Initial Problem

Start: eval_loops_start
Program_Vars: Arg_0, Arg_1, Arg_2
Temp_Vars:
Locations: eval_loops_bb0_in, eval_loops_bb1_in, eval_loops_bb2_in, eval_loops_bb3_in, eval_loops_bb4_in, eval_loops_bb5_in, eval_loops_bb6_in, eval_loops_start, eval_loops_stop
Transitions:
1:eval_loops_bb0_in(Arg_0,Arg_1,Arg_2) -> eval_loops_bb1_in(Arg_0,Arg_0,Arg_2):|:0<=Arg_0
2:eval_loops_bb0_in(Arg_0,Arg_1,Arg_2) -> eval_loops_bb6_in(Arg_0,Arg_1,Arg_2):|:Arg_0<0
3:eval_loops_bb1_in(Arg_0,Arg_1,Arg_2) -> eval_loops_bb2_in(Arg_0,Arg_1,Arg_2):|:0<=Arg_1
4:eval_loops_bb1_in(Arg_0,Arg_1,Arg_2) -> eval_loops_bb6_in(Arg_0,Arg_1,Arg_2):|:Arg_1<0
5:eval_loops_bb2_in(Arg_0,Arg_1,Arg_2) -> eval_loops_bb3_in(Arg_0,Arg_1,1):|:1<Arg_1
6:eval_loops_bb2_in(Arg_0,Arg_1,Arg_2) -> eval_loops_bb5_in(Arg_0,Arg_1,Arg_2):|:Arg_1<=1
7:eval_loops_bb3_in(Arg_0,Arg_1,Arg_2) -> eval_loops_bb4_in(Arg_0,Arg_1,Arg_2):|:Arg_2<Arg_1
8:eval_loops_bb3_in(Arg_0,Arg_1,Arg_2) -> eval_loops_bb5_in(Arg_0,Arg_1,Arg_2):|:Arg_1<=Arg_2
9:eval_loops_bb4_in(Arg_0,Arg_1,Arg_2) -> eval_loops_bb3_in(Arg_0,Arg_1,2*Arg_2)
10:eval_loops_bb5_in(Arg_0,Arg_1,Arg_2) -> eval_loops_bb1_in(Arg_0,Arg_1-1,Arg_2)
11:eval_loops_bb6_in(Arg_0,Arg_1,Arg_2) -> eval_loops_stop(Arg_0,Arg_1,Arg_2)
0:eval_loops_start(Arg_0,Arg_1,Arg_2) -> eval_loops_bb0_in(Arg_0,Arg_1,Arg_2)

Preprocessing

Found invariant Arg_1<=Arg_0 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=Arg_0 for location eval_loops_bb2_in

Found invariant Arg_1<=Arg_0 && 0<=1+Arg_1 && 0<=1+Arg_0+Arg_1 && 0<=Arg_0 for location eval_loops_bb1_in

Found invariant Arg_1<=Arg_0 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=Arg_0 for location eval_loops_bb5_in

Found invariant 1<=Arg_2 && 3<=Arg_1+Arg_2 && 3<=Arg_0+Arg_2 && Arg_1<=Arg_0 && 2<=Arg_1 && 4<=Arg_0+Arg_1 && 2<=Arg_0 for location eval_loops_bb3_in

Found invariant 1+Arg_2<=Arg_1 && 1+Arg_2<=Arg_0 && 1<=Arg_2 && 3<=Arg_1+Arg_2 && 3<=Arg_0+Arg_2 && Arg_1<=Arg_0 && 2<=Arg_1 && 4<=Arg_0+Arg_1 && 2<=Arg_0 for location eval_loops_bb4_in

Problem after Preprocessing

Start: eval_loops_start
Program_Vars: Arg_0, Arg_1, Arg_2
Temp_Vars:
Locations: eval_loops_bb0_in, eval_loops_bb1_in, eval_loops_bb2_in, eval_loops_bb3_in, eval_loops_bb4_in, eval_loops_bb5_in, eval_loops_bb6_in, eval_loops_start, eval_loops_stop
Transitions:
1:eval_loops_bb0_in(Arg_0,Arg_1,Arg_2) -> eval_loops_bb1_in(Arg_0,Arg_0,Arg_2):|:0<=Arg_0
2:eval_loops_bb0_in(Arg_0,Arg_1,Arg_2) -> eval_loops_bb6_in(Arg_0,Arg_1,Arg_2):|:Arg_0<0
3:eval_loops_bb1_in(Arg_0,Arg_1,Arg_2) -> eval_loops_bb2_in(Arg_0,Arg_1,Arg_2):|:Arg_1<=Arg_0 && 0<=1+Arg_1 && 0<=1+Arg_0+Arg_1 && 0<=Arg_0 && 0<=Arg_1
4:eval_loops_bb1_in(Arg_0,Arg_1,Arg_2) -> eval_loops_bb6_in(Arg_0,Arg_1,Arg_2):|:Arg_1<=Arg_0 && 0<=1+Arg_1 && 0<=1+Arg_0+Arg_1 && 0<=Arg_0 && Arg_1<0
5:eval_loops_bb2_in(Arg_0,Arg_1,Arg_2) -> eval_loops_bb3_in(Arg_0,Arg_1,1):|:Arg_1<=Arg_0 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=Arg_0 && 1<Arg_1
6:eval_loops_bb2_in(Arg_0,Arg_1,Arg_2) -> eval_loops_bb5_in(Arg_0,Arg_1,Arg_2):|:Arg_1<=Arg_0 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=Arg_0 && Arg_1<=1
7:eval_loops_bb3_in(Arg_0,Arg_1,Arg_2) -> eval_loops_bb4_in(Arg_0,Arg_1,Arg_2):|:1<=Arg_2 && 3<=Arg_1+Arg_2 && 3<=Arg_0+Arg_2 && Arg_1<=Arg_0 && 2<=Arg_1 && 4<=Arg_0+Arg_1 && 2<=Arg_0 && Arg_2<Arg_1
8:eval_loops_bb3_in(Arg_0,Arg_1,Arg_2) -> eval_loops_bb5_in(Arg_0,Arg_1,Arg_2):|:1<=Arg_2 && 3<=Arg_1+Arg_2 && 3<=Arg_0+Arg_2 && Arg_1<=Arg_0 && 2<=Arg_1 && 4<=Arg_0+Arg_1 && 2<=Arg_0 && Arg_1<=Arg_2
9:eval_loops_bb4_in(Arg_0,Arg_1,Arg_2) -> eval_loops_bb3_in(Arg_0,Arg_1,2*Arg_2):|:1+Arg_2<=Arg_1 && 1+Arg_2<=Arg_0 && 1<=Arg_2 && 3<=Arg_1+Arg_2 && 3<=Arg_0+Arg_2 && Arg_1<=Arg_0 && 2<=Arg_1 && 4<=Arg_0+Arg_1 && 2<=Arg_0
10:eval_loops_bb5_in(Arg_0,Arg_1,Arg_2) -> eval_loops_bb1_in(Arg_0,Arg_1-1,Arg_2):|:Arg_1<=Arg_0 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=Arg_0
11:eval_loops_bb6_in(Arg_0,Arg_1,Arg_2) -> eval_loops_stop(Arg_0,Arg_1,Arg_2)
0:eval_loops_start(Arg_0,Arg_1,Arg_2) -> eval_loops_bb0_in(Arg_0,Arg_1,Arg_2)

MPRF for transition 3:eval_loops_bb1_in(Arg_0,Arg_1,Arg_2) -> eval_loops_bb2_in(Arg_0,Arg_1,Arg_2):|:Arg_1<=Arg_0 && 0<=1+Arg_1 && 0<=1+Arg_0+Arg_1 && 0<=Arg_0 && 0<=Arg_1 of depth 1:

new bound:

Arg_0+1 {O(n)}

MPRF:

eval_loops_bb2_in [Arg_1 ]
eval_loops_bb4_in [Arg_1 ]
eval_loops_bb3_in [Arg_1 ]
eval_loops_bb5_in [Arg_1 ]
eval_loops_bb1_in [Arg_1+1 ]

MPRF for transition 5:eval_loops_bb2_in(Arg_0,Arg_1,Arg_2) -> eval_loops_bb3_in(Arg_0,Arg_1,1):|:Arg_1<=Arg_0 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=Arg_0 && 1<Arg_1 of depth 1:

new bound:

Arg_0+1 {O(n)}

MPRF:

eval_loops_bb2_in [Arg_1+1 ]
eval_loops_bb4_in [Arg_1 ]
eval_loops_bb3_in [Arg_1 ]
eval_loops_bb5_in [Arg_1 ]
eval_loops_bb1_in [Arg_1+1 ]

MPRF for transition 6:eval_loops_bb2_in(Arg_0,Arg_1,Arg_2) -> eval_loops_bb5_in(Arg_0,Arg_1,Arg_2):|:Arg_1<=Arg_0 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=Arg_0 && Arg_1<=1 of depth 1:

new bound:

Arg_0+1 {O(n)}

MPRF:

eval_loops_bb2_in [Arg_1+1 ]
eval_loops_bb4_in [Arg_1 ]
eval_loops_bb3_in [Arg_1 ]
eval_loops_bb5_in [Arg_1 ]
eval_loops_bb1_in [Arg_1+1 ]

MPRF for transition 8:eval_loops_bb3_in(Arg_0,Arg_1,Arg_2) -> eval_loops_bb5_in(Arg_0,Arg_1,Arg_2):|:1<=Arg_2 && 3<=Arg_1+Arg_2 && 3<=Arg_0+Arg_2 && Arg_1<=Arg_0 && 2<=Arg_1 && 4<=Arg_0+Arg_1 && 2<=Arg_0 && Arg_1<=Arg_2 of depth 1:

new bound:

2*Arg_0+3 {O(n)}

MPRF:

eval_loops_bb2_in [Arg_0+Arg_1-3 ]
eval_loops_bb4_in [Arg_0+Arg_1-3 ]
eval_loops_bb3_in [Arg_0+Arg_1-3 ]
eval_loops_bb5_in [Arg_0+Arg_1-4 ]
eval_loops_bb1_in [Arg_0+Arg_1-3 ]

MPRF for transition 10:eval_loops_bb5_in(Arg_0,Arg_1,Arg_2) -> eval_loops_bb1_in(Arg_0,Arg_1-1,Arg_2):|:Arg_1<=Arg_0 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=Arg_0 of depth 1:

new bound:

Arg_0+1 {O(n)}

MPRF:

eval_loops_bb2_in [Arg_1+1 ]
eval_loops_bb4_in [Arg_1+1 ]
eval_loops_bb3_in [Arg_1+1 ]
eval_loops_bb5_in [Arg_1+1 ]
eval_loops_bb1_in [Arg_1+1 ]

MPRF for transition 7:eval_loops_bb3_in(Arg_0,Arg_1,Arg_2) -> eval_loops_bb4_in(Arg_0,Arg_1,Arg_2):|:1<=Arg_2 && 3<=Arg_1+Arg_2 && 3<=Arg_0+Arg_2 && Arg_1<=Arg_0 && 2<=Arg_1 && 4<=Arg_0+Arg_1 && 2<=Arg_0 && Arg_2<Arg_1 of depth 1:

new bound:

2*Arg_0*Arg_0+4*Arg_0 {O(n^2)}

MPRF:

eval_loops_bb2_in [Arg_0 ]
eval_loops_bb4_in [Arg_0-Arg_2-1 ]
eval_loops_bb3_in [Arg_0-Arg_2 ]
eval_loops_bb5_in [Arg_0 ]
eval_loops_bb1_in [Arg_0 ]

MPRF for transition 9:eval_loops_bb4_in(Arg_0,Arg_1,Arg_2) -> eval_loops_bb3_in(Arg_0,Arg_1,2*Arg_2):|:1+Arg_2<=Arg_1 && 1+Arg_2<=Arg_0 && 1<=Arg_2 && 3<=Arg_1+Arg_2 && 3<=Arg_0+Arg_2 && Arg_1<=Arg_0 && 2<=Arg_1 && 4<=Arg_0+Arg_1 && 2<=Arg_0 of depth 1:

new bound:

2*Arg_0*Arg_0+4*Arg_0 {O(n^2)}

MPRF:

eval_loops_bb2_in [Arg_0 ]
eval_loops_bb4_in [Arg_0-Arg_2 ]
eval_loops_bb3_in [Arg_0-Arg_2 ]
eval_loops_bb5_in [Arg_0 ]
eval_loops_bb1_in [Arg_0 ]

All Bounds

Timebounds

Overall timebound:4*Arg_0*Arg_0+14*Arg_0+12 {O(n^2)}
1: eval_loops_bb0_in->eval_loops_bb1_in: 1 {O(1)}
2: eval_loops_bb0_in->eval_loops_bb6_in: 1 {O(1)}
3: eval_loops_bb1_in->eval_loops_bb2_in: Arg_0+1 {O(n)}
4: eval_loops_bb1_in->eval_loops_bb6_in: 1 {O(1)}
5: eval_loops_bb2_in->eval_loops_bb3_in: Arg_0+1 {O(n)}
6: eval_loops_bb2_in->eval_loops_bb5_in: Arg_0+1 {O(n)}
7: eval_loops_bb3_in->eval_loops_bb4_in: 2*Arg_0*Arg_0+4*Arg_0 {O(n^2)}
8: eval_loops_bb3_in->eval_loops_bb5_in: 2*Arg_0+3 {O(n)}
9: eval_loops_bb4_in->eval_loops_bb3_in: 2*Arg_0*Arg_0+4*Arg_0 {O(n^2)}
10: eval_loops_bb5_in->eval_loops_bb1_in: Arg_0+1 {O(n)}
11: eval_loops_bb6_in->eval_loops_stop: 1 {O(1)}
0: eval_loops_start->eval_loops_bb0_in: 1 {O(1)}

Costbounds

Overall costbound: 4*Arg_0*Arg_0+14*Arg_0+12 {O(n^2)}
1: eval_loops_bb0_in->eval_loops_bb1_in: 1 {O(1)}
2: eval_loops_bb0_in->eval_loops_bb6_in: 1 {O(1)}
3: eval_loops_bb1_in->eval_loops_bb2_in: Arg_0+1 {O(n)}
4: eval_loops_bb1_in->eval_loops_bb6_in: 1 {O(1)}
5: eval_loops_bb2_in->eval_loops_bb3_in: Arg_0+1 {O(n)}
6: eval_loops_bb2_in->eval_loops_bb5_in: Arg_0+1 {O(n)}
7: eval_loops_bb3_in->eval_loops_bb4_in: 2*Arg_0*Arg_0+4*Arg_0 {O(n^2)}
8: eval_loops_bb3_in->eval_loops_bb5_in: 2*Arg_0+3 {O(n)}
9: eval_loops_bb4_in->eval_loops_bb3_in: 2*Arg_0*Arg_0+4*Arg_0 {O(n^2)}
10: eval_loops_bb5_in->eval_loops_bb1_in: Arg_0+1 {O(n)}
11: eval_loops_bb6_in->eval_loops_stop: 1 {O(1)}
0: eval_loops_start->eval_loops_bb0_in: 1 {O(1)}

Sizebounds

1: eval_loops_bb0_in->eval_loops_bb1_in, Arg_0: Arg_0 {O(n)}
1: eval_loops_bb0_in->eval_loops_bb1_in, Arg_1: Arg_0 {O(n)}
1: eval_loops_bb0_in->eval_loops_bb1_in, Arg_2: Arg_2 {O(n)}
2: eval_loops_bb0_in->eval_loops_bb6_in, Arg_0: Arg_0 {O(n)}
2: eval_loops_bb0_in->eval_loops_bb6_in, Arg_1: Arg_1 {O(n)}
2: eval_loops_bb0_in->eval_loops_bb6_in, Arg_2: Arg_2 {O(n)}
3: eval_loops_bb1_in->eval_loops_bb2_in, Arg_0: Arg_0 {O(n)}
3: eval_loops_bb1_in->eval_loops_bb2_in, Arg_1: Arg_0+2 {O(n)}
3: eval_loops_bb1_in->eval_loops_bb2_in, Arg_2: 2^(2*Arg_0*Arg_0+4*Arg_0)+Arg_2 {O(EXP)}
4: eval_loops_bb1_in->eval_loops_bb6_in, Arg_0: Arg_0 {O(n)}
4: eval_loops_bb1_in->eval_loops_bb6_in, Arg_1: 1 {O(1)}
4: eval_loops_bb1_in->eval_loops_bb6_in, Arg_2: 2^(2*Arg_0*Arg_0+4*Arg_0)+Arg_2 {O(EXP)}
5: eval_loops_bb2_in->eval_loops_bb3_in, Arg_0: Arg_0 {O(n)}
5: eval_loops_bb2_in->eval_loops_bb3_in, Arg_1: Arg_0+2 {O(n)}
5: eval_loops_bb2_in->eval_loops_bb3_in, Arg_2: 1 {O(1)}
6: eval_loops_bb2_in->eval_loops_bb5_in, Arg_0: Arg_0 {O(n)}
6: eval_loops_bb2_in->eval_loops_bb5_in, Arg_1: 1 {O(1)}
6: eval_loops_bb2_in->eval_loops_bb5_in, Arg_2: 2^(2*Arg_0*Arg_0+4*Arg_0)+Arg_2 {O(EXP)}
7: eval_loops_bb3_in->eval_loops_bb4_in, Arg_0: Arg_0 {O(n)}
7: eval_loops_bb3_in->eval_loops_bb4_in, Arg_1: Arg_0+2 {O(n)}
7: eval_loops_bb3_in->eval_loops_bb4_in, Arg_2: 2^(2*Arg_0*Arg_0+4*Arg_0) {O(EXP)}
8: eval_loops_bb3_in->eval_loops_bb5_in, Arg_0: Arg_0 {O(n)}
8: eval_loops_bb3_in->eval_loops_bb5_in, Arg_1: Arg_0+2 {O(n)}
8: eval_loops_bb3_in->eval_loops_bb5_in, Arg_2: 2^(2*Arg_0*Arg_0+4*Arg_0) {O(EXP)}
9: eval_loops_bb4_in->eval_loops_bb3_in, Arg_0: Arg_0 {O(n)}
9: eval_loops_bb4_in->eval_loops_bb3_in, Arg_1: Arg_0+2 {O(n)}
9: eval_loops_bb4_in->eval_loops_bb3_in, Arg_2: 2^(2*Arg_0*Arg_0+4*Arg_0) {O(EXP)}
10: eval_loops_bb5_in->eval_loops_bb1_in, Arg_0: Arg_0 {O(n)}
10: eval_loops_bb5_in->eval_loops_bb1_in, Arg_1: Arg_0+2 {O(n)}
10: eval_loops_bb5_in->eval_loops_bb1_in, Arg_2: 2^(2*Arg_0*Arg_0+4*Arg_0)+Arg_2 {O(EXP)}
11: eval_loops_bb6_in->eval_loops_stop, Arg_0: 2*Arg_0 {O(n)}
11: eval_loops_bb6_in->eval_loops_stop, Arg_1: Arg_1+1 {O(n)}
11: eval_loops_bb6_in->eval_loops_stop, Arg_2: 2^(2*Arg_0*Arg_0+4*Arg_0)+2*Arg_2 {O(EXP)}
0: eval_loops_start->eval_loops_bb0_in, Arg_0: Arg_0 {O(n)}
0: eval_loops_start->eval_loops_bb0_in, Arg_1: Arg_1 {O(n)}
0: eval_loops_start->eval_loops_bb0_in, Arg_2: Arg_2 {O(n)}