Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1
Transitions:
t₂: l0(X₀, X₁, X₂) → l1(X₀, X₁, X₂)
t₀: l1(X₀, X₁, X₂) → l1(X₀-1, X₁, X₂-1) :|: 0 ≤ X₀ ∧ X₂ ≤ (X₁)³
t₁: l1(X₀, X₁, X₂) → l1(X₀, X₁+X₂, X₂-1) :|: 0 ≤ X₀ ∧ X₂ ≤ (X₁)³

Preprocessing

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1
Transitions:
t₂: l0(X₀, X₁, X₂) → l1(X₀, X₁, X₂)
t₀: l1(X₀, X₁, X₂) → l1(X₀-1, X₁, X₂-1) :|: 0 ≤ X₀ ∧ X₂ ≤ (X₁)³
t₁: l1(X₀, X₁, X₂) → l1(X₀, X₁+X₂, X₂-1) :|: 0 ≤ X₀ ∧ X₂ ≤ (X₁)³

MPRF for transition t₀: l1(X₀, X₁, X₂) → l1(X₀-1, X₁, X₂-1) :|: 0 ≤ X₀ ∧ X₂ ≤ (X₁)³ of depth 1:

new bound:

X₀+1 {O(n)}

MPRF:

l1 [X₀+1 ]

Found invariant 1 ≤ 0 for location l1

Analysing control-flow refined program

Eliminate variables {X₁,X₂} that do not contribute to the problem

Found invariant 0 ≤ 1+X₀ for location n_l1___2

Found invariant 0 ≤ X₀ for location n_l1___1

MPRF for transition t₆₀: n_l1___1(X₀) → n_l1___2(X₀-1) :|: 0 ≤ X₀ ∧ 0 ≤ X₀ ∧ 0 ≤ 1+X₀ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀ of depth 1:

new bound:

2⋅X₀+3 {O(n)}

MPRF:

n_l1___1 [X₀+1 ]
n_l1___2 [X₀+1 ]

MPRF for transition t₆₁: n_l1___2(X₀) → n_l1___1(X₀) :|: 0 ≤ 1+X₀ ∧ 0 ≤ X₀ ∧ 0 ≤ 1+X₀ of depth 1:

new bound:

2⋅X₀+4 {O(n)}

MPRF:

n_l1___1 [X₀+1 ]
n_l1___2 [X₀+2 ]

MPRF for transition t₆₂: n_l1___2(X₀) → n_l1___2(X₀-1) :|: 0 ≤ 1+X₀ ∧ 0 ≤ X₀ ∧ 0 ≤ 1+X₀ of depth 1:

new bound:

2⋅X₀+2 {O(n)}

MPRF:

n_l1___1 [X₀ ]
n_l1___2 [X₀+1 ]

Found invariant 0 ≤ 1+X₀ for location n_l1___2

Found invariant 0 ≤ X₀ for location n_l1___1

CFR did not improve the program. Rolling back

All Bounds

Timebounds

Overall timebound:inf {Infinity}
t₂: 1 {O(1)}
t₀: X₀+1 {O(n)}
t₁: inf {Infinity}

Costbounds

Overall costbound: inf {Infinity}
t₂: 1 {O(1)}
t₀: X₀+1 {O(n)}
t₁: inf {Infinity}

Sizebounds

t₂, X₀: X₀ {O(n)}
t₂, X₁: X₁ {O(n)}
t₂, X₂: X₂ {O(n)}
t₀, X₀: 2⋅X₀+1 {O(n)}
t₁, X₀: 2⋅X₀+1 {O(n)}