Initial Problem

Start: evalfstart
Program_Vars: Arg_0, Arg_1, Arg_2
Temp_Vars:
Locations: evalfbb1in, evalfbb2in, evalfbb3in, evalfbb4in, evalfentryin, evalfreturnin, evalfstart, evalfstop
Transitions:
6:evalfbb1in(Arg_0,Arg_1,Arg_2) -> evalfbb2in(Arg_0,Arg_1,Arg_2-1)
4:evalfbb2in(Arg_0,Arg_1,Arg_2) -> evalfbb1in(Arg_0,Arg_1,Arg_2):|:1<=Arg_2
5:evalfbb2in(Arg_0,Arg_1,Arg_2) -> evalfbb3in(Arg_0,Arg_1,Arg_2):|:Arg_2<=0
7:evalfbb3in(Arg_0,Arg_1,Arg_2) -> evalfbb4in(Arg_0,Arg_1-1,Arg_2)
2:evalfbb4in(Arg_0,Arg_1,Arg_2) -> evalfbb2in(Arg_0,Arg_1,Arg_0):|:1<=Arg_1
3:evalfbb4in(Arg_0,Arg_1,Arg_2) -> evalfreturnin(Arg_0,Arg_1,Arg_2):|:Arg_1<=0
1:evalfentryin(Arg_0,Arg_1,Arg_2) -> evalfbb4in(Arg_1,Arg_0,Arg_2)
8:evalfreturnin(Arg_0,Arg_1,Arg_2) -> evalfstop(Arg_0,Arg_1,Arg_2)
0:evalfstart(Arg_0,Arg_1,Arg_2) -> evalfentryin(Arg_0,Arg_1,Arg_2)

Preprocessing

Found invariant Arg_1<=0 for location evalfreturnin

Found invariant 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 && 1<=Arg_0 for location evalfbb1in

Found invariant Arg_2<=Arg_0 && 1<=Arg_1 for location evalfbb2in

Found invariant Arg_2<=0 && 1+Arg_2<=Arg_1 && Arg_2<=Arg_0 && 1<=Arg_1 for location evalfbb3in

Found invariant Arg_1<=0 for location evalfstop

Problem after Preprocessing

Start: evalfstart
Program_Vars: Arg_0, Arg_1, Arg_2
Temp_Vars:
Locations: evalfbb1in, evalfbb2in, evalfbb3in, evalfbb4in, evalfentryin, evalfreturnin, evalfstart, evalfstop
Transitions:
6:evalfbb1in(Arg_0,Arg_1,Arg_2) -> evalfbb2in(Arg_0,Arg_1,Arg_2-1):|: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 && 1<=Arg_0
4:evalfbb2in(Arg_0,Arg_1,Arg_2) -> evalfbb1in(Arg_0,Arg_1,Arg_2):|:Arg_2<=Arg_0 && 1<=Arg_1 && 1<=Arg_2
5:evalfbb2in(Arg_0,Arg_1,Arg_2) -> evalfbb3in(Arg_0,Arg_1,Arg_2):|:Arg_2<=Arg_0 && 1<=Arg_1 && Arg_2<=0
7:evalfbb3in(Arg_0,Arg_1,Arg_2) -> evalfbb4in(Arg_0,Arg_1-1,Arg_2):|:Arg_2<=0 && 1+Arg_2<=Arg_1 && Arg_2<=Arg_0 && 1<=Arg_1
2:evalfbb4in(Arg_0,Arg_1,Arg_2) -> evalfbb2in(Arg_0,Arg_1,Arg_0):|:1<=Arg_1
3:evalfbb4in(Arg_0,Arg_1,Arg_2) -> evalfreturnin(Arg_0,Arg_1,Arg_2):|:Arg_1<=0
1:evalfentryin(Arg_0,Arg_1,Arg_2) -> evalfbb4in(Arg_1,Arg_0,Arg_2)
8:evalfreturnin(Arg_0,Arg_1,Arg_2) -> evalfstop(Arg_0,Arg_1,Arg_2):|:Arg_1<=0
0:evalfstart(Arg_0,Arg_1,Arg_2) -> evalfentryin(Arg_0,Arg_1,Arg_2)

MPRF for transition 5:evalfbb2in(Arg_0,Arg_1,Arg_2) -> evalfbb3in(Arg_0,Arg_1,Arg_2):|:Arg_2<=Arg_0 && 1<=Arg_1 && Arg_2<=0 of depth 1:

new bound:

Arg_0 {O(n)}

MPRF:

evalfbb1in [Arg_1 ]
evalfbb3in [Arg_1-1 ]
evalfbb4in [Arg_1 ]
evalfbb2in [Arg_1 ]

MPRF for transition 7:evalfbb3in(Arg_0,Arg_1,Arg_2) -> evalfbb4in(Arg_0,Arg_1-1,Arg_2):|:Arg_2<=0 && 1+Arg_2<=Arg_1 && Arg_2<=Arg_0 && 1<=Arg_1 of depth 1:

new bound:

Arg_0 {O(n)}

MPRF:

evalfbb1in [Arg_1 ]
evalfbb3in [Arg_1 ]
evalfbb4in [Arg_1 ]
evalfbb2in [Arg_1 ]

MPRF for transition 2:evalfbb4in(Arg_0,Arg_1,Arg_2) -> evalfbb2in(Arg_0,Arg_1,Arg_0):|:1<=Arg_1 of depth 1:

new bound:

Arg_0 {O(n)}

MPRF:

evalfbb1in [Arg_1-1 ]
evalfbb3in [Arg_1-1 ]
evalfbb4in [Arg_1 ]
evalfbb2in [Arg_1-1 ]

MPRF for transition 6:evalfbb1in(Arg_0,Arg_1,Arg_2) -> evalfbb2in(Arg_0,Arg_1,Arg_2-1):|: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 && 1<=Arg_0 of depth 1:

new bound:

2*Arg_0*Arg_1 {O(n^2)}

MPRF:

evalfbb1in [Arg_2 ]
evalfbb2in [Arg_2 ]
evalfbb3in [Arg_2 ]
evalfbb4in [Arg_2 ]

MPRF for transition 4:evalfbb2in(Arg_0,Arg_1,Arg_2) -> evalfbb1in(Arg_0,Arg_1,Arg_2):|:Arg_2<=Arg_0 && 1<=Arg_1 && 1<=Arg_2 of depth 1:

new bound:

2*Arg_0*Arg_1 {O(n^2)}

MPRF:

evalfbb1in [Arg_2-1 ]
evalfbb2in [Arg_2 ]
evalfbb3in [Arg_2 ]
evalfbb4in [Arg_2 ]

All Bounds

Timebounds

Overall timebound:4*Arg_0*Arg_1+3*Arg_0+4 {O(n^2)}
6: evalfbb1in->evalfbb2in: 2*Arg_0*Arg_1 {O(n^2)}
4: evalfbb2in->evalfbb1in: 2*Arg_0*Arg_1 {O(n^2)}
5: evalfbb2in->evalfbb3in: Arg_0 {O(n)}
7: evalfbb3in->evalfbb4in: Arg_0 {O(n)}
2: evalfbb4in->evalfbb2in: Arg_0 {O(n)}
3: evalfbb4in->evalfreturnin: 1 {O(1)}
1: evalfentryin->evalfbb4in: 1 {O(1)}
8: evalfreturnin->evalfstop: 1 {O(1)}
0: evalfstart->evalfentryin: 1 {O(1)}

Costbounds

Overall costbound: 4*Arg_0*Arg_1+3*Arg_0+4 {O(n^2)}
6: evalfbb1in->evalfbb2in: 2*Arg_0*Arg_1 {O(n^2)}
4: evalfbb2in->evalfbb1in: 2*Arg_0*Arg_1 {O(n^2)}
5: evalfbb2in->evalfbb3in: Arg_0 {O(n)}
7: evalfbb3in->evalfbb4in: Arg_0 {O(n)}
2: evalfbb4in->evalfbb2in: Arg_0 {O(n)}
3: evalfbb4in->evalfreturnin: 1 {O(1)}
1: evalfentryin->evalfbb4in: 1 {O(1)}
8: evalfreturnin->evalfstop: 1 {O(1)}
0: evalfstart->evalfentryin: 1 {O(1)}

Sizebounds

6: evalfbb1in->evalfbb2in, Arg_0: Arg_1 {O(n)}
6: evalfbb1in->evalfbb2in, Arg_1: Arg_0 {O(n)}
6: evalfbb1in->evalfbb2in, Arg_2: 2*Arg_1 {O(n)}
4: evalfbb2in->evalfbb1in, Arg_0: Arg_1 {O(n)}
4: evalfbb2in->evalfbb1in, Arg_1: Arg_0 {O(n)}
4: evalfbb2in->evalfbb1in, Arg_2: 2*Arg_1 {O(n)}
5: evalfbb2in->evalfbb3in, Arg_0: Arg_1 {O(n)}
5: evalfbb2in->evalfbb3in, Arg_1: Arg_0 {O(n)}
5: evalfbb2in->evalfbb3in, Arg_2: 4*Arg_1 {O(n)}
7: evalfbb3in->evalfbb4in, Arg_0: Arg_1 {O(n)}
7: evalfbb3in->evalfbb4in, Arg_1: Arg_0 {O(n)}
7: evalfbb3in->evalfbb4in, Arg_2: 4*Arg_1 {O(n)}
2: evalfbb4in->evalfbb2in, Arg_0: Arg_1 {O(n)}
2: evalfbb4in->evalfbb2in, Arg_1: Arg_0 {O(n)}
2: evalfbb4in->evalfbb2in, Arg_2: 2*Arg_1 {O(n)}
3: evalfbb4in->evalfreturnin, Arg_0: 2*Arg_1 {O(n)}
3: evalfbb4in->evalfreturnin, Arg_1: 2*Arg_0 {O(n)}
3: evalfbb4in->evalfreturnin, Arg_2: 4*Arg_1+Arg_2 {O(n)}
1: evalfentryin->evalfbb4in, Arg_0: Arg_1 {O(n)}
1: evalfentryin->evalfbb4in, Arg_1: Arg_0 {O(n)}
1: evalfentryin->evalfbb4in, Arg_2: Arg_2 {O(n)}
8: evalfreturnin->evalfstop, Arg_0: 2*Arg_1 {O(n)}
8: evalfreturnin->evalfstop, Arg_1: 2*Arg_0 {O(n)}
8: evalfreturnin->evalfstop, Arg_2: 4*Arg_1+Arg_2 {O(n)}
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)}