Initial Problem

Start: f0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: f0, f4
Transitions:
t₂: f0(X₀, X₁, X₂) → f4(0, 0, X₂) :|: 1 ≤ X₂
t₀: f4(X₀, X₁, X₂) → f4(X₀, 1+X₁, X₂) :|: 1+X₁ ≤ X₀
t₁: f4(X₀, X₁, X₂) → f4(1+X₀, 0, X₂) :|: 2+X₀ ≤ X₂ ∧ X₀ ≤ X₁

Preprocessing

Found invariant 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location f4

Problem after Preprocessing

Start: f0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: f0, f4
Transitions:
t₂: f0(X₀, X₁, X₂) → f4(0, 0, X₂) :|: 1 ≤ X₂
t₀: f4(X₀, X₁, X₂) → f4(X₀, 1+X₁, X₂) :|: 1+X₁ ≤ X₀ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₂ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₁ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁
t₁: f4(X₀, X₁, X₂) → f4(1+X₀, 0, X₂) :|: 2+X₀ ≤ X₂ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₂ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₁ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁

MPRF for transition t₁: f4(X₀, X₁, X₂) → f4(1+X₀, 0, X₂) :|: 2+X₀ ≤ X₂ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₂ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₁ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ of depth 1:

new bound:

X₂ {O(n)}

• f4: [X₂-X₀]

MPRF for transition t₀: f4(X₀, X₁, X₂) → f4(X₀, 1+X₁, X₂) :|: 1+X₁ ≤ X₀ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₂ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₁ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ of depth 1:

new bound:

X₂⋅X₂+X₂ {O(n^2)}

• f4: [1+X₀-X₁]

Cut unsatisfiable transition [t₁₉: f4→f4_v2]

Found invariant 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location f4_v2

Found invariant 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ 0 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location f4

Found invariant 2 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2+X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location f4_v1

All Bounds

Timebounds

Overall timebound:X₂⋅X₂+2⋅X₂+1 {O(n^2)}
t₀: X₂⋅X₂+X₂ {O(n^2)}
t₁: X₂ {O(n)}
t₂: 1 {O(1)}

Costbounds

Overall costbound: X₂⋅X₂+2⋅X₂+1 {O(n^2)}
t₀: X₂⋅X₂+X₂ {O(n^2)}
t₁: X₂ {O(n)}
t₂: 1 {O(1)}

Sizebounds

t₀, X₀: X₂ {O(n)}
t₀, X₁: X₂⋅X₂+X₂ {O(n^2)}
t₀, X₂: X₂ {O(n)}
t₁, X₀: X₂ {O(n)}
t₁, X₁: 0 {O(1)}
t₁, X₂: X₂ {O(n)}
t₂, X₀: 0 {O(1)}
t₂, X₁: 0 {O(1)}
t₂, X₂: X₂ {O(n)}