Initial Problem
Start: eval_while2_start
Program_Vars: Arg_0, Arg_1, Arg_2
Temp_Vars:
Locations: eval_while2_bb0_in, eval_while2_bb1_in, eval_while2_bb2_in, eval_while2_bb3_in, eval_while2_bb4_in, eval_while2_bb5_in, eval_while2_start, eval_while2_stop
Transitions:
1:eval_while2_bb0_in(Arg_0,Arg_1,Arg_2) -> eval_while2_bb1_in(Arg_0,Arg_0,Arg_2)
2:eval_while2_bb1_in(Arg_0,Arg_1,Arg_2) -> eval_while2_bb2_in(Arg_0,Arg_1,Arg_0):|:0<Arg_1
3:eval_while2_bb1_in(Arg_0,Arg_1,Arg_2) -> eval_while2_bb5_in(Arg_0,Arg_1,Arg_2):|:Arg_1<=0
4:eval_while2_bb2_in(Arg_0,Arg_1,Arg_2) -> eval_while2_bb3_in(Arg_0,Arg_1,Arg_2):|:0<Arg_2
5:eval_while2_bb2_in(Arg_0,Arg_1,Arg_2) -> eval_while2_bb4_in(Arg_0,Arg_1,Arg_2):|:Arg_2<=0
6:eval_while2_bb3_in(Arg_0,Arg_1,Arg_2) -> eval_while2_bb2_in(Arg_0,Arg_1,Arg_2-1)
7:eval_while2_bb4_in(Arg_0,Arg_1,Arg_2) -> eval_while2_bb1_in(Arg_0,Arg_1-1,Arg_2)
8:eval_while2_bb5_in(Arg_0,Arg_1,Arg_2) -> eval_while2_stop(Arg_0,Arg_1,Arg_2)
0:eval_while2_start(Arg_0,Arg_1,Arg_2) -> eval_while2_bb0_in(Arg_0,Arg_1,Arg_2)
Preprocessing
Found invariant Arg_2<=Arg_0 && 1<=Arg_2 && 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_while2_bb3_in
Found invariant Arg_1<=Arg_0 for location eval_while2_bb1_in
Found invariant Arg_2<=Arg_0 && 0<=Arg_2 && 1<=Arg_1+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_while2_bb2_in
Found invariant Arg_1<=0 && Arg_1<=Arg_0 for location eval_while2_bb5_in
Found invariant Arg_2<=0 && 1+Arg_2<=Arg_1 && 1+Arg_2<=Arg_0 && 0<=Arg_2 && 1<=Arg_1+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_while2_bb4_in
Found invariant Arg_1<=0 && Arg_1<=Arg_0 for location eval_while2_stop
Problem after Preprocessing
Start: eval_while2_start
Program_Vars: Arg_0, Arg_1, Arg_2
Temp_Vars:
Locations: eval_while2_bb0_in, eval_while2_bb1_in, eval_while2_bb2_in, eval_while2_bb3_in, eval_while2_bb4_in, eval_while2_bb5_in, eval_while2_start, eval_while2_stop
Transitions:
1:eval_while2_bb0_in(Arg_0,Arg_1,Arg_2) -> eval_while2_bb1_in(Arg_0,Arg_0,Arg_2)
2:eval_while2_bb1_in(Arg_0,Arg_1,Arg_2) -> eval_while2_bb2_in(Arg_0,Arg_1,Arg_0):|:Arg_1<=Arg_0 && 0<Arg_1
3:eval_while2_bb1_in(Arg_0,Arg_1,Arg_2) -> eval_while2_bb5_in(Arg_0,Arg_1,Arg_2):|:Arg_1<=Arg_0 && Arg_1<=0
4:eval_while2_bb2_in(Arg_0,Arg_1,Arg_2) -> eval_while2_bb3_in(Arg_0,Arg_1,Arg_2):|:Arg_2<=Arg_0 && 0<=Arg_2 && 1<=Arg_1+Arg_2 && 1<=Arg_0+Arg_2 && Arg_1<=Arg_0 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 && 0<Arg_2
5:eval_while2_bb2_in(Arg_0,Arg_1,Arg_2) -> eval_while2_bb4_in(Arg_0,Arg_1,Arg_2):|:Arg_2<=Arg_0 && 0<=Arg_2 && 1<=Arg_1+Arg_2 && 1<=Arg_0+Arg_2 && Arg_1<=Arg_0 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 && Arg_2<=0
6:eval_while2_bb3_in(Arg_0,Arg_1,Arg_2) -> eval_while2_bb2_in(Arg_0,Arg_1,Arg_2-1):|:Arg_2<=Arg_0 && 1<=Arg_2 && 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_while2_bb4_in(Arg_0,Arg_1,Arg_2) -> eval_while2_bb1_in(Arg_0,Arg_1-1,Arg_2):|:Arg_2<=0 && 1+Arg_2<=Arg_1 && 1+Arg_2<=Arg_0 && 0<=Arg_2 && 1<=Arg_1+Arg_2 && 1<=Arg_0+Arg_2 && Arg_1<=Arg_0 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0
8:eval_while2_bb5_in(Arg_0,Arg_1,Arg_2) -> eval_while2_stop(Arg_0,Arg_1,Arg_2):|:Arg_1<=0 && Arg_1<=Arg_0
0:eval_while2_start(Arg_0,Arg_1,Arg_2) -> eval_while2_bb0_in(Arg_0,Arg_1,Arg_2)
MPRF for transition 2:eval_while2_bb1_in(Arg_0,Arg_1,Arg_2) -> eval_while2_bb2_in(Arg_0,Arg_1,Arg_0):|:Arg_1<=Arg_0 && 0<Arg_1 of depth 1:
new bound:
Arg_0 {O(n)}
MPRF:
eval_while2_bb3_in [Arg_1-1 ]
eval_while2_bb2_in [Arg_1-1 ]
eval_while2_bb4_in [Arg_1-1 ]
eval_while2_bb1_in [Arg_1 ]
MPRF for transition 5:eval_while2_bb2_in(Arg_0,Arg_1,Arg_2) -> eval_while2_bb4_in(Arg_0,Arg_1,Arg_2):|:Arg_2<=Arg_0 && 0<=Arg_2 && 1<=Arg_1+Arg_2 && 1<=Arg_0+Arg_2 && Arg_1<=Arg_0 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 && Arg_2<=0 of depth 1:
new bound:
Arg_0 {O(n)}
MPRF:
eval_while2_bb3_in [Arg_1 ]
eval_while2_bb2_in [Arg_1 ]
eval_while2_bb4_in [Arg_1-1 ]
eval_while2_bb1_in [Arg_1 ]
MPRF for transition 7:eval_while2_bb4_in(Arg_0,Arg_1,Arg_2) -> eval_while2_bb1_in(Arg_0,Arg_1-1,Arg_2):|:Arg_2<=0 && 1+Arg_2<=Arg_1 && 1+Arg_2<=Arg_0 && 0<=Arg_2 && 1<=Arg_1+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:
Arg_0 {O(n)}
MPRF:
eval_while2_bb3_in [Arg_1 ]
eval_while2_bb2_in [Arg_1 ]
eval_while2_bb4_in [Arg_1 ]
eval_while2_bb1_in [Arg_1 ]
MPRF for transition 4:eval_while2_bb2_in(Arg_0,Arg_1,Arg_2) -> eval_while2_bb3_in(Arg_0,Arg_1,Arg_2):|:Arg_2<=Arg_0 && 0<=Arg_2 && 1<=Arg_1+Arg_2 && 1<=Arg_0+Arg_2 && Arg_1<=Arg_0 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 && 0<Arg_2 of depth 1:
new bound:
Arg_0*Arg_0+3*Arg_0+2 {O(n^2)}
MPRF:
eval_while2_bb1_in [Arg_0+2 ]
eval_while2_bb4_in [0 ]
eval_while2_bb3_in [Arg_2 ]
eval_while2_bb2_in [Arg_2+1 ]
MPRF for transition 6:eval_while2_bb3_in(Arg_0,Arg_1,Arg_2) -> eval_while2_bb2_in(Arg_0,Arg_1,Arg_2-1):|:Arg_2<=Arg_0 && 1<=Arg_2 && 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:
Arg_0*Arg_0+Arg_0 {O(n^2)}
MPRF:
eval_while2_bb1_in [Arg_0 ]
eval_while2_bb4_in [0 ]
eval_while2_bb3_in [Arg_2 ]
eval_while2_bb2_in [Arg_2 ]
All Bounds
Timebounds
Overall timebound:2*Arg_0*Arg_0+7*Arg_0+6 {O(n^2)}
1: eval_while2_bb0_in->eval_while2_bb1_in: 1 {O(1)}
2: eval_while2_bb1_in->eval_while2_bb2_in: Arg_0 {O(n)}
3: eval_while2_bb1_in->eval_while2_bb5_in: 1 {O(1)}
4: eval_while2_bb2_in->eval_while2_bb3_in: Arg_0*Arg_0+3*Arg_0+2 {O(n^2)}
5: eval_while2_bb2_in->eval_while2_bb4_in: Arg_0 {O(n)}
6: eval_while2_bb3_in->eval_while2_bb2_in: Arg_0*Arg_0+Arg_0 {O(n^2)}
7: eval_while2_bb4_in->eval_while2_bb1_in: Arg_0 {O(n)}
8: eval_while2_bb5_in->eval_while2_stop: 1 {O(1)}
0: eval_while2_start->eval_while2_bb0_in: 1 {O(1)}
Costbounds
Overall costbound: 2*Arg_0*Arg_0+7*Arg_0+6 {O(n^2)}
1: eval_while2_bb0_in->eval_while2_bb1_in: 1 {O(1)}
2: eval_while2_bb1_in->eval_while2_bb2_in: Arg_0 {O(n)}
3: eval_while2_bb1_in->eval_while2_bb5_in: 1 {O(1)}
4: eval_while2_bb2_in->eval_while2_bb3_in: Arg_0*Arg_0+3*Arg_0+2 {O(n^2)}
5: eval_while2_bb2_in->eval_while2_bb4_in: Arg_0 {O(n)}
6: eval_while2_bb3_in->eval_while2_bb2_in: Arg_0*Arg_0+Arg_0 {O(n^2)}
7: eval_while2_bb4_in->eval_while2_bb1_in: Arg_0 {O(n)}
8: eval_while2_bb5_in->eval_while2_stop: 1 {O(1)}
0: eval_while2_start->eval_while2_bb0_in: 1 {O(1)}
Sizebounds
1: eval_while2_bb0_in->eval_while2_bb1_in, Arg_0: Arg_0 {O(n)}
1: eval_while2_bb0_in->eval_while2_bb1_in, Arg_1: Arg_0 {O(n)}
1: eval_while2_bb0_in->eval_while2_bb1_in, Arg_2: Arg_2 {O(n)}
2: eval_while2_bb1_in->eval_while2_bb2_in, Arg_0: Arg_0 {O(n)}
2: eval_while2_bb1_in->eval_while2_bb2_in, Arg_1: Arg_0 {O(n)}
2: eval_while2_bb1_in->eval_while2_bb2_in, Arg_2: 2*Arg_0 {O(n)}
3: eval_while2_bb1_in->eval_while2_bb5_in, Arg_0: 2*Arg_0 {O(n)}
3: eval_while2_bb1_in->eval_while2_bb5_in, Arg_1: 2*Arg_0 {O(n)}
3: eval_while2_bb1_in->eval_while2_bb5_in, Arg_2: Arg_2 {O(n)}
4: eval_while2_bb2_in->eval_while2_bb3_in, Arg_0: Arg_0 {O(n)}
4: eval_while2_bb2_in->eval_while2_bb3_in, Arg_1: Arg_0 {O(n)}
4: eval_while2_bb2_in->eval_while2_bb3_in, Arg_2: 2*Arg_0 {O(n)}
5: eval_while2_bb2_in->eval_while2_bb4_in, Arg_0: Arg_0 {O(n)}
5: eval_while2_bb2_in->eval_while2_bb4_in, Arg_1: Arg_0 {O(n)}
5: eval_while2_bb2_in->eval_while2_bb4_in, Arg_2: 0 {O(1)}
6: eval_while2_bb3_in->eval_while2_bb2_in, Arg_0: Arg_0 {O(n)}
6: eval_while2_bb3_in->eval_while2_bb2_in, Arg_1: Arg_0 {O(n)}
6: eval_while2_bb3_in->eval_while2_bb2_in, Arg_2: 2*Arg_0 {O(n)}
7: eval_while2_bb4_in->eval_while2_bb1_in, Arg_0: Arg_0 {O(n)}
7: eval_while2_bb4_in->eval_while2_bb1_in, Arg_1: Arg_0 {O(n)}
7: eval_while2_bb4_in->eval_while2_bb1_in, Arg_2: 0 {O(1)}
8: eval_while2_bb5_in->eval_while2_stop, Arg_0: 2*Arg_0 {O(n)}
8: eval_while2_bb5_in->eval_while2_stop, Arg_1: 2*Arg_0 {O(n)}
8: eval_while2_bb5_in->eval_while2_stop, Arg_2: Arg_2 {O(n)}
0: eval_while2_start->eval_while2_bb0_in, Arg_0: Arg_0 {O(n)}
0: eval_while2_start->eval_while2_bb0_in, Arg_1: Arg_1 {O(n)}
0: eval_while2_start->eval_while2_bb0_in, Arg_2: Arg_2 {O(n)}