Initial Problem

Start: eval_peed_pldi09_fig4_4_start
Program_Vars: Arg_0, Arg_1, Arg_2
Temp_Vars:
Locations: eval_peed_pldi09_fig4_4_bb0_in, eval_peed_pldi09_fig4_4_bb1_in, eval_peed_pldi09_fig4_4_bb2_in, eval_peed_pldi09_fig4_4_bb3_in, eval_peed_pldi09_fig4_4_start, eval_peed_pldi09_fig4_4_stop
Transitions:
2:eval_peed_pldi09_fig4_4_bb0_in(Arg_0,Arg_1,Arg_2) -> eval_peed_pldi09_fig4_4_bb1_in(Arg_2,Arg_1,Arg_2):|:0<Arg_1
1:eval_peed_pldi09_fig4_4_bb0_in(Arg_0,Arg_1,Arg_2) -> eval_peed_pldi09_fig4_4_bb3_in(Arg_0,Arg_1,Arg_2):|:Arg_1<=0
3:eval_peed_pldi09_fig4_4_bb1_in(Arg_0,Arg_1,Arg_2) -> eval_peed_pldi09_fig4_4_bb2_in(Arg_0,Arg_1,Arg_2):|:0<Arg_0
4:eval_peed_pldi09_fig4_4_bb1_in(Arg_0,Arg_1,Arg_2) -> eval_peed_pldi09_fig4_4_bb3_in(Arg_0,Arg_1,Arg_2):|:Arg_0<=0
5:eval_peed_pldi09_fig4_4_bb2_in(Arg_0,Arg_1,Arg_2) -> eval_peed_pldi09_fig4_4_bb1_in(Arg_0-1,Arg_1,Arg_2):|:Arg_0<Arg_1
6:eval_peed_pldi09_fig4_4_bb2_in(Arg_0,Arg_1,Arg_2) -> eval_peed_pldi09_fig4_4_bb1_in(Arg_0-Arg_1,Arg_1,Arg_2):|:Arg_1<=Arg_0
7:eval_peed_pldi09_fig4_4_bb3_in(Arg_0,Arg_1,Arg_2) -> eval_peed_pldi09_fig4_4_stop(Arg_0,Arg_1,Arg_2)
0:eval_peed_pldi09_fig4_4_start(Arg_0,Arg_1,Arg_2) -> eval_peed_pldi09_fig4_4_bb0_in(Arg_0,Arg_1,Arg_2)

Preprocessing

Found invariant 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_peed_pldi09_fig4_4_bb2_in

Found invariant Arg_0<=Arg_2 && 1<=Arg_1 for location eval_peed_pldi09_fig4_4_bb1_in

Problem after Preprocessing

Start: eval_peed_pldi09_fig4_4_start
Program_Vars: Arg_0, Arg_1, Arg_2
Temp_Vars:
Locations: eval_peed_pldi09_fig4_4_bb0_in, eval_peed_pldi09_fig4_4_bb1_in, eval_peed_pldi09_fig4_4_bb2_in, eval_peed_pldi09_fig4_4_bb3_in, eval_peed_pldi09_fig4_4_start, eval_peed_pldi09_fig4_4_stop
Transitions:
2:eval_peed_pldi09_fig4_4_bb0_in(Arg_0,Arg_1,Arg_2) -> eval_peed_pldi09_fig4_4_bb1_in(Arg_2,Arg_1,Arg_2):|:0<Arg_1
1:eval_peed_pldi09_fig4_4_bb0_in(Arg_0,Arg_1,Arg_2) -> eval_peed_pldi09_fig4_4_bb3_in(Arg_0,Arg_1,Arg_2):|:Arg_1<=0
3:eval_peed_pldi09_fig4_4_bb1_in(Arg_0,Arg_1,Arg_2) -> eval_peed_pldi09_fig4_4_bb2_in(Arg_0,Arg_1,Arg_2):|:Arg_0<=Arg_2 && 1<=Arg_1 && 0<Arg_0
4:eval_peed_pldi09_fig4_4_bb1_in(Arg_0,Arg_1,Arg_2) -> eval_peed_pldi09_fig4_4_bb3_in(Arg_0,Arg_1,Arg_2):|:Arg_0<=Arg_2 && 1<=Arg_1 && Arg_0<=0
5:eval_peed_pldi09_fig4_4_bb2_in(Arg_0,Arg_1,Arg_2) -> eval_peed_pldi09_fig4_4_bb1_in(Arg_0-1,Arg_1,Arg_2):|: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 && Arg_0<Arg_1
6:eval_peed_pldi09_fig4_4_bb2_in(Arg_0,Arg_1,Arg_2) -> eval_peed_pldi09_fig4_4_bb1_in(Arg_0-Arg_1,Arg_1,Arg_2):|: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 && Arg_1<=Arg_0
7:eval_peed_pldi09_fig4_4_bb3_in(Arg_0,Arg_1,Arg_2) -> eval_peed_pldi09_fig4_4_stop(Arg_0,Arg_1,Arg_2)
0:eval_peed_pldi09_fig4_4_start(Arg_0,Arg_1,Arg_2) -> eval_peed_pldi09_fig4_4_bb0_in(Arg_0,Arg_1,Arg_2)

MPRF for transition 3:eval_peed_pldi09_fig4_4_bb1_in(Arg_0,Arg_1,Arg_2) -> eval_peed_pldi09_fig4_4_bb2_in(Arg_0,Arg_1,Arg_2):|:Arg_0<=Arg_2 && 1<=Arg_1 && 0<Arg_0 of depth 1:

new bound:

Arg_2 {O(n)}

MPRF:

eval_peed_pldi09_fig4_4_bb2_in [Arg_0-1 ]
eval_peed_pldi09_fig4_4_bb1_in [Arg_0 ]

MPRF for transition 5:eval_peed_pldi09_fig4_4_bb2_in(Arg_0,Arg_1,Arg_2) -> eval_peed_pldi09_fig4_4_bb1_in(Arg_0-1,Arg_1,Arg_2):|: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 && Arg_0<Arg_1 of depth 1:

new bound:

Arg_2 {O(n)}

MPRF:

eval_peed_pldi09_fig4_4_bb2_in [Arg_0 ]
eval_peed_pldi09_fig4_4_bb1_in [Arg_0 ]

MPRF for transition 6:eval_peed_pldi09_fig4_4_bb2_in(Arg_0,Arg_1,Arg_2) -> eval_peed_pldi09_fig4_4_bb1_in(Arg_0-Arg_1,Arg_1,Arg_2):|: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 && Arg_1<=Arg_0 of depth 1:

new bound:

Arg_2 {O(n)}

MPRF:

eval_peed_pldi09_fig4_4_bb2_in [Arg_0 ]
eval_peed_pldi09_fig4_4_bb1_in [Arg_0 ]

All Bounds

Timebounds

Overall timebound:3*Arg_2+5 {O(n)}
1: eval_peed_pldi09_fig4_4_bb0_in->eval_peed_pldi09_fig4_4_bb3_in: 1 {O(1)}
2: eval_peed_pldi09_fig4_4_bb0_in->eval_peed_pldi09_fig4_4_bb1_in: 1 {O(1)}
3: eval_peed_pldi09_fig4_4_bb1_in->eval_peed_pldi09_fig4_4_bb2_in: Arg_2 {O(n)}
4: eval_peed_pldi09_fig4_4_bb1_in->eval_peed_pldi09_fig4_4_bb3_in: 1 {O(1)}
5: eval_peed_pldi09_fig4_4_bb2_in->eval_peed_pldi09_fig4_4_bb1_in: Arg_2 {O(n)}
6: eval_peed_pldi09_fig4_4_bb2_in->eval_peed_pldi09_fig4_4_bb1_in: Arg_2 {O(n)}
7: eval_peed_pldi09_fig4_4_bb3_in->eval_peed_pldi09_fig4_4_stop: 1 {O(1)}
0: eval_peed_pldi09_fig4_4_start->eval_peed_pldi09_fig4_4_bb0_in: 1 {O(1)}

Costbounds

Overall costbound: 3*Arg_2+5 {O(n)}
1: eval_peed_pldi09_fig4_4_bb0_in->eval_peed_pldi09_fig4_4_bb3_in: 1 {O(1)}
2: eval_peed_pldi09_fig4_4_bb0_in->eval_peed_pldi09_fig4_4_bb1_in: 1 {O(1)}
3: eval_peed_pldi09_fig4_4_bb1_in->eval_peed_pldi09_fig4_4_bb2_in: Arg_2 {O(n)}
4: eval_peed_pldi09_fig4_4_bb1_in->eval_peed_pldi09_fig4_4_bb3_in: 1 {O(1)}
5: eval_peed_pldi09_fig4_4_bb2_in->eval_peed_pldi09_fig4_4_bb1_in: Arg_2 {O(n)}
6: eval_peed_pldi09_fig4_4_bb2_in->eval_peed_pldi09_fig4_4_bb1_in: Arg_2 {O(n)}
7: eval_peed_pldi09_fig4_4_bb3_in->eval_peed_pldi09_fig4_4_stop: 1 {O(1)}
0: eval_peed_pldi09_fig4_4_start->eval_peed_pldi09_fig4_4_bb0_in: 1 {O(1)}

Sizebounds

1: eval_peed_pldi09_fig4_4_bb0_in->eval_peed_pldi09_fig4_4_bb3_in, Arg_0: Arg_0 {O(n)}
1: eval_peed_pldi09_fig4_4_bb0_in->eval_peed_pldi09_fig4_4_bb3_in, Arg_1: Arg_1 {O(n)}
1: eval_peed_pldi09_fig4_4_bb0_in->eval_peed_pldi09_fig4_4_bb3_in, Arg_2: Arg_2 {O(n)}
2: eval_peed_pldi09_fig4_4_bb0_in->eval_peed_pldi09_fig4_4_bb1_in, Arg_0: Arg_2 {O(n)}
2: eval_peed_pldi09_fig4_4_bb0_in->eval_peed_pldi09_fig4_4_bb1_in, Arg_1: Arg_1 {O(n)}
2: eval_peed_pldi09_fig4_4_bb0_in->eval_peed_pldi09_fig4_4_bb1_in, Arg_2: Arg_2 {O(n)}
3: eval_peed_pldi09_fig4_4_bb1_in->eval_peed_pldi09_fig4_4_bb2_in, Arg_0: Arg_2 {O(n)}
3: eval_peed_pldi09_fig4_4_bb1_in->eval_peed_pldi09_fig4_4_bb2_in, Arg_1: Arg_1 {O(n)}
3: eval_peed_pldi09_fig4_4_bb1_in->eval_peed_pldi09_fig4_4_bb2_in, Arg_2: Arg_2 {O(n)}
4: eval_peed_pldi09_fig4_4_bb1_in->eval_peed_pldi09_fig4_4_bb3_in, Arg_0: 3*Arg_2 {O(n)}
4: eval_peed_pldi09_fig4_4_bb1_in->eval_peed_pldi09_fig4_4_bb3_in, Arg_1: 3*Arg_1 {O(n)}
4: eval_peed_pldi09_fig4_4_bb1_in->eval_peed_pldi09_fig4_4_bb3_in, Arg_2: 3*Arg_2 {O(n)}
5: eval_peed_pldi09_fig4_4_bb2_in->eval_peed_pldi09_fig4_4_bb1_in, Arg_0: Arg_2 {O(n)}
5: eval_peed_pldi09_fig4_4_bb2_in->eval_peed_pldi09_fig4_4_bb1_in, Arg_1: Arg_1 {O(n)}
5: eval_peed_pldi09_fig4_4_bb2_in->eval_peed_pldi09_fig4_4_bb1_in, Arg_2: Arg_2 {O(n)}
6: eval_peed_pldi09_fig4_4_bb2_in->eval_peed_pldi09_fig4_4_bb1_in, Arg_0: Arg_2 {O(n)}
6: eval_peed_pldi09_fig4_4_bb2_in->eval_peed_pldi09_fig4_4_bb1_in, Arg_1: Arg_1 {O(n)}
6: eval_peed_pldi09_fig4_4_bb2_in->eval_peed_pldi09_fig4_4_bb1_in, Arg_2: Arg_2 {O(n)}
7: eval_peed_pldi09_fig4_4_bb3_in->eval_peed_pldi09_fig4_4_stop, Arg_0: 3*Arg_2+Arg_0 {O(n)}
7: eval_peed_pldi09_fig4_4_bb3_in->eval_peed_pldi09_fig4_4_stop, Arg_1: 4*Arg_1 {O(n)}
7: eval_peed_pldi09_fig4_4_bb3_in->eval_peed_pldi09_fig4_4_stop, Arg_2: 4*Arg_2 {O(n)}
0: eval_peed_pldi09_fig4_4_start->eval_peed_pldi09_fig4_4_bb0_in, Arg_0: Arg_0 {O(n)}
0: eval_peed_pldi09_fig4_4_start->eval_peed_pldi09_fig4_4_bb0_in, Arg_1: Arg_1 {O(n)}
0: eval_peed_pldi09_fig4_4_start->eval_peed_pldi09_fig4_4_bb0_in, Arg_2: Arg_2 {O(n)}