Initial Problem
Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅
Temp_Vars:
Locations: l0, l1, l2, l3, l4
Transitions:
t₁₁: l0(X₀, X₁, X₂, X₃, X₄, X₅) → l4(X₁, X₁, X₃, X₃, X₅, X₅)
t₉: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, X₁, X₂, X₃, 2+X₄, X₅) :|: X₁+1 ≤ 0 ∧ X₄ ≤ 39 ∧ 2 ≤ X₄ ∧ X₄ ≤ 41 ∧ X₂ ≤ 100 ∧ 100 ≤ X₂ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀
t₁₀: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, X₁, X₂, X₃, 2+X₄, X₅) :|: 1 ≤ X₁ ∧ X₄ ≤ 39 ∧ 2 ≤ X₄ ∧ X₄ ≤ 41 ∧ X₂ ≤ 100 ∧ 100 ≤ X₂ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀
t₈: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, X₁, X₂, X₃, 1+X₄, X₅) :|: X₄ ≤ 39 ∧ 2 ≤ X₄ ∧ X₄ ≤ 41 ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ X₂ ≤ 100 ∧ 100 ≤ X₂ ∧ X₁ ≤ 0 ∧ 0 ≤ X₁
t₇: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁, X₂, X₃, X₄, X₅) :|: 40 ≤ X₄ ∧ 2 ≤ X₄ ∧ X₄ ≤ 41 ∧ X₂ ≤ 100 ∧ 100 ≤ X₂ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀
t₅: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, X₁, X₂, X₃, 2+X₄, X₅) :|: 1 ≤ 0 ∧ X₄ ≤ 39 ∧ 1 ≤ X₄ ∧ X₄ ≤ 40 ∧ X₂ ≤ 100 ∧ 100 ≤ X₂ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ X₁ ≤ 0 ∧ 0 ≤ X₁
t₆: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, X₁, X₂, X₃, 2+X₄, X₅) :|: 1 ≤ 0 ∧ X₄ ≤ 39 ∧ 1 ≤ X₄ ∧ X₄ ≤ 40 ∧ X₂ ≤ 100 ∧ 100 ≤ X₂ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ X₁ ≤ 0 ∧ 0 ≤ X₁
t₄: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, X₁, X₂, X₃, 1+X₄, X₅) :|: X₄ ≤ 39 ∧ 1 ≤ X₄ ∧ X₄ ≤ 40 ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ X₂ ≤ 100 ∧ 100 ≤ X₂ ∧ X₁ ≤ 0 ∧ 0 ≤ X₁
t₃: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₄ ≤ 40 ∧ 40 ≤ X₄ ∧ X₂ ≤ 100 ∧ 100 ≤ X₂ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ X₁ ≤ 0 ∧ 0 ≤ X₁
t₁: l4(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, X₁, 100, X₃, 2, X₅) :|: X₁+1 ≤ 0 ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₂ ≤ X₃ ∧ X₃ ≤ X₂ ∧ X₄ ≤ X₅ ∧ X₅ ≤ X₄
t₂: l4(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, X₁, 100, X₃, 2, X₅) :|: 1 ≤ X₁ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₂ ≤ X₃ ∧ X₃ ≤ X₂ ∧ X₄ ≤ X₅ ∧ X₅ ≤ X₄
t₀: l4(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, X₁, 100, X₃, 1, X₅) :|: X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ X₂ ≤ X₃ ∧ X₃ ≤ X₂ ∧ X₄ ≤ X₅ ∧ X₅ ≤ X₄
Preprocessing
Cut unsatisfiable transition t₈: l1→l2
Cut unsatisfiable transition t₅: l2→l1
Cut unsatisfiable transition t₆: l2→l1
Found invariant X₄ ≤ 40 ∧ 60+X₄ ≤ X₂ ∧ X₂+X₄ ≤ 140 ∧ X₄ ≤ 40+X₁ ∧ X₁+X₄ ≤ 40 ∧ X₄ ≤ 40+X₀ ∧ X₀+X₄ ≤ 40 ∧ 1 ≤ X₄ ∧ 101 ≤ X₂+X₄ ∧ X₂ ≤ 99+X₄ ∧ 1 ≤ X₁+X₄ ∧ 1+X₁ ≤ X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₀ ≤ X₄ ∧ X₂ ≤ 100 ∧ X₂ ≤ 100+X₁ ∧ X₁+X₂ ≤ 100 ∧ X₂ ≤ 100+X₀ ∧ X₀+X₂ ≤ 100 ∧ 100 ≤ X₂ ∧ 100 ≤ X₁+X₂ ∧ 100+X₁ ≤ X₂ ∧ 100 ≤ X₀+X₂ ∧ 100+X₀ ≤ X₂ ∧ X₁ ≤ 0 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location l2
Found invariant X₄ ≤ 41 ∧ 59+X₄ ≤ X₂ ∧ X₂+X₄ ≤ 141 ∧ 2 ≤ X₄ ∧ 102 ≤ X₂+X₄ ∧ X₂ ≤ 98+X₄ ∧ X₂ ≤ 100 ∧ 100 ≤ X₂ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ for location l1
Found invariant X₅ ≤ X₄ ∧ X₄ ≤ X₅ ∧ X₃ ≤ X₂ ∧ X₂ ≤ X₃ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ for location l4
Found invariant X₄ ≤ 41 ∧ 59+X₄ ≤ X₂ ∧ X₂+X₄ ≤ 141 ∧ 40 ≤ X₄ ∧ 140 ≤ X₂+X₄ ∧ X₂ ≤ 60+X₄ ∧ X₂ ≤ 100 ∧ 100 ≤ X₂ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ for location l3
Problem after Preprocessing
Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅
Temp_Vars:
Locations: l0, l1, l2, l3, l4
Transitions:
t₁₁: l0(X₀, X₁, X₂, X₃, X₄, X₅) → l4(X₁, X₁, X₃, X₃, X₅, X₅)
t₉: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, X₁, X₂, X₃, 2+X₄, X₅) :|: X₁+1 ≤ 0 ∧ X₄ ≤ 39 ∧ 2 ≤ X₄ ∧ X₄ ≤ 41 ∧ X₂ ≤ 100 ∧ 100 ≤ X₂ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₄ ≤ 41 ∧ 59+X₄ ≤ X₂ ∧ X₂+X₄ ≤ 141 ∧ 2 ≤ X₄ ∧ 102 ≤ X₂+X₄ ∧ X₂ ≤ 98+X₄ ∧ X₂ ≤ 100 ∧ 100 ≤ X₂ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁
t₁₀: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, X₁, X₂, X₃, 2+X₄, X₅) :|: 1 ≤ X₁ ∧ X₄ ≤ 39 ∧ 2 ≤ X₄ ∧ X₄ ≤ 41 ∧ X₂ ≤ 100 ∧ 100 ≤ X₂ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₄ ≤ 41 ∧ 59+X₄ ≤ X₂ ∧ X₂+X₄ ≤ 141 ∧ 2 ≤ X₄ ∧ 102 ≤ X₂+X₄ ∧ X₂ ≤ 98+X₄ ∧ X₂ ≤ 100 ∧ 100 ≤ X₂ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁
t₇: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁, X₂, X₃, X₄, X₅) :|: 40 ≤ X₄ ∧ 2 ≤ X₄ ∧ X₄ ≤ 41 ∧ X₂ ≤ 100 ∧ 100 ≤ X₂ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₄ ≤ 41 ∧ 59+X₄ ≤ X₂ ∧ X₂+X₄ ≤ 141 ∧ 2 ≤ X₄ ∧ 102 ≤ X₂+X₄ ∧ X₂ ≤ 98+X₄ ∧ X₂ ≤ 100 ∧ 100 ≤ X₂ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁
t₄: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, X₁, X₂, X₃, 1+X₄, X₅) :|: X₄ ≤ 39 ∧ 1 ≤ X₄ ∧ X₄ ≤ 40 ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ X₂ ≤ 100 ∧ 100 ≤ X₂ ∧ X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ X₄ ≤ 40 ∧ 60+X₄ ≤ X₂ ∧ X₂+X₄ ≤ 140 ∧ X₄ ≤ 40+X₁ ∧ X₁+X₄ ≤ 40 ∧ X₄ ≤ 40+X₀ ∧ X₀+X₄ ≤ 40 ∧ 1 ≤ X₄ ∧ 101 ≤ X₂+X₄ ∧ X₂ ≤ 99+X₄ ∧ 1 ≤ X₁+X₄ ∧ 1+X₁ ≤ X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₀ ≤ X₄ ∧ X₂ ≤ 100 ∧ X₂ ≤ 100+X₁ ∧ X₁+X₂ ≤ 100 ∧ X₂ ≤ 100+X₀ ∧ X₀+X₂ ≤ 100 ∧ 100 ≤ X₂ ∧ 100 ≤ X₁+X₂ ∧ 100+X₁ ≤ X₂ ∧ 100 ≤ X₀+X₂ ∧ 100+X₀ ≤ X₂ ∧ X₁ ≤ 0 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀
t₃: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₄ ≤ 40 ∧ 40 ≤ X₄ ∧ X₂ ≤ 100 ∧ 100 ≤ X₂ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ X₄ ≤ 40 ∧ 60+X₄ ≤ X₂ ∧ X₂+X₄ ≤ 140 ∧ X₄ ≤ 40+X₁ ∧ X₁+X₄ ≤ 40 ∧ X₄ ≤ 40+X₀ ∧ X₀+X₄ ≤ 40 ∧ 1 ≤ X₄ ∧ 101 ≤ X₂+X₄ ∧ X₂ ≤ 99+X₄ ∧ 1 ≤ X₁+X₄ ∧ 1+X₁ ≤ X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₀ ≤ X₄ ∧ X₂ ≤ 100 ∧ X₂ ≤ 100+X₁ ∧ X₁+X₂ ≤ 100 ∧ X₂ ≤ 100+X₀ ∧ X₀+X₂ ≤ 100 ∧ 100 ≤ X₂ ∧ 100 ≤ X₁+X₂ ∧ 100+X₁ ≤ X₂ ∧ 100 ≤ X₀+X₂ ∧ 100+X₀ ≤ X₂ ∧ X₁ ≤ 0 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀
t₁: l4(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, X₁, 100, X₃, 2, X₅) :|: X₁+1 ≤ 0 ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₂ ≤ X₃ ∧ X₃ ≤ X₂ ∧ X₄ ≤ X₅ ∧ X₅ ≤ X₄ ∧ X₅ ≤ X₄ ∧ X₄ ≤ X₅ ∧ X₃ ≤ X₂ ∧ X₂ ≤ X₃ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁
t₂: l4(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, X₁, 100, X₃, 2, X₅) :|: 1 ≤ X₁ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₂ ≤ X₃ ∧ X₃ ≤ X₂ ∧ X₄ ≤ X₅ ∧ X₅ ≤ X₄ ∧ X₅ ≤ X₄ ∧ X₄ ≤ X₅ ∧ X₃ ≤ X₂ ∧ X₂ ≤ X₃ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁
t₀: l4(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, X₁, 100, X₃, 1, X₅) :|: X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ X₂ ≤ X₃ ∧ X₃ ≤ X₂ ∧ X₄ ≤ X₅ ∧ X₅ ≤ X₄ ∧ X₅ ≤ X₄ ∧ X₄ ≤ X₅ ∧ X₃ ≤ X₂ ∧ X₂ ≤ X₃ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁
MPRF for transition t₉: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, X₁, X₂, X₃, 2+X₄, X₅) :|: X₁+1 ≤ 0 ∧ X₄ ≤ 39 ∧ 2 ≤ X₄ ∧ X₄ ≤ 41 ∧ X₂ ≤ 100 ∧ 100 ≤ X₂ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₄ ≤ 41 ∧ 59+X₄ ≤ X₂ ∧ X₂+X₄ ≤ 141 ∧ 2 ≤ X₄ ∧ 102 ≤ X₂+X₄ ∧ X₂ ≤ 98+X₄ ∧ X₂ ≤ 100 ∧ 100 ≤ X₂ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ of depth 1:
new bound:
88 {O(1)}
MPRF:
l1 [42-X₄ ]
MPRF for transition t₁₀: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, X₁, X₂, X₃, 2+X₄, X₅) :|: 1 ≤ X₁ ∧ X₄ ≤ 39 ∧ 2 ≤ X₄ ∧ X₄ ≤ 41 ∧ X₂ ≤ 100 ∧ 100 ≤ X₂ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₄ ≤ 41 ∧ 59+X₄ ≤ X₂ ∧ X₂+X₄ ≤ 141 ∧ 2 ≤ X₄ ∧ 102 ≤ X₂+X₄ ∧ X₂ ≤ 98+X₄ ∧ X₂ ≤ 100 ∧ 100 ≤ X₂ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ of depth 1:
new bound:
88 {O(1)}
MPRF:
l1 [42-X₄ ]
MPRF for transition t₄: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, X₁, X₂, X₃, 1+X₄, X₅) :|: X₄ ≤ 39 ∧ 1 ≤ X₄ ∧ X₄ ≤ 40 ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ X₂ ≤ 100 ∧ 100 ≤ X₂ ∧ X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ X₄ ≤ 40 ∧ 60+X₄ ≤ X₂ ∧ X₂+X₄ ≤ 140 ∧ X₄ ≤ 40+X₁ ∧ X₁+X₄ ≤ 40 ∧ X₄ ≤ 40+X₀ ∧ X₀+X₄ ≤ 40 ∧ 1 ≤ X₄ ∧ 101 ≤ X₂+X₄ ∧ X₂ ≤ 99+X₄ ∧ 1 ≤ X₁+X₄ ∧ 1+X₁ ≤ X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₀ ≤ X₄ ∧ X₂ ≤ 100 ∧ X₂ ≤ 100+X₁ ∧ X₁+X₂ ≤ 100 ∧ X₂ ≤ 100+X₀ ∧ X₀+X₂ ≤ 100 ∧ 100 ≤ X₂ ∧ 100 ≤ X₁+X₂ ∧ 100+X₁ ≤ X₂ ∧ 100 ≤ X₀+X₂ ∧ 100+X₀ ≤ X₂ ∧ X₁ ≤ 0 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ of depth 1:
new bound:
41 {O(1)}
MPRF:
l2 [40-X₄ ]
All Bounds
Timebounds
Overall timebound:223 {O(1)}
t₁₁: 1 {O(1)}
t₇: 1 {O(1)}
t₉: 88 {O(1)}
t₁₀: 88 {O(1)}
t₃: 1 {O(1)}
t₄: 41 {O(1)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
Costbounds
Overall costbound: 223 {O(1)}
t₁₁: 1 {O(1)}
t₇: 1 {O(1)}
t₉: 88 {O(1)}
t₁₀: 88 {O(1)}
t₃: 1 {O(1)}
t₄: 41 {O(1)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
Sizebounds
t₁₁, X₀: X₁ {O(n)}
t₁₁, X₁: X₁ {O(n)}
t₁₁, X₂: X₃ {O(n)}
t₁₁, X₃: X₃ {O(n)}
t₁₁, X₄: X₅ {O(n)}
t₁₁, X₅: X₅ {O(n)}
t₇, X₀: 2⋅X₁ {O(n)}
t₇, X₁: 2⋅X₁ {O(n)}
t₇, X₂: 100 {O(1)}
t₇, X₃: 2⋅X₃ {O(n)}
t₇, X₄: 41 {O(1)}
t₇, X₅: 2⋅X₅ {O(n)}
t₉, X₀: X₁ {O(n)}
t₉, X₁: X₁ {O(n)}
t₉, X₂: 100 {O(1)}
t₉, X₃: X₃ {O(n)}
t₉, X₄: 41 {O(1)}
t₉, X₅: X₅ {O(n)}
t₁₀, X₀: X₁ {O(n)}
t₁₀, X₁: X₁ {O(n)}
t₁₀, X₂: 100 {O(1)}
t₁₀, X₃: X₃ {O(n)}
t₁₀, X₄: 41 {O(1)}
t₁₀, X₅: X₅ {O(n)}
t₃, X₀: 0 {O(1)}
t₃, X₁: 0 {O(1)}
t₃, X₂: 100 {O(1)}
t₃, X₃: X₃ {O(n)}
t₃, X₄: 40 {O(1)}
t₃, X₅: X₅ {O(n)}
t₄, X₀: 0 {O(1)}
t₄, X₁: 0 {O(1)}
t₄, X₂: 100 {O(1)}
t₄, X₃: X₃ {O(n)}
t₄, X₄: 40 {O(1)}
t₄, X₅: X₅ {O(n)}
t₀, X₀: 0 {O(1)}
t₀, X₁: 0 {O(1)}
t₀, X₂: 100 {O(1)}
t₀, X₃: X₃ {O(n)}
t₀, X₄: 1 {O(1)}
t₀, X₅: X₅ {O(n)}
t₁, X₀: X₁ {O(n)}
t₁, X₁: X₁ {O(n)}
t₁, X₂: 100 {O(1)}
t₁, X₃: X₃ {O(n)}
t₁, X₄: 2 {O(1)}
t₁, X₅: X₅ {O(n)}
t₂, X₀: X₁ {O(n)}
t₂, X₁: X₁ {O(n)}
t₂, X₂: 100 {O(1)}
t₂, X₃: X₃ {O(n)}
t₂, X₄: 2 {O(1)}
t₂, X₅: X₅ {O(n)}