Initial Problem
Start: eval_textbook_ex4_start
Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3
Temp_Vars:
Locations: eval_textbook_ex4_bb0_in, eval_textbook_ex4_bb1_in, eval_textbook_ex4_bb2_in, eval_textbook_ex4_bb3_in, eval_textbook_ex4_bb4_in, eval_textbook_ex4_bb5_in, eval_textbook_ex4_start, eval_textbook_ex4_stop
Transitions:
1:eval_textbook_ex4_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_textbook_ex4_bb1_in(Arg_0,1,Arg_2,Arg_3)
2:eval_textbook_ex4_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_textbook_ex4_bb2_in(1,Arg_1,Arg_2,Arg_3):|:Arg_1<=Arg_3
3:eval_textbook_ex4_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_textbook_ex4_bb5_in(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_3<Arg_1
4:eval_textbook_ex4_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_textbook_ex4_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_0<=Arg_2
5:eval_textbook_ex4_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_textbook_ex4_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_2<Arg_0
6:eval_textbook_ex4_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_textbook_ex4_bb2_in(Arg_0+1,Arg_1,Arg_2,Arg_3)
7:eval_textbook_ex4_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_textbook_ex4_bb1_in(Arg_0,Arg_1+1,Arg_2,Arg_3)
8:eval_textbook_ex4_bb5_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_textbook_ex4_stop(Arg_0,Arg_1,Arg_2,Arg_3)
0:eval_textbook_ex4_start(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_textbook_ex4_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3)
Preprocessing
Found invariant 1<=Arg_3 && 2<=Arg_1+Arg_3 && Arg_1<=Arg_3 && 2<=Arg_0+Arg_3 && 1+Arg_2<=Arg_0 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 for location eval_textbook_ex4_bb4_in
Found invariant 1<=Arg_3 && 2<=Arg_1+Arg_3 && Arg_1<=Arg_3 && 2<=Arg_0+Arg_3 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 for location eval_textbook_ex4_bb2_in
Found invariant 1+Arg_3<=Arg_1 && 1<=Arg_1 for location eval_textbook_ex4_stop
Found invariant 1<=Arg_3 && 2<=Arg_2+Arg_3 && 2<=Arg_1+Arg_3 && Arg_1<=Arg_3 && 2<=Arg_0+Arg_3 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && 2<=Arg_0+Arg_2 && Arg_0<=Arg_2 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 for location eval_textbook_ex4_bb3_in
Found invariant 1<=Arg_1 for location eval_textbook_ex4_bb1_in
Found invariant 1+Arg_3<=Arg_1 && 1<=Arg_1 for location eval_textbook_ex4_bb5_in
Problem after Preprocessing
Start: eval_textbook_ex4_start
Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3
Temp_Vars:
Locations: eval_textbook_ex4_bb0_in, eval_textbook_ex4_bb1_in, eval_textbook_ex4_bb2_in, eval_textbook_ex4_bb3_in, eval_textbook_ex4_bb4_in, eval_textbook_ex4_bb5_in, eval_textbook_ex4_start, eval_textbook_ex4_stop
Transitions:
1:eval_textbook_ex4_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_textbook_ex4_bb1_in(Arg_0,1,Arg_2,Arg_3)
2:eval_textbook_ex4_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_textbook_ex4_bb2_in(1,Arg_1,Arg_2,Arg_3):|:1<=Arg_1 && Arg_1<=Arg_3
3:eval_textbook_ex4_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_textbook_ex4_bb5_in(Arg_0,Arg_1,Arg_2,Arg_3):|:1<=Arg_1 && Arg_3<Arg_1
4:eval_textbook_ex4_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_textbook_ex4_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3):|:1<=Arg_3 && 2<=Arg_1+Arg_3 && Arg_1<=Arg_3 && 2<=Arg_0+Arg_3 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 && Arg_0<=Arg_2
5:eval_textbook_ex4_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_textbook_ex4_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3):|:1<=Arg_3 && 2<=Arg_1+Arg_3 && Arg_1<=Arg_3 && 2<=Arg_0+Arg_3 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 && Arg_2<Arg_0
6:eval_textbook_ex4_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_textbook_ex4_bb2_in(Arg_0+1,Arg_1,Arg_2,Arg_3):|:1<=Arg_3 && 2<=Arg_2+Arg_3 && 2<=Arg_1+Arg_3 && Arg_1<=Arg_3 && 2<=Arg_0+Arg_3 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && 2<=Arg_0+Arg_2 && Arg_0<=Arg_2 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0
7:eval_textbook_ex4_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_textbook_ex4_bb1_in(Arg_0,Arg_1+1,Arg_2,Arg_3):|:1<=Arg_3 && 2<=Arg_1+Arg_3 && Arg_1<=Arg_3 && 2<=Arg_0+Arg_3 && 1+Arg_2<=Arg_0 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0
8:eval_textbook_ex4_bb5_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_textbook_ex4_stop(Arg_0,Arg_1,Arg_2,Arg_3):|:1+Arg_3<=Arg_1 && 1<=Arg_1
0:eval_textbook_ex4_start(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_textbook_ex4_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3)
MPRF for transition 2:eval_textbook_ex4_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_textbook_ex4_bb2_in(1,Arg_1,Arg_2,Arg_3):|:1<=Arg_1 && Arg_1<=Arg_3 of depth 1:
new bound:
Arg_3+2 {O(n)}
MPRF:
eval_textbook_ex4_bb3_in [Arg_3-Arg_1 ]
eval_textbook_ex4_bb2_in [Arg_3-Arg_1 ]
eval_textbook_ex4_bb4_in [Arg_3-Arg_1 ]
eval_textbook_ex4_bb1_in [Arg_3+1-Arg_1 ]
MPRF for transition 5:eval_textbook_ex4_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_textbook_ex4_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3):|:1<=Arg_3 && 2<=Arg_1+Arg_3 && Arg_1<=Arg_3 && 2<=Arg_0+Arg_3 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 && Arg_2<Arg_0 of depth 1:
new bound:
Arg_3+2 {O(n)}
MPRF:
eval_textbook_ex4_bb3_in [Arg_3+1-Arg_1 ]
eval_textbook_ex4_bb2_in [Arg_3+1-Arg_1 ]
eval_textbook_ex4_bb4_in [Arg_3-Arg_1 ]
eval_textbook_ex4_bb1_in [Arg_3+1-Arg_1 ]
MPRF for transition 7:eval_textbook_ex4_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_textbook_ex4_bb1_in(Arg_0,Arg_1+1,Arg_2,Arg_3):|:1<=Arg_3 && 2<=Arg_1+Arg_3 && Arg_1<=Arg_3 && 2<=Arg_0+Arg_3 && 1+Arg_2<=Arg_0 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 of depth 1:
new bound:
Arg_3+2 {O(n)}
MPRF:
eval_textbook_ex4_bb3_in [Arg_3+1-Arg_1 ]
eval_textbook_ex4_bb2_in [Arg_3+1-Arg_1 ]
eval_textbook_ex4_bb4_in [Arg_3+1-Arg_1 ]
eval_textbook_ex4_bb1_in [Arg_3+1-Arg_1 ]
MPRF for transition 4:eval_textbook_ex4_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_textbook_ex4_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3):|:1<=Arg_3 && 2<=Arg_1+Arg_3 && Arg_1<=Arg_3 && 2<=Arg_0+Arg_3 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 && Arg_0<=Arg_2 of depth 1:
new bound:
Arg_2*Arg_3+3*Arg_2 {O(n^2)}
MPRF:
eval_textbook_ex4_bb1_in [Arg_2 ]
eval_textbook_ex4_bb4_in [Arg_2-Arg_0 ]
eval_textbook_ex4_bb3_in [Arg_2-Arg_0 ]
eval_textbook_ex4_bb2_in [Arg_2+1-Arg_0 ]
MPRF for transition 6:eval_textbook_ex4_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_textbook_ex4_bb2_in(Arg_0+1,Arg_1,Arg_2,Arg_3):|:1<=Arg_3 && 2<=Arg_2+Arg_3 && 2<=Arg_1+Arg_3 && Arg_1<=Arg_3 && 2<=Arg_0+Arg_3 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && 2<=Arg_0+Arg_2 && Arg_0<=Arg_2 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 of depth 1:
new bound:
Arg_2*Arg_3+3*Arg_2 {O(n^2)}
MPRF:
eval_textbook_ex4_bb1_in [Arg_2 ]
eval_textbook_ex4_bb4_in [Arg_2-Arg_0 ]
eval_textbook_ex4_bb3_in [Arg_2+1-Arg_0 ]
eval_textbook_ex4_bb2_in [Arg_2+1-Arg_0 ]
All Bounds
Timebounds
Overall timebound:2*Arg_2*Arg_3+3*Arg_3+6*Arg_2+10 {O(n^2)}
1: eval_textbook_ex4_bb0_in->eval_textbook_ex4_bb1_in: 1 {O(1)}
2: eval_textbook_ex4_bb1_in->eval_textbook_ex4_bb2_in: Arg_3+2 {O(n)}
3: eval_textbook_ex4_bb1_in->eval_textbook_ex4_bb5_in: 1 {O(1)}
4: eval_textbook_ex4_bb2_in->eval_textbook_ex4_bb3_in: Arg_2*Arg_3+3*Arg_2 {O(n^2)}
5: eval_textbook_ex4_bb2_in->eval_textbook_ex4_bb4_in: Arg_3+2 {O(n)}
6: eval_textbook_ex4_bb3_in->eval_textbook_ex4_bb2_in: Arg_2*Arg_3+3*Arg_2 {O(n^2)}
7: eval_textbook_ex4_bb4_in->eval_textbook_ex4_bb1_in: Arg_3+2 {O(n)}
8: eval_textbook_ex4_bb5_in->eval_textbook_ex4_stop: 1 {O(1)}
0: eval_textbook_ex4_start->eval_textbook_ex4_bb0_in: 1 {O(1)}
Costbounds
Overall costbound: 2*Arg_2*Arg_3+3*Arg_3+6*Arg_2+10 {O(n^2)}
1: eval_textbook_ex4_bb0_in->eval_textbook_ex4_bb1_in: 1 {O(1)}
2: eval_textbook_ex4_bb1_in->eval_textbook_ex4_bb2_in: Arg_3+2 {O(n)}
3: eval_textbook_ex4_bb1_in->eval_textbook_ex4_bb5_in: 1 {O(1)}
4: eval_textbook_ex4_bb2_in->eval_textbook_ex4_bb3_in: Arg_2*Arg_3+3*Arg_2 {O(n^2)}
5: eval_textbook_ex4_bb2_in->eval_textbook_ex4_bb4_in: Arg_3+2 {O(n)}
6: eval_textbook_ex4_bb3_in->eval_textbook_ex4_bb2_in: Arg_2*Arg_3+3*Arg_2 {O(n^2)}
7: eval_textbook_ex4_bb4_in->eval_textbook_ex4_bb1_in: Arg_3+2 {O(n)}
8: eval_textbook_ex4_bb5_in->eval_textbook_ex4_stop: 1 {O(1)}
0: eval_textbook_ex4_start->eval_textbook_ex4_bb0_in: 1 {O(1)}
Sizebounds
1: eval_textbook_ex4_bb0_in->eval_textbook_ex4_bb1_in, Arg_0: Arg_0 {O(n)}
1: eval_textbook_ex4_bb0_in->eval_textbook_ex4_bb1_in, Arg_1: 1 {O(1)}
1: eval_textbook_ex4_bb0_in->eval_textbook_ex4_bb1_in, Arg_2: Arg_2 {O(n)}
1: eval_textbook_ex4_bb0_in->eval_textbook_ex4_bb1_in, Arg_3: Arg_3 {O(n)}
2: eval_textbook_ex4_bb1_in->eval_textbook_ex4_bb2_in, Arg_0: 1 {O(1)}
2: eval_textbook_ex4_bb1_in->eval_textbook_ex4_bb2_in, Arg_1: Arg_3+3 {O(n)}
2: eval_textbook_ex4_bb1_in->eval_textbook_ex4_bb2_in, Arg_2: Arg_2 {O(n)}
2: eval_textbook_ex4_bb1_in->eval_textbook_ex4_bb2_in, Arg_3: Arg_3 {O(n)}
3: eval_textbook_ex4_bb1_in->eval_textbook_ex4_bb5_in, Arg_0: Arg_2*Arg_3+3*Arg_2+Arg_0+2 {O(n^2)}
3: eval_textbook_ex4_bb1_in->eval_textbook_ex4_bb5_in, Arg_1: Arg_3+4 {O(n)}
3: eval_textbook_ex4_bb1_in->eval_textbook_ex4_bb5_in, Arg_2: 2*Arg_2 {O(n)}
3: eval_textbook_ex4_bb1_in->eval_textbook_ex4_bb5_in, Arg_3: 2*Arg_3 {O(n)}
4: eval_textbook_ex4_bb2_in->eval_textbook_ex4_bb3_in, Arg_0: Arg_2*Arg_3+3*Arg_2+1 {O(n^2)}
4: eval_textbook_ex4_bb2_in->eval_textbook_ex4_bb3_in, Arg_1: Arg_3+3 {O(n)}
4: eval_textbook_ex4_bb2_in->eval_textbook_ex4_bb3_in, Arg_2: Arg_2 {O(n)}
4: eval_textbook_ex4_bb2_in->eval_textbook_ex4_bb3_in, Arg_3: Arg_3 {O(n)}
5: eval_textbook_ex4_bb2_in->eval_textbook_ex4_bb4_in, Arg_0: Arg_2*Arg_3+3*Arg_2+2 {O(n^2)}
5: eval_textbook_ex4_bb2_in->eval_textbook_ex4_bb4_in, Arg_1: Arg_3+3 {O(n)}
5: eval_textbook_ex4_bb2_in->eval_textbook_ex4_bb4_in, Arg_2: Arg_2 {O(n)}
5: eval_textbook_ex4_bb2_in->eval_textbook_ex4_bb4_in, Arg_3: Arg_3 {O(n)}
6: eval_textbook_ex4_bb3_in->eval_textbook_ex4_bb2_in, Arg_0: Arg_2*Arg_3+3*Arg_2+1 {O(n^2)}
6: eval_textbook_ex4_bb3_in->eval_textbook_ex4_bb2_in, Arg_1: Arg_3+3 {O(n)}
6: eval_textbook_ex4_bb3_in->eval_textbook_ex4_bb2_in, Arg_2: Arg_2 {O(n)}
6: eval_textbook_ex4_bb3_in->eval_textbook_ex4_bb2_in, Arg_3: Arg_3 {O(n)}
7: eval_textbook_ex4_bb4_in->eval_textbook_ex4_bb1_in, Arg_0: Arg_2*Arg_3+3*Arg_2+2 {O(n^2)}
7: eval_textbook_ex4_bb4_in->eval_textbook_ex4_bb1_in, Arg_1: Arg_3+3 {O(n)}
7: eval_textbook_ex4_bb4_in->eval_textbook_ex4_bb1_in, Arg_2: Arg_2 {O(n)}
7: eval_textbook_ex4_bb4_in->eval_textbook_ex4_bb1_in, Arg_3: Arg_3 {O(n)}
8: eval_textbook_ex4_bb5_in->eval_textbook_ex4_stop, Arg_0: Arg_2*Arg_3+3*Arg_2+Arg_0+2 {O(n^2)}
8: eval_textbook_ex4_bb5_in->eval_textbook_ex4_stop, Arg_1: Arg_3+4 {O(n)}
8: eval_textbook_ex4_bb5_in->eval_textbook_ex4_stop, Arg_2: 2*Arg_2 {O(n)}
8: eval_textbook_ex4_bb5_in->eval_textbook_ex4_stop, Arg_3: 2*Arg_3 {O(n)}
0: eval_textbook_ex4_start->eval_textbook_ex4_bb0_in, Arg_0: Arg_0 {O(n)}
0: eval_textbook_ex4_start->eval_textbook_ex4_bb0_in, Arg_1: Arg_1 {O(n)}
0: eval_textbook_ex4_start->eval_textbook_ex4_bb0_in, Arg_2: Arg_2 {O(n)}
0: eval_textbook_ex4_start->eval_textbook_ex4_bb0_in, Arg_3: Arg_3 {O(n)}