Initial Problem
Start: eval_ex_paper2_start
Program_Vars: Arg_0, Arg_1, Arg_2
Temp_Vars:
Locations: eval_ex_paper2_bb0_in, eval_ex_paper2_bb1_in, eval_ex_paper2_bb2_in, eval_ex_paper2_bb3_in, eval_ex_paper2_bb4_in, eval_ex_paper2_bb5_in, eval_ex_paper2_start, eval_ex_paper2_stop
Transitions:
1:eval_ex_paper2_bb0_in(Arg_0,Arg_1,Arg_2) -> eval_ex_paper2_bb1_in(Arg_0,1,Arg_2)
2:eval_ex_paper2_bb1_in(Arg_0,Arg_1,Arg_2) -> eval_ex_paper2_bb2_in(Arg_0,Arg_1,Arg_1):|:Arg_1<=Arg_0
3:eval_ex_paper2_bb1_in(Arg_0,Arg_1,Arg_2) -> eval_ex_paper2_bb5_in(Arg_0,Arg_1,Arg_2):|:Arg_0<Arg_1
4:eval_ex_paper2_bb2_in(Arg_0,Arg_1,Arg_2) -> eval_ex_paper2_bb3_in(Arg_0,Arg_1,Arg_2):|:Arg_2<=Arg_0
5:eval_ex_paper2_bb2_in(Arg_0,Arg_1,Arg_2) -> eval_ex_paper2_bb4_in(Arg_0,Arg_1,Arg_2):|:Arg_0<Arg_2
6:eval_ex_paper2_bb3_in(Arg_0,Arg_1,Arg_2) -> eval_ex_paper2_bb2_in(Arg_0,Arg_1,Arg_2+1)
7:eval_ex_paper2_bb4_in(Arg_0,Arg_1,Arg_2) -> eval_ex_paper2_bb1_in(Arg_0,Arg_1+1,Arg_2)
8:eval_ex_paper2_bb5_in(Arg_0,Arg_1,Arg_2) -> eval_ex_paper2_stop(Arg_0,Arg_1,Arg_2)
0:eval_ex_paper2_start(Arg_0,Arg_1,Arg_2) -> eval_ex_paper2_bb0_in(Arg_0,Arg_1,Arg_2)
Preprocessing
Found invariant 1<=Arg_1 && 1+Arg_0<=Arg_1 for location eval_ex_paper2_bb5_in
Found invariant 1<=Arg_1 for location eval_ex_paper2_bb1_in
Found invariant Arg_2<=Arg_0 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 2<=Arg_0+Arg_2 && Arg_1<=Arg_0 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 for location eval_ex_paper2_bb3_in
Found invariant Arg_2<=1+Arg_0 && 2<=Arg_2 && 3<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 3<=Arg_0+Arg_2 && 1+Arg_0<=Arg_2 && Arg_1<=Arg_0 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 for location eval_ex_paper2_bb4_in
Found invariant 1<=Arg_1 && 1+Arg_0<=Arg_1 for location eval_ex_paper2_stop
Found invariant Arg_2<=1+Arg_0 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 2<=Arg_0+Arg_2 && Arg_1<=Arg_0 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 for location eval_ex_paper2_bb2_in
Problem after Preprocessing
Start: eval_ex_paper2_start
Program_Vars: Arg_0, Arg_1, Arg_2
Temp_Vars:
Locations: eval_ex_paper2_bb0_in, eval_ex_paper2_bb1_in, eval_ex_paper2_bb2_in, eval_ex_paper2_bb3_in, eval_ex_paper2_bb4_in, eval_ex_paper2_bb5_in, eval_ex_paper2_start, eval_ex_paper2_stop
Transitions:
1:eval_ex_paper2_bb0_in(Arg_0,Arg_1,Arg_2) -> eval_ex_paper2_bb1_in(Arg_0,1,Arg_2)
2:eval_ex_paper2_bb1_in(Arg_0,Arg_1,Arg_2) -> eval_ex_paper2_bb2_in(Arg_0,Arg_1,Arg_1):|:1<=Arg_1 && Arg_1<=Arg_0
3:eval_ex_paper2_bb1_in(Arg_0,Arg_1,Arg_2) -> eval_ex_paper2_bb5_in(Arg_0,Arg_1,Arg_2):|:1<=Arg_1 && Arg_0<Arg_1
4:eval_ex_paper2_bb2_in(Arg_0,Arg_1,Arg_2) -> eval_ex_paper2_bb3_in(Arg_0,Arg_1,Arg_2):|:Arg_2<=1+Arg_0 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 2<=Arg_0+Arg_2 && Arg_1<=Arg_0 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 && Arg_2<=Arg_0
5:eval_ex_paper2_bb2_in(Arg_0,Arg_1,Arg_2) -> eval_ex_paper2_bb4_in(Arg_0,Arg_1,Arg_2):|:Arg_2<=1+Arg_0 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 2<=Arg_0+Arg_2 && Arg_1<=Arg_0 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 && Arg_0<Arg_2
6:eval_ex_paper2_bb3_in(Arg_0,Arg_1,Arg_2) -> eval_ex_paper2_bb2_in(Arg_0,Arg_1,Arg_2+1):|:Arg_2<=Arg_0 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 2<=Arg_0+Arg_2 && Arg_1<=Arg_0 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0
7:eval_ex_paper2_bb4_in(Arg_0,Arg_1,Arg_2) -> eval_ex_paper2_bb1_in(Arg_0,Arg_1+1,Arg_2):|:Arg_2<=1+Arg_0 && 2<=Arg_2 && 3<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 3<=Arg_0+Arg_2 && 1+Arg_0<=Arg_2 && Arg_1<=Arg_0 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0
8:eval_ex_paper2_bb5_in(Arg_0,Arg_1,Arg_2) -> eval_ex_paper2_stop(Arg_0,Arg_1,Arg_2):|:1<=Arg_1 && 1+Arg_0<=Arg_1
0:eval_ex_paper2_start(Arg_0,Arg_1,Arg_2) -> eval_ex_paper2_bb0_in(Arg_0,Arg_1,Arg_2)
MPRF for transition 2:eval_ex_paper2_bb1_in(Arg_0,Arg_1,Arg_2) -> eval_ex_paper2_bb2_in(Arg_0,Arg_1,Arg_1):|:1<=Arg_1 && Arg_1<=Arg_0 of depth 1:
new bound:
Arg_0+2 {O(n)}
MPRF:
eval_ex_paper2_bb3_in [Arg_0-Arg_1 ]
eval_ex_paper2_bb2_in [Arg_0-Arg_1 ]
eval_ex_paper2_bb4_in [Arg_0-Arg_1 ]
eval_ex_paper2_bb1_in [Arg_0+1-Arg_1 ]
MPRF for transition 5:eval_ex_paper2_bb2_in(Arg_0,Arg_1,Arg_2) -> eval_ex_paper2_bb4_in(Arg_0,Arg_1,Arg_2):|:Arg_2<=1+Arg_0 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 2<=Arg_0+Arg_2 && Arg_1<=Arg_0 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 && Arg_0<Arg_2 of depth 1:
new bound:
Arg_0+2 {O(n)}
MPRF:
eval_ex_paper2_bb3_in [Arg_0+1-Arg_1 ]
eval_ex_paper2_bb2_in [Arg_0+1-Arg_1 ]
eval_ex_paper2_bb4_in [Arg_0-Arg_1 ]
eval_ex_paper2_bb1_in [Arg_0+1-Arg_1 ]
MPRF for transition 7:eval_ex_paper2_bb4_in(Arg_0,Arg_1,Arg_2) -> eval_ex_paper2_bb1_in(Arg_0,Arg_1+1,Arg_2):|:Arg_2<=1+Arg_0 && 2<=Arg_2 && 3<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 3<=Arg_0+Arg_2 && 1+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_0+1 {O(n)}
MPRF:
eval_ex_paper2_bb3_in [2*Arg_0-Arg_1 ]
eval_ex_paper2_bb2_in [2*Arg_0-Arg_1 ]
eval_ex_paper2_bb4_in [2*Arg_0-Arg_1 ]
eval_ex_paper2_bb1_in [2*Arg_0-Arg_1 ]
MPRF for transition 4:eval_ex_paper2_bb2_in(Arg_0,Arg_1,Arg_2) -> eval_ex_paper2_bb3_in(Arg_0,Arg_1,Arg_2):|:Arg_2<=1+Arg_0 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 2<=Arg_0+Arg_2 && Arg_1<=Arg_0 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 && Arg_2<=Arg_0 of depth 1:
new bound:
2*Arg_0*Arg_0+2*Arg_0 {O(n^2)}
MPRF:
eval_ex_paper2_bb1_in [Arg_0 ]
eval_ex_paper2_bb4_in [Arg_0-Arg_2 ]
eval_ex_paper2_bb3_in [Arg_0-Arg_2 ]
eval_ex_paper2_bb2_in [Arg_0+1-Arg_2 ]
MPRF for transition 6:eval_ex_paper2_bb3_in(Arg_0,Arg_1,Arg_2) -> eval_ex_paper2_bb2_in(Arg_0,Arg_1,Arg_2+1):|:Arg_2<=Arg_0 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 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_0*Arg_0+2*Arg_0 {O(n^2)}
MPRF:
eval_ex_paper2_bb1_in [Arg_0 ]
eval_ex_paper2_bb4_in [Arg_0-Arg_2 ]
eval_ex_paper2_bb3_in [Arg_0+1-Arg_2 ]
eval_ex_paper2_bb2_in [Arg_0+1-Arg_2 ]
All Bounds
Timebounds
Overall timebound:4*Arg_0*Arg_0+8*Arg_0+9 {O(n^2)}
1: eval_ex_paper2_bb0_in->eval_ex_paper2_bb1_in: 1 {O(1)}
2: eval_ex_paper2_bb1_in->eval_ex_paper2_bb2_in: Arg_0+2 {O(n)}
3: eval_ex_paper2_bb1_in->eval_ex_paper2_bb5_in: 1 {O(1)}
4: eval_ex_paper2_bb2_in->eval_ex_paper2_bb3_in: 2*Arg_0*Arg_0+2*Arg_0 {O(n^2)}
5: eval_ex_paper2_bb2_in->eval_ex_paper2_bb4_in: Arg_0+2 {O(n)}
6: eval_ex_paper2_bb3_in->eval_ex_paper2_bb2_in: 2*Arg_0*Arg_0+2*Arg_0 {O(n^2)}
7: eval_ex_paper2_bb4_in->eval_ex_paper2_bb1_in: 2*Arg_0+1 {O(n)}
8: eval_ex_paper2_bb5_in->eval_ex_paper2_stop: 1 {O(1)}
0: eval_ex_paper2_start->eval_ex_paper2_bb0_in: 1 {O(1)}
Costbounds
Overall costbound: 4*Arg_0*Arg_0+8*Arg_0+9 {O(n^2)}
1: eval_ex_paper2_bb0_in->eval_ex_paper2_bb1_in: 1 {O(1)}
2: eval_ex_paper2_bb1_in->eval_ex_paper2_bb2_in: Arg_0+2 {O(n)}
3: eval_ex_paper2_bb1_in->eval_ex_paper2_bb5_in: 1 {O(1)}
4: eval_ex_paper2_bb2_in->eval_ex_paper2_bb3_in: 2*Arg_0*Arg_0+2*Arg_0 {O(n^2)}
5: eval_ex_paper2_bb2_in->eval_ex_paper2_bb4_in: Arg_0+2 {O(n)}
6: eval_ex_paper2_bb3_in->eval_ex_paper2_bb2_in: 2*Arg_0*Arg_0+2*Arg_0 {O(n^2)}
7: eval_ex_paper2_bb4_in->eval_ex_paper2_bb1_in: 2*Arg_0+1 {O(n)}
8: eval_ex_paper2_bb5_in->eval_ex_paper2_stop: 1 {O(1)}
0: eval_ex_paper2_start->eval_ex_paper2_bb0_in: 1 {O(1)}
Sizebounds
1: eval_ex_paper2_bb0_in->eval_ex_paper2_bb1_in, Arg_0: Arg_0 {O(n)}
1: eval_ex_paper2_bb0_in->eval_ex_paper2_bb1_in, Arg_1: 1 {O(1)}
1: eval_ex_paper2_bb0_in->eval_ex_paper2_bb1_in, Arg_2: Arg_2 {O(n)}
2: eval_ex_paper2_bb1_in->eval_ex_paper2_bb2_in, Arg_0: Arg_0 {O(n)}
2: eval_ex_paper2_bb1_in->eval_ex_paper2_bb2_in, Arg_1: 2*Arg_0+2 {O(n)}
2: eval_ex_paper2_bb1_in->eval_ex_paper2_bb2_in, Arg_2: 2*Arg_0+3 {O(n)}
3: eval_ex_paper2_bb1_in->eval_ex_paper2_bb5_in, Arg_0: 2*Arg_0 {O(n)}
3: eval_ex_paper2_bb1_in->eval_ex_paper2_bb5_in, Arg_1: 2*Arg_0+3 {O(n)}
3: eval_ex_paper2_bb1_in->eval_ex_paper2_bb5_in, Arg_2: 2*Arg_0*Arg_0+4*Arg_0+Arg_2+3 {O(n^2)}
4: eval_ex_paper2_bb2_in->eval_ex_paper2_bb3_in, Arg_0: Arg_0 {O(n)}
4: eval_ex_paper2_bb2_in->eval_ex_paper2_bb3_in, Arg_1: 2*Arg_0+2 {O(n)}
4: eval_ex_paper2_bb2_in->eval_ex_paper2_bb3_in, Arg_2: 2*Arg_0*Arg_0+4*Arg_0+3 {O(n^2)}
5: eval_ex_paper2_bb2_in->eval_ex_paper2_bb4_in, Arg_0: Arg_0 {O(n)}
5: eval_ex_paper2_bb2_in->eval_ex_paper2_bb4_in, Arg_1: 2*Arg_0+2 {O(n)}
5: eval_ex_paper2_bb2_in->eval_ex_paper2_bb4_in, Arg_2: 2*Arg_0*Arg_0+4*Arg_0+3 {O(n^2)}
6: eval_ex_paper2_bb3_in->eval_ex_paper2_bb2_in, Arg_0: Arg_0 {O(n)}
6: eval_ex_paper2_bb3_in->eval_ex_paper2_bb2_in, Arg_1: 2*Arg_0+2 {O(n)}
6: eval_ex_paper2_bb3_in->eval_ex_paper2_bb2_in, Arg_2: 2*Arg_0*Arg_0+4*Arg_0+3 {O(n^2)}
7: eval_ex_paper2_bb4_in->eval_ex_paper2_bb1_in, Arg_0: Arg_0 {O(n)}
7: eval_ex_paper2_bb4_in->eval_ex_paper2_bb1_in, Arg_1: 2*Arg_0+2 {O(n)}
7: eval_ex_paper2_bb4_in->eval_ex_paper2_bb1_in, Arg_2: 2*Arg_0*Arg_0+4*Arg_0+3 {O(n^2)}
8: eval_ex_paper2_bb5_in->eval_ex_paper2_stop, Arg_0: 2*Arg_0 {O(n)}
8: eval_ex_paper2_bb5_in->eval_ex_paper2_stop, Arg_1: 2*Arg_0+3 {O(n)}
8: eval_ex_paper2_bb5_in->eval_ex_paper2_stop, Arg_2: 2*Arg_0*Arg_0+4*Arg_0+Arg_2+3 {O(n^2)}
0: eval_ex_paper2_start->eval_ex_paper2_bb0_in, Arg_0: Arg_0 {O(n)}
0: eval_ex_paper2_start->eval_ex_paper2_bb0_in, Arg_1: Arg_1 {O(n)}
0: eval_ex_paper2_start->eval_ex_paper2_bb0_in, Arg_2: Arg_2 {O(n)}