Initial Problem

Start: eval_insertsort_start
Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3, Arg_4
Temp_Vars: nondef_0, nondef_1
Locations: eval_insertsort_0, eval_insertsort_1, eval_insertsort_2, eval_insertsort_25, eval_insertsort_26, eval_insertsort_3, eval_insertsort_4, eval_insertsort_5, eval_insertsort_6, eval_insertsort_bb0_in, eval_insertsort_bb1_in, eval_insertsort_bb2_in, eval_insertsort_bb3_in, eval_insertsort_bb4_in, eval_insertsort_bb5_in, eval_insertsort_bb6_in, eval_insertsort_bb7_in, eval_insertsort_start, eval_insertsort_stop
Transitions:
2:eval_insertsort_0(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_insertsort_1(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4)
3:eval_insertsort_1(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_insertsort_2(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4)
4:eval_insertsort_2(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_insertsort_3(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4)
18:eval_insertsort_25(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_insertsort_26(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4)
19:eval_insertsort_26(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_insertsort_bb1_in(Arg_0,Arg_1,Arg_0,Arg_3,Arg_4)
5:eval_insertsort_3(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_insertsort_4(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4)
6:eval_insertsort_4(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_insertsort_5(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4)
7:eval_insertsort_5(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_insertsort_6(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4)
8:eval_insertsort_6(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_insertsort_bb1_in(Arg_0,Arg_1,1,Arg_3,Arg_4)
1:eval_insertsort_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_insertsort_0(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4)
9:eval_insertsort_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_insertsort_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:Arg_2<Arg_4
10:eval_insertsort_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_insertsort_bb7_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:Arg_4<=Arg_2
11:eval_insertsort_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_insertsort_bb3_in(Arg_0,nondef_0,Arg_2,Arg_2-1,Arg_4)
12:eval_insertsort_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_insertsort_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:0<=Arg_3
13:eval_insertsort_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_insertsort_bb6_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:Arg_3<0
14:eval_insertsort_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_insertsort_bb5_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:Arg_1<nondef_1
15:eval_insertsort_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_insertsort_bb6_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:nondef_1<=Arg_1
16:eval_insertsort_bb5_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_insertsort_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3-1,Arg_4)
17:eval_insertsort_bb6_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_insertsort_25(Arg_2+1,Arg_1,Arg_2,Arg_3,Arg_4)
20:eval_insertsort_bb7_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_insertsort_stop(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4)
0:eval_insertsort_start(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_insertsort_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4)

Preprocessing

Found invariant 2<=Arg_4 && 2+Arg_3<=Arg_4 && 3<=Arg_2+Arg_4 && 1+Arg_2<=Arg_4 && 4<=Arg_0+Arg_4 && Arg_0<=Arg_4 && 1+Arg_3<=Arg_2 && 2+Arg_3<=Arg_0 && 1+Arg_2<=Arg_0 && 1<=Arg_2 && 3<=Arg_0+Arg_2 && Arg_0<=1+Arg_2 && 2<=Arg_0 for location eval_insertsort_25

Found invariant 2<=Arg_4 && 2<=Arg_3+Arg_4 && 2+Arg_3<=Arg_4 && 3<=Arg_2+Arg_4 && 1+Arg_2<=Arg_4 && 1+Arg_3<=Arg_2 && 0<=Arg_3 && 1<=Arg_2+Arg_3 && 1<=Arg_2 for location eval_insertsort_bb4_in

Found invariant Arg_4<=Arg_2 && 1<=Arg_2 for location eval_insertsort_bb7_in

Found invariant 2<=Arg_4 && 2<=Arg_3+Arg_4 && 2+Arg_3<=Arg_4 && 3<=Arg_2+Arg_4 && 1+Arg_2<=Arg_4 && 1+Arg_3<=Arg_2 && 0<=Arg_3 && 1<=Arg_2+Arg_3 && 1<=Arg_2 for location eval_insertsort_bb5_in

Found invariant 2<=Arg_4 && 1<=Arg_3+Arg_4 && 2+Arg_3<=Arg_4 && 3<=Arg_2+Arg_4 && 1+Arg_2<=Arg_4 && 1+Arg_3<=Arg_2 && 0<=1+Arg_3 && 0<=Arg_2+Arg_3 && 1<=Arg_2 for location eval_insertsort_bb3_in

Found invariant 2<=Arg_4 && 2+Arg_3<=Arg_4 && 3<=Arg_2+Arg_4 && 1+Arg_2<=Arg_4 && 4<=Arg_0+Arg_4 && Arg_0<=Arg_4 && 1+Arg_3<=Arg_2 && 2+Arg_3<=Arg_0 && 1+Arg_2<=Arg_0 && 1<=Arg_2 && 3<=Arg_0+Arg_2 && Arg_0<=1+Arg_2 && 2<=Arg_0 for location eval_insertsort_26

Found invariant 2<=Arg_4 && 3<=Arg_2+Arg_4 && 1+Arg_2<=Arg_4 && 1<=Arg_2 for location eval_insertsort_bb2_in

Found invariant 2<=Arg_4 && 1<=Arg_3+Arg_4 && 2+Arg_3<=Arg_4 && 3<=Arg_2+Arg_4 && 1+Arg_2<=Arg_4 && 1+Arg_3<=Arg_2 && 0<=1+Arg_3 && 0<=Arg_2+Arg_3 && 1<=Arg_2 for location eval_insertsort_bb6_in

Found invariant Arg_4<=Arg_2 && 1<=Arg_2 for location eval_insertsort_stop

Found invariant 1<=Arg_2 for location eval_insertsort_bb1_in

Problem after Preprocessing

Start: eval_insertsort_start
Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3, Arg_4
Temp_Vars: nondef_0, nondef_1
Locations: eval_insertsort_0, eval_insertsort_1, eval_insertsort_2, eval_insertsort_25, eval_insertsort_26, eval_insertsort_3, eval_insertsort_4, eval_insertsort_5, eval_insertsort_6, eval_insertsort_bb0_in, eval_insertsort_bb1_in, eval_insertsort_bb2_in, eval_insertsort_bb3_in, eval_insertsort_bb4_in, eval_insertsort_bb5_in, eval_insertsort_bb6_in, eval_insertsort_bb7_in, eval_insertsort_start, eval_insertsort_stop
Transitions:
2:eval_insertsort_0(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_insertsort_1(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4)
3:eval_insertsort_1(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_insertsort_2(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4)
4:eval_insertsort_2(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_insertsort_3(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4)
18:eval_insertsort_25(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_insertsort_26(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:2<=Arg_4 && 2+Arg_3<=Arg_4 && 3<=Arg_2+Arg_4 && 1+Arg_2<=Arg_4 && 4<=Arg_0+Arg_4 && Arg_0<=Arg_4 && 1+Arg_3<=Arg_2 && 2+Arg_3<=Arg_0 && 1+Arg_2<=Arg_0 && 1<=Arg_2 && 3<=Arg_0+Arg_2 && Arg_0<=1+Arg_2 && 2<=Arg_0
19:eval_insertsort_26(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_insertsort_bb1_in(Arg_0,Arg_1,Arg_0,Arg_3,Arg_4):|:2<=Arg_4 && 2+Arg_3<=Arg_4 && 3<=Arg_2+Arg_4 && 1+Arg_2<=Arg_4 && 4<=Arg_0+Arg_4 && Arg_0<=Arg_4 && 1+Arg_3<=Arg_2 && 2+Arg_3<=Arg_0 && 1+Arg_2<=Arg_0 && 1<=Arg_2 && 3<=Arg_0+Arg_2 && Arg_0<=1+Arg_2 && 2<=Arg_0
5:eval_insertsort_3(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_insertsort_4(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4)
6:eval_insertsort_4(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_insertsort_5(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4)
7:eval_insertsort_5(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_insertsort_6(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4)
8:eval_insertsort_6(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_insertsort_bb1_in(Arg_0,Arg_1,1,Arg_3,Arg_4)
1:eval_insertsort_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_insertsort_0(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4)
9:eval_insertsort_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_insertsort_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:1<=Arg_2 && Arg_2<Arg_4
10:eval_insertsort_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_insertsort_bb7_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:1<=Arg_2 && Arg_4<=Arg_2
11:eval_insertsort_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_insertsort_bb3_in(Arg_0,nondef_0,Arg_2,Arg_2-1,Arg_4):|:2<=Arg_4 && 3<=Arg_2+Arg_4 && 1+Arg_2<=Arg_4 && 1<=Arg_2
12:eval_insertsort_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_insertsort_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:2<=Arg_4 && 1<=Arg_3+Arg_4 && 2+Arg_3<=Arg_4 && 3<=Arg_2+Arg_4 && 1+Arg_2<=Arg_4 && 1+Arg_3<=Arg_2 && 0<=1+Arg_3 && 0<=Arg_2+Arg_3 && 1<=Arg_2 && 0<=Arg_3
13:eval_insertsort_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_insertsort_bb6_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:2<=Arg_4 && 1<=Arg_3+Arg_4 && 2+Arg_3<=Arg_4 && 3<=Arg_2+Arg_4 && 1+Arg_2<=Arg_4 && 1+Arg_3<=Arg_2 && 0<=1+Arg_3 && 0<=Arg_2+Arg_3 && 1<=Arg_2 && Arg_3<0
14:eval_insertsort_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_insertsort_bb5_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:2<=Arg_4 && 2<=Arg_3+Arg_4 && 2+Arg_3<=Arg_4 && 3<=Arg_2+Arg_4 && 1+Arg_2<=Arg_4 && 1+Arg_3<=Arg_2 && 0<=Arg_3 && 1<=Arg_2+Arg_3 && 1<=Arg_2 && Arg_1<nondef_1
15:eval_insertsort_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_insertsort_bb6_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:2<=Arg_4 && 2<=Arg_3+Arg_4 && 2+Arg_3<=Arg_4 && 3<=Arg_2+Arg_4 && 1+Arg_2<=Arg_4 && 1+Arg_3<=Arg_2 && 0<=Arg_3 && 1<=Arg_2+Arg_3 && 1<=Arg_2 && nondef_1<=Arg_1
16:eval_insertsort_bb5_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_insertsort_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3-1,Arg_4):|:2<=Arg_4 && 2<=Arg_3+Arg_4 && 2+Arg_3<=Arg_4 && 3<=Arg_2+Arg_4 && 1+Arg_2<=Arg_4 && 1+Arg_3<=Arg_2 && 0<=Arg_3 && 1<=Arg_2+Arg_3 && 1<=Arg_2
17:eval_insertsort_bb6_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_insertsort_25(Arg_2+1,Arg_1,Arg_2,Arg_3,Arg_4):|:2<=Arg_4 && 1<=Arg_3+Arg_4 && 2+Arg_3<=Arg_4 && 3<=Arg_2+Arg_4 && 1+Arg_2<=Arg_4 && 1+Arg_3<=Arg_2 && 0<=1+Arg_3 && 0<=Arg_2+Arg_3 && 1<=Arg_2
20:eval_insertsort_bb7_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_insertsort_stop(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:Arg_4<=Arg_2 && 1<=Arg_2
0:eval_insertsort_start(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_insertsort_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4)

MPRF for transition 18:eval_insertsort_25(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_insertsort_26(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:2<=Arg_4 && 2+Arg_3<=Arg_4 && 3<=Arg_2+Arg_4 && 1+Arg_2<=Arg_4 && 4<=Arg_0+Arg_4 && Arg_0<=Arg_4 && 1+Arg_3<=Arg_2 && 2+Arg_3<=Arg_0 && 1+Arg_2<=Arg_0 && 1<=Arg_2 && 3<=Arg_0+Arg_2 && Arg_0<=1+Arg_2 && 2<=Arg_0 of depth 1:

new bound:

Arg_4+1 {O(n)}

MPRF:

eval_insertsort_26 [Arg_4-Arg_0 ]
eval_insertsort_bb1_in [Arg_4-Arg_2 ]
eval_insertsort_bb2_in [Arg_4-Arg_2 ]
eval_insertsort_bb4_in [Arg_4-Arg_2 ]
eval_insertsort_bb5_in [Arg_4-Arg_2 ]
eval_insertsort_bb3_in [Arg_4-Arg_2 ]
eval_insertsort_bb6_in [Arg_4-Arg_2 ]
eval_insertsort_25 [Arg_4+1-Arg_0 ]

MPRF for transition 19:eval_insertsort_26(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_insertsort_bb1_in(Arg_0,Arg_1,Arg_0,Arg_3,Arg_4):|:2<=Arg_4 && 2+Arg_3<=Arg_4 && 3<=Arg_2+Arg_4 && 1+Arg_2<=Arg_4 && 4<=Arg_0+Arg_4 && Arg_0<=Arg_4 && 1+Arg_3<=Arg_2 && 2+Arg_3<=Arg_0 && 1+Arg_2<=Arg_0 && 1<=Arg_2 && 3<=Arg_0+Arg_2 && Arg_0<=1+Arg_2 && 2<=Arg_0 of depth 1:

new bound:

Arg_4+1 {O(n)}

MPRF:

eval_insertsort_26 [Arg_4-Arg_2 ]
eval_insertsort_bb1_in [Arg_4-Arg_2 ]
eval_insertsort_bb2_in [Arg_4-Arg_2 ]
eval_insertsort_bb4_in [Arg_4-Arg_2 ]
eval_insertsort_bb5_in [Arg_4-Arg_2 ]
eval_insertsort_bb3_in [Arg_4-Arg_2 ]
eval_insertsort_bb6_in [Arg_4-Arg_2 ]
eval_insertsort_25 [Arg_4-Arg_2 ]

MPRF for transition 9:eval_insertsort_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_insertsort_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:1<=Arg_2 && Arg_2<Arg_4 of depth 1:

new bound:

Arg_4+1 {O(n)}

MPRF:

eval_insertsort_26 [Arg_4-Arg_2-1 ]
eval_insertsort_bb1_in [Arg_4-Arg_2 ]
eval_insertsort_bb2_in [Arg_4-Arg_2-1 ]
eval_insertsort_bb4_in [Arg_4-Arg_2-1 ]
eval_insertsort_bb5_in [Arg_4-Arg_2-1 ]
eval_insertsort_bb3_in [Arg_4-Arg_2-1 ]
eval_insertsort_bb6_in [Arg_4-Arg_2-1 ]
eval_insertsort_25 [Arg_4-Arg_2-1 ]

MPRF for transition 11:eval_insertsort_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_insertsort_bb3_in(Arg_0,nondef_0,Arg_2,Arg_2-1,Arg_4):|:2<=Arg_4 && 3<=Arg_2+Arg_4 && 1+Arg_2<=Arg_4 && 1<=Arg_2 of depth 1:

new bound:

Arg_4+1 {O(n)}

MPRF:

eval_insertsort_26 [Arg_4-Arg_0 ]
eval_insertsort_bb1_in [Arg_4-Arg_2 ]
eval_insertsort_bb2_in [Arg_4-Arg_2 ]
eval_insertsort_bb4_in [Arg_4-Arg_2-1 ]
eval_insertsort_bb5_in [Arg_4-Arg_2-1 ]
eval_insertsort_bb3_in [Arg_4-Arg_2-1 ]
eval_insertsort_bb6_in [Arg_4-Arg_2-1 ]
eval_insertsort_25 [Arg_4-Arg_0 ]

MPRF for transition 13:eval_insertsort_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_insertsort_bb6_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:2<=Arg_4 && 1<=Arg_3+Arg_4 && 2+Arg_3<=Arg_4 && 3<=Arg_2+Arg_4 && 1+Arg_2<=Arg_4 && 1+Arg_3<=Arg_2 && 0<=1+Arg_3 && 0<=Arg_2+Arg_3 && 1<=Arg_2 && Arg_3<0 of depth 1:

new bound:

Arg_4+1 {O(n)}

MPRF:

eval_insertsort_26 [Arg_4-Arg_0 ]
eval_insertsort_bb1_in [Arg_4-Arg_2 ]
eval_insertsort_bb2_in [Arg_4-Arg_2 ]
eval_insertsort_bb4_in [Arg_4-Arg_2 ]
eval_insertsort_bb5_in [Arg_4-Arg_2 ]
eval_insertsort_bb3_in [Arg_4-Arg_2 ]
eval_insertsort_bb6_in [Arg_4-Arg_2-1 ]
eval_insertsort_25 [Arg_4-Arg_2-1 ]

MPRF for transition 15:eval_insertsort_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_insertsort_bb6_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:2<=Arg_4 && 2<=Arg_3+Arg_4 && 2+Arg_3<=Arg_4 && 3<=Arg_2+Arg_4 && 1+Arg_2<=Arg_4 && 1+Arg_3<=Arg_2 && 0<=Arg_3 && 1<=Arg_2+Arg_3 && 1<=Arg_2 && nondef_1<=Arg_1 of depth 1:

new bound:

Arg_4+1 {O(n)}

MPRF:

eval_insertsort_26 [Arg_4-Arg_0 ]
eval_insertsort_bb1_in [Arg_4-Arg_2 ]
eval_insertsort_bb2_in [Arg_4-Arg_2 ]
eval_insertsort_bb4_in [Arg_4-Arg_2 ]
eval_insertsort_bb5_in [Arg_4-Arg_2 ]
eval_insertsort_bb3_in [Arg_4-Arg_2 ]
eval_insertsort_bb6_in [Arg_4-Arg_2-1 ]
eval_insertsort_25 [Arg_4-Arg_0 ]

MPRF for transition 17:eval_insertsort_bb6_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_insertsort_25(Arg_2+1,Arg_1,Arg_2,Arg_3,Arg_4):|:2<=Arg_4 && 1<=Arg_3+Arg_4 && 2+Arg_3<=Arg_4 && 3<=Arg_2+Arg_4 && 1+Arg_2<=Arg_4 && 1+Arg_3<=Arg_2 && 0<=1+Arg_3 && 0<=Arg_2+Arg_3 && 1<=Arg_2 of depth 1:

new bound:

Arg_4+1 {O(n)}

MPRF:

eval_insertsort_26 [Arg_4-Arg_0 ]
eval_insertsort_bb1_in [Arg_4-Arg_2 ]
eval_insertsort_bb2_in [Arg_4-Arg_2 ]
eval_insertsort_bb4_in [Arg_4-Arg_2 ]
eval_insertsort_bb5_in [Arg_4-Arg_2 ]
eval_insertsort_bb3_in [Arg_4-Arg_2 ]
eval_insertsort_bb6_in [Arg_4-Arg_2 ]
eval_insertsort_25 [Arg_4-Arg_0 ]

MPRF for transition 12:eval_insertsort_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_insertsort_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:2<=Arg_4 && 1<=Arg_3+Arg_4 && 2+Arg_3<=Arg_4 && 3<=Arg_2+Arg_4 && 1+Arg_2<=Arg_4 && 1+Arg_3<=Arg_2 && 0<=1+Arg_3 && 0<=Arg_2+Arg_3 && 1<=Arg_2 && 0<=Arg_3 of depth 1:

new bound:

Arg_4*Arg_4+5*Arg_4+7 {O(n^2)}

MPRF:

eval_insertsort_25 [Arg_0+2 ]
eval_insertsort_26 [Arg_0+2 ]
eval_insertsort_bb1_in [Arg_2+2 ]
eval_insertsort_bb2_in [Arg_2+2 ]
eval_insertsort_bb4_in [Arg_3+2 ]
eval_insertsort_bb6_in [Arg_3 ]
eval_insertsort_bb5_in [Arg_3+2 ]
eval_insertsort_bb3_in [Arg_3+3 ]

MPRF for transition 14:eval_insertsort_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_insertsort_bb5_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:2<=Arg_4 && 2<=Arg_3+Arg_4 && 2+Arg_3<=Arg_4 && 3<=Arg_2+Arg_4 && 1+Arg_2<=Arg_4 && 1+Arg_3<=Arg_2 && 0<=Arg_3 && 1<=Arg_2+Arg_3 && 1<=Arg_2 && Arg_1<nondef_1 of depth 1:

new bound:

Arg_4*Arg_4+3*Arg_4+3 {O(n^2)}

MPRF:

eval_insertsort_25 [Arg_0 ]
eval_insertsort_26 [Arg_0 ]
eval_insertsort_bb1_in [Arg_2 ]
eval_insertsort_bb2_in [Arg_2 ]
eval_insertsort_bb4_in [Arg_3+1 ]
eval_insertsort_bb6_in [Arg_3 ]
eval_insertsort_bb5_in [Arg_3 ]
eval_insertsort_bb3_in [Arg_3+1 ]

MPRF for transition 16:eval_insertsort_bb5_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_insertsort_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3-1,Arg_4):|:2<=Arg_4 && 2<=Arg_3+Arg_4 && 2+Arg_3<=Arg_4 && 3<=Arg_2+Arg_4 && 1+Arg_2<=Arg_4 && 1+Arg_3<=Arg_2 && 0<=Arg_3 && 1<=Arg_2+Arg_3 && 1<=Arg_2 of depth 1:

new bound:

Arg_4*Arg_4+3*Arg_4+3 {O(n^2)}

MPRF:

eval_insertsort_25 [Arg_0 ]
eval_insertsort_26 [Arg_0 ]
eval_insertsort_bb1_in [Arg_2 ]
eval_insertsort_bb2_in [Arg_2 ]
eval_insertsort_bb4_in [Arg_3+1 ]
eval_insertsort_bb6_in [Arg_3 ]
eval_insertsort_bb5_in [Arg_3+1 ]
eval_insertsort_bb3_in [Arg_3+1 ]

All Bounds

Timebounds

Overall timebound:3*Arg_4*Arg_4+18*Arg_4+31 {O(n^2)}
2: eval_insertsort_0->eval_insertsort_1: 1 {O(1)}
3: eval_insertsort_1->eval_insertsort_2: 1 {O(1)}
4: eval_insertsort_2->eval_insertsort_3: 1 {O(1)}
18: eval_insertsort_25->eval_insertsort_26: Arg_4+1 {O(n)}
19: eval_insertsort_26->eval_insertsort_bb1_in: Arg_4+1 {O(n)}
5: eval_insertsort_3->eval_insertsort_4: 1 {O(1)}
6: eval_insertsort_4->eval_insertsort_5: 1 {O(1)}
7: eval_insertsort_5->eval_insertsort_6: 1 {O(1)}
8: eval_insertsort_6->eval_insertsort_bb1_in: 1 {O(1)}
1: eval_insertsort_bb0_in->eval_insertsort_0: 1 {O(1)}
9: eval_insertsort_bb1_in->eval_insertsort_bb2_in: Arg_4+1 {O(n)}
10: eval_insertsort_bb1_in->eval_insertsort_bb7_in: 1 {O(1)}
11: eval_insertsort_bb2_in->eval_insertsort_bb3_in: Arg_4+1 {O(n)}
12: eval_insertsort_bb3_in->eval_insertsort_bb4_in: Arg_4*Arg_4+5*Arg_4+7 {O(n^2)}
13: eval_insertsort_bb3_in->eval_insertsort_bb6_in: Arg_4+1 {O(n)}
14: eval_insertsort_bb4_in->eval_insertsort_bb5_in: Arg_4*Arg_4+3*Arg_4+3 {O(n^2)}
15: eval_insertsort_bb4_in->eval_insertsort_bb6_in: Arg_4+1 {O(n)}
16: eval_insertsort_bb5_in->eval_insertsort_bb3_in: Arg_4*Arg_4+3*Arg_4+3 {O(n^2)}
17: eval_insertsort_bb6_in->eval_insertsort_25: Arg_4+1 {O(n)}
20: eval_insertsort_bb7_in->eval_insertsort_stop: 1 {O(1)}
0: eval_insertsort_start->eval_insertsort_bb0_in: 1 {O(1)}

Costbounds

Overall costbound: 3*Arg_4*Arg_4+18*Arg_4+31 {O(n^2)}
2: eval_insertsort_0->eval_insertsort_1: 1 {O(1)}
3: eval_insertsort_1->eval_insertsort_2: 1 {O(1)}
4: eval_insertsort_2->eval_insertsort_3: 1 {O(1)}
18: eval_insertsort_25->eval_insertsort_26: Arg_4+1 {O(n)}
19: eval_insertsort_26->eval_insertsort_bb1_in: Arg_4+1 {O(n)}
5: eval_insertsort_3->eval_insertsort_4: 1 {O(1)}
6: eval_insertsort_4->eval_insertsort_5: 1 {O(1)}
7: eval_insertsort_5->eval_insertsort_6: 1 {O(1)}
8: eval_insertsort_6->eval_insertsort_bb1_in: 1 {O(1)}
1: eval_insertsort_bb0_in->eval_insertsort_0: 1 {O(1)}
9: eval_insertsort_bb1_in->eval_insertsort_bb2_in: Arg_4+1 {O(n)}
10: eval_insertsort_bb1_in->eval_insertsort_bb7_in: 1 {O(1)}
11: eval_insertsort_bb2_in->eval_insertsort_bb3_in: Arg_4+1 {O(n)}
12: eval_insertsort_bb3_in->eval_insertsort_bb4_in: Arg_4*Arg_4+5*Arg_4+7 {O(n^2)}
13: eval_insertsort_bb3_in->eval_insertsort_bb6_in: Arg_4+1 {O(n)}
14: eval_insertsort_bb4_in->eval_insertsort_bb5_in: Arg_4*Arg_4+3*Arg_4+3 {O(n^2)}
15: eval_insertsort_bb4_in->eval_insertsort_bb6_in: Arg_4+1 {O(n)}
16: eval_insertsort_bb5_in->eval_insertsort_bb3_in: Arg_4*Arg_4+3*Arg_4+3 {O(n^2)}
17: eval_insertsort_bb6_in->eval_insertsort_25: Arg_4+1 {O(n)}
20: eval_insertsort_bb7_in->eval_insertsort_stop: 1 {O(1)}
0: eval_insertsort_start->eval_insertsort_bb0_in: 1 {O(1)}

Sizebounds

2: eval_insertsort_0->eval_insertsort_1, Arg_0: Arg_0 {O(n)}
2: eval_insertsort_0->eval_insertsort_1, Arg_1: Arg_1 {O(n)}
2: eval_insertsort_0->eval_insertsort_1, Arg_2: Arg_2 {O(n)}
2: eval_insertsort_0->eval_insertsort_1, Arg_3: Arg_3 {O(n)}
2: eval_insertsort_0->eval_insertsort_1, Arg_4: Arg_4 {O(n)}
3: eval_insertsort_1->eval_insertsort_2, Arg_0: Arg_0 {O(n)}
3: eval_insertsort_1->eval_insertsort_2, Arg_1: Arg_1 {O(n)}
3: eval_insertsort_1->eval_insertsort_2, Arg_2: Arg_2 {O(n)}
3: eval_insertsort_1->eval_insertsort_2, Arg_3: Arg_3 {O(n)}
3: eval_insertsort_1->eval_insertsort_2, Arg_4: Arg_4 {O(n)}
4: eval_insertsort_2->eval_insertsort_3, Arg_0: Arg_0 {O(n)}
4: eval_insertsort_2->eval_insertsort_3, Arg_1: Arg_1 {O(n)}
4: eval_insertsort_2->eval_insertsort_3, Arg_2: Arg_2 {O(n)}
4: eval_insertsort_2->eval_insertsort_3, Arg_3: Arg_3 {O(n)}
4: eval_insertsort_2->eval_insertsort_3, Arg_4: Arg_4 {O(n)}
18: eval_insertsort_25->eval_insertsort_26, Arg_0: Arg_4+2 {O(n)}
18: eval_insertsort_25->eval_insertsort_26, Arg_2: 2*Arg_4+4 {O(n)}
18: eval_insertsort_25->eval_insertsort_26, Arg_3: Arg_4+4 {O(n)}
18: eval_insertsort_25->eval_insertsort_26, Arg_4: Arg_4 {O(n)}
19: eval_insertsort_26->eval_insertsort_bb1_in, Arg_0: Arg_4+2 {O(n)}
19: eval_insertsort_26->eval_insertsort_bb1_in, Arg_2: Arg_4+2 {O(n)}
19: eval_insertsort_26->eval_insertsort_bb1_in, Arg_3: Arg_4+4 {O(n)}
19: eval_insertsort_26->eval_insertsort_bb1_in, Arg_4: Arg_4 {O(n)}
5: eval_insertsort_3->eval_insertsort_4, Arg_0: Arg_0 {O(n)}
5: eval_insertsort_3->eval_insertsort_4, Arg_1: Arg_1 {O(n)}
5: eval_insertsort_3->eval_insertsort_4, Arg_2: Arg_2 {O(n)}
5: eval_insertsort_3->eval_insertsort_4, Arg_3: Arg_3 {O(n)}
5: eval_insertsort_3->eval_insertsort_4, Arg_4: Arg_4 {O(n)}
6: eval_insertsort_4->eval_insertsort_5, Arg_0: Arg_0 {O(n)}
6: eval_insertsort_4->eval_insertsort_5, Arg_1: Arg_1 {O(n)}
6: eval_insertsort_4->eval_insertsort_5, Arg_2: Arg_2 {O(n)}
6: eval_insertsort_4->eval_insertsort_5, Arg_3: Arg_3 {O(n)}
6: eval_insertsort_4->eval_insertsort_5, Arg_4: Arg_4 {O(n)}
7: eval_insertsort_5->eval_insertsort_6, Arg_0: Arg_0 {O(n)}
7: eval_insertsort_5->eval_insertsort_6, Arg_1: Arg_1 {O(n)}
7: eval_insertsort_5->eval_insertsort_6, Arg_2: Arg_2 {O(n)}
7: eval_insertsort_5->eval_insertsort_6, Arg_3: Arg_3 {O(n)}
7: eval_insertsort_5->eval_insertsort_6, Arg_4: Arg_4 {O(n)}
8: eval_insertsort_6->eval_insertsort_bb1_in, Arg_0: Arg_0 {O(n)}
8: eval_insertsort_6->eval_insertsort_bb1_in, Arg_1: Arg_1 {O(n)}
8: eval_insertsort_6->eval_insertsort_bb1_in, Arg_2: 1 {O(1)}
8: eval_insertsort_6->eval_insertsort_bb1_in, Arg_3: Arg_3 {O(n)}
8: eval_insertsort_6->eval_insertsort_bb1_in, Arg_4: Arg_4 {O(n)}
1: eval_insertsort_bb0_in->eval_insertsort_0, Arg_0: Arg_0 {O(n)}
1: eval_insertsort_bb0_in->eval_insertsort_0, Arg_1: Arg_1 {O(n)}
1: eval_insertsort_bb0_in->eval_insertsort_0, Arg_2: Arg_2 {O(n)}
1: eval_insertsort_bb0_in->eval_insertsort_0, Arg_3: Arg_3 {O(n)}
1: eval_insertsort_bb0_in->eval_insertsort_0, Arg_4: Arg_4 {O(n)}
9: eval_insertsort_bb1_in->eval_insertsort_bb2_in, Arg_0: Arg_0+Arg_4+2 {O(n)}
9: eval_insertsort_bb1_in->eval_insertsort_bb2_in, Arg_2: Arg_4+2 {O(n)}
9: eval_insertsort_bb1_in->eval_insertsort_bb2_in, Arg_3: Arg_3+Arg_4+4 {O(n)}
9: eval_insertsort_bb1_in->eval_insertsort_bb2_in, Arg_4: Arg_4 {O(n)}
10: eval_insertsort_bb1_in->eval_insertsort_bb7_in, Arg_0: Arg_0+Arg_4+2 {O(n)}
10: eval_insertsort_bb1_in->eval_insertsort_bb7_in, Arg_2: Arg_4+3 {O(n)}
10: eval_insertsort_bb1_in->eval_insertsort_bb7_in, Arg_3: Arg_3+Arg_4+4 {O(n)}
10: eval_insertsort_bb1_in->eval_insertsort_bb7_in, Arg_4: 2*Arg_4 {O(n)}
11: eval_insertsort_bb2_in->eval_insertsort_bb3_in, Arg_0: Arg_0+Arg_4+2 {O(n)}
11: eval_insertsort_bb2_in->eval_insertsort_bb3_in, Arg_2: Arg_4+2 {O(n)}
11: eval_insertsort_bb2_in->eval_insertsort_bb3_in, Arg_3: Arg_4+2 {O(n)}
11: eval_insertsort_bb2_in->eval_insertsort_bb3_in, Arg_4: Arg_4 {O(n)}
12: eval_insertsort_bb3_in->eval_insertsort_bb4_in, Arg_0: Arg_0+Arg_4+2 {O(n)}
12: eval_insertsort_bb3_in->eval_insertsort_bb4_in, Arg_2: Arg_4+2 {O(n)}
12: eval_insertsort_bb3_in->eval_insertsort_bb4_in, Arg_3: Arg_4+3 {O(n)}
12: eval_insertsort_bb3_in->eval_insertsort_bb4_in, Arg_4: Arg_4 {O(n)}
13: eval_insertsort_bb3_in->eval_insertsort_bb6_in, Arg_0: Arg_0+Arg_4+2 {O(n)}
13: eval_insertsort_bb3_in->eval_insertsort_bb6_in, Arg_2: Arg_4+2 {O(n)}
13: eval_insertsort_bb3_in->eval_insertsort_bb6_in, Arg_3: 1 {O(1)}
13: eval_insertsort_bb3_in->eval_insertsort_bb6_in, Arg_4: Arg_4 {O(n)}
14: eval_insertsort_bb4_in->eval_insertsort_bb5_in, Arg_0: Arg_0+Arg_4+2 {O(n)}
14: eval_insertsort_bb4_in->eval_insertsort_bb5_in, Arg_2: Arg_4+2 {O(n)}
14: eval_insertsort_bb4_in->eval_insertsort_bb5_in, Arg_3: Arg_4+3 {O(n)}
14: eval_insertsort_bb4_in->eval_insertsort_bb5_in, Arg_4: Arg_4 {O(n)}
15: eval_insertsort_bb4_in->eval_insertsort_bb6_in, Arg_0: Arg_0+Arg_4+2 {O(n)}
15: eval_insertsort_bb4_in->eval_insertsort_bb6_in, Arg_2: Arg_4+2 {O(n)}
15: eval_insertsort_bb4_in->eval_insertsort_bb6_in, Arg_3: Arg_4+3 {O(n)}
15: eval_insertsort_bb4_in->eval_insertsort_bb6_in, Arg_4: Arg_4 {O(n)}
16: eval_insertsort_bb5_in->eval_insertsort_bb3_in, Arg_0: Arg_0+Arg_4+2 {O(n)}
16: eval_insertsort_bb5_in->eval_insertsort_bb3_in, Arg_2: Arg_4+2 {O(n)}
16: eval_insertsort_bb5_in->eval_insertsort_bb3_in, Arg_3: Arg_4+3 {O(n)}
16: eval_insertsort_bb5_in->eval_insertsort_bb3_in, Arg_4: Arg_4 {O(n)}
17: eval_insertsort_bb6_in->eval_insertsort_25, Arg_0: Arg_4+2 {O(n)}
17: eval_insertsort_bb6_in->eval_insertsort_25, Arg_2: 2*Arg_4+4 {O(n)}
17: eval_insertsort_bb6_in->eval_insertsort_25, Arg_3: Arg_4+4 {O(n)}
17: eval_insertsort_bb6_in->eval_insertsort_25, Arg_4: Arg_4 {O(n)}
20: eval_insertsort_bb7_in->eval_insertsort_stop, Arg_0: Arg_0+Arg_4+2 {O(n)}
20: eval_insertsort_bb7_in->eval_insertsort_stop, Arg_2: Arg_4+3 {O(n)}
20: eval_insertsort_bb7_in->eval_insertsort_stop, Arg_3: Arg_3+Arg_4+4 {O(n)}
20: eval_insertsort_bb7_in->eval_insertsort_stop, Arg_4: 2*Arg_4 {O(n)}
0: eval_insertsort_start->eval_insertsort_bb0_in, Arg_0: Arg_0 {O(n)}
0: eval_insertsort_start->eval_insertsort_bb0_in, Arg_1: Arg_1 {O(n)}
0: eval_insertsort_start->eval_insertsort_bb0_in, Arg_2: Arg_2 {O(n)}
0: eval_insertsort_start->eval_insertsort_bb0_in, Arg_3: Arg_3 {O(n)}
0: eval_insertsort_start->eval_insertsort_bb0_in, Arg_4: Arg_4 {O(n)}