Initial Problem

Start: eval_sipmabubble_start
Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3
Temp_Vars: nondef_0, nondef_1
Locations: eval_sipmabubble_0, eval_sipmabubble_1, eval_sipmabubble_2, eval_sipmabubble_29, eval_sipmabubble_3, eval_sipmabubble_30, eval_sipmabubble_4, eval_sipmabubble_5, eval_sipmabubble_6, eval_sipmabubble_bb0_in, eval_sipmabubble_bb1_in, eval_sipmabubble_bb2_in, eval_sipmabubble_bb3_in, eval_sipmabubble_bb4_in, eval_sipmabubble_bb5_in, eval_sipmabubble_bb6_in, eval_sipmabubble_bb7_in, eval_sipmabubble_start, eval_sipmabubble_stop
Transitions:
2:eval_sipmabubble_0(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_sipmabubble_1(Arg_0,Arg_1,Arg_2,Arg_3)
3:eval_sipmabubble_1(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_sipmabubble_2(Arg_0,Arg_1,Arg_2,Arg_3)
4:eval_sipmabubble_2(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_sipmabubble_3(Arg_0,Arg_1,Arg_2,Arg_3)
18:eval_sipmabubble_29(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_sipmabubble_30(Arg_0,Arg_1,Arg_2,Arg_3)
5:eval_sipmabubble_3(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_sipmabubble_4(Arg_0,Arg_1,Arg_2,Arg_3)
19:eval_sipmabubble_30(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_sipmabubble_bb1_in(Arg_0,Arg_0,Arg_2,Arg_3)
6:eval_sipmabubble_4(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_sipmabubble_5(Arg_0,Arg_1,Arg_2,Arg_3)
7:eval_sipmabubble_5(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_sipmabubble_6(Arg_0,Arg_1,Arg_2,Arg_3)
8:eval_sipmabubble_6(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_sipmabubble_bb1_in(Arg_0,Arg_3,Arg_2,Arg_3)
1:eval_sipmabubble_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_sipmabubble_0(Arg_0,Arg_1,Arg_2,Arg_3)
9:eval_sipmabubble_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_sipmabubble_bb2_in(Arg_0,Arg_1,0,Arg_3):|:0<=Arg_1
10:eval_sipmabubble_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_sipmabubble_bb7_in(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_1<0
11:eval_sipmabubble_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_sipmabubble_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_2+1<=Arg_1
12:eval_sipmabubble_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_sipmabubble_bb6_in(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_1<1+Arg_2
13:eval_sipmabubble_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_sipmabubble_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3):|:nondef_1<nondef_0
14:eval_sipmabubble_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_sipmabubble_bb5_in(Arg_0,Arg_1,Arg_2,Arg_3):|:nondef_0<=nondef_1
15:eval_sipmabubble_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_sipmabubble_bb5_in(Arg_0,Arg_1,Arg_2,Arg_3)
16:eval_sipmabubble_bb5_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_sipmabubble_bb2_in(Arg_0,Arg_1,Arg_2+1,Arg_3)
17:eval_sipmabubble_bb6_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_sipmabubble_29(Arg_1-1,Arg_1,Arg_2,Arg_3)
20:eval_sipmabubble_bb7_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_sipmabubble_stop(Arg_0,Arg_1,Arg_2,Arg_3)
0:eval_sipmabubble_start(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_sipmabubble_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3)

Preprocessing

Found invariant Arg_1<=Arg_3 && 1+Arg_1<=0 for location eval_sipmabubble_bb7_in

Found invariant 1<=Arg_3 && 1<=Arg_2+Arg_3 && 1+Arg_2<=Arg_3 && 2<=Arg_1+Arg_3 && Arg_1<=Arg_3 && 1+Arg_2<=Arg_1 && 0<=Arg_2 && 1<=Arg_1+Arg_2 && 1<=Arg_1 for location eval_sipmabubble_bb4_in

Found invariant 0<=Arg_3 && 0<=Arg_2+Arg_3 && Arg_2<=Arg_3 && 0<=Arg_1+Arg_3 && Arg_1<=Arg_3 && Arg_2<=Arg_1 && 0<=Arg_2 && 0<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 0<=Arg_1 for location eval_sipmabubble_bb6_in

Found invariant Arg_1<=Arg_3 && 1+Arg_1<=0 for location eval_sipmabubble_stop

Found invariant 0<=Arg_3 && 0<=Arg_2+Arg_3 && Arg_2<=Arg_3 && 0<=Arg_1+Arg_3 && Arg_1<=Arg_3 && 0<=1+Arg_0+Arg_3 && 1+Arg_0<=Arg_3 && Arg_2<=Arg_1 && Arg_2<=1+Arg_0 && 0<=Arg_2 && 0<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 0<=1+Arg_0+Arg_2 && 1+Arg_0<=Arg_2 && Arg_1<=1+Arg_0 && 0<=Arg_1 && 0<=1+Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 0<=1+Arg_0 for location eval_sipmabubble_29

Found invariant 0<=Arg_3 && 0<=Arg_2+Arg_3 && Arg_2<=Arg_3 && 0<=Arg_1+Arg_3 && Arg_1<=Arg_3 && Arg_2<=Arg_1 && 0<=Arg_2 && 0<=Arg_1+Arg_2 && 0<=Arg_1 for location eval_sipmabubble_bb2_in

Found invariant 0<=Arg_3 && 0<=Arg_2+Arg_3 && Arg_2<=Arg_3 && 0<=Arg_1+Arg_3 && Arg_1<=Arg_3 && 0<=1+Arg_0+Arg_3 && 1+Arg_0<=Arg_3 && Arg_2<=Arg_1 && Arg_2<=1+Arg_0 && 0<=Arg_2 && 0<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 0<=1+Arg_0+Arg_2 && 1+Arg_0<=Arg_2 && Arg_1<=1+Arg_0 && 0<=Arg_1 && 0<=1+Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 0<=1+Arg_0 for location eval_sipmabubble_30

Found invariant Arg_1<=Arg_3 for location eval_sipmabubble_bb1_in

Found invariant 1<=Arg_3 && 1<=Arg_2+Arg_3 && 1+Arg_2<=Arg_3 && 2<=Arg_1+Arg_3 && Arg_1<=Arg_3 && 1+Arg_2<=Arg_1 && 0<=Arg_2 && 1<=Arg_1+Arg_2 && 1<=Arg_1 for location eval_sipmabubble_bb5_in

Found invariant 1<=Arg_3 && 1<=Arg_2+Arg_3 && 1+Arg_2<=Arg_3 && 2<=Arg_1+Arg_3 && Arg_1<=Arg_3 && 1+Arg_2<=Arg_1 && 0<=Arg_2 && 1<=Arg_1+Arg_2 && 1<=Arg_1 for location eval_sipmabubble_bb3_in

Problem after Preprocessing

Start: eval_sipmabubble_start
Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3
Temp_Vars: nondef_0, nondef_1
Locations: eval_sipmabubble_0, eval_sipmabubble_1, eval_sipmabubble_2, eval_sipmabubble_29, eval_sipmabubble_3, eval_sipmabubble_30, eval_sipmabubble_4, eval_sipmabubble_5, eval_sipmabubble_6, eval_sipmabubble_bb0_in, eval_sipmabubble_bb1_in, eval_sipmabubble_bb2_in, eval_sipmabubble_bb3_in, eval_sipmabubble_bb4_in, eval_sipmabubble_bb5_in, eval_sipmabubble_bb6_in, eval_sipmabubble_bb7_in, eval_sipmabubble_start, eval_sipmabubble_stop
Transitions:
2:eval_sipmabubble_0(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_sipmabubble_1(Arg_0,Arg_1,Arg_2,Arg_3)
3:eval_sipmabubble_1(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_sipmabubble_2(Arg_0,Arg_1,Arg_2,Arg_3)
4:eval_sipmabubble_2(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_sipmabubble_3(Arg_0,Arg_1,Arg_2,Arg_3)
18:eval_sipmabubble_29(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_sipmabubble_30(Arg_0,Arg_1,Arg_2,Arg_3):|:0<=Arg_3 && 0<=Arg_2+Arg_3 && Arg_2<=Arg_3 && 0<=Arg_1+Arg_3 && Arg_1<=Arg_3 && 0<=1+Arg_0+Arg_3 && 1+Arg_0<=Arg_3 && Arg_2<=Arg_1 && Arg_2<=1+Arg_0 && 0<=Arg_2 && 0<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 0<=1+Arg_0+Arg_2 && 1+Arg_0<=Arg_2 && Arg_1<=1+Arg_0 && 0<=Arg_1 && 0<=1+Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 0<=1+Arg_0
5:eval_sipmabubble_3(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_sipmabubble_4(Arg_0,Arg_1,Arg_2,Arg_3)
19:eval_sipmabubble_30(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_sipmabubble_bb1_in(Arg_0,Arg_0,Arg_2,Arg_3):|:0<=Arg_3 && 0<=Arg_2+Arg_3 && Arg_2<=Arg_3 && 0<=Arg_1+Arg_3 && Arg_1<=Arg_3 && 0<=1+Arg_0+Arg_3 && 1+Arg_0<=Arg_3 && Arg_2<=Arg_1 && Arg_2<=1+Arg_0 && 0<=Arg_2 && 0<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 0<=1+Arg_0+Arg_2 && 1+Arg_0<=Arg_2 && Arg_1<=1+Arg_0 && 0<=Arg_1 && 0<=1+Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 0<=1+Arg_0
6:eval_sipmabubble_4(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_sipmabubble_5(Arg_0,Arg_1,Arg_2,Arg_3)
7:eval_sipmabubble_5(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_sipmabubble_6(Arg_0,Arg_1,Arg_2,Arg_3)
8:eval_sipmabubble_6(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_sipmabubble_bb1_in(Arg_0,Arg_3,Arg_2,Arg_3)
1:eval_sipmabubble_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_sipmabubble_0(Arg_0,Arg_1,Arg_2,Arg_3)
9:eval_sipmabubble_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_sipmabubble_bb2_in(Arg_0,Arg_1,0,Arg_3):|:Arg_1<=Arg_3 && 0<=Arg_1
10:eval_sipmabubble_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_sipmabubble_bb7_in(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_1<=Arg_3 && Arg_1<0
11:eval_sipmabubble_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_sipmabubble_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3):|:0<=Arg_3 && 0<=Arg_2+Arg_3 && Arg_2<=Arg_3 && 0<=Arg_1+Arg_3 && Arg_1<=Arg_3 && Arg_2<=Arg_1 && 0<=Arg_2 && 0<=Arg_1+Arg_2 && 0<=Arg_1 && Arg_2+1<=Arg_1
12:eval_sipmabubble_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_sipmabubble_bb6_in(Arg_0,Arg_1,Arg_2,Arg_3):|:0<=Arg_3 && 0<=Arg_2+Arg_3 && Arg_2<=Arg_3 && 0<=Arg_1+Arg_3 && Arg_1<=Arg_3 && Arg_2<=Arg_1 && 0<=Arg_2 && 0<=Arg_1+Arg_2 && 0<=Arg_1 && Arg_1<1+Arg_2
13:eval_sipmabubble_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_sipmabubble_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3):|:1<=Arg_3 && 1<=Arg_2+Arg_3 && 1+Arg_2<=Arg_3 && 2<=Arg_1+Arg_3 && Arg_1<=Arg_3 && 1+Arg_2<=Arg_1 && 0<=Arg_2 && 1<=Arg_1+Arg_2 && 1<=Arg_1 && nondef_1<nondef_0
14:eval_sipmabubble_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_sipmabubble_bb5_in(Arg_0,Arg_1,Arg_2,Arg_3):|:1<=Arg_3 && 1<=Arg_2+Arg_3 && 1+Arg_2<=Arg_3 && 2<=Arg_1+Arg_3 && Arg_1<=Arg_3 && 1+Arg_2<=Arg_1 && 0<=Arg_2 && 1<=Arg_1+Arg_2 && 1<=Arg_1 && nondef_0<=nondef_1
15:eval_sipmabubble_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_sipmabubble_bb5_in(Arg_0,Arg_1,Arg_2,Arg_3):|:1<=Arg_3 && 1<=Arg_2+Arg_3 && 1+Arg_2<=Arg_3 && 2<=Arg_1+Arg_3 && Arg_1<=Arg_3 && 1+Arg_2<=Arg_1 && 0<=Arg_2 && 1<=Arg_1+Arg_2 && 1<=Arg_1
16:eval_sipmabubble_bb5_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_sipmabubble_bb2_in(Arg_0,Arg_1,Arg_2+1,Arg_3):|:1<=Arg_3 && 1<=Arg_2+Arg_3 && 1+Arg_2<=Arg_3 && 2<=Arg_1+Arg_3 && Arg_1<=Arg_3 && 1+Arg_2<=Arg_1 && 0<=Arg_2 && 1<=Arg_1+Arg_2 && 1<=Arg_1
17:eval_sipmabubble_bb6_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_sipmabubble_29(Arg_1-1,Arg_1,Arg_2,Arg_3):|:0<=Arg_3 && 0<=Arg_2+Arg_3 && Arg_2<=Arg_3 && 0<=Arg_1+Arg_3 && Arg_1<=Arg_3 && Arg_2<=Arg_1 && 0<=Arg_2 && 0<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 0<=Arg_1
20:eval_sipmabubble_bb7_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_sipmabubble_stop(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_1<=Arg_3 && 1+Arg_1<=0
0:eval_sipmabubble_start(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_sipmabubble_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3)

MPRF for transition 18:eval_sipmabubble_29(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_sipmabubble_30(Arg_0,Arg_1,Arg_2,Arg_3):|:0<=Arg_3 && 0<=Arg_2+Arg_3 && Arg_2<=Arg_3 && 0<=Arg_1+Arg_3 && Arg_1<=Arg_3 && 0<=1+Arg_0+Arg_3 && 1+Arg_0<=Arg_3 && Arg_2<=Arg_1 && Arg_2<=1+Arg_0 && 0<=Arg_2 && 0<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 0<=1+Arg_0+Arg_2 && 1+Arg_0<=Arg_2 && Arg_1<=1+Arg_0 && 0<=Arg_1 && 0<=1+Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 0<=1+Arg_0 of depth 1:

new bound:

Arg_3+1 {O(n)}

MPRF:

eval_sipmabubble_30 [Arg_1 ]
eval_sipmabubble_bb1_in [Arg_1+1 ]
eval_sipmabubble_bb3_in [Arg_1+1 ]
eval_sipmabubble_bb4_in [Arg_1+1 ]
eval_sipmabubble_bb5_in [Arg_1+1 ]
eval_sipmabubble_bb2_in [Arg_1+1 ]
eval_sipmabubble_bb6_in [Arg_1+1 ]
eval_sipmabubble_29 [Arg_2+1 ]

MPRF for transition 19:eval_sipmabubble_30(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_sipmabubble_bb1_in(Arg_0,Arg_0,Arg_2,Arg_3):|:0<=Arg_3 && 0<=Arg_2+Arg_3 && Arg_2<=Arg_3 && 0<=Arg_1+Arg_3 && Arg_1<=Arg_3 && 0<=1+Arg_0+Arg_3 && 1+Arg_0<=Arg_3 && Arg_2<=Arg_1 && Arg_2<=1+Arg_0 && 0<=Arg_2 && 0<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 0<=1+Arg_0+Arg_2 && 1+Arg_0<=Arg_2 && Arg_1<=1+Arg_0 && 0<=Arg_1 && 0<=1+Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 0<=1+Arg_0 of depth 1:

new bound:

Arg_3+1 {O(n)}

MPRF:

eval_sipmabubble_30 [Arg_2+1 ]
eval_sipmabubble_bb1_in [Arg_1+1 ]
eval_sipmabubble_bb3_in [Arg_1+1 ]
eval_sipmabubble_bb4_in [Arg_1+1 ]
eval_sipmabubble_bb5_in [Arg_1+1 ]
eval_sipmabubble_bb2_in [Arg_1+1 ]
eval_sipmabubble_bb6_in [Arg_1+1 ]
eval_sipmabubble_29 [Arg_1+1 ]

MPRF for transition 9:eval_sipmabubble_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_sipmabubble_bb2_in(Arg_0,Arg_1,0,Arg_3):|:Arg_1<=Arg_3 && 0<=Arg_1 of depth 1:

new bound:

Arg_3+1 {O(n)}

MPRF:

eval_sipmabubble_30 [Arg_1 ]
eval_sipmabubble_bb1_in [Arg_1+1 ]
eval_sipmabubble_bb3_in [Arg_1 ]
eval_sipmabubble_bb4_in [Arg_1 ]
eval_sipmabubble_bb5_in [Arg_1 ]
eval_sipmabubble_bb2_in [Arg_1 ]
eval_sipmabubble_bb6_in [Arg_2 ]
eval_sipmabubble_29 [Arg_2 ]

MPRF for transition 12:eval_sipmabubble_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_sipmabubble_bb6_in(Arg_0,Arg_1,Arg_2,Arg_3):|:0<=Arg_3 && 0<=Arg_2+Arg_3 && Arg_2<=Arg_3 && 0<=Arg_1+Arg_3 && Arg_1<=Arg_3 && Arg_2<=Arg_1 && 0<=Arg_2 && 0<=Arg_1+Arg_2 && 0<=Arg_1 && Arg_1<1+Arg_2 of depth 1:

new bound:

Arg_3+1 {O(n)}

MPRF:

eval_sipmabubble_30 [Arg_1 ]
eval_sipmabubble_bb1_in [Arg_1+1 ]
eval_sipmabubble_bb3_in [Arg_1+1 ]
eval_sipmabubble_bb4_in [Arg_1+1 ]
eval_sipmabubble_bb5_in [Arg_1+1 ]
eval_sipmabubble_bb2_in [Arg_1+1 ]
eval_sipmabubble_bb6_in [Arg_1 ]
eval_sipmabubble_29 [Arg_2 ]

MPRF for transition 17:eval_sipmabubble_bb6_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_sipmabubble_29(Arg_1-1,Arg_1,Arg_2,Arg_3):|:0<=Arg_3 && 0<=Arg_2+Arg_3 && Arg_2<=Arg_3 && 0<=Arg_1+Arg_3 && Arg_1<=Arg_3 && Arg_2<=Arg_1 && 0<=Arg_2 && 0<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 0<=Arg_1 of depth 1:

new bound:

Arg_3+1 {O(n)}

MPRF:

eval_sipmabubble_30 [Arg_0+1 ]
eval_sipmabubble_bb1_in [Arg_1+1 ]
eval_sipmabubble_bb3_in [Arg_1+1 ]
eval_sipmabubble_bb4_in [Arg_1+1 ]
eval_sipmabubble_bb5_in [Arg_1+1 ]
eval_sipmabubble_bb2_in [Arg_1+1 ]
eval_sipmabubble_bb6_in [Arg_2+1 ]
eval_sipmabubble_29 [Arg_0+Arg_2+1-Arg_1 ]

MPRF for transition 11:eval_sipmabubble_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_sipmabubble_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3):|:0<=Arg_3 && 0<=Arg_2+Arg_3 && Arg_2<=Arg_3 && 0<=Arg_1+Arg_3 && Arg_1<=Arg_3 && Arg_2<=Arg_1 && 0<=Arg_2 && 0<=Arg_1+Arg_2 && 0<=Arg_1 && Arg_2+1<=Arg_1 of depth 1:

new bound:

Arg_3*Arg_3+4*Arg_3+3 {O(n^2)}

MPRF:

eval_sipmabubble_29 [Arg_0+1 ]
eval_sipmabubble_30 [Arg_0+1 ]
eval_sipmabubble_bb1_in [Arg_1+1 ]
eval_sipmabubble_bb6_in [1 ]
eval_sipmabubble_bb3_in [Arg_1-Arg_2 ]
eval_sipmabubble_bb4_in [Arg_1-Arg_2 ]
eval_sipmabubble_bb5_in [Arg_1-Arg_2 ]
eval_sipmabubble_bb2_in [Arg_1+1-Arg_2 ]

MPRF for transition 13:eval_sipmabubble_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_sipmabubble_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3):|:1<=Arg_3 && 1<=Arg_2+Arg_3 && 1+Arg_2<=Arg_3 && 2<=Arg_1+Arg_3 && Arg_1<=Arg_3 && 1+Arg_2<=Arg_1 && 0<=Arg_2 && 1<=Arg_1+Arg_2 && 1<=Arg_1 && nondef_1<nondef_0 of depth 1:

new bound:

Arg_3*Arg_3+3*Arg_3+2 {O(n^2)}

MPRF:

eval_sipmabubble_29 [Arg_3+1 ]
eval_sipmabubble_30 [Arg_3+1 ]
eval_sipmabubble_bb1_in [Arg_3+1 ]
eval_sipmabubble_bb6_in [Arg_3+1-Arg_2 ]
eval_sipmabubble_bb3_in [Arg_3+1-Arg_2 ]
eval_sipmabubble_bb4_in [Arg_3-Arg_2 ]
eval_sipmabubble_bb5_in [Arg_3-Arg_2 ]
eval_sipmabubble_bb2_in [Arg_3+1-Arg_2 ]

MPRF for transition 14:eval_sipmabubble_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_sipmabubble_bb5_in(Arg_0,Arg_1,Arg_2,Arg_3):|:1<=Arg_3 && 1<=Arg_2+Arg_3 && 1+Arg_2<=Arg_3 && 2<=Arg_1+Arg_3 && Arg_1<=Arg_3 && 1+Arg_2<=Arg_1 && 0<=Arg_2 && 1<=Arg_1+Arg_2 && 1<=Arg_1 && nondef_0<=nondef_1 of depth 1:

new bound:

Arg_3*Arg_3+3*Arg_3+2 {O(n^2)}

MPRF:

eval_sipmabubble_29 [Arg_3+1 ]
eval_sipmabubble_30 [Arg_3+1 ]
eval_sipmabubble_bb1_in [Arg_3+1 ]
eval_sipmabubble_bb6_in [Arg_3+1-Arg_2 ]
eval_sipmabubble_bb3_in [Arg_3+1-Arg_2 ]
eval_sipmabubble_bb4_in [Arg_3-Arg_2 ]
eval_sipmabubble_bb5_in [Arg_3-Arg_2 ]
eval_sipmabubble_bb2_in [Arg_3+1-Arg_2 ]

MPRF for transition 15:eval_sipmabubble_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_sipmabubble_bb5_in(Arg_0,Arg_1,Arg_2,Arg_3):|:1<=Arg_3 && 1<=Arg_2+Arg_3 && 1+Arg_2<=Arg_3 && 2<=Arg_1+Arg_3 && Arg_1<=Arg_3 && 1+Arg_2<=Arg_1 && 0<=Arg_2 && 1<=Arg_1+Arg_2 && 1<=Arg_1 of depth 1:

new bound:

Arg_3*Arg_3+3*Arg_3+2 {O(n^2)}

MPRF:

eval_sipmabubble_29 [Arg_3+1 ]
eval_sipmabubble_30 [Arg_3+1 ]
eval_sipmabubble_bb1_in [Arg_3+1 ]
eval_sipmabubble_bb6_in [2*Arg_1+1-Arg_2-Arg_3 ]
eval_sipmabubble_bb3_in [Arg_3+1-Arg_2 ]
eval_sipmabubble_bb4_in [Arg_3+1-Arg_2 ]
eval_sipmabubble_bb5_in [Arg_3-Arg_2 ]
eval_sipmabubble_bb2_in [Arg_3+1-Arg_2 ]

MPRF for transition 16:eval_sipmabubble_bb5_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_sipmabubble_bb2_in(Arg_0,Arg_1,Arg_2+1,Arg_3):|:1<=Arg_3 && 1<=Arg_2+Arg_3 && 1+Arg_2<=Arg_3 && 2<=Arg_1+Arg_3 && Arg_1<=Arg_3 && 1+Arg_2<=Arg_1 && 0<=Arg_2 && 1<=Arg_1+Arg_2 && 1<=Arg_1 of depth 1:

new bound:

Arg_3*Arg_3+3*Arg_3+2 {O(n^2)}

MPRF:

eval_sipmabubble_29 [Arg_3+1 ]
eval_sipmabubble_30 [Arg_3+1 ]
eval_sipmabubble_bb1_in [Arg_3+1 ]
eval_sipmabubble_bb6_in [Arg_3+1-Arg_2 ]
eval_sipmabubble_bb3_in [Arg_3+1-Arg_2 ]
eval_sipmabubble_bb4_in [Arg_3+1-Arg_2 ]
eval_sipmabubble_bb5_in [Arg_3+1-Arg_2 ]
eval_sipmabubble_bb2_in [Arg_3+1-Arg_2 ]

All Bounds

Timebounds

Overall timebound:5*Arg_3*Arg_3+21*Arg_3+27 {O(n^2)}
2: eval_sipmabubble_0->eval_sipmabubble_1: 1 {O(1)}
3: eval_sipmabubble_1->eval_sipmabubble_2: 1 {O(1)}
4: eval_sipmabubble_2->eval_sipmabubble_3: 1 {O(1)}
18: eval_sipmabubble_29->eval_sipmabubble_30: Arg_3+1 {O(n)}
5: eval_sipmabubble_3->eval_sipmabubble_4: 1 {O(1)}
19: eval_sipmabubble_30->eval_sipmabubble_bb1_in: Arg_3+1 {O(n)}
6: eval_sipmabubble_4->eval_sipmabubble_5: 1 {O(1)}
7: eval_sipmabubble_5->eval_sipmabubble_6: 1 {O(1)}
8: eval_sipmabubble_6->eval_sipmabubble_bb1_in: 1 {O(1)}
1: eval_sipmabubble_bb0_in->eval_sipmabubble_0: 1 {O(1)}
9: eval_sipmabubble_bb1_in->eval_sipmabubble_bb2_in: Arg_3+1 {O(n)}
10: eval_sipmabubble_bb1_in->eval_sipmabubble_bb7_in: 1 {O(1)}
11: eval_sipmabubble_bb2_in->eval_sipmabubble_bb3_in: Arg_3*Arg_3+4*Arg_3+3 {O(n^2)}
12: eval_sipmabubble_bb2_in->eval_sipmabubble_bb6_in: Arg_3+1 {O(n)}
13: eval_sipmabubble_bb3_in->eval_sipmabubble_bb4_in: Arg_3*Arg_3+3*Arg_3+2 {O(n^2)}
14: eval_sipmabubble_bb3_in->eval_sipmabubble_bb5_in: Arg_3*Arg_3+3*Arg_3+2 {O(n^2)}
15: eval_sipmabubble_bb4_in->eval_sipmabubble_bb5_in: Arg_3*Arg_3+3*Arg_3+2 {O(n^2)}
16: eval_sipmabubble_bb5_in->eval_sipmabubble_bb2_in: Arg_3*Arg_3+3*Arg_3+2 {O(n^2)}
17: eval_sipmabubble_bb6_in->eval_sipmabubble_29: Arg_3+1 {O(n)}
20: eval_sipmabubble_bb7_in->eval_sipmabubble_stop: 1 {O(1)}
0: eval_sipmabubble_start->eval_sipmabubble_bb0_in: 1 {O(1)}

Costbounds

Overall costbound: 5*Arg_3*Arg_3+21*Arg_3+27 {O(n^2)}
2: eval_sipmabubble_0->eval_sipmabubble_1: 1 {O(1)}
3: eval_sipmabubble_1->eval_sipmabubble_2: 1 {O(1)}
4: eval_sipmabubble_2->eval_sipmabubble_3: 1 {O(1)}
18: eval_sipmabubble_29->eval_sipmabubble_30: Arg_3+1 {O(n)}
5: eval_sipmabubble_3->eval_sipmabubble_4: 1 {O(1)}
19: eval_sipmabubble_30->eval_sipmabubble_bb1_in: Arg_3+1 {O(n)}
6: eval_sipmabubble_4->eval_sipmabubble_5: 1 {O(1)}
7: eval_sipmabubble_5->eval_sipmabubble_6: 1 {O(1)}
8: eval_sipmabubble_6->eval_sipmabubble_bb1_in: 1 {O(1)}
1: eval_sipmabubble_bb0_in->eval_sipmabubble_0: 1 {O(1)}
9: eval_sipmabubble_bb1_in->eval_sipmabubble_bb2_in: Arg_3+1 {O(n)}
10: eval_sipmabubble_bb1_in->eval_sipmabubble_bb7_in: 1 {O(1)}
11: eval_sipmabubble_bb2_in->eval_sipmabubble_bb3_in: Arg_3*Arg_3+4*Arg_3+3 {O(n^2)}
12: eval_sipmabubble_bb2_in->eval_sipmabubble_bb6_in: Arg_3+1 {O(n)}
13: eval_sipmabubble_bb3_in->eval_sipmabubble_bb4_in: Arg_3*Arg_3+3*Arg_3+2 {O(n^2)}
14: eval_sipmabubble_bb3_in->eval_sipmabubble_bb5_in: Arg_3*Arg_3+3*Arg_3+2 {O(n^2)}
15: eval_sipmabubble_bb4_in->eval_sipmabubble_bb5_in: Arg_3*Arg_3+3*Arg_3+2 {O(n^2)}
16: eval_sipmabubble_bb5_in->eval_sipmabubble_bb2_in: Arg_3*Arg_3+3*Arg_3+2 {O(n^2)}
17: eval_sipmabubble_bb6_in->eval_sipmabubble_29: Arg_3+1 {O(n)}
20: eval_sipmabubble_bb7_in->eval_sipmabubble_stop: 1 {O(1)}
0: eval_sipmabubble_start->eval_sipmabubble_bb0_in: 1 {O(1)}

Sizebounds

2: eval_sipmabubble_0->eval_sipmabubble_1, Arg_0: Arg_0 {O(n)}
2: eval_sipmabubble_0->eval_sipmabubble_1, Arg_1: Arg_1 {O(n)}
2: eval_sipmabubble_0->eval_sipmabubble_1, Arg_2: Arg_2 {O(n)}
2: eval_sipmabubble_0->eval_sipmabubble_1, Arg_3: Arg_3 {O(n)}
3: eval_sipmabubble_1->eval_sipmabubble_2, Arg_0: Arg_0 {O(n)}
3: eval_sipmabubble_1->eval_sipmabubble_2, Arg_1: Arg_1 {O(n)}
3: eval_sipmabubble_1->eval_sipmabubble_2, Arg_2: Arg_2 {O(n)}
3: eval_sipmabubble_1->eval_sipmabubble_2, Arg_3: Arg_3 {O(n)}
4: eval_sipmabubble_2->eval_sipmabubble_3, Arg_0: Arg_0 {O(n)}
4: eval_sipmabubble_2->eval_sipmabubble_3, Arg_1: Arg_1 {O(n)}
4: eval_sipmabubble_2->eval_sipmabubble_3, Arg_2: Arg_2 {O(n)}
4: eval_sipmabubble_2->eval_sipmabubble_3, Arg_3: Arg_3 {O(n)}
18: eval_sipmabubble_29->eval_sipmabubble_30, Arg_0: Arg_3+1 {O(n)}
18: eval_sipmabubble_29->eval_sipmabubble_30, Arg_1: Arg_3+1 {O(n)}
18: eval_sipmabubble_29->eval_sipmabubble_30, Arg_2: Arg_3*Arg_3+3*Arg_3+2 {O(n^2)}
18: eval_sipmabubble_29->eval_sipmabubble_30, Arg_3: Arg_3 {O(n)}
5: eval_sipmabubble_3->eval_sipmabubble_4, Arg_0: Arg_0 {O(n)}
5: eval_sipmabubble_3->eval_sipmabubble_4, Arg_1: Arg_1 {O(n)}
5: eval_sipmabubble_3->eval_sipmabubble_4, Arg_2: Arg_2 {O(n)}
5: eval_sipmabubble_3->eval_sipmabubble_4, Arg_3: Arg_3 {O(n)}
19: eval_sipmabubble_30->eval_sipmabubble_bb1_in, Arg_0: Arg_3+1 {O(n)}
19: eval_sipmabubble_30->eval_sipmabubble_bb1_in, Arg_1: Arg_3+1 {O(n)}
19: eval_sipmabubble_30->eval_sipmabubble_bb1_in, Arg_2: Arg_3*Arg_3+3*Arg_3+2 {O(n^2)}
19: eval_sipmabubble_30->eval_sipmabubble_bb1_in, Arg_3: Arg_3 {O(n)}
6: eval_sipmabubble_4->eval_sipmabubble_5, Arg_0: Arg_0 {O(n)}
6: eval_sipmabubble_4->eval_sipmabubble_5, Arg_1: Arg_1 {O(n)}
6: eval_sipmabubble_4->eval_sipmabubble_5, Arg_2: Arg_2 {O(n)}
6: eval_sipmabubble_4->eval_sipmabubble_5, Arg_3: Arg_3 {O(n)}
7: eval_sipmabubble_5->eval_sipmabubble_6, Arg_0: Arg_0 {O(n)}
7: eval_sipmabubble_5->eval_sipmabubble_6, Arg_1: Arg_1 {O(n)}
7: eval_sipmabubble_5->eval_sipmabubble_6, Arg_2: Arg_2 {O(n)}
7: eval_sipmabubble_5->eval_sipmabubble_6, Arg_3: Arg_3 {O(n)}
8: eval_sipmabubble_6->eval_sipmabubble_bb1_in, Arg_0: Arg_0 {O(n)}
8: eval_sipmabubble_6->eval_sipmabubble_bb1_in, Arg_1: Arg_3 {O(n)}
8: eval_sipmabubble_6->eval_sipmabubble_bb1_in, Arg_2: Arg_2 {O(n)}
8: eval_sipmabubble_6->eval_sipmabubble_bb1_in, Arg_3: Arg_3 {O(n)}
1: eval_sipmabubble_bb0_in->eval_sipmabubble_0, Arg_0: Arg_0 {O(n)}
1: eval_sipmabubble_bb0_in->eval_sipmabubble_0, Arg_1: Arg_1 {O(n)}
1: eval_sipmabubble_bb0_in->eval_sipmabubble_0, Arg_2: Arg_2 {O(n)}
1: eval_sipmabubble_bb0_in->eval_sipmabubble_0, Arg_3: Arg_3 {O(n)}
9: eval_sipmabubble_bb1_in->eval_sipmabubble_bb2_in, Arg_0: Arg_0+Arg_3+1 {O(n)}
9: eval_sipmabubble_bb1_in->eval_sipmabubble_bb2_in, Arg_1: Arg_3+1 {O(n)}
9: eval_sipmabubble_bb1_in->eval_sipmabubble_bb2_in, Arg_2: 0 {O(1)}
9: eval_sipmabubble_bb1_in->eval_sipmabubble_bb2_in, Arg_3: Arg_3 {O(n)}
10: eval_sipmabubble_bb1_in->eval_sipmabubble_bb7_in, Arg_0: Arg_0+Arg_3+1 {O(n)}
10: eval_sipmabubble_bb1_in->eval_sipmabubble_bb7_in, Arg_1: 2*Arg_3+1 {O(n)}
10: eval_sipmabubble_bb1_in->eval_sipmabubble_bb7_in, Arg_2: Arg_3*Arg_3+3*Arg_3+Arg_2+2 {O(n^2)}
10: eval_sipmabubble_bb1_in->eval_sipmabubble_bb7_in, Arg_3: 2*Arg_3 {O(n)}
11: eval_sipmabubble_bb2_in->eval_sipmabubble_bb3_in, Arg_0: Arg_0+Arg_3+1 {O(n)}
11: eval_sipmabubble_bb2_in->eval_sipmabubble_bb3_in, Arg_1: Arg_3+1 {O(n)}
11: eval_sipmabubble_bb2_in->eval_sipmabubble_bb3_in, Arg_2: Arg_3*Arg_3+3*Arg_3+2 {O(n^2)}
11: eval_sipmabubble_bb2_in->eval_sipmabubble_bb3_in, Arg_3: Arg_3 {O(n)}
12: eval_sipmabubble_bb2_in->eval_sipmabubble_bb6_in, Arg_0: 2*Arg_0+2*Arg_3+2 {O(n)}
12: eval_sipmabubble_bb2_in->eval_sipmabubble_bb6_in, Arg_1: Arg_3+1 {O(n)}
12: eval_sipmabubble_bb2_in->eval_sipmabubble_bb6_in, Arg_2: Arg_3*Arg_3+3*Arg_3+2 {O(n^2)}
12: eval_sipmabubble_bb2_in->eval_sipmabubble_bb6_in, Arg_3: Arg_3 {O(n)}
13: eval_sipmabubble_bb3_in->eval_sipmabubble_bb4_in, Arg_0: Arg_0+Arg_3+1 {O(n)}
13: eval_sipmabubble_bb3_in->eval_sipmabubble_bb4_in, Arg_1: Arg_3+1 {O(n)}
13: eval_sipmabubble_bb3_in->eval_sipmabubble_bb4_in, Arg_2: Arg_3*Arg_3+3*Arg_3+2 {O(n^2)}
13: eval_sipmabubble_bb3_in->eval_sipmabubble_bb4_in, Arg_3: Arg_3 {O(n)}
14: eval_sipmabubble_bb3_in->eval_sipmabubble_bb5_in, Arg_0: Arg_0+Arg_3+1 {O(n)}
14: eval_sipmabubble_bb3_in->eval_sipmabubble_bb5_in, Arg_1: Arg_3+1 {O(n)}
14: eval_sipmabubble_bb3_in->eval_sipmabubble_bb5_in, Arg_2: Arg_3*Arg_3+3*Arg_3+2 {O(n^2)}
14: eval_sipmabubble_bb3_in->eval_sipmabubble_bb5_in, Arg_3: Arg_3 {O(n)}
15: eval_sipmabubble_bb4_in->eval_sipmabubble_bb5_in, Arg_0: Arg_0+Arg_3+1 {O(n)}
15: eval_sipmabubble_bb4_in->eval_sipmabubble_bb5_in, Arg_1: Arg_3+1 {O(n)}
15: eval_sipmabubble_bb4_in->eval_sipmabubble_bb5_in, Arg_2: Arg_3*Arg_3+3*Arg_3+2 {O(n^2)}
15: eval_sipmabubble_bb4_in->eval_sipmabubble_bb5_in, Arg_3: Arg_3 {O(n)}
16: eval_sipmabubble_bb5_in->eval_sipmabubble_bb2_in, Arg_0: Arg_0+Arg_3+1 {O(n)}
16: eval_sipmabubble_bb5_in->eval_sipmabubble_bb2_in, Arg_1: Arg_3+1 {O(n)}
16: eval_sipmabubble_bb5_in->eval_sipmabubble_bb2_in, Arg_2: Arg_3*Arg_3+3*Arg_3+2 {O(n^2)}
16: eval_sipmabubble_bb5_in->eval_sipmabubble_bb2_in, Arg_3: Arg_3 {O(n)}
17: eval_sipmabubble_bb6_in->eval_sipmabubble_29, Arg_0: Arg_3+1 {O(n)}
17: eval_sipmabubble_bb6_in->eval_sipmabubble_29, Arg_1: Arg_3+1 {O(n)}
17: eval_sipmabubble_bb6_in->eval_sipmabubble_29, Arg_2: Arg_3*Arg_3+3*Arg_3+2 {O(n^2)}
17: eval_sipmabubble_bb6_in->eval_sipmabubble_29, Arg_3: Arg_3 {O(n)}
20: eval_sipmabubble_bb7_in->eval_sipmabubble_stop, Arg_0: Arg_0+Arg_3+1 {O(n)}
20: eval_sipmabubble_bb7_in->eval_sipmabubble_stop, Arg_1: 2*Arg_3+1 {O(n)}
20: eval_sipmabubble_bb7_in->eval_sipmabubble_stop, Arg_2: Arg_3*Arg_3+3*Arg_3+Arg_2+2 {O(n^2)}
20: eval_sipmabubble_bb7_in->eval_sipmabubble_stop, Arg_3: 2*Arg_3 {O(n)}
0: eval_sipmabubble_start->eval_sipmabubble_bb0_in, Arg_0: Arg_0 {O(n)}
0: eval_sipmabubble_start->eval_sipmabubble_bb0_in, Arg_1: Arg_1 {O(n)}
0: eval_sipmabubble_start->eval_sipmabubble_bb0_in, Arg_2: Arg_2 {O(n)}
0: eval_sipmabubble_start->eval_sipmabubble_bb0_in, Arg_3: Arg_3 {O(n)}