Initial Problem

Start: evalfstart
Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3, Arg_4
Temp_Vars:
Locations: evalfbb10in, evalfbb3in, evalfbb4in, evalfbb5in, evalfbb6in, evalfbb7in, evalfbb8in, evalfentryin, evalfreturnin, evalfstart, evalfstop
Transitions:
2:evalfbb10in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> evalfbb8in(Arg_0,Arg_1,1,Arg_3,Arg_4):|:Arg_0<=Arg_1
3:evalfbb10in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> evalfreturnin(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:Arg_1+1<=Arg_0
10:evalfbb3in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> evalfbb4in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4+1)
8:evalfbb4in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> evalfbb3in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:Arg_4<=Arg_3
9:evalfbb4in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> evalfbb5in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:Arg_3+1<=Arg_4
11:evalfbb5in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> evalfbb6in(Arg_0,Arg_1,Arg_2,Arg_3+1,Arg_4)
6:evalfbb6in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> evalfbb4in(Arg_0,Arg_1,Arg_2,Arg_3,1):|:Arg_3<=Arg_1
7:evalfbb6in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> evalfbb7in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:Arg_1+1<=Arg_3
12:evalfbb7in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> evalfbb8in(Arg_0,Arg_1,Arg_2+1,Arg_3,Arg_4)
5:evalfbb8in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> evalfbb10in(Arg_0+1,Arg_1,Arg_2,Arg_3,Arg_4):|:Arg_0+1<=Arg_2
4:evalfbb8in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> evalfbb6in(Arg_0,Arg_1,Arg_2,Arg_0+1,Arg_4):|:Arg_2<=Arg_0
1:evalfentryin(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> evalfbb10in(1,Arg_1,Arg_2,Arg_3,Arg_4)
13: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 Arg_4<=1+Arg_3 && Arg_4<=1+Arg_1 && 3<=Arg_4 && 5<=Arg_3+Arg_4 && 1+Arg_3<=Arg_4 && 4<=Arg_2+Arg_4 && 2+Arg_2<=Arg_4 && 5<=Arg_1+Arg_4 && 4<=Arg_0+Arg_4 && 2+Arg_0<=Arg_4 && Arg_3<=Arg_1 && 2<=Arg_3 && 3<=Arg_2+Arg_3 && 1+Arg_2<=Arg_3 && 4<=Arg_1+Arg_3 && 3<=Arg_0+Arg_3 && 1+Arg_0<=Arg_3 && 1+Arg_2<=Arg_1 && Arg_2<=Arg_0 && 1<=Arg_2 && 3<=Arg_1+Arg_2 && 2<=Arg_0+Arg_2 && 2<=Arg_1 && 3<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 1<=Arg_0 for location evalfbb5in

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

Found invariant 1<=Arg_0 for location evalfbb10in

Found invariant Arg_4<=Arg_3 && Arg_4<=Arg_1 && 1<=Arg_4 && 3<=Arg_3+Arg_4 && 2<=Arg_2+Arg_4 && 3<=Arg_1+Arg_4 && 2<=Arg_0+Arg_4 && Arg_3<=Arg_1 && 2<=Arg_3 && 3<=Arg_2+Arg_3 && 1+Arg_2<=Arg_3 && 4<=Arg_1+Arg_3 && 3<=Arg_0+Arg_3 && 1+Arg_0<=Arg_3 && 1+Arg_2<=Arg_1 && Arg_2<=Arg_0 && 1<=Arg_2 && 3<=Arg_1+Arg_2 && 2<=Arg_0+Arg_2 && 2<=Arg_1 && 3<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 1<=Arg_0 for location evalfbb3in

Found invariant Arg_3<=1+Arg_1 && 2<=Arg_3 && 3<=Arg_2+Arg_3 && 1+Arg_2<=Arg_3 && 3<=Arg_1+Arg_3 && 3<=Arg_0+Arg_3 && 1+Arg_0<=Arg_3 && Arg_2<=Arg_1 && Arg_2<=Arg_0 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && 2<=Arg_0+Arg_2 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 1<=Arg_0 for location evalfbb6in

Found invariant Arg_3<=1+Arg_1 && 2<=Arg_3 && 3<=Arg_2+Arg_3 && 1+Arg_2<=Arg_3 && 3<=Arg_1+Arg_3 && 1+Arg_1<=Arg_3 && 3<=Arg_0+Arg_3 && 1+Arg_0<=Arg_3 && Arg_2<=Arg_1 && Arg_2<=Arg_0 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && 2<=Arg_0+Arg_2 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 1<=Arg_0 for location evalfbb7in

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

Found invariant Arg_4<=1+Arg_3 && Arg_4<=1+Arg_1 && 1<=Arg_4 && 3<=Arg_3+Arg_4 && 2<=Arg_2+Arg_4 && 3<=Arg_1+Arg_4 && 2<=Arg_0+Arg_4 && Arg_3<=Arg_1 && 2<=Arg_3 && 3<=Arg_2+Arg_3 && 1+Arg_2<=Arg_3 && 4<=Arg_1+Arg_3 && 3<=Arg_0+Arg_3 && 1+Arg_0<=Arg_3 && 1+Arg_2<=Arg_1 && Arg_2<=Arg_0 && 1<=Arg_2 && 3<=Arg_1+Arg_2 && 2<=Arg_0+Arg_2 && 2<=Arg_1 && 3<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 1<=Arg_0 for location evalfbb4in

Found invariant Arg_2<=1+Arg_1 && Arg_2<=1+Arg_0 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && 2<=Arg_0+Arg_2 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 1<=Arg_0 for location evalfbb8in

Problem after Preprocessing

Start: evalfstart
Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3, Arg_4
Temp_Vars:
Locations: evalfbb10in, evalfbb3in, evalfbb4in, evalfbb5in, evalfbb6in, evalfbb7in, evalfbb8in, evalfentryin, evalfreturnin, evalfstart, evalfstop
Transitions:
2:evalfbb10in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> evalfbb8in(Arg_0,Arg_1,1,Arg_3,Arg_4):|:1<=Arg_0 && Arg_0<=Arg_1
3:evalfbb10in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> evalfreturnin(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:1<=Arg_0 && Arg_1+1<=Arg_0
10:evalfbb3in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> evalfbb4in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4+1):|:Arg_4<=Arg_3 && Arg_4<=Arg_1 && 1<=Arg_4 && 3<=Arg_3+Arg_4 && 2<=Arg_2+Arg_4 && 3<=Arg_1+Arg_4 && 2<=Arg_0+Arg_4 && Arg_3<=Arg_1 && 2<=Arg_3 && 3<=Arg_2+Arg_3 && 1+Arg_2<=Arg_3 && 4<=Arg_1+Arg_3 && 3<=Arg_0+Arg_3 && 1+Arg_0<=Arg_3 && 1+Arg_2<=Arg_1 && Arg_2<=Arg_0 && 1<=Arg_2 && 3<=Arg_1+Arg_2 && 2<=Arg_0+Arg_2 && 2<=Arg_1 && 3<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 1<=Arg_0
8:evalfbb4in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> evalfbb3in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:Arg_4<=1+Arg_3 && Arg_4<=1+Arg_1 && 1<=Arg_4 && 3<=Arg_3+Arg_4 && 2<=Arg_2+Arg_4 && 3<=Arg_1+Arg_4 && 2<=Arg_0+Arg_4 && Arg_3<=Arg_1 && 2<=Arg_3 && 3<=Arg_2+Arg_3 && 1+Arg_2<=Arg_3 && 4<=Arg_1+Arg_3 && 3<=Arg_0+Arg_3 && 1+Arg_0<=Arg_3 && 1+Arg_2<=Arg_1 && Arg_2<=Arg_0 && 1<=Arg_2 && 3<=Arg_1+Arg_2 && 2<=Arg_0+Arg_2 && 2<=Arg_1 && 3<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 1<=Arg_0 && Arg_4<=Arg_3
9:evalfbb4in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> evalfbb5in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:Arg_4<=1+Arg_3 && Arg_4<=1+Arg_1 && 1<=Arg_4 && 3<=Arg_3+Arg_4 && 2<=Arg_2+Arg_4 && 3<=Arg_1+Arg_4 && 2<=Arg_0+Arg_4 && Arg_3<=Arg_1 && 2<=Arg_3 && 3<=Arg_2+Arg_3 && 1+Arg_2<=Arg_3 && 4<=Arg_1+Arg_3 && 3<=Arg_0+Arg_3 && 1+Arg_0<=Arg_3 && 1+Arg_2<=Arg_1 && Arg_2<=Arg_0 && 1<=Arg_2 && 3<=Arg_1+Arg_2 && 2<=Arg_0+Arg_2 && 2<=Arg_1 && 3<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 1<=Arg_0 && Arg_3+1<=Arg_4
11:evalfbb5in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> evalfbb6in(Arg_0,Arg_1,Arg_2,Arg_3+1,Arg_4):|:Arg_4<=1+Arg_3 && Arg_4<=1+Arg_1 && 3<=Arg_4 && 5<=Arg_3+Arg_4 && 1+Arg_3<=Arg_4 && 4<=Arg_2+Arg_4 && 2+Arg_2<=Arg_4 && 5<=Arg_1+Arg_4 && 4<=Arg_0+Arg_4 && 2+Arg_0<=Arg_4 && Arg_3<=Arg_1 && 2<=Arg_3 && 3<=Arg_2+Arg_3 && 1+Arg_2<=Arg_3 && 4<=Arg_1+Arg_3 && 3<=Arg_0+Arg_3 && 1+Arg_0<=Arg_3 && 1+Arg_2<=Arg_1 && Arg_2<=Arg_0 && 1<=Arg_2 && 3<=Arg_1+Arg_2 && 2<=Arg_0+Arg_2 && 2<=Arg_1 && 3<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 1<=Arg_0
6:evalfbb6in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> evalfbb4in(Arg_0,Arg_1,Arg_2,Arg_3,1):|:Arg_3<=1+Arg_1 && 2<=Arg_3 && 3<=Arg_2+Arg_3 && 1+Arg_2<=Arg_3 && 3<=Arg_1+Arg_3 && 3<=Arg_0+Arg_3 && 1+Arg_0<=Arg_3 && Arg_2<=Arg_1 && Arg_2<=Arg_0 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && 2<=Arg_0+Arg_2 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 1<=Arg_0 && Arg_3<=Arg_1
7:evalfbb6in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> evalfbb7in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:Arg_3<=1+Arg_1 && 2<=Arg_3 && 3<=Arg_2+Arg_3 && 1+Arg_2<=Arg_3 && 3<=Arg_1+Arg_3 && 3<=Arg_0+Arg_3 && 1+Arg_0<=Arg_3 && Arg_2<=Arg_1 && Arg_2<=Arg_0 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && 2<=Arg_0+Arg_2 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 1<=Arg_0 && Arg_1+1<=Arg_3
12:evalfbb7in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> evalfbb8in(Arg_0,Arg_1,Arg_2+1,Arg_3,Arg_4):|:Arg_3<=1+Arg_1 && 2<=Arg_3 && 3<=Arg_2+Arg_3 && 1+Arg_2<=Arg_3 && 3<=Arg_1+Arg_3 && 1+Arg_1<=Arg_3 && 3<=Arg_0+Arg_3 && 1+Arg_0<=Arg_3 && Arg_2<=Arg_1 && Arg_2<=Arg_0 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && 2<=Arg_0+Arg_2 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 1<=Arg_0
5:evalfbb8in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> evalfbb10in(Arg_0+1,Arg_1,Arg_2,Arg_3,Arg_4):|:Arg_2<=1+Arg_1 && Arg_2<=1+Arg_0 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && 2<=Arg_0+Arg_2 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 1<=Arg_0 && Arg_0+1<=Arg_2
4:evalfbb8in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> evalfbb6in(Arg_0,Arg_1,Arg_2,Arg_0+1,Arg_4):|:Arg_2<=1+Arg_1 && Arg_2<=1+Arg_0 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && 2<=Arg_0+Arg_2 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 1<=Arg_0 && Arg_2<=Arg_0
1:evalfentryin(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> evalfbb10in(1,Arg_1,Arg_2,Arg_3,Arg_4)
13:evalfreturnin(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> evalfstop(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:1+Arg_1<=Arg_0 && 1<=Arg_0
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 2:evalfbb10in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> evalfbb8in(Arg_0,Arg_1,1,Arg_3,Arg_4):|:1<=Arg_0 && Arg_0<=Arg_1 of depth 1:

new bound:

Arg_1+2 {O(n)}

MPRF:

evalfbb3in [Arg_1-Arg_0 ]
evalfbb5in [Arg_1-Arg_0 ]
evalfbb4in [Arg_1-Arg_0 ]
evalfbb7in [Arg_1-Arg_0 ]
evalfbb6in [Arg_1-Arg_0 ]
evalfbb8in [Arg_1-Arg_0 ]
evalfbb10in [Arg_1+1-Arg_0 ]

MPRF for transition 5:evalfbb8in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> evalfbb10in(Arg_0+1,Arg_1,Arg_2,Arg_3,Arg_4):|:Arg_2<=1+Arg_1 && Arg_2<=1+Arg_0 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && 2<=Arg_0+Arg_2 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 1<=Arg_0 && Arg_0+1<=Arg_2 of depth 1:

new bound:

2*Arg_1+1 {O(n)}

MPRF:

evalfbb3in [2*Arg_1-Arg_0 ]
evalfbb5in [2*Arg_1-Arg_0 ]
evalfbb4in [2*Arg_1-Arg_0 ]
evalfbb7in [2*Arg_1-Arg_0 ]
evalfbb6in [2*Arg_1-Arg_0 ]
evalfbb8in [2*Arg_1-Arg_0 ]
evalfbb10in [2*Arg_1-Arg_0 ]

MPRF for transition 7:evalfbb6in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> evalfbb7in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:Arg_3<=1+Arg_1 && 2<=Arg_3 && 3<=Arg_2+Arg_3 && 1+Arg_2<=Arg_3 && 3<=Arg_1+Arg_3 && 3<=Arg_0+Arg_3 && 1+Arg_0<=Arg_3 && Arg_2<=Arg_1 && Arg_2<=Arg_0 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && 2<=Arg_0+Arg_2 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 1<=Arg_0 && Arg_1+1<=Arg_3 of depth 1:

new bound:

4*Arg_1*Arg_1+6*Arg_1+3 {O(n^2)}

MPRF:

evalfbb10in [Arg_0 ]
evalfbb3in [Arg_0+1-Arg_2 ]
evalfbb5in [Arg_0+1-Arg_2 ]
evalfbb4in [Arg_0+1-Arg_2 ]
evalfbb7in [Arg_0-Arg_2 ]
evalfbb8in [Arg_0+1-Arg_2 ]
evalfbb6in [Arg_0+1-Arg_2 ]

MPRF for transition 12:evalfbb7in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> evalfbb8in(Arg_0,Arg_1,Arg_2+1,Arg_3,Arg_4):|:Arg_3<=1+Arg_1 && 2<=Arg_3 && 3<=Arg_2+Arg_3 && 1+Arg_2<=Arg_3 && 3<=Arg_1+Arg_3 && 1+Arg_1<=Arg_3 && 3<=Arg_0+Arg_3 && 1+Arg_0<=Arg_3 && Arg_2<=Arg_1 && Arg_2<=Arg_0 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && 2<=Arg_0+Arg_2 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 1<=Arg_0 of depth 1:

new bound:

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

MPRF:

evalfbb10in [2*Arg_1 ]
evalfbb3in [2*Arg_1-Arg_2 ]
evalfbb5in [2*Arg_1-Arg_2 ]
evalfbb4in [2*Arg_1-Arg_2 ]
evalfbb7in [2*Arg_1-Arg_2 ]
evalfbb8in [2*Arg_1-Arg_2 ]
evalfbb6in [2*Arg_1-Arg_2 ]

MPRF for transition 4:evalfbb8in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> evalfbb6in(Arg_0,Arg_1,Arg_2,Arg_0+1,Arg_4):|:Arg_2<=1+Arg_1 && Arg_2<=1+Arg_0 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && 2<=Arg_0+Arg_2 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 1<=Arg_0 && Arg_2<=Arg_0 of depth 1:

new bound:

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

MPRF:

evalfbb10in [Arg_1 ]
evalfbb3in [Arg_1-Arg_2 ]
evalfbb5in [Arg_1-Arg_2 ]
evalfbb4in [Arg_1-Arg_2 ]
evalfbb7in [Arg_1-Arg_2 ]
evalfbb8in [Arg_1+1-Arg_2 ]
evalfbb6in [Arg_1-Arg_2 ]

MPRF for transition 9:evalfbb4in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> evalfbb5in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:Arg_4<=1+Arg_3 && Arg_4<=1+Arg_1 && 1<=Arg_4 && 3<=Arg_3+Arg_4 && 2<=Arg_2+Arg_4 && 3<=Arg_1+Arg_4 && 2<=Arg_0+Arg_4 && Arg_3<=Arg_1 && 2<=Arg_3 && 3<=Arg_2+Arg_3 && 1+Arg_2<=Arg_3 && 4<=Arg_1+Arg_3 && 3<=Arg_0+Arg_3 && 1+Arg_0<=Arg_3 && 1+Arg_2<=Arg_1 && Arg_2<=Arg_0 && 1<=Arg_2 && 3<=Arg_1+Arg_2 && 2<=Arg_0+Arg_2 && 2<=Arg_1 && 3<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 1<=Arg_0 && Arg_3+1<=Arg_4 of depth 1:

new bound:

10*Arg_1*Arg_1*Arg_1+24*Arg_1*Arg_1+14*Arg_1 {O(n^3)}

MPRF:

evalfbb3in [Arg_1+1-Arg_3 ]
evalfbb5in [Arg_1-Arg_3 ]
evalfbb4in [Arg_1+1-Arg_3 ]
evalfbb6in [Arg_1+1-Arg_3 ]
evalfbb7in [Arg_1+1-Arg_3 ]
evalfbb8in [0 ]
evalfbb10in [0 ]

MPRF for transition 11:evalfbb5in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> evalfbb6in(Arg_0,Arg_1,Arg_2,Arg_3+1,Arg_4):|:Arg_4<=1+Arg_3 && Arg_4<=1+Arg_1 && 3<=Arg_4 && 5<=Arg_3+Arg_4 && 1+Arg_3<=Arg_4 && 4<=Arg_2+Arg_4 && 2+Arg_2<=Arg_4 && 5<=Arg_1+Arg_4 && 4<=Arg_0+Arg_4 && 2+Arg_0<=Arg_4 && Arg_3<=Arg_1 && 2<=Arg_3 && 3<=Arg_2+Arg_3 && 1+Arg_2<=Arg_3 && 4<=Arg_1+Arg_3 && 3<=Arg_0+Arg_3 && 1+Arg_0<=Arg_3 && 1+Arg_2<=Arg_1 && Arg_2<=Arg_0 && 1<=Arg_2 && 3<=Arg_1+Arg_2 && 2<=Arg_0+Arg_2 && 2<=Arg_1 && 3<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 1<=Arg_0 of depth 1:

new bound:

14*Arg_1*Arg_1*Arg_1+28*Arg_1*Arg_1+16*Arg_1 {O(n^3)}

MPRF:

evalfbb3in [3*Arg_1+1-Arg_3 ]
evalfbb5in [3*Arg_1+1-Arg_3 ]
evalfbb4in [3*Arg_1+1-Arg_3 ]
evalfbb6in [3*Arg_1+1-Arg_3 ]
evalfbb7in [3*Arg_1+1-Arg_3 ]
evalfbb8in [2*Arg_1 ]
evalfbb10in [2*Arg_1 ]

MPRF for transition 6:evalfbb6in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> evalfbb4in(Arg_0,Arg_1,Arg_2,Arg_3,1):|:Arg_3<=1+Arg_1 && 2<=Arg_3 && 3<=Arg_2+Arg_3 && 1+Arg_2<=Arg_3 && 3<=Arg_1+Arg_3 && 3<=Arg_0+Arg_3 && 1+Arg_0<=Arg_3 && Arg_2<=Arg_1 && Arg_2<=Arg_0 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && 2<=Arg_0+Arg_2 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 1<=Arg_0 && Arg_3<=Arg_1 of depth 1:

new bound:

10*Arg_1*Arg_1*Arg_1+24*Arg_1*Arg_1+14*Arg_1 {O(n^3)}

MPRF:

evalfbb3in [Arg_1-Arg_3 ]
evalfbb5in [Arg_1-Arg_3 ]
evalfbb4in [Arg_1-Arg_3 ]
evalfbb6in [Arg_1+1-Arg_3 ]
evalfbb7in [0 ]
evalfbb8in [0 ]
evalfbb10in [0 ]

MPRF for transition 10:evalfbb3in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> evalfbb4in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4+1):|:Arg_4<=Arg_3 && Arg_4<=Arg_1 && 1<=Arg_4 && 3<=Arg_3+Arg_4 && 2<=Arg_2+Arg_4 && 3<=Arg_1+Arg_4 && 2<=Arg_0+Arg_4 && Arg_3<=Arg_1 && 2<=Arg_3 && 3<=Arg_2+Arg_3 && 1+Arg_2<=Arg_3 && 4<=Arg_1+Arg_3 && 3<=Arg_0+Arg_3 && 1+Arg_0<=Arg_3 && 1+Arg_2<=Arg_1 && Arg_2<=Arg_0 && 1<=Arg_2 && 3<=Arg_1+Arg_2 && 2<=Arg_0+Arg_2 && 2<=Arg_1 && 3<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 1<=Arg_0 of depth 1:

new bound:

140*Arg_1*Arg_1*Arg_1*Arg_1*Arg_1*Arg_1+616*Arg_1*Arg_1*Arg_1*Arg_1*Arg_1+1068*Arg_1*Arg_1*Arg_1*Arg_1+952*Arg_1*Arg_1*Arg_1+472*Arg_1*Arg_1+112*Arg_1 {O(n^6)}

MPRF:

evalfbb3in [Arg_3+1-Arg_4 ]
evalfbb4in [Arg_3+1-Arg_4 ]
evalfbb5in [0 ]
evalfbb7in [0 ]
evalfbb6in [0 ]
evalfbb8in [0 ]
evalfbb10in [0 ]

MPRF for transition 8:evalfbb4in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> evalfbb3in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:Arg_4<=1+Arg_3 && Arg_4<=1+Arg_1 && 1<=Arg_4 && 3<=Arg_3+Arg_4 && 2<=Arg_2+Arg_4 && 3<=Arg_1+Arg_4 && 2<=Arg_0+Arg_4 && Arg_3<=Arg_1 && 2<=Arg_3 && 3<=Arg_2+Arg_3 && 1+Arg_2<=Arg_3 && 4<=Arg_1+Arg_3 && 3<=Arg_0+Arg_3 && 1+Arg_0<=Arg_3 && 1+Arg_2<=Arg_1 && Arg_2<=Arg_0 && 1<=Arg_2 && 3<=Arg_1+Arg_2 && 2<=Arg_0+Arg_2 && 2<=Arg_1 && 3<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 1<=Arg_0 && Arg_4<=Arg_3 of depth 1:

new bound:

140*Arg_1*Arg_1*Arg_1*Arg_1*Arg_1*Arg_1+616*Arg_1*Arg_1*Arg_1*Arg_1*Arg_1+1068*Arg_1*Arg_1*Arg_1*Arg_1+962*Arg_1*Arg_1*Arg_1+496*Arg_1*Arg_1+126*Arg_1 {O(n^6)}

MPRF:

evalfbb3in [Arg_3+1-Arg_4 ]
evalfbb4in [Arg_3+2-Arg_4 ]
evalfbb5in [Arg_3+2-Arg_4 ]
evalfbb7in [0 ]
evalfbb6in [0 ]
evalfbb8in [0 ]
evalfbb10in [0 ]

All Bounds

Timebounds

Overall timebound:280*Arg_1*Arg_1*Arg_1*Arg_1*Arg_1*Arg_1+1232*Arg_1*Arg_1*Arg_1*Arg_1*Arg_1+2136*Arg_1*Arg_1*Arg_1*Arg_1+1948*Arg_1*Arg_1*Arg_1+1054*Arg_1*Arg_1+297*Arg_1+10 {O(n^6)}
2: evalfbb10in->evalfbb8in: Arg_1+2 {O(n)}
3: evalfbb10in->evalfreturnin: 1 {O(1)}
10: evalfbb3in->evalfbb4in: 140*Arg_1*Arg_1*Arg_1*Arg_1*Arg_1*Arg_1+616*Arg_1*Arg_1*Arg_1*Arg_1*Arg_1+1068*Arg_1*Arg_1*Arg_1*Arg_1+952*Arg_1*Arg_1*Arg_1+472*Arg_1*Arg_1+112*Arg_1 {O(n^6)}
8: evalfbb4in->evalfbb3in: 140*Arg_1*Arg_1*Arg_1*Arg_1*Arg_1*Arg_1+616*Arg_1*Arg_1*Arg_1*Arg_1*Arg_1+1068*Arg_1*Arg_1*Arg_1*Arg_1+962*Arg_1*Arg_1*Arg_1+496*Arg_1*Arg_1+126*Arg_1 {O(n^6)}
9: evalfbb4in->evalfbb5in: 10*Arg_1*Arg_1*Arg_1+24*Arg_1*Arg_1+14*Arg_1 {O(n^3)}
11: evalfbb5in->evalfbb6in: 14*Arg_1*Arg_1*Arg_1+28*Arg_1*Arg_1+16*Arg_1 {O(n^3)}
6: evalfbb6in->evalfbb4in: 10*Arg_1*Arg_1*Arg_1+24*Arg_1*Arg_1+14*Arg_1 {O(n^3)}
7: evalfbb6in->evalfbb7in: 4*Arg_1*Arg_1+6*Arg_1+3 {O(n^2)}
12: evalfbb7in->evalfbb8in: 4*Arg_1*Arg_1+4*Arg_1 {O(n^2)}
4: evalfbb8in->evalfbb6in: 2*Arg_1*Arg_1+2*Arg_1 {O(n^2)}
5: evalfbb8in->evalfbb10in: 2*Arg_1+1 {O(n)}
1: evalfentryin->evalfbb10in: 1 {O(1)}
13: evalfreturnin->evalfstop: 1 {O(1)}
0: evalfstart->evalfentryin: 1 {O(1)}

Costbounds

Overall costbound: 280*Arg_1*Arg_1*Arg_1*Arg_1*Arg_1*Arg_1+1232*Arg_1*Arg_1*Arg_1*Arg_1*Arg_1+2136*Arg_1*Arg_1*Arg_1*Arg_1+1948*Arg_1*Arg_1*Arg_1+1054*Arg_1*Arg_1+297*Arg_1+10 {O(n^6)}
2: evalfbb10in->evalfbb8in: Arg_1+2 {O(n)}
3: evalfbb10in->evalfreturnin: 1 {O(1)}
10: evalfbb3in->evalfbb4in: 140*Arg_1*Arg_1*Arg_1*Arg_1*Arg_1*Arg_1+616*Arg_1*Arg_1*Arg_1*Arg_1*Arg_1+1068*Arg_1*Arg_1*Arg_1*Arg_1+952*Arg_1*Arg_1*Arg_1+472*Arg_1*Arg_1+112*Arg_1 {O(n^6)}
8: evalfbb4in->evalfbb3in: 140*Arg_1*Arg_1*Arg_1*Arg_1*Arg_1*Arg_1+616*Arg_1*Arg_1*Arg_1*Arg_1*Arg_1+1068*Arg_1*Arg_1*Arg_1*Arg_1+962*Arg_1*Arg_1*Arg_1+496*Arg_1*Arg_1+126*Arg_1 {O(n^6)}
9: evalfbb4in->evalfbb5in: 10*Arg_1*Arg_1*Arg_1+24*Arg_1*Arg_1+14*Arg_1 {O(n^3)}
11: evalfbb5in->evalfbb6in: 14*Arg_1*Arg_1*Arg_1+28*Arg_1*Arg_1+16*Arg_1 {O(n^3)}
6: evalfbb6in->evalfbb4in: 10*Arg_1*Arg_1*Arg_1+24*Arg_1*Arg_1+14*Arg_1 {O(n^3)}
7: evalfbb6in->evalfbb7in: 4*Arg_1*Arg_1+6*Arg_1+3 {O(n^2)}
12: evalfbb7in->evalfbb8in: 4*Arg_1*Arg_1+4*Arg_1 {O(n^2)}
4: evalfbb8in->evalfbb6in: 2*Arg_1*Arg_1+2*Arg_1 {O(n^2)}
5: evalfbb8in->evalfbb10in: 2*Arg_1+1 {O(n)}
1: evalfentryin->evalfbb10in: 1 {O(1)}
13: evalfreturnin->evalfstop: 1 {O(1)}
0: evalfstart->evalfentryin: 1 {O(1)}

Sizebounds

2: evalfbb10in->evalfbb8in, Arg_0: 2*Arg_1+2 {O(n)}
2: evalfbb10in->evalfbb8in, Arg_1: Arg_1 {O(n)}
2: evalfbb10in->evalfbb8in, Arg_2: 1 {O(1)}
2: evalfbb10in->evalfbb8in, Arg_3: 14*Arg_1*Arg_1*Arg_1+28*Arg_1*Arg_1+24*Arg_1+Arg_3+12 {O(n^3)}
2: evalfbb10in->evalfbb8in, Arg_4: 140*Arg_1*Arg_1*Arg_1*Arg_1*Arg_1*Arg_1+616*Arg_1*Arg_1*Arg_1*Arg_1*Arg_1+1068*Arg_1*Arg_1*Arg_1*Arg_1+952*Arg_1*Arg_1*Arg_1+472*Arg_1*Arg_1+112*Arg_1+Arg_4+1 {O(n^6)}
3: evalfbb10in->evalfreturnin, Arg_0: 2*Arg_1+3 {O(n)}
3: evalfbb10in->evalfreturnin, Arg_1: 2*Arg_1 {O(n)}
3: evalfbb10in->evalfreturnin, Arg_2: 4*Arg_1*Arg_1+4*Arg_1+Arg_2+1 {O(n^2)}
3: evalfbb10in->evalfreturnin, Arg_3: 14*Arg_1*Arg_1*Arg_1+28*Arg_1*Arg_1+24*Arg_1+Arg_3+12 {O(n^3)}
3: evalfbb10in->evalfreturnin, Arg_4: 140*Arg_1*Arg_1*Arg_1*Arg_1*Arg_1*Arg_1+616*Arg_1*Arg_1*Arg_1*Arg_1*Arg_1+1068*Arg_1*Arg_1*Arg_1*Arg_1+952*Arg_1*Arg_1*Arg_1+472*Arg_1*Arg_1+112*Arg_1+2*Arg_4+1 {O(n^6)}
10: evalfbb3in->evalfbb4in, Arg_0: 2*Arg_1+2 {O(n)}
10: evalfbb3in->evalfbb4in, Arg_1: Arg_1 {O(n)}
10: evalfbb3in->evalfbb4in, Arg_2: 4*Arg_1*Arg_1+4*Arg_1+1 {O(n^2)}
10: evalfbb3in->evalfbb4in, Arg_3: 14*Arg_1*Arg_1*Arg_1+28*Arg_1*Arg_1+20*Arg_1+6 {O(n^3)}
10: evalfbb3in->evalfbb4in, Arg_4: 140*Arg_1*Arg_1*Arg_1*Arg_1*Arg_1*Arg_1+616*Arg_1*Arg_1*Arg_1*Arg_1*Arg_1+1068*Arg_1*Arg_1*Arg_1*Arg_1+952*Arg_1*Arg_1*Arg_1+472*Arg_1*Arg_1+112*Arg_1+1 {O(n^6)}
8: evalfbb4in->evalfbb3in, Arg_0: 2*Arg_1+2 {O(n)}
8: evalfbb4in->evalfbb3in, Arg_1: Arg_1 {O(n)}
8: evalfbb4in->evalfbb3in, Arg_2: 4*Arg_1*Arg_1+4*Arg_1+1 {O(n^2)}
8: evalfbb4in->evalfbb3in, Arg_3: 14*Arg_1*Arg_1*Arg_1+28*Arg_1*Arg_1+20*Arg_1+6 {O(n^3)}
8: evalfbb4in->evalfbb3in, Arg_4: 140*Arg_1*Arg_1*Arg_1*Arg_1*Arg_1*Arg_1+616*Arg_1*Arg_1*Arg_1*Arg_1*Arg_1+1068*Arg_1*Arg_1*Arg_1*Arg_1+952*Arg_1*Arg_1*Arg_1+472*Arg_1*Arg_1+112*Arg_1+1 {O(n^6)}
9: evalfbb4in->evalfbb5in, Arg_0: 2*Arg_1+2 {O(n)}
9: evalfbb4in->evalfbb5in, Arg_1: Arg_1 {O(n)}
9: evalfbb4in->evalfbb5in, Arg_2: 4*Arg_1*Arg_1+4*Arg_1+1 {O(n^2)}
9: evalfbb4in->evalfbb5in, Arg_3: 14*Arg_1*Arg_1*Arg_1+28*Arg_1*Arg_1+20*Arg_1+6 {O(n^3)}
9: evalfbb4in->evalfbb5in, Arg_4: 140*Arg_1*Arg_1*Arg_1*Arg_1*Arg_1*Arg_1+616*Arg_1*Arg_1*Arg_1*Arg_1*Arg_1+1068*Arg_1*Arg_1*Arg_1*Arg_1+952*Arg_1*Arg_1*Arg_1+472*Arg_1*Arg_1+112*Arg_1+1 {O(n^6)}
11: evalfbb5in->evalfbb6in, Arg_0: 2*Arg_1+2 {O(n)}
11: evalfbb5in->evalfbb6in, Arg_1: Arg_1 {O(n)}
11: evalfbb5in->evalfbb6in, Arg_2: 4*Arg_1*Arg_1+4*Arg_1+1 {O(n^2)}
11: evalfbb5in->evalfbb6in, Arg_3: 14*Arg_1*Arg_1*Arg_1+28*Arg_1*Arg_1+20*Arg_1+6 {O(n^3)}
11: evalfbb5in->evalfbb6in, Arg_4: 140*Arg_1*Arg_1*Arg_1*Arg_1*Arg_1*Arg_1+616*Arg_1*Arg_1*Arg_1*Arg_1*Arg_1+1068*Arg_1*Arg_1*Arg_1*Arg_1+952*Arg_1*Arg_1*Arg_1+472*Arg_1*Arg_1+112*Arg_1+1 {O(n^6)}
6: evalfbb6in->evalfbb4in, Arg_0: 2*Arg_1+2 {O(n)}
6: evalfbb6in->evalfbb4in, Arg_1: Arg_1 {O(n)}
6: evalfbb6in->evalfbb4in, Arg_2: 4*Arg_1*Arg_1+4*Arg_1+1 {O(n^2)}
6: evalfbb6in->evalfbb4in, Arg_3: 14*Arg_1*Arg_1*Arg_1+28*Arg_1*Arg_1+20*Arg_1+6 {O(n^3)}
6: evalfbb6in->evalfbb4in, Arg_4: 1 {O(1)}
7: evalfbb6in->evalfbb7in, Arg_0: 2*Arg_1+2 {O(n)}
7: evalfbb6in->evalfbb7in, Arg_1: Arg_1 {O(n)}
7: evalfbb6in->evalfbb7in, Arg_2: 4*Arg_1*Arg_1+4*Arg_1+1 {O(n^2)}
7: evalfbb6in->evalfbb7in, Arg_3: 14*Arg_1*Arg_1*Arg_1+28*Arg_1*Arg_1+24*Arg_1+12 {O(n^3)}
7: evalfbb6in->evalfbb7in, Arg_4: 140*Arg_1*Arg_1*Arg_1*Arg_1*Arg_1*Arg_1+616*Arg_1*Arg_1*Arg_1*Arg_1*Arg_1+1068*Arg_1*Arg_1*Arg_1*Arg_1+952*Arg_1*Arg_1*Arg_1+472*Arg_1*Arg_1+112*Arg_1+Arg_4+1 {O(n^6)}
12: evalfbb7in->evalfbb8in, Arg_0: 2*Arg_1+2 {O(n)}
12: evalfbb7in->evalfbb8in, Arg_1: Arg_1 {O(n)}
12: evalfbb7in->evalfbb8in, Arg_2: 4*Arg_1*Arg_1+4*Arg_1+1 {O(n^2)}
12: evalfbb7in->evalfbb8in, Arg_3: 14*Arg_1*Arg_1*Arg_1+28*Arg_1*Arg_1+24*Arg_1+12 {O(n^3)}
12: evalfbb7in->evalfbb8in, Arg_4: 140*Arg_1*Arg_1*Arg_1*Arg_1*Arg_1*Arg_1+616*Arg_1*Arg_1*Arg_1*Arg_1*Arg_1+1068*Arg_1*Arg_1*Arg_1*Arg_1+952*Arg_1*Arg_1*Arg_1+472*Arg_1*Arg_1+112*Arg_1+Arg_4+1 {O(n^6)}
4: evalfbb8in->evalfbb6in, Arg_0: 2*Arg_1+2 {O(n)}
4: evalfbb8in->evalfbb6in, Arg_1: Arg_1 {O(n)}
4: evalfbb8in->evalfbb6in, Arg_2: 4*Arg_1*Arg_1+4*Arg_1+1 {O(n^2)}
4: evalfbb8in->evalfbb6in, Arg_3: 4*Arg_1+6 {O(n)}
4: evalfbb8in->evalfbb6in, Arg_4: 140*Arg_1*Arg_1*Arg_1*Arg_1*Arg_1*Arg_1+616*Arg_1*Arg_1*Arg_1*Arg_1*Arg_1+1068*Arg_1*Arg_1*Arg_1*Arg_1+952*Arg_1*Arg_1*Arg_1+472*Arg_1*Arg_1+112*Arg_1+Arg_4+1 {O(n^6)}
5: evalfbb8in->evalfbb10in, Arg_0: 2*Arg_1+2 {O(n)}
5: evalfbb8in->evalfbb10in, Arg_1: Arg_1 {O(n)}
5: evalfbb8in->evalfbb10in, Arg_2: 4*Arg_1*Arg_1+4*Arg_1+1 {O(n^2)}
5: evalfbb8in->evalfbb10in, Arg_3: 14*Arg_1*Arg_1*Arg_1+28*Arg_1*Arg_1+24*Arg_1+12 {O(n^3)}
5: evalfbb8in->evalfbb10in, Arg_4: 140*Arg_1*Arg_1*Arg_1*Arg_1*Arg_1*Arg_1+616*Arg_1*Arg_1*Arg_1*Arg_1*Arg_1+1068*Arg_1*Arg_1*Arg_1*Arg_1+952*Arg_1*Arg_1*Arg_1+472*Arg_1*Arg_1+112*Arg_1+Arg_4+1 {O(n^6)}
1: evalfentryin->evalfbb10in, Arg_0: 1 {O(1)}
1: evalfentryin->evalfbb10in, Arg_1: Arg_1 {O(n)}
1: evalfentryin->evalfbb10in, Arg_2: Arg_2 {O(n)}
1: evalfentryin->evalfbb10in, Arg_3: Arg_3 {O(n)}
1: evalfentryin->evalfbb10in, Arg_4: Arg_4 {O(n)}
13: evalfreturnin->evalfstop, Arg_0: 2*Arg_1+3 {O(n)}
13: evalfreturnin->evalfstop, Arg_1: 2*Arg_1 {O(n)}
13: evalfreturnin->evalfstop, Arg_2: 4*Arg_1*Arg_1+4*Arg_1+Arg_2+1 {O(n^2)}
13: evalfreturnin->evalfstop, Arg_3: 14*Arg_1*Arg_1*Arg_1+28*Arg_1*Arg_1+24*Arg_1+Arg_3+12 {O(n^3)}
13: evalfreturnin->evalfstop, Arg_4: 140*Arg_1*Arg_1*Arg_1*Arg_1*Arg_1*Arg_1+616*Arg_1*Arg_1*Arg_1*Arg_1*Arg_1+1068*Arg_1*Arg_1*Arg_1*Arg_1+952*Arg_1*Arg_1*Arg_1+472*Arg_1*Arg_1+112*Arg_1+2*Arg_4+1 {O(n^6)}
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)}