Initial Problem
Start: eval_start_start
Program_Vars: Arg_0, Arg_1, Arg_2
Temp_Vars:
Locations: eval_start_0, eval_start_1, eval_start_2, eval_start_3, eval_start_4, eval_start_5, eval_start_6, eval_start_bb0_in, eval_start_bb1_in, eval_start_bb2_in, eval_start_bb3_in, eval_start_bb4_in, eval_start_bb5_in, eval_start_start, eval_start_stop
Transitions:
2:eval_start_0(Arg_0,Arg_1,Arg_2) -> eval_start_1(Arg_0,Arg_1,Arg_2)
3:eval_start_1(Arg_0,Arg_1,Arg_2) -> eval_start_2(Arg_0,Arg_1,Arg_2)
4:eval_start_2(Arg_0,Arg_1,Arg_2) -> eval_start_3(Arg_0,Arg_1,Arg_2)
5:eval_start_3(Arg_0,Arg_1,Arg_2) -> eval_start_4(Arg_0,Arg_1,Arg_2)
6:eval_start_4(Arg_0,Arg_1,Arg_2) -> eval_start_5(Arg_0,Arg_1,Arg_2)
7:eval_start_5(Arg_0,Arg_1,Arg_2) -> eval_start_6(Arg_0,Arg_1,Arg_2)
8:eval_start_6(Arg_0,Arg_1,Arg_2) -> eval_start_bb1_in(Arg_0,0,0)
1:eval_start_bb0_in(Arg_0,Arg_1,Arg_2) -> eval_start_0(Arg_0,Arg_1,Arg_2)
9:eval_start_bb1_in(Arg_0,Arg_1,Arg_2) -> eval_start_bb2_in(Arg_0,Arg_1,Arg_2):|:Arg_1<Arg_0
10:eval_start_bb1_in(Arg_0,Arg_1,Arg_2) -> eval_start_bb3_in(Arg_0,Arg_1,Arg_2):|:Arg_0<=Arg_1
11:eval_start_bb2_in(Arg_0,Arg_1,Arg_2) -> eval_start_bb1_in(Arg_0,Arg_1+1,Arg_2+1)
12:eval_start_bb3_in(Arg_0,Arg_1,Arg_2) -> eval_start_bb4_in(Arg_0,Arg_1,Arg_2):|:0<Arg_2
13:eval_start_bb3_in(Arg_0,Arg_1,Arg_2) -> eval_start_bb5_in(Arg_0,Arg_1,Arg_2):|:Arg_2<=0
14:eval_start_bb4_in(Arg_0,Arg_1,Arg_2) -> eval_start_bb1_in(Arg_0,Arg_1,Arg_2-1)
15:eval_start_bb5_in(Arg_0,Arg_1,Arg_2) -> eval_start_stop(Arg_0,Arg_1,Arg_2)
0:eval_start_start(Arg_0,Arg_1,Arg_2) -> eval_start_bb0_in(Arg_0,Arg_1,Arg_2)
Preprocessing
Found invariant Arg_2<=Arg_1 && 0<=Arg_2 && 0<=Arg_1+Arg_2 && 0<=Arg_1 for location eval_start_bb1_in
Found invariant Arg_2<=0 && Arg_2<=Arg_1 && 0<=Arg_2 && 0<=Arg_1+Arg_2 && 0<=Arg_1 && Arg_0<=Arg_1 for location eval_start_stop
Found invariant Arg_2<=0 && Arg_2<=Arg_1 && 0<=Arg_2 && 0<=Arg_1+Arg_2 && 0<=Arg_1 && Arg_0<=Arg_1 for location eval_start_bb5_in
Found invariant Arg_2<=Arg_1 && 1+Arg_2<=Arg_0 && 0<=Arg_2 && 0<=Arg_1+Arg_2 && 1<=Arg_0+Arg_2 && 1+Arg_1<=Arg_0 && 0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 for location eval_start_bb2_in
Found invariant Arg_2<=Arg_1 && 0<=Arg_2 && 0<=Arg_1+Arg_2 && 0<=Arg_1 && Arg_0<=Arg_1 for location eval_start_bb3_in
Found invariant Arg_2<=Arg_1 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && 1<=Arg_1 && Arg_0<=Arg_1 for location eval_start_bb4_in
Problem after Preprocessing
Start: eval_start_start
Program_Vars: Arg_0, Arg_1, Arg_2
Temp_Vars:
Locations: eval_start_0, eval_start_1, eval_start_2, eval_start_3, eval_start_4, eval_start_5, eval_start_6, eval_start_bb0_in, eval_start_bb1_in, eval_start_bb2_in, eval_start_bb3_in, eval_start_bb4_in, eval_start_bb5_in, eval_start_start, eval_start_stop
Transitions:
2:eval_start_0(Arg_0,Arg_1,Arg_2) -> eval_start_1(Arg_0,Arg_1,Arg_2)
3:eval_start_1(Arg_0,Arg_1,Arg_2) -> eval_start_2(Arg_0,Arg_1,Arg_2)
4:eval_start_2(Arg_0,Arg_1,Arg_2) -> eval_start_3(Arg_0,Arg_1,Arg_2)
5:eval_start_3(Arg_0,Arg_1,Arg_2) -> eval_start_4(Arg_0,Arg_1,Arg_2)
6:eval_start_4(Arg_0,Arg_1,Arg_2) -> eval_start_5(Arg_0,Arg_1,Arg_2)
7:eval_start_5(Arg_0,Arg_1,Arg_2) -> eval_start_6(Arg_0,Arg_1,Arg_2)
8:eval_start_6(Arg_0,Arg_1,Arg_2) -> eval_start_bb1_in(Arg_0,0,0)
1:eval_start_bb0_in(Arg_0,Arg_1,Arg_2) -> eval_start_0(Arg_0,Arg_1,Arg_2)
9:eval_start_bb1_in(Arg_0,Arg_1,Arg_2) -> eval_start_bb2_in(Arg_0,Arg_1,Arg_2):|:Arg_2<=Arg_1 && 0<=Arg_2 && 0<=Arg_1+Arg_2 && 0<=Arg_1 && Arg_1<Arg_0
10:eval_start_bb1_in(Arg_0,Arg_1,Arg_2) -> eval_start_bb3_in(Arg_0,Arg_1,Arg_2):|:Arg_2<=Arg_1 && 0<=Arg_2 && 0<=Arg_1+Arg_2 && 0<=Arg_1 && Arg_0<=Arg_1
11:eval_start_bb2_in(Arg_0,Arg_1,Arg_2) -> eval_start_bb1_in(Arg_0,Arg_1+1,Arg_2+1):|:Arg_2<=Arg_1 && 1+Arg_2<=Arg_0 && 0<=Arg_2 && 0<=Arg_1+Arg_2 && 1<=Arg_0+Arg_2 && 1+Arg_1<=Arg_0 && 0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0
12:eval_start_bb3_in(Arg_0,Arg_1,Arg_2) -> eval_start_bb4_in(Arg_0,Arg_1,Arg_2):|:Arg_2<=Arg_1 && 0<=Arg_2 && 0<=Arg_1+Arg_2 && 0<=Arg_1 && Arg_0<=Arg_1 && 0<Arg_2
13:eval_start_bb3_in(Arg_0,Arg_1,Arg_2) -> eval_start_bb5_in(Arg_0,Arg_1,Arg_2):|:Arg_2<=Arg_1 && 0<=Arg_2 && 0<=Arg_1+Arg_2 && 0<=Arg_1 && Arg_0<=Arg_1 && Arg_2<=0
14:eval_start_bb4_in(Arg_0,Arg_1,Arg_2) -> eval_start_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<=Arg_1
15:eval_start_bb5_in(Arg_0,Arg_1,Arg_2) -> eval_start_stop(Arg_0,Arg_1,Arg_2):|:Arg_2<=0 && Arg_2<=Arg_1 && 0<=Arg_2 && 0<=Arg_1+Arg_2 && 0<=Arg_1 && Arg_0<=Arg_1
0:eval_start_start(Arg_0,Arg_1,Arg_2) -> eval_start_bb0_in(Arg_0,Arg_1,Arg_2)
MPRF for transition 9:eval_start_bb1_in(Arg_0,Arg_1,Arg_2) -> eval_start_bb2_in(Arg_0,Arg_1,Arg_2):|:Arg_2<=Arg_1 && 0<=Arg_2 && 0<=Arg_1+Arg_2 && 0<=Arg_1 && Arg_1<Arg_0 of depth 1:
new bound:
Arg_0 {O(n)}
MPRF:
eval_start_bb2_in [Arg_0-Arg_1-1 ]
eval_start_bb3_in [Arg_0-Arg_1 ]
eval_start_bb4_in [Arg_0-Arg_1 ]
eval_start_bb1_in [Arg_0-Arg_1 ]
MPRF for transition 11:eval_start_bb2_in(Arg_0,Arg_1,Arg_2) -> eval_start_bb1_in(Arg_0,Arg_1+1,Arg_2+1):|:Arg_2<=Arg_1 && 1+Arg_2<=Arg_0 && 0<=Arg_2 && 0<=Arg_1+Arg_2 && 1<=Arg_0+Arg_2 && 1+Arg_1<=Arg_0 && 0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 of depth 1:
new bound:
Arg_0 {O(n)}
MPRF:
eval_start_bb2_in [Arg_0-Arg_1 ]
eval_start_bb3_in [Arg_0-Arg_1 ]
eval_start_bb4_in [Arg_0-Arg_1 ]
eval_start_bb1_in [Arg_0-Arg_1 ]
MPRF for transition 10:eval_start_bb1_in(Arg_0,Arg_1,Arg_2) -> eval_start_bb3_in(Arg_0,Arg_1,Arg_2):|:Arg_2<=Arg_1 && 0<=Arg_2 && 0<=Arg_1+Arg_2 && 0<=Arg_1 && Arg_0<=Arg_1 of depth 1:
new bound:
Arg_0*Arg_0+Arg_0+1 {O(n^2)}
MPRF:
eval_start_bb2_in [Arg_2+1 ]
eval_start_bb3_in [Arg_2 ]
eval_start_bb4_in [Arg_2 ]
eval_start_bb1_in [Arg_2+1 ]
MPRF for transition 12:eval_start_bb3_in(Arg_0,Arg_1,Arg_2) -> eval_start_bb4_in(Arg_0,Arg_1,Arg_2):|:Arg_2<=Arg_1 && 0<=Arg_2 && 0<=Arg_1+Arg_2 && 0<=Arg_1 && Arg_0<=Arg_1 && 0<Arg_2 of depth 1:
new bound:
Arg_0*Arg_0+Arg_0+1 {O(n^2)}
MPRF:
eval_start_bb2_in [Arg_2+1 ]
eval_start_bb3_in [Arg_2+1 ]
eval_start_bb4_in [Arg_2 ]
eval_start_bb1_in [Arg_2+1 ]
MPRF for transition 14:eval_start_bb4_in(Arg_0,Arg_1,Arg_2) -> eval_start_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<=Arg_1 of depth 1:
new bound:
Arg_0*Arg_0 {O(n^2)}
MPRF:
eval_start_bb2_in [Arg_2 ]
eval_start_bb3_in [Arg_2 ]
eval_start_bb4_in [Arg_2 ]
eval_start_bb1_in [Arg_2 ]
All Bounds
Timebounds
Overall timebound:3*Arg_0*Arg_0+4*Arg_0+13 {O(n^2)}
2: eval_start_0->eval_start_1: 1 {O(1)}
3: eval_start_1->eval_start_2: 1 {O(1)}
4: eval_start_2->eval_start_3: 1 {O(1)}
5: eval_start_3->eval_start_4: 1 {O(1)}
6: eval_start_4->eval_start_5: 1 {O(1)}
7: eval_start_5->eval_start_6: 1 {O(1)}
8: eval_start_6->eval_start_bb1_in: 1 {O(1)}
1: eval_start_bb0_in->eval_start_0: 1 {O(1)}
9: eval_start_bb1_in->eval_start_bb2_in: Arg_0 {O(n)}
10: eval_start_bb1_in->eval_start_bb3_in: Arg_0*Arg_0+Arg_0+1 {O(n^2)}
11: eval_start_bb2_in->eval_start_bb1_in: Arg_0 {O(n)}
12: eval_start_bb3_in->eval_start_bb4_in: Arg_0*Arg_0+Arg_0+1 {O(n^2)}
13: eval_start_bb3_in->eval_start_bb5_in: 1 {O(1)}
14: eval_start_bb4_in->eval_start_bb1_in: Arg_0*Arg_0 {O(n^2)}
15: eval_start_bb5_in->eval_start_stop: 1 {O(1)}
0: eval_start_start->eval_start_bb0_in: 1 {O(1)}
Costbounds
Overall costbound: 3*Arg_0*Arg_0+4*Arg_0+13 {O(n^2)}
2: eval_start_0->eval_start_1: 1 {O(1)}
3: eval_start_1->eval_start_2: 1 {O(1)}
4: eval_start_2->eval_start_3: 1 {O(1)}
5: eval_start_3->eval_start_4: 1 {O(1)}
6: eval_start_4->eval_start_5: 1 {O(1)}
7: eval_start_5->eval_start_6: 1 {O(1)}
8: eval_start_6->eval_start_bb1_in: 1 {O(1)}
1: eval_start_bb0_in->eval_start_0: 1 {O(1)}
9: eval_start_bb1_in->eval_start_bb2_in: Arg_0 {O(n)}
10: eval_start_bb1_in->eval_start_bb3_in: Arg_0*Arg_0+Arg_0+1 {O(n^2)}
11: eval_start_bb2_in->eval_start_bb1_in: Arg_0 {O(n)}
12: eval_start_bb3_in->eval_start_bb4_in: Arg_0*Arg_0+Arg_0+1 {O(n^2)}
13: eval_start_bb3_in->eval_start_bb5_in: 1 {O(1)}
14: eval_start_bb4_in->eval_start_bb1_in: Arg_0*Arg_0 {O(n^2)}
15: eval_start_bb5_in->eval_start_stop: 1 {O(1)}
0: eval_start_start->eval_start_bb0_in: 1 {O(1)}
Sizebounds
2: eval_start_0->eval_start_1, Arg_0: Arg_0 {O(n)}
2: eval_start_0->eval_start_1, Arg_1: Arg_1 {O(n)}
2: eval_start_0->eval_start_1, Arg_2: Arg_2 {O(n)}
3: eval_start_1->eval_start_2, Arg_0: Arg_0 {O(n)}
3: eval_start_1->eval_start_2, Arg_1: Arg_1 {O(n)}
3: eval_start_1->eval_start_2, Arg_2: Arg_2 {O(n)}
4: eval_start_2->eval_start_3, Arg_0: Arg_0 {O(n)}
4: eval_start_2->eval_start_3, Arg_1: Arg_1 {O(n)}
4: eval_start_2->eval_start_3, Arg_2: Arg_2 {O(n)}
5: eval_start_3->eval_start_4, Arg_0: Arg_0 {O(n)}
5: eval_start_3->eval_start_4, Arg_1: Arg_1 {O(n)}
5: eval_start_3->eval_start_4, Arg_2: Arg_2 {O(n)}
6: eval_start_4->eval_start_5, Arg_0: Arg_0 {O(n)}
6: eval_start_4->eval_start_5, Arg_1: Arg_1 {O(n)}
6: eval_start_4->eval_start_5, Arg_2: Arg_2 {O(n)}
7: eval_start_5->eval_start_6, Arg_0: Arg_0 {O(n)}
7: eval_start_5->eval_start_6, Arg_1: Arg_1 {O(n)}
7: eval_start_5->eval_start_6, Arg_2: Arg_2 {O(n)}
8: eval_start_6->eval_start_bb1_in, Arg_0: Arg_0 {O(n)}
8: eval_start_6->eval_start_bb1_in, Arg_1: 0 {O(1)}
8: eval_start_6->eval_start_bb1_in, Arg_2: 0 {O(1)}
1: eval_start_bb0_in->eval_start_0, Arg_0: Arg_0 {O(n)}
1: eval_start_bb0_in->eval_start_0, Arg_1: Arg_1 {O(n)}
1: eval_start_bb0_in->eval_start_0, Arg_2: Arg_2 {O(n)}
9: eval_start_bb1_in->eval_start_bb2_in, Arg_0: Arg_0 {O(n)}
9: eval_start_bb1_in->eval_start_bb2_in, Arg_1: Arg_0 {O(n)}
9: eval_start_bb1_in->eval_start_bb2_in, Arg_2: Arg_0 {O(n)}
10: eval_start_bb1_in->eval_start_bb3_in, Arg_0: 2*Arg_0 {O(n)}
10: eval_start_bb1_in->eval_start_bb3_in, Arg_1: Arg_0 {O(n)}
10: eval_start_bb1_in->eval_start_bb3_in, Arg_2: Arg_0 {O(n)}
11: eval_start_bb2_in->eval_start_bb1_in, Arg_0: Arg_0 {O(n)}
11: eval_start_bb2_in->eval_start_bb1_in, Arg_1: Arg_0 {O(n)}
11: eval_start_bb2_in->eval_start_bb1_in, Arg_2: Arg_0 {O(n)}
12: eval_start_bb3_in->eval_start_bb4_in, Arg_0: 2*Arg_0 {O(n)}
12: eval_start_bb3_in->eval_start_bb4_in, Arg_1: Arg_0 {O(n)}
12: eval_start_bb3_in->eval_start_bb4_in, Arg_2: Arg_0 {O(n)}
13: eval_start_bb3_in->eval_start_bb5_in, Arg_0: 2*Arg_0 {O(n)}
13: eval_start_bb3_in->eval_start_bb5_in, Arg_1: Arg_0 {O(n)}
13: eval_start_bb3_in->eval_start_bb5_in, Arg_2: 0 {O(1)}
14: eval_start_bb4_in->eval_start_bb1_in, Arg_0: 2*Arg_0 {O(n)}
14: eval_start_bb4_in->eval_start_bb1_in, Arg_1: Arg_0 {O(n)}
14: eval_start_bb4_in->eval_start_bb1_in, Arg_2: Arg_0 {O(n)}
15: eval_start_bb5_in->eval_start_stop, Arg_0: 2*Arg_0 {O(n)}
15: eval_start_bb5_in->eval_start_stop, Arg_1: Arg_0 {O(n)}
15: eval_start_bb5_in->eval_start_stop, Arg_2: 0 {O(1)}
0: eval_start_start->eval_start_bb0_in, Arg_0: Arg_0 {O(n)}
0: eval_start_start->eval_start_bb0_in, Arg_1: Arg_1 {O(n)}
0: eval_start_start->eval_start_bb0_in, Arg_2: Arg_2 {O(n)}