Initial Problem

Start: eval_peed_pldi09_fig4_2_start
Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3
Temp_Vars:
Locations: eval_peed_pldi09_fig4_2_bb0_in, eval_peed_pldi09_fig4_2_bb1_in, eval_peed_pldi09_fig4_2_bb2_in, eval_peed_pldi09_fig4_2_bb3_in, eval_peed_pldi09_fig4_2_bb4_in, eval_peed_pldi09_fig4_2_start, eval_peed_pldi09_fig4_2_stop
Transitions:
2:eval_peed_pldi09_fig4_2_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_peed_pldi09_fig4_2_bb1_in(Arg_0,Arg_1,Arg_1,0):|:0<Arg_0
1:eval_peed_pldi09_fig4_2_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_peed_pldi09_fig4_2_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_0<=0
3:eval_peed_pldi09_fig4_2_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_peed_pldi09_fig4_2_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3):|:0<Arg_2
4:eval_peed_pldi09_fig4_2_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_peed_pldi09_fig4_2_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_2<=0
6:eval_peed_pldi09_fig4_2_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_peed_pldi09_fig4_2_bb1_in(Arg_0,Arg_1,Arg_2,0):|:Arg_0<=Arg_3
5:eval_peed_pldi09_fig4_2_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_peed_pldi09_fig4_2_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_3<Arg_0
7:eval_peed_pldi09_fig4_2_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_peed_pldi09_fig4_2_bb1_in(Arg_0,Arg_1,Arg_2-1,Arg_3+1)
8:eval_peed_pldi09_fig4_2_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_peed_pldi09_fig4_2_stop(Arg_0,Arg_1,Arg_2,Arg_3)
0:eval_peed_pldi09_fig4_2_start(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_peed_pldi09_fig4_2_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3)

Preprocessing

Found invariant Arg_3<=Arg_0 && 0<=Arg_3 && 1<=Arg_2+Arg_3 && 1<=Arg_1+Arg_3 && 1<=Arg_0+Arg_3 && Arg_2<=Arg_1 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && 2<=Arg_0+Arg_2 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 for location eval_peed_pldi09_fig4_2_bb2_in

Found invariant Arg_3<=Arg_0 && 0<=Arg_3 && 1<=Arg_0+Arg_3 && Arg_2<=Arg_1 && 1<=Arg_0 for location eval_peed_pldi09_fig4_2_bb1_in

Found invariant 1+Arg_3<=Arg_0 && 0<=Arg_3 && 1<=Arg_2+Arg_3 && 1<=Arg_1+Arg_3 && 1<=Arg_0+Arg_3 && Arg_2<=Arg_1 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && 2<=Arg_0+Arg_2 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 for location eval_peed_pldi09_fig4_2_bb3_in

Problem after Preprocessing

Start: eval_peed_pldi09_fig4_2_start
Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3
Temp_Vars:
Locations: eval_peed_pldi09_fig4_2_bb0_in, eval_peed_pldi09_fig4_2_bb1_in, eval_peed_pldi09_fig4_2_bb2_in, eval_peed_pldi09_fig4_2_bb3_in, eval_peed_pldi09_fig4_2_bb4_in, eval_peed_pldi09_fig4_2_start, eval_peed_pldi09_fig4_2_stop
Transitions:
2:eval_peed_pldi09_fig4_2_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_peed_pldi09_fig4_2_bb1_in(Arg_0,Arg_1,Arg_1,0):|:0<Arg_0
1:eval_peed_pldi09_fig4_2_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_peed_pldi09_fig4_2_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_0<=0
3:eval_peed_pldi09_fig4_2_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_peed_pldi09_fig4_2_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_3<=Arg_0 && 0<=Arg_3 && 1<=Arg_0+Arg_3 && Arg_2<=Arg_1 && 1<=Arg_0 && 0<Arg_2
4:eval_peed_pldi09_fig4_2_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_peed_pldi09_fig4_2_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_3<=Arg_0 && 0<=Arg_3 && 1<=Arg_0+Arg_3 && Arg_2<=Arg_1 && 1<=Arg_0 && Arg_2<=0
6:eval_peed_pldi09_fig4_2_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_peed_pldi09_fig4_2_bb1_in(Arg_0,Arg_1,Arg_2,0):|:Arg_3<=Arg_0 && 0<=Arg_3 && 1<=Arg_2+Arg_3 && 1<=Arg_1+Arg_3 && 1<=Arg_0+Arg_3 && Arg_2<=Arg_1 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && 2<=Arg_0+Arg_2 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 && Arg_0<=Arg_3
5:eval_peed_pldi09_fig4_2_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_peed_pldi09_fig4_2_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_3<=Arg_0 && 0<=Arg_3 && 1<=Arg_2+Arg_3 && 1<=Arg_1+Arg_3 && 1<=Arg_0+Arg_3 && Arg_2<=Arg_1 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && 2<=Arg_0+Arg_2 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 && Arg_3<Arg_0
7:eval_peed_pldi09_fig4_2_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_peed_pldi09_fig4_2_bb1_in(Arg_0,Arg_1,Arg_2-1,Arg_3+1):|:1+Arg_3<=Arg_0 && 0<=Arg_3 && 1<=Arg_2+Arg_3 && 1<=Arg_1+Arg_3 && 1<=Arg_0+Arg_3 && Arg_2<=Arg_1 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && 2<=Arg_0+Arg_2 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0
8:eval_peed_pldi09_fig4_2_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_peed_pldi09_fig4_2_stop(Arg_0,Arg_1,Arg_2,Arg_3)
0:eval_peed_pldi09_fig4_2_start(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_peed_pldi09_fig4_2_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3)

MPRF for transition 3:eval_peed_pldi09_fig4_2_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_peed_pldi09_fig4_2_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_3<=Arg_0 && 0<=Arg_3 && 1<=Arg_0+Arg_3 && Arg_2<=Arg_1 && 1<=Arg_0 && 0<Arg_2 of depth 1:

new bound:

2*Arg_1+1 {O(n)}

MPRF:

eval_peed_pldi09_fig4_2_bb2_in [2*Arg_2+Arg_3-2 ]
eval_peed_pldi09_fig4_2_bb3_in [2*Arg_2+Arg_3-2 ]
eval_peed_pldi09_fig4_2_bb1_in [2*Arg_2+Arg_3-1 ]

MPRF for transition 5:eval_peed_pldi09_fig4_2_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_peed_pldi09_fig4_2_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_3<=Arg_0 && 0<=Arg_3 && 1<=Arg_2+Arg_3 && 1<=Arg_1+Arg_3 && 1<=Arg_0+Arg_3 && Arg_2<=Arg_1 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && 2<=Arg_0+Arg_2 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 && Arg_3<Arg_0 of depth 1:

new bound:

Arg_1 {O(n)}

MPRF:

eval_peed_pldi09_fig4_2_bb2_in [Arg_2 ]
eval_peed_pldi09_fig4_2_bb3_in [Arg_2-1 ]
eval_peed_pldi09_fig4_2_bb1_in [Arg_2 ]

MPRF for transition 6:eval_peed_pldi09_fig4_2_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_peed_pldi09_fig4_2_bb1_in(Arg_0,Arg_1,Arg_2,0):|:Arg_3<=Arg_0 && 0<=Arg_3 && 1<=Arg_2+Arg_3 && 1<=Arg_1+Arg_3 && 1<=Arg_0+Arg_3 && Arg_2<=Arg_1 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && 2<=Arg_0+Arg_2 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 && Arg_0<=Arg_3 of depth 1:

new bound:

Arg_1 {O(n)}

MPRF:

eval_peed_pldi09_fig4_2_bb2_in [Arg_2+Arg_3 ]
eval_peed_pldi09_fig4_2_bb3_in [Arg_2+Arg_3 ]
eval_peed_pldi09_fig4_2_bb1_in [Arg_2+Arg_3 ]

MPRF for transition 7:eval_peed_pldi09_fig4_2_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_peed_pldi09_fig4_2_bb1_in(Arg_0,Arg_1,Arg_2-1,Arg_3+1):|:1+Arg_3<=Arg_0 && 0<=Arg_3 && 1<=Arg_2+Arg_3 && 1<=Arg_1+Arg_3 && 1<=Arg_0+Arg_3 && Arg_2<=Arg_1 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && 2<=Arg_0+Arg_2 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 of depth 1:

new bound:

Arg_1 {O(n)}

MPRF:

eval_peed_pldi09_fig4_2_bb2_in [Arg_2 ]
eval_peed_pldi09_fig4_2_bb3_in [Arg_2 ]
eval_peed_pldi09_fig4_2_bb1_in [Arg_2 ]

All Bounds

Timebounds

Overall timebound:5*Arg_1+6 {O(n)}
1: eval_peed_pldi09_fig4_2_bb0_in->eval_peed_pldi09_fig4_2_bb4_in: 1 {O(1)}
2: eval_peed_pldi09_fig4_2_bb0_in->eval_peed_pldi09_fig4_2_bb1_in: 1 {O(1)}
3: eval_peed_pldi09_fig4_2_bb1_in->eval_peed_pldi09_fig4_2_bb2_in: 2*Arg_1+1 {O(n)}
4: eval_peed_pldi09_fig4_2_bb1_in->eval_peed_pldi09_fig4_2_bb4_in: 1 {O(1)}
5: eval_peed_pldi09_fig4_2_bb2_in->eval_peed_pldi09_fig4_2_bb3_in: Arg_1 {O(n)}
6: eval_peed_pldi09_fig4_2_bb2_in->eval_peed_pldi09_fig4_2_bb1_in: Arg_1 {O(n)}
7: eval_peed_pldi09_fig4_2_bb3_in->eval_peed_pldi09_fig4_2_bb1_in: Arg_1 {O(n)}
8: eval_peed_pldi09_fig4_2_bb4_in->eval_peed_pldi09_fig4_2_stop: 1 {O(1)}
0: eval_peed_pldi09_fig4_2_start->eval_peed_pldi09_fig4_2_bb0_in: 1 {O(1)}

Costbounds

Overall costbound: 5*Arg_1+6 {O(n)}
1: eval_peed_pldi09_fig4_2_bb0_in->eval_peed_pldi09_fig4_2_bb4_in: 1 {O(1)}
2: eval_peed_pldi09_fig4_2_bb0_in->eval_peed_pldi09_fig4_2_bb1_in: 1 {O(1)}
3: eval_peed_pldi09_fig4_2_bb1_in->eval_peed_pldi09_fig4_2_bb2_in: 2*Arg_1+1 {O(n)}
4: eval_peed_pldi09_fig4_2_bb1_in->eval_peed_pldi09_fig4_2_bb4_in: 1 {O(1)}
5: eval_peed_pldi09_fig4_2_bb2_in->eval_peed_pldi09_fig4_2_bb3_in: Arg_1 {O(n)}
6: eval_peed_pldi09_fig4_2_bb2_in->eval_peed_pldi09_fig4_2_bb1_in: Arg_1 {O(n)}
7: eval_peed_pldi09_fig4_2_bb3_in->eval_peed_pldi09_fig4_2_bb1_in: Arg_1 {O(n)}
8: eval_peed_pldi09_fig4_2_bb4_in->eval_peed_pldi09_fig4_2_stop: 1 {O(1)}
0: eval_peed_pldi09_fig4_2_start->eval_peed_pldi09_fig4_2_bb0_in: 1 {O(1)}

Sizebounds

1: eval_peed_pldi09_fig4_2_bb0_in->eval_peed_pldi09_fig4_2_bb4_in, Arg_0: Arg_0 {O(n)}
1: eval_peed_pldi09_fig4_2_bb0_in->eval_peed_pldi09_fig4_2_bb4_in, Arg_1: Arg_1 {O(n)}
1: eval_peed_pldi09_fig4_2_bb0_in->eval_peed_pldi09_fig4_2_bb4_in, Arg_2: Arg_2 {O(n)}
1: eval_peed_pldi09_fig4_2_bb0_in->eval_peed_pldi09_fig4_2_bb4_in, Arg_3: Arg_3 {O(n)}
2: eval_peed_pldi09_fig4_2_bb0_in->eval_peed_pldi09_fig4_2_bb1_in, Arg_0: Arg_0 {O(n)}
2: eval_peed_pldi09_fig4_2_bb0_in->eval_peed_pldi09_fig4_2_bb1_in, Arg_1: Arg_1 {O(n)}
2: eval_peed_pldi09_fig4_2_bb0_in->eval_peed_pldi09_fig4_2_bb1_in, Arg_2: Arg_1 {O(n)}
2: eval_peed_pldi09_fig4_2_bb0_in->eval_peed_pldi09_fig4_2_bb1_in, Arg_3: 0 {O(1)}
3: eval_peed_pldi09_fig4_2_bb1_in->eval_peed_pldi09_fig4_2_bb2_in, Arg_0: Arg_0 {O(n)}
3: eval_peed_pldi09_fig4_2_bb1_in->eval_peed_pldi09_fig4_2_bb2_in, Arg_1: Arg_1 {O(n)}
3: eval_peed_pldi09_fig4_2_bb1_in->eval_peed_pldi09_fig4_2_bb2_in, Arg_2: Arg_1 {O(n)}
3: eval_peed_pldi09_fig4_2_bb1_in->eval_peed_pldi09_fig4_2_bb2_in, Arg_3: Arg_1 {O(n)}
4: eval_peed_pldi09_fig4_2_bb1_in->eval_peed_pldi09_fig4_2_bb4_in, Arg_0: 2*Arg_0 {O(n)}
4: eval_peed_pldi09_fig4_2_bb1_in->eval_peed_pldi09_fig4_2_bb4_in, Arg_1: 2*Arg_1 {O(n)}
4: eval_peed_pldi09_fig4_2_bb1_in->eval_peed_pldi09_fig4_2_bb4_in, Arg_2: 2*Arg_1 {O(n)}
4: eval_peed_pldi09_fig4_2_bb1_in->eval_peed_pldi09_fig4_2_bb4_in, Arg_3: Arg_1 {O(n)}
5: eval_peed_pldi09_fig4_2_bb2_in->eval_peed_pldi09_fig4_2_bb3_in, Arg_0: Arg_0 {O(n)}
5: eval_peed_pldi09_fig4_2_bb2_in->eval_peed_pldi09_fig4_2_bb3_in, Arg_1: Arg_1 {O(n)}
5: eval_peed_pldi09_fig4_2_bb2_in->eval_peed_pldi09_fig4_2_bb3_in, Arg_2: Arg_1 {O(n)}
5: eval_peed_pldi09_fig4_2_bb2_in->eval_peed_pldi09_fig4_2_bb3_in, Arg_3: Arg_1 {O(n)}
6: eval_peed_pldi09_fig4_2_bb2_in->eval_peed_pldi09_fig4_2_bb1_in, Arg_0: Arg_0 {O(n)}
6: eval_peed_pldi09_fig4_2_bb2_in->eval_peed_pldi09_fig4_2_bb1_in, Arg_1: Arg_1 {O(n)}
6: eval_peed_pldi09_fig4_2_bb2_in->eval_peed_pldi09_fig4_2_bb1_in, Arg_2: Arg_1 {O(n)}
6: eval_peed_pldi09_fig4_2_bb2_in->eval_peed_pldi09_fig4_2_bb1_in, Arg_3: 0 {O(1)}
7: eval_peed_pldi09_fig4_2_bb3_in->eval_peed_pldi09_fig4_2_bb1_in, Arg_0: Arg_0 {O(n)}
7: eval_peed_pldi09_fig4_2_bb3_in->eval_peed_pldi09_fig4_2_bb1_in, Arg_1: Arg_1 {O(n)}
7: eval_peed_pldi09_fig4_2_bb3_in->eval_peed_pldi09_fig4_2_bb1_in, Arg_2: Arg_1 {O(n)}
7: eval_peed_pldi09_fig4_2_bb3_in->eval_peed_pldi09_fig4_2_bb1_in, Arg_3: Arg_1 {O(n)}
8: eval_peed_pldi09_fig4_2_bb4_in->eval_peed_pldi09_fig4_2_stop, Arg_0: 3*Arg_0 {O(n)}
8: eval_peed_pldi09_fig4_2_bb4_in->eval_peed_pldi09_fig4_2_stop, Arg_1: 3*Arg_1 {O(n)}
8: eval_peed_pldi09_fig4_2_bb4_in->eval_peed_pldi09_fig4_2_stop, Arg_2: 2*Arg_1+Arg_2 {O(n)}
8: eval_peed_pldi09_fig4_2_bb4_in->eval_peed_pldi09_fig4_2_stop, Arg_3: Arg_1+Arg_3 {O(n)}
0: eval_peed_pldi09_fig4_2_start->eval_peed_pldi09_fig4_2_bb0_in, Arg_0: Arg_0 {O(n)}
0: eval_peed_pldi09_fig4_2_start->eval_peed_pldi09_fig4_2_bb0_in, Arg_1: Arg_1 {O(n)}
0: eval_peed_pldi09_fig4_2_start->eval_peed_pldi09_fig4_2_bb0_in, Arg_2: Arg_2 {O(n)}
0: eval_peed_pldi09_fig4_2_start->eval_peed_pldi09_fig4_2_bb0_in, Arg_3: Arg_3 {O(n)}