Initial Problem

Start: evalfstart
Program_Vars: Arg_0, Arg_1, Arg_2
Temp_Vars: D
Locations: evalfbb1in, evalfbb3in, evalfbb4in, evalfbbin, evalfentryin, evalfreturnin, evalfstart, evalfstop
Transitions:
9:evalfbb1in(Arg_0,Arg_1,Arg_2) -> evalfbb3in(Arg_0,Arg_1-1,Arg_2+1)
3:evalfbb3in(Arg_0,Arg_1,Arg_2) -> evalfbb4in(Arg_0,Arg_1,Arg_2):|:1<=Arg_1
2:evalfbb3in(Arg_0,Arg_1,Arg_2) -> evalfreturnin(Arg_0,Arg_1,Arg_2):|:Arg_1<=0
4:evalfbb4in(Arg_0,Arg_1,Arg_2) -> evalfbbin(Arg_0,Arg_1,Arg_2):|:D+1<=0
5:evalfbb4in(Arg_0,Arg_1,Arg_2) -> evalfbbin(Arg_0,Arg_1,Arg_2):|:1<=D
6:evalfbb4in(Arg_0,Arg_1,Arg_2) -> evalfreturnin(Arg_0,Arg_1,Arg_2)
7:evalfbbin(Arg_0,Arg_1,Arg_2) -> evalfbb1in(Arg_0,Arg_1,Arg_2):|:Arg_2+1<=Arg_0
8:evalfbbin(Arg_0,Arg_1,Arg_2) -> evalfbb3in(Arg_0,Arg_1,0):|:Arg_0<=Arg_2
1:evalfentryin(Arg_0,Arg_1,Arg_2) -> evalfbb3in(Arg_1,Arg_0,0):|:1<=Arg_0 && 1<=Arg_1
10: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_2<=Arg_0 && 0<=Arg_2 && 1<=Arg_1+Arg_2 && 1<=Arg_0+Arg_2 && 0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 for location evalfreturnin

Found invariant 1+Arg_2<=Arg_0 && 0<=Arg_2 && 1<=Arg_1+Arg_2 && 1<=Arg_0+Arg_2 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 for location evalfbb1in

Found invariant Arg_2<=Arg_0 && 0<=Arg_2 && 1<=Arg_1+Arg_2 && 1<=Arg_0+Arg_2 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 for location evalfbbin

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

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

Found invariant Arg_2<=Arg_0 && 0<=Arg_2 && 1<=Arg_1+Arg_2 && 1<=Arg_0+Arg_2 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 for location evalfbb4in

Problem after Preprocessing

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

MPRF for transition 9:evalfbb1in(Arg_0,Arg_1,Arg_2) -> evalfbb3in(Arg_0,Arg_1-1,Arg_2+1):|:1+Arg_2<=Arg_0 && 0<=Arg_2 && 1<=Arg_1+Arg_2 && 1<=Arg_0+Arg_2 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 of depth 1:

new bound:

Arg_0 {O(n)}

MPRF:

evalfbb4in [Arg_1 ]
evalfbb1in [Arg_1 ]
evalfbbin [Arg_1 ]
evalfbb3in [Arg_1 ]

MPRF for transition 3:evalfbb3in(Arg_0,Arg_1,Arg_2) -> evalfbb4in(Arg_0,Arg_1,Arg_2):|:Arg_2<=Arg_0 && 0<=Arg_2 && 1<=Arg_1+Arg_2 && 1<=Arg_0+Arg_2 && 0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 && 1<=Arg_1 of depth 1:

new bound:

2*Arg_0+1 {O(n)}

MPRF:

evalfbb4in [2*Arg_1+Arg_2 ]
evalfbb1in [2*Arg_1+Arg_2 ]
evalfbbin [2*Arg_1+Arg_2 ]
evalfbb3in [2*Arg_1+Arg_2+1 ]

MPRF for transition 4:evalfbb4in(Arg_0,Arg_1,Arg_2) -> evalfbbin(Arg_0,Arg_1,Arg_2):|:Arg_2<=Arg_0 && 0<=Arg_2 && 1<=Arg_1+Arg_2 && 1<=Arg_0+Arg_2 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 && D+1<=0 of depth 1:

new bound:

2*Arg_0+2 {O(n)}

MPRF:

evalfbb4in [2*Arg_1+Arg_2+2 ]
evalfbb1in [2*Arg_1+Arg_2+1 ]
evalfbbin [2*Arg_1+Arg_2+1 ]
evalfbb3in [2*Arg_1+Arg_2+2 ]

MPRF for transition 5:evalfbb4in(Arg_0,Arg_1,Arg_2) -> evalfbbin(Arg_0,Arg_1,Arg_2):|:Arg_2<=Arg_0 && 0<=Arg_2 && 1<=Arg_1+Arg_2 && 1<=Arg_0+Arg_2 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 && 1<=D of depth 1:

new bound:

2*Arg_0+1 {O(n)}

MPRF:

evalfbb4in [2*Arg_1+Arg_2-1 ]
evalfbb1in [2*Arg_1+Arg_2-2 ]
evalfbbin [2*Arg_1+Arg_2-2 ]
evalfbb3in [2*Arg_1+Arg_2-1 ]

MPRF for transition 7:evalfbbin(Arg_0,Arg_1,Arg_2) -> evalfbb1in(Arg_0,Arg_1,Arg_2):|:Arg_2<=Arg_0 && 0<=Arg_2 && 1<=Arg_1+Arg_2 && 1<=Arg_0+Arg_2 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 && Arg_2+1<=Arg_0 of depth 1:

new bound:

Arg_0 {O(n)}

MPRF:

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

MPRF for transition 8:evalfbbin(Arg_0,Arg_1,Arg_2) -> evalfbb3in(Arg_0,Arg_1,0):|:Arg_2<=Arg_0 && 0<=Arg_2 && 1<=Arg_1+Arg_2 && 1<=Arg_0+Arg_2 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 && Arg_0<=Arg_2 of depth 1:

new bound:

Arg_0 {O(n)}

MPRF:

evalfbb4in [Arg_1+Arg_2 ]
evalfbb1in [Arg_1+Arg_2 ]
evalfbbin [Arg_1+Arg_2 ]
evalfbb3in [Arg_1+Arg_2 ]

All Bounds

Timebounds

Overall timebound:9*Arg_0+9 {O(n)}
9: evalfbb1in->evalfbb3in: Arg_0 {O(n)}
2: evalfbb3in->evalfreturnin: 1 {O(1)}
3: evalfbb3in->evalfbb4in: 2*Arg_0+1 {O(n)}
4: evalfbb4in->evalfbbin: 2*Arg_0+2 {O(n)}
5: evalfbb4in->evalfbbin: 2*Arg_0+1 {O(n)}
6: evalfbb4in->evalfreturnin: 1 {O(1)}
7: evalfbbin->evalfbb1in: Arg_0 {O(n)}
8: evalfbbin->evalfbb3in: Arg_0 {O(n)}
1: evalfentryin->evalfbb3in: 1 {O(1)}
10: evalfreturnin->evalfstop: 1 {O(1)}
0: evalfstart->evalfentryin: 1 {O(1)}

Costbounds

Overall costbound: 9*Arg_0+9 {O(n)}
9: evalfbb1in->evalfbb3in: Arg_0 {O(n)}
2: evalfbb3in->evalfreturnin: 1 {O(1)}
3: evalfbb3in->evalfbb4in: 2*Arg_0+1 {O(n)}
4: evalfbb4in->evalfbbin: 2*Arg_0+2 {O(n)}
5: evalfbb4in->evalfbbin: 2*Arg_0+1 {O(n)}
6: evalfbb4in->evalfreturnin: 1 {O(1)}
7: evalfbbin->evalfbb1in: Arg_0 {O(n)}
8: evalfbbin->evalfbb3in: Arg_0 {O(n)}
1: evalfentryin->evalfbb3in: 1 {O(1)}
10: evalfreturnin->evalfstop: 1 {O(1)}
0: evalfstart->evalfentryin: 1 {O(1)}

Sizebounds

9: evalfbb1in->evalfbb3in, Arg_0: Arg_1 {O(n)}
9: evalfbb1in->evalfbb3in, Arg_1: Arg_0 {O(n)}
9: evalfbb1in->evalfbb3in, Arg_2: Arg_0 {O(n)}
2: evalfbb3in->evalfreturnin, Arg_0: Arg_1 {O(n)}
2: evalfbb3in->evalfreturnin, Arg_1: 0 {O(1)}
2: evalfbb3in->evalfreturnin, Arg_2: Arg_0 {O(n)}
3: evalfbb3in->evalfbb4in, Arg_0: Arg_1 {O(n)}
3: evalfbb3in->evalfbb4in, Arg_1: Arg_0 {O(n)}
3: evalfbb3in->evalfbb4in, Arg_2: Arg_0 {O(n)}
4: evalfbb4in->evalfbbin, Arg_0: Arg_1 {O(n)}
4: evalfbb4in->evalfbbin, Arg_1: Arg_0 {O(n)}
4: evalfbb4in->evalfbbin, Arg_2: Arg_0 {O(n)}
5: evalfbb4in->evalfbbin, Arg_0: Arg_1 {O(n)}
5: evalfbb4in->evalfbbin, Arg_1: Arg_0 {O(n)}
5: evalfbb4in->evalfbbin, Arg_2: Arg_0 {O(n)}
6: evalfbb4in->evalfreturnin, Arg_0: Arg_1 {O(n)}
6: evalfbb4in->evalfreturnin, Arg_1: Arg_0 {O(n)}
6: evalfbb4in->evalfreturnin, Arg_2: Arg_0 {O(n)}
7: evalfbbin->evalfbb1in, Arg_0: Arg_1 {O(n)}
7: evalfbbin->evalfbb1in, Arg_1: Arg_0 {O(n)}
7: evalfbbin->evalfbb1in, Arg_2: Arg_0 {O(n)}
8: evalfbbin->evalfbb3in, Arg_0: Arg_1 {O(n)}
8: evalfbbin->evalfbb3in, Arg_1: Arg_0 {O(n)}
8: evalfbbin->evalfbb3in, Arg_2: 0 {O(1)}
1: evalfentryin->evalfbb3in, Arg_0: Arg_1 {O(n)}
1: evalfentryin->evalfbb3in, Arg_1: Arg_0 {O(n)}
1: evalfentryin->evalfbb3in, Arg_2: 0 {O(1)}
10: evalfreturnin->evalfstop, Arg_0: 2*Arg_1 {O(n)}
10: evalfreturnin->evalfstop, Arg_1: Arg_0 {O(n)}
10: evalfreturnin->evalfstop, Arg_2: 2*Arg_0 {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)}