Initial Problem

Start: evalNestedSinglestart
Program_Vars: Arg_0, Arg_1, Arg_2
Temp_Vars: D
Locations: evalNestedSinglebb1in, evalNestedSinglebb2in, evalNestedSinglebb3in, evalNestedSinglebb4in, evalNestedSinglebb5in, evalNestedSingleentryin, evalNestedSinglereturnin, evalNestedSinglestart, evalNestedSinglestop
Transitions:
9:evalNestedSinglebb1in(Arg_0,Arg_1,Arg_2) -> evalNestedSinglebb2in(Arg_0,Arg_1,Arg_2+1)
5:evalNestedSinglebb2in(Arg_0,Arg_1,Arg_2) -> evalNestedSinglebb3in(Arg_0,Arg_1,Arg_2):|:Arg_2+1<=Arg_1
4:evalNestedSinglebb2in(Arg_0,Arg_1,Arg_2) -> evalNestedSinglebb4in(Arg_0,Arg_1,Arg_2):|:Arg_1<=Arg_2
6:evalNestedSinglebb3in(Arg_0,Arg_1,Arg_2) -> evalNestedSinglebb1in(Arg_0,Arg_1,Arg_2):|:D+1<=0
7:evalNestedSinglebb3in(Arg_0,Arg_1,Arg_2) -> evalNestedSinglebb1in(Arg_0,Arg_1,Arg_2):|:1<=D
8:evalNestedSinglebb3in(Arg_0,Arg_1,Arg_2) -> evalNestedSinglebb4in(Arg_0,Arg_1,Arg_2)
10:evalNestedSinglebb4in(Arg_0,Arg_1,Arg_2) -> evalNestedSinglebb5in(Arg_2+1,Arg_1,Arg_2)
2:evalNestedSinglebb5in(Arg_0,Arg_1,Arg_2) -> evalNestedSinglebb2in(Arg_0,Arg_1,Arg_0):|:Arg_0+1<=Arg_1
3:evalNestedSinglebb5in(Arg_0,Arg_1,Arg_2) -> evalNestedSinglereturnin(Arg_0,Arg_1,Arg_2):|:Arg_1<=Arg_0
1:evalNestedSingleentryin(Arg_0,Arg_1,Arg_2) -> evalNestedSinglebb5in(0,Arg_1,Arg_2)
11:evalNestedSinglereturnin(Arg_0,Arg_1,Arg_2) -> evalNestedSinglestop(Arg_0,Arg_1,Arg_2)
0:evalNestedSinglestart(Arg_0,Arg_1,Arg_2) -> evalNestedSingleentryin(Arg_0,Arg_1,Arg_2)

Preprocessing

Found invariant 0<=Arg_0 for location evalNestedSinglebb5in

Found invariant Arg_1<=Arg_0 && 0<=Arg_0 for location evalNestedSinglereturnin

Found invariant 1+Arg_2<=Arg_1 && 0<=Arg_2 && 1<=Arg_1+Arg_2 && 0<=Arg_0+Arg_2 && Arg_0<=Arg_2 && 1<=Arg_1 && 1<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 0<=Arg_0 for location evalNestedSinglebb3in

Found invariant Arg_1<=Arg_0 && 0<=Arg_0 for location evalNestedSinglestop

Found invariant Arg_2<=Arg_1 && 0<=Arg_2 && 1<=Arg_1+Arg_2 && 0<=Arg_0+Arg_2 && Arg_0<=Arg_2 && 1<=Arg_1 && 1<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 0<=Arg_0 for location evalNestedSinglebb2in

Found invariant Arg_2<=Arg_1 && 0<=Arg_2 && 1<=Arg_1+Arg_2 && 0<=Arg_0+Arg_2 && Arg_0<=Arg_2 && 1<=Arg_1 && 1<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 0<=Arg_0 for location evalNestedSinglebb4in

Found invariant 1+Arg_2<=Arg_1 && 0<=Arg_2 && 1<=Arg_1+Arg_2 && 0<=Arg_0+Arg_2 && Arg_0<=Arg_2 && 1<=Arg_1 && 1<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 0<=Arg_0 for location evalNestedSinglebb1in

Problem after Preprocessing

Start: evalNestedSinglestart
Program_Vars: Arg_0, Arg_1, Arg_2
Temp_Vars: D
Locations: evalNestedSinglebb1in, evalNestedSinglebb2in, evalNestedSinglebb3in, evalNestedSinglebb4in, evalNestedSinglebb5in, evalNestedSingleentryin, evalNestedSinglereturnin, evalNestedSinglestart, evalNestedSinglestop
Transitions:
9:evalNestedSinglebb1in(Arg_0,Arg_1,Arg_2) -> evalNestedSinglebb2in(Arg_0,Arg_1,Arg_2+1):|:1+Arg_2<=Arg_1 && 0<=Arg_2 && 1<=Arg_1+Arg_2 && 0<=Arg_0+Arg_2 && Arg_0<=Arg_2 && 1<=Arg_1 && 1<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 0<=Arg_0
5:evalNestedSinglebb2in(Arg_0,Arg_1,Arg_2) -> evalNestedSinglebb3in(Arg_0,Arg_1,Arg_2):|:Arg_2<=Arg_1 && 0<=Arg_2 && 1<=Arg_1+Arg_2 && 0<=Arg_0+Arg_2 && Arg_0<=Arg_2 && 1<=Arg_1 && 1<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 0<=Arg_0 && Arg_2+1<=Arg_1
4:evalNestedSinglebb2in(Arg_0,Arg_1,Arg_2) -> evalNestedSinglebb4in(Arg_0,Arg_1,Arg_2):|:Arg_2<=Arg_1 && 0<=Arg_2 && 1<=Arg_1+Arg_2 && 0<=Arg_0+Arg_2 && Arg_0<=Arg_2 && 1<=Arg_1 && 1<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 0<=Arg_0 && Arg_1<=Arg_2
6:evalNestedSinglebb3in(Arg_0,Arg_1,Arg_2) -> evalNestedSinglebb1in(Arg_0,Arg_1,Arg_2):|:1+Arg_2<=Arg_1 && 0<=Arg_2 && 1<=Arg_1+Arg_2 && 0<=Arg_0+Arg_2 && Arg_0<=Arg_2 && 1<=Arg_1 && 1<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 0<=Arg_0 && D+1<=0
7:evalNestedSinglebb3in(Arg_0,Arg_1,Arg_2) -> evalNestedSinglebb1in(Arg_0,Arg_1,Arg_2):|:1+Arg_2<=Arg_1 && 0<=Arg_2 && 1<=Arg_1+Arg_2 && 0<=Arg_0+Arg_2 && Arg_0<=Arg_2 && 1<=Arg_1 && 1<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 0<=Arg_0 && 1<=D
8:evalNestedSinglebb3in(Arg_0,Arg_1,Arg_2) -> evalNestedSinglebb4in(Arg_0,Arg_1,Arg_2):|:1+Arg_2<=Arg_1 && 0<=Arg_2 && 1<=Arg_1+Arg_2 && 0<=Arg_0+Arg_2 && Arg_0<=Arg_2 && 1<=Arg_1 && 1<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 0<=Arg_0
10:evalNestedSinglebb4in(Arg_0,Arg_1,Arg_2) -> evalNestedSinglebb5in(Arg_2+1,Arg_1,Arg_2):|:Arg_2<=Arg_1 && 0<=Arg_2 && 1<=Arg_1+Arg_2 && 0<=Arg_0+Arg_2 && Arg_0<=Arg_2 && 1<=Arg_1 && 1<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 0<=Arg_0
2:evalNestedSinglebb5in(Arg_0,Arg_1,Arg_2) -> evalNestedSinglebb2in(Arg_0,Arg_1,Arg_0):|:0<=Arg_0 && Arg_0+1<=Arg_1
3:evalNestedSinglebb5in(Arg_0,Arg_1,Arg_2) -> evalNestedSinglereturnin(Arg_0,Arg_1,Arg_2):|:0<=Arg_0 && Arg_1<=Arg_0
1:evalNestedSingleentryin(Arg_0,Arg_1,Arg_2) -> evalNestedSinglebb5in(0,Arg_1,Arg_2)
11:evalNestedSinglereturnin(Arg_0,Arg_1,Arg_2) -> evalNestedSinglestop(Arg_0,Arg_1,Arg_2):|:Arg_1<=Arg_0 && 0<=Arg_0
0:evalNestedSinglestart(Arg_0,Arg_1,Arg_2) -> evalNestedSingleentryin(Arg_0,Arg_1,Arg_2)

MPRF for transition 9:evalNestedSinglebb1in(Arg_0,Arg_1,Arg_2) -> evalNestedSinglebb2in(Arg_0,Arg_1,Arg_2+1):|:1+Arg_2<=Arg_1 && 0<=Arg_2 && 1<=Arg_1+Arg_2 && 0<=Arg_0+Arg_2 && Arg_0<=Arg_2 && 1<=Arg_1 && 1<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 0<=Arg_0 of depth 1:

new bound:

Arg_1 {O(n)}

MPRF:

evalNestedSinglebb1in [Arg_1-Arg_2 ]
evalNestedSinglebb3in [Arg_1-Arg_2 ]
evalNestedSinglebb4in [Arg_1-Arg_2 ]
evalNestedSinglebb5in [Arg_1-Arg_0 ]
evalNestedSinglebb2in [Arg_1-Arg_2 ]

MPRF for transition 4:evalNestedSinglebb2in(Arg_0,Arg_1,Arg_2) -> evalNestedSinglebb4in(Arg_0,Arg_1,Arg_2):|:Arg_2<=Arg_1 && 0<=Arg_2 && 1<=Arg_1+Arg_2 && 0<=Arg_0+Arg_2 && Arg_0<=Arg_2 && 1<=Arg_1 && 1<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 0<=Arg_0 && Arg_1<=Arg_2 of depth 1:

new bound:

Arg_1+1 {O(n)}

MPRF:

evalNestedSinglebb1in [Arg_1+1-Arg_0 ]
evalNestedSinglebb3in [Arg_1+1-Arg_0 ]
evalNestedSinglebb4in [Arg_1-Arg_2 ]
evalNestedSinglebb5in [Arg_1+1-Arg_0 ]
evalNestedSinglebb2in [Arg_1+1-Arg_0 ]

MPRF for transition 5:evalNestedSinglebb2in(Arg_0,Arg_1,Arg_2) -> evalNestedSinglebb3in(Arg_0,Arg_1,Arg_2):|:Arg_2<=Arg_1 && 0<=Arg_2 && 1<=Arg_1+Arg_2 && 0<=Arg_0+Arg_2 && Arg_0<=Arg_2 && 1<=Arg_1 && 1<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 0<=Arg_0 && Arg_2+1<=Arg_1 of depth 1:

new bound:

Arg_1+1 {O(n)}

MPRF:

evalNestedSinglebb1in [Arg_1-Arg_2 ]
evalNestedSinglebb3in [Arg_1-Arg_2 ]
evalNestedSinglebb4in [Arg_1-Arg_2 ]
evalNestedSinglebb5in [Arg_1+1-Arg_0 ]
evalNestedSinglebb2in [Arg_1+1-Arg_2 ]

MPRF for transition 6:evalNestedSinglebb3in(Arg_0,Arg_1,Arg_2) -> evalNestedSinglebb1in(Arg_0,Arg_1,Arg_2):|:1+Arg_2<=Arg_1 && 0<=Arg_2 && 1<=Arg_1+Arg_2 && 0<=Arg_0+Arg_2 && Arg_0<=Arg_2 && 1<=Arg_1 && 1<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 0<=Arg_0 && D+1<=0 of depth 1:

new bound:

Arg_1 {O(n)}

MPRF:

evalNestedSinglebb1in [Arg_1-Arg_2-1 ]
evalNestedSinglebb3in [Arg_1-Arg_2 ]
evalNestedSinglebb4in [Arg_1-Arg_2 ]
evalNestedSinglebb5in [Arg_1-Arg_0 ]
evalNestedSinglebb2in [Arg_1-Arg_2 ]

MPRF for transition 7:evalNestedSinglebb3in(Arg_0,Arg_1,Arg_2) -> evalNestedSinglebb1in(Arg_0,Arg_1,Arg_2):|:1+Arg_2<=Arg_1 && 0<=Arg_2 && 1<=Arg_1+Arg_2 && 0<=Arg_0+Arg_2 && Arg_0<=Arg_2 && 1<=Arg_1 && 1<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 0<=Arg_0 && 1<=D of depth 1:

new bound:

Arg_1 {O(n)}

MPRF:

evalNestedSinglebb1in [Arg_1-Arg_2-1 ]
evalNestedSinglebb3in [Arg_1-Arg_2 ]
evalNestedSinglebb4in [Arg_1-Arg_2 ]
evalNestedSinglebb5in [Arg_1-Arg_0 ]
evalNestedSinglebb2in [Arg_1-Arg_2 ]

MPRF for transition 8:evalNestedSinglebb3in(Arg_0,Arg_1,Arg_2) -> evalNestedSinglebb4in(Arg_0,Arg_1,Arg_2):|:1+Arg_2<=Arg_1 && 0<=Arg_2 && 1<=Arg_1+Arg_2 && 0<=Arg_0+Arg_2 && Arg_0<=Arg_2 && 1<=Arg_1 && 1<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 0<=Arg_0 of depth 1:

new bound:

Arg_1 {O(n)}

MPRF:

evalNestedSinglebb1in [Arg_1-Arg_2-1 ]
evalNestedSinglebb3in [Arg_1-Arg_2 ]
evalNestedSinglebb4in [Arg_1-Arg_2-1 ]
evalNestedSinglebb5in [Arg_1-Arg_0 ]
evalNestedSinglebb2in [Arg_1-Arg_2 ]

MPRF for transition 10:evalNestedSinglebb4in(Arg_0,Arg_1,Arg_2) -> evalNestedSinglebb5in(Arg_2+1,Arg_1,Arg_2):|:Arg_2<=Arg_1 && 0<=Arg_2 && 1<=Arg_1+Arg_2 && 0<=Arg_0+Arg_2 && Arg_0<=Arg_2 && 1<=Arg_1 && 1<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 0<=Arg_0 of depth 1:

new bound:

Arg_1+1 {O(n)}

MPRF:

evalNestedSinglebb1in [Arg_1+1-Arg_2 ]
evalNestedSinglebb3in [Arg_1+1-Arg_2 ]
evalNestedSinglebb4in [Arg_1+1-Arg_2 ]
evalNestedSinglebb5in [Arg_1+1-Arg_0 ]
evalNestedSinglebb2in [Arg_1+1-Arg_2 ]

MPRF for transition 2:evalNestedSinglebb5in(Arg_0,Arg_1,Arg_2) -> evalNestedSinglebb2in(Arg_0,Arg_1,Arg_0):|:0<=Arg_0 && Arg_0+1<=Arg_1 of depth 1:

new bound:

Arg_1 {O(n)}

MPRF:

evalNestedSinglebb1in [Arg_1-Arg_0-1 ]
evalNestedSinglebb3in [Arg_1-Arg_0-1 ]
evalNestedSinglebb4in [Arg_1-Arg_0-1 ]
evalNestedSinglebb5in [Arg_1-Arg_0 ]
evalNestedSinglebb2in [Arg_1-Arg_0-1 ]

All Bounds

Timebounds

Overall timebound:8*Arg_1+7 {O(n)}
9: evalNestedSinglebb1in->evalNestedSinglebb2in: Arg_1 {O(n)}
4: evalNestedSinglebb2in->evalNestedSinglebb4in: Arg_1+1 {O(n)}
5: evalNestedSinglebb2in->evalNestedSinglebb3in: Arg_1+1 {O(n)}
6: evalNestedSinglebb3in->evalNestedSinglebb1in: Arg_1 {O(n)}
7: evalNestedSinglebb3in->evalNestedSinglebb1in: Arg_1 {O(n)}
8: evalNestedSinglebb3in->evalNestedSinglebb4in: Arg_1 {O(n)}
10: evalNestedSinglebb4in->evalNestedSinglebb5in: Arg_1+1 {O(n)}
2: evalNestedSinglebb5in->evalNestedSinglebb2in: Arg_1 {O(n)}
3: evalNestedSinglebb5in->evalNestedSinglereturnin: 1 {O(1)}
1: evalNestedSingleentryin->evalNestedSinglebb5in: 1 {O(1)}
11: evalNestedSinglereturnin->evalNestedSinglestop: 1 {O(1)}
0: evalNestedSinglestart->evalNestedSingleentryin: 1 {O(1)}

Costbounds

Overall costbound: 8*Arg_1+7 {O(n)}
9: evalNestedSinglebb1in->evalNestedSinglebb2in: Arg_1 {O(n)}
4: evalNestedSinglebb2in->evalNestedSinglebb4in: Arg_1+1 {O(n)}
5: evalNestedSinglebb2in->evalNestedSinglebb3in: Arg_1+1 {O(n)}
6: evalNestedSinglebb3in->evalNestedSinglebb1in: Arg_1 {O(n)}
7: evalNestedSinglebb3in->evalNestedSinglebb1in: Arg_1 {O(n)}
8: evalNestedSinglebb3in->evalNestedSinglebb4in: Arg_1 {O(n)}
10: evalNestedSinglebb4in->evalNestedSinglebb5in: Arg_1+1 {O(n)}
2: evalNestedSinglebb5in->evalNestedSinglebb2in: Arg_1 {O(n)}
3: evalNestedSinglebb5in->evalNestedSinglereturnin: 1 {O(1)}
1: evalNestedSingleentryin->evalNestedSinglebb5in: 1 {O(1)}
11: evalNestedSinglereturnin->evalNestedSinglestop: 1 {O(1)}
0: evalNestedSinglestart->evalNestedSingleentryin: 1 {O(1)}

Sizebounds

9: evalNestedSinglebb1in->evalNestedSinglebb2in, Arg_0: 2*Arg_1+1 {O(n)}
9: evalNestedSinglebb1in->evalNestedSinglebb2in, Arg_1: Arg_1 {O(n)}
9: evalNestedSinglebb1in->evalNestedSinglebb2in, Arg_2: 2*Arg_1+1 {O(n)}
4: evalNestedSinglebb2in->evalNestedSinglebb4in, Arg_0: 2*Arg_1+1 {O(n)}
4: evalNestedSinglebb2in->evalNestedSinglebb4in, Arg_1: Arg_1 {O(n)}
4: evalNestedSinglebb2in->evalNestedSinglebb4in, Arg_2: 2*Arg_1+1 {O(n)}
5: evalNestedSinglebb2in->evalNestedSinglebb3in, Arg_0: 2*Arg_1+1 {O(n)}
5: evalNestedSinglebb2in->evalNestedSinglebb3in, Arg_1: Arg_1 {O(n)}
5: evalNestedSinglebb2in->evalNestedSinglebb3in, Arg_2: 2*Arg_1+1 {O(n)}
6: evalNestedSinglebb3in->evalNestedSinglebb1in, Arg_0: 2*Arg_1+1 {O(n)}
6: evalNestedSinglebb3in->evalNestedSinglebb1in, Arg_1: Arg_1 {O(n)}
6: evalNestedSinglebb3in->evalNestedSinglebb1in, Arg_2: 2*Arg_1+1 {O(n)}
7: evalNestedSinglebb3in->evalNestedSinglebb1in, Arg_0: 2*Arg_1+1 {O(n)}
7: evalNestedSinglebb3in->evalNestedSinglebb1in, Arg_1: Arg_1 {O(n)}
7: evalNestedSinglebb3in->evalNestedSinglebb1in, Arg_2: 2*Arg_1+1 {O(n)}
8: evalNestedSinglebb3in->evalNestedSinglebb4in, Arg_0: 2*Arg_1+1 {O(n)}
8: evalNestedSinglebb3in->evalNestedSinglebb4in, Arg_1: Arg_1 {O(n)}
8: evalNestedSinglebb3in->evalNestedSinglebb4in, Arg_2: 2*Arg_1+1 {O(n)}
10: evalNestedSinglebb4in->evalNestedSinglebb5in, Arg_0: 2*Arg_1+1 {O(n)}
10: evalNestedSinglebb4in->evalNestedSinglebb5in, Arg_1: Arg_1 {O(n)}
10: evalNestedSinglebb4in->evalNestedSinglebb5in, Arg_2: 4*Arg_1+2 {O(n)}
2: evalNestedSinglebb5in->evalNestedSinglebb2in, Arg_0: 2*Arg_1+1 {O(n)}
2: evalNestedSinglebb5in->evalNestedSinglebb2in, Arg_1: Arg_1 {O(n)}
2: evalNestedSinglebb5in->evalNestedSinglebb2in, Arg_2: 2*Arg_1+1 {O(n)}
3: evalNestedSinglebb5in->evalNestedSinglereturnin, Arg_0: 2*Arg_1+1 {O(n)}
3: evalNestedSinglebb5in->evalNestedSinglereturnin, Arg_1: 2*Arg_1 {O(n)}
3: evalNestedSinglebb5in->evalNestedSinglereturnin, Arg_2: 4*Arg_1+Arg_2+2 {O(n)}
1: evalNestedSingleentryin->evalNestedSinglebb5in, Arg_0: 0 {O(1)}
1: evalNestedSingleentryin->evalNestedSinglebb5in, Arg_1: Arg_1 {O(n)}
1: evalNestedSingleentryin->evalNestedSinglebb5in, Arg_2: Arg_2 {O(n)}
11: evalNestedSinglereturnin->evalNestedSinglestop, Arg_0: 2*Arg_1+1 {O(n)}
11: evalNestedSinglereturnin->evalNestedSinglestop, Arg_1: 2*Arg_1 {O(n)}
11: evalNestedSinglereturnin->evalNestedSinglestop, Arg_2: 4*Arg_1+Arg_2+2 {O(n)}
0: evalNestedSinglestart->evalNestedSingleentryin, Arg_0: Arg_0 {O(n)}
0: evalNestedSinglestart->evalNestedSingleentryin, Arg_1: Arg_1 {O(n)}
0: evalNestedSinglestart->evalNestedSingleentryin, Arg_2: Arg_2 {O(n)}