Initial Problem

Start: eval_realheapsort_step1_start
Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3, Arg_4
Temp_Vars: nondef.0, nondef.1, nondef.3
Locations: eval_realheapsort_step1_.critedge_in, eval_realheapsort_step1_2, eval_realheapsort_step1_3, eval_realheapsort_step1_4, eval_realheapsort_step1_5, eval_realheapsort_step1_6, eval_realheapsort_step1_bb0_in, eval_realheapsort_step1_bb1_in, eval_realheapsort_step1_bb2_in, eval_realheapsort_step1_bb3_in, eval_realheapsort_step1_bb4_in, eval_realheapsort_step1_bb5_in, eval_realheapsort_step1_start, eval_realheapsort_step1_stop
Transitions:
20:eval_realheapsort_step1_.critedge_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_realheapsort_step1_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4+1)
9:eval_realheapsort_step1_2(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_realheapsort_step1_3(nondef.0,Arg_1,Arg_2,Arg_3,Arg_4)
11:eval_realheapsort_step1_3(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_realheapsort_step1_4(Arg_0,nondef.1,Arg_2,Arg_3,Arg_4)
13:eval_realheapsort_step1_4(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_realheapsort_step1_.critedge_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:Arg_0<=Arg_1
12:eval_realheapsort_step1_4(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_realheapsort_step1_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:Arg_1<Arg_0
16:eval_realheapsort_step1_5(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_realheapsort_step1_6(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4)
17:eval_realheapsort_step1_6(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_realheapsort_step1_bb2_in(Arg_0,Arg_1,Arg_2,nondef.3-1,Arg_4):|:Arg_3+1<=0 && 0<=1+Arg_3 && nondef.3<=0 && 0<=nondef.3
18:eval_realheapsort_step1_6(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_realheapsort_step1_bb2_in(Arg_0,Arg_1,Arg_2,nondef.3-1,Arg_4):|:0<1+Arg_3 && 0<=nondef.3 && 2*nondef.3<=1+Arg_3 && Arg_3<2*nondef.3+1
19:eval_realheapsort_step1_6(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_realheapsort_step1_bb2_in(Arg_0,Arg_1,Arg_2,nondef.3-1,Arg_4):|:Arg_3+1<0 && nondef.3<=0 && 1+Arg_3<=2*nondef.3 && 2*nondef.3<Arg_3+3
1:eval_realheapsort_step1_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_realheapsort_step1_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3,1):|:2<Arg_2
2:eval_realheapsort_step1_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_realheapsort_step1_bb5_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:Arg_2<=2
3:eval_realheapsort_step1_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_realheapsort_step1_bb2_in(Arg_0,Arg_1,Arg_2,Arg_4,Arg_4):|:Arg_4+1<=Arg_2
4:eval_realheapsort_step1_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_realheapsort_step1_bb5_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:Arg_2<1+Arg_4
6:eval_realheapsort_step1_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_realheapsort_step1_.critedge_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:Arg_3<=0
5:eval_realheapsort_step1_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_realheapsort_step1_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:0<Arg_3
7:eval_realheapsort_step1_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_realheapsort_step1_2(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4)
14:eval_realheapsort_step1_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_realheapsort_step1_5(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4)
21:eval_realheapsort_step1_bb5_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_realheapsort_step1_stop(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4)
0:eval_realheapsort_step1_start(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_realheapsort_step1_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4)

Preprocessing

Found invariant 1+Arg_4<=Arg_2 && 1<=Arg_4 && 2<=Arg_3+Arg_4 && Arg_3<=Arg_4 && 4<=Arg_2+Arg_4 && 1+Arg_3<=Arg_2 && 1<=Arg_3 && 4<=Arg_2+Arg_3 && 3<=Arg_2 for location eval_realheapsort_step1_4

Found invariant 1+Arg_4<=Arg_2 && 1<=Arg_4 && 2<=Arg_3+Arg_4 && Arg_3<=Arg_4 && 4<=Arg_2+Arg_4 && 1+Arg_3<=Arg_2 && 1<=Arg_3 && 4<=Arg_2+Arg_3 && 3<=Arg_2 && 1+Arg_1<=Arg_0 for location eval_realheapsort_step1_bb4_in

Found invariant 1+Arg_4<=Arg_2 && 1<=Arg_4 && 2<=Arg_3+Arg_4 && Arg_3<=Arg_4 && 4<=Arg_2+Arg_4 && 1+Arg_3<=Arg_2 && 1<=Arg_3 && 4<=Arg_2+Arg_3 && 3<=Arg_2 for location eval_realheapsort_step1_2

Found invariant Arg_4<=Arg_2 && 1<=Arg_4 && 4<=Arg_2+Arg_4 && 3<=Arg_2 for location eval_realheapsort_step1_bb1_in

Found invariant 1+Arg_4<=Arg_2 && 1<=Arg_4 && 1<=Arg_3+Arg_4 && Arg_3<=Arg_4 && 4<=Arg_2+Arg_4 && 1+Arg_3<=Arg_2 && 0<=Arg_3 && 3<=Arg_2+Arg_3 && 3<=Arg_2 for location eval_realheapsort_step1_.critedge_in

Found invariant 1+Arg_4<=Arg_2 && 1<=Arg_4 && 2<=Arg_3+Arg_4 && Arg_3<=Arg_4 && 4<=Arg_2+Arg_4 && 1+Arg_3<=Arg_2 && 1<=Arg_3 && 4<=Arg_2+Arg_3 && 3<=Arg_2 && 1+Arg_1<=Arg_0 for location eval_realheapsort_step1_5

Found invariant 1+Arg_4<=Arg_2 && 1<=Arg_4 && 2<=Arg_3+Arg_4 && Arg_3<=Arg_4 && 4<=Arg_2+Arg_4 && 1+Arg_3<=Arg_2 && 1<=Arg_3 && 4<=Arg_2+Arg_3 && 3<=Arg_2 && 1+Arg_1<=Arg_0 for location eval_realheapsort_step1_6

Found invariant 1+Arg_4<=Arg_2 && 1<=Arg_4 && 1<=Arg_3+Arg_4 && Arg_3<=Arg_4 && 4<=Arg_2+Arg_4 && 1+Arg_3<=Arg_2 && 0<=Arg_3 && 3<=Arg_2+Arg_3 && 3<=Arg_2 for location eval_realheapsort_step1_bb2_in

Found invariant 1+Arg_4<=Arg_2 && 1<=Arg_4 && 2<=Arg_3+Arg_4 && Arg_3<=Arg_4 && 4<=Arg_2+Arg_4 && 1+Arg_3<=Arg_2 && 1<=Arg_3 && 4<=Arg_2+Arg_3 && 3<=Arg_2 for location eval_realheapsort_step1_bb3_in

Found invariant 1+Arg_4<=Arg_2 && 1<=Arg_4 && 2<=Arg_3+Arg_4 && Arg_3<=Arg_4 && 4<=Arg_2+Arg_4 && 1+Arg_3<=Arg_2 && 1<=Arg_3 && 4<=Arg_2+Arg_3 && 3<=Arg_2 for location eval_realheapsort_step1_3

Cut unsatisfiable transition 17: eval_realheapsort_step1_6->eval_realheapsort_step1_bb2_in

Cut unsatisfiable transition 19: eval_realheapsort_step1_6->eval_realheapsort_step1_bb2_in

Problem after Preprocessing

Start: eval_realheapsort_step1_start
Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3, Arg_4
Temp_Vars: nondef.0, nondef.1, nondef.3
Locations: eval_realheapsort_step1_.critedge_in, eval_realheapsort_step1_2, eval_realheapsort_step1_3, eval_realheapsort_step1_4, eval_realheapsort_step1_5, eval_realheapsort_step1_6, eval_realheapsort_step1_bb0_in, eval_realheapsort_step1_bb1_in, eval_realheapsort_step1_bb2_in, eval_realheapsort_step1_bb3_in, eval_realheapsort_step1_bb4_in, eval_realheapsort_step1_bb5_in, eval_realheapsort_step1_start, eval_realheapsort_step1_stop
Transitions:
20:eval_realheapsort_step1_.critedge_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_realheapsort_step1_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4+1):|:1+Arg_4<=Arg_2 && 1<=Arg_4 && 1<=Arg_3+Arg_4 && Arg_3<=Arg_4 && 4<=Arg_2+Arg_4 && 1+Arg_3<=Arg_2 && 0<=Arg_3 && 3<=Arg_2+Arg_3 && 3<=Arg_2
9:eval_realheapsort_step1_2(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_realheapsort_step1_3(nondef.0,Arg_1,Arg_2,Arg_3,Arg_4):|:1+Arg_4<=Arg_2 && 1<=Arg_4 && 2<=Arg_3+Arg_4 && Arg_3<=Arg_4 && 4<=Arg_2+Arg_4 && 1+Arg_3<=Arg_2 && 1<=Arg_3 && 4<=Arg_2+Arg_3 && 3<=Arg_2
11:eval_realheapsort_step1_3(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_realheapsort_step1_4(Arg_0,nondef.1,Arg_2,Arg_3,Arg_4):|:1+Arg_4<=Arg_2 && 1<=Arg_4 && 2<=Arg_3+Arg_4 && Arg_3<=Arg_4 && 4<=Arg_2+Arg_4 && 1+Arg_3<=Arg_2 && 1<=Arg_3 && 4<=Arg_2+Arg_3 && 3<=Arg_2
13:eval_realheapsort_step1_4(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_realheapsort_step1_.critedge_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:1+Arg_4<=Arg_2 && 1<=Arg_4 && 2<=Arg_3+Arg_4 && Arg_3<=Arg_4 && 4<=Arg_2+Arg_4 && 1+Arg_3<=Arg_2 && 1<=Arg_3 && 4<=Arg_2+Arg_3 && 3<=Arg_2 && Arg_0<=Arg_1
12:eval_realheapsort_step1_4(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_realheapsort_step1_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:1+Arg_4<=Arg_2 && 1<=Arg_4 && 2<=Arg_3+Arg_4 && Arg_3<=Arg_4 && 4<=Arg_2+Arg_4 && 1+Arg_3<=Arg_2 && 1<=Arg_3 && 4<=Arg_2+Arg_3 && 3<=Arg_2 && Arg_1<Arg_0
16:eval_realheapsort_step1_5(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_realheapsort_step1_6(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:1+Arg_4<=Arg_2 && 1<=Arg_4 && 2<=Arg_3+Arg_4 && Arg_3<=Arg_4 && 4<=Arg_2+Arg_4 && 1+Arg_3<=Arg_2 && 1<=Arg_3 && 4<=Arg_2+Arg_3 && 3<=Arg_2 && 1+Arg_1<=Arg_0
18:eval_realheapsort_step1_6(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_realheapsort_step1_bb2_in(Arg_0,Arg_1,Arg_2,nondef.3-1,Arg_4):|:1+Arg_4<=Arg_2 && 1<=Arg_4 && 2<=Arg_3+Arg_4 && Arg_3<=Arg_4 && 4<=Arg_2+Arg_4 && 1+Arg_3<=Arg_2 && 1<=Arg_3 && 4<=Arg_2+Arg_3 && 3<=Arg_2 && 1+Arg_1<=Arg_0 && 0<1+Arg_3 && 0<=nondef.3 && 2*nondef.3<=1+Arg_3 && Arg_3<2*nondef.3+1
1:eval_realheapsort_step1_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_realheapsort_step1_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3,1):|:2<Arg_2
2:eval_realheapsort_step1_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_realheapsort_step1_bb5_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:Arg_2<=2
3:eval_realheapsort_step1_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_realheapsort_step1_bb2_in(Arg_0,Arg_1,Arg_2,Arg_4,Arg_4):|:Arg_4<=Arg_2 && 1<=Arg_4 && 4<=Arg_2+Arg_4 && 3<=Arg_2 && Arg_4+1<=Arg_2
4:eval_realheapsort_step1_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_realheapsort_step1_bb5_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:Arg_4<=Arg_2 && 1<=Arg_4 && 4<=Arg_2+Arg_4 && 3<=Arg_2 && Arg_2<1+Arg_4
6:eval_realheapsort_step1_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_realheapsort_step1_.critedge_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:1+Arg_4<=Arg_2 && 1<=Arg_4 && 1<=Arg_3+Arg_4 && Arg_3<=Arg_4 && 4<=Arg_2+Arg_4 && 1+Arg_3<=Arg_2 && 0<=Arg_3 && 3<=Arg_2+Arg_3 && 3<=Arg_2 && Arg_3<=0
5:eval_realheapsort_step1_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_realheapsort_step1_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:1+Arg_4<=Arg_2 && 1<=Arg_4 && 1<=Arg_3+Arg_4 && Arg_3<=Arg_4 && 4<=Arg_2+Arg_4 && 1+Arg_3<=Arg_2 && 0<=Arg_3 && 3<=Arg_2+Arg_3 && 3<=Arg_2 && 0<Arg_3
7:eval_realheapsort_step1_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_realheapsort_step1_2(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:1+Arg_4<=Arg_2 && 1<=Arg_4 && 2<=Arg_3+Arg_4 && Arg_3<=Arg_4 && 4<=Arg_2+Arg_4 && 1+Arg_3<=Arg_2 && 1<=Arg_3 && 4<=Arg_2+Arg_3 && 3<=Arg_2
14:eval_realheapsort_step1_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_realheapsort_step1_5(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:1+Arg_4<=Arg_2 && 1<=Arg_4 && 2<=Arg_3+Arg_4 && Arg_3<=Arg_4 && 4<=Arg_2+Arg_4 && 1+Arg_3<=Arg_2 && 1<=Arg_3 && 4<=Arg_2+Arg_3 && 3<=Arg_2 && 1+Arg_1<=Arg_0
21:eval_realheapsort_step1_bb5_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_realheapsort_step1_stop(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4)
0:eval_realheapsort_step1_start(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_realheapsort_step1_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4)

MPRF for transition 20:eval_realheapsort_step1_.critedge_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_realheapsort_step1_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4+1):|:1+Arg_4<=Arg_2 && 1<=Arg_4 && 1<=Arg_3+Arg_4 && Arg_3<=Arg_4 && 4<=Arg_2+Arg_4 && 1+Arg_3<=Arg_2 && 0<=Arg_3 && 3<=Arg_2+Arg_3 && 3<=Arg_2 of depth 1:

new bound:

Arg_2+3 {O(n)}

MPRF:

eval_realheapsort_step1_3 [Arg_2+2-Arg_4 ]
eval_realheapsort_step1_4 [Arg_2+2-Arg_4 ]
eval_realheapsort_step1_6 [Arg_2+2-Arg_4 ]
eval_realheapsort_step1_bb1_in [Arg_2+2-Arg_4 ]
eval_realheapsort_step1_bb2_in [Arg_2+2-Arg_4 ]
eval_realheapsort_step1_.critedge_in [Arg_2+2-Arg_4 ]
eval_realheapsort_step1_bb3_in [Arg_2+2-Arg_4 ]
eval_realheapsort_step1_2 [Arg_2+2-Arg_4 ]
eval_realheapsort_step1_bb4_in [Arg_2+2-Arg_4 ]
eval_realheapsort_step1_5 [Arg_2+2-Arg_4 ]

MPRF for transition 13:eval_realheapsort_step1_4(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_realheapsort_step1_.critedge_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:1+Arg_4<=Arg_2 && 1<=Arg_4 && 2<=Arg_3+Arg_4 && Arg_3<=Arg_4 && 4<=Arg_2+Arg_4 && 1+Arg_3<=Arg_2 && 1<=Arg_3 && 4<=Arg_2+Arg_3 && 3<=Arg_2 && Arg_0<=Arg_1 of depth 1:

new bound:

Arg_2+1 {O(n)}

MPRF:

eval_realheapsort_step1_3 [Arg_2-Arg_4 ]
eval_realheapsort_step1_4 [Arg_2-Arg_4 ]
eval_realheapsort_step1_6 [Arg_2-Arg_4 ]
eval_realheapsort_step1_bb1_in [Arg_2-Arg_4 ]
eval_realheapsort_step1_bb2_in [Arg_2-Arg_4 ]
eval_realheapsort_step1_.critedge_in [Arg_2-Arg_4-1 ]
eval_realheapsort_step1_bb3_in [Arg_2-Arg_4 ]
eval_realheapsort_step1_2 [Arg_2-Arg_4 ]
eval_realheapsort_step1_bb4_in [Arg_2-Arg_4 ]
eval_realheapsort_step1_5 [Arg_2-Arg_4 ]

MPRF for transition 3:eval_realheapsort_step1_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_realheapsort_step1_bb2_in(Arg_0,Arg_1,Arg_2,Arg_4,Arg_4):|:Arg_4<=Arg_2 && 1<=Arg_4 && 4<=Arg_2+Arg_4 && 3<=Arg_2 && Arg_4+1<=Arg_2 of depth 1:

new bound:

Arg_2+2 {O(n)}

MPRF:

eval_realheapsort_step1_3 [Arg_2-Arg_4 ]
eval_realheapsort_step1_4 [Arg_2-Arg_4 ]
eval_realheapsort_step1_6 [Arg_2-Arg_4 ]
eval_realheapsort_step1_bb1_in [Arg_2+1-Arg_4 ]
eval_realheapsort_step1_bb2_in [Arg_2-Arg_4 ]
eval_realheapsort_step1_.critedge_in [Arg_2-Arg_4 ]
eval_realheapsort_step1_bb3_in [Arg_2-Arg_4 ]
eval_realheapsort_step1_2 [Arg_2-Arg_4 ]
eval_realheapsort_step1_bb4_in [Arg_2-Arg_4 ]
eval_realheapsort_step1_5 [Arg_2-Arg_4 ]

MPRF for transition 6:eval_realheapsort_step1_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_realheapsort_step1_.critedge_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:1+Arg_4<=Arg_2 && 1<=Arg_4 && 1<=Arg_3+Arg_4 && Arg_3<=Arg_4 && 4<=Arg_2+Arg_4 && 1+Arg_3<=Arg_2 && 0<=Arg_3 && 3<=Arg_2+Arg_3 && 3<=Arg_2 && Arg_3<=0 of depth 1:

new bound:

Arg_2+1 {O(n)}

MPRF:

eval_realheapsort_step1_3 [Arg_2-Arg_4 ]
eval_realheapsort_step1_4 [Arg_2-Arg_4 ]
eval_realheapsort_step1_6 [Arg_2-Arg_4 ]
eval_realheapsort_step1_bb1_in [Arg_2-Arg_4 ]
eval_realheapsort_step1_bb2_in [Arg_2-Arg_4 ]
eval_realheapsort_step1_.critedge_in [Arg_2-Arg_4-1 ]
eval_realheapsort_step1_bb3_in [Arg_2-Arg_4 ]
eval_realheapsort_step1_2 [Arg_2-Arg_4 ]
eval_realheapsort_step1_bb4_in [Arg_2-Arg_4 ]
eval_realheapsort_step1_5 [Arg_2-Arg_4 ]

MPRF for transition 9:eval_realheapsort_step1_2(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_realheapsort_step1_3(nondef.0,Arg_1,Arg_2,Arg_3,Arg_4):|:1+Arg_4<=Arg_2 && 1<=Arg_4 && 2<=Arg_3+Arg_4 && Arg_3<=Arg_4 && 4<=Arg_2+Arg_4 && 1+Arg_3<=Arg_2 && 1<=Arg_3 && 4<=Arg_2+Arg_3 && 3<=Arg_2 of depth 1:

new bound:

2*Arg_2*Arg_2+14*Arg_2+20 {O(n^2)}

MPRF:

eval_realheapsort_step1_bb1_in [-2 ]
eval_realheapsort_step1_3 [Arg_3-1 ]
eval_realheapsort_step1_4 [Arg_3-1 ]
eval_realheapsort_step1_6 [Arg_3-1 ]
eval_realheapsort_step1_bb2_in [2*Arg_3 ]
eval_realheapsort_step1_.critedge_in [Arg_3-2 ]
eval_realheapsort_step1_bb3_in [Arg_3 ]
eval_realheapsort_step1_2 [Arg_3 ]
eval_realheapsort_step1_bb4_in [Arg_3-1 ]
eval_realheapsort_step1_5 [Arg_3-1 ]

MPRF for transition 11:eval_realheapsort_step1_3(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_realheapsort_step1_4(Arg_0,nondef.1,Arg_2,Arg_3,Arg_4):|:1+Arg_4<=Arg_2 && 1<=Arg_4 && 2<=Arg_3+Arg_4 && Arg_3<=Arg_4 && 4<=Arg_2+Arg_4 && 1+Arg_3<=Arg_2 && 1<=Arg_3 && 4<=Arg_2+Arg_3 && 3<=Arg_2 of depth 1:

new bound:

4*Arg_2*Arg_2+23*Arg_2+30 {O(n^2)}

MPRF:

eval_realheapsort_step1_bb1_in [Arg_2-Arg_4 ]
eval_realheapsort_step1_3 [Arg_2+Arg_3-Arg_4-1 ]
eval_realheapsort_step1_4 [Arg_2+Arg_3-Arg_4-2 ]
eval_realheapsort_step1_6 [Arg_2+Arg_3-Arg_4-2 ]
eval_realheapsort_step1_bb2_in [Arg_2+2*Arg_3-Arg_4-1 ]
eval_realheapsort_step1_.critedge_in [Arg_2-Arg_4-1 ]
eval_realheapsort_step1_bb3_in [Arg_2+Arg_3-Arg_4-1 ]
eval_realheapsort_step1_2 [Arg_2+Arg_3-Arg_4-1 ]
eval_realheapsort_step1_bb4_in [Arg_2+Arg_3-Arg_4-2 ]
eval_realheapsort_step1_5 [Arg_2+Arg_3-Arg_4-2 ]

MPRF for transition 12:eval_realheapsort_step1_4(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_realheapsort_step1_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:1+Arg_4<=Arg_2 && 1<=Arg_4 && 2<=Arg_3+Arg_4 && Arg_3<=Arg_4 && 4<=Arg_2+Arg_4 && 1+Arg_3<=Arg_2 && 1<=Arg_3 && 4<=Arg_2+Arg_3 && 3<=Arg_2 && Arg_1<Arg_0 of depth 1:

new bound:

2*Arg_2*Arg_2+19*Arg_2+30 {O(n^2)}

MPRF:

eval_realheapsort_step1_bb1_in [0 ]
eval_realheapsort_step1_3 [Arg_3+5 ]
eval_realheapsort_step1_4 [Arg_3+5 ]
eval_realheapsort_step1_6 [Arg_3+4 ]
eval_realheapsort_step1_bb2_in [2*Arg_3+5 ]
eval_realheapsort_step1_.critedge_in [Arg_3 ]
eval_realheapsort_step1_bb3_in [Arg_3+5 ]
eval_realheapsort_step1_2 [Arg_3+5 ]
eval_realheapsort_step1_bb4_in [Arg_3+4 ]
eval_realheapsort_step1_5 [Arg_3+4 ]

MPRF for transition 16:eval_realheapsort_step1_5(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_realheapsort_step1_6(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:1+Arg_4<=Arg_2 && 1<=Arg_4 && 2<=Arg_3+Arg_4 && Arg_3<=Arg_4 && 4<=Arg_2+Arg_4 && 1+Arg_3<=Arg_2 && 1<=Arg_3 && 4<=Arg_2+Arg_3 && 3<=Arg_2 && 1+Arg_1<=Arg_0 of depth 1:

new bound:

2*Arg_2*Arg_2+14*Arg_2+20 {O(n^2)}

MPRF:

eval_realheapsort_step1_bb1_in [0 ]
eval_realheapsort_step1_3 [Arg_3 ]
eval_realheapsort_step1_4 [Arg_3 ]
eval_realheapsort_step1_6 [Arg_3-1 ]
eval_realheapsort_step1_bb2_in [2*Arg_3 ]
eval_realheapsort_step1_.critedge_in [Arg_3 ]
eval_realheapsort_step1_bb3_in [Arg_3 ]
eval_realheapsort_step1_2 [Arg_3 ]
eval_realheapsort_step1_bb4_in [Arg_3 ]
eval_realheapsort_step1_5 [Arg_3 ]

MPRF for transition 18:eval_realheapsort_step1_6(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_realheapsort_step1_bb2_in(Arg_0,Arg_1,Arg_2,nondef.3-1,Arg_4):|:1+Arg_4<=Arg_2 && 1<=Arg_4 && 2<=Arg_3+Arg_4 && Arg_3<=Arg_4 && 4<=Arg_2+Arg_4 && 1+Arg_3<=Arg_2 && 1<=Arg_3 && 4<=Arg_2+Arg_3 && 3<=Arg_2 && 1+Arg_1<=Arg_0 && 0<1+Arg_3 && 0<=nondef.3 && 2*nondef.3<=1+Arg_3 && Arg_3<2*nondef.3+1 of depth 1:

new bound:

2*Arg_2*Arg_2+14*Arg_2+20 {O(n^2)}

MPRF:

eval_realheapsort_step1_bb1_in [0 ]
eval_realheapsort_step1_3 [2*Arg_3 ]
eval_realheapsort_step1_4 [2*Arg_3 ]
eval_realheapsort_step1_6 [Arg_3+1 ]
eval_realheapsort_step1_bb2_in [2*Arg_3 ]
eval_realheapsort_step1_.critedge_in [2*Arg_3 ]
eval_realheapsort_step1_bb3_in [2*Arg_3 ]
eval_realheapsort_step1_2 [2*Arg_3 ]
eval_realheapsort_step1_bb4_in [2*Arg_3 ]
eval_realheapsort_step1_5 [2*Arg_3 ]

MPRF for transition 5:eval_realheapsort_step1_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_realheapsort_step1_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:1+Arg_4<=Arg_2 && 1<=Arg_4 && 1<=Arg_3+Arg_4 && Arg_3<=Arg_4 && 4<=Arg_2+Arg_4 && 1+Arg_3<=Arg_2 && 0<=Arg_3 && 3<=Arg_2+Arg_3 && 3<=Arg_2 && 0<Arg_3 of depth 1:

new bound:

2*Arg_2*Arg_2+15*Arg_2+22 {O(n^2)}

MPRF:

eval_realheapsort_step1_bb1_in [0 ]
eval_realheapsort_step1_3 [Arg_3 ]
eval_realheapsort_step1_4 [Arg_3 ]
eval_realheapsort_step1_6 [Arg_3 ]
eval_realheapsort_step1_bb2_in [2*Arg_3+1 ]
eval_realheapsort_step1_.critedge_in [Arg_3 ]
eval_realheapsort_step1_bb3_in [Arg_3 ]
eval_realheapsort_step1_2 [Arg_3 ]
eval_realheapsort_step1_bb4_in [Arg_3 ]
eval_realheapsort_step1_5 [Arg_3 ]

MPRF for transition 7:eval_realheapsort_step1_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_realheapsort_step1_2(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:1+Arg_4<=Arg_2 && 1<=Arg_4 && 2<=Arg_3+Arg_4 && Arg_3<=Arg_4 && 4<=Arg_2+Arg_4 && 1+Arg_3<=Arg_2 && 1<=Arg_3 && 4<=Arg_2+Arg_3 && 3<=Arg_2 of depth 1:

new bound:

2*Arg_2*Arg_2+15*Arg_2+22 {O(n^2)}

MPRF:

eval_realheapsort_step1_bb1_in [0 ]
eval_realheapsort_step1_3 [Arg_3 ]
eval_realheapsort_step1_4 [Arg_3 ]
eval_realheapsort_step1_6 [Arg_3 ]
eval_realheapsort_step1_bb2_in [2*Arg_3+1 ]
eval_realheapsort_step1_.critedge_in [Arg_3 ]
eval_realheapsort_step1_bb3_in [Arg_3+2 ]
eval_realheapsort_step1_2 [Arg_3 ]
eval_realheapsort_step1_bb4_in [Arg_3 ]
eval_realheapsort_step1_5 [Arg_3 ]

MPRF for transition 14:eval_realheapsort_step1_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_realheapsort_step1_5(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:1+Arg_4<=Arg_2 && 1<=Arg_4 && 2<=Arg_3+Arg_4 && Arg_3<=Arg_4 && 4<=Arg_2+Arg_4 && 1+Arg_3<=Arg_2 && 1<=Arg_3 && 4<=Arg_2+Arg_3 && 3<=Arg_2 && 1+Arg_1<=Arg_0 of depth 1:

new bound:

6*Arg_2*Arg_2+31*Arg_2+38 {O(n^2)}

MPRF:

eval_realheapsort_step1_bb1_in [2*Arg_2-2*Arg_4 ]
eval_realheapsort_step1_3 [2*Arg_2+2*Arg_3-2*Arg_4-1 ]
eval_realheapsort_step1_4 [2*Arg_2+2*Arg_3-2*Arg_4-1 ]
eval_realheapsort_step1_6 [2*Arg_2+Arg_3-2*Arg_4-2 ]
eval_realheapsort_step1_bb2_in [2*Arg_2+2*Arg_3-2*Arg_4-1 ]
eval_realheapsort_step1_.critedge_in [2*Arg_2+2*Arg_3-2*Arg_4-1 ]
eval_realheapsort_step1_bb3_in [2*Arg_2+2*Arg_3-2*Arg_4-1 ]
eval_realheapsort_step1_2 [2*Arg_2+2*Arg_3-2*Arg_4-1 ]
eval_realheapsort_step1_bb4_in [2*Arg_2+2*Arg_3-2*Arg_4-1 ]
eval_realheapsort_step1_5 [2*Arg_2+Arg_3-2*Arg_4-2 ]

All Bounds

Timebounds

Overall timebound:22*Arg_2*Arg_2+149*Arg_2+214 {O(n^2)}
20: eval_realheapsort_step1_.critedge_in->eval_realheapsort_step1_bb1_in: Arg_2+3 {O(n)}
9: eval_realheapsort_step1_2->eval_realheapsort_step1_3: 2*Arg_2*Arg_2+14*Arg_2+20 {O(n^2)}
11: eval_realheapsort_step1_3->eval_realheapsort_step1_4: 4*Arg_2*Arg_2+23*Arg_2+30 {O(n^2)}
12: eval_realheapsort_step1_4->eval_realheapsort_step1_bb4_in: 2*Arg_2*Arg_2+19*Arg_2+30 {O(n^2)}
13: eval_realheapsort_step1_4->eval_realheapsort_step1_.critedge_in: Arg_2+1 {O(n)}
16: eval_realheapsort_step1_5->eval_realheapsort_step1_6: 2*Arg_2*Arg_2+14*Arg_2+20 {O(n^2)}
18: eval_realheapsort_step1_6->eval_realheapsort_step1_bb2_in: 2*Arg_2*Arg_2+14*Arg_2+20 {O(n^2)}
1: eval_realheapsort_step1_bb0_in->eval_realheapsort_step1_bb1_in: 1 {O(1)}
2: eval_realheapsort_step1_bb0_in->eval_realheapsort_step1_bb5_in: 1 {O(1)}
3: eval_realheapsort_step1_bb1_in->eval_realheapsort_step1_bb2_in: Arg_2+2 {O(n)}
4: eval_realheapsort_step1_bb1_in->eval_realheapsort_step1_bb5_in: 1 {O(1)}
5: eval_realheapsort_step1_bb2_in->eval_realheapsort_step1_bb3_in: 2*Arg_2*Arg_2+15*Arg_2+22 {O(n^2)}
6: eval_realheapsort_step1_bb2_in->eval_realheapsort_step1_.critedge_in: Arg_2+1 {O(n)}
7: eval_realheapsort_step1_bb3_in->eval_realheapsort_step1_2: 2*Arg_2*Arg_2+15*Arg_2+22 {O(n^2)}
14: eval_realheapsort_step1_bb4_in->eval_realheapsort_step1_5: 6*Arg_2*Arg_2+31*Arg_2+38 {O(n^2)}
21: eval_realheapsort_step1_bb5_in->eval_realheapsort_step1_stop: 1 {O(1)}
0: eval_realheapsort_step1_start->eval_realheapsort_step1_bb0_in: 1 {O(1)}

Costbounds

Overall costbound: 22*Arg_2*Arg_2+149*Arg_2+214 {O(n^2)}
20: eval_realheapsort_step1_.critedge_in->eval_realheapsort_step1_bb1_in: Arg_2+3 {O(n)}
9: eval_realheapsort_step1_2->eval_realheapsort_step1_3: 2*Arg_2*Arg_2+14*Arg_2+20 {O(n^2)}
11: eval_realheapsort_step1_3->eval_realheapsort_step1_4: 4*Arg_2*Arg_2+23*Arg_2+30 {O(n^2)}
12: eval_realheapsort_step1_4->eval_realheapsort_step1_bb4_in: 2*Arg_2*Arg_2+19*Arg_2+30 {O(n^2)}
13: eval_realheapsort_step1_4->eval_realheapsort_step1_.critedge_in: Arg_2+1 {O(n)}
16: eval_realheapsort_step1_5->eval_realheapsort_step1_6: 2*Arg_2*Arg_2+14*Arg_2+20 {O(n^2)}
18: eval_realheapsort_step1_6->eval_realheapsort_step1_bb2_in: 2*Arg_2*Arg_2+14*Arg_2+20 {O(n^2)}
1: eval_realheapsort_step1_bb0_in->eval_realheapsort_step1_bb1_in: 1 {O(1)}
2: eval_realheapsort_step1_bb0_in->eval_realheapsort_step1_bb5_in: 1 {O(1)}
3: eval_realheapsort_step1_bb1_in->eval_realheapsort_step1_bb2_in: Arg_2+2 {O(n)}
4: eval_realheapsort_step1_bb1_in->eval_realheapsort_step1_bb5_in: 1 {O(1)}
5: eval_realheapsort_step1_bb2_in->eval_realheapsort_step1_bb3_in: 2*Arg_2*Arg_2+15*Arg_2+22 {O(n^2)}
6: eval_realheapsort_step1_bb2_in->eval_realheapsort_step1_.critedge_in: Arg_2+1 {O(n)}
7: eval_realheapsort_step1_bb3_in->eval_realheapsort_step1_2: 2*Arg_2*Arg_2+15*Arg_2+22 {O(n^2)}
14: eval_realheapsort_step1_bb4_in->eval_realheapsort_step1_5: 6*Arg_2*Arg_2+31*Arg_2+38 {O(n^2)}
21: eval_realheapsort_step1_bb5_in->eval_realheapsort_step1_stop: 1 {O(1)}
0: eval_realheapsort_step1_start->eval_realheapsort_step1_bb0_in: 1 {O(1)}

Sizebounds

20: eval_realheapsort_step1_.critedge_in->eval_realheapsort_step1_bb1_in, Arg_2: Arg_2 {O(n)}
20: eval_realheapsort_step1_.critedge_in->eval_realheapsort_step1_bb1_in, Arg_3: Arg_2+5 {O(n)}
20: eval_realheapsort_step1_.critedge_in->eval_realheapsort_step1_bb1_in, Arg_4: Arg_2+4 {O(n)}
9: eval_realheapsort_step1_2->eval_realheapsort_step1_3, Arg_2: Arg_2 {O(n)}
9: eval_realheapsort_step1_2->eval_realheapsort_step1_3, Arg_3: Arg_2+5 {O(n)}
9: eval_realheapsort_step1_2->eval_realheapsort_step1_3, Arg_4: Arg_2+4 {O(n)}
11: eval_realheapsort_step1_3->eval_realheapsort_step1_4, Arg_2: Arg_2 {O(n)}
11: eval_realheapsort_step1_3->eval_realheapsort_step1_4, Arg_3: Arg_2+5 {O(n)}
11: eval_realheapsort_step1_3->eval_realheapsort_step1_4, Arg_4: Arg_2+4 {O(n)}
12: eval_realheapsort_step1_4->eval_realheapsort_step1_bb4_in, Arg_2: Arg_2 {O(n)}
12: eval_realheapsort_step1_4->eval_realheapsort_step1_bb4_in, Arg_3: Arg_2+5 {O(n)}
12: eval_realheapsort_step1_4->eval_realheapsort_step1_bb4_in, Arg_4: Arg_2+4 {O(n)}
13: eval_realheapsort_step1_4->eval_realheapsort_step1_.critedge_in, Arg_2: Arg_2 {O(n)}
13: eval_realheapsort_step1_4->eval_realheapsort_step1_.critedge_in, Arg_3: Arg_2+5 {O(n)}
13: eval_realheapsort_step1_4->eval_realheapsort_step1_.critedge_in, Arg_4: Arg_2+4 {O(n)}
16: eval_realheapsort_step1_5->eval_realheapsort_step1_6, Arg_2: Arg_2 {O(n)}
16: eval_realheapsort_step1_5->eval_realheapsort_step1_6, Arg_3: Arg_2+5 {O(n)}
16: eval_realheapsort_step1_5->eval_realheapsort_step1_6, Arg_4: Arg_2+4 {O(n)}
18: eval_realheapsort_step1_6->eval_realheapsort_step1_bb2_in, Arg_2: Arg_2 {O(n)}
18: eval_realheapsort_step1_6->eval_realheapsort_step1_bb2_in, Arg_3: Arg_2+5 {O(n)}
18: eval_realheapsort_step1_6->eval_realheapsort_step1_bb2_in, Arg_4: Arg_2+4 {O(n)}
1: eval_realheapsort_step1_bb0_in->eval_realheapsort_step1_bb1_in, Arg_0: Arg_0 {O(n)}
1: eval_realheapsort_step1_bb0_in->eval_realheapsort_step1_bb1_in, Arg_1: Arg_1 {O(n)}
1: eval_realheapsort_step1_bb0_in->eval_realheapsort_step1_bb1_in, Arg_2: Arg_2 {O(n)}
1: eval_realheapsort_step1_bb0_in->eval_realheapsort_step1_bb1_in, Arg_3: Arg_3 {O(n)}
1: eval_realheapsort_step1_bb0_in->eval_realheapsort_step1_bb1_in, Arg_4: 1 {O(1)}
2: eval_realheapsort_step1_bb0_in->eval_realheapsort_step1_bb5_in, Arg_0: Arg_0 {O(n)}
2: eval_realheapsort_step1_bb0_in->eval_realheapsort_step1_bb5_in, Arg_1: Arg_1 {O(n)}
2: eval_realheapsort_step1_bb0_in->eval_realheapsort_step1_bb5_in, Arg_2: Arg_2 {O(n)}
2: eval_realheapsort_step1_bb0_in->eval_realheapsort_step1_bb5_in, Arg_3: Arg_3 {O(n)}
2: eval_realheapsort_step1_bb0_in->eval_realheapsort_step1_bb5_in, Arg_4: Arg_4 {O(n)}
3: eval_realheapsort_step1_bb1_in->eval_realheapsort_step1_bb2_in, Arg_2: Arg_2 {O(n)}
3: eval_realheapsort_step1_bb1_in->eval_realheapsort_step1_bb2_in, Arg_3: Arg_2+5 {O(n)}
3: eval_realheapsort_step1_bb1_in->eval_realheapsort_step1_bb2_in, Arg_4: Arg_2+4 {O(n)}
4: eval_realheapsort_step1_bb1_in->eval_realheapsort_step1_bb5_in, Arg_2: Arg_2 {O(n)}
4: eval_realheapsort_step1_bb1_in->eval_realheapsort_step1_bb5_in, Arg_3: Arg_2+5 {O(n)}
4: eval_realheapsort_step1_bb1_in->eval_realheapsort_step1_bb5_in, Arg_4: Arg_2+4 {O(n)}
5: eval_realheapsort_step1_bb2_in->eval_realheapsort_step1_bb3_in, Arg_2: Arg_2 {O(n)}
5: eval_realheapsort_step1_bb2_in->eval_realheapsort_step1_bb3_in, Arg_3: Arg_2+5 {O(n)}
5: eval_realheapsort_step1_bb2_in->eval_realheapsort_step1_bb3_in, Arg_4: Arg_2+4 {O(n)}
6: eval_realheapsort_step1_bb2_in->eval_realheapsort_step1_.critedge_in, Arg_2: Arg_2 {O(n)}
6: eval_realheapsort_step1_bb2_in->eval_realheapsort_step1_.critedge_in, Arg_3: 0 {O(1)}
6: eval_realheapsort_step1_bb2_in->eval_realheapsort_step1_.critedge_in, Arg_4: Arg_2+4 {O(n)}
7: eval_realheapsort_step1_bb3_in->eval_realheapsort_step1_2, Arg_2: Arg_2 {O(n)}
7: eval_realheapsort_step1_bb3_in->eval_realheapsort_step1_2, Arg_3: Arg_2+5 {O(n)}
7: eval_realheapsort_step1_bb3_in->eval_realheapsort_step1_2, Arg_4: Arg_2+4 {O(n)}
14: eval_realheapsort_step1_bb4_in->eval_realheapsort_step1_5, Arg_2: Arg_2 {O(n)}
14: eval_realheapsort_step1_bb4_in->eval_realheapsort_step1_5, Arg_3: Arg_2+5 {O(n)}
14: eval_realheapsort_step1_bb4_in->eval_realheapsort_step1_5, Arg_4: Arg_2+4 {O(n)}
21: eval_realheapsort_step1_bb5_in->eval_realheapsort_step1_stop, Arg_2: 2*Arg_2 {O(n)}
21: eval_realheapsort_step1_bb5_in->eval_realheapsort_step1_stop, Arg_3: Arg_2+Arg_3+5 {O(n)}
21: eval_realheapsort_step1_bb5_in->eval_realheapsort_step1_stop, Arg_4: Arg_2+Arg_4+4 {O(n)}
0: eval_realheapsort_step1_start->eval_realheapsort_step1_bb0_in, Arg_0: Arg_0 {O(n)}
0: eval_realheapsort_step1_start->eval_realheapsort_step1_bb0_in, Arg_1: Arg_1 {O(n)}
0: eval_realheapsort_step1_start->eval_realheapsort_step1_bb0_in, Arg_2: Arg_2 {O(n)}
0: eval_realheapsort_step1_start->eval_realheapsort_step1_bb0_in, Arg_3: Arg_3 {O(n)}
0: eval_realheapsort_step1_start->eval_realheapsort_step1_bb0_in, Arg_4: Arg_4 {O(n)}