Initial Problem

Start: evalSimpleSinglestart
Program_Vars: Arg_0, Arg_1
Temp_Vars:
Locations: evalSimpleSinglebb3in, evalSimpleSinglebbin, evalSimpleSingleentryin, evalSimpleSinglereturnin, evalSimpleSinglestart, evalSimpleSinglestop
Transitions:
2:evalSimpleSinglebb3in(Arg_0,Arg_1) -> evalSimpleSinglebbin(Arg_0,Arg_1):|:Arg_0+1<=Arg_1
3:evalSimpleSinglebb3in(Arg_0,Arg_1) -> evalSimpleSinglereturnin(Arg_0,Arg_1):|:Arg_1<=Arg_0
4:evalSimpleSinglebbin(Arg_0,Arg_1) -> evalSimpleSinglebb3in(Arg_0+1,Arg_1)
1:evalSimpleSingleentryin(Arg_0,Arg_1) -> evalSimpleSinglebb3in(0,Arg_1)
5:evalSimpleSinglereturnin(Arg_0,Arg_1) -> evalSimpleSinglestop(Arg_0,Arg_1)
0:evalSimpleSinglestart(Arg_0,Arg_1) -> evalSimpleSingleentryin(Arg_0,Arg_1)

Preprocessing

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

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

Found invariant 0<=Arg_0 for location evalSimpleSinglebb3in

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

Problem after Preprocessing

Start: evalSimpleSinglestart
Program_Vars: Arg_0, Arg_1
Temp_Vars:
Locations: evalSimpleSinglebb3in, evalSimpleSinglebbin, evalSimpleSingleentryin, evalSimpleSinglereturnin, evalSimpleSinglestart, evalSimpleSinglestop
Transitions:
2:evalSimpleSinglebb3in(Arg_0,Arg_1) -> evalSimpleSinglebbin(Arg_0,Arg_1):|:0<=Arg_0 && Arg_0+1<=Arg_1
3:evalSimpleSinglebb3in(Arg_0,Arg_1) -> evalSimpleSinglereturnin(Arg_0,Arg_1):|:0<=Arg_0 && Arg_1<=Arg_0
4:evalSimpleSinglebbin(Arg_0,Arg_1) -> evalSimpleSinglebb3in(Arg_0+1,Arg_1):|:1<=Arg_1 && 1<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 0<=Arg_0
1:evalSimpleSingleentryin(Arg_0,Arg_1) -> evalSimpleSinglebb3in(0,Arg_1)
5:evalSimpleSinglereturnin(Arg_0,Arg_1) -> evalSimpleSinglestop(Arg_0,Arg_1):|:Arg_1<=Arg_0 && 0<=Arg_0
0:evalSimpleSinglestart(Arg_0,Arg_1) -> evalSimpleSingleentryin(Arg_0,Arg_1)

MPRF for transition 2:evalSimpleSinglebb3in(Arg_0,Arg_1) -> evalSimpleSinglebbin(Arg_0,Arg_1):|:0<=Arg_0 && Arg_0+1<=Arg_1 of depth 1:

new bound:

Arg_1 {O(n)}

MPRF:

evalSimpleSinglebbin [Arg_1-Arg_0-1 ]
evalSimpleSinglebb3in [Arg_1-Arg_0 ]

MPRF for transition 4:evalSimpleSinglebbin(Arg_0,Arg_1) -> evalSimpleSinglebb3in(Arg_0+1,Arg_1):|: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:

evalSimpleSinglebbin [Arg_1-Arg_0 ]
evalSimpleSinglebb3in [Arg_1-Arg_0 ]

All Bounds

Timebounds

Overall timebound:2*Arg_1+4 {O(n)}
2: evalSimpleSinglebb3in->evalSimpleSinglebbin: Arg_1 {O(n)}
3: evalSimpleSinglebb3in->evalSimpleSinglereturnin: 1 {O(1)}
4: evalSimpleSinglebbin->evalSimpleSinglebb3in: Arg_1 {O(n)}
1: evalSimpleSingleentryin->evalSimpleSinglebb3in: 1 {O(1)}
5: evalSimpleSinglereturnin->evalSimpleSinglestop: 1 {O(1)}
0: evalSimpleSinglestart->evalSimpleSingleentryin: 1 {O(1)}

Costbounds

Overall costbound: 2*Arg_1+4 {O(n)}
2: evalSimpleSinglebb3in->evalSimpleSinglebbin: Arg_1 {O(n)}
3: evalSimpleSinglebb3in->evalSimpleSinglereturnin: 1 {O(1)}
4: evalSimpleSinglebbin->evalSimpleSinglebb3in: Arg_1 {O(n)}
1: evalSimpleSingleentryin->evalSimpleSinglebb3in: 1 {O(1)}
5: evalSimpleSinglereturnin->evalSimpleSinglestop: 1 {O(1)}
0: evalSimpleSinglestart->evalSimpleSingleentryin: 1 {O(1)}

Sizebounds

2: evalSimpleSinglebb3in->evalSimpleSinglebbin, Arg_0: Arg_1 {O(n)}
2: evalSimpleSinglebb3in->evalSimpleSinglebbin, Arg_1: Arg_1 {O(n)}
3: evalSimpleSinglebb3in->evalSimpleSinglereturnin, Arg_0: Arg_1 {O(n)}
3: evalSimpleSinglebb3in->evalSimpleSinglereturnin, Arg_1: 2*Arg_1 {O(n)}
4: evalSimpleSinglebbin->evalSimpleSinglebb3in, Arg_0: Arg_1 {O(n)}
4: evalSimpleSinglebbin->evalSimpleSinglebb3in, Arg_1: Arg_1 {O(n)}
1: evalSimpleSingleentryin->evalSimpleSinglebb3in, Arg_0: 0 {O(1)}
1: evalSimpleSingleentryin->evalSimpleSinglebb3in, Arg_1: Arg_1 {O(n)}
5: evalSimpleSinglereturnin->evalSimpleSinglestop, Arg_0: Arg_1 {O(n)}
5: evalSimpleSinglereturnin->evalSimpleSinglestop, Arg_1: 2*Arg_1 {O(n)}
0: evalSimpleSinglestart->evalSimpleSingleentryin, Arg_0: Arg_0 {O(n)}
0: evalSimpleSinglestart->evalSimpleSingleentryin, Arg_1: Arg_1 {O(n)}