Initial Problem

Start: n_start
Program_Vars: Arg_0, Arg_1
Temp_Vars:
Locations: n_eval1___1, n_eval1___4, n_eval1___6, n_eval2___2, n_eval2___3, n_eval2___5, n_start
Transitions:
0:n_eval1___1(Arg_0,Arg_1) -> n_eval2___5(Arg_0,1):|:0<=Arg_0 && 0<=Arg_0 && 0<=1+Arg_0 && 1<=Arg_1 && 1+Arg_0<=Arg_1 && 0<=Arg_0
1:n_eval1___4(Arg_0,Arg_1) -> n_eval2___2(Arg_0,1):|:Arg_0<=1 && 0<=1+Arg_0 && 1<=Arg_1 && 1+Arg_0<=Arg_1 && 0<=Arg_0
2:n_eval1___6(Arg_0,Arg_1) -> n_eval2___5(Arg_0,1):|:0<=Arg_0
3:n_eval2___2(Arg_0,Arg_1) -> n_eval1___4(Arg_0-1,Arg_1):|:Arg_0<=Arg_1 && 0<=Arg_0 && 1<=Arg_1 && Arg_1<=1 && 1<=Arg_1 && 0<=Arg_0 && 0<=Arg_0 && Arg_0<=Arg_1 && 1<=Arg_1 && 0<=Arg_0 && 1<=Arg_1 && Arg_0<=Arg_1
4:n_eval2___3(Arg_0,Arg_1) -> n_eval1___1(Arg_0-1,Arg_1):|:0<=Arg_0 && 1<=Arg_1 && 2<=Arg_1 && 2+Arg_1<=2*Arg_0 && 0<=Arg_0 && 1<=Arg_1 && Arg_0<=Arg_1
5:n_eval2___3(Arg_0,Arg_1) -> n_eval2___3(Arg_0,2*Arg_1):|:0<=Arg_0 && 1<=Arg_1 && 2<=Arg_1 && 2+Arg_1<=2*Arg_0 && 1+Arg_1<=Arg_0 && 1<=Arg_1
6:n_eval2___5(Arg_0,Arg_1) -> n_eval1___4(Arg_0-1,Arg_1):|:0<=Arg_0 && 1<=Arg_1 && Arg_1<=1 && 1<=Arg_1 && 0<=Arg_0 && 0<=Arg_0 && 1<=Arg_1 && Arg_0<=Arg_1
7:n_eval2___5(Arg_0,Arg_1) -> n_eval2___3(Arg_0,2*Arg_1):|:0<=Arg_0 && 1<=Arg_1 && Arg_1<=1 && 1<=Arg_1 && 0<=Arg_0 && 1+Arg_1<=Arg_0 && 1<=Arg_1
8:n_start(Arg_0,Arg_1) -> n_eval1___6(Arg_0,Arg_1)

Preprocessing

Found invariant Arg_1<=1 && Arg_1<=2+Arg_0 && Arg_0+Arg_1<=1 && 1<=Arg_1 && 0<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && Arg_0<=0 && 0<=1+Arg_0 for location n_eval1___4

Found invariant Arg_1<=1 && Arg_1<=1+Arg_0 && Arg_0+Arg_1<=1 && 1<=Arg_1 && 1<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && Arg_0<=0 && 0<=Arg_0 for location n_eval2___2

Found invariant 2<=Arg_1 && 3<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 1<=Arg_0 for location n_eval1___1

Found invariant Arg_1<=1 && Arg_1<=1+Arg_0 && 1<=Arg_1 && 1<=Arg_0+Arg_1 && 0<=Arg_0 for location n_eval2___5

Found invariant 2<=Arg_1 && 4<=Arg_0+Arg_1 && 2<=Arg_0 for location n_eval2___3

Problem after Preprocessing

Start: n_start
Program_Vars: Arg_0, Arg_1
Temp_Vars:
Locations: n_eval1___1, n_eval1___4, n_eval1___6, n_eval2___2, n_eval2___3, n_eval2___5, n_start
Transitions:
0:n_eval1___1(Arg_0,Arg_1) -> n_eval2___5(Arg_0,1):|:2<=Arg_1 && 3<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 1<=Arg_0 && 0<=Arg_0 && 0<=Arg_0 && 0<=1+Arg_0 && 1<=Arg_1 && 1+Arg_0<=Arg_1 && 0<=Arg_0
1:n_eval1___4(Arg_0,Arg_1) -> n_eval2___2(Arg_0,1):|:Arg_1<=1 && Arg_1<=2+Arg_0 && Arg_0+Arg_1<=1 && 1<=Arg_1 && 0<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && Arg_0<=0 && 0<=1+Arg_0 && Arg_0<=1 && 0<=1+Arg_0 && 1<=Arg_1 && 1+Arg_0<=Arg_1 && 0<=Arg_0
2:n_eval1___6(Arg_0,Arg_1) -> n_eval2___5(Arg_0,1):|:0<=Arg_0
3:n_eval2___2(Arg_0,Arg_1) -> n_eval1___4(Arg_0-1,Arg_1):|:Arg_1<=1 && Arg_1<=1+Arg_0 && Arg_0+Arg_1<=1 && 1<=Arg_1 && 1<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && Arg_0<=0 && 0<=Arg_0 && Arg_0<=Arg_1 && 0<=Arg_0 && 1<=Arg_1 && Arg_1<=1 && 1<=Arg_1 && 0<=Arg_0 && 0<=Arg_0 && Arg_0<=Arg_1 && 1<=Arg_1 && 0<=Arg_0 && 1<=Arg_1 && Arg_0<=Arg_1
4:n_eval2___3(Arg_0,Arg_1) -> n_eval1___1(Arg_0-1,Arg_1):|:2<=Arg_1 && 4<=Arg_0+Arg_1 && 2<=Arg_0 && 0<=Arg_0 && 1<=Arg_1 && 2<=Arg_1 && 2+Arg_1<=2*Arg_0 && 0<=Arg_0 && 1<=Arg_1 && Arg_0<=Arg_1
5:n_eval2___3(Arg_0,Arg_1) -> n_eval2___3(Arg_0,2*Arg_1):|:2<=Arg_1 && 4<=Arg_0+Arg_1 && 2<=Arg_0 && 0<=Arg_0 && 1<=Arg_1 && 2<=Arg_1 && 2+Arg_1<=2*Arg_0 && 1+Arg_1<=Arg_0 && 1<=Arg_1
6:n_eval2___5(Arg_0,Arg_1) -> n_eval1___4(Arg_0-1,Arg_1):|:Arg_1<=1 && Arg_1<=1+Arg_0 && 1<=Arg_1 && 1<=Arg_0+Arg_1 && 0<=Arg_0 && 0<=Arg_0 && 1<=Arg_1 && Arg_1<=1 && 1<=Arg_1 && 0<=Arg_0 && 0<=Arg_0 && 1<=Arg_1 && Arg_0<=Arg_1
7:n_eval2___5(Arg_0,Arg_1) -> n_eval2___3(Arg_0,2*Arg_1):|:Arg_1<=1 && Arg_1<=1+Arg_0 && 1<=Arg_1 && 1<=Arg_0+Arg_1 && 0<=Arg_0 && 0<=Arg_0 && 1<=Arg_1 && Arg_1<=1 && 1<=Arg_1 && 0<=Arg_0 && 1+Arg_1<=Arg_0 && 1<=Arg_1
8:n_start(Arg_0,Arg_1) -> n_eval1___6(Arg_0,Arg_1)

MPRF for transition 0:n_eval1___1(Arg_0,Arg_1) -> n_eval2___5(Arg_0,1):|:2<=Arg_1 && 3<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 1<=Arg_0 && 0<=Arg_0 && 0<=Arg_0 && 0<=1+Arg_0 && 1<=Arg_1 && 1+Arg_0<=Arg_1 && 0<=Arg_0 of depth 1:

new bound:

Arg_0 {O(n)}

MPRF:

n_eval1___1 [Arg_0+1 ]
n_eval2___5 [Arg_0 ]
n_eval2___3 [Arg_0 ]

MPRF for transition 4:n_eval2___3(Arg_0,Arg_1) -> n_eval1___1(Arg_0-1,Arg_1):|:2<=Arg_1 && 4<=Arg_0+Arg_1 && 2<=Arg_0 && 0<=Arg_0 && 1<=Arg_1 && 2<=Arg_1 && 2+Arg_1<=2*Arg_0 && 0<=Arg_0 && 1<=Arg_1 && Arg_0<=Arg_1 of depth 1:

new bound:

Arg_0+1 {O(n)}

MPRF:

n_eval1___1 [Arg_0+1 ]
n_eval2___5 [Arg_0+Arg_1 ]
n_eval2___3 [Arg_0+1 ]

MPRF for transition 7:n_eval2___5(Arg_0,Arg_1) -> n_eval2___3(Arg_0,2*Arg_1):|:Arg_1<=1 && Arg_1<=1+Arg_0 && 1<=Arg_1 && 1<=Arg_0+Arg_1 && 0<=Arg_0 && 0<=Arg_0 && 1<=Arg_1 && Arg_1<=1 && 1<=Arg_1 && 0<=Arg_0 && 1+Arg_1<=Arg_0 && 1<=Arg_1 of depth 1:

new bound:

2*Arg_0+1 {O(n)}

MPRF:

n_eval1___1 [2*Arg_0+1 ]
n_eval2___5 [2*Arg_0+1 ]
n_eval2___3 [2*Arg_0 ]

MPRF for transition 5:n_eval2___3(Arg_0,Arg_1) -> n_eval2___3(Arg_0,2*Arg_1):|:2<=Arg_1 && 4<=Arg_0+Arg_1 && 2<=Arg_0 && 0<=Arg_0 && 1<=Arg_1 && 2<=Arg_1 && 2+Arg_1<=2*Arg_0 && 1+Arg_1<=Arg_0 && 1<=Arg_1 of depth 1:

new bound:

8*Arg_0*Arg_0+8*Arg_0+2 {O(n^2)}

MPRF:

n_eval2___5 [2*Arg_0 ]
n_eval1___1 [2*Arg_0 ]
n_eval2___3 [4*Arg_0-Arg_1 ]

knowledge_propagation leads to new time bound 1 {O(1)} for transition 1:n_eval1___4(Arg_0,Arg_1) -> n_eval2___2(Arg_0,1):|:Arg_1<=1 && Arg_1<=2+Arg_0 && Arg_0+Arg_1<=1 && 1<=Arg_1 && 0<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && Arg_0<=0 && 0<=1+Arg_0 && Arg_0<=1 && 0<=1+Arg_0 && 1<=Arg_1 && 1+Arg_0<=Arg_1 && 0<=Arg_0

knowledge_propagation leads to new time bound 1 {O(1)} for transition 3:n_eval2___2(Arg_0,Arg_1) -> n_eval1___4(Arg_0-1,Arg_1):|:Arg_1<=1 && Arg_1<=1+Arg_0 && Arg_0+Arg_1<=1 && 1<=Arg_1 && 1<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && Arg_0<=0 && 0<=Arg_0 && Arg_0<=Arg_1 && 0<=Arg_0 && 1<=Arg_1 && Arg_1<=1 && 1<=Arg_1 && 0<=Arg_0 && 0<=Arg_0 && Arg_0<=Arg_1 && 1<=Arg_1 && 0<=Arg_0 && 1<=Arg_1 && Arg_0<=Arg_1

All Bounds

Timebounds

Overall timebound:8*Arg_0*Arg_0+12*Arg_0+9 {O(n^2)}
0: n_eval1___1->n_eval2___5: Arg_0 {O(n)}
1: n_eval1___4->n_eval2___2: 1 {O(1)}
2: n_eval1___6->n_eval2___5: 1 {O(1)}
3: n_eval2___2->n_eval1___4: 1 {O(1)}
4: n_eval2___3->n_eval1___1: Arg_0+1 {O(n)}
5: n_eval2___3->n_eval2___3: 8*Arg_0*Arg_0+8*Arg_0+2 {O(n^2)}
6: n_eval2___5->n_eval1___4: 1 {O(1)}
7: n_eval2___5->n_eval2___3: 2*Arg_0+1 {O(n)}
8: n_start->n_eval1___6: 1 {O(1)}

Costbounds

Overall costbound: 8*Arg_0*Arg_0+12*Arg_0+9 {O(n^2)}
0: n_eval1___1->n_eval2___5: Arg_0 {O(n)}
1: n_eval1___4->n_eval2___2: 1 {O(1)}
2: n_eval1___6->n_eval2___5: 1 {O(1)}
3: n_eval2___2->n_eval1___4: 1 {O(1)}
4: n_eval2___3->n_eval1___1: Arg_0+1 {O(n)}
5: n_eval2___3->n_eval2___3: 8*Arg_0*Arg_0+8*Arg_0+2 {O(n^2)}
6: n_eval2___5->n_eval1___4: 1 {O(1)}
7: n_eval2___5->n_eval2___3: 2*Arg_0+1 {O(n)}
8: n_start->n_eval1___6: 1 {O(1)}

Sizebounds

0: n_eval1___1->n_eval2___5, Arg_0: Arg_0 {O(n)}
0: n_eval1___1->n_eval2___5, Arg_1: 1 {O(1)}
1: n_eval1___4->n_eval2___2, Arg_0: 0 {O(1)}
1: n_eval1___4->n_eval2___2, Arg_1: 1 {O(1)}
2: n_eval1___6->n_eval2___5, Arg_0: Arg_0 {O(n)}
2: n_eval1___6->n_eval2___5, Arg_1: 1 {O(1)}
3: n_eval2___2->n_eval1___4, Arg_0: 1 {O(1)}
3: n_eval2___2->n_eval1___4, Arg_1: 1 {O(1)}
4: n_eval2___3->n_eval1___1, Arg_0: Arg_0 {O(n)}
4: n_eval2___3->n_eval1___1, Arg_1: 2*2^(8*Arg_0*Arg_0+8*Arg_0+2)+2 {O(EXP)}
5: n_eval2___3->n_eval2___3, Arg_0: Arg_0 {O(n)}
5: n_eval2___3->n_eval2___3, Arg_1: 2*2^(8*Arg_0*Arg_0+8*Arg_0+2) {O(EXP)}
6: n_eval2___5->n_eval1___4, Arg_0: 1 {O(1)}
6: n_eval2___5->n_eval1___4, Arg_1: 1 {O(1)}
7: n_eval2___5->n_eval2___3, Arg_0: Arg_0 {O(n)}
7: n_eval2___5->n_eval2___3, Arg_1: 2 {O(1)}
8: n_start->n_eval1___6, Arg_0: Arg_0 {O(n)}
8: n_start->n_eval1___6, Arg_1: Arg_1 {O(n)}