Initial Problem

Start: eval_random1d_start
Program_Vars: Arg_0, Arg_1, Arg_2
Temp_Vars: nondef_0
Locations: eval_random1d_0, eval_random1d_1, eval_random1d_2, eval_random1d_3, eval_random1d_bb0_in, eval_random1d_bb1_in, eval_random1d_bb2_in, eval_random1d_bb3_in, eval_random1d_start, eval_random1d_stop
Transitions:
2:eval_random1d_0(Arg_0,Arg_1,Arg_2) -> eval_random1d_1(Arg_0,Arg_1,Arg_2)
3:eval_random1d_1(Arg_0,Arg_1,Arg_2) -> eval_random1d_bb1_in(Arg_0,Arg_1,1):|:0<Arg_1
4:eval_random1d_1(Arg_0,Arg_1,Arg_2) -> eval_random1d_bb3_in(Arg_0,Arg_1,Arg_2):|:Arg_1<=0
8:eval_random1d_2(Arg_0,Arg_1,Arg_2) -> eval_random1d_3(nondef_0,Arg_1,Arg_2)
9:eval_random1d_3(Arg_0,Arg_1,Arg_2) -> eval_random1d_bb1_in(Arg_0,Arg_1,Arg_2+1):|:0<Arg_0
10:eval_random1d_3(Arg_0,Arg_1,Arg_2) -> eval_random1d_bb1_in(Arg_0,Arg_1,Arg_2+1):|:Arg_0<=0
1:eval_random1d_bb0_in(Arg_0,Arg_1,Arg_2) -> eval_random1d_0(Arg_0,Arg_1,Arg_2)
5:eval_random1d_bb1_in(Arg_0,Arg_1,Arg_2) -> eval_random1d_bb2_in(Arg_0,Arg_1,Arg_2):|:Arg_2<=Arg_1
6:eval_random1d_bb1_in(Arg_0,Arg_1,Arg_2) -> eval_random1d_bb3_in(Arg_0,Arg_1,Arg_2):|:Arg_1<Arg_2
7:eval_random1d_bb2_in(Arg_0,Arg_1,Arg_2) -> eval_random1d_2(Arg_0,Arg_1,Arg_2)
11:eval_random1d_bb3_in(Arg_0,Arg_1,Arg_2) -> eval_random1d_stop(Arg_0,Arg_1,Arg_2)
0:eval_random1d_start(Arg_0,Arg_1,Arg_2) -> eval_random1d_bb0_in(Arg_0,Arg_1,Arg_2)

Preprocessing

Found invariant Arg_2<=Arg_1 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && 1<=Arg_1 for location eval_random1d_2

Found invariant Arg_2<=Arg_1 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && 1<=Arg_1 for location eval_random1d_3

Found invariant Arg_2<=1+Arg_1 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && 1<=Arg_1 for location eval_random1d_bb1_in

Found invariant Arg_2<=Arg_1 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && 1<=Arg_1 for location eval_random1d_bb2_in

Problem after Preprocessing

Start: eval_random1d_start
Program_Vars: Arg_0, Arg_1, Arg_2
Temp_Vars: nondef_0
Locations: eval_random1d_0, eval_random1d_1, eval_random1d_2, eval_random1d_3, eval_random1d_bb0_in, eval_random1d_bb1_in, eval_random1d_bb2_in, eval_random1d_bb3_in, eval_random1d_start, eval_random1d_stop
Transitions:
2:eval_random1d_0(Arg_0,Arg_1,Arg_2) -> eval_random1d_1(Arg_0,Arg_1,Arg_2)
3:eval_random1d_1(Arg_0,Arg_1,Arg_2) -> eval_random1d_bb1_in(Arg_0,Arg_1,1):|:0<Arg_1
4:eval_random1d_1(Arg_0,Arg_1,Arg_2) -> eval_random1d_bb3_in(Arg_0,Arg_1,Arg_2):|:Arg_1<=0
8:eval_random1d_2(Arg_0,Arg_1,Arg_2) -> eval_random1d_3(nondef_0,Arg_1,Arg_2):|:Arg_2<=Arg_1 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && 1<=Arg_1
9:eval_random1d_3(Arg_0,Arg_1,Arg_2) -> eval_random1d_bb1_in(Arg_0,Arg_1,Arg_2+1):|:Arg_2<=Arg_1 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && 1<=Arg_1 && 0<Arg_0
10:eval_random1d_3(Arg_0,Arg_1,Arg_2) -> eval_random1d_bb1_in(Arg_0,Arg_1,Arg_2+1):|:Arg_2<=Arg_1 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && 1<=Arg_1 && Arg_0<=0
1:eval_random1d_bb0_in(Arg_0,Arg_1,Arg_2) -> eval_random1d_0(Arg_0,Arg_1,Arg_2)
5:eval_random1d_bb1_in(Arg_0,Arg_1,Arg_2) -> eval_random1d_bb2_in(Arg_0,Arg_1,Arg_2):|:Arg_2<=1+Arg_1 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && 1<=Arg_1 && Arg_2<=Arg_1
6:eval_random1d_bb1_in(Arg_0,Arg_1,Arg_2) -> eval_random1d_bb3_in(Arg_0,Arg_1,Arg_2):|:Arg_2<=1+Arg_1 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && 1<=Arg_1 && Arg_1<Arg_2
7:eval_random1d_bb2_in(Arg_0,Arg_1,Arg_2) -> eval_random1d_2(Arg_0,Arg_1,Arg_2):|:Arg_2<=Arg_1 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && 1<=Arg_1
11:eval_random1d_bb3_in(Arg_0,Arg_1,Arg_2) -> eval_random1d_stop(Arg_0,Arg_1,Arg_2)
0:eval_random1d_start(Arg_0,Arg_1,Arg_2) -> eval_random1d_bb0_in(Arg_0,Arg_1,Arg_2)

MPRF for transition 8:eval_random1d_2(Arg_0,Arg_1,Arg_2) -> eval_random1d_3(nondef_0,Arg_1,Arg_2):|:Arg_2<=Arg_1 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && 1<=Arg_1 of depth 1:

new bound:

2*Arg_1+1 {O(n)}

MPRF:

eval_random1d_3 [2*Arg_1-Arg_2-1 ]
eval_random1d_bb1_in [2*Arg_1-Arg_2 ]
eval_random1d_bb2_in [2*Arg_1-Arg_2 ]
eval_random1d_2 [2*Arg_1-Arg_2 ]

MPRF for transition 9:eval_random1d_3(Arg_0,Arg_1,Arg_2) -> eval_random1d_bb1_in(Arg_0,Arg_1,Arg_2+1):|:Arg_2<=Arg_1 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && 1<=Arg_1 && 0<Arg_0 of depth 1:

new bound:

Arg_1+2 {O(n)}

MPRF:

eval_random1d_3 [Arg_1+1-Arg_2 ]
eval_random1d_bb1_in [Arg_1+1-Arg_2 ]
eval_random1d_bb2_in [Arg_1+1-Arg_2 ]
eval_random1d_2 [Arg_1+1-Arg_2 ]

MPRF for transition 10:eval_random1d_3(Arg_0,Arg_1,Arg_2) -> eval_random1d_bb1_in(Arg_0,Arg_1,Arg_2+1):|:Arg_2<=Arg_1 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && 1<=Arg_1 && Arg_0<=0 of depth 1:

new bound:

Arg_1+2 {O(n)}

MPRF:

eval_random1d_3 [Arg_1+1-Arg_2 ]
eval_random1d_bb1_in [Arg_1+1-Arg_2 ]
eval_random1d_bb2_in [Arg_1+1-Arg_2 ]
eval_random1d_2 [Arg_1+1-Arg_2 ]

MPRF for transition 5:eval_random1d_bb1_in(Arg_0,Arg_1,Arg_2) -> eval_random1d_bb2_in(Arg_0,Arg_1,Arg_2):|:Arg_2<=1+Arg_1 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && 1<=Arg_1 && Arg_2<=Arg_1 of depth 1:

new bound:

Arg_1+2 {O(n)}

MPRF:

eval_random1d_3 [Arg_1-Arg_2 ]
eval_random1d_bb1_in [Arg_1+1-Arg_2 ]
eval_random1d_bb2_in [Arg_1-Arg_2 ]
eval_random1d_2 [Arg_1-Arg_2 ]

MPRF for transition 7:eval_random1d_bb2_in(Arg_0,Arg_1,Arg_2) -> eval_random1d_2(Arg_0,Arg_1,Arg_2):|:Arg_2<=Arg_1 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && 1<=Arg_1 of depth 1:

new bound:

Arg_1+2 {O(n)}

MPRF:

eval_random1d_3 [Arg_1-Arg_2 ]
eval_random1d_bb1_in [Arg_1+1-Arg_2 ]
eval_random1d_bb2_in [Arg_1+1-Arg_2 ]
eval_random1d_2 [Arg_1-Arg_2 ]

All Bounds

Timebounds

Overall timebound:6*Arg_1+16 {O(n)}
2: eval_random1d_0->eval_random1d_1: 1 {O(1)}
3: eval_random1d_1->eval_random1d_bb1_in: 1 {O(1)}
4: eval_random1d_1->eval_random1d_bb3_in: 1 {O(1)}
8: eval_random1d_2->eval_random1d_3: 2*Arg_1+1 {O(n)}
9: eval_random1d_3->eval_random1d_bb1_in: Arg_1+2 {O(n)}
10: eval_random1d_3->eval_random1d_bb1_in: Arg_1+2 {O(n)}
1: eval_random1d_bb0_in->eval_random1d_0: 1 {O(1)}
5: eval_random1d_bb1_in->eval_random1d_bb2_in: Arg_1+2 {O(n)}
6: eval_random1d_bb1_in->eval_random1d_bb3_in: 1 {O(1)}
7: eval_random1d_bb2_in->eval_random1d_2: Arg_1+2 {O(n)}
11: eval_random1d_bb3_in->eval_random1d_stop: 1 {O(1)}
0: eval_random1d_start->eval_random1d_bb0_in: 1 {O(1)}

Costbounds

Overall costbound: 6*Arg_1+16 {O(n)}
2: eval_random1d_0->eval_random1d_1: 1 {O(1)}
3: eval_random1d_1->eval_random1d_bb1_in: 1 {O(1)}
4: eval_random1d_1->eval_random1d_bb3_in: 1 {O(1)}
8: eval_random1d_2->eval_random1d_3: 2*Arg_1+1 {O(n)}
9: eval_random1d_3->eval_random1d_bb1_in: Arg_1+2 {O(n)}
10: eval_random1d_3->eval_random1d_bb1_in: Arg_1+2 {O(n)}
1: eval_random1d_bb0_in->eval_random1d_0: 1 {O(1)}
5: eval_random1d_bb1_in->eval_random1d_bb2_in: Arg_1+2 {O(n)}
6: eval_random1d_bb1_in->eval_random1d_bb3_in: 1 {O(1)}
7: eval_random1d_bb2_in->eval_random1d_2: Arg_1+2 {O(n)}
11: eval_random1d_bb3_in->eval_random1d_stop: 1 {O(1)}
0: eval_random1d_start->eval_random1d_bb0_in: 1 {O(1)}

Sizebounds

2: eval_random1d_0->eval_random1d_1, Arg_0: Arg_0 {O(n)}
2: eval_random1d_0->eval_random1d_1, Arg_1: Arg_1 {O(n)}
2: eval_random1d_0->eval_random1d_1, Arg_2: Arg_2 {O(n)}
3: eval_random1d_1->eval_random1d_bb1_in, Arg_0: Arg_0 {O(n)}
3: eval_random1d_1->eval_random1d_bb1_in, Arg_1: Arg_1 {O(n)}
3: eval_random1d_1->eval_random1d_bb1_in, Arg_2: 1 {O(1)}
4: eval_random1d_1->eval_random1d_bb3_in, Arg_0: Arg_0 {O(n)}
4: eval_random1d_1->eval_random1d_bb3_in, Arg_1: Arg_1 {O(n)}
4: eval_random1d_1->eval_random1d_bb3_in, Arg_2: Arg_2 {O(n)}
8: eval_random1d_2->eval_random1d_3, Arg_1: Arg_1 {O(n)}
8: eval_random1d_2->eval_random1d_3, Arg_2: 2*Arg_1+5 {O(n)}
9: eval_random1d_3->eval_random1d_bb1_in, Arg_1: Arg_1 {O(n)}
9: eval_random1d_3->eval_random1d_bb1_in, Arg_2: 2*Arg_1+5 {O(n)}
10: eval_random1d_3->eval_random1d_bb1_in, Arg_1: Arg_1 {O(n)}
10: eval_random1d_3->eval_random1d_bb1_in, Arg_2: 2*Arg_1+5 {O(n)}
1: eval_random1d_bb0_in->eval_random1d_0, Arg_0: Arg_0 {O(n)}
1: eval_random1d_bb0_in->eval_random1d_0, Arg_1: Arg_1 {O(n)}
1: eval_random1d_bb0_in->eval_random1d_0, Arg_2: Arg_2 {O(n)}
5: eval_random1d_bb1_in->eval_random1d_bb2_in, Arg_1: Arg_1 {O(n)}
5: eval_random1d_bb1_in->eval_random1d_bb2_in, Arg_2: 2*Arg_1+5 {O(n)}
6: eval_random1d_bb1_in->eval_random1d_bb3_in, Arg_1: 2*Arg_1 {O(n)}
6: eval_random1d_bb1_in->eval_random1d_bb3_in, Arg_2: 4*Arg_1+10 {O(n)}
7: eval_random1d_bb2_in->eval_random1d_2, Arg_1: Arg_1 {O(n)}
7: eval_random1d_bb2_in->eval_random1d_2, Arg_2: 2*Arg_1+5 {O(n)}
11: eval_random1d_bb3_in->eval_random1d_stop, Arg_1: 3*Arg_1 {O(n)}
11: eval_random1d_bb3_in->eval_random1d_stop, Arg_2: 4*Arg_1+Arg_2+10 {O(n)}
0: eval_random1d_start->eval_random1d_bb0_in, Arg_0: Arg_0 {O(n)}
0: eval_random1d_start->eval_random1d_bb0_in, Arg_1: Arg_1 {O(n)}
0: eval_random1d_start->eval_random1d_bb0_in, Arg_2: Arg_2 {O(n)}