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):|:Arg_2<=Arg_1
5:evalfbb2in(Arg_0,Arg_1,Arg_2) -> evalfbb3in(Arg_0,Arg_1,Arg_2):|:Arg_1+1<=Arg_2
7:evalfbb3in(Arg_0,Arg_1,Arg_2) -> evalfbb4in(Arg_0+1,Arg_1,Arg_2)
2:evalfbb4in(Arg_0,Arg_1,Arg_2) -> evalfbb2in(Arg_0,Arg_1,Arg_0):|:Arg_0<=Arg_1
3:evalfbb4in(Arg_0,Arg_1,Arg_2) -> evalfreturnin(Arg_0,Arg_1,Arg_2):|:Arg_1+1<=Arg_0
1:evalfentryin(Arg_0,Arg_1,Arg_2) -> evalfbb4in(1,Arg_1,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 1+Arg_1<=Arg_0 && 1<=Arg_0 for location evalfreturnin
Found invariant Arg_2<=Arg_1 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && 2<=Arg_0+Arg_2 && Arg_0<=Arg_2 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 1<=Arg_0 for location evalfbb1in
Found invariant Arg_2<=1+Arg_1 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && 2<=Arg_0+Arg_2 && Arg_0<=Arg_2 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 1<=Arg_0 for location evalfbb2in
Found invariant Arg_2<=1+Arg_1 && 2<=Arg_2 && 3<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 3<=Arg_0+Arg_2 && 1+Arg_0<=Arg_2 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 1<=Arg_0 for location evalfbb3in
Found invariant 1+Arg_1<=Arg_0 && 1<=Arg_0 for location evalfstop
Found invariant 1<=Arg_0 for location evalfbb4in
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_1 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && 2<=Arg_0+Arg_2 && Arg_0<=Arg_2 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 1<=Arg_0
4:evalfbb2in(Arg_0,Arg_1,Arg_2) -> evalfbb1in(Arg_0,Arg_1,Arg_2):|:Arg_2<=1+Arg_1 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && 2<=Arg_0+Arg_2 && Arg_0<=Arg_2 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 1<=Arg_0 && Arg_2<=Arg_1
5:evalfbb2in(Arg_0,Arg_1,Arg_2) -> evalfbb3in(Arg_0,Arg_1,Arg_2):|:Arg_2<=1+Arg_1 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && 2<=Arg_0+Arg_2 && Arg_0<=Arg_2 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 1<=Arg_0 && Arg_1+1<=Arg_2
7:evalfbb3in(Arg_0,Arg_1,Arg_2) -> evalfbb4in(Arg_0+1,Arg_1,Arg_2):|:Arg_2<=1+Arg_1 && 2<=Arg_2 && 3<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 3<=Arg_0+Arg_2 && 1+Arg_0<=Arg_2 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 1<=Arg_0
2:evalfbb4in(Arg_0,Arg_1,Arg_2) -> evalfbb2in(Arg_0,Arg_1,Arg_0):|:1<=Arg_0 && Arg_0<=Arg_1
3:evalfbb4in(Arg_0,Arg_1,Arg_2) -> evalfreturnin(Arg_0,Arg_1,Arg_2):|:1<=Arg_0 && Arg_1+1<=Arg_0
1:evalfentryin(Arg_0,Arg_1,Arg_2) -> evalfbb4in(1,Arg_1,Arg_2)
8:evalfreturnin(Arg_0,Arg_1,Arg_2) -> evalfstop(Arg_0,Arg_1,Arg_2):|:1+Arg_1<=Arg_0 && 1<=Arg_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<=1+Arg_1 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && 2<=Arg_0+Arg_2 && Arg_0<=Arg_2 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 1<=Arg_0 && Arg_1+1<=Arg_2 of depth 1:
new bound:
Arg_1+3 {O(n)}
MPRF:
evalfbb1in [Arg_1+2-Arg_0 ]
evalfbb3in [Arg_1+1-Arg_0 ]
evalfbb4in [Arg_1+2-Arg_0 ]
evalfbb2in [Arg_1+2-Arg_0 ]
MPRF for transition 7:evalfbb3in(Arg_0,Arg_1,Arg_2) -> evalfbb4in(Arg_0+1,Arg_1,Arg_2):|:Arg_2<=1+Arg_1 && 2<=Arg_2 && 3<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 3<=Arg_0+Arg_2 && 1+Arg_0<=Arg_2 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 1<=Arg_0 of depth 1:
new bound:
Arg_1+2 {O(n)}
MPRF:
evalfbb1in [Arg_1+1-Arg_0 ]
evalfbb3in [Arg_1+1-Arg_0 ]
evalfbb4in [Arg_1+1-Arg_0 ]
evalfbb2in [Arg_1+1-Arg_0 ]
MPRF for transition 2:evalfbb4in(Arg_0,Arg_1,Arg_2) -> evalfbb2in(Arg_0,Arg_1,Arg_0):|:1<=Arg_0 && Arg_0<=Arg_1 of depth 1:
new bound:
Arg_1+2 {O(n)}
MPRF:
evalfbb1in [Arg_1-Arg_0 ]
evalfbb3in [Arg_1-Arg_0 ]
evalfbb4in [Arg_1+1-Arg_0 ]
evalfbb2in [Arg_1-Arg_0 ]
MPRF for transition 6:evalfbb1in(Arg_0,Arg_1,Arg_2) -> evalfbb2in(Arg_0,Arg_1,Arg_2+1):|:Arg_2<=Arg_1 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && 2<=Arg_0+Arg_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:
2*Arg_1*Arg_1+9*Arg_1+10 {O(n^2)}
MPRF:
evalfbb1in [Arg_1+1-Arg_2 ]
evalfbb2in [Arg_1+1-Arg_2 ]
evalfbb3in [Arg_1-Arg_2 ]
evalfbb4in [-1 ]
MPRF for transition 4:evalfbb2in(Arg_0,Arg_1,Arg_2) -> evalfbb1in(Arg_0,Arg_1,Arg_2):|:Arg_2<=1+Arg_1 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && 2<=Arg_0+Arg_2 && Arg_0<=Arg_2 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 1<=Arg_0 && Arg_2<=Arg_1 of depth 1:
new bound:
2*Arg_1*Arg_1+9*Arg_1+10 {O(n^2)}
MPRF:
evalfbb1in [Arg_1-Arg_2 ]
evalfbb2in [Arg_1+1-Arg_2 ]
evalfbb3in [0 ]
evalfbb4in [0 ]
All Bounds
Timebounds
Overall timebound:4*Arg_1*Arg_1+21*Arg_1+31 {O(n^2)}
6: evalfbb1in->evalfbb2in: 2*Arg_1*Arg_1+9*Arg_1+10 {O(n^2)}
4: evalfbb2in->evalfbb1in: 2*Arg_1*Arg_1+9*Arg_1+10 {O(n^2)}
5: evalfbb2in->evalfbb3in: Arg_1+3 {O(n)}
7: evalfbb3in->evalfbb4in: Arg_1+2 {O(n)}
2: evalfbb4in->evalfbb2in: Arg_1+2 {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_1*Arg_1+21*Arg_1+31 {O(n^2)}
6: evalfbb1in->evalfbb2in: 2*Arg_1*Arg_1+9*Arg_1+10 {O(n^2)}
4: evalfbb2in->evalfbb1in: 2*Arg_1*Arg_1+9*Arg_1+10 {O(n^2)}
5: evalfbb2in->evalfbb3in: Arg_1+3 {O(n)}
7: evalfbb3in->evalfbb4in: Arg_1+2 {O(n)}
2: evalfbb4in->evalfbb2in: Arg_1+2 {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+3 {O(n)}
6: evalfbb1in->evalfbb2in, Arg_1: Arg_1 {O(n)}
6: evalfbb1in->evalfbb2in, Arg_2: 2*Arg_1*Arg_1+10*Arg_1+14 {O(n^2)}
4: evalfbb2in->evalfbb1in, Arg_0: Arg_1+3 {O(n)}
4: evalfbb2in->evalfbb1in, Arg_1: Arg_1 {O(n)}
4: evalfbb2in->evalfbb1in, Arg_2: 2*Arg_1*Arg_1+10*Arg_1+14 {O(n^2)}
5: evalfbb2in->evalfbb3in, Arg_0: Arg_1+3 {O(n)}
5: evalfbb2in->evalfbb3in, Arg_1: Arg_1 {O(n)}
5: evalfbb2in->evalfbb3in, Arg_2: 2*Arg_1*Arg_1+10*Arg_1+14 {O(n^2)}
7: evalfbb3in->evalfbb4in, Arg_0: Arg_1+3 {O(n)}
7: evalfbb3in->evalfbb4in, Arg_1: Arg_1 {O(n)}
7: evalfbb3in->evalfbb4in, Arg_2: 2*Arg_1*Arg_1+10*Arg_1+14 {O(n^2)}
2: evalfbb4in->evalfbb2in, Arg_0: Arg_1+3 {O(n)}
2: evalfbb4in->evalfbb2in, Arg_1: Arg_1 {O(n)}
2: evalfbb4in->evalfbb2in, Arg_2: Arg_1+4 {O(n)}
3: evalfbb4in->evalfreturnin, Arg_0: Arg_1+4 {O(n)}
3: evalfbb4in->evalfreturnin, Arg_1: 2*Arg_1 {O(n)}
3: evalfbb4in->evalfreturnin, Arg_2: 2*Arg_1*Arg_1+10*Arg_1+Arg_2+14 {O(n^2)}
1: evalfentryin->evalfbb4in, Arg_0: 1 {O(1)}
1: evalfentryin->evalfbb4in, Arg_1: Arg_1 {O(n)}
1: evalfentryin->evalfbb4in, Arg_2: Arg_2 {O(n)}
8: evalfreturnin->evalfstop, Arg_0: Arg_1+4 {O(n)}
8: evalfreturnin->evalfstop, Arg_1: 2*Arg_1 {O(n)}
8: evalfreturnin->evalfstop, Arg_2: 2*Arg_1*Arg_1+10*Arg_1+Arg_2+14 {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)}