Initial Problem

Start: evalEx2start
Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3
Temp_Vars: E
Locations: evalEx2bb1in, evalEx2bb2in, evalEx2bb3in, evalEx2bbin, evalEx2entryin, evalEx2returnin, evalEx2start, evalEx2stop
Transitions:
9:evalEx2bb1in(Arg_0,Arg_1,Arg_2,Arg_3) -> evalEx2bb2in(Arg_0,Arg_1,Arg_2+1,Arg_3-1)
6:evalEx2bb2in(Arg_0,Arg_1,Arg_2,Arg_3) -> evalEx2bb1in(Arg_0,Arg_1,Arg_2,Arg_3):|:E+1<=0
7:evalEx2bb2in(Arg_0,Arg_1,Arg_2,Arg_3) -> evalEx2bb1in(Arg_0,Arg_1,Arg_2,Arg_3):|:1<=E
8:evalEx2bb2in(Arg_0,Arg_1,Arg_2,Arg_3) -> evalEx2bb3in(Arg_2,Arg_3,Arg_2,Arg_3)
2:evalEx2bb3in(Arg_0,Arg_1,Arg_2,Arg_3) -> evalEx2bbin(Arg_0,Arg_1,Arg_2,Arg_3):|:1<=Arg_1 && 1<=Arg_0
3:evalEx2bb3in(Arg_0,Arg_1,Arg_2,Arg_3) -> evalEx2returnin(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_1<=0
4:evalEx2bb3in(Arg_0,Arg_1,Arg_2,Arg_3) -> evalEx2returnin(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_0<=0
5:evalEx2bbin(Arg_0,Arg_1,Arg_2,Arg_3) -> evalEx2bb2in(Arg_0,Arg_1,Arg_0-1,Arg_1-1)
1:evalEx2entryin(Arg_0,Arg_1,Arg_2,Arg_3) -> evalEx2bb3in(Arg_1,Arg_0,Arg_2,Arg_3)
10:evalEx2returnin(Arg_0,Arg_1,Arg_2,Arg_3) -> evalEx2stop(Arg_0,Arg_1,Arg_2,Arg_3)
0:evalEx2start(Arg_0,Arg_1,Arg_2,Arg_3) -> evalEx2entryin(Arg_0,Arg_1,Arg_2,Arg_3)

Preprocessing

Found invariant 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 for location evalEx2bbin

Found invariant 1+Arg_3<=Arg_1 && 0<=Arg_2+Arg_3 && 0<=Arg_2 && 1<=Arg_1+Arg_2 && 1<=Arg_0+Arg_2 && Arg_0<=1+Arg_2 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 for location evalEx2bb2in

Found invariant 1+Arg_3<=Arg_1 && 0<=Arg_2+Arg_3 && 0<=Arg_2 && 1<=Arg_1+Arg_2 && 1<=Arg_0+Arg_2 && Arg_0<=1+Arg_2 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 for location evalEx2bb1in

Problem after Preprocessing

Start: evalEx2start
Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3
Temp_Vars: E
Locations: evalEx2bb1in, evalEx2bb2in, evalEx2bb3in, evalEx2bbin, evalEx2entryin, evalEx2returnin, evalEx2start, evalEx2stop
Transitions:
9:evalEx2bb1in(Arg_0,Arg_1,Arg_2,Arg_3) -> evalEx2bb2in(Arg_0,Arg_1,Arg_2+1,Arg_3-1):|:1+Arg_3<=Arg_1 && 0<=Arg_2+Arg_3 && 0<=Arg_2 && 1<=Arg_1+Arg_2 && 1<=Arg_0+Arg_2 && Arg_0<=1+Arg_2 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0
6:evalEx2bb2in(Arg_0,Arg_1,Arg_2,Arg_3) -> evalEx2bb1in(Arg_0,Arg_1,Arg_2,Arg_3):|:1+Arg_3<=Arg_1 && 0<=Arg_2+Arg_3 && 0<=Arg_2 && 1<=Arg_1+Arg_2 && 1<=Arg_0+Arg_2 && Arg_0<=1+Arg_2 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 && E+1<=0
7:evalEx2bb2in(Arg_0,Arg_1,Arg_2,Arg_3) -> evalEx2bb1in(Arg_0,Arg_1,Arg_2,Arg_3):|:1+Arg_3<=Arg_1 && 0<=Arg_2+Arg_3 && 0<=Arg_2 && 1<=Arg_1+Arg_2 && 1<=Arg_0+Arg_2 && Arg_0<=1+Arg_2 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 && 1<=E
8:evalEx2bb2in(Arg_0,Arg_1,Arg_2,Arg_3) -> evalEx2bb3in(Arg_2,Arg_3,Arg_2,Arg_3):|:1+Arg_3<=Arg_1 && 0<=Arg_2+Arg_3 && 0<=Arg_2 && 1<=Arg_1+Arg_2 && 1<=Arg_0+Arg_2 && Arg_0<=1+Arg_2 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0
2:evalEx2bb3in(Arg_0,Arg_1,Arg_2,Arg_3) -> evalEx2bbin(Arg_0,Arg_1,Arg_2,Arg_3):|:1<=Arg_1 && 1<=Arg_0
3:evalEx2bb3in(Arg_0,Arg_1,Arg_2,Arg_3) -> evalEx2returnin(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_1<=0
4:evalEx2bb3in(Arg_0,Arg_1,Arg_2,Arg_3) -> evalEx2returnin(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_0<=0
5:evalEx2bbin(Arg_0,Arg_1,Arg_2,Arg_3) -> evalEx2bb2in(Arg_0,Arg_1,Arg_0-1,Arg_1-1):|:1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0
1:evalEx2entryin(Arg_0,Arg_1,Arg_2,Arg_3) -> evalEx2bb3in(Arg_1,Arg_0,Arg_2,Arg_3)
10:evalEx2returnin(Arg_0,Arg_1,Arg_2,Arg_3) -> evalEx2stop(Arg_0,Arg_1,Arg_2,Arg_3)
0:evalEx2start(Arg_0,Arg_1,Arg_2,Arg_3) -> evalEx2entryin(Arg_0,Arg_1,Arg_2,Arg_3)

MPRF for transition 8:evalEx2bb2in(Arg_0,Arg_1,Arg_2,Arg_3) -> evalEx2bb3in(Arg_2,Arg_3,Arg_2,Arg_3):|:1+Arg_3<=Arg_1 && 0<=Arg_2+Arg_3 && 0<=Arg_2 && 1<=Arg_1+Arg_2 && 1<=Arg_0+Arg_2 && Arg_0<=1+Arg_2 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 of depth 1:

new bound:

Arg_0 {O(n)}

MPRF:

evalEx2bb1in [Arg_1 ]
evalEx2bb3in [Arg_1 ]
evalEx2bbin [Arg_1 ]
evalEx2bb2in [Arg_1 ]

MPRF for transition 2:evalEx2bb3in(Arg_0,Arg_1,Arg_2,Arg_3) -> evalEx2bbin(Arg_0,Arg_1,Arg_2,Arg_3):|:1<=Arg_1 && 1<=Arg_0 of depth 1:

new bound:

Arg_0 {O(n)}

MPRF:

evalEx2bb1in [Arg_1-1 ]
evalEx2bb3in [Arg_1 ]
evalEx2bbin [Arg_1-1 ]
evalEx2bb2in [Arg_1-1 ]

MPRF for transition 5:evalEx2bbin(Arg_0,Arg_1,Arg_2,Arg_3) -> evalEx2bb2in(Arg_0,Arg_1,Arg_0-1,Arg_1-1):|:1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 of depth 1:

new bound:

Arg_0 {O(n)}

MPRF:

evalEx2bb1in [Arg_1-1 ]
evalEx2bb3in [Arg_1 ]
evalEx2bbin [Arg_1 ]
evalEx2bb2in [Arg_1-1 ]

Analysing control-flow refined program

Found invariant 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 for location evalEx2bbin

Found invariant 2+Arg_3<=Arg_1 && 0<=Arg_2+Arg_3 && 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 && 1<=Arg_0 for location n_evalEx2bb1in___1

Found invariant 1+Arg_3<=Arg_1 && 0<=Arg_3 && 0<=Arg_2+Arg_3 && 1<=Arg_1+Arg_3 && Arg_1<=1+Arg_3 && 1<=Arg_0+Arg_3 && 1+Arg_2<=Arg_0 && 0<=Arg_2 && 1<=Arg_1+Arg_2 && 1<=Arg_0+Arg_2 && Arg_0<=1+Arg_2 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 for location evalEx2bb2in

Found invariant 1+Arg_3<=Arg_1 && 0<=Arg_3 && 0<=Arg_2+Arg_3 && 1<=Arg_1+Arg_3 && Arg_1<=1+Arg_3 && 1<=Arg_0+Arg_3 && 1+Arg_2<=Arg_0 && 0<=Arg_2 && 1<=Arg_1+Arg_2 && 1<=Arg_0+Arg_2 && Arg_0<=1+Arg_2 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 for location n_evalEx2bb1in___3

Found invariant 2+Arg_3<=Arg_1 && 0<=Arg_2+Arg_3 && 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 && 1<=Arg_0 for location n_evalEx2bb2in___2

knowledge_propagation leads to new time bound Arg_0 {O(n)} for transition 81:evalEx2bb2in(Arg_0,Arg_1,Arg_2,Arg_3) -> n_evalEx2bb1in___3(Arg_0,Arg_1,Arg_2,Arg_3):|:1+Arg_3<=Arg_1 && 0<=Arg_3 && 0<=Arg_2+Arg_3 && 1<=Arg_1+Arg_3 && Arg_1<=1+Arg_3 && 1<=Arg_0+Arg_3 && 1+Arg_2<=Arg_0 && 0<=Arg_2 && 1<=Arg_1+Arg_2 && 1<=Arg_0+Arg_2 && Arg_0<=1+Arg_2 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 && 1+Arg_3<=Arg_1 && 1<=Arg_0 && 0<=Arg_2+Arg_3 && Arg_0<=1+Arg_2 && 1<=Arg_1 && 1<=Arg_1 && Arg_0<=1+Arg_2 && 0<=Arg_2+Arg_3 && 1<=Arg_0 && 1+Arg_3<=Arg_1 && 1<=Arg_1 && Arg_0<=1+Arg_2 && 0<=Arg_2+Arg_3 && 1<=Arg_0 && 1+Arg_3<=Arg_1 && Arg_1<=1+Arg_3 && 1+Arg_3<=Arg_1 && Arg_0<=1+Arg_2 && 1+Arg_2<=Arg_0 && 1<=Arg_0 && 1<=Arg_1 && 1+Arg_3<=Arg_1 && 1<=Arg_0 && 0<=Arg_2+Arg_3 && Arg_0<=1+Arg_2 && 1<=Arg_1

knowledge_propagation leads to new time bound Arg_0 {O(n)} for transition 82:evalEx2bb2in(Arg_0,Arg_1,Arg_2,Arg_3) -> n_evalEx2bb1in___3(Arg_0,Arg_1,Arg_2,Arg_3):|:1+Arg_3<=Arg_1 && 0<=Arg_3 && 0<=Arg_2+Arg_3 && 1<=Arg_1+Arg_3 && Arg_1<=1+Arg_3 && 1<=Arg_0+Arg_3 && 1+Arg_2<=Arg_0 && 0<=Arg_2 && 1<=Arg_1+Arg_2 && 1<=Arg_0+Arg_2 && Arg_0<=1+Arg_2 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 && 1+Arg_3<=Arg_1 && 1<=Arg_0 && 0<=Arg_2+Arg_3 && Arg_0<=1+Arg_2 && 1<=Arg_1 && 1<=Arg_1 && Arg_0<=1+Arg_2 && 0<=Arg_2+Arg_3 && 1<=Arg_0 && 1+Arg_3<=Arg_1 && 1<=Arg_1 && Arg_0<=1+Arg_2 && 0<=Arg_2+Arg_3 && 1<=Arg_0 && 1+Arg_3<=Arg_1 && Arg_1<=1+Arg_3 && 1+Arg_3<=Arg_1 && Arg_0<=1+Arg_2 && 1+Arg_2<=Arg_0 && 1<=Arg_0 && 1<=Arg_1 && 1+Arg_3<=Arg_1 && 1<=Arg_0 && 0<=Arg_2+Arg_3 && Arg_0<=1+Arg_2 && 1<=Arg_1

knowledge_propagation leads to new time bound 2*Arg_0 {O(n)} for transition 78:n_evalEx2bb1in___3(Arg_0,Arg_1,Arg_2,Arg_3) -> n_evalEx2bb2in___2(Arg_0,Arg_1,Arg_2+1,Arg_3-1):|:1+Arg_3<=Arg_1 && 0<=Arg_3 && 0<=Arg_2+Arg_3 && 1<=Arg_1+Arg_3 && Arg_1<=1+Arg_3 && 1<=Arg_0+Arg_3 && 1+Arg_2<=Arg_0 && 0<=Arg_2 && 1<=Arg_1+Arg_2 && 1<=Arg_0+Arg_2 && Arg_0<=1+Arg_2 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 && 1<=Arg_1 && 1<=Arg_0 && Arg_1<=Arg_3+1 && 1+Arg_3<=Arg_1 && Arg_0<=Arg_2+1 && 1+Arg_2<=Arg_0 && 1<=Arg_1 && 1+Arg_3<=Arg_1 && 0<=Arg_2+Arg_3 && 1<=Arg_0 && Arg_0<=1+Arg_2

MPRF for transition 89:n_evalEx2bb2in___2(Arg_0,Arg_1,Arg_2,Arg_3) -> evalEx2bb3in(Arg_2,Arg_3,Arg_2,Arg_3):|:2+Arg_3<=Arg_1 && 0<=Arg_2+Arg_3 && 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 && 1<=Arg_0 && 1+Arg_3<=Arg_1 && 0<=Arg_2+Arg_3 && 0<=Arg_2 && 1<=Arg_1+Arg_2 && 1<=Arg_0+Arg_2 && Arg_0<=1+Arg_2 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 of depth 1:

new bound:

Arg_0 {O(n)}

MPRF:

evalEx2bbin [Arg_1 ]
evalEx2bb2in [Arg_0+Arg_3-Arg_2 ]
n_evalEx2bb1in___3 [Arg_1 ]
n_evalEx2bb1in___1 [Arg_1 ]
n_evalEx2bb2in___2 [Arg_1 ]
evalEx2bb3in [Arg_1 ]

CFR did not improve the program. Rolling back

All Bounds

Timebounds

Overall timebound:inf {Infinity}
9: evalEx2bb1in->evalEx2bb2in: inf {Infinity}
6: evalEx2bb2in->evalEx2bb1in: inf {Infinity}
7: evalEx2bb2in->evalEx2bb1in: inf {Infinity}
8: evalEx2bb2in->evalEx2bb3in: Arg_0 {O(n)}
2: evalEx2bb3in->evalEx2bbin: Arg_0 {O(n)}
3: evalEx2bb3in->evalEx2returnin: 1 {O(1)}
4: evalEx2bb3in->evalEx2returnin: 1 {O(1)}
5: evalEx2bbin->evalEx2bb2in: Arg_0 {O(n)}
1: evalEx2entryin->evalEx2bb3in: 1 {O(1)}
10: evalEx2returnin->evalEx2stop: 1 {O(1)}
0: evalEx2start->evalEx2entryin: 1 {O(1)}

Costbounds

Overall costbound: inf {Infinity}
9: evalEx2bb1in->evalEx2bb2in: inf {Infinity}
6: evalEx2bb2in->evalEx2bb1in: inf {Infinity}
7: evalEx2bb2in->evalEx2bb1in: inf {Infinity}
8: evalEx2bb2in->evalEx2bb3in: Arg_0 {O(n)}
2: evalEx2bb3in->evalEx2bbin: Arg_0 {O(n)}
3: evalEx2bb3in->evalEx2returnin: 1 {O(1)}
4: evalEx2bb3in->evalEx2returnin: 1 {O(1)}
5: evalEx2bbin->evalEx2bb2in: Arg_0 {O(n)}
1: evalEx2entryin->evalEx2bb3in: 1 {O(1)}
10: evalEx2returnin->evalEx2stop: 1 {O(1)}
0: evalEx2start->evalEx2entryin: 1 {O(1)}

Sizebounds

1: evalEx2entryin->evalEx2bb3in, Arg_0: Arg_1 {O(n)}
1: evalEx2entryin->evalEx2bb3in, Arg_1: Arg_0 {O(n)}
1: evalEx2entryin->evalEx2bb3in, Arg_2: Arg_2 {O(n)}
1: evalEx2entryin->evalEx2bb3in, Arg_3: Arg_3 {O(n)}
0: evalEx2start->evalEx2entryin, Arg_0: Arg_0 {O(n)}
0: evalEx2start->evalEx2entryin, Arg_1: Arg_1 {O(n)}
0: evalEx2start->evalEx2entryin, Arg_2: Arg_2 {O(n)}
0: evalEx2start->evalEx2entryin, Arg_3: Arg_3 {O(n)}