Initial Problem
Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l1(X₀, X₁, 2, X₃) :|: 0 ≤ X₀ ∧ X₀ ≤ 3 ∧ X₁ ≤ 3 ∧ 0 ≤ X₁
t₁: l1(X₀, X₁, X₂, X₃) → l1(X₀, X₁+1, X₂, X₁+1) :|: 2⋅X₁+1 ≤ X₂+X₀ ∧ 2 ≤ 0
t₂: l1(X₀, X₁, X₂, X₃) → l1(X₀, X₁+1, X₂, X₁+1) :|: 2⋅X₁+1 ≤ X₂+X₀
t₃: l1(X₀, X₁, X₂, X₃) → l1(X₀, X₁-1, X₂, X₁-1) :|: 2+X₂+X₀ ≤ 2⋅X₁
t₄: l1(X₀, X₁, X₂, X₃) → l1(X₀, X₁-1, X₂, X₁-1) :|: 2+X₂+X₀ ≤ 2⋅X₁ ∧ 2 ≤ 0
t₅: l1(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, X₁) :|: 1 ≤ 0 ∧ X₂+X₀ ≤ 2⋅X₁ ∧ 2⋅X₁ ≤ X₂+X₀+1
t₆: l1(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, X₁) :|: 1 ≤ 0 ∧ X₂+X₀ ≤ 2⋅X₁ ∧ 2⋅X₁ ≤ X₂+X₀+1
Preprocessing
Cut unsatisfiable transition t₁: l1→l1
Cut unsatisfiable transition t₄: l1→l1
Cut unsatisfiable transition t₅: l1→l1
Cut unsatisfiable transition t₆: l1→l1
Eliminate variables {X₃} that do not contribute to the problem
Found invariant X₂ ≤ 2 ∧ X₂ ≤ 2+X₁ ∧ X₁+X₂ ≤ 5 ∧ X₂ ≤ 2+X₀ ∧ X₀+X₂ ≤ 5 ∧ 2 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ 1+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ X₁ ≤ 3 ∧ X₁ ≤ 3+X₀ ∧ X₀+X₁ ≤ 6 ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ 3+X₁ ∧ X₀ ≤ 3 ∧ 0 ≤ X₀ for location l1
Problem after Preprocessing
Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1
Transitions:
t₅₀: l0(X₀, X₁, X₂) → l1(X₀, X₁, 2) :|: 0 ≤ X₀ ∧ X₀ ≤ 3 ∧ X₁ ≤ 3 ∧ 0 ≤ X₁
t₅₁: l1(X₀, X₁, X₂) → l1(X₀, X₁+1, X₂) :|: 2⋅X₁+1 ≤ X₂+X₀ ∧ X₂ ≤ 2 ∧ X₂ ≤ 2+X₁ ∧ X₁+X₂ ≤ 5 ∧ X₂ ≤ 2+X₀ ∧ X₀+X₂ ≤ 5 ∧ 2 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ 1+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ X₁ ≤ 3 ∧ X₁ ≤ 3+X₀ ∧ X₀+X₁ ≤ 6 ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ 3+X₁ ∧ X₀ ≤ 3 ∧ 0 ≤ X₀
t₅₂: l1(X₀, X₁, X₂) → l1(X₀, X₁-1, X₂) :|: 2+X₂+X₀ ≤ 2⋅X₁ ∧ X₂ ≤ 2 ∧ X₂ ≤ 2+X₁ ∧ X₁+X₂ ≤ 5 ∧ X₂ ≤ 2+X₀ ∧ X₀+X₂ ≤ 5 ∧ 2 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ 1+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ X₁ ≤ 3 ∧ X₁ ≤ 3+X₀ ∧ X₀+X₁ ≤ 6 ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ 3+X₁ ∧ X₀ ≤ 3 ∧ 0 ≤ X₀
MPRF for transition t₅₁: l1(X₀, X₁, X₂) → l1(X₀, X₁+1, X₂) :|: 2⋅X₁+1 ≤ X₂+X₀ ∧ X₂ ≤ 2 ∧ X₂ ≤ 2+X₁ ∧ X₁+X₂ ≤ 5 ∧ X₂ ≤ 2+X₀ ∧ X₀+X₂ ≤ 5 ∧ 2 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ 1+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ X₁ ≤ 3 ∧ X₁ ≤ 3+X₀ ∧ X₀+X₁ ≤ 6 ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ 3+X₁ ∧ X₀ ≤ 3 ∧ 0 ≤ X₀ of depth 1:
new bound:
7 {O(1)}
MPRF:
l1 [4-X₁ ]
MPRF for transition t₅₂: l1(X₀, X₁, X₂) → l1(X₀, X₁-1, X₂) :|: 2+X₂+X₀ ≤ 2⋅X₁ ∧ X₂ ≤ 2 ∧ X₂ ≤ 2+X₁ ∧ X₁+X₂ ≤ 5 ∧ X₂ ≤ 2+X₀ ∧ X₀+X₂ ≤ 5 ∧ 2 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ 1+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ X₁ ≤ 3 ∧ X₁ ≤ 3+X₀ ∧ X₀+X₁ ≤ 6 ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ 3+X₁ ∧ X₀ ≤ 3 ∧ 0 ≤ X₀ of depth 1:
new bound:
4 {O(1)}
MPRF:
l1 [X₁+1 ]
All Bounds
Timebounds
Overall timebound:12 {O(1)}
t₅₀: 1 {O(1)}
t₅₁: 7 {O(1)}
t₅₂: 4 {O(1)}
Costbounds
Overall costbound: 12 {O(1)}
t₅₀: 1 {O(1)}
t₅₁: 7 {O(1)}
t₅₂: 4 {O(1)}
Sizebounds
t₅₀, X₀: 3 {O(1)}
t₅₀, X₁: 3 {O(1)}
t₅₀, X₂: 2 {O(1)}
t₅₁, X₀: 3 {O(1)}
t₅₁, X₁: 3 {O(1)}
t₅₁, X₂: 2 {O(1)}
t₅₂, X₀: 2 {O(1)}
t₅₂, X₁: 2 {O(1)}
t₅₂, X₂: 2 {O(1)}