Initial Problem

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_start, eval_foo_stop
Transitions:
1:eval_foo_bb0_in(Arg_0,Arg_1,Arg_2) -> eval_foo_bb1_in(Arg_1,Arg_1,Arg_2):|:1<=2*Arg_2
2:eval_foo_bb0_in(Arg_0,Arg_1,Arg_2) -> eval_foo_bb3_in(Arg_0,Arg_1,Arg_2):|:2*Arg_2<1
3:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2) -> eval_foo_bb2_in(Arg_0,Arg_1,Arg_2):|:0<=Arg_0
4:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2) -> eval_foo_bb3_in(Arg_0,Arg_1,Arg_2):|:Arg_0<0
5:eval_foo_bb2_in(Arg_0,Arg_1,Arg_2) -> eval_foo_bb1_in(Arg_0+1-2*Arg_2,Arg_1,Arg_2)
6: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_2 && 1<=Arg_1+Arg_2 && 1<=Arg_0+Arg_2 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 0<=Arg_0 for location eval_foo_bb2_in

Found invariant 1<=Arg_2 && Arg_0<=Arg_1 for location eval_foo_bb1_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_start, eval_foo_stop
Transitions:
1:eval_foo_bb0_in(Arg_0,Arg_1,Arg_2) -> eval_foo_bb1_in(Arg_1,Arg_1,Arg_2):|:1<=2*Arg_2
2:eval_foo_bb0_in(Arg_0,Arg_1,Arg_2) -> eval_foo_bb3_in(Arg_0,Arg_1,Arg_2):|:2*Arg_2<1
3:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2) -> eval_foo_bb2_in(Arg_0,Arg_1,Arg_2):|:1<=Arg_2 && Arg_0<=Arg_1 && 0<=Arg_0
4:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2) -> eval_foo_bb3_in(Arg_0,Arg_1,Arg_2):|:1<=Arg_2 && Arg_0<=Arg_1 && Arg_0<0
5:eval_foo_bb2_in(Arg_0,Arg_1,Arg_2) -> eval_foo_bb1_in(Arg_0+1-2*Arg_2,Arg_1,Arg_2):|:1<=Arg_2 && 1<=Arg_1+Arg_2 && 1<=Arg_0+Arg_2 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 0<=Arg_0
6: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 3:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2) -> eval_foo_bb2_in(Arg_0,Arg_1,Arg_2):|:1<=Arg_2 && Arg_0<=Arg_1 && 0<=Arg_0 of depth 1:

new bound:

Arg_1+1 {O(n)}

MPRF:

eval_foo_bb2_in [Arg_0 ]
eval_foo_bb1_in [Arg_0+1 ]

MPRF for transition 5:eval_foo_bb2_in(Arg_0,Arg_1,Arg_2) -> eval_foo_bb1_in(Arg_0+1-2*Arg_2,Arg_1,Arg_2):|:1<=Arg_2 && 1<=Arg_1+Arg_2 && 1<=Arg_0+Arg_2 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 0<=Arg_0 of depth 1:

new bound:

2*Arg_2+Arg_1+1 {O(n)}

MPRF:

eval_foo_bb2_in [Arg_0+1 ]
eval_foo_bb1_in [Arg_0+2*Arg_2-1 ]

All Bounds

Timebounds

Overall timebound:2*Arg_1+2*Arg_2+7 {O(n)}
1: eval_foo_bb0_in->eval_foo_bb1_in: 1 {O(1)}
2: eval_foo_bb0_in->eval_foo_bb3_in: 1 {O(1)}
3: eval_foo_bb1_in->eval_foo_bb2_in: Arg_1+1 {O(n)}
4: eval_foo_bb1_in->eval_foo_bb3_in: 1 {O(1)}
5: eval_foo_bb2_in->eval_foo_bb1_in: 2*Arg_2+Arg_1+1 {O(n)}
6: eval_foo_bb3_in->eval_foo_stop: 1 {O(1)}
0: eval_foo_start->eval_foo_bb0_in: 1 {O(1)}

Costbounds

Overall costbound: 2*Arg_1+2*Arg_2+7 {O(n)}
1: eval_foo_bb0_in->eval_foo_bb1_in: 1 {O(1)}
2: eval_foo_bb0_in->eval_foo_bb3_in: 1 {O(1)}
3: eval_foo_bb1_in->eval_foo_bb2_in: Arg_1+1 {O(n)}
4: eval_foo_bb1_in->eval_foo_bb3_in: 1 {O(1)}
5: eval_foo_bb2_in->eval_foo_bb1_in: 2*Arg_2+Arg_1+1 {O(n)}
6: eval_foo_bb3_in->eval_foo_stop: 1 {O(1)}
0: eval_foo_start->eval_foo_bb0_in: 1 {O(1)}

Sizebounds

1: eval_foo_bb0_in->eval_foo_bb1_in, Arg_0: Arg_1 {O(n)}
1: eval_foo_bb0_in->eval_foo_bb1_in, Arg_1: Arg_1 {O(n)}
1: eval_foo_bb0_in->eval_foo_bb1_in, Arg_2: Arg_2 {O(n)}
2: eval_foo_bb0_in->eval_foo_bb3_in, Arg_0: Arg_0 {O(n)}
2: eval_foo_bb0_in->eval_foo_bb3_in, Arg_1: Arg_1 {O(n)}
2: eval_foo_bb0_in->eval_foo_bb3_in, Arg_2: Arg_2 {O(n)}
3: eval_foo_bb1_in->eval_foo_bb2_in, Arg_0: 2*2^(2*Arg_2+Arg_1+1)*Arg_2+2*2^(2*Arg_2+Arg_1+1)*Arg_2*Arg_2+2^(2*Arg_2+Arg_1+1)*Arg_1+2^(2*Arg_2+Arg_1+1)*Arg_1*Arg_2 {O(EXP)}
3: eval_foo_bb1_in->eval_foo_bb2_in, Arg_1: Arg_1 {O(n)}
3: eval_foo_bb1_in->eval_foo_bb2_in, Arg_2: Arg_2 {O(n)}
4: eval_foo_bb1_in->eval_foo_bb3_in, Arg_0: 2*2^(2*Arg_2+Arg_1+1)*Arg_2+2*2^(2*Arg_2+Arg_1+1)*Arg_2*Arg_2+2^(2*Arg_2+Arg_1+1)*Arg_1+2^(2*Arg_2+Arg_1+1)*Arg_1*Arg_2+Arg_1 {O(EXP)}
4: eval_foo_bb1_in->eval_foo_bb3_in, Arg_1: 2*Arg_1 {O(n)}
4: eval_foo_bb1_in->eval_foo_bb3_in, Arg_2: 2*Arg_2 {O(n)}
5: eval_foo_bb2_in->eval_foo_bb1_in, Arg_0: 2*2^(2*Arg_2+Arg_1+1)*Arg_2+2*2^(2*Arg_2+Arg_1+1)*Arg_2*Arg_2+2^(2*Arg_2+Arg_1+1)*Arg_1+2^(2*Arg_2+Arg_1+1)*Arg_1*Arg_2 {O(EXP)}
5: eval_foo_bb2_in->eval_foo_bb1_in, Arg_1: Arg_1 {O(n)}
5: eval_foo_bb2_in->eval_foo_bb1_in, Arg_2: Arg_2 {O(n)}
6: eval_foo_bb3_in->eval_foo_stop, Arg_0: 2*2^(2*Arg_2+Arg_1+1)*Arg_2+2*2^(2*Arg_2+Arg_1+1)*Arg_2*Arg_2+2^(2*Arg_2+Arg_1+1)*Arg_1+2^(2*Arg_2+Arg_1+1)*Arg_1*Arg_2+Arg_0+Arg_1 {O(EXP)}
6: eval_foo_bb3_in->eval_foo_stop, Arg_1: 3*Arg_1 {O(n)}
6: eval_foo_bb3_in->eval_foo_stop, Arg_2: 3*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)}