Initial Problem
Start: n_start
Program_Vars: Arg_0, Arg_1
Temp_Vars: A_P, B_P
Locations: n_eval___1, n_eval___2, n_eval___3, n_eval___4, n_eval___5, n_start
Transitions:
0:n_eval___1(Arg_0,Arg_1) -> n_eval___3(A_P,B_P):|:0<=Arg_0 && 2<=Arg_0+Arg_1 && 0<=Arg_0 && 1<=Arg_1 && 2+2*Arg_0<=3*Arg_1 && 1+A_P<=Arg_1 && 0<=A_P && 2*B_P<=Arg_1+A_P && 1+Arg_1+A_P<=3*B_P && Arg_0<=A_P && A_P<=Arg_0
1:n_eval___1(Arg_0,Arg_1) -> n_eval___4(A_P,Arg_1):|: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*A_P<=2+Arg_0+Arg_1 && 4+Arg_0+Arg_1<=3*A_P
2:n_eval___2(Arg_0,Arg_1) -> n_eval___1(A_P,B_P):|: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+A_P<=Arg_1 && 0<=A_P && 2*B_P<=Arg_1+A_P && 1+Arg_1+A_P<=3*B_P && Arg_0<=A_P && A_P<=Arg_0
3:n_eval___2(Arg_0,Arg_1) -> n_eval___2(A_P,Arg_1):|: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+Arg_0<=Arg_1 && 0<=Arg_0 && 2*A_P<=2+Arg_0+Arg_1 && 4+Arg_0+Arg_1<=3*A_P
4:n_eval___3(Arg_0,Arg_1) -> n_eval___3(A_P,B_P):|:0<=Arg_0 && 0<=Arg_0 && 1<=Arg_1 && 2+2*Arg_0<=3*Arg_1 && 1+A_P<=Arg_1 && 0<=A_P && 2*B_P<=Arg_1+A_P && 1+Arg_1+A_P<=3*B_P && Arg_0<=A_P && A_P<=Arg_0
5:n_eval___3(Arg_0,Arg_1) -> n_eval___4(A_P,Arg_1):|: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*A_P<=2+Arg_0+Arg_1 && 4+Arg_0+Arg_1<=3*A_P
6:n_eval___4(Arg_0,Arg_1) -> n_eval___1(A_P,B_P):|: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+A_P<=Arg_1 && 0<=A_P && 2*B_P<=Arg_1+A_P && 1+Arg_1+A_P<=3*B_P && Arg_0<=A_P && A_P<=Arg_0
7:n_eval___4(Arg_0,Arg_1) -> n_eval___2(A_P,Arg_1):|: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*A_P<=2+Arg_0+Arg_1 && 4+Arg_0+Arg_1<=3*A_P
8:n_eval___5(Arg_0,Arg_1) -> n_eval___3(A_P,B_P):|:1+A_P<=Arg_1 && 0<=A_P && 2*B_P<=Arg_1+A_P && 1+Arg_1+A_P<=3*B_P && Arg_0<=A_P && A_P<=Arg_0
9:n_eval___5(Arg_0,Arg_1) -> n_eval___4(A_P,Arg_1):|:1+Arg_0<=Arg_1 && 0<=Arg_0 && 2*A_P<=2+Arg_0+Arg_1 && 4+Arg_0+Arg_1<=3*A_P
10:n_start(Arg_0,Arg_1) -> n_eval___5(Arg_0,Arg_1)
Preprocessing
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
Problem after Preprocessing
Start: n_start
Program_Vars: Arg_0, Arg_1
Temp_Vars: A_P, B_P
Locations: n_eval___1, n_eval___2, n_eval___3, n_eval___4, n_eval___5, n_start
Transitions:
0:n_eval___1(Arg_0,Arg_1) -> n_eval___3(A_P,B_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+A_P<=Arg_1 && 0<=A_P && 2*B_P<=Arg_1+A_P && 1+Arg_1+A_P<=3*B_P && Arg_0<=A_P && A_P<=Arg_0
1:n_eval___1(Arg_0,Arg_1) -> n_eval___4(A_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*A_P<=2+Arg_0+Arg_1 && 4+Arg_0+Arg_1<=3*A_P
2:n_eval___2(Arg_0,Arg_1) -> n_eval___1(A_P,B_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+A_P<=Arg_1 && 0<=A_P && 2*B_P<=Arg_1+A_P && 1+Arg_1+A_P<=3*B_P && Arg_0<=A_P && A_P<=Arg_0
3:n_eval___2(Arg_0,Arg_1) -> n_eval___2(A_P,Arg_1):|: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+Arg_0<=Arg_1 && 0<=Arg_0 && 2*A_P<=2+Arg_0+Arg_1 && 4+Arg_0+Arg_1<=3*A_P
4:n_eval___3(Arg_0,Arg_1) -> n_eval___3(A_P,B_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+A_P<=Arg_1 && 0<=A_P && 2*B_P<=Arg_1+A_P && 1+Arg_1+A_P<=3*B_P && Arg_0<=A_P && A_P<=Arg_0
5:n_eval___3(Arg_0,Arg_1) -> n_eval___4(A_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*A_P<=2+Arg_0+Arg_1 && 4+Arg_0+Arg_1<=3*A_P
6:n_eval___4(Arg_0,Arg_1) -> n_eval___1(A_P,B_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+A_P<=Arg_1 && 0<=A_P && 2*B_P<=Arg_1+A_P && 1+Arg_1+A_P<=3*B_P && Arg_0<=A_P && A_P<=Arg_0
7:n_eval___4(Arg_0,Arg_1) -> n_eval___2(A_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*A_P<=2+Arg_0+Arg_1 && 4+Arg_0+Arg_1<=3*A_P
8:n_eval___5(Arg_0,Arg_1) -> n_eval___3(A_P,B_P):|:1+A_P<=Arg_1 && 0<=A_P && 2*B_P<=Arg_1+A_P && 1+Arg_1+A_P<=3*B_P && Arg_0<=A_P && A_P<=Arg_0
9:n_eval___5(Arg_0,Arg_1) -> n_eval___4(A_P,Arg_1):|:1+Arg_0<=Arg_1 && 0<=Arg_0 && 2*A_P<=2+Arg_0+Arg_1 && 4+Arg_0+Arg_1<=3*A_P
10:n_start(Arg_0,Arg_1) -> n_eval___5(Arg_0,Arg_1)
MPRF for transition 0:n_eval___1(Arg_0,Arg_1) -> n_eval___3(A_P,B_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+A_P<=Arg_1 && 0<=A_P && 2*B_P<=Arg_1+A_P && 1+Arg_1+A_P<=3*B_P && Arg_0<=A_P && A_P<=Arg_0 of depth 1:
new bound:
4*Arg_1+6 {O(n)}
MPRF:
n_eval___3 [2*Arg_1-3 ]
n_eval___1 [4*Arg_1-2*Arg_0-3 ]
n_eval___4 [2*Arg_1-3 ]
n_eval___2 [2*Arg_1-3 ]
MPRF for transition 1:n_eval___1(Arg_0,Arg_1) -> n_eval___4(A_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*A_P<=2+Arg_0+Arg_1 && 4+Arg_0+Arg_1<=3*A_P of depth 1:
new bound:
4*Arg_1+6 {O(n)}
MPRF:
n_eval___3 [2*Arg_1-3 ]
n_eval___1 [4*Arg_1-2*Arg_0-3 ]
n_eval___4 [2*Arg_1-3 ]
n_eval___2 [2*Arg_1-3 ]
MPRF for transition 2:n_eval___2(Arg_0,Arg_1) -> n_eval___1(A_P,B_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+A_P<=Arg_1 && 0<=A_P && 2*B_P<=Arg_1+A_P && 1+Arg_1+A_P<=3*B_P && Arg_0<=A_P && A_P<=Arg_0 of depth 1:
new bound:
4*Arg_1+14 {O(n)}
MPRF:
n_eval___3 [2*Arg_1-7 ]
n_eval___1 [4*Arg_1-2*Arg_0-9 ]
n_eval___4 [2*Arg_1-7 ]
n_eval___2 [2*Arg_1-7 ]
MPRF for transition 4:n_eval___3(Arg_0,Arg_1) -> n_eval___3(A_P,B_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+A_P<=Arg_1 && 0<=A_P && 2*B_P<=Arg_1+A_P && 1+Arg_1+A_P<=3*B_P && Arg_0<=A_P && A_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 5:n_eval___3(Arg_0,Arg_1) -> n_eval___4(A_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*A_P<=2+Arg_0+Arg_1 && 4+Arg_0+Arg_1<=3*A_P of depth 1:
new bound:
20*Arg_1+23 {O(n)}
MPRF:
n_eval___3 [10*Arg_1-9 ]
n_eval___1 [12*Arg_1-2*Arg_0-16 ]
n_eval___4 [10*Arg_1-14 ]
n_eval___2 [10*Arg_1-14 ]
MPRF for transition 6:n_eval___4(Arg_0,Arg_1) -> n_eval___1(A_P,B_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+A_P<=Arg_1 && 0<=A_P && 2*B_P<=Arg_1+A_P && 1+Arg_1+A_P<=3*B_P && Arg_0<=A_P && A_P<=Arg_0 of depth 1:
new bound:
3*Arg_0+5*Arg_1+1 {O(n)}
MPRF:
n_eval___3 [4*Arg_1-3*Arg_0-1 ]
n_eval___1 [2*Arg_1-Arg_0-1 ]
n_eval___4 [Arg_1 ]
n_eval___2 [Arg_1 ]
MPRF for transition 7:n_eval___4(Arg_0,Arg_1) -> n_eval___2(A_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*A_P<=2+Arg_0+Arg_1 && 4+Arg_0+Arg_1<=3*A_P of depth 1:
new bound:
20*Arg_1+4 {O(n)}
MPRF:
n_eval___3 [10*Arg_1+2 ]
n_eval___1 [12*Arg_1-2*Arg_0 ]
n_eval___4 [10*Arg_1+2 ]
n_eval___2 [10*Arg_1-4 ]
All Bounds
Timebounds
Overall timebound:inf {Infinity}
0: n_eval___1->n_eval___3: 4*Arg_1+6 {O(n)}
1: n_eval___1->n_eval___4: 4*Arg_1+6 {O(n)}
2: n_eval___2->n_eval___1: 4*Arg_1+14 {O(n)}
3: n_eval___2->n_eval___2: inf {Infinity}
4: n_eval___3->n_eval___3: 20*Arg_1 {O(n)}
5: n_eval___3->n_eval___4: 20*Arg_1+23 {O(n)}
6: n_eval___4->n_eval___1: 3*Arg_0+5*Arg_1+1 {O(n)}
7: n_eval___4->n_eval___2: 20*Arg_1+4 {O(n)}
8: n_eval___5->n_eval___3: 1 {O(1)}
9: n_eval___5->n_eval___4: 1 {O(1)}
10: n_start->n_eval___5: 1 {O(1)}
Costbounds
Overall costbound: inf {Infinity}
0: n_eval___1->n_eval___3: 4*Arg_1+6 {O(n)}
1: n_eval___1->n_eval___4: 4*Arg_1+6 {O(n)}
2: n_eval___2->n_eval___1: 4*Arg_1+14 {O(n)}
3: n_eval___2->n_eval___2: inf {Infinity}
4: n_eval___3->n_eval___3: 20*Arg_1 {O(n)}
5: n_eval___3->n_eval___4: 20*Arg_1+23 {O(n)}
6: n_eval___4->n_eval___1: 3*Arg_0+5*Arg_1+1 {O(n)}
7: n_eval___4->n_eval___2: 20*Arg_1+4 {O(n)}
8: n_eval___5->n_eval___3: 1 {O(1)}
9: n_eval___5->n_eval___4: 1 {O(1)}
10: n_start->n_eval___5: 1 {O(1)}
Sizebounds
0: n_eval___1->n_eval___3, Arg_1: 4*Arg_1 {O(n)}
1: n_eval___1->n_eval___4, Arg_1: 4*Arg_1 {O(n)}
2: n_eval___2->n_eval___1, Arg_1: 4*Arg_1 {O(n)}
3: n_eval___2->n_eval___2, Arg_1: 4*Arg_1 {O(n)}
4: n_eval___3->n_eval___3, Arg_1: 4*Arg_1 {O(n)}
5: n_eval___3->n_eval___4, Arg_1: 4*Arg_1 {O(n)}
6: n_eval___4->n_eval___1, Arg_1: 4*Arg_1 {O(n)}
7: n_eval___4->n_eval___2, Arg_1: 4*Arg_1 {O(n)}
8: n_eval___5->n_eval___3, Arg_0: Arg_0 {O(n)}
8: n_eval___5->n_eval___3, Arg_1: Arg_1 {O(n)}
9: n_eval___5->n_eval___4, Arg_1: Arg_1 {O(n)}
10: n_start->n_eval___5, Arg_0: Arg_0 {O(n)}
10: n_start->n_eval___5, Arg_1: Arg_1 {O(n)}