Initial Problem

Start: f0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: f0, f6, f8
Transitions:
t₀: f0(X₀, X₁, X₂) → f8(0, 10, 0)
t₂: f8(X₀, X₁, X₂) → f6(X₀, X₁, X₂) :|: 1+X₀ ≤ 2⋅X₁ ∧ X₁ ≤ X₂
t₃: f8(X₀, X₁, X₂) → f6(X₀, X₁, X₂) :|: 2⋅X₁ ≤ X₀ ∧ X₁ ≤ X₂
t₁: f8(X₀, X₁, X₂) → f8(2+X₀, X₁, 1+X₂) :|: 1+X₂ ≤ X₁

Preprocessing

Found invariant X₂ ≤ 10 ∧ X₂ ≤ X₁ ∧ X₁+X₂ ≤ 20 ∧ X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 10 ≤ X₁+X₂ ∧ X₁ ≤ 10+X₂ ∧ 0 ≤ X₀+X₂ ∧ X₁ ≤ 10 ∧ X₁ ≤ 10+X₀ ∧ 10 ≤ X₁ ∧ 10 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location f8

Found invariant X₂ ≤ 10 ∧ X₂ ≤ X₁ ∧ X₁+X₂ ≤ 20 ∧ X₂ ≤ X₀ ∧ 10 ≤ X₂ ∧ 20 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 20 ≤ X₀+X₂ ∧ X₁ ≤ 10 ∧ X₁ ≤ X₀ ∧ 10 ≤ X₁ ∧ 20 ≤ X₀+X₁ ∧ 10 ≤ X₀ for location f6

Problem after Preprocessing

Start: f0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: f0, f6, f8
Transitions:
t₀: f0(X₀, X₁, X₂) → f8(0, 10, 0)
t₂: f8(X₀, X₁, X₂) → f6(X₀, X₁, X₂) :|: 1+X₀ ≤ 2⋅X₁ ∧ X₁ ≤ X₂ ∧ X₁+X₂ ≤ 20 ∧ X₁ ≤ 10+X₀ ∧ X₁ ≤ 10 ∧ X₁ ≤ 10+X₂ ∧ X₂ ≤ 10 ∧ 10 ≤ X₀+X₁ ∧ 10 ≤ X₁ ∧ 10 ≤ X₁+X₂ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₂ ∧ X₂ ≤ X₀ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂
t₃: f8(X₀, X₁, X₂) → f6(X₀, X₁, X₂) :|: 2⋅X₁ ≤ X₀ ∧ X₁ ≤ X₂ ∧ X₁+X₂ ≤ 20 ∧ X₁ ≤ 10+X₀ ∧ X₁ ≤ 10 ∧ X₁ ≤ 10+X₂ ∧ X₂ ≤ 10 ∧ 10 ≤ X₀+X₁ ∧ 10 ≤ X₁ ∧ 10 ≤ X₁+X₂ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₂ ∧ X₂ ≤ X₀ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂
t₁: f8(X₀, X₁, X₂) → f8(2+X₀, X₁, 1+X₂) :|: 1+X₂ ≤ X₁ ∧ X₁+X₂ ≤ 20 ∧ X₁ ≤ 10+X₀ ∧ X₁ ≤ 10 ∧ X₁ ≤ 10+X₂ ∧ X₂ ≤ 10 ∧ 10 ≤ X₀+X₁ ∧ 10 ≤ X₁ ∧ 10 ≤ X₁+X₂ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₂ ∧ X₂ ≤ X₀ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂

MPRF for transition t₁: f8(X₀, X₁, X₂) → f8(2+X₀, X₁, 1+X₂) :|: 1+X₂ ≤ X₁ ∧ X₁+X₂ ≤ 20 ∧ X₁ ≤ 10+X₀ ∧ X₁ ≤ 10 ∧ X₁ ≤ 10+X₂ ∧ X₂ ≤ 10 ∧ 10 ≤ X₀+X₁ ∧ 10 ≤ X₁ ∧ 10 ≤ X₁+X₂ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₂ ∧ X₂ ≤ X₀ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ of depth 1:

new bound:

11 {O(1)}

MPRF:

• f8: [1+X₁-X₂]

All Bounds

Timebounds

Overall timebound:14 {O(1)}
t₀: 1 {O(1)}
t₁: 11 {O(1)}
t₂: 1 {O(1)}
t₃: 1 {O(1)}

Costbounds

Overall costbound: 14 {O(1)}
t₀: 1 {O(1)}
t₁: 11 {O(1)}
t₂: 1 {O(1)}
t₃: 1 {O(1)}

Sizebounds

t₀, X₀: 0 {O(1)}
t₀, X₁: 10 {O(1)}
t₀, X₂: 0 {O(1)}
t₁, X₀: 22 {O(1)}
t₁, X₁: 10 {O(1)}
t₁, X₂: 10 {O(1)}
t₂, X₀: 19 {O(1)}
t₂, X₁: 10 {O(1)}
t₂, X₂: 10 {O(1)}
t₃, X₀: 22 {O(1)}
t₃, X₁: 10 {O(1)}
t₃, X₂: 10 {O(1)}