Infinity}
10: eval_foo_bb3_in->eval_foo_stop: 1 {O(1)}
0: eval_foo_start->eval_foo_bb0_in: 1 {O(1)}

Costbounds

Overall costbound: inf {Infinity}
3: eval_foo_0->eval_foo_1: 1 {O(1)}
4: eval_foo_1->eval_foo_bb1_in: 1 {O(1)}
5: eval_foo_1->eval_foo_bb3_in: 1 {O(1)}
1: eval_foo_bb0_in->eval_foo_0: 1 {O(1)}
6: eval_foo_bb1_in->eval_foo_bb2_in: inf {Infinity}
7: eval_foo_bb1_in->eval_foo_bb2_in: Arg_2 {O(n)}
8: eval_foo_bb1_in->eval_foo_bb3_in: 1 {O(1)}
9: eval_foo_bb2_in->eval_foo_bb1_in: inf {Infinity}
10: eval_foo_bb3_in->eval_foo_stop: 1 {O(1)}
0: eval_foo_start->eval_foo_bb0_in: 1 {O(1)}

Sizebounds

3: eval_foo_0->eval_foo_1, Arg_0: Arg_0 {O(n)}
3: eval_foo_0->eval_foo_1, Arg_2: Arg_2 {O(n)}
4: eval_foo_1->eval_foo_bb1_in, Arg_0: Arg_2 {O(n)}
4: eval_foo_1->eval_foo_bb1_in, Arg_2: Arg_2 {O(n)}
5: eval_foo_1->eval_foo_bb3_in, Arg_0: Arg_0 {O(n)}
5: eval_foo_1->eval_foo_bb3_in, Arg_2: Arg_2 {O(n)}
1: eval_foo_bb0_in->eval_foo_0, Arg_0: Arg_0 {O(n)}
1: eval_foo_bb0_in->eval_foo_0, Arg_1: Arg_1 {O(n)}
1: eval_foo_bb0_in->eval_foo_0, Arg_2: Arg_2 {O(n)}
6: eval_foo_bb1_in->eval_foo_bb2_in, Arg_2: 2*Arg_2 {O(n)}
7: eval_foo_bb1_in->eval_foo_bb2_in, Arg_2: 2*Arg_2 {O(n)}
8: eval_foo_bb1_in->eval_foo_bb3_in, Arg_0: 0 {O(1)}
8: eval_foo_bb1_in->eval_foo_bb3_in, Arg_2: 3*Arg_2 {O(n)}
9: eval_foo_bb2_in->eval_foo_bb1_in, Arg_2: 2*Arg_2 {O(n)}
10: eval_foo_bb3_in->eval_foo_stop, Arg_0: Arg_0 {O(n)}
10: eval_foo_bb3_in->eval_foo_stop, Arg_2: 4*Arg_2 {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)}