Initial Problem

Start: evalloopsstart
Program_Vars: Arg_0, Arg_1
Temp_Vars: C
Locations: evalloopsbb1in, evalloopsbb3in, evalloopsbb4in, evalloopsbb5in, evalloopsbb6in, evalloopsentryin, evalloopsreturnin, evalloopsstart, evalloopsstop
Transitions:
5:evalloopsbb1in(Arg_0,Arg_1) -> evalloopsbb4in(Arg_0,1):|:2<=Arg_0
6:evalloopsbb1in(Arg_0,Arg_1) -> evalloopsbb5in(Arg_0,C):|:Arg_0<=1
9:evalloopsbb3in(Arg_0,Arg_1) -> evalloopsbb4in(Arg_0,2*Arg_1)
7:evalloopsbb4in(Arg_0,Arg_1) -> evalloopsbb3in(Arg_0,Arg_1):|:Arg_1+1<=Arg_0
8:evalloopsbb4in(Arg_0,Arg_1) -> evalloopsbb5in(Arg_0,Arg_1):|:Arg_0<=Arg_1
10:evalloopsbb5in(Arg_0,Arg_1) -> evalloopsbb6in(Arg_0-1,Arg_1)
3:evalloopsbb6in(Arg_0,Arg_1) -> evalloopsbb1in(Arg_0,Arg_1):|:0<=Arg_0
4:evalloopsbb6in(Arg_0,Arg_1) -> evalloopsreturnin(Arg_0,Arg_1):|:Arg_0+1<=0
1:evalloopsentryin(Arg_0,Arg_1) -> evalloopsbb6in(Arg_0,Arg_1):|:0<=Arg_0
2:evalloopsentryin(Arg_0,Arg_1) -> evalloopsreturnin(Arg_0,Arg_1):|:Arg_0+1<=0
11:evalloopsreturnin(Arg_0,Arg_1) -> evalloopsstop(Arg_0,Arg_1)
0:evalloopsstart(Arg_0,Arg_1) -> evalloopsentryin(Arg_0,Arg_1)

Preprocessing

Found invariant 1+Arg_0<=0 for location evalloopsstop

Found invariant 1+Arg_1<=Arg_0 && 1<=Arg_1 && 3<=Arg_0+Arg_1 && 2<=Arg_0 for location evalloopsbb3in

Found invariant 0<=Arg_0 for location evalloopsbb1in

Found invariant 1<=Arg_1 && 3<=Arg_0+Arg_1 && 2<=Arg_0 for location evalloopsbb4in

Found invariant 0<=1+Arg_0 for location evalloopsbb6in

Found invariant 1+Arg_0<=0 for location evalloopsreturnin

Found invariant 0<=Arg_0 for location evalloopsbb5in

Problem after Preprocessing

Start: evalloopsstart
Program_Vars: Arg_0, Arg_1
Temp_Vars: C
Locations: evalloopsbb1in, evalloopsbb3in, evalloopsbb4in, evalloopsbb5in, evalloopsbb6in, evalloopsentryin, evalloopsreturnin, evalloopsstart, evalloopsstop
Transitions:
5:evalloopsbb1in(Arg_0,Arg_1) -> evalloopsbb4in(Arg_0,1):|:0<=Arg_0 && 2<=Arg_0
6:evalloopsbb1in(Arg_0,Arg_1) -> evalloopsbb5in(Arg_0,C):|:0<=Arg_0 && Arg_0<=1
9:evalloopsbb3in(Arg_0,Arg_1) -> evalloopsbb4in(Arg_0,2*Arg_1):|:1+Arg_1<=Arg_0 && 1<=Arg_1 && 3<=Arg_0+Arg_1 && 2<=Arg_0
7:evalloopsbb4in(Arg_0,Arg_1) -> evalloopsbb3in(Arg_0,Arg_1):|:1<=Arg_1 && 3<=Arg_0+Arg_1 && 2<=Arg_0 && Arg_1+1<=Arg_0
8:evalloopsbb4in(Arg_0,Arg_1) -> evalloopsbb5in(Arg_0,Arg_1):|:1<=Arg_1 && 3<=Arg_0+Arg_1 && 2<=Arg_0 && Arg_0<=Arg_1
10:evalloopsbb5in(Arg_0,Arg_1) -> evalloopsbb6in(Arg_0-1,Arg_1):|:0<=Arg_0
3:evalloopsbb6in(Arg_0,Arg_1) -> evalloopsbb1in(Arg_0,Arg_1):|:0<=1+Arg_0 && 0<=Arg_0
4:evalloopsbb6in(Arg_0,Arg_1) -> evalloopsreturnin(Arg_0,Arg_1):|:0<=1+Arg_0 && Arg_0+1<=0
1:evalloopsentryin(Arg_0,Arg_1) -> evalloopsbb6in(Arg_0,Arg_1):|:0<=Arg_0
2:evalloopsentryin(Arg_0,Arg_1) -> evalloopsreturnin(Arg_0,Arg_1):|:Arg_0+1<=0
11:evalloopsreturnin(Arg_0,Arg_1) -> evalloopsstop(Arg_0,Arg_1):|:1+Arg_0<=0
0:evalloopsstart(Arg_0,Arg_1) -> evalloopsentryin(Arg_0,Arg_1)

MPRF for transition 5:evalloopsbb1in(Arg_0,Arg_1) -> evalloopsbb4in(Arg_0,1):|:0<=Arg_0 && 2<=Arg_0 of depth 1:

new bound:

Arg_0+1 {O(n)}

MPRF:

evalloopsbb3in [Arg_0 ]
evalloopsbb4in [Arg_0 ]
evalloopsbb5in [Arg_0 ]
evalloopsbb6in [Arg_0+1 ]
evalloopsbb1in [Arg_0+1 ]

MPRF for transition 6:evalloopsbb1in(Arg_0,Arg_1) -> evalloopsbb5in(Arg_0,C):|:0<=Arg_0 && Arg_0<=1 of depth 1:

new bound:

Arg_0+1 {O(n)}

MPRF:

evalloopsbb3in [Arg_0 ]
evalloopsbb4in [Arg_0 ]
evalloopsbb5in [Arg_0 ]
evalloopsbb6in [Arg_0+1 ]
evalloopsbb1in [Arg_0+1 ]

MPRF for transition 8:evalloopsbb4in(Arg_0,Arg_1) -> evalloopsbb5in(Arg_0,Arg_1):|:1<=Arg_1 && 3<=Arg_0+Arg_1 && 2<=Arg_0 && Arg_0<=Arg_1 of depth 1:

new bound:

Arg_0+1 {O(n)}

MPRF:

evalloopsbb3in [Arg_0-1 ]
evalloopsbb4in [Arg_0-1 ]
evalloopsbb5in [Arg_0-2 ]
evalloopsbb6in [Arg_0-1 ]
evalloopsbb1in [Arg_0-1 ]

MPRF for transition 10:evalloopsbb5in(Arg_0,Arg_1) -> evalloopsbb6in(Arg_0-1,Arg_1):|:0<=Arg_0 of depth 1:

new bound:

Arg_0+1 {O(n)}

MPRF:

evalloopsbb3in [Arg_0+1 ]
evalloopsbb4in [Arg_0+1 ]
evalloopsbb5in [Arg_0+1 ]
evalloopsbb6in [Arg_0+1 ]
evalloopsbb1in [Arg_0+1 ]

MPRF for transition 3:evalloopsbb6in(Arg_0,Arg_1) -> evalloopsbb1in(Arg_0,Arg_1):|:0<=1+Arg_0 && 0<=Arg_0 of depth 1:

new bound:

Arg_0+1 {O(n)}

MPRF:

evalloopsbb3in [Arg_0 ]
evalloopsbb4in [Arg_0 ]
evalloopsbb5in [Arg_0 ]
evalloopsbb6in [Arg_0+1 ]
evalloopsbb1in [Arg_0 ]

MPRF for transition 9:evalloopsbb3in(Arg_0,Arg_1) -> evalloopsbb4in(Arg_0,2*Arg_1):|:1+Arg_1<=Arg_0 && 1<=Arg_1 && 3<=Arg_0+Arg_1 && 2<=Arg_0 of depth 1:

new bound:

Arg_0*Arg_0+4*Arg_0+2 {O(n^2)}

MPRF:

evalloopsbb4in [Arg_0-Arg_1 ]
evalloopsbb3in [Arg_0-Arg_1 ]
evalloopsbb5in [Arg_0 ]
evalloopsbb6in [Arg_0 ]
evalloopsbb1in [Arg_0 ]

MPRF for transition 7:evalloopsbb4in(Arg_0,Arg_1) -> evalloopsbb3in(Arg_0,Arg_1):|:1<=Arg_1 && 3<=Arg_0+Arg_1 && 2<=Arg_0 && Arg_1+1<=Arg_0 of depth 1:

new bound:

Arg_0*Arg_0+4*Arg_0+2 {O(n^2)}

MPRF:

evalloopsbb4in [Arg_0-Arg_1 ]
evalloopsbb3in [Arg_0-Arg_1-1 ]
evalloopsbb5in [Arg_0 ]
evalloopsbb6in [Arg_0 ]
evalloopsbb1in [Arg_0 ]

All Bounds

Timebounds

Overall timebound:2*Arg_0*Arg_0+13*Arg_0+14 {O(n^2)}
5: evalloopsbb1in->evalloopsbb4in: Arg_0+1 {O(n)}
6: evalloopsbb1in->evalloopsbb5in: Arg_0+1 {O(n)}
9: evalloopsbb3in->evalloopsbb4in: Arg_0*Arg_0+4*Arg_0+2 {O(n^2)}
7: evalloopsbb4in->evalloopsbb3in: Arg_0*Arg_0+4*Arg_0+2 {O(n^2)}
8: evalloopsbb4in->evalloopsbb5in: Arg_0+1 {O(n)}
10: evalloopsbb5in->evalloopsbb6in: Arg_0+1 {O(n)}
3: evalloopsbb6in->evalloopsbb1in: Arg_0+1 {O(n)}
4: evalloopsbb6in->evalloopsreturnin: 1 {O(1)}
1: evalloopsentryin->evalloopsbb6in: 1 {O(1)}
2: evalloopsentryin->evalloopsreturnin: 1 {O(1)}
11: evalloopsreturnin->evalloopsstop: 1 {O(1)}
0: evalloopsstart->evalloopsentryin: 1 {O(1)}

Costbounds

Overall costbound: 2*Arg_0*Arg_0+13*Arg_0+14 {O(n^2)}
5: evalloopsbb1in->evalloopsbb4in: Arg_0+1 {O(n)}
6: evalloopsbb1in->evalloopsbb5in: Arg_0+1 {O(n)}
9: evalloopsbb3in->evalloopsbb4in: Arg_0*Arg_0+4*Arg_0+2 {O(n^2)}
7: evalloopsbb4in->evalloopsbb3in: Arg_0*Arg_0+4*Arg_0+2 {O(n^2)}
8: evalloopsbb4in->evalloopsbb5in: Arg_0+1 {O(n)}
10: evalloopsbb5in->evalloopsbb6in: Arg_0+1 {O(n)}
3: evalloopsbb6in->evalloopsbb1in: Arg_0+1 {O(n)}
4: evalloopsbb6in->evalloopsreturnin: 1 {O(1)}
1: evalloopsentryin->evalloopsbb6in: 1 {O(1)}
2: evalloopsentryin->evalloopsreturnin: 1 {O(1)}
11: evalloopsreturnin->evalloopsstop: 1 {O(1)}
0: evalloopsstart->evalloopsentryin: 1 {O(1)}

Sizebounds

5: evalloopsbb1in->evalloopsbb4in, Arg_0: Arg_0+2 {O(n)}
5: evalloopsbb1in->evalloopsbb4in, Arg_1: 1 {O(1)}
6: evalloopsbb1in->evalloopsbb5in, Arg_0: 1 {O(1)}
9: evalloopsbb3in->evalloopsbb4in, Arg_0: Arg_0+2 {O(n)}
9: evalloopsbb3in->evalloopsbb4in, Arg_1: 2^(Arg_0*Arg_0+4*Arg_0+2) {O(EXP)}
7: evalloopsbb4in->evalloopsbb3in, Arg_0: Arg_0+2 {O(n)}
7: evalloopsbb4in->evalloopsbb3in, Arg_1: 2^(Arg_0*Arg_0+4*Arg_0+2) {O(EXP)}
8: evalloopsbb4in->evalloopsbb5in, Arg_0: Arg_0+2 {O(n)}
8: evalloopsbb4in->evalloopsbb5in, Arg_1: 2^(Arg_0*Arg_0+4*Arg_0+2) {O(EXP)}
10: evalloopsbb5in->evalloopsbb6in, Arg_0: Arg_0+2 {O(n)}
3: evalloopsbb6in->evalloopsbb1in, Arg_0: Arg_0+2 {O(n)}
4: evalloopsbb6in->evalloopsreturnin, Arg_0: 1 {O(1)}
1: evalloopsentryin->evalloopsbb6in, Arg_0: Arg_0 {O(n)}
1: evalloopsentryin->evalloopsbb6in, Arg_1: Arg_1 {O(n)}
2: evalloopsentryin->evalloopsreturnin, Arg_0: Arg_0 {O(n)}
2: evalloopsentryin->evalloopsreturnin, Arg_1: Arg_1 {O(n)}
11: evalloopsreturnin->evalloopsstop, Arg_0: Arg_0+1 {O(n)}
0: evalloopsstart->evalloopsentryin, Arg_0: Arg_0 {O(n)}
0: evalloopsstart->evalloopsentryin, Arg_1: Arg_1 {O(n)}