Initial Problem
Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆
Temp_Vars: H
Locations: l0, l1, l2, l3, l4, l5, l6, l7
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₈: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l1(X₀, X₁, X₂, X₃, X₄, X₅+1, X₆) :|: X₅+1 ≤ X₆
t₇: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l2(X₀, X₅+1, X₄, X₃, X₄, X₅, X₆) :|: X₆ ≤ X₅
t₃: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l3(X₀, X₁, X₂, X₃, X₂+1, X₅, X₆) :|: X₂+1 ≤ X₃
t₂: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₃ ≤ X₂
t₄: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l1(X₀, X₁, X₂, X₃, X₄, X₁, X₆) :|: H+1 ≤ 0
t₅: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l1(X₀, X₁, X₂, X₃, X₄, X₁, X₆) :|: 1 ≤ H
t₆: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l4(X₀, X₁, X₂, X₃, X₄, X₀, X₆)
t₉: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l2(X₅+1, X₁, X₄, X₃, X₄, X₅, X₆) :|: X₆ ≤ X₅
t₁₀: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l4(X₀, X₁, X₂, X₃, X₄, X₅+1, X₆) :|: X₅+1 ≤ X₆
t₁₁: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₁: l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l2(0, 0, 0, X₃, X₄, X₅, X₆)
Preprocessing
Found invariant 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location l2
Found invariant X₃ ≤ X₂ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location l7
Found invariant X₃ ≤ X₂ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location l5
Found invariant 0 ≤ X₅ ∧ 1 ≤ X₄+X₅ ∧ 1 ≤ X₃+X₅ ∧ 0 ≤ X₂+X₅ ∧ 0 ≤ X₁+X₅ ∧ X₁ ≤ X₅ ∧ 0 ≤ X₀+X₅ ∧ X₄ ≤ X₃ ∧ X₄ ≤ 1+X₂ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 1 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 1 ≤ X₁+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location l1
Found invariant 0 ≤ X₅ ∧ 1 ≤ X₄+X₅ ∧ 1 ≤ X₃+X₅ ∧ 0 ≤ X₂+X₅ ∧ 0 ≤ X₁+X₅ ∧ 0 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ X₄ ≤ X₃ ∧ X₄ ≤ 1+X₂ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 1 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 1 ≤ X₁+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location l4
Found invariant X₄ ≤ X₃ ∧ X₄ ≤ 1+X₂ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 1 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 1 ≤ X₁+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location l3
Problem after Preprocessing
Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆
Temp_Vars: H
Locations: l0, l1, l2, l3, l4, l5, l6, l7
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₈: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l1(X₀, X₁, X₂, X₃, X₄, X₅+1, X₆) :|: X₅+1 ≤ X₆ ∧ 0 ≤ X₅ ∧ 1 ≤ X₄+X₅ ∧ 1 ≤ X₃+X₅ ∧ 0 ≤ X₂+X₅ ∧ 0 ≤ X₁+X₅ ∧ X₁ ≤ X₅ ∧ 0 ≤ X₀+X₅ ∧ X₄ ≤ X₃ ∧ X₄ ≤ 1+X₂ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 1 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 1 ≤ X₁+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀
t₇: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l2(X₀, X₅+1, X₄, X₃, X₄, X₅, X₆) :|: X₆ ≤ X₅ ∧ 0 ≤ X₅ ∧ 1 ≤ X₄+X₅ ∧ 1 ≤ X₃+X₅ ∧ 0 ≤ X₂+X₅ ∧ 0 ≤ X₁+X₅ ∧ X₁ ≤ X₅ ∧ 0 ≤ X₀+X₅ ∧ X₄ ≤ X₃ ∧ X₄ ≤ 1+X₂ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 1 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 1 ≤ X₁+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀
t₃: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l3(X₀, X₁, X₂, X₃, X₂+1, X₅, X₆) :|: X₂+1 ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀
t₂: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₃ ≤ X₂ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀
t₄: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l1(X₀, X₁, X₂, X₃, X₄, X₁, X₆) :|: H+1 ≤ 0 ∧ X₄ ≤ X₃ ∧ X₄ ≤ 1+X₂ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 1 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 1 ≤ X₁+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀
t₅: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l1(X₀, X₁, X₂, X₃, X₄, X₁, X₆) :|: 1 ≤ H ∧ X₄ ≤ X₃ ∧ X₄ ≤ 1+X₂ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 1 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 1 ≤ X₁+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀
t₆: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l4(X₀, X₁, X₂, X₃, X₄, X₀, X₆) :|: X₄ ≤ X₃ ∧ X₄ ≤ 1+X₂ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 1 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 1 ≤ X₁+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀
t₉: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l2(X₅+1, X₁, X₄, X₃, X₄, X₅, X₆) :|: X₆ ≤ X₅ ∧ 0 ≤ X₅ ∧ 1 ≤ X₄+X₅ ∧ 1 ≤ X₃+X₅ ∧ 0 ≤ X₂+X₅ ∧ 0 ≤ X₁+X₅ ∧ 0 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ X₄ ≤ X₃ ∧ X₄ ≤ 1+X₂ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 1 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 1 ≤ X₁+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀
t₁₀: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l4(X₀, X₁, X₂, X₃, X₄, X₅+1, X₆) :|: X₅+1 ≤ X₆ ∧ 0 ≤ X₅ ∧ 1 ≤ X₄+X₅ ∧ 1 ≤ X₃+X₅ ∧ 0 ≤ X₂+X₅ ∧ 0 ≤ X₁+X₅ ∧ 0 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ X₄ ≤ X₃ ∧ X₄ ≤ 1+X₂ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 1 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 1 ≤ X₁+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀
t₁₁: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₃ ≤ X₂ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀
t₁: l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l2(0, 0, 0, X₃, X₄, X₅, X₆)
MPRF for transition t₇: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l2(X₀, X₅+1, X₄, X₃, X₄, X₅, X₆) :|: X₆ ≤ X₅ ∧ 0 ≤ X₅ ∧ 1 ≤ X₄+X₅ ∧ 1 ≤ X₃+X₅ ∧ 0 ≤ X₂+X₅ ∧ 0 ≤ X₁+X₅ ∧ X₁ ≤ X₅ ∧ 0 ≤ X₀+X₅ ∧ X₄ ≤ X₃ ∧ X₄ ≤ 1+X₂ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 1 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 1 ≤ X₁+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ of depth 1:
new bound:
X₃ {O(n)}
MPRF:
l1 [X₃-X₂ ]
l3 [X₃-X₂ ]
l2 [X₃-X₂ ]
l4 [X₃-X₂ ]
MPRF for transition t₈: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l1(X₀, X₁, X₂, X₃, X₄, X₅+1, X₆) :|: X₅+1 ≤ X₆ ∧ 0 ≤ X₅ ∧ 1 ≤ X₄+X₅ ∧ 1 ≤ X₃+X₅ ∧ 0 ≤ X₂+X₅ ∧ 0 ≤ X₁+X₅ ∧ X₁ ≤ X₅ ∧ 0 ≤ X₀+X₅ ∧ X₄ ≤ X₃ ∧ X₄ ≤ 1+X₂ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 1 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 1 ≤ X₁+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ of depth 1:
new bound:
X₆ {O(n)}
MPRF:
l1 [X₆-X₅ ]
l3 [X₆-X₁ ]
l2 [X₆-X₁ ]
l4 [X₆-X₁ ]
MPRF for transition t₃: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l3(X₀, X₁, X₂, X₃, X₂+1, X₅, X₆) :|: X₂+1 ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ of depth 1:
new bound:
X₃ {O(n)}
MPRF:
l1 [X₃-X₄ ]
l3 [X₃-X₄ ]
l2 [X₃-X₂ ]
l4 [X₃-X₄ ]
MPRF for transition t₄: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l1(X₀, X₁, X₂, X₃, X₄, X₁, X₆) :|: H+1 ≤ 0 ∧ X₄ ≤ X₃ ∧ X₄ ≤ 1+X₂ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 1 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 1 ≤ X₁+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ of depth 1:
new bound:
X₃ {O(n)}
MPRF:
l1 [X₃-X₄ ]
l3 [X₃+1-X₄ ]
l2 [X₃-X₂ ]
l4 [X₃-X₄ ]
MPRF for transition t₅: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l1(X₀, X₁, X₂, X₃, X₄, X₁, X₆) :|: 1 ≤ H ∧ X₄ ≤ X₃ ∧ X₄ ≤ 1+X₂ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 1 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 1 ≤ X₁+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ of depth 1:
new bound:
X₃ {O(n)}
MPRF:
l1 [X₃-X₄ ]
l3 [X₃+1-X₄ ]
l2 [X₃-X₂ ]
l4 [X₃-X₄ ]
MPRF for transition t₆: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l4(X₀, X₁, X₂, X₃, X₄, X₀, X₆) :|: X₄ ≤ X₃ ∧ X₄ ≤ 1+X₂ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 1 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 1 ≤ X₁+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ of depth 1:
new bound:
X₃ {O(n)}
MPRF:
l1 [X₃-X₄ ]
l3 [X₃+1-X₄ ]
l2 [X₃-X₂ ]
l4 [X₃-X₄ ]
MPRF for transition t₉: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l2(X₅+1, X₁, X₄, X₃, X₄, X₅, X₆) :|: X₆ ≤ X₅ ∧ 0 ≤ X₅ ∧ 1 ≤ X₄+X₅ ∧ 1 ≤ X₃+X₅ ∧ 0 ≤ X₂+X₅ ∧ 0 ≤ X₁+X₅ ∧ 0 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ X₄ ≤ X₃ ∧ X₄ ≤ 1+X₂ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 1 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 1 ≤ X₁+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ of depth 1:
new bound:
X₃ {O(n)}
MPRF:
l1 [X₃-X₂ ]
l3 [X₃-X₂ ]
l2 [X₃-X₂ ]
l4 [X₃+1-X₄ ]
MPRF for transition t₁₀: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l4(X₀, X₁, X₂, X₃, X₄, X₅+1, X₆) :|: X₅+1 ≤ X₆ ∧ 0 ≤ X₅ ∧ 1 ≤ X₄+X₅ ∧ 1 ≤ X₃+X₅ ∧ 0 ≤ X₂+X₅ ∧ 0 ≤ X₁+X₅ ∧ 0 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ X₄ ≤ X₃ ∧ X₄ ≤ 1+X₂ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 1 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 1 ≤ X₁+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ of depth 1:
new bound:
X₆ {O(n)}
MPRF:
l1 [X₆-X₀ ]
l3 [X₆-X₀ ]
l2 [X₆-X₀ ]
l4 [X₆-X₅ ]
All Bounds
Timebounds
Overall timebound:2⋅X₆+6⋅X₃+4 {O(n)}
t₀: 1 {O(1)}
t₇: X₃ {O(n)}
t₈: X₆ {O(n)}
t₂: 1 {O(1)}
t₃: X₃ {O(n)}
t₄: X₃ {O(n)}
t₅: X₃ {O(n)}
t₆: X₃ {O(n)}
t₉: X₃ {O(n)}
t₁₀: X₆ {O(n)}
t₁₁: 1 {O(1)}
t₁: 1 {O(1)}
Costbounds
Overall costbound: 2⋅X₆+6⋅X₃+4 {O(n)}
t₀: 1 {O(1)}
t₇: X₃ {O(n)}
t₈: X₆ {O(n)}
t₂: 1 {O(1)}
t₃: X₃ {O(n)}
t₄: X₃ {O(n)}
t₅: X₃ {O(n)}
t₆: X₃ {O(n)}
t₉: X₃ {O(n)}
t₁₀: X₆ {O(n)}
t₁₁: 1 {O(1)}
t₁: 1 {O(1)}
Sizebounds
t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₀, X₃: X₃ {O(n)}
t₀, X₄: X₄ {O(n)}
t₀, X₅: X₅ {O(n)}
t₀, X₆: X₆ {O(n)}
t₇, X₀: X₃+X₆ {O(n)}
t₇, X₁: X₃+X₆ {O(n)}
t₇, X₂: 2⋅X₃ {O(n)}
t₇, X₃: X₃ {O(n)}
t₇, X₄: 16⋅X₃+12 {O(n)}
t₇, X₅: 3⋅X₃+3⋅X₆ {O(n)}
t₇, X₆: X₆ {O(n)}
t₈, X₀: X₃+X₆ {O(n)}
t₈, X₁: 2⋅X₃+2⋅X₆ {O(n)}
t₈, X₂: 2⋅X₃ {O(n)}
t₈, X₃: X₃ {O(n)}
t₈, X₄: 8⋅X₃+6 {O(n)}
t₈, X₅: X₃+X₆ {O(n)}
t₈, X₆: X₆ {O(n)}
t₂, X₀: 2⋅X₃+2⋅X₆ {O(n)}
t₂, X₁: 2⋅X₃+2⋅X₆ {O(n)}
t₂, X₂: 4⋅X₃ {O(n)}
t₂, X₃: 3⋅X₃ {O(n)}
t₂, X₄: 24⋅X₃+X₄+18 {O(n)}
t₂, X₅: 5⋅X₃+5⋅X₆+X₅ {O(n)}
t₂, X₆: 3⋅X₆ {O(n)}
t₃, X₀: X₃+X₆ {O(n)}
t₃, X₁: X₃+X₆ {O(n)}
t₃, X₂: 2⋅X₃ {O(n)}
t₃, X₃: X₃ {O(n)}
t₃, X₄: 4⋅X₃+3 {O(n)}
t₃, X₅: 5⋅X₃+5⋅X₆+X₅ {O(n)}
t₃, X₆: X₆ {O(n)}
t₄, X₀: X₃+X₆ {O(n)}
t₄, X₁: X₃+X₆ {O(n)}
t₄, X₂: 2⋅X₃ {O(n)}
t₄, X₃: X₃ {O(n)}
t₄, X₄: 4⋅X₃+3 {O(n)}
t₄, X₅: X₃+X₆ {O(n)}
t₄, X₆: X₆ {O(n)}
t₅, X₀: X₃+X₆ {O(n)}
t₅, X₁: X₃+X₆ {O(n)}
t₅, X₂: 2⋅X₃ {O(n)}
t₅, X₃: X₃ {O(n)}
t₅, X₄: 4⋅X₃+3 {O(n)}
t₅, X₅: X₃+X₆ {O(n)}
t₅, X₆: X₆ {O(n)}
t₆, X₀: X₃+X₆ {O(n)}
t₆, X₁: X₃+X₆ {O(n)}
t₆, X₂: 2⋅X₃ {O(n)}
t₆, X₃: X₃ {O(n)}
t₆, X₄: 4⋅X₃+3 {O(n)}
t₆, X₅: X₃+X₆ {O(n)}
t₆, X₆: X₆ {O(n)}
t₉, X₀: X₃+X₆ {O(n)}
t₉, X₁: X₃+X₆ {O(n)}
t₉, X₂: 2⋅X₃ {O(n)}
t₉, X₃: X₃ {O(n)}
t₉, X₄: 8⋅X₃+6 {O(n)}
t₉, X₅: 2⋅X₃+2⋅X₆ {O(n)}
t₉, X₆: X₆ {O(n)}
t₁₀, X₀: X₃+X₆ {O(n)}
t₁₀, X₁: X₃+X₆ {O(n)}
t₁₀, X₂: 2⋅X₃ {O(n)}
t₁₀, X₃: X₃ {O(n)}
t₁₀, X₄: 4⋅X₃+3 {O(n)}
t₁₀, X₅: X₃+X₆ {O(n)}
t₁₀, X₆: X₆ {O(n)}
t₁₁, X₀: 2⋅X₃+2⋅X₆ {O(n)}
t₁₁, X₁: 2⋅X₃+2⋅X₆ {O(n)}
t₁₁, X₂: 4⋅X₃ {O(n)}
t₁₁, X₃: 3⋅X₃ {O(n)}
t₁₁, X₄: 24⋅X₃+X₄+18 {O(n)}
t₁₁, X₅: 5⋅X₃+5⋅X₆+X₅ {O(n)}
t₁₁, X₆: 3⋅X₆ {O(n)}
t₁, X₀: 0 {O(1)}
t₁, X₁: 0 {O(1)}
t₁, X₂: 0 {O(1)}
t₁, X₃: X₃ {O(n)}
t₁, X₄: X₄ {O(n)}
t₁, X₅: X₅ {O(n)}
t₁, X₆: X₆ {O(n)}