Initial Problem

Start: eval_sipmabubble_start
Program_Vars: Arg_0, Arg_1, Arg_2
Temp_Vars:
Locations: eval_sipmabubble_2, eval_sipmabubble_3, eval_sipmabubble_4, 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_start, eval_sipmabubble_stop
Transitions:
8:eval_sipmabubble_2(Arg_0,Arg_1,Arg_2) -> eval_sipmabubble_3(Arg_0,Arg_1,Arg_2)
10:eval_sipmabubble_3(Arg_0,Arg_1,Arg_2) -> eval_sipmabubble_4(Arg_0,Arg_1,Arg_2)
11:eval_sipmabubble_4(Arg_0,Arg_1,Arg_2) -> eval_sipmabubble_bb2_in(Arg_0,Arg_1+1,Arg_2)
1:eval_sipmabubble_bb0_in(Arg_0,Arg_1,Arg_2) -> eval_sipmabubble_bb1_in(Arg_2,Arg_1,Arg_2)
2:eval_sipmabubble_bb1_in(Arg_0,Arg_1,Arg_2) -> eval_sipmabubble_bb2_in(Arg_0,0,Arg_2):|:0<=Arg_0
3:eval_sipmabubble_bb1_in(Arg_0,Arg_1,Arg_2) -> eval_sipmabubble_bb5_in(Arg_0,Arg_1,Arg_2):|:Arg_0<0
4:eval_sipmabubble_bb2_in(Arg_0,Arg_1,Arg_2) -> eval_sipmabubble_bb3_in(Arg_0,Arg_1,Arg_2):|:Arg_1+1<=Arg_0
5:eval_sipmabubble_bb2_in(Arg_0,Arg_1,Arg_2) -> eval_sipmabubble_bb4_in(Arg_0,Arg_1,Arg_2):|:Arg_0<1+Arg_1
6:eval_sipmabubble_bb3_in(Arg_0,Arg_1,Arg_2) -> eval_sipmabubble_2(Arg_0,Arg_1,Arg_2)
12:eval_sipmabubble_bb4_in(Arg_0,Arg_1,Arg_2) -> eval_sipmabubble_bb1_in(Arg_0-1,Arg_1,Arg_2)
13:eval_sipmabubble_bb5_in(Arg_0,Arg_1,Arg_2) -> eval_sipmabubble_stop(Arg_0,Arg_1,Arg_2)
0:eval_sipmabubble_start(Arg_0,Arg_1,Arg_2) -> eval_sipmabubble_bb0_in(Arg_0,Arg_1,Arg_2)

Preprocessing

Found invariant 1<=Arg_2 && 1<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 2<=Arg_0+Arg_2 && Arg_0<=Arg_2 && 1+Arg_1<=Arg_0 && 0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 for location eval_sipmabubble_3

Found invariant 0<=Arg_2 && 0<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 0<=Arg_0+Arg_2 && Arg_0<=Arg_2 && Arg_1<=Arg_0 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 0<=Arg_0 for location eval_sipmabubble_bb4_in

Found invariant Arg_0<=Arg_2 && 1+Arg_0<=0 for location eval_sipmabubble_stop

Found invariant 1<=Arg_2 && 1<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 2<=Arg_0+Arg_2 && Arg_0<=Arg_2 && 1+Arg_1<=Arg_0 && 0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 for location eval_sipmabubble_2

Found invariant 0<=Arg_2 && 0<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 0<=Arg_0+Arg_2 && Arg_0<=Arg_2 && Arg_1<=Arg_0 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=Arg_0 for location eval_sipmabubble_bb2_in

Found invariant Arg_0<=Arg_2 for location eval_sipmabubble_bb1_in

Found invariant Arg_0<=Arg_2 && 1+Arg_0<=0 for location eval_sipmabubble_bb5_in

Found invariant 1<=Arg_2 && 1<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 2<=Arg_0+Arg_2 && Arg_0<=Arg_2 && 1+Arg_1<=Arg_0 && 0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 for location eval_sipmabubble_4

Found invariant 1<=Arg_2 && 1<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 2<=Arg_0+Arg_2 && Arg_0<=Arg_2 && 1+Arg_1<=Arg_0 && 0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 for location eval_sipmabubble_bb3_in

Problem after Preprocessing

Start: eval_sipmabubble_start
Program_Vars: Arg_0, Arg_1, Arg_2
Temp_Vars:
Locations: eval_sipmabubble_2, eval_sipmabubble_3, eval_sipmabubble_4, 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_start, eval_sipmabubble_stop
Transitions:
8:eval_sipmabubble_2(Arg_0,Arg_1,Arg_2) -> eval_sipmabubble_3(Arg_0,Arg_1,Arg_2):|:1<=Arg_2 && 1<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 2<=Arg_0+Arg_2 && Arg_0<=Arg_2 && 1+Arg_1<=Arg_0 && 0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0
10:eval_sipmabubble_3(Arg_0,Arg_1,Arg_2) -> eval_sipmabubble_4(Arg_0,Arg_1,Arg_2):|:1<=Arg_2 && 1<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 2<=Arg_0+Arg_2 && Arg_0<=Arg_2 && 1+Arg_1<=Arg_0 && 0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0
11:eval_sipmabubble_4(Arg_0,Arg_1,Arg_2) -> eval_sipmabubble_bb2_in(Arg_0,Arg_1+1,Arg_2):|:1<=Arg_2 && 1<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 2<=Arg_0+Arg_2 && Arg_0<=Arg_2 && 1+Arg_1<=Arg_0 && 0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0
1:eval_sipmabubble_bb0_in(Arg_0,Arg_1,Arg_2) -> eval_sipmabubble_bb1_in(Arg_2,Arg_1,Arg_2)
2:eval_sipmabubble_bb1_in(Arg_0,Arg_1,Arg_2) -> eval_sipmabubble_bb2_in(Arg_0,0,Arg_2):|:Arg_0<=Arg_2 && 0<=Arg_0
3:eval_sipmabubble_bb1_in(Arg_0,Arg_1,Arg_2) -> eval_sipmabubble_bb5_in(Arg_0,Arg_1,Arg_2):|:Arg_0<=Arg_2 && Arg_0<0
4:eval_sipmabubble_bb2_in(Arg_0,Arg_1,Arg_2) -> eval_sipmabubble_bb3_in(Arg_0,Arg_1,Arg_2):|:0<=Arg_2 && 0<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 0<=Arg_0+Arg_2 && Arg_0<=Arg_2 && Arg_1<=Arg_0 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=Arg_0 && Arg_1+1<=Arg_0
5:eval_sipmabubble_bb2_in(Arg_0,Arg_1,Arg_2) -> eval_sipmabubble_bb4_in(Arg_0,Arg_1,Arg_2):|:0<=Arg_2 && 0<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 0<=Arg_0+Arg_2 && Arg_0<=Arg_2 && Arg_1<=Arg_0 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=Arg_0 && Arg_0<1+Arg_1
6:eval_sipmabubble_bb3_in(Arg_0,Arg_1,Arg_2) -> eval_sipmabubble_2(Arg_0,Arg_1,Arg_2):|:1<=Arg_2 && 1<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 2<=Arg_0+Arg_2 && Arg_0<=Arg_2 && 1+Arg_1<=Arg_0 && 0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0
12:eval_sipmabubble_bb4_in(Arg_0,Arg_1,Arg_2) -> eval_sipmabubble_bb1_in(Arg_0-1,Arg_1,Arg_2):|:0<=Arg_2 && 0<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 0<=Arg_0+Arg_2 && Arg_0<=Arg_2 && Arg_1<=Arg_0 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 0<=Arg_0
13:eval_sipmabubble_bb5_in(Arg_0,Arg_1,Arg_2) -> eval_sipmabubble_stop(Arg_0,Arg_1,Arg_2):|:Arg_0<=Arg_2 && 1+Arg_0<=0
0:eval_sipmabubble_start(Arg_0,Arg_1,Arg_2) -> eval_sipmabubble_bb0_in(Arg_0,Arg_1,Arg_2)

MPRF for transition 2:eval_sipmabubble_bb1_in(Arg_0,Arg_1,Arg_2) -> eval_sipmabubble_bb2_in(Arg_0,0,Arg_2):|:Arg_0<=Arg_2 && 0<=Arg_0 of depth 1:

new bound:

Arg_2+1 {O(n)}

MPRF:

eval_sipmabubble_3 [Arg_0 ]
eval_sipmabubble_4 [Arg_0 ]
eval_sipmabubble_bb2_in [Arg_0 ]
eval_sipmabubble_bb3_in [Arg_0 ]
eval_sipmabubble_2 [Arg_0 ]
eval_sipmabubble_bb4_in [Arg_1 ]
eval_sipmabubble_bb1_in [Arg_0+1 ]

MPRF for transition 5:eval_sipmabubble_bb2_in(Arg_0,Arg_1,Arg_2) -> eval_sipmabubble_bb4_in(Arg_0,Arg_1,Arg_2):|:0<=Arg_2 && 0<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 0<=Arg_0+Arg_2 && Arg_0<=Arg_2 && Arg_1<=Arg_0 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=Arg_0 && Arg_0<1+Arg_1 of depth 1:

new bound:

Arg_2+1 {O(n)}

MPRF:

eval_sipmabubble_3 [Arg_0+1 ]
eval_sipmabubble_4 [Arg_0+1 ]
eval_sipmabubble_bb2_in [Arg_0+1 ]
eval_sipmabubble_bb3_in [Arg_0+1 ]
eval_sipmabubble_2 [Arg_0+1 ]
eval_sipmabubble_bb4_in [Arg_0 ]
eval_sipmabubble_bb1_in [Arg_0+1 ]

MPRF for transition 12:eval_sipmabubble_bb4_in(Arg_0,Arg_1,Arg_2) -> eval_sipmabubble_bb1_in(Arg_0-1,Arg_1,Arg_2):|:0<=Arg_2 && 0<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 0<=Arg_0+Arg_2 && Arg_0<=Arg_2 && Arg_1<=Arg_0 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 0<=Arg_0 of depth 1:

new bound:

Arg_2+1 {O(n)}

MPRF:

eval_sipmabubble_3 [Arg_0+1 ]
eval_sipmabubble_4 [Arg_0+1 ]
eval_sipmabubble_bb2_in [Arg_0+1 ]
eval_sipmabubble_bb3_in [Arg_0+1 ]
eval_sipmabubble_2 [Arg_0+1 ]
eval_sipmabubble_bb4_in [Arg_1+1 ]
eval_sipmabubble_bb1_in [Arg_0+1 ]

MPRF for transition 8:eval_sipmabubble_2(Arg_0,Arg_1,Arg_2) -> eval_sipmabubble_3(Arg_0,Arg_1,Arg_2):|:1<=Arg_2 && 1<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 2<=Arg_0+Arg_2 && Arg_0<=Arg_2 && 1+Arg_1<=Arg_0 && 0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 of depth 1:

new bound:

Arg_2*Arg_2+3*Arg_2+2 {O(n^2)}

MPRF:

eval_sipmabubble_3 [Arg_2-Arg_1 ]
eval_sipmabubble_4 [Arg_2-Arg_1 ]
eval_sipmabubble_bb1_in [Arg_2+1 ]
eval_sipmabubble_bb2_in [Arg_2+1-Arg_1 ]
eval_sipmabubble_bb4_in [Arg_2+1-Arg_1 ]
eval_sipmabubble_bb3_in [Arg_2+1-Arg_1 ]
eval_sipmabubble_2 [Arg_2+1-Arg_1 ]

MPRF for transition 10:eval_sipmabubble_3(Arg_0,Arg_1,Arg_2) -> eval_sipmabubble_4(Arg_0,Arg_1,Arg_2):|:1<=Arg_2 && 1<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 2<=Arg_0+Arg_2 && Arg_0<=Arg_2 && 1+Arg_1<=Arg_0 && 0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 of depth 1:

new bound:

Arg_2*Arg_2+3*Arg_2+2 {O(n^2)}

MPRF:

eval_sipmabubble_3 [Arg_2+1-Arg_1 ]
eval_sipmabubble_4 [Arg_2-Arg_1 ]
eval_sipmabubble_bb1_in [Arg_2+1 ]
eval_sipmabubble_bb2_in [Arg_2+1-Arg_1 ]
eval_sipmabubble_bb4_in [Arg_2+1-Arg_1 ]
eval_sipmabubble_bb3_in [Arg_2+1-Arg_1 ]
eval_sipmabubble_2 [Arg_2+1-Arg_1 ]

MPRF for transition 11:eval_sipmabubble_4(Arg_0,Arg_1,Arg_2) -> eval_sipmabubble_bb2_in(Arg_0,Arg_1+1,Arg_2):|:1<=Arg_2 && 1<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 2<=Arg_0+Arg_2 && Arg_0<=Arg_2 && 1+Arg_1<=Arg_0 && 0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 of depth 1:

new bound:

Arg_2*Arg_2+4*Arg_2+3 {O(n^2)}

MPRF:

eval_sipmabubble_3 [Arg_0+1-Arg_1 ]
eval_sipmabubble_4 [Arg_0+1-Arg_1 ]
eval_sipmabubble_bb1_in [Arg_0+1 ]
eval_sipmabubble_bb2_in [Arg_0+1-Arg_1 ]
eval_sipmabubble_bb4_in [Arg_0+1-Arg_1 ]
eval_sipmabubble_bb3_in [Arg_0+1-Arg_1 ]
eval_sipmabubble_2 [Arg_0+1-Arg_1 ]

MPRF for transition 4:eval_sipmabubble_bb2_in(Arg_0,Arg_1,Arg_2) -> eval_sipmabubble_bb3_in(Arg_0,Arg_1,Arg_2):|:0<=Arg_2 && 0<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 0<=Arg_0+Arg_2 && Arg_0<=Arg_2 && Arg_1<=Arg_0 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=Arg_0 && Arg_1+1<=Arg_0 of depth 1:

new bound:

Arg_2*Arg_2+4*Arg_2+3 {O(n^2)}

MPRF:

eval_sipmabubble_3 [Arg_0-Arg_1 ]
eval_sipmabubble_4 [Arg_0-Arg_1 ]
eval_sipmabubble_bb1_in [Arg_0+1 ]
eval_sipmabubble_bb2_in [Arg_0+1-Arg_1 ]
eval_sipmabubble_bb4_in [1 ]
eval_sipmabubble_bb3_in [Arg_0-Arg_1 ]
eval_sipmabubble_2 [Arg_0-Arg_1 ]

MPRF for transition 6:eval_sipmabubble_bb3_in(Arg_0,Arg_1,Arg_2) -> eval_sipmabubble_2(Arg_0,Arg_1,Arg_2):|:1<=Arg_2 && 1<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 2<=Arg_0+Arg_2 && Arg_0<=Arg_2 && 1+Arg_1<=Arg_0 && 0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 of depth 1:

new bound:

Arg_2*Arg_2+3*Arg_2+2 {O(n^2)}

MPRF:

eval_sipmabubble_3 [Arg_2-Arg_1 ]
eval_sipmabubble_4 [Arg_2-Arg_1 ]
eval_sipmabubble_bb1_in [Arg_2+1 ]
eval_sipmabubble_bb2_in [Arg_2+1-Arg_1 ]
eval_sipmabubble_bb4_in [Arg_2+1-Arg_1 ]
eval_sipmabubble_bb3_in [Arg_2+1-Arg_1 ]
eval_sipmabubble_2 [Arg_2-Arg_1 ]

Analysing control-flow refined program

Found invariant 0<=Arg_2 && 0<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 0<=Arg_0+Arg_2 && Arg_0<=Arg_2 && Arg_1<=Arg_0 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 0<=Arg_0 for location eval_sipmabubble_bb4_in

Found invariant Arg_0<=Arg_2 && 1+Arg_0<=0 for location eval_sipmabubble_stop

Found invariant 2<=Arg_2 && 3<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 4<=Arg_0+Arg_2 && Arg_0<=Arg_2 && 1+Arg_1<=Arg_0 && 1<=Arg_1 && 3<=Arg_0+Arg_1 && 2<=Arg_0 for location n_eval_sipmabubble_3___2

Found invariant 1<=Arg_2 && 1<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 2<=Arg_0+Arg_2 && Arg_0<=Arg_2 && Arg_1<=0 && 1+Arg_1<=Arg_0 && 0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 for location n_eval_sipmabubble_bb3_in___9

Found invariant 1<=Arg_2 && 1<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 2<=Arg_0+Arg_2 && Arg_0<=Arg_2 && Arg_1<=0 && 1+Arg_1<=Arg_0 && 0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 for location n_eval_sipmabubble_2___8

Found invariant 1<=Arg_2 && 2<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 2<=Arg_0+Arg_2 && Arg_0<=Arg_2 && Arg_1<=Arg_0 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 for location n_eval_sipmabubble_bb2_in___5

Found invariant 0<=Arg_2 && 0<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 0<=Arg_0+Arg_2 && Arg_0<=Arg_2 && Arg_1<=0 && Arg_1<=Arg_0 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=Arg_0 for location eval_sipmabubble_bb2_in

Found invariant 2<=Arg_2 && 3<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 4<=Arg_0+Arg_2 && Arg_0<=Arg_2 && 1+Arg_1<=Arg_0 && 1<=Arg_1 && 3<=Arg_0+Arg_1 && 2<=Arg_0 for location n_eval_sipmabubble_4___1

Found invariant 2<=Arg_2 && 3<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 4<=Arg_0+Arg_2 && Arg_0<=Arg_2 && 1+Arg_1<=Arg_0 && 1<=Arg_1 && 3<=Arg_0+Arg_1 && 2<=Arg_0 for location n_eval_sipmabubble_bb3_in___4

Found invariant Arg_0<=Arg_2 for location eval_sipmabubble_bb1_in

Found invariant Arg_0<=Arg_2 && 1+Arg_0<=0 for location eval_sipmabubble_bb5_in

Found invariant 1<=Arg_2 && 1<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 2<=Arg_0+Arg_2 && Arg_0<=Arg_2 && Arg_1<=0 && 1+Arg_1<=Arg_0 && 0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 for location n_eval_sipmabubble_4___6

Found invariant 2<=Arg_2 && 3<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 4<=Arg_0+Arg_2 && Arg_0<=Arg_2 && 1+Arg_1<=Arg_0 && 1<=Arg_1 && 3<=Arg_0+Arg_1 && 2<=Arg_0 for location n_eval_sipmabubble_2___3

Found invariant 1<=Arg_2 && 1<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 2<=Arg_0+Arg_2 && Arg_0<=Arg_2 && Arg_1<=0 && 1+Arg_1<=Arg_0 && 0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 for location n_eval_sipmabubble_3___7

knowledge_propagation leads to new time bound Arg_2+1 {O(n)} for transition 91:eval_sipmabubble_bb2_in(Arg_0,Arg_1,Arg_2) -> n_eval_sipmabubble_bb3_in___9(Arg_0,Arg_1,Arg_2):|:0<=Arg_2 && 0<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 0<=Arg_0+Arg_2 && Arg_0<=Arg_2 && Arg_1<=0 && Arg_1<=Arg_0 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=Arg_0 && Arg_0<=Arg_2 && 0<=Arg_1 && Arg_1<=0 && 0<=Arg_1 && 0<=Arg_0 && Arg_0<=Arg_2 && 0<=Arg_1 && 1+Arg_1<=Arg_0 && Arg_0<=Arg_2

knowledge_propagation leads to new time bound Arg_2+1 {O(n)} for transition 94:n_eval_sipmabubble_bb3_in___9(Arg_0,Arg_1,Arg_2) -> n_eval_sipmabubble_2___8(Arg_0,Arg_1,Arg_2):|:1<=Arg_2 && 1<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 2<=Arg_0+Arg_2 && Arg_0<=Arg_2 && Arg_1<=0 && 1+Arg_1<=Arg_0 && 0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 && Arg_0<=Arg_2 && 1<=Arg_0 && Arg_1<=0 && 0<=Arg_1 && 0<=Arg_1 && 1+Arg_1<=Arg_0 && Arg_0<=Arg_2

knowledge_propagation leads to new time bound Arg_2+1 {O(n)} for transition 86:n_eval_sipmabubble_2___8(Arg_0,Arg_1,Arg_2) -> n_eval_sipmabubble_3___7(Arg_0,Arg_1,Arg_2):|:1<=Arg_2 && 1<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 2<=Arg_0+Arg_2 && Arg_0<=Arg_2 && Arg_1<=0 && 1+Arg_1<=Arg_0 && 0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 && Arg_0<=Arg_2 && 1<=Arg_0 && Arg_1<=0 && 0<=Arg_1 && 0<=Arg_1 && 1+Arg_1<=Arg_0 && Arg_0<=Arg_2

knowledge_propagation leads to new time bound Arg_2+1 {O(n)} for transition 88:n_eval_sipmabubble_3___7(Arg_0,Arg_1,Arg_2) -> n_eval_sipmabubble_4___6(Arg_0,Arg_1,Arg_2):|:1<=Arg_2 && 1<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 2<=Arg_0+Arg_2 && Arg_0<=Arg_2 && Arg_1<=0 && 1+Arg_1<=Arg_0 && 0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 && Arg_0<=Arg_2 && 1<=Arg_0 && Arg_1<=0 && 0<=Arg_1 && 0<=Arg_1 && 1+Arg_1<=Arg_0 && Arg_0<=Arg_2

knowledge_propagation leads to new time bound Arg_2+1 {O(n)} for transition 90:n_eval_sipmabubble_4___6(Arg_0,Arg_1,Arg_2) -> n_eval_sipmabubble_bb2_in___5(Arg_0,Arg_1+1,Arg_2):|:1<=Arg_2 && 1<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 2<=Arg_0+Arg_2 && Arg_0<=Arg_2 && Arg_1<=0 && 1+Arg_1<=Arg_0 && 0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 && Arg_0<=Arg_2 && 1<=Arg_0 && Arg_1<=0 && 0<=Arg_1 && 0<=Arg_1 && 1+Arg_1<=Arg_0 && Arg_0<=Arg_2

MPRF for transition 85:n_eval_sipmabubble_2___3(Arg_0,Arg_1,Arg_2) -> n_eval_sipmabubble_3___2(Arg_0,Arg_1,Arg_2):|:2<=Arg_2 && 3<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 4<=Arg_0+Arg_2 && Arg_0<=Arg_2 && 1+Arg_1<=Arg_0 && 1<=Arg_1 && 3<=Arg_0+Arg_1 && 2<=Arg_0 && Arg_0<=Arg_2 && 1+Arg_1<=Arg_0 && 1<=Arg_1 && 0<=Arg_1 && 1+Arg_1<=Arg_0 && Arg_0<=Arg_2 of depth 1:

new bound:

Arg_2*Arg_2+2*Arg_2+1 {O(n^2)}

MPRF:

eval_sipmabubble_bb2_in [0 ]
n_eval_sipmabubble_bb3_in___9 [0 ]
eval_sipmabubble_bb1_in [0 ]
n_eval_sipmabubble_2___8 [Arg_0 ]
n_eval_sipmabubble_3___2 [Arg_0-Arg_1-1 ]
n_eval_sipmabubble_3___7 [Arg_0 ]
n_eval_sipmabubble_4___1 [Arg_0-Arg_1-1 ]
n_eval_sipmabubble_4___6 [Arg_0 ]
n_eval_sipmabubble_bb2_in___5 [Arg_0-Arg_1 ]
eval_sipmabubble_bb4_in [0 ]
n_eval_sipmabubble_bb3_in___4 [Arg_0-Arg_1 ]
n_eval_sipmabubble_2___3 [Arg_0-Arg_1 ]

MPRF for transition 87:n_eval_sipmabubble_3___2(Arg_0,Arg_1,Arg_2) -> n_eval_sipmabubble_4___1(Arg_0,Arg_1,Arg_2):|:2<=Arg_2 && 3<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 4<=Arg_0+Arg_2 && Arg_0<=Arg_2 && 1+Arg_1<=Arg_0 && 1<=Arg_1 && 3<=Arg_0+Arg_1 && 2<=Arg_0 && Arg_0<=Arg_2 && 1+Arg_1<=Arg_0 && 1<=Arg_1 && 0<=Arg_1 && 1+Arg_1<=Arg_0 && Arg_0<=Arg_2 of depth 1:

new bound:

Arg_2*Arg_2+2*Arg_2+1 {O(n^2)}

MPRF:

eval_sipmabubble_bb2_in [0 ]
n_eval_sipmabubble_bb3_in___9 [0 ]
eval_sipmabubble_bb1_in [0 ]
n_eval_sipmabubble_2___8 [Arg_0 ]
n_eval_sipmabubble_3___2 [Arg_0-Arg_1 ]
n_eval_sipmabubble_3___7 [Arg_0 ]
n_eval_sipmabubble_4___1 [Arg_0-Arg_1-1 ]
n_eval_sipmabubble_4___6 [Arg_0 ]
n_eval_sipmabubble_bb2_in___5 [Arg_0-Arg_1 ]
eval_sipmabubble_bb4_in [0 ]
n_eval_sipmabubble_bb3_in___4 [Arg_0-Arg_1 ]
n_eval_sipmabubble_2___3 [Arg_0-Arg_1 ]

MPRF for transition 89:n_eval_sipmabubble_4___1(Arg_0,Arg_1,Arg_2) -> n_eval_sipmabubble_bb2_in___5(Arg_0,Arg_1+1,Arg_2):|:2<=Arg_2 && 3<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 4<=Arg_0+Arg_2 && Arg_0<=Arg_2 && 1+Arg_1<=Arg_0 && 1<=Arg_1 && 3<=Arg_0+Arg_1 && 2<=Arg_0 && Arg_0<=Arg_2 && 1+Arg_1<=Arg_0 && 1<=Arg_1 && 0<=Arg_1 && 1+Arg_1<=Arg_0 && Arg_0<=Arg_2 of depth 1:

new bound:

2*Arg_2*Arg_2+4*Arg_2+1 {O(n^2)}

MPRF:

eval_sipmabubble_bb2_in [Arg_2 ]
n_eval_sipmabubble_bb3_in___9 [Arg_2 ]
eval_sipmabubble_bb1_in [Arg_2 ]
n_eval_sipmabubble_2___8 [Arg_0+Arg_2 ]
n_eval_sipmabubble_3___2 [Arg_0+Arg_2+1-Arg_1 ]
n_eval_sipmabubble_3___7 [Arg_0+Arg_2 ]
n_eval_sipmabubble_4___1 [Arg_0+Arg_2+1-Arg_1 ]
n_eval_sipmabubble_4___6 [Arg_0+Arg_2 ]
n_eval_sipmabubble_bb2_in___5 [Arg_0+Arg_2+1-Arg_1 ]
eval_sipmabubble_bb4_in [Arg_2 ]
n_eval_sipmabubble_bb3_in___4 [Arg_0+Arg_2+1-Arg_1 ]
n_eval_sipmabubble_2___3 [Arg_0+Arg_2+1-Arg_1 ]

MPRF for transition 92:n_eval_sipmabubble_bb2_in___5(Arg_0,Arg_1,Arg_2) -> n_eval_sipmabubble_bb3_in___4(Arg_0,Arg_1,Arg_2):|:1<=Arg_2 && 2<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 2<=Arg_0+Arg_2 && Arg_0<=Arg_2 && Arg_1<=Arg_0 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 && Arg_0<=Arg_2 && 0<=Arg_1 && 1<=Arg_1 && Arg_1<=Arg_0 && Arg_0<=Arg_2 && 0<=Arg_1 && 1+Arg_1<=Arg_0 && Arg_0<=Arg_2 of depth 1:

new bound:

2*Arg_2*Arg_2+4*Arg_2+1 {O(n^2)}

MPRF:

eval_sipmabubble_bb2_in [Arg_2 ]
n_eval_sipmabubble_bb3_in___9 [Arg_2 ]
eval_sipmabubble_bb1_in [Arg_2 ]
n_eval_sipmabubble_2___8 [Arg_0+Arg_2 ]
n_eval_sipmabubble_3___2 [Arg_0+Arg_2-Arg_1-1 ]
n_eval_sipmabubble_3___7 [Arg_0+Arg_2 ]
n_eval_sipmabubble_4___1 [Arg_0+Arg_2-Arg_1-1 ]
n_eval_sipmabubble_4___6 [Arg_0+Arg_2 ]
n_eval_sipmabubble_bb2_in___5 [Arg_0+Arg_2-Arg_1 ]
eval_sipmabubble_bb4_in [Arg_2 ]
n_eval_sipmabubble_bb3_in___4 [Arg_0+Arg_2-Arg_1-1 ]
n_eval_sipmabubble_2___3 [Arg_0+Arg_2-Arg_1-1 ]

MPRF for transition 102:n_eval_sipmabubble_bb2_in___5(Arg_0,Arg_1,Arg_2) -> eval_sipmabubble_bb4_in(Arg_0,Arg_1,Arg_2):|:1<=Arg_2 && 2<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 2<=Arg_0+Arg_2 && Arg_0<=Arg_2 && Arg_1<=Arg_0 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 && 0<=Arg_2 && 0<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 0<=Arg_0+Arg_2 && Arg_0<=Arg_2 && Arg_1<=Arg_0 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=Arg_0 && Arg_0<1+Arg_1 of depth 1:

new bound:

2*Arg_2 {O(n)}

MPRF:

eval_sipmabubble_bb2_in [Arg_0+Arg_2 ]
eval_sipmabubble_bb1_in [Arg_0+Arg_2 ]
n_eval_sipmabubble_3___2 [Arg_0+Arg_2 ]
n_eval_sipmabubble_3___7 [Arg_0+Arg_2 ]
n_eval_sipmabubble_4___1 [Arg_0+Arg_2 ]
n_eval_sipmabubble_4___6 [Arg_0+Arg_2 ]
n_eval_sipmabubble_bb2_in___5 [Arg_0+Arg_2 ]
eval_sipmabubble_bb4_in [Arg_0+Arg_2-1 ]
n_eval_sipmabubble_bb3_in___4 [Arg_0+Arg_2 ]
n_eval_sipmabubble_2___3 [Arg_0+Arg_2 ]
n_eval_sipmabubble_bb3_in___9 [Arg_0+Arg_2 ]
n_eval_sipmabubble_2___8 [Arg_0+Arg_2 ]

MPRF for transition 93:n_eval_sipmabubble_bb3_in___4(Arg_0,Arg_1,Arg_2) -> n_eval_sipmabubble_2___3(Arg_0,Arg_1,Arg_2):|:2<=Arg_2 && 3<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 4<=Arg_0+Arg_2 && Arg_0<=Arg_2 && 1+Arg_1<=Arg_0 && 1<=Arg_1 && 3<=Arg_0+Arg_1 && 2<=Arg_0 && Arg_0<=Arg_2 && 1+Arg_1<=Arg_0 && 1<=Arg_1 && 0<=Arg_1 && 1+Arg_1<=Arg_0 && Arg_0<=Arg_2 of depth 1:

new bound:

Arg_2*Arg_2+2*Arg_2+1 {O(n^2)}

MPRF:

eval_sipmabubble_bb2_in [0 ]
n_eval_sipmabubble_bb3_in___9 [0 ]
eval_sipmabubble_bb1_in [0 ]
n_eval_sipmabubble_2___8 [Arg_0 ]
n_eval_sipmabubble_3___2 [Arg_0-Arg_1-1 ]
n_eval_sipmabubble_3___7 [Arg_0 ]
n_eval_sipmabubble_4___1 [Arg_0-Arg_1-1 ]
n_eval_sipmabubble_4___6 [Arg_0 ]
n_eval_sipmabubble_bb2_in___5 [Arg_0-Arg_1 ]
eval_sipmabubble_bb4_in [0 ]
n_eval_sipmabubble_bb3_in___4 [Arg_0-Arg_1 ]
n_eval_sipmabubble_2___3 [Arg_0-Arg_1-1 ]

CFR did not improve the program. Rolling back

All Bounds

Timebounds

Overall timebound:5*Arg_2*Arg_2+20*Arg_2+19 {O(n^2)}
8: eval_sipmabubble_2->eval_sipmabubble_3: Arg_2*Arg_2+3*Arg_2+2 {O(n^2)}
10: eval_sipmabubble_3->eval_sipmabubble_4: Arg_2*Arg_2+3*Arg_2+2 {O(n^2)}
11: eval_sipmabubble_4->eval_sipmabubble_bb2_in: Arg_2*Arg_2+4*Arg_2+3 {O(n^2)}
1: eval_sipmabubble_bb0_in->eval_sipmabubble_bb1_in: 1 {O(1)}
2: eval_sipmabubble_bb1_in->eval_sipmabubble_bb2_in: Arg_2+1 {O(n)}
3: eval_sipmabubble_bb1_in->eval_sipmabubble_bb5_in: 1 {O(1)}
4: eval_sipmabubble_bb2_in->eval_sipmabubble_bb3_in: Arg_2*Arg_2+4*Arg_2+3 {O(n^2)}
5: eval_sipmabubble_bb2_in->eval_sipmabubble_bb4_in: Arg_2+1 {O(n)}
6: eval_sipmabubble_bb3_in->eval_sipmabubble_2: Arg_2*Arg_2+3*Arg_2+2 {O(n^2)}
12: eval_sipmabubble_bb4_in->eval_sipmabubble_bb1_in: Arg_2+1 {O(n)}
13: eval_sipmabubble_bb5_in->eval_sipmabubble_stop: 1 {O(1)}
0: eval_sipmabubble_start->eval_sipmabubble_bb0_in: 1 {O(1)}

Costbounds

Overall costbound: 5*Arg_2*Arg_2+20*Arg_2+19 {O(n^2)}
8: eval_sipmabubble_2->eval_sipmabubble_3: Arg_2*Arg_2+3*Arg_2+2 {O(n^2)}
10: eval_sipmabubble_3->eval_sipmabubble_4: Arg_2*Arg_2+3*Arg_2+2 {O(n^2)}
11: eval_sipmabubble_4->eval_sipmabubble_bb2_in: Arg_2*Arg_2+4*Arg_2+3 {O(n^2)}
1: eval_sipmabubble_bb0_in->eval_sipmabubble_bb1_in: 1 {O(1)}
2: eval_sipmabubble_bb1_in->eval_sipmabubble_bb2_in: Arg_2+1 {O(n)}
3: eval_sipmabubble_bb1_in->eval_sipmabubble_bb5_in: 1 {O(1)}
4: eval_sipmabubble_bb2_in->eval_sipmabubble_bb3_in: Arg_2*Arg_2+4*Arg_2+3 {O(n^2)}
5: eval_sipmabubble_bb2_in->eval_sipmabubble_bb4_in: Arg_2+1 {O(n)}
6: eval_sipmabubble_bb3_in->eval_sipmabubble_2: Arg_2*Arg_2+3*Arg_2+2 {O(n^2)}
12: eval_sipmabubble_bb4_in->eval_sipmabubble_bb1_in: Arg_2+1 {O(n)}
13: eval_sipmabubble_bb5_in->eval_sipmabubble_stop: 1 {O(1)}
0: eval_sipmabubble_start->eval_sipmabubble_bb0_in: 1 {O(1)}

Sizebounds

8: eval_sipmabubble_2->eval_sipmabubble_3, Arg_0: Arg_2+1 {O(n)}
8: eval_sipmabubble_2->eval_sipmabubble_3, Arg_1: Arg_2*Arg_2+4*Arg_2+3 {O(n^2)}
8: eval_sipmabubble_2->eval_sipmabubble_3, Arg_2: Arg_2 {O(n)}
10: eval_sipmabubble_3->eval_sipmabubble_4, Arg_0: Arg_2+1 {O(n)}
10: eval_sipmabubble_3->eval_sipmabubble_4, Arg_1: Arg_2*Arg_2+4*Arg_2+3 {O(n^2)}
10: eval_sipmabubble_3->eval_sipmabubble_4, Arg_2: Arg_2 {O(n)}
11: eval_sipmabubble_4->eval_sipmabubble_bb2_in, Arg_0: Arg_2+1 {O(n)}
11: eval_sipmabubble_4->eval_sipmabubble_bb2_in, Arg_1: Arg_2*Arg_2+4*Arg_2+3 {O(n^2)}
11: eval_sipmabubble_4->eval_sipmabubble_bb2_in, Arg_2: Arg_2 {O(n)}
1: eval_sipmabubble_bb0_in->eval_sipmabubble_bb1_in, Arg_0: Arg_2 {O(n)}
1: eval_sipmabubble_bb0_in->eval_sipmabubble_bb1_in, Arg_1: Arg_1 {O(n)}
1: eval_sipmabubble_bb0_in->eval_sipmabubble_bb1_in, Arg_2: Arg_2 {O(n)}
2: eval_sipmabubble_bb1_in->eval_sipmabubble_bb2_in, Arg_0: Arg_2+1 {O(n)}
2: eval_sipmabubble_bb1_in->eval_sipmabubble_bb2_in, Arg_1: 0 {O(1)}
2: eval_sipmabubble_bb1_in->eval_sipmabubble_bb2_in, Arg_2: Arg_2 {O(n)}
3: eval_sipmabubble_bb1_in->eval_sipmabubble_bb5_in, Arg_0: 2*Arg_2+1 {O(n)}
3: eval_sipmabubble_bb1_in->eval_sipmabubble_bb5_in, Arg_1: Arg_2*Arg_2+4*Arg_2+Arg_1+3 {O(n^2)}
3: eval_sipmabubble_bb1_in->eval_sipmabubble_bb5_in, Arg_2: 2*Arg_2 {O(n)}
4: eval_sipmabubble_bb2_in->eval_sipmabubble_bb3_in, Arg_0: Arg_2+1 {O(n)}
4: eval_sipmabubble_bb2_in->eval_sipmabubble_bb3_in, Arg_1: Arg_2*Arg_2+4*Arg_2+3 {O(n^2)}
4: eval_sipmabubble_bb2_in->eval_sipmabubble_bb3_in, Arg_2: Arg_2 {O(n)}
5: eval_sipmabubble_bb2_in->eval_sipmabubble_bb4_in, Arg_0: Arg_2+1 {O(n)}
5: eval_sipmabubble_bb2_in->eval_sipmabubble_bb4_in, Arg_1: Arg_2*Arg_2+4*Arg_2+3 {O(n^2)}
5: eval_sipmabubble_bb2_in->eval_sipmabubble_bb4_in, Arg_2: Arg_2 {O(n)}
6: eval_sipmabubble_bb3_in->eval_sipmabubble_2, Arg_0: Arg_2+1 {O(n)}
6: eval_sipmabubble_bb3_in->eval_sipmabubble_2, Arg_1: Arg_2*Arg_2+4*Arg_2+3 {O(n^2)}
6: eval_sipmabubble_bb3_in->eval_sipmabubble_2, Arg_2: Arg_2 {O(n)}
12: eval_sipmabubble_bb4_in->eval_sipmabubble_bb1_in, Arg_0: Arg_2+1 {O(n)}
12: eval_sipmabubble_bb4_in->eval_sipmabubble_bb1_in, Arg_1: Arg_2*Arg_2+4*Arg_2+3 {O(n^2)}
12: eval_sipmabubble_bb4_in->eval_sipmabubble_bb1_in, Arg_2: Arg_2 {O(n)}
13: eval_sipmabubble_bb5_in->eval_sipmabubble_stop, Arg_0: 2*Arg_2+1 {O(n)}
13: eval_sipmabubble_bb5_in->eval_sipmabubble_stop, Arg_1: Arg_2*Arg_2+4*Arg_2+Arg_1+3 {O(n^2)}
13: eval_sipmabubble_bb5_in->eval_sipmabubble_stop, Arg_2: 2*Arg_2 {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)}