Initial Problem

Start: n_eval_jama_ex1_start
Program_Vars: Arg_0, Arg_1, Arg_2
Temp_Vars:
Locations: n_eval_jama_ex1_bb0_in___18, n_eval_jama_ex1_bb1_in___10, n_eval_jama_ex1_bb1_in___17, n_eval_jama_ex1_bb1_in___6, n_eval_jama_ex1_bb2_in___13, n_eval_jama_ex1_bb2_in___16, n_eval_jama_ex1_bb2_in___5, n_eval_jama_ex1_bb2_in___9, n_eval_jama_ex1_bb3_in___12, n_eval_jama_ex1_bb3_in___14, n_eval_jama_ex1_bb4_in___11, n_eval_jama_ex1_bb4_in___7, n_eval_jama_ex1_bb5_in___15, n_eval_jama_ex1_bb5_in___4, n_eval_jama_ex1_bb5_in___8, n_eval_jama_ex1_start, n_eval_jama_ex1_stop___1, n_eval_jama_ex1_stop___2, n_eval_jama_ex1_stop___3
Transitions:
0:n_eval_jama_ex1_bb0_in___18(Arg_0,Arg_1,Arg_2) -> n_eval_jama_ex1_bb1_in___17(1,Arg_1,Arg_2)
1:n_eval_jama_ex1_bb1_in___10(Arg_0,Arg_1,Arg_2) -> n_eval_jama_ex1_bb2_in___9(Arg_0,1,Arg_2):|:Arg_0<=Arg_2
2:n_eval_jama_ex1_bb1_in___10(Arg_0,Arg_1,Arg_2) -> n_eval_jama_ex1_bb5_in___8(Arg_0,Arg_1,Arg_2):|:Arg_2<Arg_0
3:n_eval_jama_ex1_bb1_in___17(Arg_0,Arg_1,Arg_2) -> n_eval_jama_ex1_bb2_in___16(Arg_0,1,Arg_2):|:Arg_0<=1 && 1<=Arg_0 && Arg_0<=Arg_2
4:n_eval_jama_ex1_bb1_in___17(Arg_0,Arg_1,Arg_2) -> n_eval_jama_ex1_bb5_in___15(Arg_0,Arg_1,Arg_2):|:Arg_0<=1 && 1<=Arg_0 && Arg_2<Arg_0
5:n_eval_jama_ex1_bb1_in___6(Arg_0,Arg_1,Arg_2) -> n_eval_jama_ex1_bb2_in___5(Arg_0,1,Arg_2):|:Arg_2<1 && Arg_0<=Arg_2
6:n_eval_jama_ex1_bb1_in___6(Arg_0,Arg_1,Arg_2) -> n_eval_jama_ex1_bb5_in___4(Arg_0,Arg_1,Arg_2):|:Arg_2<1 && Arg_2<Arg_0
7:n_eval_jama_ex1_bb2_in___13(Arg_0,Arg_1,Arg_2) -> n_eval_jama_ex1_bb3_in___12(Arg_0,Arg_1,Arg_2):|:Arg_1<=Arg_2
8:n_eval_jama_ex1_bb2_in___13(Arg_0,Arg_1,Arg_2) -> n_eval_jama_ex1_bb4_in___11(Arg_0,Arg_1,Arg_2):|:Arg_2<Arg_1
9:n_eval_jama_ex1_bb2_in___16(Arg_0,Arg_1,Arg_2) -> n_eval_jama_ex1_bb3_in___14(Arg_0,Arg_1,Arg_2):|:Arg_1<=Arg_2 && Arg_1<=1 && 1<=Arg_1 && Arg_0<=Arg_2 && Arg_1<=Arg_2 && Arg_1<=Arg_2
10:n_eval_jama_ex1_bb2_in___5(Arg_0,Arg_1,Arg_2) -> n_eval_jama_ex1_bb4_in___7(Arg_0,Arg_1,Arg_2):|:Arg_2<Arg_1 && Arg_1<=1 && 1<=Arg_1 && Arg_0<=Arg_2 && Arg_2<Arg_1
11:n_eval_jama_ex1_bb2_in___9(Arg_0,Arg_1,Arg_2) -> n_eval_jama_ex1_bb3_in___14(Arg_0,Arg_1,Arg_2):|:Arg_1<=1 && 1<=Arg_1 && Arg_0<=Arg_2 && Arg_1<=Arg_2
12:n_eval_jama_ex1_bb2_in___9(Arg_0,Arg_1,Arg_2) -> n_eval_jama_ex1_bb4_in___7(Arg_0,Arg_1,Arg_2):|:Arg_1<=1 && 1<=Arg_1 && Arg_0<=Arg_2 && Arg_2<Arg_1
13:n_eval_jama_ex1_bb3_in___12(Arg_0,Arg_1,Arg_2) -> n_eval_jama_ex1_bb2_in___13(Arg_0,Arg_1+1,Arg_2):|:Arg_1<=Arg_2
14:n_eval_jama_ex1_bb3_in___14(Arg_0,Arg_1,Arg_2) -> n_eval_jama_ex1_bb2_in___13(Arg_0,Arg_1+1,Arg_2):|:Arg_0<=Arg_2 && 1<=Arg_2 && Arg_1<=1 && 1<=Arg_1
15:n_eval_jama_ex1_bb4_in___11(Arg_0,Arg_1,Arg_2) -> n_eval_jama_ex1_bb1_in___10(Arg_0+1,Arg_1,Arg_2):|:Arg_2<Arg_1
16:n_eval_jama_ex1_bb4_in___7(Arg_0,Arg_1,Arg_2) -> n_eval_jama_ex1_bb1_in___6(Arg_0+1,Arg_1,Arg_2):|:Arg_2<1 && Arg_0<=Arg_2 && Arg_1<=1 && 1<=Arg_1
17:n_eval_jama_ex1_bb5_in___15(Arg_0,Arg_1,Arg_2) -> n_eval_jama_ex1_stop___1(Arg_0,Arg_1,Arg_2):|:Arg_2<1 && Arg_0<=1 && 1<=Arg_0
18:n_eval_jama_ex1_bb5_in___4(Arg_0,Arg_1,Arg_2) -> n_eval_jama_ex1_stop___3(Arg_0,Arg_1,Arg_2):|:Arg_2<1 && Arg_2<Arg_0
19:n_eval_jama_ex1_bb5_in___8(Arg_0,Arg_1,Arg_2) -> n_eval_jama_ex1_stop___2(Arg_0,Arg_1,Arg_2):|:Arg_2<Arg_0
20:n_eval_jama_ex1_start(Arg_0,Arg_1,Arg_2) -> n_eval_jama_ex1_bb0_in___18(Arg_0,Arg_1,Arg_2)

Preprocessing

Found invariant Arg_0<=1 && 1<=Arg_0 for location n_eval_jama_ex1_bb1_in___17

Found invariant 1<=0 for location n_eval_jama_ex1_bb1_in___6

Found invariant 1<=0 for location n_eval_jama_ex1_bb4_in___7

Found invariant 1+Arg_2<=Arg_1 && 1+Arg_2<=Arg_0 && 1<=Arg_2 && 3<=Arg_1+Arg_2 && Arg_1<=1+Arg_2 && 3<=Arg_0+Arg_2 && Arg_1<=Arg_0 && 2<=Arg_1 && 4<=Arg_0+Arg_1 && 2<=Arg_0 for location n_eval_jama_ex1_bb5_in___8

Found invariant Arg_2<=0 && 1+Arg_2<=Arg_0 && Arg_0+Arg_2<=1 && Arg_0<=1 && 1<=Arg_0 for location n_eval_jama_ex1_bb5_in___15

Found invariant 1<=Arg_2 && 3<=Arg_1+Arg_2 && Arg_1<=1+Arg_2 && 2<=Arg_0+Arg_2 && 2<=Arg_1 && 3<=Arg_0+Arg_1 && 1<=Arg_0 for location n_eval_jama_ex1_bb2_in___13

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<=1 && Arg_1<=Arg_0 && Arg_0+Arg_1<=2 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && Arg_0<=Arg_1 && Arg_0<=1 && 1<=Arg_0 for location n_eval_jama_ex1_bb2_in___16

Found invariant 1<=0 for location n_eval_jama_ex1_bb2_in___5

Found invariant 1<=0 for location n_eval_jama_ex1_bb5_in___4

Found invariant 1<=0 for location n_eval_jama_ex1_stop___3

Found invariant 1+Arg_2<=Arg_1 && 1<=Arg_2 && 3<=Arg_1+Arg_2 && Arg_1<=1+Arg_2 && 3<=Arg_0+Arg_2 && 2<=Arg_1 && 4<=Arg_0+Arg_1 && 2<=Arg_0 for location n_eval_jama_ex1_bb1_in___10

Found invariant 2<=Arg_2 && 3<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 4<=Arg_0+Arg_2 && Arg_0<=Arg_2 && Arg_1<=1 && 1+Arg_1<=Arg_0 && 1<=Arg_1 && 3<=Arg_0+Arg_1 && 2<=Arg_0 for location n_eval_jama_ex1_bb2_in___9

Found invariant Arg_2<=0 && 1+Arg_2<=Arg_0 && Arg_0+Arg_2<=1 && Arg_0<=1 && 1<=Arg_0 for location n_eval_jama_ex1_stop___1

Found invariant 1+Arg_2<=Arg_1 && 1+Arg_2<=Arg_0 && 1<=Arg_2 && 3<=Arg_1+Arg_2 && Arg_1<=1+Arg_2 && 3<=Arg_0+Arg_2 && Arg_1<=Arg_0 && 2<=Arg_1 && 4<=Arg_0+Arg_1 && 2<=Arg_0 for location n_eval_jama_ex1_stop___2

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<=1 && Arg_1<=Arg_0 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 for location n_eval_jama_ex1_bb3_in___14

Found invariant 1+Arg_2<=Arg_1 && 1<=Arg_2 && 3<=Arg_1+Arg_2 && Arg_1<=1+Arg_2 && 2<=Arg_0+Arg_2 && 2<=Arg_1 && 3<=Arg_0+Arg_1 && 1<=Arg_0 for location n_eval_jama_ex1_bb4_in___11

Found invariant 2<=Arg_2 && 4<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 3<=Arg_0+Arg_2 && 2<=Arg_1 && 3<=Arg_0+Arg_1 && 1<=Arg_0 for location n_eval_jama_ex1_bb3_in___12

Cut unsatisfiable transition 5: n_eval_jama_ex1_bb1_in___6->n_eval_jama_ex1_bb2_in___5

Cut unsatisfiable transition 6: n_eval_jama_ex1_bb1_in___6->n_eval_jama_ex1_bb5_in___4

Cut unsatisfiable transition 10: n_eval_jama_ex1_bb2_in___5->n_eval_jama_ex1_bb4_in___7

Cut unsatisfiable transition 12: n_eval_jama_ex1_bb2_in___9->n_eval_jama_ex1_bb4_in___7

Cut unsatisfiable transition 16: n_eval_jama_ex1_bb4_in___7->n_eval_jama_ex1_bb1_in___6

Cut unsatisfiable transition 18: n_eval_jama_ex1_bb5_in___4->n_eval_jama_ex1_stop___3

Cut unreachable locations [n_eval_jama_ex1_bb1_in___6; n_eval_jama_ex1_bb2_in___5; n_eval_jama_ex1_bb4_in___7; n_eval_jama_ex1_bb5_in___4; n_eval_jama_ex1_stop___3] from the program graph

Problem after Preprocessing

Start: n_eval_jama_ex1_start
Program_Vars: Arg_0, Arg_1, Arg_2
Temp_Vars:
Locations: n_eval_jama_ex1_bb0_in___18, n_eval_jama_ex1_bb1_in___10, n_eval_jama_ex1_bb1_in___17, n_eval_jama_ex1_bb2_in___13, n_eval_jama_ex1_bb2_in___16, n_eval_jama_ex1_bb2_in___9, n_eval_jama_ex1_bb3_in___12, n_eval_jama_ex1_bb3_in___14, n_eval_jama_ex1_bb4_in___11, n_eval_jama_ex1_bb5_in___15, n_eval_jama_ex1_bb5_in___8, n_eval_jama_ex1_start, n_eval_jama_ex1_stop___1, n_eval_jama_ex1_stop___2
Transitions:
0:n_eval_jama_ex1_bb0_in___18(Arg_0,Arg_1,Arg_2) -> n_eval_jama_ex1_bb1_in___17(1,Arg_1,Arg_2)
1:n_eval_jama_ex1_bb1_in___10(Arg_0,Arg_1,Arg_2) -> n_eval_jama_ex1_bb2_in___9(Arg_0,1,Arg_2):|:1+Arg_2<=Arg_1 && 1<=Arg_2 && 3<=Arg_1+Arg_2 && Arg_1<=1+Arg_2 && 3<=Arg_0+Arg_2 && 2<=Arg_1 && 4<=Arg_0+Arg_1 && 2<=Arg_0 && Arg_0<=Arg_2
2:n_eval_jama_ex1_bb1_in___10(Arg_0,Arg_1,Arg_2) -> n_eval_jama_ex1_bb5_in___8(Arg_0,Arg_1,Arg_2):|:1+Arg_2<=Arg_1 && 1<=Arg_2 && 3<=Arg_1+Arg_2 && Arg_1<=1+Arg_2 && 3<=Arg_0+Arg_2 && 2<=Arg_1 && 4<=Arg_0+Arg_1 && 2<=Arg_0 && Arg_2<Arg_0
3:n_eval_jama_ex1_bb1_in___17(Arg_0,Arg_1,Arg_2) -> n_eval_jama_ex1_bb2_in___16(Arg_0,1,Arg_2):|:Arg_0<=1 && 1<=Arg_0 && Arg_0<=1 && 1<=Arg_0 && Arg_0<=Arg_2
4:n_eval_jama_ex1_bb1_in___17(Arg_0,Arg_1,Arg_2) -> n_eval_jama_ex1_bb5_in___15(Arg_0,Arg_1,Arg_2):|:Arg_0<=1 && 1<=Arg_0 && Arg_0<=1 && 1<=Arg_0 && Arg_2<Arg_0
7:n_eval_jama_ex1_bb2_in___13(Arg_0,Arg_1,Arg_2) -> n_eval_jama_ex1_bb3_in___12(Arg_0,Arg_1,Arg_2):|:1<=Arg_2 && 3<=Arg_1+Arg_2 && Arg_1<=1+Arg_2 && 2<=Arg_0+Arg_2 && 2<=Arg_1 && 3<=Arg_0+Arg_1 && 1<=Arg_0 && Arg_1<=Arg_2
8:n_eval_jama_ex1_bb2_in___13(Arg_0,Arg_1,Arg_2) -> n_eval_jama_ex1_bb4_in___11(Arg_0,Arg_1,Arg_2):|:1<=Arg_2 && 3<=Arg_1+Arg_2 && Arg_1<=1+Arg_2 && 2<=Arg_0+Arg_2 && 2<=Arg_1 && 3<=Arg_0+Arg_1 && 1<=Arg_0 && Arg_2<Arg_1
9:n_eval_jama_ex1_bb2_in___16(Arg_0,Arg_1,Arg_2) -> n_eval_jama_ex1_bb3_in___14(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<=1 && Arg_1<=Arg_0 && Arg_0+Arg_1<=2 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && Arg_0<=Arg_1 && Arg_0<=1 && 1<=Arg_0 && Arg_1<=Arg_2 && Arg_1<=1 && 1<=Arg_1 && Arg_0<=Arg_2 && Arg_1<=Arg_2 && Arg_1<=Arg_2
11:n_eval_jama_ex1_bb2_in___9(Arg_0,Arg_1,Arg_2) -> n_eval_jama_ex1_bb3_in___14(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 && Arg_1<=1 && 1+Arg_1<=Arg_0 && 1<=Arg_1 && 3<=Arg_0+Arg_1 && 2<=Arg_0 && Arg_1<=1 && 1<=Arg_1 && Arg_0<=Arg_2 && Arg_1<=Arg_2
13:n_eval_jama_ex1_bb3_in___12(Arg_0,Arg_1,Arg_2) -> n_eval_jama_ex1_bb2_in___13(Arg_0,Arg_1+1,Arg_2):|:2<=Arg_2 && 4<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 3<=Arg_0+Arg_2 && 2<=Arg_1 && 3<=Arg_0+Arg_1 && 1<=Arg_0 && Arg_1<=Arg_2
14:n_eval_jama_ex1_bb3_in___14(Arg_0,Arg_1,Arg_2) -> n_eval_jama_ex1_bb2_in___13(Arg_0,Arg_1+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<=1 && Arg_1<=Arg_0 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 && Arg_0<=Arg_2 && 1<=Arg_2 && Arg_1<=1 && 1<=Arg_1
15:n_eval_jama_ex1_bb4_in___11(Arg_0,Arg_1,Arg_2) -> n_eval_jama_ex1_bb1_in___10(Arg_0+1,Arg_1,Arg_2):|:1+Arg_2<=Arg_1 && 1<=Arg_2 && 3<=Arg_1+Arg_2 && Arg_1<=1+Arg_2 && 2<=Arg_0+Arg_2 && 2<=Arg_1 && 3<=Arg_0+Arg_1 && 1<=Arg_0 && Arg_2<Arg_1
17:n_eval_jama_ex1_bb5_in___15(Arg_0,Arg_1,Arg_2) -> n_eval_jama_ex1_stop___1(Arg_0,Arg_1,Arg_2):|:Arg_2<=0 && 1+Arg_2<=Arg_0 && Arg_0+Arg_2<=1 && Arg_0<=1 && 1<=Arg_0 && Arg_2<1 && Arg_0<=1 && 1<=Arg_0
19:n_eval_jama_ex1_bb5_in___8(Arg_0,Arg_1,Arg_2) -> n_eval_jama_ex1_stop___2(Arg_0,Arg_1,Arg_2):|:1+Arg_2<=Arg_1 && 1+Arg_2<=Arg_0 && 1<=Arg_2 && 3<=Arg_1+Arg_2 && Arg_1<=1+Arg_2 && 3<=Arg_0+Arg_2 && Arg_1<=Arg_0 && 2<=Arg_1 && 4<=Arg_0+Arg_1 && 2<=Arg_0 && Arg_2<Arg_0
20:n_eval_jama_ex1_start(Arg_0,Arg_1,Arg_2) -> n_eval_jama_ex1_bb0_in___18(Arg_0,Arg_1,Arg_2)

MPRF for transition 1:n_eval_jama_ex1_bb1_in___10(Arg_0,Arg_1,Arg_2) -> n_eval_jama_ex1_bb2_in___9(Arg_0,1,Arg_2):|:1+Arg_2<=Arg_1 && 1<=Arg_2 && 3<=Arg_1+Arg_2 && Arg_1<=1+Arg_2 && 3<=Arg_0+Arg_2 && 2<=Arg_1 && 4<=Arg_0+Arg_1 && 2<=Arg_0 && Arg_0<=Arg_2 of depth 1:

new bound:

Arg_2+1 {O(n)}

MPRF:

n_eval_jama_ex1_bb2_in___9 [Arg_2-Arg_0 ]
n_eval_jama_ex1_bb3_in___12 [Arg_2-Arg_0 ]
n_eval_jama_ex1_bb3_in___14 [Arg_2-Arg_0 ]
n_eval_jama_ex1_bb2_in___13 [Arg_2-Arg_0 ]
n_eval_jama_ex1_bb4_in___11 [Arg_2-Arg_0 ]
n_eval_jama_ex1_bb1_in___10 [Arg_2+1-Arg_0 ]

MPRF for transition 11:n_eval_jama_ex1_bb2_in___9(Arg_0,Arg_1,Arg_2) -> n_eval_jama_ex1_bb3_in___14(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 && Arg_1<=1 && 1+Arg_1<=Arg_0 && 1<=Arg_1 && 3<=Arg_0+Arg_1 && 2<=Arg_0 && Arg_1<=1 && 1<=Arg_1 && Arg_0<=Arg_2 && Arg_1<=Arg_2 of depth 1:

new bound:

Arg_2+1 {O(n)}

MPRF:

n_eval_jama_ex1_bb2_in___9 [Arg_2+1-Arg_0 ]
n_eval_jama_ex1_bb3_in___12 [Arg_2-Arg_0 ]
n_eval_jama_ex1_bb3_in___14 [Arg_2-Arg_0 ]
n_eval_jama_ex1_bb2_in___13 [Arg_2-Arg_0 ]
n_eval_jama_ex1_bb4_in___11 [Arg_2-Arg_0 ]
n_eval_jama_ex1_bb1_in___10 [Arg_2+1-Arg_0 ]

MPRF for transition 14:n_eval_jama_ex1_bb3_in___14(Arg_0,Arg_1,Arg_2) -> n_eval_jama_ex1_bb2_in___13(Arg_0,Arg_1+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<=1 && Arg_1<=Arg_0 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 && Arg_0<=Arg_2 && 1<=Arg_2 && Arg_1<=1 && 1<=Arg_1 of depth 1:

new bound:

2*Arg_2+1 {O(n)}

MPRF:

n_eval_jama_ex1_bb2_in___9 [2*Arg_2-Arg_0 ]
n_eval_jama_ex1_bb3_in___12 [2*Arg_2-Arg_0-1 ]
n_eval_jama_ex1_bb3_in___14 [2*Arg_2-Arg_0 ]
n_eval_jama_ex1_bb2_in___13 [2*Arg_2-Arg_0-1 ]
n_eval_jama_ex1_bb4_in___11 [2*Arg_2-Arg_0-1 ]
n_eval_jama_ex1_bb1_in___10 [2*Arg_2-Arg_0 ]

MPRF for transition 7:n_eval_jama_ex1_bb2_in___13(Arg_0,Arg_1,Arg_2) -> n_eval_jama_ex1_bb3_in___12(Arg_0,Arg_1,Arg_2):|:1<=Arg_2 && 3<=Arg_1+Arg_2 && Arg_1<=1+Arg_2 && 2<=Arg_0+Arg_2 && 2<=Arg_1 && 3<=Arg_0+Arg_1 && 1<=Arg_0 && Arg_1<=Arg_2 of depth 1:

new bound:

2*Arg_2*Arg_2+7*Arg_2+3 {O(n^2)}

MPRF:

n_eval_jama_ex1_bb2_in___9 [0 ]
n_eval_jama_ex1_bb3_in___14 [-Arg_1 ]
n_eval_jama_ex1_bb3_in___12 [Arg_2-Arg_1 ]
n_eval_jama_ex1_bb2_in___13 [Arg_2+1-Arg_1 ]
n_eval_jama_ex1_bb4_in___11 [0 ]
n_eval_jama_ex1_bb1_in___10 [0 ]

MPRF for transition 8:n_eval_jama_ex1_bb2_in___13(Arg_0,Arg_1,Arg_2) -> n_eval_jama_ex1_bb4_in___11(Arg_0,Arg_1,Arg_2):|:1<=Arg_2 && 3<=Arg_1+Arg_2 && Arg_1<=1+Arg_2 && 2<=Arg_0+Arg_2 && 2<=Arg_1 && 3<=Arg_0+Arg_1 && 1<=Arg_0 && Arg_2<Arg_1 of depth 1:

new bound:

2*Arg_2+1 {O(n)}

MPRF:

n_eval_jama_ex1_bb2_in___9 [1-Arg_1 ]
n_eval_jama_ex1_bb3_in___14 [0 ]
n_eval_jama_ex1_bb3_in___12 [1 ]
n_eval_jama_ex1_bb2_in___13 [1 ]
n_eval_jama_ex1_bb4_in___11 [0 ]
n_eval_jama_ex1_bb1_in___10 [0 ]

MPRF for transition 13:n_eval_jama_ex1_bb3_in___12(Arg_0,Arg_1,Arg_2) -> n_eval_jama_ex1_bb2_in___13(Arg_0,Arg_1+1,Arg_2):|:2<=Arg_2 && 4<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 3<=Arg_0+Arg_2 && 2<=Arg_1 && 3<=Arg_0+Arg_1 && 1<=Arg_0 && Arg_1<=Arg_2 of depth 1:

new bound:

2*Arg_2*Arg_2+7*Arg_2+3 {O(n^2)}

MPRF:

n_eval_jama_ex1_bb2_in___9 [-Arg_2 ]
n_eval_jama_ex1_bb3_in___14 [-Arg_2 ]
n_eval_jama_ex1_bb3_in___12 [Arg_2+1-Arg_1 ]
n_eval_jama_ex1_bb2_in___13 [Arg_2+1-Arg_1 ]
n_eval_jama_ex1_bb4_in___11 [Arg_2-Arg_1 ]
n_eval_jama_ex1_bb1_in___10 [-Arg_2 ]

MPRF for transition 15:n_eval_jama_ex1_bb4_in___11(Arg_0,Arg_1,Arg_2) -> n_eval_jama_ex1_bb1_in___10(Arg_0+1,Arg_1,Arg_2):|:1+Arg_2<=Arg_1 && 1<=Arg_2 && 3<=Arg_1+Arg_2 && Arg_1<=1+Arg_2 && 2<=Arg_0+Arg_2 && 2<=Arg_1 && 3<=Arg_0+Arg_1 && 1<=Arg_0 && Arg_2<Arg_1 of depth 1:

new bound:

2*Arg_2*Arg_2+3*Arg_2+1 {O(n^2)}

MPRF:

n_eval_jama_ex1_bb2_in___9 [Arg_2 ]
n_eval_jama_ex1_bb3_in___14 [Arg_2+2-2*Arg_1 ]
n_eval_jama_ex1_bb3_in___12 [Arg_2+1 ]
n_eval_jama_ex1_bb2_in___13 [Arg_2+1 ]
n_eval_jama_ex1_bb4_in___11 [Arg_1 ]
n_eval_jama_ex1_bb1_in___10 [Arg_2 ]

knowledge_propagation leads to new time bound 2*Arg_2+1 {O(n)} for transition 15:n_eval_jama_ex1_bb4_in___11(Arg_0,Arg_1,Arg_2) -> n_eval_jama_ex1_bb1_in___10(Arg_0+1,Arg_1,Arg_2):|:1+Arg_2<=Arg_1 && 1<=Arg_2 && 3<=Arg_1+Arg_2 && Arg_1<=1+Arg_2 && 2<=Arg_0+Arg_2 && 2<=Arg_1 && 3<=Arg_0+Arg_1 && 1<=Arg_0 && Arg_2<Arg_1

All Bounds

Timebounds

Overall timebound:4*Arg_2*Arg_2+22*Arg_2+19 {O(n^2)}
0: n_eval_jama_ex1_bb0_in___18->n_eval_jama_ex1_bb1_in___17: 1 {O(1)}
1: n_eval_jama_ex1_bb1_in___10->n_eval_jama_ex1_bb2_in___9: Arg_2+1 {O(n)}
2: n_eval_jama_ex1_bb1_in___10->n_eval_jama_ex1_bb5_in___8: 1 {O(1)}
3: n_eval_jama_ex1_bb1_in___17->n_eval_jama_ex1_bb2_in___16: 1 {O(1)}
4: n_eval_jama_ex1_bb1_in___17->n_eval_jama_ex1_bb5_in___15: 1 {O(1)}
7: n_eval_jama_ex1_bb2_in___13->n_eval_jama_ex1_bb3_in___12: 2*Arg_2*Arg_2+7*Arg_2+3 {O(n^2)}
8: n_eval_jama_ex1_bb2_in___13->n_eval_jama_ex1_bb4_in___11: 2*Arg_2+1 {O(n)}
9: n_eval_jama_ex1_bb2_in___16->n_eval_jama_ex1_bb3_in___14: 1 {O(1)}
11: n_eval_jama_ex1_bb2_in___9->n_eval_jama_ex1_bb3_in___14: Arg_2+1 {O(n)}
13: n_eval_jama_ex1_bb3_in___12->n_eval_jama_ex1_bb2_in___13: 2*Arg_2*Arg_2+7*Arg_2+3 {O(n^2)}
14: n_eval_jama_ex1_bb3_in___14->n_eval_jama_ex1_bb2_in___13: 2*Arg_2+1 {O(n)}
15: n_eval_jama_ex1_bb4_in___11->n_eval_jama_ex1_bb1_in___10: 2*Arg_2+1 {O(n)}
17: n_eval_jama_ex1_bb5_in___15->n_eval_jama_ex1_stop___1: 1 {O(1)}
19: n_eval_jama_ex1_bb5_in___8->n_eval_jama_ex1_stop___2: 1 {O(1)}
20: n_eval_jama_ex1_start->n_eval_jama_ex1_bb0_in___18: 1 {O(1)}

Costbounds

Overall costbound: 4*Arg_2*Arg_2+22*Arg_2+19 {O(n^2)}
0: n_eval_jama_ex1_bb0_in___18->n_eval_jama_ex1_bb1_in___17: 1 {O(1)}
1: n_eval_jama_ex1_bb1_in___10->n_eval_jama_ex1_bb2_in___9: Arg_2+1 {O(n)}
2: n_eval_jama_ex1_bb1_in___10->n_eval_jama_ex1_bb5_in___8: 1 {O(1)}
3: n_eval_jama_ex1_bb1_in___17->n_eval_jama_ex1_bb2_in___16: 1 {O(1)}
4: n_eval_jama_ex1_bb1_in___17->n_eval_jama_ex1_bb5_in___15: 1 {O(1)}
7: n_eval_jama_ex1_bb2_in___13->n_eval_jama_ex1_bb3_in___12: 2*Arg_2*Arg_2+7*Arg_2+3 {O(n^2)}
8: n_eval_jama_ex1_bb2_in___13->n_eval_jama_ex1_bb4_in___11: 2*Arg_2+1 {O(n)}
9: n_eval_jama_ex1_bb2_in___16->n_eval_jama_ex1_bb3_in___14: 1 {O(1)}
11: n_eval_jama_ex1_bb2_in___9->n_eval_jama_ex1_bb3_in___14: Arg_2+1 {O(n)}
13: n_eval_jama_ex1_bb3_in___12->n_eval_jama_ex1_bb2_in___13: 2*Arg_2*Arg_2+7*Arg_2+3 {O(n^2)}
14: n_eval_jama_ex1_bb3_in___14->n_eval_jama_ex1_bb2_in___13: 2*Arg_2+1 {O(n)}
15: n_eval_jama_ex1_bb4_in___11->n_eval_jama_ex1_bb1_in___10: 2*Arg_2+1 {O(n)}
17: n_eval_jama_ex1_bb5_in___15->n_eval_jama_ex1_stop___1: 1 {O(1)}
19: n_eval_jama_ex1_bb5_in___8->n_eval_jama_ex1_stop___2: 1 {O(1)}
20: n_eval_jama_ex1_start->n_eval_jama_ex1_bb0_in___18: 1 {O(1)}

Sizebounds

0: n_eval_jama_ex1_bb0_in___18->n_eval_jama_ex1_bb1_in___17, Arg_0: 1 {O(1)}
0: n_eval_jama_ex1_bb0_in___18->n_eval_jama_ex1_bb1_in___17, Arg_1: Arg_1 {O(n)}
0: n_eval_jama_ex1_bb0_in___18->n_eval_jama_ex1_bb1_in___17, Arg_2: Arg_2 {O(n)}
1: n_eval_jama_ex1_bb1_in___10->n_eval_jama_ex1_bb2_in___9, Arg_0: 2*Arg_2+2 {O(n)}
1: n_eval_jama_ex1_bb1_in___10->n_eval_jama_ex1_bb2_in___9, Arg_1: 1 {O(1)}
1: n_eval_jama_ex1_bb1_in___10->n_eval_jama_ex1_bb2_in___9, Arg_2: Arg_2 {O(n)}
2: n_eval_jama_ex1_bb1_in___10->n_eval_jama_ex1_bb5_in___8, Arg_0: 2*Arg_2+2 {O(n)}
2: n_eval_jama_ex1_bb1_in___10->n_eval_jama_ex1_bb5_in___8, Arg_1: 2*Arg_2*Arg_2+7*Arg_2+7 {O(n^2)}
2: n_eval_jama_ex1_bb1_in___10->n_eval_jama_ex1_bb5_in___8, Arg_2: Arg_2 {O(n)}
3: n_eval_jama_ex1_bb1_in___17->n_eval_jama_ex1_bb2_in___16, Arg_0: 1 {O(1)}
3: n_eval_jama_ex1_bb1_in___17->n_eval_jama_ex1_bb2_in___16, Arg_1: 1 {O(1)}
3: n_eval_jama_ex1_bb1_in___17->n_eval_jama_ex1_bb2_in___16, Arg_2: Arg_2 {O(n)}
4: n_eval_jama_ex1_bb1_in___17->n_eval_jama_ex1_bb5_in___15, Arg_0: 1 {O(1)}
4: n_eval_jama_ex1_bb1_in___17->n_eval_jama_ex1_bb5_in___15, Arg_1: Arg_1 {O(n)}
4: n_eval_jama_ex1_bb1_in___17->n_eval_jama_ex1_bb5_in___15, Arg_2: Arg_2 {O(n)}
7: n_eval_jama_ex1_bb2_in___13->n_eval_jama_ex1_bb3_in___12, Arg_0: 2*Arg_2+2 {O(n)}
7: n_eval_jama_ex1_bb2_in___13->n_eval_jama_ex1_bb3_in___12, Arg_1: 2*Arg_2*Arg_2+7*Arg_2+5 {O(n^2)}
7: n_eval_jama_ex1_bb2_in___13->n_eval_jama_ex1_bb3_in___12, Arg_2: Arg_2 {O(n)}
8: n_eval_jama_ex1_bb2_in___13->n_eval_jama_ex1_bb4_in___11, Arg_0: 2*Arg_2+2 {O(n)}
8: n_eval_jama_ex1_bb2_in___13->n_eval_jama_ex1_bb4_in___11, Arg_1: 2*Arg_2*Arg_2+7*Arg_2+7 {O(n^2)}
8: n_eval_jama_ex1_bb2_in___13->n_eval_jama_ex1_bb4_in___11, Arg_2: Arg_2 {O(n)}
9: n_eval_jama_ex1_bb2_in___16->n_eval_jama_ex1_bb3_in___14, Arg_0: 1 {O(1)}
9: n_eval_jama_ex1_bb2_in___16->n_eval_jama_ex1_bb3_in___14, Arg_1: 1 {O(1)}
9: n_eval_jama_ex1_bb2_in___16->n_eval_jama_ex1_bb3_in___14, Arg_2: Arg_2 {O(n)}
11: n_eval_jama_ex1_bb2_in___9->n_eval_jama_ex1_bb3_in___14, Arg_0: 2*Arg_2+2 {O(n)}
11: n_eval_jama_ex1_bb2_in___9->n_eval_jama_ex1_bb3_in___14, Arg_1: 1 {O(1)}
11: n_eval_jama_ex1_bb2_in___9->n_eval_jama_ex1_bb3_in___14, Arg_2: Arg_2 {O(n)}
13: n_eval_jama_ex1_bb3_in___12->n_eval_jama_ex1_bb2_in___13, Arg_0: 2*Arg_2+2 {O(n)}
13: n_eval_jama_ex1_bb3_in___12->n_eval_jama_ex1_bb2_in___13, Arg_1: 2*Arg_2*Arg_2+7*Arg_2+5 {O(n^2)}
13: n_eval_jama_ex1_bb3_in___12->n_eval_jama_ex1_bb2_in___13, Arg_2: Arg_2 {O(n)}
14: n_eval_jama_ex1_bb3_in___14->n_eval_jama_ex1_bb2_in___13, Arg_0: 2*Arg_2+2 {O(n)}
14: n_eval_jama_ex1_bb3_in___14->n_eval_jama_ex1_bb2_in___13, Arg_1: 2 {O(1)}
14: n_eval_jama_ex1_bb3_in___14->n_eval_jama_ex1_bb2_in___13, Arg_2: Arg_2 {O(n)}
15: n_eval_jama_ex1_bb4_in___11->n_eval_jama_ex1_bb1_in___10, Arg_0: 2*Arg_2+2 {O(n)}
15: n_eval_jama_ex1_bb4_in___11->n_eval_jama_ex1_bb1_in___10, Arg_1: 2*Arg_2*Arg_2+7*Arg_2+7 {O(n^2)}
15: n_eval_jama_ex1_bb4_in___11->n_eval_jama_ex1_bb1_in___10, Arg_2: Arg_2 {O(n)}
17: n_eval_jama_ex1_bb5_in___15->n_eval_jama_ex1_stop___1, Arg_0: 1 {O(1)}
17: n_eval_jama_ex1_bb5_in___15->n_eval_jama_ex1_stop___1, Arg_1: Arg_1 {O(n)}
17: n_eval_jama_ex1_bb5_in___15->n_eval_jama_ex1_stop___1, Arg_2: Arg_2 {O(n)}
19: n_eval_jama_ex1_bb5_in___8->n_eval_jama_ex1_stop___2, Arg_0: 2*Arg_2+2 {O(n)}
19: n_eval_jama_ex1_bb5_in___8->n_eval_jama_ex1_stop___2, Arg_1: 2*Arg_2*Arg_2+7*Arg_2+7 {O(n^2)}
19: n_eval_jama_ex1_bb5_in___8->n_eval_jama_ex1_stop___2, Arg_2: Arg_2 {O(n)}
20: n_eval_jama_ex1_start->n_eval_jama_ex1_bb0_in___18, Arg_0: Arg_0 {O(n)}
20: n_eval_jama_ex1_start->n_eval_jama_ex1_bb0_in___18, Arg_1: Arg_1 {O(n)}
20: n_eval_jama_ex1_start->n_eval_jama_ex1_bb0_in___18, Arg_2: Arg_2 {O(n)}