Initial Problem
Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6
Transitions:
t₁₃: l0(X₀, X₁, X₂, X₃) → l4(X₀, X₂, X₂, X₀)
t₇: l2(X₀, X₁, X₂, X₃) → l2(X₀, X₁-X₃, X₂, X₃) :|: X₃+1 ≤ X₁ ∧ X₃ ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₃ ∧ X₃+X₁ ≤ X₂
t₈: l2(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃-X₁) :|: X₁+1 ≤ X₃ ∧ X₃ ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₃ ∧ X₃+X₁ ≤ X₂
t₆: l2(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2⋅X₁ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₃
t₁₀: l3(X₀, X₁, X₂, X₃) → l2(X₀, X₁-X₃, X₂, X₃) :|: X₃+1 ≤ X₁ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₃ ∧ X₃+X₁ ≤ X₀
t₁₁: l3(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃-X₁) :|: X₁+1 ≤ X₃ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₃ ∧ X₃+X₁ ≤ X₀
t₉: l3(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₁ ≤ X₂ ∧ 1 ≤ X₁ ∧ 2⋅X₁ ≤ X₀ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₃
t₀: l4(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, X₃) :|: X₀ ≤ 0 ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃
t₃: l4(X₀, X₁, X₂, X₃) → l2(X₀, X₁-X₃, X₂, X₃) :|: 1 ≤ X₀ ∧ X₀+1 ≤ X₂ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃
t₄: l4(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃-X₁) :|: X₂+1 ≤ X₀ ∧ 1 ≤ X₂ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃
t₂: l4(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: 1 ≤ X₀ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂
t₁: l4(X₀, X₁, X₂, X₃) → l6(X₀, X₁, X₂, X₃) :|: 1 ≤ X₀ ∧ X₂ ≤ 0 ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃
t₁₂: l5(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, X₃) :|: X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₃
t₅: l6(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, X₃) :|: 1 ≤ X₀ ∧ X₂ ≤ 0 ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁
Preprocessing
Found invariant 1+X₃ ≤ X₂ ∧ X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l2
Found invariant X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 1+X₂ ≤ X₃ ∧ 1+X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ X₁+X₂ ≤ 0 ∧ 1+X₂ ≤ X₀ ∧ X₁ ≤ X₂ ∧ X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀ for location l6
Found invariant X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l5
Found invariant X₃ ≤ X₀ ∧ X₁ ≤ X₂ for location l1
Found invariant X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂ for location l4
Found invariant 1+X₃ ≤ X₀ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 3 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location l3
Problem after Preprocessing
Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6
Transitions:
t₁₃: l0(X₀, X₁, X₂, X₃) → l4(X₀, X₂, X₂, X₀)
t₇: l2(X₀, X₁, X₂, X₃) → l2(X₀, X₁-X₃, X₂, X₃) :|: X₃+1 ≤ X₁ ∧ X₃ ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₃ ∧ X₃+X₁ ≤ X₂ ∧ 1+X₃ ≤ X₂ ∧ X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₈: l2(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃-X₁) :|: X₁+1 ≤ X₃ ∧ X₃ ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₃ ∧ X₃+X₁ ≤ X₂ ∧ 1+X₃ ≤ X₂ ∧ X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₆: l2(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2⋅X₁ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₃ ∧ 1+X₃ ≤ X₂ ∧ X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₁₀: l3(X₀, X₁, X₂, X₃) → l2(X₀, X₁-X₃, X₂, X₃) :|: X₃+1 ≤ X₁ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₃ ∧ X₃+X₁ ≤ X₀ ∧ 1+X₃ ≤ X₀ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 3 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀
t₁₁: l3(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃-X₁) :|: X₁+1 ≤ X₃ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₃ ∧ X₃+X₁ ≤ X₀ ∧ 1+X₃ ≤ X₀ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 3 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀
t₉: l3(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₁ ≤ X₂ ∧ 1 ≤ X₁ ∧ 2⋅X₁ ≤ X₀ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₃ ∧ 1+X₃ ≤ X₀ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 3 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀
t₀: l4(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, X₃) :|: X₀ ≤ 0 ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂
t₃: l4(X₀, X₁, X₂, X₃) → l2(X₀, X₁-X₃, X₂, X₃) :|: 1 ≤ X₀ ∧ X₀+1 ≤ X₂ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂
t₄: l4(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃-X₁) :|: X₂+1 ≤ X₀ ∧ 1 ≤ X₂ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂
t₂: l4(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: 1 ≤ X₀ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂
t₁: l4(X₀, X₁, X₂, X₃) → l6(X₀, X₁, X₂, X₃) :|: 1 ≤ X₀ ∧ X₂ ≤ 0 ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂
t₁₂: l5(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, X₃) :|: X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₃ ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₅: l6(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, X₃) :|: 1 ≤ X₀ ∧ X₂ ≤ 0 ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 1+X₂ ≤ X₃ ∧ 1+X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ X₁+X₂ ≤ 0 ∧ 1+X₂ ≤ X₀ ∧ X₁ ≤ X₂ ∧ X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀
MPRF for transition t₇: l2(X₀, X₁, X₂, X₃) → l2(X₀, X₁-X₃, X₂, X₃) :|: X₃+1 ≤ X₁ ∧ X₃ ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₃ ∧ X₃+X₁ ≤ X₂ ∧ 1+X₃ ≤ X₂ ∧ X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
2⋅X₂ {O(n)}
MPRF for transition t₈: l2(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃-X₁) :|: X₁+1 ≤ X₃ ∧ X₃ ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₃ ∧ X₃+X₁ ≤ X₂ ∧ 1+X₃ ≤ X₂ ∧ X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
2⋅X₀+X₂+1 {O(n)}
MPRF for transition t₁₀: l3(X₀, X₁, X₂, X₃) → l2(X₀, X₁-X₃, X₂, X₃) :|: X₃+1 ≤ X₁ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₃ ∧ X₃+X₁ ≤ X₀ ∧ 1+X₃ ≤ X₀ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 3 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ of depth 1:
new bound:
2⋅X₂ {O(n)}
MPRF for transition t₁₁: l3(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃-X₁) :|: X₁+1 ≤ X₃ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₃ ∧ X₃+X₁ ≤ X₀ ∧ 1+X₃ ≤ X₀ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 3 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ of depth 1:
new bound:
2⋅X₀ {O(n)}
All Bounds
Timebounds
Overall timebound:4⋅X₀+5⋅X₂+11 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₅: 1 {O(1)}
t₆: 1 {O(1)}
t₇: 2⋅X₂ {O(n)}
t₈: 2⋅X₀+X₂+1 {O(n)}
t₉: 1 {O(1)}
t₁₀: 2⋅X₂ {O(n)}
t₁₁: 2⋅X₀ {O(n)}
t₁₂: 1 {O(1)}
t₁₃: 1 {O(1)}
Costbounds
Overall costbound: 4⋅X₀+5⋅X₂+11 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₅: 1 {O(1)}
t₆: 1 {O(1)}
t₇: 2⋅X₂ {O(n)}
t₈: 2⋅X₀+X₂+1 {O(n)}
t₉: 1 {O(1)}
t₁₀: 2⋅X₂ {O(n)}
t₁₁: 2⋅X₀ {O(n)}
t₁₂: 1 {O(1)}
t₁₃: 1 {O(1)}
Sizebounds
t₀, X₀: X₀ {O(n)}
t₀, X₁: X₂ {O(n)}
t₀, X₂: X₂ {O(n)}
t₀, X₃: X₀ {O(n)}
t₁, X₀: X₀ {O(n)}
t₁, X₁: X₂ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₀ {O(n)}
t₂, X₀: X₀ {O(n)}
t₂, X₁: X₂ {O(n)}
t₂, X₂: X₂ {O(n)}
t₂, X₃: X₀ {O(n)}
t₃, X₀: X₀ {O(n)}
t₃, X₁: X₂ {O(n)}
t₃, X₂: X₂ {O(n)}
t₃, X₃: X₀ {O(n)}
t₄, X₀: X₀ {O(n)}
t₄, X₁: X₂ {O(n)}
t₄, X₂: X₂ {O(n)}
t₄, X₃: X₀ {O(n)}
t₅, X₀: X₀ {O(n)}
t₅, X₁: X₂ {O(n)}
t₅, X₂: X₂ {O(n)}
t₅, X₃: X₀ {O(n)}
t₆, X₀: 5⋅X₀ {O(n)}
t₆, X₁: 5⋅X₂ {O(n)}
t₆, X₂: 5⋅X₂ {O(n)}
t₆, X₃: 5⋅X₀ {O(n)}
t₇, X₀: 2⋅X₀ {O(n)}
t₇, X₁: 2⋅X₂ {O(n)}
t₇, X₂: 2⋅X₂ {O(n)}
t₇, X₃: 2⋅X₀ {O(n)}
t₈, X₀: 2⋅X₀ {O(n)}
t₈, X₁: 2⋅X₂ {O(n)}
t₈, X₂: 2⋅X₂ {O(n)}
t₈, X₃: 2⋅X₀ {O(n)}
t₉, X₀: 5⋅X₀ {O(n)}
t₉, X₁: 5⋅X₂ {O(n)}
t₉, X₂: 5⋅X₂ {O(n)}
t₉, X₃: 5⋅X₀ {O(n)}
t₁₀, X₀: 2⋅X₀ {O(n)}
t₁₀, X₁: 2⋅X₂ {O(n)}
t₁₀, X₂: 2⋅X₂ {O(n)}
t₁₀, X₃: 2⋅X₀ {O(n)}
t₁₁, X₀: 2⋅X₀ {O(n)}
t₁₁, X₁: 2⋅X₂ {O(n)}
t₁₁, X₂: 2⋅X₂ {O(n)}
t₁₁, X₃: 2⋅X₀ {O(n)}
t₁₂, X₀: 11⋅X₀ {O(n)}
t₁₂, X₁: 11⋅X₂ {O(n)}
t₁₂, X₂: 11⋅X₂ {O(n)}
t₁₂, X₃: 11⋅X₀ {O(n)}
t₁₃, X₀: X₀ {O(n)}
t₁₃, X₁: X₂ {O(n)}
t₁₃, X₂: X₂ {O(n)}
t₁₃, X₃: X₀ {O(n)}