Initial Problem

Start: evalfstart
Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3, Arg_4
Temp_Vars: F
Locations: evalfbb2in, evalfbb3in, evalfbb4in, evalfbb5in, evalfbb6in, evalfbb7in, evalfbbin, evalfentryin, evalfreturnin, evalfstart, evalfstop
Transitions:
13:evalfbb2in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> evalfbb3in(Arg_0,Arg_1,Arg_2,Arg_3+1,Arg_4)
9:evalfbb3in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> evalfbb4in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:Arg_3<=Arg_1
8:evalfbb3in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> evalfbb5in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:Arg_1+1<=Arg_3
10:evalfbb4in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> evalfbb2in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:F+1<=0
11:evalfbb4in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> evalfbb2in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:1<=F
12:evalfbb4in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> evalfbb5in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4)
14:evalfbb5in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> evalfbb6in(Arg_0,Arg_1,Arg_2,Arg_0-1,Arg_3)
15:evalfbb6in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> evalfbb7in(Arg_3,Arg_1,Arg_4-1,Arg_3,Arg_4)
2:evalfbb7in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> evalfbbin(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:0<=Arg_0 && 0<=Arg_2
3:evalfbb7in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> evalfreturnin(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:Arg_0+1<=0
4:evalfbb7in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> evalfreturnin(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:Arg_2+1<=0
5:evalfbbin(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> evalfbb3in(Arg_0,Arg_1,Arg_2,Arg_2,Arg_4):|:F+1<=0
6:evalfbbin(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> evalfbb3in(Arg_0,Arg_1,Arg_2,Arg_2,Arg_4):|:1<=F
7:evalfbbin(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> evalfbb6in(Arg_0,Arg_1,Arg_2,Arg_0,Arg_2)
1:evalfentryin(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> evalfbb7in(Arg_1,Arg_1,0,Arg_3,Arg_4)
16:evalfreturnin(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> evalfstop(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4)
0:evalfstart(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> evalfentryin(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4)

Preprocessing

Found invariant 0<=Arg_3 && 0<=Arg_2+Arg_3 && Arg_2<=Arg_3 && 0<=Arg_1+Arg_3 && 0<=Arg_0+Arg_3 && 0<=Arg_2 && 0<=Arg_1+Arg_2 && 0<=Arg_0+Arg_2 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 0<=Arg_0 for location evalfbb5in

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

Found invariant Arg_3<=Arg_1 && 0<=Arg_3 && 0<=Arg_2+Arg_3 && Arg_2<=Arg_3 && 0<=Arg_1+Arg_3 && 0<=Arg_0+Arg_3 && Arg_2<=Arg_1 && 0<=Arg_2 && 0<=Arg_1+Arg_2 && 0<=Arg_0+Arg_2 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 0<=Arg_0 for location evalfbb2in

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

Found invariant 0<=Arg_3 && 0<=Arg_2+Arg_3 && Arg_2<=Arg_3 && 0<=Arg_1+Arg_3 && 0<=Arg_0+Arg_3 && 0<=Arg_2 && 0<=Arg_1+Arg_2 && 0<=Arg_0+Arg_2 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 0<=Arg_0 for location evalfbb3in

Found invariant 0<=Arg_4 && 0<=1+Arg_3+Arg_4 && 0<=Arg_2+Arg_4 && Arg_2<=Arg_4 && 0<=Arg_1+Arg_4 && 0<=Arg_0+Arg_4 && Arg_3<=Arg_1 && Arg_3<=Arg_0 && 0<=1+Arg_3 && 0<=1+Arg_2+Arg_3 && 0<=1+Arg_1+Arg_3 && 0<=1+Arg_0+Arg_3 && Arg_0<=1+Arg_3 && 0<=Arg_2 && 0<=Arg_1+Arg_2 && 0<=Arg_0+Arg_2 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 0<=Arg_0 for location evalfbb6in

Found invariant 0<=1+Arg_2 && Arg_0<=Arg_1 for location evalfbb7in

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

Found invariant Arg_3<=Arg_1 && 0<=Arg_3 && 0<=Arg_2+Arg_3 && Arg_2<=Arg_3 && 0<=Arg_1+Arg_3 && 0<=Arg_0+Arg_3 && Arg_2<=Arg_1 && 0<=Arg_2 && 0<=Arg_1+Arg_2 && 0<=Arg_0+Arg_2 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 0<=Arg_0 for location evalfbb4in

Problem after Preprocessing

Start: evalfstart
Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3, Arg_4
Temp_Vars: F
Locations: evalfbb2in, evalfbb3in, evalfbb4in, evalfbb5in, evalfbb6in, evalfbb7in, evalfbbin, evalfentryin, evalfreturnin, evalfstart, evalfstop
Transitions:
13:evalfbb2in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> evalfbb3in(Arg_0,Arg_1,Arg_2,Arg_3+1,Arg_4):|:Arg_3<=Arg_1 && 0<=Arg_3 && 0<=Arg_2+Arg_3 && Arg_2<=Arg_3 && 0<=Arg_1+Arg_3 && 0<=Arg_0+Arg_3 && Arg_2<=Arg_1 && 0<=Arg_2 && 0<=Arg_1+Arg_2 && 0<=Arg_0+Arg_2 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 0<=Arg_0
9:evalfbb3in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> evalfbb4in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:0<=Arg_3 && 0<=Arg_2+Arg_3 && Arg_2<=Arg_3 && 0<=Arg_1+Arg_3 && 0<=Arg_0+Arg_3 && 0<=Arg_2 && 0<=Arg_1+Arg_2 && 0<=Arg_0+Arg_2 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 0<=Arg_0 && Arg_3<=Arg_1
8:evalfbb3in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> evalfbb5in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:0<=Arg_3 && 0<=Arg_2+Arg_3 && Arg_2<=Arg_3 && 0<=Arg_1+Arg_3 && 0<=Arg_0+Arg_3 && 0<=Arg_2 && 0<=Arg_1+Arg_2 && 0<=Arg_0+Arg_2 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 0<=Arg_0 && Arg_1+1<=Arg_3
10:evalfbb4in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> evalfbb2in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:Arg_3<=Arg_1 && 0<=Arg_3 && 0<=Arg_2+Arg_3 && Arg_2<=Arg_3 && 0<=Arg_1+Arg_3 && 0<=Arg_0+Arg_3 && Arg_2<=Arg_1 && 0<=Arg_2 && 0<=Arg_1+Arg_2 && 0<=Arg_0+Arg_2 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 0<=Arg_0 && F+1<=0
11:evalfbb4in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> evalfbb2in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:Arg_3<=Arg_1 && 0<=Arg_3 && 0<=Arg_2+Arg_3 && Arg_2<=Arg_3 && 0<=Arg_1+Arg_3 && 0<=Arg_0+Arg_3 && Arg_2<=Arg_1 && 0<=Arg_2 && 0<=Arg_1+Arg_2 && 0<=Arg_0+Arg_2 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 0<=Arg_0 && 1<=F
12:evalfbb4in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> evalfbb5in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:Arg_3<=Arg_1 && 0<=Arg_3 && 0<=Arg_2+Arg_3 && Arg_2<=Arg_3 && 0<=Arg_1+Arg_3 && 0<=Arg_0+Arg_3 && Arg_2<=Arg_1 && 0<=Arg_2 && 0<=Arg_1+Arg_2 && 0<=Arg_0+Arg_2 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 0<=Arg_0
14:evalfbb5in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> evalfbb6in(Arg_0,Arg_1,Arg_2,Arg_0-1,Arg_3):|:0<=Arg_3 && 0<=Arg_2+Arg_3 && Arg_2<=Arg_3 && 0<=Arg_1+Arg_3 && 0<=Arg_0+Arg_3 && 0<=Arg_2 && 0<=Arg_1+Arg_2 && 0<=Arg_0+Arg_2 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 0<=Arg_0
15:evalfbb6in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> evalfbb7in(Arg_3,Arg_1,Arg_4-1,Arg_3,Arg_4):|:0<=Arg_4 && 0<=1+Arg_3+Arg_4 && 0<=Arg_2+Arg_4 && Arg_2<=Arg_4 && 0<=Arg_1+Arg_4 && 0<=Arg_0+Arg_4 && Arg_3<=Arg_1 && Arg_3<=Arg_0 && 0<=1+Arg_3 && 0<=1+Arg_2+Arg_3 && 0<=1+Arg_1+Arg_3 && 0<=1+Arg_0+Arg_3 && Arg_0<=1+Arg_3 && 0<=Arg_2 && 0<=Arg_1+Arg_2 && 0<=Arg_0+Arg_2 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 0<=Arg_0
2:evalfbb7in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> evalfbbin(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:0<=1+Arg_2 && Arg_0<=Arg_1 && 0<=Arg_0 && 0<=Arg_2
3:evalfbb7in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> evalfreturnin(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:0<=1+Arg_2 && Arg_0<=Arg_1 && Arg_0+1<=0
4:evalfbb7in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> evalfreturnin(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:0<=1+Arg_2 && Arg_0<=Arg_1 && Arg_2+1<=0
5:evalfbbin(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> evalfbb3in(Arg_0,Arg_1,Arg_2,Arg_2,Arg_4):|:0<=Arg_2 && 0<=Arg_1+Arg_2 && 0<=Arg_0+Arg_2 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 0<=Arg_0 && F+1<=0
6:evalfbbin(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> evalfbb3in(Arg_0,Arg_1,Arg_2,Arg_2,Arg_4):|:0<=Arg_2 && 0<=Arg_1+Arg_2 && 0<=Arg_0+Arg_2 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 0<=Arg_0 && 1<=F
7:evalfbbin(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> evalfbb6in(Arg_0,Arg_1,Arg_2,Arg_0,Arg_2):|:0<=Arg_2 && 0<=Arg_1+Arg_2 && 0<=Arg_0+Arg_2 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 0<=Arg_0
1:evalfentryin(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> evalfbb7in(Arg_1,Arg_1,0,Arg_3,Arg_4)
16:evalfreturnin(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> evalfstop(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:0<=1+Arg_2 && Arg_0<=Arg_1
0:evalfstart(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> evalfentryin(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4)

MPRF for transition 8:evalfbb3in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> evalfbb5in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:0<=Arg_3 && 0<=Arg_2+Arg_3 && Arg_2<=Arg_3 && 0<=Arg_1+Arg_3 && 0<=Arg_0+Arg_3 && 0<=Arg_2 && 0<=Arg_1+Arg_2 && 0<=Arg_0+Arg_2 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 0<=Arg_0 && Arg_1+1<=Arg_3 of depth 1:

new bound:

Arg_1+1 {O(n)}

MPRF:

evalfbb2in [Arg_0+1 ]
evalfbb4in [Arg_0+1 ]
evalfbb5in [Arg_0 ]
evalfbb7in [Arg_0+1 ]
evalfbb3in [Arg_0+1 ]
evalfbbin [Arg_0+1 ]
evalfbb6in [Arg_3+1 ]

MPRF for transition 12:evalfbb4in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> evalfbb5in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:Arg_3<=Arg_1 && 0<=Arg_3 && 0<=Arg_2+Arg_3 && Arg_2<=Arg_3 && 0<=Arg_1+Arg_3 && 0<=Arg_0+Arg_3 && Arg_2<=Arg_1 && 0<=Arg_2 && 0<=Arg_1+Arg_2 && 0<=Arg_0+Arg_2 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 0<=Arg_0 of depth 1:

new bound:

Arg_1+1 {O(n)}

MPRF:

evalfbb2in [Arg_0+1 ]
evalfbb4in [Arg_0+1 ]
evalfbb5in [Arg_0 ]
evalfbb7in [Arg_0+1 ]
evalfbb3in [Arg_0+1 ]
evalfbbin [Arg_0+1 ]
evalfbb6in [Arg_3+1 ]

MPRF for transition 14:evalfbb5in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> evalfbb6in(Arg_0,Arg_1,Arg_2,Arg_0-1,Arg_3):|:0<=Arg_3 && 0<=Arg_2+Arg_3 && Arg_2<=Arg_3 && 0<=Arg_1+Arg_3 && 0<=Arg_0+Arg_3 && 0<=Arg_2 && 0<=Arg_1+Arg_2 && 0<=Arg_0+Arg_2 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 0<=Arg_0 of depth 1:

new bound:

Arg_1+1 {O(n)}

MPRF:

evalfbb2in [Arg_0+1 ]
evalfbb4in [Arg_0+1 ]
evalfbb5in [Arg_0+1 ]
evalfbb7in [Arg_0+1 ]
evalfbb3in [Arg_0+1 ]
evalfbbin [Arg_0+1 ]
evalfbb6in [Arg_3+1 ]

MPRF for transition 5:evalfbbin(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> evalfbb3in(Arg_0,Arg_1,Arg_2,Arg_2,Arg_4):|:0<=Arg_2 && 0<=Arg_1+Arg_2 && 0<=Arg_0+Arg_2 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 0<=Arg_0 && F+1<=0 of depth 1:

new bound:

Arg_1+1 {O(n)}

MPRF:

evalfbb2in [Arg_0 ]
evalfbb4in [Arg_0 ]
evalfbb5in [Arg_0 ]
evalfbb7in [Arg_0+1 ]
evalfbb3in [Arg_0 ]
evalfbbin [Arg_0+1 ]
evalfbb6in [Arg_3+1 ]

MPRF for transition 6:evalfbbin(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> evalfbb3in(Arg_0,Arg_1,Arg_2,Arg_2,Arg_4):|:0<=Arg_2 && 0<=Arg_1+Arg_2 && 0<=Arg_0+Arg_2 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 0<=Arg_0 && 1<=F of depth 1:

new bound:

Arg_1+1 {O(n)}

MPRF:

evalfbb2in [Arg_0 ]
evalfbb4in [Arg_0 ]
evalfbb5in [Arg_0 ]
evalfbb7in [Arg_0+1 ]
evalfbb3in [Arg_0 ]
evalfbbin [Arg_0+1 ]
evalfbb6in [Arg_3+1 ]

MPRF for transition 13:evalfbb2in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> evalfbb3in(Arg_0,Arg_1,Arg_2,Arg_3+1,Arg_4):|:Arg_3<=Arg_1 && 0<=Arg_3 && 0<=Arg_2+Arg_3 && Arg_2<=Arg_3 && 0<=Arg_1+Arg_3 && 0<=Arg_0+Arg_3 && Arg_2<=Arg_1 && 0<=Arg_2 && 0<=Arg_1+Arg_2 && 0<=Arg_0+Arg_2 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 0<=Arg_0 of depth 1:

new bound:

6*Arg_1*Arg_1+15*Arg_1+4 {O(n^2)}

MPRF:

evalfbb2in [2*Arg_0+Arg_1+1-Arg_3 ]
evalfbb4in [2*Arg_0+Arg_1+1-Arg_3 ]
evalfbb5in [2*Arg_0+Arg_1-Arg_3 ]
evalfbb7in [2*Arg_0+4*Arg_1+1 ]
evalfbb3in [2*Arg_0+Arg_1+1-Arg_3 ]
evalfbbin [2*Arg_0+4*Arg_1+1 ]
evalfbb6in [2*Arg_0+4*Arg_1+1 ]

MPRF for transition 9:evalfbb3in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> evalfbb4in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:0<=Arg_3 && 0<=Arg_2+Arg_3 && Arg_2<=Arg_3 && 0<=Arg_1+Arg_3 && 0<=Arg_0+Arg_3 && 0<=Arg_2 && 0<=Arg_1+Arg_2 && 0<=Arg_0+Arg_2 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 0<=Arg_0 && Arg_3<=Arg_1 of depth 1:

new bound:

3*Arg_1*Arg_1+7*Arg_1+2 {O(n^2)}

MPRF:

evalfbb2in [2*Arg_0+Arg_1-Arg_3 ]
evalfbb4in [2*Arg_0+Arg_1-Arg_3 ]
evalfbb5in [2*Arg_0+Arg_1-Arg_3 ]
evalfbb7in [3*Arg_1+1 ]
evalfbb3in [2*Arg_0+Arg_1+1-Arg_3 ]
evalfbbin [3*Arg_1+1 ]
evalfbb6in [3*Arg_1+1 ]

MPRF for transition 10:evalfbb4in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> evalfbb2in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:Arg_3<=Arg_1 && 0<=Arg_3 && 0<=Arg_2+Arg_3 && Arg_2<=Arg_3 && 0<=Arg_1+Arg_3 && 0<=Arg_0+Arg_3 && Arg_2<=Arg_1 && 0<=Arg_2 && 0<=Arg_1+Arg_2 && 0<=Arg_0+Arg_2 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 0<=Arg_0 && F+1<=0 of depth 1:

new bound:

Arg_1*Arg_1+3*Arg_1+2 {O(n^2)}

MPRF:

evalfbb2in [Arg_1-Arg_3 ]
evalfbb4in [Arg_1+1-Arg_3 ]
evalfbb5in [Arg_1+1-Arg_3 ]
evalfbb7in [Arg_1+1 ]
evalfbb3in [Arg_1+1-Arg_3 ]
evalfbbin [Arg_1+1 ]
evalfbb6in [Arg_1+1 ]

MPRF for transition 11:evalfbb4in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> evalfbb2in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:Arg_3<=Arg_1 && 0<=Arg_3 && 0<=Arg_2+Arg_3 && Arg_2<=Arg_3 && 0<=Arg_1+Arg_3 && 0<=Arg_0+Arg_3 && Arg_2<=Arg_1 && 0<=Arg_2 && 0<=Arg_1+Arg_2 && 0<=Arg_0+Arg_2 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 0<=Arg_0 && 1<=F of depth 1:

new bound:

3*Arg_1*Arg_1+7*Arg_1+2 {O(n^2)}

MPRF:

evalfbb2in [Arg_0+Arg_1-Arg_3 ]
evalfbb4in [Arg_0+Arg_1+1-Arg_3 ]
evalfbb5in [Arg_0+Arg_1+1-Arg_3 ]
evalfbb7in [3*Arg_1+1 ]
evalfbb3in [Arg_0+Arg_1+1-Arg_3 ]
evalfbbin [3*Arg_1+1 ]
evalfbb6in [3*Arg_1+1 ]

MPRF for transition 15:evalfbb6in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> evalfbb7in(Arg_3,Arg_1,Arg_4-1,Arg_3,Arg_4):|:0<=Arg_4 && 0<=1+Arg_3+Arg_4 && 0<=Arg_2+Arg_4 && Arg_2<=Arg_4 && 0<=Arg_1+Arg_4 && 0<=Arg_0+Arg_4 && Arg_3<=Arg_1 && Arg_3<=Arg_0 && 0<=1+Arg_3 && 0<=1+Arg_2+Arg_3 && 0<=1+Arg_1+Arg_3 && 0<=1+Arg_0+Arg_3 && Arg_0<=1+Arg_3 && 0<=Arg_2 && 0<=Arg_1+Arg_2 && 0<=Arg_0+Arg_2 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 0<=Arg_0 of depth 1:

new bound:

6*Arg_1*Arg_1*Arg_1+21*Arg_1*Arg_1+21*Arg_1+7 {O(n^3)}

MPRF:

evalfbb2in [1 ]
evalfbb4in [1 ]
evalfbb5in [1 ]
evalfbb7in [Arg_2+1 ]
evalfbb3in [1 ]
evalfbbin [Arg_2+1 ]
evalfbb6in [Arg_4+1 ]

MPRF for transition 2:evalfbb7in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> evalfbbin(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:0<=1+Arg_2 && Arg_0<=Arg_1 && 0<=Arg_0 && 0<=Arg_2 of depth 1:

new bound:

6*Arg_1*Arg_1*Arg_1+21*Arg_1*Arg_1+21*Arg_1+8 {O(n^3)}

MPRF:

evalfbb2in [1 ]
evalfbb4in [1 ]
evalfbb5in [1 ]
evalfbb7in [Arg_2+2 ]
evalfbb3in [1 ]
evalfbbin [Arg_2+1 ]
evalfbb6in [Arg_4+1 ]

MPRF for transition 7:evalfbbin(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> evalfbb6in(Arg_0,Arg_1,Arg_2,Arg_0,Arg_2):|:0<=Arg_2 && 0<=Arg_1+Arg_2 && 0<=Arg_0+Arg_2 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 0<=Arg_0 of depth 1:

new bound:

6*Arg_1*Arg_1*Arg_1+21*Arg_1*Arg_1+20*Arg_1+6 {O(n^3)}

MPRF:

evalfbb2in [1 ]
evalfbb4in [1 ]
evalfbb5in [1 ]
evalfbb7in [Arg_2+1 ]
evalfbb3in [1 ]
evalfbbin [Arg_2+1 ]
evalfbb6in [Arg_4 ]

All Bounds

Timebounds

Overall timebound:18*Arg_1*Arg_1*Arg_1+76*Arg_1*Arg_1+99*Arg_1+41 {O(n^3)}
13: evalfbb2in->evalfbb3in: 6*Arg_1*Arg_1+15*Arg_1+4 {O(n^2)}
8: evalfbb3in->evalfbb5in: Arg_1+1 {O(n)}
9: evalfbb3in->evalfbb4in: 3*Arg_1*Arg_1+7*Arg_1+2 {O(n^2)}
10: evalfbb4in->evalfbb2in: Arg_1*Arg_1+3*Arg_1+2 {O(n^2)}
11: evalfbb4in->evalfbb2in: 3*Arg_1*Arg_1+7*Arg_1+2 {O(n^2)}
12: evalfbb4in->evalfbb5in: Arg_1+1 {O(n)}
14: evalfbb5in->evalfbb6in: Arg_1+1 {O(n)}
15: evalfbb6in->evalfbb7in: 6*Arg_1*Arg_1*Arg_1+21*Arg_1*Arg_1+21*Arg_1+7 {O(n^3)}
2: evalfbb7in->evalfbbin: 6*Arg_1*Arg_1*Arg_1+21*Arg_1*Arg_1+21*Arg_1+8 {O(n^3)}
3: evalfbb7in->evalfreturnin: 1 {O(1)}
4: evalfbb7in->evalfreturnin: 1 {O(1)}
5: evalfbbin->evalfbb3in: Arg_1+1 {O(n)}
6: evalfbbin->evalfbb3in: Arg_1+1 {O(n)}
7: evalfbbin->evalfbb6in: 6*Arg_1*Arg_1*Arg_1+21*Arg_1*Arg_1+20*Arg_1+6 {O(n^3)}
1: evalfentryin->evalfbb7in: 1 {O(1)}
16: evalfreturnin->evalfstop: 1 {O(1)}
0: evalfstart->evalfentryin: 1 {O(1)}

Costbounds

Overall costbound: 18*Arg_1*Arg_1*Arg_1+76*Arg_1*Arg_1+99*Arg_1+41 {O(n^3)}
13: evalfbb2in->evalfbb3in: 6*Arg_1*Arg_1+15*Arg_1+4 {O(n^2)}
8: evalfbb3in->evalfbb5in: Arg_1+1 {O(n)}
9: evalfbb3in->evalfbb4in: 3*Arg_1*Arg_1+7*Arg_1+2 {O(n^2)}
10: evalfbb4in->evalfbb2in: Arg_1*Arg_1+3*Arg_1+2 {O(n^2)}
11: evalfbb4in->evalfbb2in: 3*Arg_1*Arg_1+7*Arg_1+2 {O(n^2)}
12: evalfbb4in->evalfbb5in: Arg_1+1 {O(n)}
14: evalfbb5in->evalfbb6in: Arg_1+1 {O(n)}
15: evalfbb6in->evalfbb7in: 6*Arg_1*Arg_1*Arg_1+21*Arg_1*Arg_1+21*Arg_1+7 {O(n^3)}
2: evalfbb7in->evalfbbin: 6*Arg_1*Arg_1*Arg_1+21*Arg_1*Arg_1+21*Arg_1+8 {O(n^3)}
3: evalfbb7in->evalfreturnin: 1 {O(1)}
4: evalfbb7in->evalfreturnin: 1 {O(1)}
5: evalfbbin->evalfbb3in: Arg_1+1 {O(n)}
6: evalfbbin->evalfbb3in: Arg_1+1 {O(n)}
7: evalfbbin->evalfbb6in: 6*Arg_1*Arg_1*Arg_1+21*Arg_1*Arg_1+20*Arg_1+6 {O(n^3)}
1: evalfentryin->evalfbb7in: 1 {O(1)}
16: evalfreturnin->evalfstop: 1 {O(1)}
0: evalfstart->evalfentryin: 1 {O(1)}

Sizebounds

13: evalfbb2in->evalfbb3in, Arg_0: Arg_1+1 {O(n)}
13: evalfbb2in->evalfbb3in, Arg_1: Arg_1 {O(n)}
13: evalfbb2in->evalfbb3in, Arg_2: 12*Arg_1*Arg_1+30*Arg_1+10 {O(n^2)}
13: evalfbb2in->evalfbb3in, Arg_3: 6*Arg_1*Arg_1+15*Arg_1+5 {O(n^2)}
13: evalfbb2in->evalfbb3in, Arg_4: 24*Arg_1*Arg_1+2*Arg_4+60*Arg_1+20 {O(n^2)}
8: evalfbb3in->evalfbb5in, Arg_0: Arg_1+1 {O(n)}
8: evalfbb3in->evalfbb5in, Arg_1: Arg_1 {O(n)}
8: evalfbb3in->evalfbb5in, Arg_2: 24*Arg_1*Arg_1+60*Arg_1+20 {O(n^2)}
8: evalfbb3in->evalfbb5in, Arg_3: 6*Arg_1*Arg_1+15*Arg_1+5 {O(n^2)}
8: evalfbb3in->evalfbb5in, Arg_4: 48*Arg_1*Arg_1+120*Arg_1+4*Arg_4+40 {O(n^2)}
9: evalfbb3in->evalfbb4in, Arg_0: Arg_1+1 {O(n)}
9: evalfbb3in->evalfbb4in, Arg_1: Arg_1 {O(n)}
9: evalfbb3in->evalfbb4in, Arg_2: 12*Arg_1*Arg_1+30*Arg_1+10 {O(n^2)}
9: evalfbb3in->evalfbb4in, Arg_3: 6*Arg_1*Arg_1+15*Arg_1+5 {O(n^2)}
9: evalfbb3in->evalfbb4in, Arg_4: 24*Arg_1*Arg_1+2*Arg_4+60*Arg_1+20 {O(n^2)}
10: evalfbb4in->evalfbb2in, Arg_0: Arg_1+1 {O(n)}
10: evalfbb4in->evalfbb2in, Arg_1: Arg_1 {O(n)}
10: evalfbb4in->evalfbb2in, Arg_2: 12*Arg_1*Arg_1+30*Arg_1+10 {O(n^2)}
10: evalfbb4in->evalfbb2in, Arg_3: 6*Arg_1*Arg_1+15*Arg_1+5 {O(n^2)}
10: evalfbb4in->evalfbb2in, Arg_4: 24*Arg_1*Arg_1+2*Arg_4+60*Arg_1+20 {O(n^2)}
11: evalfbb4in->evalfbb2in, Arg_0: Arg_1+1 {O(n)}
11: evalfbb4in->evalfbb2in, Arg_1: Arg_1 {O(n)}
11: evalfbb4in->evalfbb2in, Arg_2: 12*Arg_1*Arg_1+30*Arg_1+10 {O(n^2)}
11: evalfbb4in->evalfbb2in, Arg_3: 6*Arg_1*Arg_1+15*Arg_1+5 {O(n^2)}
11: evalfbb4in->evalfbb2in, Arg_4: 24*Arg_1*Arg_1+2*Arg_4+60*Arg_1+20 {O(n^2)}
12: evalfbb4in->evalfbb5in, Arg_0: Arg_1+1 {O(n)}
12: evalfbb4in->evalfbb5in, Arg_1: Arg_1 {O(n)}
12: evalfbb4in->evalfbb5in, Arg_2: 12*Arg_1*Arg_1+30*Arg_1+10 {O(n^2)}
12: evalfbb4in->evalfbb5in, Arg_3: 6*Arg_1*Arg_1+15*Arg_1+5 {O(n^2)}
12: evalfbb4in->evalfbb5in, Arg_4: 24*Arg_1*Arg_1+2*Arg_4+60*Arg_1+20 {O(n^2)}
14: evalfbb5in->evalfbb6in, Arg_0: Arg_1+1 {O(n)}
14: evalfbb5in->evalfbb6in, Arg_1: Arg_1 {O(n)}
14: evalfbb5in->evalfbb6in, Arg_2: 36*Arg_1*Arg_1+90*Arg_1+30 {O(n^2)}
14: evalfbb5in->evalfbb6in, Arg_3: 2*Arg_1+4 {O(n)}
14: evalfbb5in->evalfbb6in, Arg_4: 6*Arg_1*Arg_1+15*Arg_1+5 {O(n^2)}
15: evalfbb6in->evalfbb7in, Arg_0: Arg_1+1 {O(n)}
15: evalfbb6in->evalfbb7in, Arg_1: Arg_1 {O(n)}
15: evalfbb6in->evalfbb7in, Arg_2: 6*Arg_1*Arg_1+15*Arg_1+5 {O(n^2)}
15: evalfbb6in->evalfbb7in, Arg_3: 3*Arg_1+5 {O(n)}
15: evalfbb6in->evalfbb7in, Arg_4: 12*Arg_1*Arg_1+30*Arg_1+10 {O(n^2)}
2: evalfbb7in->evalfbbin, Arg_0: Arg_1+1 {O(n)}
2: evalfbb7in->evalfbbin, Arg_1: Arg_1 {O(n)}
2: evalfbb7in->evalfbbin, Arg_2: 6*Arg_1*Arg_1+15*Arg_1+5 {O(n^2)}
2: evalfbb7in->evalfbbin, Arg_3: 3*Arg_1+Arg_3+5 {O(n)}
2: evalfbb7in->evalfbbin, Arg_4: 12*Arg_1*Arg_1+30*Arg_1+Arg_4+10 {O(n^2)}
3: evalfbb7in->evalfreturnin, Arg_0: 2*Arg_1+1 {O(n)}
3: evalfbb7in->evalfreturnin, Arg_1: 2*Arg_1 {O(n)}
3: evalfbb7in->evalfreturnin, Arg_2: 6*Arg_1*Arg_1+15*Arg_1+5 {O(n^2)}
3: evalfbb7in->evalfreturnin, Arg_3: 3*Arg_1+Arg_3+5 {O(n)}
3: evalfbb7in->evalfreturnin, Arg_4: 12*Arg_1*Arg_1+30*Arg_1+Arg_4+10 {O(n^2)}
4: evalfbb7in->evalfreturnin, Arg_0: Arg_1+1 {O(n)}
4: evalfbb7in->evalfreturnin, Arg_1: Arg_1 {O(n)}
4: evalfbb7in->evalfreturnin, Arg_2: 1 {O(1)}
4: evalfbb7in->evalfreturnin, Arg_3: 3*Arg_1+5 {O(n)}
4: evalfbb7in->evalfreturnin, Arg_4: 12*Arg_1*Arg_1+30*Arg_1+10 {O(n^2)}
5: evalfbbin->evalfbb3in, Arg_0: Arg_1+1 {O(n)}
5: evalfbbin->evalfbb3in, Arg_1: Arg_1 {O(n)}
5: evalfbbin->evalfbb3in, Arg_2: 6*Arg_1*Arg_1+15*Arg_1+5 {O(n^2)}
5: evalfbbin->evalfbb3in, Arg_3: 6*Arg_1*Arg_1+15*Arg_1+5 {O(n^2)}
5: evalfbbin->evalfbb3in, Arg_4: 12*Arg_1*Arg_1+30*Arg_1+Arg_4+10 {O(n^2)}
6: evalfbbin->evalfbb3in, Arg_0: Arg_1+1 {O(n)}
6: evalfbbin->evalfbb3in, Arg_1: Arg_1 {O(n)}
6: evalfbbin->evalfbb3in, Arg_2: 6*Arg_1*Arg_1+15*Arg_1+5 {O(n^2)}
6: evalfbbin->evalfbb3in, Arg_3: 6*Arg_1*Arg_1+15*Arg_1+5 {O(n^2)}
6: evalfbbin->evalfbb3in, Arg_4: 12*Arg_1*Arg_1+30*Arg_1+Arg_4+10 {O(n^2)}
7: evalfbbin->evalfbb6in, Arg_0: Arg_1+1 {O(n)}
7: evalfbbin->evalfbb6in, Arg_1: Arg_1 {O(n)}
7: evalfbbin->evalfbb6in, Arg_2: 6*Arg_1*Arg_1+15*Arg_1+5 {O(n^2)}
7: evalfbbin->evalfbb6in, Arg_3: Arg_1+1 {O(n)}
7: evalfbbin->evalfbb6in, Arg_4: 6*Arg_1*Arg_1+15*Arg_1+5 {O(n^2)}
1: evalfentryin->evalfbb7in, Arg_0: Arg_1 {O(n)}
1: evalfentryin->evalfbb7in, Arg_1: Arg_1 {O(n)}
1: evalfentryin->evalfbb7in, Arg_2: 0 {O(1)}
1: evalfentryin->evalfbb7in, Arg_3: Arg_3 {O(n)}
1: evalfentryin->evalfbb7in, Arg_4: Arg_4 {O(n)}
16: evalfreturnin->evalfstop, Arg_0: 3*Arg_1+2 {O(n)}
16: evalfreturnin->evalfstop, Arg_1: 3*Arg_1 {O(n)}
16: evalfreturnin->evalfstop, Arg_2: 6*Arg_1*Arg_1+15*Arg_1+6 {O(n^2)}
16: evalfreturnin->evalfstop, Arg_3: 6*Arg_1+Arg_3+10 {O(n)}
16: evalfreturnin->evalfstop, Arg_4: 24*Arg_1*Arg_1+60*Arg_1+Arg_4+20 {O(n^2)}
0: evalfstart->evalfentryin, Arg_0: Arg_0 {O(n)}
0: evalfstart->evalfentryin, Arg_1: Arg_1 {O(n)}
0: evalfstart->evalfentryin, Arg_2: Arg_2 {O(n)}
0: evalfstart->evalfentryin, Arg_3: Arg_3 {O(n)}
0: evalfstart->evalfentryin, Arg_4: Arg_4 {O(n)}