Initial Problem

Start: eval_jama_ex2_start
Program_Vars: Arg_0, Arg_1, Arg_2
Temp_Vars:
Locations: eval_jama_ex2_bb0_in, eval_jama_ex2_bb1_in, eval_jama_ex2_bb2_in, eval_jama_ex2_bb3_in, eval_jama_ex2_bb4_in, eval_jama_ex2_bb5_in, eval_jama_ex2_start, eval_jama_ex2_stop
Transitions:
1:eval_jama_ex2_bb0_in(Arg_0,Arg_1,Arg_2) -> eval_jama_ex2_bb1_in(1,Arg_1,Arg_2)
2:eval_jama_ex2_bb1_in(Arg_0,Arg_1,Arg_2) -> eval_jama_ex2_bb2_in(Arg_0,1,Arg_2):|:Arg_0<=Arg_2
3:eval_jama_ex2_bb1_in(Arg_0,Arg_1,Arg_2) -> eval_jama_ex2_bb5_in(Arg_0,Arg_1,Arg_2):|:Arg_2<Arg_0
4:eval_jama_ex2_bb2_in(Arg_0,Arg_1,Arg_2) -> eval_jama_ex2_bb3_in(Arg_0,Arg_1,Arg_2):|:Arg_1<=Arg_0
5:eval_jama_ex2_bb2_in(Arg_0,Arg_1,Arg_2) -> eval_jama_ex2_bb4_in(Arg_0,Arg_1,Arg_2):|:Arg_0<Arg_1
6:eval_jama_ex2_bb3_in(Arg_0,Arg_1,Arg_2) -> eval_jama_ex2_bb2_in(Arg_0,Arg_1+1,Arg_2)
7:eval_jama_ex2_bb4_in(Arg_0,Arg_1,Arg_2) -> eval_jama_ex2_bb1_in(Arg_0+1,Arg_1,Arg_2)
8:eval_jama_ex2_bb5_in(Arg_0,Arg_1,Arg_2) -> eval_jama_ex2_stop(Arg_0,Arg_1,Arg_2)
0:eval_jama_ex2_start(Arg_0,Arg_1,Arg_2) -> eval_jama_ex2_bb0_in(Arg_0,Arg_1,Arg_2)

Preprocessing

Found invariant 1<=Arg_2 && 3<=Arg_1+Arg_2 && Arg_1<=1+Arg_2 && 2<=Arg_0+Arg_2 && Arg_0<=Arg_2 && Arg_1<=1+Arg_0 && 2<=Arg_1 && 3<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 1<=Arg_0 for location eval_jama_ex2_bb4_in

Found invariant 1+Arg_2<=Arg_0 && 1<=Arg_0 for location eval_jama_ex2_stop

Found invariant 1<=Arg_0 for location eval_jama_ex2_bb1_in

Found invariant 1<=Arg_2 && 2<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 2<=Arg_0+Arg_2 && Arg_0<=Arg_2 && Arg_1<=Arg_0 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 for location eval_jama_ex2_bb3_in

Found invariant 1<=Arg_2 && 2<=Arg_1+Arg_2 && Arg_1<=1+Arg_2 && 2<=Arg_0+Arg_2 && Arg_0<=Arg_2 && Arg_1<=1+Arg_0 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 for location eval_jama_ex2_bb2_in

Found invariant 1+Arg_2<=Arg_0 && 1<=Arg_0 for location eval_jama_ex2_bb5_in

Problem after Preprocessing

Start: eval_jama_ex2_start
Program_Vars: Arg_0, Arg_1, Arg_2
Temp_Vars:
Locations: eval_jama_ex2_bb0_in, eval_jama_ex2_bb1_in, eval_jama_ex2_bb2_in, eval_jama_ex2_bb3_in, eval_jama_ex2_bb4_in, eval_jama_ex2_bb5_in, eval_jama_ex2_start, eval_jama_ex2_stop
Transitions:
1:eval_jama_ex2_bb0_in(Arg_0,Arg_1,Arg_2) -> eval_jama_ex2_bb1_in(1,Arg_1,Arg_2)
2:eval_jama_ex2_bb1_in(Arg_0,Arg_1,Arg_2) -> eval_jama_ex2_bb2_in(Arg_0,1,Arg_2):|:1<=Arg_0 && Arg_0<=Arg_2
3:eval_jama_ex2_bb1_in(Arg_0,Arg_1,Arg_2) -> eval_jama_ex2_bb5_in(Arg_0,Arg_1,Arg_2):|:1<=Arg_0 && Arg_2<Arg_0
4:eval_jama_ex2_bb2_in(Arg_0,Arg_1,Arg_2) -> eval_jama_ex2_bb3_in(Arg_0,Arg_1,Arg_2):|:1<=Arg_2 && 2<=Arg_1+Arg_2 && Arg_1<=1+Arg_2 && 2<=Arg_0+Arg_2 && Arg_0<=Arg_2 && Arg_1<=1+Arg_0 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 && Arg_1<=Arg_0
5:eval_jama_ex2_bb2_in(Arg_0,Arg_1,Arg_2) -> eval_jama_ex2_bb4_in(Arg_0,Arg_1,Arg_2):|:1<=Arg_2 && 2<=Arg_1+Arg_2 && Arg_1<=1+Arg_2 && 2<=Arg_0+Arg_2 && Arg_0<=Arg_2 && Arg_1<=1+Arg_0 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 && Arg_0<Arg_1
6:eval_jama_ex2_bb3_in(Arg_0,Arg_1,Arg_2) -> eval_jama_ex2_bb2_in(Arg_0,Arg_1+1,Arg_2):|:1<=Arg_2 && 2<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 2<=Arg_0+Arg_2 && Arg_0<=Arg_2 && Arg_1<=Arg_0 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0
7:eval_jama_ex2_bb4_in(Arg_0,Arg_1,Arg_2) -> eval_jama_ex2_bb1_in(Arg_0+1,Arg_1,Arg_2):|:1<=Arg_2 && 3<=Arg_1+Arg_2 && Arg_1<=1+Arg_2 && 2<=Arg_0+Arg_2 && Arg_0<=Arg_2 && Arg_1<=1+Arg_0 && 2<=Arg_1 && 3<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 1<=Arg_0
8:eval_jama_ex2_bb5_in(Arg_0,Arg_1,Arg_2) -> eval_jama_ex2_stop(Arg_0,Arg_1,Arg_2):|:1+Arg_2<=Arg_0 && 1<=Arg_0
0:eval_jama_ex2_start(Arg_0,Arg_1,Arg_2) -> eval_jama_ex2_bb0_in(Arg_0,Arg_1,Arg_2)

MPRF for transition 2:eval_jama_ex2_bb1_in(Arg_0,Arg_1,Arg_2) -> eval_jama_ex2_bb2_in(Arg_0,1,Arg_2):|:1<=Arg_0 && Arg_0<=Arg_2 of depth 1:

new bound:

Arg_2+2 {O(n)}

MPRF:

eval_jama_ex2_bb3_in [Arg_2-Arg_0 ]
eval_jama_ex2_bb2_in [Arg_2-Arg_0 ]
eval_jama_ex2_bb4_in [Arg_2-Arg_0 ]
eval_jama_ex2_bb1_in [Arg_2+1-Arg_0 ]

MPRF for transition 5:eval_jama_ex2_bb2_in(Arg_0,Arg_1,Arg_2) -> eval_jama_ex2_bb4_in(Arg_0,Arg_1,Arg_2):|:1<=Arg_2 && 2<=Arg_1+Arg_2 && Arg_1<=1+Arg_2 && 2<=Arg_0+Arg_2 && Arg_0<=Arg_2 && Arg_1<=1+Arg_0 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 && Arg_0<Arg_1 of depth 1:

new bound:

Arg_2+2 {O(n)}

MPRF:

eval_jama_ex2_bb3_in [Arg_2+1-Arg_0 ]
eval_jama_ex2_bb2_in [Arg_2+1-Arg_0 ]
eval_jama_ex2_bb4_in [Arg_2-Arg_0 ]
eval_jama_ex2_bb1_in [Arg_2+1-Arg_0 ]

MPRF for transition 7:eval_jama_ex2_bb4_in(Arg_0,Arg_1,Arg_2) -> eval_jama_ex2_bb1_in(Arg_0+1,Arg_1,Arg_2):|:1<=Arg_2 && 3<=Arg_1+Arg_2 && Arg_1<=1+Arg_2 && 2<=Arg_0+Arg_2 && Arg_0<=Arg_2 && Arg_1<=1+Arg_0 && 2<=Arg_1 && 3<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 1<=Arg_0 of depth 1:

new bound:

2*Arg_2+1 {O(n)}

MPRF:

eval_jama_ex2_bb3_in [2*Arg_2-Arg_0 ]
eval_jama_ex2_bb2_in [2*Arg_2-Arg_0 ]
eval_jama_ex2_bb4_in [Arg_1+2*Arg_2-2*Arg_0-1 ]
eval_jama_ex2_bb1_in [2*Arg_2-Arg_0 ]

MPRF for transition 4:eval_jama_ex2_bb2_in(Arg_0,Arg_1,Arg_2) -> eval_jama_ex2_bb3_in(Arg_0,Arg_1,Arg_2):|:1<=Arg_2 && 2<=Arg_1+Arg_2 && Arg_1<=1+Arg_2 && 2<=Arg_0+Arg_2 && Arg_0<=Arg_2 && Arg_1<=1+Arg_0 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 && Arg_1<=Arg_0 of depth 1:

new bound:

4*Arg_2*Arg_2+6*Arg_2+3 {O(n^2)}

MPRF:

eval_jama_ex2_bb1_in [Arg_0 ]
eval_jama_ex2_bb4_in [Arg_0-Arg_1 ]
eval_jama_ex2_bb3_in [Arg_0-Arg_1 ]
eval_jama_ex2_bb2_in [Arg_0+1-Arg_1 ]

MPRF for transition 6:eval_jama_ex2_bb3_in(Arg_0,Arg_1,Arg_2) -> eval_jama_ex2_bb2_in(Arg_0,Arg_1+1,Arg_2):|:1<=Arg_2 && 2<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 2<=Arg_0+Arg_2 && Arg_0<=Arg_2 && Arg_1<=Arg_0 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 of depth 1:

new bound:

2*Arg_2*Arg_2+2*Arg_2 {O(n^2)}

MPRF:

eval_jama_ex2_bb1_in [Arg_2 ]
eval_jama_ex2_bb4_in [Arg_2-Arg_1 ]
eval_jama_ex2_bb3_in [Arg_2+1-Arg_1 ]
eval_jama_ex2_bb2_in [Arg_2+1-Arg_1 ]

All Bounds

Timebounds

Overall timebound:6*Arg_2*Arg_2+12*Arg_2+12 {O(n^2)}
1: eval_jama_ex2_bb0_in->eval_jama_ex2_bb1_in: 1 {O(1)}
2: eval_jama_ex2_bb1_in->eval_jama_ex2_bb2_in: Arg_2+2 {O(n)}
3: eval_jama_ex2_bb1_in->eval_jama_ex2_bb5_in: 1 {O(1)}
4: eval_jama_ex2_bb2_in->eval_jama_ex2_bb3_in: 4*Arg_2*Arg_2+6*Arg_2+3 {O(n^2)}
5: eval_jama_ex2_bb2_in->eval_jama_ex2_bb4_in: Arg_2+2 {O(n)}
6: eval_jama_ex2_bb3_in->eval_jama_ex2_bb2_in: 2*Arg_2*Arg_2+2*Arg_2 {O(n^2)}
7: eval_jama_ex2_bb4_in->eval_jama_ex2_bb1_in: 2*Arg_2+1 {O(n)}
8: eval_jama_ex2_bb5_in->eval_jama_ex2_stop: 1 {O(1)}
0: eval_jama_ex2_start->eval_jama_ex2_bb0_in: 1 {O(1)}

Costbounds

Overall costbound: 6*Arg_2*Arg_2+12*Arg_2+12 {O(n^2)}
1: eval_jama_ex2_bb0_in->eval_jama_ex2_bb1_in: 1 {O(1)}
2: eval_jama_ex2_bb1_in->eval_jama_ex2_bb2_in: Arg_2+2 {O(n)}
3: eval_jama_ex2_bb1_in->eval_jama_ex2_bb5_in: 1 {O(1)}
4: eval_jama_ex2_bb2_in->eval_jama_ex2_bb3_in: 4*Arg_2*Arg_2+6*Arg_2+3 {O(n^2)}
5: eval_jama_ex2_bb2_in->eval_jama_ex2_bb4_in: Arg_2+2 {O(n)}
6: eval_jama_ex2_bb3_in->eval_jama_ex2_bb2_in: 2*Arg_2*Arg_2+2*Arg_2 {O(n^2)}
7: eval_jama_ex2_bb4_in->eval_jama_ex2_bb1_in: 2*Arg_2+1 {O(n)}
8: eval_jama_ex2_bb5_in->eval_jama_ex2_stop: 1 {O(1)}
0: eval_jama_ex2_start->eval_jama_ex2_bb0_in: 1 {O(1)}

Sizebounds

1: eval_jama_ex2_bb0_in->eval_jama_ex2_bb1_in, Arg_0: 1 {O(1)}
1: eval_jama_ex2_bb0_in->eval_jama_ex2_bb1_in, Arg_1: Arg_1 {O(n)}
1: eval_jama_ex2_bb0_in->eval_jama_ex2_bb1_in, Arg_2: Arg_2 {O(n)}
2: eval_jama_ex2_bb1_in->eval_jama_ex2_bb2_in, Arg_0: 2*Arg_2+2 {O(n)}
2: eval_jama_ex2_bb1_in->eval_jama_ex2_bb2_in, Arg_1: 1 {O(1)}
2: eval_jama_ex2_bb1_in->eval_jama_ex2_bb2_in, Arg_2: Arg_2 {O(n)}
3: eval_jama_ex2_bb1_in->eval_jama_ex2_bb5_in, Arg_0: 2*Arg_2+3 {O(n)}
3: eval_jama_ex2_bb1_in->eval_jama_ex2_bb5_in, Arg_1: 2*Arg_2*Arg_2+2*Arg_2+Arg_1+1 {O(n^2)}
3: eval_jama_ex2_bb1_in->eval_jama_ex2_bb5_in, Arg_2: 2*Arg_2 {O(n)}
4: eval_jama_ex2_bb2_in->eval_jama_ex2_bb3_in, Arg_0: 2*Arg_2+2 {O(n)}
4: eval_jama_ex2_bb2_in->eval_jama_ex2_bb3_in, Arg_1: 2*Arg_2*Arg_2+2*Arg_2+1 {O(n^2)}
4: eval_jama_ex2_bb2_in->eval_jama_ex2_bb3_in, Arg_2: Arg_2 {O(n)}
5: eval_jama_ex2_bb2_in->eval_jama_ex2_bb4_in, Arg_0: 2*Arg_2+2 {O(n)}
5: eval_jama_ex2_bb2_in->eval_jama_ex2_bb4_in, Arg_1: 2*Arg_2*Arg_2+2*Arg_2+1 {O(n^2)}
5: eval_jama_ex2_bb2_in->eval_jama_ex2_bb4_in, Arg_2: Arg_2 {O(n)}
6: eval_jama_ex2_bb3_in->eval_jama_ex2_bb2_in, Arg_0: 2*Arg_2+2 {O(n)}
6: eval_jama_ex2_bb3_in->eval_jama_ex2_bb2_in, Arg_1: 2*Arg_2*Arg_2+2*Arg_2+1 {O(n^2)}
6: eval_jama_ex2_bb3_in->eval_jama_ex2_bb2_in, Arg_2: Arg_2 {O(n)}
7: eval_jama_ex2_bb4_in->eval_jama_ex2_bb1_in, Arg_0: 2*Arg_2+2 {O(n)}
7: eval_jama_ex2_bb4_in->eval_jama_ex2_bb1_in, Arg_1: 2*Arg_2*Arg_2+2*Arg_2+1 {O(n^2)}
7: eval_jama_ex2_bb4_in->eval_jama_ex2_bb1_in, Arg_2: Arg_2 {O(n)}
8: eval_jama_ex2_bb5_in->eval_jama_ex2_stop, Arg_0: 2*Arg_2+3 {O(n)}
8: eval_jama_ex2_bb5_in->eval_jama_ex2_stop, Arg_1: 2*Arg_2*Arg_2+2*Arg_2+Arg_1+1 {O(n^2)}
8: eval_jama_ex2_bb5_in->eval_jama_ex2_stop, Arg_2: 2*Arg_2 {O(n)}
0: eval_jama_ex2_start->eval_jama_ex2_bb0_in, Arg_0: Arg_0 {O(n)}
0: eval_jama_ex2_start->eval_jama_ex2_bb0_in, Arg_1: Arg_1 {O(n)}
0: eval_jama_ex2_start->eval_jama_ex2_bb0_in, Arg_2: Arg_2 {O(n)}