Initial Problem

Start: start
Program_Vars: Arg_0, Arg_1
Temp_Vars: C, D, E
Locations: eval, start
Transitions:
0:eval(Arg_0,Arg_1) -> eval(D,Arg_1):|:0<=Arg_0 && 0<=Arg_1 && Arg_0+1<=Arg_1 && 2*C<=Arg_0+Arg_1 && Arg_0+Arg_1+1<=3*C && C+1<=D && 2*E<=Arg_0+Arg_1 && Arg_0+Arg_1+1<=3*E && D<=E+1
1:eval(Arg_0,Arg_1) -> eval(Arg_0,D):|:0<=Arg_0 && 0<=Arg_1 && Arg_0+1<=Arg_1 && 2*C<=Arg_0+Arg_1 && Arg_0+Arg_1+1<=3*C && C<=D && 2*E<=Arg_0+Arg_1 && Arg_0+Arg_1+1<=3*E && D<=E
2:start(Arg_0,Arg_1) -> eval(Arg_0,Arg_1)

Preprocessing

Problem after Preprocessing

Start: start
Program_Vars: Arg_0, Arg_1
Temp_Vars: C, D, E
Locations: eval, start
Transitions:
0:eval(Arg_0,Arg_1) -> eval(D,Arg_1):|:0<=Arg_0 && 0<=Arg_1 && Arg_0+1<=Arg_1 && 2*C<=Arg_0+Arg_1 && Arg_0+Arg_1+1<=3*C && C+1<=D && 2*E<=Arg_0+Arg_1 && Arg_0+Arg_1+1<=3*E && D<=E+1
1:eval(Arg_0,Arg_1) -> eval(Arg_0,D):|:0<=Arg_0 && 0<=Arg_1 && Arg_0+1<=Arg_1 && 2*C<=Arg_0+Arg_1 && Arg_0+Arg_1+1<=3*C && C<=D && 2*E<=Arg_0+Arg_1 && Arg_0+Arg_1+1<=3*E && D<=E
2:start(Arg_0,Arg_1) -> eval(Arg_0,Arg_1)

MPRF for transition 1:eval(Arg_0,Arg_1) -> eval(Arg_0,D):|:0<=Arg_0 && 0<=Arg_1 && Arg_0+1<=Arg_1 && 2*C<=Arg_0+Arg_1 && Arg_0+Arg_1+1<=3*C && C<=D && 2*E<=Arg_0+Arg_1 && Arg_0+Arg_1+1<=3*E && D<=E of depth 1:

new bound:

2*Arg_1+1 {O(n)}

MPRF:

eval [2*Arg_1+1 ]

Analysing control-flow refined program

Found invariant 2<=Arg_1 && 4<=Arg_0+Arg_1 && 2<=Arg_0 for location n_eval___1

Found invariant 4<=Arg_1 && 8<=Arg_0+Arg_1 && 4<=Arg_0 for location n_eval___2

Found invariant 1<=Arg_1 && 1<=Arg_0+Arg_1 && 0<=Arg_0 for location n_eval___3

Found invariant 1<=Arg_1 && 3<=Arg_0+Arg_1 && 2<=Arg_0 for location n_eval___4

MPRF for transition 29:n_eval___1(Arg_0,Arg_1) -> n_eval___3(Arg0_P,Arg1_P):|:2<=Arg_1 && 4<=Arg_0+Arg_1 && 2<=Arg_0 && 0<=Arg_0 && 2<=Arg_0+Arg_1 && 0<=Arg_0 && 1<=Arg_1 && 2+2*Arg_0<=3*Arg_1 && 1+Arg0_P<=Arg_1 && 0<=Arg0_P && 2*Arg1_P<=Arg_1+Arg0_P && 1+Arg_1+Arg0_P<=3*Arg1_P && Arg_0<=Arg0_P && Arg0_P<=Arg_0 of depth 1:

new bound:

3*Arg_0+5*Arg_1+9 {O(n)}

MPRF:

n_eval___3 [4*Arg_1-3*Arg_0-6 ]
n_eval___1 [2*Arg_1-Arg_0-3 ]
n_eval___4 [Arg_1-3 ]
n_eval___2 [Arg_1-3 ]

MPRF for transition 30:n_eval___1(Arg_0,Arg_1) -> n_eval___4(Arg0_P,Arg_1):|:2<=Arg_1 && 4<=Arg_0+Arg_1 && 2<=Arg_0 && 0<=Arg_0 && 2<=Arg_0+Arg_1 && 0<=Arg_0 && 1<=Arg_1 && 2+2*Arg_0<=3*Arg_1 && 1+Arg_0<=Arg_1 && 0<=Arg_0 && 2*Arg0_P<=2+Arg_0+Arg_1 && 4+Arg_0+Arg_1<=3*Arg0_P of depth 1:

new bound:

8*Arg_1+4 {O(n)}

MPRF:

n_eval___3 [4*Arg_1 ]
n_eval___1 [4*Arg_1-2 ]
n_eval___4 [4*Arg_1-4 ]
n_eval___2 [4*Arg_1-4 ]

MPRF for transition 31:n_eval___2(Arg_0,Arg_1) -> n_eval___1(Arg0_P,Arg1_P):|:4<=Arg_1 && 8<=Arg_0+Arg_1 && 4<=Arg_0 && 0<=Arg_0 && 2<=Arg_0+Arg_1 && 4+Arg_1<=3*Arg_0 && 2<=Arg_0 && 2*Arg_0<=1+2*Arg_1 && 0<=Arg_0 && 1<=Arg_1 && 2+2*Arg_0<=3*Arg_1 && 1+Arg0_P<=Arg_1 && 0<=Arg0_P && 2*Arg1_P<=Arg_1+Arg0_P && 1+Arg_1+Arg0_P<=3*Arg1_P && Arg_0<=Arg0_P && Arg0_P<=Arg_0 of depth 1:

new bound:

4*Arg_1+2 {O(n)}

MPRF:

n_eval___3 [2*Arg_1-1 ]
n_eval___1 [4*Arg_1-2*Arg_0-3 ]
n_eval___4 [2*Arg_1-1 ]
n_eval___2 [2*Arg_1-1 ]

MPRF for transition 33:n_eval___3(Arg_0,Arg_1) -> n_eval___3(Arg0_P,Arg1_P):|:1<=Arg_1 && 1<=Arg_0+Arg_1 && 0<=Arg_0 && 0<=Arg_0 && 0<=Arg_0 && 1<=Arg_1 && 2+2*Arg_0<=3*Arg_1 && 1+Arg0_P<=Arg_1 && 0<=Arg0_P && 2*Arg1_P<=Arg_1+Arg0_P && 1+Arg_1+Arg0_P<=3*Arg1_P && Arg_0<=Arg0_P && Arg0_P<=Arg_0 of depth 1:

new bound:

20*Arg_1 {O(n)}

MPRF:

n_eval___3 [10*Arg_1 ]
n_eval___1 [20*Arg_1-10*Arg_0-10 ]
n_eval___4 [10*Arg_1 ]
n_eval___2 [10*Arg_1-10 ]

MPRF for transition 34:n_eval___3(Arg_0,Arg_1) -> n_eval___4(Arg0_P,Arg_1):|:1<=Arg_1 && 1<=Arg_0+Arg_1 && 0<=Arg_0 && 0<=Arg_0 && 0<=Arg_0 && 1<=Arg_1 && 2+2*Arg_0<=3*Arg_1 && 1+Arg_0<=Arg_1 && 0<=Arg_0 && 2*Arg0_P<=2+Arg_0+Arg_1 && 4+Arg_0+Arg_1<=3*Arg0_P of depth 1:

new bound:

18*Arg_1+6*Arg_0+17 {O(n)}

MPRF:

n_eval___3 [12*Arg_1-6*Arg_0-7 ]
n_eval___1 [6*Arg_1-7 ]
n_eval___4 [6*Arg_1-10 ]
n_eval___2 [6*Arg_1-10 ]

MPRF for transition 35:n_eval___4(Arg_0,Arg_1) -> n_eval___1(Arg0_P,Arg1_P):|:1<=Arg_1 && 3<=Arg_0+Arg_1 && 2<=Arg_0 && 0<=Arg_0 && 2<=Arg_0+Arg_1 && 4+Arg_1<=3*Arg_0 && 2<=Arg_0 && 2*Arg_0<=1+2*Arg_1 && 1+Arg0_P<=Arg_1 && 0<=Arg0_P && 2*Arg1_P<=Arg_1+Arg0_P && 1+Arg_1+Arg0_P<=3*Arg1_P && Arg_0<=Arg0_P && Arg0_P<=Arg_0 of depth 1:

new bound:

12*Arg_1+7 {O(n)}

MPRF:

n_eval___3 [6*Arg_1-2 ]
n_eval___1 [6*Arg_1-5 ]
n_eval___4 [6*Arg_1-5 ]
n_eval___2 [6*Arg_1-5 ]

MPRF for transition 36:n_eval___4(Arg_0,Arg_1) -> n_eval___2(Arg0_P,Arg_1):|:1<=Arg_1 && 3<=Arg_0+Arg_1 && 2<=Arg_0 && 0<=Arg_0 && 2<=Arg_0+Arg_1 && 4+Arg_1<=3*Arg_0 && 2<=Arg_0 && 2*Arg_0<=1+2*Arg_1 && 1+Arg_0<=Arg_1 && 0<=Arg_0 && 2*Arg0_P<=2+Arg_0+Arg_1 && 4+Arg_0+Arg_1<=3*Arg0_P of depth 1:

new bound:

4*Arg_1+1 {O(n)}

MPRF:

n_eval___3 [2*Arg_1 ]
n_eval___1 [2*Arg_1-1 ]
n_eval___4 [2*Arg_1-1 ]
n_eval___2 [2*Arg_1-2 ]

CFR did not improve the program. Rolling back

All Bounds

Timebounds

Overall timebound:inf {Infinity}
0: eval->eval: inf {Infinity}
1: eval->eval: 2*Arg_1+1 {O(n)}
2: start->eval: 1 {O(1)}

Costbounds

Overall costbound: inf {Infinity}
0: eval->eval: inf {Infinity}
1: eval->eval: 2*Arg_1+1 {O(n)}
2: start->eval: 1 {O(1)}

Sizebounds

0: eval->eval, Arg_1: 2*Arg_1 {O(n)}
1: eval->eval, Arg_1: 2*Arg_1 {O(n)}
2: start->eval, Arg_0: Arg_0 {O(n)}
2: start->eval, Arg_1: Arg_1 {O(n)}