Initial Problem

Start: l0
Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3
Temp_Vars:
Locations: l0, l1, l2
Transitions:
0:l0(Arg_0,Arg_1,Arg_2,Arg_3) -> l1(Arg_0,Arg_1,Arg_2,Arg_3)
1:l1(Arg_0,Arg_1,Arg_2,Arg_3) -> l1(Arg_0+Arg_1,Arg_1+Arg_2,Arg_2-1,Arg_3):|:1<=Arg_0
2:l1(Arg_0,Arg_1,Arg_2,Arg_3) -> l2(Arg_0,Arg_1,Arg_2,Arg_3-1):|:Arg_0<=0
3:l2(Arg_0,Arg_1,Arg_2,Arg_3) -> l1(Arg_3,Arg_3,Arg_3,Arg_3):|:1<=Arg_3

Preprocessing

Found invariant Arg_0<=0 for location l2

Problem after Preprocessing

Start: l0
Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3
Temp_Vars:
Locations: l0, l1, l2
Transitions:
0:l0(Arg_0,Arg_1,Arg_2,Arg_3) -> l1(Arg_0,Arg_1,Arg_2,Arg_3)
1:l1(Arg_0,Arg_1,Arg_2,Arg_3) -> l1(Arg_0+Arg_1,Arg_1+Arg_2,Arg_2-1,Arg_3):|:1<=Arg_0
2:l1(Arg_0,Arg_1,Arg_2,Arg_3) -> l2(Arg_0,Arg_1,Arg_2,Arg_3-1):|:Arg_0<=0
3:l2(Arg_0,Arg_1,Arg_2,Arg_3) -> l1(Arg_3,Arg_3,Arg_3,Arg_3):|:Arg_0<=0 && 1<=Arg_3

MPRF for transition 3:l2(Arg_0,Arg_1,Arg_2,Arg_3) -> l1(Arg_3,Arg_3,Arg_3,Arg_3):|:Arg_0<=0 && 1<=Arg_3 of depth 1:

new bound:

Arg_3+1 {O(n)}

MPRF:

l2 [Arg_3 ]
l1 [Arg_3-1 ]

MPRF for transition 2:l1(Arg_0,Arg_1,Arg_2,Arg_3) -> l2(Arg_0,Arg_1,Arg_2,Arg_3-1):|:Arg_0<=0 of depth 1:

new bound:

Arg_3+2 {O(n)}

MPRF:

l1 [1 ]
l2 [0 ]

Analysing control-flow refined program

Found invariant Arg_3<=Arg_2 && Arg_3<=Arg_1 && Arg_3<=Arg_0 && 1<=Arg_3 && 2<=Arg_2+Arg_3 && Arg_2<=Arg_3 && 2<=Arg_1+Arg_3 && Arg_1<=Arg_3 && 2<=Arg_0+Arg_3 && Arg_0<=Arg_3 && Arg_2<=Arg_1 && Arg_2<=Arg_0 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 2<=Arg_0+Arg_2 && Arg_0<=Arg_2 && Arg_1<=Arg_0 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 1<=Arg_0 for location n_l1___2

Found invariant Arg_0<=0 for location n_l2___3

Found invariant Arg_3<=1+Arg_2 && 1+Arg_3<=Arg_1 && 1+Arg_3<=Arg_0 && 1<=Arg_3 && 1<=Arg_2+Arg_3 && 1+Arg_2<=Arg_3 && 3<=Arg_1+Arg_3 && 3<=Arg_0+Arg_3 && 2+Arg_2<=Arg_1 && 2+Arg_2<=Arg_0 && 0<=Arg_2 && 2<=Arg_1+Arg_2 && 2<=Arg_0+Arg_2 && 2<=Arg_1 && 4<=Arg_0+Arg_1 && 2<=Arg_0 for location n_l1___1

Found invariant Arg_0<=0 for location n_l2___4

MPRF for transition 42:n_l1___1(Arg_0,Arg_1,Arg_2,Arg_3) -> n_l1___5(Arg_0+Arg_1,Arg_1+Arg_2,Arg_2-1,Arg_3):|:Arg_3<=1+Arg_2 && 1+Arg_3<=Arg_1 && 1+Arg_3<=Arg_0 && 1<=Arg_3 && 1<=Arg_2+Arg_3 && 1+Arg_2<=Arg_3 && 3<=Arg_1+Arg_3 && 3<=Arg_0+Arg_3 && 2+Arg_2<=Arg_1 && 2+Arg_2<=Arg_0 && 0<=Arg_2 && 2<=Arg_1+Arg_2 && 2<=Arg_0+Arg_2 && 2<=Arg_1 && 4<=Arg_0+Arg_1 && 2<=Arg_0 && 1<=Arg_0 && 1<=Arg_0 && Arg_1<=Arg_0+Arg_2 && 1<=Arg_0 of depth 1:

new bound:

2*Arg_3+2 {O(n)}

MPRF:

n_l1___1 [Arg_3 ]
n_l1___5 [Arg_3-1 ]
n_l2___3 [Arg_3 ]
n_l1___2 [Arg_1 ]

MPRF for transition 43:n_l1___2(Arg_0,Arg_1,Arg_2,Arg_3) -> n_l1___1(Arg_0+Arg_1,Arg_1+Arg_2,Arg_2-1,Arg_3):|:Arg_3<=Arg_2 && Arg_3<=Arg_1 && Arg_3<=Arg_0 && 1<=Arg_3 && 2<=Arg_2+Arg_3 && Arg_2<=Arg_3 && 2<=Arg_1+Arg_3 && Arg_1<=Arg_3 && 2<=Arg_0+Arg_3 && Arg_0<=Arg_3 && Arg_2<=Arg_1 && Arg_2<=Arg_0 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 2<=Arg_0+Arg_2 && Arg_0<=Arg_2 && Arg_1<=Arg_0 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 1<=Arg_0 && 1<=Arg_0 && 1<=Arg_0 && Arg_1<=Arg_0+Arg_2 && Arg_0<=Arg_2 && Arg_2<=Arg_0 && Arg_0<=Arg_3 && Arg_3<=Arg_0 && Arg_0<=Arg_1 && Arg_1<=Arg_0 && 1<=Arg_0 && 1<=Arg_0 of depth 1:

new bound:

2*Arg_3+2 {O(n)}

MPRF:

n_l1___1 [Arg_3-1 ]
n_l1___5 [Arg_3-1 ]
n_l2___3 [Arg_3 ]
n_l1___2 [Arg_2 ]

MPRF for transition 48:n_l2___3(Arg_0,Arg_1,Arg_2,Arg_3) -> n_l1___2(Arg_3,Arg_3,Arg_3,Arg_3):|:Arg_0<=0 && Arg_0<=0 && Arg_1<=Arg_0+Arg_2 && 1<=Arg_3 && Arg_0<=0 of depth 1:

new bound:

2*Arg_3+3 {O(n)}

MPRF:

n_l1___1 [Arg_3-1 ]
n_l1___5 [Arg_3-1 ]
n_l2___3 [Arg_3 ]
n_l1___2 [Arg_0-1 ]

MPRF for transition 45:n_l1___5(Arg_0,Arg_1,Arg_2,Arg_3) -> n_l2___3(Arg_0,Arg_1,Arg_2,Arg_3-1):|:Arg_1<=Arg_0+Arg_2 && Arg_0<=0 of depth 1:

new bound:

2*Arg_3+5 {O(n)}

MPRF:

n_l1___2 [1 ]
n_l1___1 [1 ]
n_l1___5 [1 ]
n_l2___3 [0 ]

CFR did not improve the program. Rolling back

All Bounds

Timebounds

Overall timebound:inf {Infinity}
0: l0->l1: 1 {O(1)}
1: l1->l1: inf {Infinity}
2: l1->l2: Arg_3+2 {O(n)}
3: l2->l1: Arg_3+1 {O(n)}

Costbounds

Overall costbound: inf {Infinity}
0: l0->l1: 1 {O(1)}
1: l1->l1: inf {Infinity}
2: l1->l2: Arg_3+2 {O(n)}
3: l2->l1: Arg_3+1 {O(n)}

Sizebounds

0: l0->l1, Arg_0: Arg_0 {O(n)}
0: l0->l1, Arg_1: Arg_1 {O(n)}
0: l0->l1, Arg_2: Arg_2 {O(n)}
0: l0->l1, Arg_3: Arg_3 {O(n)}
1: l1->l1, Arg_3: 3*Arg_3+2 {O(n)}
2: l1->l2, Arg_3: 3*Arg_3+2 {O(n)}
3: l2->l1, Arg_0: 3*Arg_3+2 {O(n)}
3: l2->l1, Arg_1: 3*Arg_3+2 {O(n)}
3: l2->l1, Arg_2: 3*Arg_3+2 {O(n)}
3: l2->l1, Arg_3: 3*Arg_3+2 {O(n)}