Initial Problem

Start: evalfstart
Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3
Temp_Vars:
Locations: evalfbb1in, evalfbb2in, evalfbb3in, evalfbbin, evalfentryin, evalfreturnin, evalfstart, evalfstop
Transitions:
6:evalfbb1in(Arg_0,Arg_1,Arg_2,Arg_3) -> evalfbb3in(Arg_0+1,Arg_1,Arg_2,Arg_3)
7:evalfbb2in(Arg_0,Arg_1,Arg_2,Arg_3) -> evalfbb3in(0,Arg_1+1,Arg_2,Arg_3)
2:evalfbb3in(Arg_0,Arg_1,Arg_2,Arg_3) -> evalfbbin(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_1+1<=Arg_2
3:evalfbb3in(Arg_0,Arg_1,Arg_2,Arg_3) -> evalfreturnin(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_2<=Arg_1
4:evalfbbin(Arg_0,Arg_1,Arg_2,Arg_3) -> evalfbb1in(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_0+1<=Arg_3
5:evalfbbin(Arg_0,Arg_1,Arg_2,Arg_3) -> evalfbb2in(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_3<=Arg_0
1:evalfentryin(Arg_0,Arg_1,Arg_2,Arg_3) -> evalfbb3in(0,0,Arg_2,Arg_3)
8:evalfreturnin(Arg_0,Arg_1,Arg_2,Arg_3) -> evalfstop(Arg_0,Arg_1,Arg_2,Arg_3)
0:evalfstart(Arg_0,Arg_1,Arg_2,Arg_3) -> evalfentryin(Arg_0,Arg_1,Arg_2,Arg_3)

Preprocessing

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

Found invariant 1<=Arg_3 && 2<=Arg_2+Arg_3 && 1<=Arg_1+Arg_3 && 1<=Arg_0+Arg_3 && 1+Arg_0<=Arg_3 && 1<=Arg_2 && 1<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 1<=Arg_0+Arg_2 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=Arg_0 for location evalfbb1in

Found invariant Arg_3<=Arg_0 && 1<=Arg_2 && 1<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 1<=Arg_0+Arg_2 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=Arg_0 for location evalfbb2in

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

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

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

Problem after Preprocessing

Start: evalfstart
Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3
Temp_Vars:
Locations: evalfbb1in, evalfbb2in, evalfbb3in, evalfbbin, evalfentryin, evalfreturnin, evalfstart, evalfstop
Transitions:
6:evalfbb1in(Arg_0,Arg_1,Arg_2,Arg_3) -> evalfbb3in(Arg_0+1,Arg_1,Arg_2,Arg_3):|:1<=Arg_3 && 2<=Arg_2+Arg_3 && 1<=Arg_1+Arg_3 && 1<=Arg_0+Arg_3 && 1+Arg_0<=Arg_3 && 1<=Arg_2 && 1<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 1<=Arg_0+Arg_2 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=Arg_0
7:evalfbb2in(Arg_0,Arg_1,Arg_2,Arg_3) -> evalfbb3in(0,Arg_1+1,Arg_2,Arg_3):|:Arg_3<=Arg_0 && 1<=Arg_2 && 1<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 1<=Arg_0+Arg_2 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=Arg_0
2:evalfbb3in(Arg_0,Arg_1,Arg_2,Arg_3) -> evalfbbin(Arg_0,Arg_1,Arg_2,Arg_3):|:0<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=Arg_0 && Arg_1+1<=Arg_2
3:evalfbb3in(Arg_0,Arg_1,Arg_2,Arg_3) -> evalfreturnin(Arg_0,Arg_1,Arg_2,Arg_3):|:0<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=Arg_0 && Arg_2<=Arg_1
4:evalfbbin(Arg_0,Arg_1,Arg_2,Arg_3) -> evalfbb1in(Arg_0,Arg_1,Arg_2,Arg_3):|:1<=Arg_2 && 1<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 1<=Arg_0+Arg_2 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=Arg_0 && Arg_0+1<=Arg_3
5:evalfbbin(Arg_0,Arg_1,Arg_2,Arg_3) -> evalfbb2in(Arg_0,Arg_1,Arg_2,Arg_3):|:1<=Arg_2 && 1<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 1<=Arg_0+Arg_2 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=Arg_0 && Arg_3<=Arg_0
1:evalfentryin(Arg_0,Arg_1,Arg_2,Arg_3) -> evalfbb3in(0,0,Arg_2,Arg_3)
8:evalfreturnin(Arg_0,Arg_1,Arg_2,Arg_3) -> evalfstop(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_2<=Arg_1 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=Arg_0
0:evalfstart(Arg_0,Arg_1,Arg_2,Arg_3) -> evalfentryin(Arg_0,Arg_1,Arg_2,Arg_3)

MPRF for transition 7:evalfbb2in(Arg_0,Arg_1,Arg_2,Arg_3) -> evalfbb3in(0,Arg_1+1,Arg_2,Arg_3):|:Arg_3<=Arg_0 && 1<=Arg_2 && 1<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 1<=Arg_0+Arg_2 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=Arg_0 of depth 1:

new bound:

Arg_2 {O(n)}

MPRF:

evalfbb3in [Arg_2-Arg_1 ]
evalfbb1in [Arg_2-Arg_1 ]
evalfbbin [Arg_2-Arg_1 ]
evalfbb2in [Arg_2-Arg_1 ]

MPRF for transition 5:evalfbbin(Arg_0,Arg_1,Arg_2,Arg_3) -> evalfbb2in(Arg_0,Arg_1,Arg_2,Arg_3):|:1<=Arg_2 && 1<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 1<=Arg_0+Arg_2 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=Arg_0 && Arg_3<=Arg_0 of depth 1:

new bound:

Arg_2 {O(n)}

MPRF:

evalfbb3in [Arg_2-Arg_1 ]
evalfbb1in [Arg_2-Arg_1 ]
evalfbbin [Arg_2-Arg_1 ]
evalfbb2in [Arg_2-Arg_1-1 ]

MPRF for transition 6:evalfbb1in(Arg_0,Arg_1,Arg_2,Arg_3) -> evalfbb3in(Arg_0+1,Arg_1,Arg_2,Arg_3):|:1<=Arg_3 && 2<=Arg_2+Arg_3 && 1<=Arg_1+Arg_3 && 1<=Arg_0+Arg_3 && 1+Arg_0<=Arg_3 && 1<=Arg_2 && 1<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 1<=Arg_0+Arg_2 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=Arg_0 of depth 1:

new bound:

Arg_2*Arg_3+Arg_3 {O(n^2)}

MPRF:

evalfbb2in [Arg_3 ]
evalfbb3in [Arg_3-Arg_0 ]
evalfbbin [Arg_3-Arg_0 ]
evalfbb1in [Arg_3-Arg_0 ]

MPRF for transition 4:evalfbbin(Arg_0,Arg_1,Arg_2,Arg_3) -> evalfbb1in(Arg_0,Arg_1,Arg_2,Arg_3):|:1<=Arg_2 && 1<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 1<=Arg_0+Arg_2 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=Arg_0 && Arg_0+1<=Arg_3 of depth 1:

new bound:

Arg_2*Arg_3+Arg_3 {O(n^2)}

MPRF:

evalfbb2in [Arg_3 ]
evalfbb3in [Arg_3-Arg_0 ]
evalfbbin [Arg_3-Arg_0 ]
evalfbb1in [Arg_3-Arg_0-1 ]

knowledge_propagation leads to new time bound Arg_2*Arg_3+Arg_2+Arg_3+1 {O(n^2)} for transition 2:evalfbb3in(Arg_0,Arg_1,Arg_2,Arg_3) -> evalfbbin(Arg_0,Arg_1,Arg_2,Arg_3):|:0<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=Arg_0 && Arg_1+1<=Arg_2

All Bounds

Timebounds

Overall timebound:3*Arg_2*Arg_3+3*Arg_2+3*Arg_3+5 {O(n^2)}
6: evalfbb1in->evalfbb3in: Arg_2*Arg_3+Arg_3 {O(n^2)}
7: evalfbb2in->evalfbb3in: Arg_2 {O(n)}
2: evalfbb3in->evalfbbin: Arg_2*Arg_3+Arg_2+Arg_3+1 {O(n^2)}
3: evalfbb3in->evalfreturnin: 1 {O(1)}
4: evalfbbin->evalfbb1in: Arg_2*Arg_3+Arg_3 {O(n^2)}
5: evalfbbin->evalfbb2in: Arg_2 {O(n)}
1: evalfentryin->evalfbb3in: 1 {O(1)}
8: evalfreturnin->evalfstop: 1 {O(1)}
0: evalfstart->evalfentryin: 1 {O(1)}

Costbounds

Overall costbound: 3*Arg_2*Arg_3+3*Arg_2+3*Arg_3+5 {O(n^2)}
6: evalfbb1in->evalfbb3in: Arg_2*Arg_3+Arg_3 {O(n^2)}
7: evalfbb2in->evalfbb3in: Arg_2 {O(n)}
2: evalfbb3in->evalfbbin: Arg_2*Arg_3+Arg_2+Arg_3+1 {O(n^2)}
3: evalfbb3in->evalfreturnin: 1 {O(1)}
4: evalfbbin->evalfbb1in: Arg_2*Arg_3+Arg_3 {O(n^2)}
5: evalfbbin->evalfbb2in: Arg_2 {O(n)}
1: evalfentryin->evalfbb3in: 1 {O(1)}
8: evalfreturnin->evalfstop: 1 {O(1)}
0: evalfstart->evalfentryin: 1 {O(1)}

Sizebounds

6: evalfbb1in->evalfbb3in, Arg_0: Arg_2*Arg_3+Arg_3 {O(n^2)}
6: evalfbb1in->evalfbb3in, Arg_1: Arg_2 {O(n)}
6: evalfbb1in->evalfbb3in, Arg_2: Arg_2 {O(n)}
6: evalfbb1in->evalfbb3in, Arg_3: Arg_3 {O(n)}
7: evalfbb2in->evalfbb3in, Arg_0: 0 {O(1)}
7: evalfbb2in->evalfbb3in, Arg_1: Arg_2 {O(n)}
7: evalfbb2in->evalfbb3in, Arg_2: Arg_2 {O(n)}
7: evalfbb2in->evalfbb3in, Arg_3: Arg_3 {O(n)}
2: evalfbb3in->evalfbbin, Arg_0: Arg_2*Arg_3+Arg_3 {O(n^2)}
2: evalfbb3in->evalfbbin, Arg_1: Arg_2 {O(n)}
2: evalfbb3in->evalfbbin, Arg_2: Arg_2 {O(n)}
2: evalfbb3in->evalfbbin, Arg_3: Arg_3 {O(n)}
3: evalfbb3in->evalfreturnin, Arg_0: 0 {O(1)}
3: evalfbb3in->evalfreturnin, Arg_1: Arg_2 {O(n)}
3: evalfbb3in->evalfreturnin, Arg_2: 2*Arg_2 {O(n)}
3: evalfbb3in->evalfreturnin, Arg_3: 2*Arg_3 {O(n)}
4: evalfbbin->evalfbb1in, Arg_0: Arg_2*Arg_3+Arg_3 {O(n^2)}
4: evalfbbin->evalfbb1in, Arg_1: Arg_2 {O(n)}
4: evalfbbin->evalfbb1in, Arg_2: Arg_2 {O(n)}
4: evalfbbin->evalfbb1in, Arg_3: Arg_3 {O(n)}
5: evalfbbin->evalfbb2in, Arg_0: Arg_2*Arg_3+Arg_3 {O(n^2)}
5: evalfbbin->evalfbb2in, Arg_1: Arg_2 {O(n)}
5: evalfbbin->evalfbb2in, Arg_2: Arg_2 {O(n)}
5: evalfbbin->evalfbb2in, Arg_3: Arg_3 {O(n)}
1: evalfentryin->evalfbb3in, Arg_0: 0 {O(1)}
1: evalfentryin->evalfbb3in, Arg_1: 0 {O(1)}
1: evalfentryin->evalfbb3in, Arg_2: Arg_2 {O(n)}
1: evalfentryin->evalfbb3in, Arg_3: Arg_3 {O(n)}
8: evalfreturnin->evalfstop, Arg_0: 0 {O(1)}
8: evalfreturnin->evalfstop, Arg_1: Arg_2 {O(n)}
8: evalfreturnin->evalfstop, Arg_2: 2*Arg_2 {O(n)}
8: evalfreturnin->evalfstop, Arg_3: 2*Arg_3 {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)}
0: evalfstart->evalfentryin, Arg_3: Arg_3 {O(n)}