Initial Problem

Start: eval_jama_ex4_start
Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3, Arg_4, Arg_5
Temp_Vars:
Locations: eval_jama_ex4_bb0_in, eval_jama_ex4_bb1_in, eval_jama_ex4_bb2_in, eval_jama_ex4_bb3_in, eval_jama_ex4_bb4_in, eval_jama_ex4_bb5_in, eval_jama_ex4_start, eval_jama_ex4_stop
Transitions:
1:eval_jama_ex4_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_jama_ex4_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_0,Arg_5)
2:eval_jama_ex4_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_jama_ex4_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_2):|:Arg_4<=Arg_1
3:eval_jama_ex4_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_jama_ex4_bb5_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5):|:Arg_1<Arg_4
4:eval_jama_ex4_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_jama_ex4_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5):|:Arg_5<=Arg_3
5:eval_jama_ex4_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_jama_ex4_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5):|:Arg_3<Arg_5
6:eval_jama_ex4_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_jama_ex4_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5+1)
7:eval_jama_ex4_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_jama_ex4_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4+1,Arg_5)
8:eval_jama_ex4_bb5_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_jama_ex4_stop(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5)
0:eval_jama_ex4_start(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_jama_ex4_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5)

Preprocessing

Found invariant Arg_5<=Arg_3 && Arg_2<=Arg_5 && Arg_4<=Arg_1 && Arg_0<=Arg_4 && Arg_2<=Arg_3 && Arg_0<=Arg_1 for location eval_jama_ex4_bb3_in

Found invariant 1+Arg_1<=Arg_4 && Arg_0<=Arg_4 for location eval_jama_ex4_stop

Found invariant 1+Arg_3<=Arg_5 && Arg_2<=Arg_5 && Arg_4<=Arg_1 && Arg_0<=Arg_4 && Arg_0<=Arg_1 for location eval_jama_ex4_bb4_in

Found invariant 1+Arg_1<=Arg_4 && Arg_0<=Arg_4 for location eval_jama_ex4_bb5_in

Found invariant Arg_0<=Arg_4 for location eval_jama_ex4_bb1_in

Found invariant Arg_2<=Arg_5 && Arg_4<=Arg_1 && Arg_0<=Arg_4 && Arg_0<=Arg_1 for location eval_jama_ex4_bb2_in

Problem after Preprocessing

Start: eval_jama_ex4_start
Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3, Arg_4, Arg_5
Temp_Vars:
Locations: eval_jama_ex4_bb0_in, eval_jama_ex4_bb1_in, eval_jama_ex4_bb2_in, eval_jama_ex4_bb3_in, eval_jama_ex4_bb4_in, eval_jama_ex4_bb5_in, eval_jama_ex4_start, eval_jama_ex4_stop
Transitions:
1:eval_jama_ex4_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_jama_ex4_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_0,Arg_5)
2:eval_jama_ex4_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_jama_ex4_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_2):|:Arg_0<=Arg_4 && Arg_4<=Arg_1
3:eval_jama_ex4_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_jama_ex4_bb5_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5):|:Arg_0<=Arg_4 && Arg_1<Arg_4
4:eval_jama_ex4_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_jama_ex4_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5):|:Arg_2<=Arg_5 && Arg_4<=Arg_1 && Arg_0<=Arg_4 && Arg_0<=Arg_1 && Arg_5<=Arg_3
5:eval_jama_ex4_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_jama_ex4_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5):|:Arg_2<=Arg_5 && Arg_4<=Arg_1 && Arg_0<=Arg_4 && Arg_0<=Arg_1 && Arg_3<Arg_5
6:eval_jama_ex4_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_jama_ex4_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5+1):|:Arg_5<=Arg_3 && Arg_2<=Arg_5 && Arg_4<=Arg_1 && Arg_0<=Arg_4 && Arg_2<=Arg_3 && Arg_0<=Arg_1
7:eval_jama_ex4_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_jama_ex4_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4+1,Arg_5):|:1+Arg_3<=Arg_5 && Arg_2<=Arg_5 && Arg_4<=Arg_1 && Arg_0<=Arg_4 && Arg_0<=Arg_1
8:eval_jama_ex4_bb5_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_jama_ex4_stop(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5):|:1+Arg_1<=Arg_4 && Arg_0<=Arg_4
0:eval_jama_ex4_start(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_jama_ex4_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5)

MPRF for transition 2:eval_jama_ex4_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_jama_ex4_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_2):|:Arg_0<=Arg_4 && Arg_4<=Arg_1 of depth 1:

new bound:

Arg_0+Arg_1+1 {O(n)}

MPRF:

eval_jama_ex4_bb3_in [Arg_1-Arg_4 ]
eval_jama_ex4_bb2_in [Arg_1-Arg_4 ]
eval_jama_ex4_bb4_in [Arg_1-Arg_4 ]
eval_jama_ex4_bb1_in [Arg_1+1-Arg_4 ]

MPRF for transition 5:eval_jama_ex4_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_jama_ex4_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5):|:Arg_2<=Arg_5 && Arg_4<=Arg_1 && Arg_0<=Arg_4 && Arg_0<=Arg_1 && Arg_3<Arg_5 of depth 1:

new bound:

Arg_0+Arg_1+1 {O(n)}

MPRF:

eval_jama_ex4_bb3_in [Arg_1+1-Arg_4 ]
eval_jama_ex4_bb2_in [Arg_1+1-Arg_4 ]
eval_jama_ex4_bb4_in [Arg_1-Arg_4 ]
eval_jama_ex4_bb1_in [Arg_1+1-Arg_4 ]

MPRF for transition 7:eval_jama_ex4_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_jama_ex4_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4+1,Arg_5):|:1+Arg_3<=Arg_5 && Arg_2<=Arg_5 && Arg_4<=Arg_1 && Arg_0<=Arg_4 && Arg_0<=Arg_1 of depth 1:

new bound:

Arg_0+Arg_1+1 {O(n)}

MPRF:

eval_jama_ex4_bb3_in [Arg_1+1-Arg_4 ]
eval_jama_ex4_bb2_in [Arg_1+1-Arg_4 ]
eval_jama_ex4_bb4_in [Arg_1+1-Arg_4 ]
eval_jama_ex4_bb1_in [Arg_1+1-Arg_4 ]

MPRF for transition 4:eval_jama_ex4_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_jama_ex4_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5):|:Arg_2<=Arg_5 && Arg_4<=Arg_1 && Arg_0<=Arg_4 && Arg_0<=Arg_1 && Arg_5<=Arg_3 of depth 1:

new bound:

Arg_0*Arg_2+Arg_0*Arg_3+Arg_1*Arg_2+Arg_1*Arg_3+2*Arg_2+2*Arg_3+Arg_0+Arg_1+2 {O(n^2)}

MPRF:

eval_jama_ex4_bb1_in [Arg_3+1-Arg_2 ]
eval_jama_ex4_bb4_in [Arg_3-Arg_5 ]
eval_jama_ex4_bb3_in [Arg_3-Arg_5 ]
eval_jama_ex4_bb2_in [Arg_3+1-Arg_5 ]

MPRF for transition 6:eval_jama_ex4_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_jama_ex4_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5+1):|:Arg_5<=Arg_3 && Arg_2<=Arg_5 && Arg_4<=Arg_1 && Arg_0<=Arg_4 && Arg_2<=Arg_3 && Arg_0<=Arg_1 of depth 1:

new bound:

Arg_0*Arg_2+Arg_0*Arg_3+Arg_1*Arg_2+Arg_1*Arg_3+2*Arg_2+2*Arg_3+Arg_0+Arg_1+2 {O(n^2)}

MPRF:

eval_jama_ex4_bb1_in [Arg_3+1-Arg_2 ]
eval_jama_ex4_bb4_in [Arg_3-Arg_5 ]
eval_jama_ex4_bb3_in [Arg_3+1-Arg_5 ]
eval_jama_ex4_bb2_in [Arg_3+1-Arg_5 ]

All Bounds

Timebounds

Overall timebound:2*Arg_0*Arg_2+2*Arg_0*Arg_3+2*Arg_1*Arg_2+2*Arg_1*Arg_3+4*Arg_2+4*Arg_3+5*Arg_0+5*Arg_1+11 {O(n^2)}
1: eval_jama_ex4_bb0_in->eval_jama_ex4_bb1_in: 1 {O(1)}
2: eval_jama_ex4_bb1_in->eval_jama_ex4_bb2_in: Arg_0+Arg_1+1 {O(n)}
3: eval_jama_ex4_bb1_in->eval_jama_ex4_bb5_in: 1 {O(1)}
4: eval_jama_ex4_bb2_in->eval_jama_ex4_bb3_in: Arg_0*Arg_2+Arg_0*Arg_3+Arg_1*Arg_2+Arg_1*Arg_3+2*Arg_2+2*Arg_3+Arg_0+Arg_1+2 {O(n^2)}
5: eval_jama_ex4_bb2_in->eval_jama_ex4_bb4_in: Arg_0+Arg_1+1 {O(n)}
6: eval_jama_ex4_bb3_in->eval_jama_ex4_bb2_in: Arg_0*Arg_2+Arg_0*Arg_3+Arg_1*Arg_2+Arg_1*Arg_3+2*Arg_2+2*Arg_3+Arg_0+Arg_1+2 {O(n^2)}
7: eval_jama_ex4_bb4_in->eval_jama_ex4_bb1_in: Arg_0+Arg_1+1 {O(n)}
8: eval_jama_ex4_bb5_in->eval_jama_ex4_stop: 1 {O(1)}
0: eval_jama_ex4_start->eval_jama_ex4_bb0_in: 1 {O(1)}

Costbounds

Overall costbound: 2*Arg_0*Arg_2+2*Arg_0*Arg_3+2*Arg_1*Arg_2+2*Arg_1*Arg_3+4*Arg_2+4*Arg_3+5*Arg_0+5*Arg_1+11 {O(n^2)}
1: eval_jama_ex4_bb0_in->eval_jama_ex4_bb1_in: 1 {O(1)}
2: eval_jama_ex4_bb1_in->eval_jama_ex4_bb2_in: Arg_0+Arg_1+1 {O(n)}
3: eval_jama_ex4_bb1_in->eval_jama_ex4_bb5_in: 1 {O(1)}
4: eval_jama_ex4_bb2_in->eval_jama_ex4_bb3_in: Arg_0*Arg_2+Arg_0*Arg_3+Arg_1*Arg_2+Arg_1*Arg_3+2*Arg_2+2*Arg_3+Arg_0+Arg_1+2 {O(n^2)}
5: eval_jama_ex4_bb2_in->eval_jama_ex4_bb4_in: Arg_0+Arg_1+1 {O(n)}
6: eval_jama_ex4_bb3_in->eval_jama_ex4_bb2_in: Arg_0*Arg_2+Arg_0*Arg_3+Arg_1*Arg_2+Arg_1*Arg_3+2*Arg_2+2*Arg_3+Arg_0+Arg_1+2 {O(n^2)}
7: eval_jama_ex4_bb4_in->eval_jama_ex4_bb1_in: Arg_0+Arg_1+1 {O(n)}
8: eval_jama_ex4_bb5_in->eval_jama_ex4_stop: 1 {O(1)}
0: eval_jama_ex4_start->eval_jama_ex4_bb0_in: 1 {O(1)}

Sizebounds

1: eval_jama_ex4_bb0_in->eval_jama_ex4_bb1_in, Arg_0: Arg_0 {O(n)}
1: eval_jama_ex4_bb0_in->eval_jama_ex4_bb1_in, Arg_1: Arg_1 {O(n)}
1: eval_jama_ex4_bb0_in->eval_jama_ex4_bb1_in, Arg_2: Arg_2 {O(n)}
1: eval_jama_ex4_bb0_in->eval_jama_ex4_bb1_in, Arg_3: Arg_3 {O(n)}
1: eval_jama_ex4_bb0_in->eval_jama_ex4_bb1_in, Arg_4: Arg_0 {O(n)}
1: eval_jama_ex4_bb0_in->eval_jama_ex4_bb1_in, Arg_5: Arg_5 {O(n)}
2: eval_jama_ex4_bb1_in->eval_jama_ex4_bb2_in, Arg_0: Arg_0 {O(n)}
2: eval_jama_ex4_bb1_in->eval_jama_ex4_bb2_in, Arg_1: Arg_1 {O(n)}
2: eval_jama_ex4_bb1_in->eval_jama_ex4_bb2_in, Arg_2: Arg_2 {O(n)}
2: eval_jama_ex4_bb1_in->eval_jama_ex4_bb2_in, Arg_3: Arg_3 {O(n)}
2: eval_jama_ex4_bb1_in->eval_jama_ex4_bb2_in, Arg_4: 2*Arg_0+Arg_1+1 {O(n)}
2: eval_jama_ex4_bb1_in->eval_jama_ex4_bb2_in, Arg_5: 2*Arg_2 {O(n)}
3: eval_jama_ex4_bb1_in->eval_jama_ex4_bb5_in, Arg_0: 2*Arg_0 {O(n)}
3: eval_jama_ex4_bb1_in->eval_jama_ex4_bb5_in, Arg_1: 2*Arg_1 {O(n)}
3: eval_jama_ex4_bb1_in->eval_jama_ex4_bb5_in, Arg_2: 2*Arg_2 {O(n)}
3: eval_jama_ex4_bb1_in->eval_jama_ex4_bb5_in, Arg_3: 2*Arg_3 {O(n)}
3: eval_jama_ex4_bb1_in->eval_jama_ex4_bb5_in, Arg_4: 3*Arg_0+Arg_1+1 {O(n)}
3: eval_jama_ex4_bb1_in->eval_jama_ex4_bb5_in, Arg_5: Arg_0*Arg_2+Arg_0*Arg_3+Arg_1*Arg_2+Arg_1*Arg_3+2*Arg_3+6*Arg_2+Arg_0+Arg_1+Arg_5+2 {O(n^2)}
4: eval_jama_ex4_bb2_in->eval_jama_ex4_bb3_in, Arg_0: Arg_0 {O(n)}
4: eval_jama_ex4_bb2_in->eval_jama_ex4_bb3_in, Arg_1: Arg_1 {O(n)}
4: eval_jama_ex4_bb2_in->eval_jama_ex4_bb3_in, Arg_2: Arg_2 {O(n)}
4: eval_jama_ex4_bb2_in->eval_jama_ex4_bb3_in, Arg_3: Arg_3 {O(n)}
4: eval_jama_ex4_bb2_in->eval_jama_ex4_bb3_in, Arg_4: 2*Arg_0+Arg_1+1 {O(n)}
4: eval_jama_ex4_bb2_in->eval_jama_ex4_bb3_in, Arg_5: Arg_0*Arg_2+Arg_0*Arg_3+Arg_1*Arg_2+Arg_1*Arg_3+2*Arg_3+4*Arg_2+Arg_0+Arg_1+2 {O(n^2)}
5: eval_jama_ex4_bb2_in->eval_jama_ex4_bb4_in, Arg_0: Arg_0 {O(n)}
5: eval_jama_ex4_bb2_in->eval_jama_ex4_bb4_in, Arg_1: Arg_1 {O(n)}
5: eval_jama_ex4_bb2_in->eval_jama_ex4_bb4_in, Arg_2: Arg_2 {O(n)}
5: eval_jama_ex4_bb2_in->eval_jama_ex4_bb4_in, Arg_3: Arg_3 {O(n)}
5: eval_jama_ex4_bb2_in->eval_jama_ex4_bb4_in, Arg_4: 2*Arg_0+Arg_1+1 {O(n)}
5: eval_jama_ex4_bb2_in->eval_jama_ex4_bb4_in, Arg_5: Arg_0*Arg_2+Arg_0*Arg_3+Arg_1*Arg_2+Arg_1*Arg_3+2*Arg_3+6*Arg_2+Arg_0+Arg_1+2 {O(n^2)}
6: eval_jama_ex4_bb3_in->eval_jama_ex4_bb2_in, Arg_0: Arg_0 {O(n)}
6: eval_jama_ex4_bb3_in->eval_jama_ex4_bb2_in, Arg_1: Arg_1 {O(n)}
6: eval_jama_ex4_bb3_in->eval_jama_ex4_bb2_in, Arg_2: Arg_2 {O(n)}
6: eval_jama_ex4_bb3_in->eval_jama_ex4_bb2_in, Arg_3: Arg_3 {O(n)}
6: eval_jama_ex4_bb3_in->eval_jama_ex4_bb2_in, Arg_4: 2*Arg_0+Arg_1+1 {O(n)}
6: eval_jama_ex4_bb3_in->eval_jama_ex4_bb2_in, Arg_5: Arg_0*Arg_2+Arg_0*Arg_3+Arg_1*Arg_2+Arg_1*Arg_3+2*Arg_3+4*Arg_2+Arg_0+Arg_1+2 {O(n^2)}
7: eval_jama_ex4_bb4_in->eval_jama_ex4_bb1_in, Arg_0: Arg_0 {O(n)}
7: eval_jama_ex4_bb4_in->eval_jama_ex4_bb1_in, Arg_1: Arg_1 {O(n)}
7: eval_jama_ex4_bb4_in->eval_jama_ex4_bb1_in, Arg_2: Arg_2 {O(n)}
7: eval_jama_ex4_bb4_in->eval_jama_ex4_bb1_in, Arg_3: Arg_3 {O(n)}
7: eval_jama_ex4_bb4_in->eval_jama_ex4_bb1_in, Arg_4: 2*Arg_0+Arg_1+1 {O(n)}
7: eval_jama_ex4_bb4_in->eval_jama_ex4_bb1_in, Arg_5: Arg_0*Arg_2+Arg_0*Arg_3+Arg_1*Arg_2+Arg_1*Arg_3+2*Arg_3+6*Arg_2+Arg_0+Arg_1+2 {O(n^2)}
8: eval_jama_ex4_bb5_in->eval_jama_ex4_stop, Arg_0: 2*Arg_0 {O(n)}
8: eval_jama_ex4_bb5_in->eval_jama_ex4_stop, Arg_1: 2*Arg_1 {O(n)}
8: eval_jama_ex4_bb5_in->eval_jama_ex4_stop, Arg_2: 2*Arg_2 {O(n)}
8: eval_jama_ex4_bb5_in->eval_jama_ex4_stop, Arg_3: 2*Arg_3 {O(n)}
8: eval_jama_ex4_bb5_in->eval_jama_ex4_stop, Arg_4: 3*Arg_0+Arg_1+1 {O(n)}
8: eval_jama_ex4_bb5_in->eval_jama_ex4_stop, Arg_5: Arg_0*Arg_2+Arg_0*Arg_3+Arg_1*Arg_2+Arg_1*Arg_3+2*Arg_3+6*Arg_2+Arg_0+Arg_1+Arg_5+2 {O(n^2)}
0: eval_jama_ex4_start->eval_jama_ex4_bb0_in, Arg_0: Arg_0 {O(n)}
0: eval_jama_ex4_start->eval_jama_ex4_bb0_in, Arg_1: Arg_1 {O(n)}
0: eval_jama_ex4_start->eval_jama_ex4_bb0_in, Arg_2: Arg_2 {O(n)}
0: eval_jama_ex4_start->eval_jama_ex4_bb0_in, Arg_3: Arg_3 {O(n)}
0: eval_jama_ex4_start->eval_jama_ex4_bb0_in, Arg_4: Arg_4 {O(n)}
0: eval_jama_ex4_start->eval_jama_ex4_bb0_in, Arg_5: Arg_5 {O(n)}