Initial Problem

Start: eval_Loopus2015_ex2_start
Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3, Arg_4, Arg_5, Arg_6
Temp_Vars: nondef.0
Locations: eval_Loopus2015_ex2_0, eval_Loopus2015_ex2_1, eval_Loopus2015_ex2_bb0_in, eval_Loopus2015_ex2_bb1_in, eval_Loopus2015_ex2_bb2_in, eval_Loopus2015_ex2_bb3_in, eval_Loopus2015_ex2_bb4_in, eval_Loopus2015_ex2_bb5_in, eval_Loopus2015_ex2_bb6_in, eval_Loopus2015_ex2_start, eval_Loopus2015_ex2_stop
Transitions:
7:eval_Loopus2015_ex2_0(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6) -> eval_Loopus2015_ex2_1(nondef.0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6)
8:eval_Loopus2015_ex2_1(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6) -> eval_Loopus2015_ex2_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_1,Arg_3,Arg_6):|:0<Arg_0
9:eval_Loopus2015_ex2_1(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6) -> eval_Loopus2015_ex2_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_2,Arg_3,Arg_6):|:Arg_0<=0
4:eval_Loopus2015_ex2_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6) -> eval_Loopus2015_ex2_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6):|:0<=Arg_3 && 0<=Arg_1 && 0<=Arg_2
1:eval_Loopus2015_ex2_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6) -> eval_Loopus2015_ex2_bb6_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6):|:Arg_3<0
2:eval_Loopus2015_ex2_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6) -> eval_Loopus2015_ex2_bb6_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6):|:Arg_1<0
3:eval_Loopus2015_ex2_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6) -> eval_Loopus2015_ex2_bb6_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6):|:Arg_2<0
5:eval_Loopus2015_ex2_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6) -> eval_Loopus2015_ex2_0(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6)
10:eval_Loopus2015_ex2_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6) -> eval_Loopus2015_ex2_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6):|:0<Arg_5
11:eval_Loopus2015_ex2_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6) -> eval_Loopus2015_ex2_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_4):|:Arg_5<=0
12:eval_Loopus2015_ex2_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6) -> eval_Loopus2015_ex2_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4+2,Arg_5-1,Arg_6)
13:eval_Loopus2015_ex2_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6) -> eval_Loopus2015_ex2_bb5_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6):|:0<Arg_6
14:eval_Loopus2015_ex2_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6) -> eval_Loopus2015_ex2_bb6_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6):|:Arg_6<=0
15:eval_Loopus2015_ex2_bb5_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6) -> eval_Loopus2015_ex2_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6-1)
16:eval_Loopus2015_ex2_bb6_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6) -> eval_Loopus2015_ex2_stop(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6)
0:eval_Loopus2015_ex2_start(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6) -> eval_Loopus2015_ex2_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6)

Preprocessing

Found invariant Arg_6<=Arg_4 && 1<=Arg_6 && 1<=Arg_5+Arg_6 && 1+Arg_5<=Arg_6 && 2<=Arg_4+Arg_6 && 1<=Arg_3+Arg_6 && 1<=Arg_2+Arg_6 && 1<=Arg_1+Arg_6 && Arg_5<=0 && 1+Arg_5<=Arg_4 && Arg_5<=Arg_3 && Arg_5<=Arg_2 && Arg_5<=Arg_1 && 0<=Arg_5 && 1<=Arg_4+Arg_5 && 0<=Arg_3+Arg_5 && 0<=Arg_2+Arg_5 && 0<=Arg_1+Arg_5 && 1<=Arg_4 && 1<=Arg_3+Arg_4 && 1<=Arg_2+Arg_4 && 1<=Arg_1+Arg_4 && 0<=Arg_3 && 0<=Arg_2+Arg_3 && 0<=Arg_1+Arg_3 && 0<=Arg_2 && 0<=Arg_1+Arg_2 && 0<=Arg_1 for location eval_Loopus2015_ex2_bb5_in

Found invariant Arg_6<=Arg_4 && 0<=Arg_6 && 0<=Arg_5+Arg_6 && Arg_5<=Arg_6 && 0<=Arg_4+Arg_6 && 0<=Arg_3+Arg_6 && 0<=Arg_2+Arg_6 && 0<=Arg_1+Arg_6 && Arg_5<=0 && Arg_5<=Arg_4 && Arg_5<=Arg_3 && Arg_5<=Arg_2 && Arg_5<=Arg_1 && 0<=Arg_5 && 0<=Arg_4+Arg_5 && 0<=Arg_3+Arg_5 && 0<=Arg_2+Arg_5 && 0<=Arg_1+Arg_5 && 0<=Arg_4 && 0<=Arg_3+Arg_4 && 0<=Arg_2+Arg_4 && 0<=Arg_1+Arg_4 && 0<=Arg_3 && 0<=Arg_2+Arg_3 && 0<=Arg_1+Arg_3 && 0<=Arg_2 && 0<=Arg_1+Arg_2 && 0<=Arg_1 for location eval_Loopus2015_ex2_bb4_in

Found invariant Arg_5<=Arg_3 && 1<=Arg_5 && 1<=Arg_4+Arg_5 && 2<=Arg_3+Arg_5 && 1<=Arg_2+Arg_5 && 1<=Arg_1+Arg_5 && 0<=Arg_4 && 1<=Arg_3+Arg_4 && 0<=Arg_2+Arg_4 && 0<=Arg_1+Arg_4 && 1<=Arg_3 && 1<=Arg_2+Arg_3 && 1<=Arg_1+Arg_3 && 0<=Arg_2 && 0<=Arg_1+Arg_2 && 0<=Arg_1 for location eval_Loopus2015_ex2_bb3_in

Found invariant 0<=Arg_3 && 0<=Arg_2+Arg_3 && 0<=Arg_1+Arg_3 && 0<=Arg_2 && 0<=Arg_1+Arg_2 && 0<=Arg_1 for location eval_Loopus2015_ex2_bb1_in

Found invariant 0<=Arg_3 && 0<=Arg_2+Arg_3 && 0<=Arg_1+Arg_3 && 0<=Arg_2 && 0<=Arg_1+Arg_2 && 0<=Arg_1 for location eval_Loopus2015_ex2_1

Found invariant 0<=Arg_3 && 0<=Arg_2+Arg_3 && 0<=Arg_1+Arg_3 && 0<=Arg_2 && 0<=Arg_1+Arg_2 && 0<=Arg_1 for location eval_Loopus2015_ex2_0

Found invariant Arg_5<=Arg_3 && 0<=Arg_5 && 0<=Arg_4+Arg_5 && 0<=Arg_3+Arg_5 && 0<=Arg_2+Arg_5 && 0<=Arg_1+Arg_5 && 0<=Arg_4 && 0<=Arg_3+Arg_4 && 0<=Arg_2+Arg_4 && 0<=Arg_1+Arg_4 && 0<=Arg_3 && 0<=Arg_2+Arg_3 && 0<=Arg_1+Arg_3 && 0<=Arg_2 && 0<=Arg_1+Arg_2 && 0<=Arg_1 for location eval_Loopus2015_ex2_bb2_in

Problem after Preprocessing

Start: eval_Loopus2015_ex2_start
Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3, Arg_4, Arg_5, Arg_6
Temp_Vars: nondef.0
Locations: eval_Loopus2015_ex2_0, eval_Loopus2015_ex2_1, eval_Loopus2015_ex2_bb0_in, eval_Loopus2015_ex2_bb1_in, eval_Loopus2015_ex2_bb2_in, eval_Loopus2015_ex2_bb3_in, eval_Loopus2015_ex2_bb4_in, eval_Loopus2015_ex2_bb5_in, eval_Loopus2015_ex2_bb6_in, eval_Loopus2015_ex2_start, eval_Loopus2015_ex2_stop
Transitions:
7:eval_Loopus2015_ex2_0(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6) -> eval_Loopus2015_ex2_1(nondef.0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6):|:0<=Arg_3 && 0<=Arg_2+Arg_3 && 0<=Arg_1+Arg_3 && 0<=Arg_2 && 0<=Arg_1+Arg_2 && 0<=Arg_1
8:eval_Loopus2015_ex2_1(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6) -> eval_Loopus2015_ex2_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_1,Arg_3,Arg_6):|:0<=Arg_3 && 0<=Arg_2+Arg_3 && 0<=Arg_1+Arg_3 && 0<=Arg_2 && 0<=Arg_1+Arg_2 && 0<=Arg_1 && 0<Arg_0
9:eval_Loopus2015_ex2_1(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6) -> eval_Loopus2015_ex2_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_2,Arg_3,Arg_6):|:0<=Arg_3 && 0<=Arg_2+Arg_3 && 0<=Arg_1+Arg_3 && 0<=Arg_2 && 0<=Arg_1+Arg_2 && 0<=Arg_1 && Arg_0<=0
4:eval_Loopus2015_ex2_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6) -> eval_Loopus2015_ex2_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6):|:0<=Arg_3 && 0<=Arg_1 && 0<=Arg_2
1:eval_Loopus2015_ex2_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6) -> eval_Loopus2015_ex2_bb6_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6):|:Arg_3<0
2:eval_Loopus2015_ex2_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6) -> eval_Loopus2015_ex2_bb6_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6):|:Arg_1<0
3:eval_Loopus2015_ex2_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6) -> eval_Loopus2015_ex2_bb6_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6):|:Arg_2<0
5:eval_Loopus2015_ex2_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6) -> eval_Loopus2015_ex2_0(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6):|:0<=Arg_3 && 0<=Arg_2+Arg_3 && 0<=Arg_1+Arg_3 && 0<=Arg_2 && 0<=Arg_1+Arg_2 && 0<=Arg_1
10:eval_Loopus2015_ex2_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6) -> eval_Loopus2015_ex2_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6):|:Arg_5<=Arg_3 && 0<=Arg_5 && 0<=Arg_4+Arg_5 && 0<=Arg_3+Arg_5 && 0<=Arg_2+Arg_5 && 0<=Arg_1+Arg_5 && 0<=Arg_4 && 0<=Arg_3+Arg_4 && 0<=Arg_2+Arg_4 && 0<=Arg_1+Arg_4 && 0<=Arg_3 && 0<=Arg_2+Arg_3 && 0<=Arg_1+Arg_3 && 0<=Arg_2 && 0<=Arg_1+Arg_2 && 0<=Arg_1 && 0<Arg_5
11:eval_Loopus2015_ex2_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6) -> eval_Loopus2015_ex2_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_4):|:Arg_5<=Arg_3 && 0<=Arg_5 && 0<=Arg_4+Arg_5 && 0<=Arg_3+Arg_5 && 0<=Arg_2+Arg_5 && 0<=Arg_1+Arg_5 && 0<=Arg_4 && 0<=Arg_3+Arg_4 && 0<=Arg_2+Arg_4 && 0<=Arg_1+Arg_4 && 0<=Arg_3 && 0<=Arg_2+Arg_3 && 0<=Arg_1+Arg_3 && 0<=Arg_2 && 0<=Arg_1+Arg_2 && 0<=Arg_1 && Arg_5<=0
12:eval_Loopus2015_ex2_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6) -> eval_Loopus2015_ex2_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4+2,Arg_5-1,Arg_6):|:Arg_5<=Arg_3 && 1<=Arg_5 && 1<=Arg_4+Arg_5 && 2<=Arg_3+Arg_5 && 1<=Arg_2+Arg_5 && 1<=Arg_1+Arg_5 && 0<=Arg_4 && 1<=Arg_3+Arg_4 && 0<=Arg_2+Arg_4 && 0<=Arg_1+Arg_4 && 1<=Arg_3 && 1<=Arg_2+Arg_3 && 1<=Arg_1+Arg_3 && 0<=Arg_2 && 0<=Arg_1+Arg_2 && 0<=Arg_1
13:eval_Loopus2015_ex2_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6) -> eval_Loopus2015_ex2_bb5_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6):|:Arg_6<=Arg_4 && 0<=Arg_6 && 0<=Arg_5+Arg_6 && Arg_5<=Arg_6 && 0<=Arg_4+Arg_6 && 0<=Arg_3+Arg_6 && 0<=Arg_2+Arg_6 && 0<=Arg_1+Arg_6 && Arg_5<=0 && Arg_5<=Arg_4 && Arg_5<=Arg_3 && Arg_5<=Arg_2 && Arg_5<=Arg_1 && 0<=Arg_5 && 0<=Arg_4+Arg_5 && 0<=Arg_3+Arg_5 && 0<=Arg_2+Arg_5 && 0<=Arg_1+Arg_5 && 0<=Arg_4 && 0<=Arg_3+Arg_4 && 0<=Arg_2+Arg_4 && 0<=Arg_1+Arg_4 && 0<=Arg_3 && 0<=Arg_2+Arg_3 && 0<=Arg_1+Arg_3 && 0<=Arg_2 && 0<=Arg_1+Arg_2 && 0<=Arg_1 && 0<Arg_6
14:eval_Loopus2015_ex2_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6) -> eval_Loopus2015_ex2_bb6_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6):|:Arg_6<=Arg_4 && 0<=Arg_6 && 0<=Arg_5+Arg_6 && Arg_5<=Arg_6 && 0<=Arg_4+Arg_6 && 0<=Arg_3+Arg_6 && 0<=Arg_2+Arg_6 && 0<=Arg_1+Arg_6 && Arg_5<=0 && Arg_5<=Arg_4 && Arg_5<=Arg_3 && Arg_5<=Arg_2 && Arg_5<=Arg_1 && 0<=Arg_5 && 0<=Arg_4+Arg_5 && 0<=Arg_3+Arg_5 && 0<=Arg_2+Arg_5 && 0<=Arg_1+Arg_5 && 0<=Arg_4 && 0<=Arg_3+Arg_4 && 0<=Arg_2+Arg_4 && 0<=Arg_1+Arg_4 && 0<=Arg_3 && 0<=Arg_2+Arg_3 && 0<=Arg_1+Arg_3 && 0<=Arg_2 && 0<=Arg_1+Arg_2 && 0<=Arg_1 && Arg_6<=0
15:eval_Loopus2015_ex2_bb5_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6) -> eval_Loopus2015_ex2_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6-1):|:Arg_6<=Arg_4 && 1<=Arg_6 && 1<=Arg_5+Arg_6 && 1+Arg_5<=Arg_6 && 2<=Arg_4+Arg_6 && 1<=Arg_3+Arg_6 && 1<=Arg_2+Arg_6 && 1<=Arg_1+Arg_6 && Arg_5<=0 && 1+Arg_5<=Arg_4 && Arg_5<=Arg_3 && Arg_5<=Arg_2 && Arg_5<=Arg_1 && 0<=Arg_5 && 1<=Arg_4+Arg_5 && 0<=Arg_3+Arg_5 && 0<=Arg_2+Arg_5 && 0<=Arg_1+Arg_5 && 1<=Arg_4 && 1<=Arg_3+Arg_4 && 1<=Arg_2+Arg_4 && 1<=Arg_1+Arg_4 && 0<=Arg_3 && 0<=Arg_2+Arg_3 && 0<=Arg_1+Arg_3 && 0<=Arg_2 && 0<=Arg_1+Arg_2 && 0<=Arg_1
16:eval_Loopus2015_ex2_bb6_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6) -> eval_Loopus2015_ex2_stop(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6)
0:eval_Loopus2015_ex2_start(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6) -> eval_Loopus2015_ex2_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6)

MPRF for transition 10:eval_Loopus2015_ex2_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6) -> eval_Loopus2015_ex2_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6):|:Arg_5<=Arg_3 && 0<=Arg_5 && 0<=Arg_4+Arg_5 && 0<=Arg_3+Arg_5 && 0<=Arg_2+Arg_5 && 0<=Arg_1+Arg_5 && 0<=Arg_4 && 0<=Arg_3+Arg_4 && 0<=Arg_2+Arg_4 && 0<=Arg_1+Arg_4 && 0<=Arg_3 && 0<=Arg_2+Arg_3 && 0<=Arg_1+Arg_3 && 0<=Arg_2 && 0<=Arg_1+Arg_2 && 0<=Arg_1 && 0<Arg_5 of depth 1:

new bound:

2*Arg_3+2 {O(n)}

MPRF:

eval_Loopus2015_ex2_bb3_in [Arg_5 ]
eval_Loopus2015_ex2_bb2_in [Arg_5+1 ]

MPRF for transition 12:eval_Loopus2015_ex2_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6) -> eval_Loopus2015_ex2_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4+2,Arg_5-1,Arg_6):|:Arg_5<=Arg_3 && 1<=Arg_5 && 1<=Arg_4+Arg_5 && 2<=Arg_3+Arg_5 && 1<=Arg_2+Arg_5 && 1<=Arg_1+Arg_5 && 0<=Arg_4 && 1<=Arg_3+Arg_4 && 0<=Arg_2+Arg_4 && 0<=Arg_1+Arg_4 && 1<=Arg_3 && 1<=Arg_2+Arg_3 && 1<=Arg_1+Arg_3 && 0<=Arg_2 && 0<=Arg_1+Arg_2 && 0<=Arg_1 of depth 1:

new bound:

2*Arg_3 {O(n)}

MPRF:

eval_Loopus2015_ex2_bb3_in [Arg_5 ]
eval_Loopus2015_ex2_bb2_in [Arg_5 ]

MPRF for transition 13:eval_Loopus2015_ex2_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6) -> eval_Loopus2015_ex2_bb5_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6):|:Arg_6<=Arg_4 && 0<=Arg_6 && 0<=Arg_5+Arg_6 && Arg_5<=Arg_6 && 0<=Arg_4+Arg_6 && 0<=Arg_3+Arg_6 && 0<=Arg_2+Arg_6 && 0<=Arg_1+Arg_6 && Arg_5<=0 && Arg_5<=Arg_4 && Arg_5<=Arg_3 && Arg_5<=Arg_2 && Arg_5<=Arg_1 && 0<=Arg_5 && 0<=Arg_4+Arg_5 && 0<=Arg_3+Arg_5 && 0<=Arg_2+Arg_5 && 0<=Arg_1+Arg_5 && 0<=Arg_4 && 0<=Arg_3+Arg_4 && 0<=Arg_2+Arg_4 && 0<=Arg_1+Arg_4 && 0<=Arg_3 && 0<=Arg_2+Arg_3 && 0<=Arg_1+Arg_3 && 0<=Arg_2 && 0<=Arg_1+Arg_2 && 0<=Arg_1 && 0<Arg_6 of depth 1:

new bound:

2*Arg_1+2*Arg_2+4*Arg_3+1 {O(n)}

MPRF:

eval_Loopus2015_ex2_bb5_in [Arg_6 ]
eval_Loopus2015_ex2_bb4_in [Arg_6+1 ]

MPRF for transition 15:eval_Loopus2015_ex2_bb5_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6) -> eval_Loopus2015_ex2_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6-1):|:Arg_6<=Arg_4 && 1<=Arg_6 && 1<=Arg_5+Arg_6 && 1+Arg_5<=Arg_6 && 2<=Arg_4+Arg_6 && 1<=Arg_3+Arg_6 && 1<=Arg_2+Arg_6 && 1<=Arg_1+Arg_6 && Arg_5<=0 && 1+Arg_5<=Arg_4 && Arg_5<=Arg_3 && Arg_5<=Arg_2 && Arg_5<=Arg_1 && 0<=Arg_5 && 1<=Arg_4+Arg_5 && 0<=Arg_3+Arg_5 && 0<=Arg_2+Arg_5 && 0<=Arg_1+Arg_5 && 1<=Arg_4 && 1<=Arg_3+Arg_4 && 1<=Arg_2+Arg_4 && 1<=Arg_1+Arg_4 && 0<=Arg_3 && 0<=Arg_2+Arg_3 && 0<=Arg_1+Arg_3 && 0<=Arg_2 && 0<=Arg_1+Arg_2 && 0<=Arg_1 of depth 1:

new bound:

2*Arg_1+2*Arg_2+4*Arg_3 {O(n)}

MPRF:

eval_Loopus2015_ex2_bb5_in [Arg_6 ]
eval_Loopus2015_ex2_bb4_in [Arg_6 ]

All Bounds

Timebounds

Overall timebound:12*Arg_3+4*Arg_1+4*Arg_2+15 {O(n)}
7: eval_Loopus2015_ex2_0->eval_Loopus2015_ex2_1: 1 {O(1)}
8: eval_Loopus2015_ex2_1->eval_Loopus2015_ex2_bb2_in: 1 {O(1)}
9: eval_Loopus2015_ex2_1->eval_Loopus2015_ex2_bb2_in: 1 {O(1)}
1: eval_Loopus2015_ex2_bb0_in->eval_Loopus2015_ex2_bb6_in: 1 {O(1)}
2: eval_Loopus2015_ex2_bb0_in->eval_Loopus2015_ex2_bb6_in: 1 {O(1)}
3: eval_Loopus2015_ex2_bb0_in->eval_Loopus2015_ex2_bb6_in: 1 {O(1)}
4: eval_Loopus2015_ex2_bb0_in->eval_Loopus2015_ex2_bb1_in: 1 {O(1)}
5: eval_Loopus2015_ex2_bb1_in->eval_Loopus2015_ex2_0: 1 {O(1)}
10: eval_Loopus2015_ex2_bb2_in->eval_Loopus2015_ex2_bb3_in: 2*Arg_3+2 {O(n)}
11: eval_Loopus2015_ex2_bb2_in->eval_Loopus2015_ex2_bb4_in: 1 {O(1)}
12: eval_Loopus2015_ex2_bb3_in->eval_Loopus2015_ex2_bb2_in: 2*Arg_3 {O(n)}
13: eval_Loopus2015_ex2_bb4_in->eval_Loopus2015_ex2_bb5_in: 2*Arg_1+2*Arg_2+4*Arg_3+1 {O(n)}
14: eval_Loopus2015_ex2_bb4_in->eval_Loopus2015_ex2_bb6_in: 1 {O(1)}
15: eval_Loopus2015_ex2_bb5_in->eval_Loopus2015_ex2_bb4_in: 2*Arg_1+2*Arg_2+4*Arg_3 {O(n)}
16: eval_Loopus2015_ex2_bb6_in->eval_Loopus2015_ex2_stop: 1 {O(1)}
0: eval_Loopus2015_ex2_start->eval_Loopus2015_ex2_bb0_in: 1 {O(1)}

Costbounds

Overall costbound: 12*Arg_3+4*Arg_1+4*Arg_2+15 {O(n)}
7: eval_Loopus2015_ex2_0->eval_Loopus2015_ex2_1: 1 {O(1)}
8: eval_Loopus2015_ex2_1->eval_Loopus2015_ex2_bb2_in: 1 {O(1)}
9: eval_Loopus2015_ex2_1->eval_Loopus2015_ex2_bb2_in: 1 {O(1)}
1: eval_Loopus2015_ex2_bb0_in->eval_Loopus2015_ex2_bb6_in: 1 {O(1)}
2: eval_Loopus2015_ex2_bb0_in->eval_Loopus2015_ex2_bb6_in: 1 {O(1)}
3: eval_Loopus2015_ex2_bb0_in->eval_Loopus2015_ex2_bb6_in: 1 {O(1)}
4: eval_Loopus2015_ex2_bb0_in->eval_Loopus2015_ex2_bb1_in: 1 {O(1)}
5: eval_Loopus2015_ex2_bb1_in->eval_Loopus2015_ex2_0: 1 {O(1)}
10: eval_Loopus2015_ex2_bb2_in->eval_Loopus2015_ex2_bb3_in: 2*Arg_3+2 {O(n)}
11: eval_Loopus2015_ex2_bb2_in->eval_Loopus2015_ex2_bb4_in: 1 {O(1)}
12: eval_Loopus2015_ex2_bb3_in->eval_Loopus2015_ex2_bb2_in: 2*Arg_3 {O(n)}
13: eval_Loopus2015_ex2_bb4_in->eval_Loopus2015_ex2_bb5_in: 2*Arg_1+2*Arg_2+4*Arg_3+1 {O(n)}
14: eval_Loopus2015_ex2_bb4_in->eval_Loopus2015_ex2_bb6_in: 1 {O(1)}
15: eval_Loopus2015_ex2_bb5_in->eval_Loopus2015_ex2_bb4_in: 2*Arg_1+2*Arg_2+4*Arg_3 {O(n)}
16: eval_Loopus2015_ex2_bb6_in->eval_Loopus2015_ex2_stop: 1 {O(1)}
0: eval_Loopus2015_ex2_start->eval_Loopus2015_ex2_bb0_in: 1 {O(1)}

Sizebounds

7: eval_Loopus2015_ex2_0->eval_Loopus2015_ex2_1, Arg_1: Arg_1 {O(n)}
7: eval_Loopus2015_ex2_0->eval_Loopus2015_ex2_1, Arg_2: Arg_2 {O(n)}
7: eval_Loopus2015_ex2_0->eval_Loopus2015_ex2_1, Arg_3: Arg_3 {O(n)}
7: eval_Loopus2015_ex2_0->eval_Loopus2015_ex2_1, Arg_4: Arg_4 {O(n)}
7: eval_Loopus2015_ex2_0->eval_Loopus2015_ex2_1, Arg_5: Arg_5 {O(n)}
7: eval_Loopus2015_ex2_0->eval_Loopus2015_ex2_1, Arg_6: Arg_6 {O(n)}
8: eval_Loopus2015_ex2_1->eval_Loopus2015_ex2_bb2_in, Arg_1: Arg_1 {O(n)}
8: eval_Loopus2015_ex2_1->eval_Loopus2015_ex2_bb2_in, Arg_2: Arg_2 {O(n)}
8: eval_Loopus2015_ex2_1->eval_Loopus2015_ex2_bb2_in, Arg_3: Arg_3 {O(n)}
8: eval_Loopus2015_ex2_1->eval_Loopus2015_ex2_bb2_in, Arg_4: Arg_1 {O(n)}
8: eval_Loopus2015_ex2_1->eval_Loopus2015_ex2_bb2_in, Arg_5: Arg_3 {O(n)}
8: eval_Loopus2015_ex2_1->eval_Loopus2015_ex2_bb2_in, Arg_6: Arg_6 {O(n)}
9: eval_Loopus2015_ex2_1->eval_Loopus2015_ex2_bb2_in, Arg_1: Arg_1 {O(n)}
9: eval_Loopus2015_ex2_1->eval_Loopus2015_ex2_bb2_in, Arg_2: Arg_2 {O(n)}
9: eval_Loopus2015_ex2_1->eval_Loopus2015_ex2_bb2_in, Arg_3: Arg_3 {O(n)}
9: eval_Loopus2015_ex2_1->eval_Loopus2015_ex2_bb2_in, Arg_4: Arg_2 {O(n)}
9: eval_Loopus2015_ex2_1->eval_Loopus2015_ex2_bb2_in, Arg_5: Arg_3 {O(n)}
9: eval_Loopus2015_ex2_1->eval_Loopus2015_ex2_bb2_in, Arg_6: Arg_6 {O(n)}
1: eval_Loopus2015_ex2_bb0_in->eval_Loopus2015_ex2_bb6_in, Arg_0: Arg_0 {O(n)}
1: eval_Loopus2015_ex2_bb0_in->eval_Loopus2015_ex2_bb6_in, Arg_1: Arg_1 {O(n)}
1: eval_Loopus2015_ex2_bb0_in->eval_Loopus2015_ex2_bb6_in, Arg_2: Arg_2 {O(n)}
1: eval_Loopus2015_ex2_bb0_in->eval_Loopus2015_ex2_bb6_in, Arg_3: Arg_3 {O(n)}
1: eval_Loopus2015_ex2_bb0_in->eval_Loopus2015_ex2_bb6_in, Arg_4: Arg_4 {O(n)}
1: eval_Loopus2015_ex2_bb0_in->eval_Loopus2015_ex2_bb6_in, Arg_5: Arg_5 {O(n)}
1: eval_Loopus2015_ex2_bb0_in->eval_Loopus2015_ex2_bb6_in, Arg_6: Arg_6 {O(n)}
2: eval_Loopus2015_ex2_bb0_in->eval_Loopus2015_ex2_bb6_in, Arg_0: Arg_0 {O(n)}
2: eval_Loopus2015_ex2_bb0_in->eval_Loopus2015_ex2_bb6_in, Arg_1: Arg_1 {O(n)}
2: eval_Loopus2015_ex2_bb0_in->eval_Loopus2015_ex2_bb6_in, Arg_2: Arg_2 {O(n)}
2: eval_Loopus2015_ex2_bb0_in->eval_Loopus2015_ex2_bb6_in, Arg_3: Arg_3 {O(n)}
2: eval_Loopus2015_ex2_bb0_in->eval_Loopus2015_ex2_bb6_in, Arg_4: Arg_4 {O(n)}
2: eval_Loopus2015_ex2_bb0_in->eval_Loopus2015_ex2_bb6_in, Arg_5: Arg_5 {O(n)}
2: eval_Loopus2015_ex2_bb0_in->eval_Loopus2015_ex2_bb6_in, Arg_6: Arg_6 {O(n)}
3: eval_Loopus2015_ex2_bb0_in->eval_Loopus2015_ex2_bb6_in, Arg_0: Arg_0 {O(n)}
3: eval_Loopus2015_ex2_bb0_in->eval_Loopus2015_ex2_bb6_in, Arg_1: Arg_1 {O(n)}
3: eval_Loopus2015_ex2_bb0_in->eval_Loopus2015_ex2_bb6_in, Arg_2: Arg_2 {O(n)}
3: eval_Loopus2015_ex2_bb0_in->eval_Loopus2015_ex2_bb6_in, Arg_3: Arg_3 {O(n)}
3: eval_Loopus2015_ex2_bb0_in->eval_Loopus2015_ex2_bb6_in, Arg_4: Arg_4 {O(n)}
3: eval_Loopus2015_ex2_bb0_in->eval_Loopus2015_ex2_bb6_in, Arg_5: Arg_5 {O(n)}
3: eval_Loopus2015_ex2_bb0_in->eval_Loopus2015_ex2_bb6_in, Arg_6: Arg_6 {O(n)}
4: eval_Loopus2015_ex2_bb0_in->eval_Loopus2015_ex2_bb1_in, Arg_0: Arg_0 {O(n)}
4: eval_Loopus2015_ex2_bb0_in->eval_Loopus2015_ex2_bb1_in, Arg_1: Arg_1 {O(n)}
4: eval_Loopus2015_ex2_bb0_in->eval_Loopus2015_ex2_bb1_in, Arg_2: Arg_2 {O(n)}
4: eval_Loopus2015_ex2_bb0_in->eval_Loopus2015_ex2_bb1_in, Arg_3: Arg_3 {O(n)}
4: eval_Loopus2015_ex2_bb0_in->eval_Loopus2015_ex2_bb1_in, Arg_4: Arg_4 {O(n)}
4: eval_Loopus2015_ex2_bb0_in->eval_Loopus2015_ex2_bb1_in, Arg_5: Arg_5 {O(n)}
4: eval_Loopus2015_ex2_bb0_in->eval_Loopus2015_ex2_bb1_in, Arg_6: Arg_6 {O(n)}
5: eval_Loopus2015_ex2_bb1_in->eval_Loopus2015_ex2_0, Arg_0: Arg_0 {O(n)}
5: eval_Loopus2015_ex2_bb1_in->eval_Loopus2015_ex2_0, Arg_1: Arg_1 {O(n)}
5: eval_Loopus2015_ex2_bb1_in->eval_Loopus2015_ex2_0, Arg_2: Arg_2 {O(n)}
5: eval_Loopus2015_ex2_bb1_in->eval_Loopus2015_ex2_0, Arg_3: Arg_3 {O(n)}
5: eval_Loopus2015_ex2_bb1_in->eval_Loopus2015_ex2_0, Arg_4: Arg_4 {O(n)}
5: eval_Loopus2015_ex2_bb1_in->eval_Loopus2015_ex2_0, Arg_5: Arg_5 {O(n)}
5: eval_Loopus2015_ex2_bb1_in->eval_Loopus2015_ex2_0, Arg_6: Arg_6 {O(n)}
10: eval_Loopus2015_ex2_bb2_in->eval_Loopus2015_ex2_bb3_in, Arg_1: 2*Arg_1 {O(n)}
10: eval_Loopus2015_ex2_bb2_in->eval_Loopus2015_ex2_bb3_in, Arg_2: 2*Arg_2 {O(n)}
10: eval_Loopus2015_ex2_bb2_in->eval_Loopus2015_ex2_bb3_in, Arg_3: 2*Arg_3 {O(n)}
10: eval_Loopus2015_ex2_bb2_in->eval_Loopus2015_ex2_bb3_in, Arg_4: 4*Arg_3+Arg_1+Arg_2 {O(n)}
10: eval_Loopus2015_ex2_bb2_in->eval_Loopus2015_ex2_bb3_in, Arg_5: 2*Arg_3 {O(n)}
10: eval_Loopus2015_ex2_bb2_in->eval_Loopus2015_ex2_bb3_in, Arg_6: 2*Arg_6 {O(n)}
11: eval_Loopus2015_ex2_bb2_in->eval_Loopus2015_ex2_bb4_in, Arg_1: 4*Arg_1 {O(n)}
11: eval_Loopus2015_ex2_bb2_in->eval_Loopus2015_ex2_bb4_in, Arg_2: 4*Arg_2 {O(n)}
11: eval_Loopus2015_ex2_bb2_in->eval_Loopus2015_ex2_bb4_in, Arg_3: 4*Arg_3 {O(n)}
11: eval_Loopus2015_ex2_bb2_in->eval_Loopus2015_ex2_bb4_in, Arg_4: 2*Arg_1+2*Arg_2+4*Arg_3 {O(n)}
11: eval_Loopus2015_ex2_bb2_in->eval_Loopus2015_ex2_bb4_in, Arg_5: 0 {O(1)}
11: eval_Loopus2015_ex2_bb2_in->eval_Loopus2015_ex2_bb4_in, Arg_6: 2*Arg_1+2*Arg_2+4*Arg_3 {O(n)}
12: eval_Loopus2015_ex2_bb3_in->eval_Loopus2015_ex2_bb2_in, Arg_1: 2*Arg_1 {O(n)}
12: eval_Loopus2015_ex2_bb3_in->eval_Loopus2015_ex2_bb2_in, Arg_2: 2*Arg_2 {O(n)}
12: eval_Loopus2015_ex2_bb3_in->eval_Loopus2015_ex2_bb2_in, Arg_3: 2*Arg_3 {O(n)}
12: eval_Loopus2015_ex2_bb3_in->eval_Loopus2015_ex2_bb2_in, Arg_4: 4*Arg_3+Arg_1+Arg_2 {O(n)}
12: eval_Loopus2015_ex2_bb3_in->eval_Loopus2015_ex2_bb2_in, Arg_5: 2*Arg_3 {O(n)}
12: eval_Loopus2015_ex2_bb3_in->eval_Loopus2015_ex2_bb2_in, Arg_6: 2*Arg_6 {O(n)}
13: eval_Loopus2015_ex2_bb4_in->eval_Loopus2015_ex2_bb5_in, Arg_1: 4*Arg_1 {O(n)}
13: eval_Loopus2015_ex2_bb4_in->eval_Loopus2015_ex2_bb5_in, Arg_2: 4*Arg_2 {O(n)}
13: eval_Loopus2015_ex2_bb4_in->eval_Loopus2015_ex2_bb5_in, Arg_3: 4*Arg_3 {O(n)}
13: eval_Loopus2015_ex2_bb4_in->eval_Loopus2015_ex2_bb5_in, Arg_4: 2*Arg_1+2*Arg_2+4*Arg_3 {O(n)}
13: eval_Loopus2015_ex2_bb4_in->eval_Loopus2015_ex2_bb5_in, Arg_5: 0 {O(1)}
13: eval_Loopus2015_ex2_bb4_in->eval_Loopus2015_ex2_bb5_in, Arg_6: 2*Arg_1+2*Arg_2+4*Arg_3 {O(n)}
14: eval_Loopus2015_ex2_bb4_in->eval_Loopus2015_ex2_bb6_in, Arg_1: 8*Arg_1 {O(n)}
14: eval_Loopus2015_ex2_bb4_in->eval_Loopus2015_ex2_bb6_in, Arg_2: 8*Arg_2 {O(n)}
14: eval_Loopus2015_ex2_bb4_in->eval_Loopus2015_ex2_bb6_in, Arg_3: 8*Arg_3 {O(n)}
14: eval_Loopus2015_ex2_bb4_in->eval_Loopus2015_ex2_bb6_in, Arg_4: 4*Arg_1+4*Arg_2+8*Arg_3 {O(n)}
14: eval_Loopus2015_ex2_bb4_in->eval_Loopus2015_ex2_bb6_in, Arg_5: 0 {O(1)}
14: eval_Loopus2015_ex2_bb4_in->eval_Loopus2015_ex2_bb6_in, Arg_6: 0 {O(1)}
15: eval_Loopus2015_ex2_bb5_in->eval_Loopus2015_ex2_bb4_in, Arg_1: 4*Arg_1 {O(n)}
15: eval_Loopus2015_ex2_bb5_in->eval_Loopus2015_ex2_bb4_in, Arg_2: 4*Arg_2 {O(n)}
15: eval_Loopus2015_ex2_bb5_in->eval_Loopus2015_ex2_bb4_in, Arg_3: 4*Arg_3 {O(n)}
15: eval_Loopus2015_ex2_bb5_in->eval_Loopus2015_ex2_bb4_in, Arg_4: 2*Arg_1+2*Arg_2+4*Arg_3 {O(n)}
15: eval_Loopus2015_ex2_bb5_in->eval_Loopus2015_ex2_bb4_in, Arg_5: 0 {O(1)}
15: eval_Loopus2015_ex2_bb5_in->eval_Loopus2015_ex2_bb4_in, Arg_6: 2*Arg_1+2*Arg_2+4*Arg_3 {O(n)}
16: eval_Loopus2015_ex2_bb6_in->eval_Loopus2015_ex2_stop, Arg_1: 11*Arg_1 {O(n)}
16: eval_Loopus2015_ex2_bb6_in->eval_Loopus2015_ex2_stop, Arg_2: 11*Arg_2 {O(n)}
16: eval_Loopus2015_ex2_bb6_in->eval_Loopus2015_ex2_stop, Arg_3: 11*Arg_3 {O(n)}
16: eval_Loopus2015_ex2_bb6_in->eval_Loopus2015_ex2_stop, Arg_4: 3*Arg_4+4*Arg_1+4*Arg_2+8*Arg_3 {O(n)}
16: eval_Loopus2015_ex2_bb6_in->eval_Loopus2015_ex2_stop, Arg_5: 3*Arg_5 {O(n)}
16: eval_Loopus2015_ex2_bb6_in->eval_Loopus2015_ex2_stop, Arg_6: 3*Arg_6 {O(n)}
0: eval_Loopus2015_ex2_start->eval_Loopus2015_ex2_bb0_in, Arg_0: Arg_0 {O(n)}
0: eval_Loopus2015_ex2_start->eval_Loopus2015_ex2_bb0_in, Arg_1: Arg_1 {O(n)}
0: eval_Loopus2015_ex2_start->eval_Loopus2015_ex2_bb0_in, Arg_2: Arg_2 {O(n)}
0: eval_Loopus2015_ex2_start->eval_Loopus2015_ex2_bb0_in, Arg_3: Arg_3 {O(n)}
0: eval_Loopus2015_ex2_start->eval_Loopus2015_ex2_bb0_in, Arg_4: Arg_4 {O(n)}
0: eval_Loopus2015_ex2_start->eval_Loopus2015_ex2_bb0_in, Arg_5: Arg_5 {O(n)}
0: eval_Loopus2015_ex2_start->eval_Loopus2015_ex2_bb0_in, Arg_6: Arg_6 {O(n)}