Initial Problem
Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7, l8
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₂: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 0 < X₀+X₁
t₃: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₀+X₁ ≤ 0
t₁: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l1(X₅, X₆, X₂, X₃, X₄, X₅, X₆)
t₄: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₁ < X₀
t₅: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₀ ≤ X₁
t₁₇: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l8(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₁₆: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l1(X₂, X₃, X₂, X₃, X₄, X₅, X₆)
t₆: l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l5(X₀, X₁, X₀-1, X₁, X₄, X₅, X₆)
t₇: l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l5(X₀, X₁, X₀-1, X₁, X₄, X₅, X₆) :|: X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀
t₈: l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l5(X₀, X₁, X₀, X₁, X₄, X₅, X₆) :|: X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₀ < X₁
t₉: l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l5(X₀, X₁, X₀, X₁, X₄, X₅, X₆) :|: X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₁ < X₀
t₁₀: l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l5(X₀, X₁, X₀-1, X₁-1, X₄, X₅, X₆) :|: X₀ < X₁ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀
t₁₁: l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l5(X₀, X₁, X₀-1, X₁-1, X₄, X₅, X₆) :|: X₁ < X₀ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀
t₁₂: l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l5(X₀, X₁, X₀, X₁-1, X₄, X₅, X₆) :|: X₀ < X₁ ∧ X₀ < X₁
t₁₃: l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l5(X₀, X₁, X₀, X₁-1, X₄, X₅, X₆) :|: X₀ < X₁ ∧ X₁ < X₀
t₁₄: l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l5(X₀, X₁, X₀, X₁-1, X₄, X₅, X₆) :|: X₁ < X₀ ∧ X₀ < X₁
t₁₅: l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l5(X₀, X₁, X₀, X₁-1, X₄, X₅, X₆) :|: X₁ < X₀ ∧ X₁ < X₀
Preprocessing
Cut unsatisfiable transition t₈: l7→l5
Cut unsatisfiable transition t₉: l7→l5
Cut unsatisfiable transition t₁₀: l7→l5
Cut unsatisfiable transition t₁₁: l7→l5
Cut unsatisfiable transition t₁₃: l7→l5
Cut unsatisfiable transition t₁₄: l7→l5
Cut unsatisfiable transition t₁₅: l7→l5
Eliminate variables {X₄} that do not contribute to the problem
Found invariant 1 ≤ X₄+X₅ ∧ X₁ ≤ X₅ ∧ 1 ≤ X₀+X₅ ∧ 1 ≤ X₄ ∧ 1 ≤ X₁+X₄ ∧ 1+X₁ ≤ X₄ ∧ 2 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l6
Found invariant 1 ≤ X₅ ∧ 1 ≤ X₄+X₅ ∧ 2 ≤ X₁+X₅ ∧ X₁ ≤ X₅ ∧ 1 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₁+X₄ ∧ X₀ ≤ X₄ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ X₀ ≤ X₁ for location l7
Found invariant 1 ≤ X₄+X₅ ∧ X₃ ≤ X₅ ∧ 0 ≤ X₂+X₅ ∧ X₁ ≤ X₅ ∧ 1 ≤ X₀+X₅ ∧ 0 ≤ X₃+X₄ ∧ X₂ ≤ X₄ ∧ 1 ≤ X₁+X₄ ∧ X₀ ≤ X₄ ∧ X₃ ≤ X₁ ∧ 0 ≤ X₂+X₃ ∧ X₁ ≤ 1+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁+X₂ ∧ X₀ ≤ 1+X₂ ∧ 1 ≤ X₀+X₁ for location l5
Found invariant X₁ ≤ X₅ ∧ X₀ ≤ X₄ ∧ X₀+X₁ ≤ 0 for location l8
Found invariant X₁ ≤ X₅ ∧ X₀ ≤ X₄ for location l1
Found invariant X₁ ≤ X₅ ∧ X₀ ≤ X₄ ∧ X₀+X₁ ≤ 0 for location l4
Found invariant 1 ≤ X₄+X₅ ∧ X₁ ≤ X₅ ∧ 1 ≤ X₀+X₅ ∧ 1 ≤ X₁+X₄ ∧ X₀ ≤ X₄ ∧ 1 ≤ 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, l5, l6, l7, l8
Transitions:
t₃₅: l0(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, X₁, X₂, X₃, X₄, X₅)
t₃₆: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁, X₂, X₃, X₄, X₅) :|: 0 < X₀+X₁ ∧ X₁ ≤ X₅ ∧ X₀ ≤ X₄
t₃₇: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l4(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₀+X₁ ≤ 0 ∧ X₁ ≤ X₅ ∧ X₀ ≤ X₄
t₃₈: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₄, X₅, X₂, X₃, X₄, X₅)
t₃₉: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l6(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₁ < X₀ ∧ 1 ≤ X₄+X₅ ∧ X₁ ≤ X₅ ∧ 1 ≤ X₀+X₅ ∧ 1 ≤ X₁+X₄ ∧ X₀ ≤ X₄ ∧ 1 ≤ X₀+X₁
t₄₀: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l7(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₀ ≤ X₁ ∧ 1 ≤ X₄+X₅ ∧ X₁ ≤ X₅ ∧ 1 ≤ X₀+X₅ ∧ 1 ≤ X₁+X₄ ∧ X₀ ≤ X₄ ∧ 1 ≤ X₀+X₁
t₄₁: l4(X₀, X₁, X₂, X₃, X₄, X₅) → l8(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₁ ≤ X₅ ∧ X₀ ≤ X₄ ∧ X₀+X₁ ≤ 0
t₄₂: l5(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₂, X₃, X₂, X₃, X₄, X₅) :|: 1 ≤ X₄+X₅ ∧ X₃ ≤ X₅ ∧ 0 ≤ X₂+X₅ ∧ X₁ ≤ X₅ ∧ 1 ≤ X₀+X₅ ∧ 0 ≤ X₃+X₄ ∧ X₂ ≤ X₄ ∧ 1 ≤ X₁+X₄ ∧ X₀ ≤ X₄ ∧ X₃ ≤ X₁ ∧ 0 ≤ X₂+X₃ ∧ X₁ ≤ 1+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁+X₂ ∧ X₀ ≤ 1+X₂ ∧ 1 ≤ X₀+X₁
t₄₃: l6(X₀, X₁, X₂, X₃, X₄, X₅) → l5(X₀, X₁, X₀-1, X₁, X₄, X₅) :|: 1 ≤ X₄+X₅ ∧ X₁ ≤ X₅ ∧ 1 ≤ X₀+X₅ ∧ 1 ≤ X₄ ∧ 1 ≤ X₁+X₄ ∧ 1+X₁ ≤ X₄ ∧ 2 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₄₄: l7(X₀, X₁, X₂, X₃, X₄, X₅) → l5(X₀, X₁, X₀-1, X₁, X₄, X₅) :|: X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₅ ∧ 1 ≤ X₄+X₅ ∧ 2 ≤ X₁+X₅ ∧ X₁ ≤ X₅ ∧ 1 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₁+X₄ ∧ X₀ ≤ X₄ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ X₀ ≤ X₁
t₄₅: l7(X₀, X₁, X₂, X₃, X₄, X₅) → l5(X₀, X₁, X₀, X₁-1, X₄, X₅) :|: X₀ < X₁ ∧ X₀ < X₁ ∧ 1 ≤ X₅ ∧ 1 ≤ X₄+X₅ ∧ 2 ≤ X₁+X₅ ∧ X₁ ≤ X₅ ∧ 1 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₁+X₄ ∧ X₀ ≤ X₄ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ X₀ ≤ X₁
MPRF for transition t₃₆: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁, X₂, X₃, X₄, X₅) :|: 0 < X₀+X₁ ∧ X₁ ≤ X₅ ∧ X₀ ≤ X₄ of depth 1:
new bound:
2⋅X₄+2⋅X₅+1 {O(n)}
MPRF for transition t₃₉: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l6(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₁ < X₀ ∧ 1 ≤ X₄+X₅ ∧ X₁ ≤ X₅ ∧ 1 ≤ X₀+X₅ ∧ 1 ≤ X₁+X₄ ∧ X₀ ≤ X₄ ∧ 1 ≤ X₀+X₁ of depth 1:
new bound:
2⋅X₄ {O(n)}
MPRF for transition t₄₀: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l7(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₀ ≤ X₁ ∧ 1 ≤ X₄+X₅ ∧ X₁ ≤ X₅ ∧ 1 ≤ X₀+X₅ ∧ 1 ≤ X₁+X₄ ∧ X₀ ≤ X₄ ∧ 1 ≤ X₀+X₁ of depth 1:
new bound:
X₄+X₅+1 {O(n)}
MPRF for transition t₄₂: l5(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₂, X₃, X₂, X₃, X₄, X₅) :|: 1 ≤ X₄+X₅ ∧ X₃ ≤ X₅ ∧ 0 ≤ X₂+X₅ ∧ X₁ ≤ X₅ ∧ 1 ≤ X₀+X₅ ∧ 0 ≤ X₃+X₄ ∧ X₂ ≤ X₄ ∧ 1 ≤ X₁+X₄ ∧ X₀ ≤ X₄ ∧ X₃ ≤ X₁ ∧ 0 ≤ X₂+X₃ ∧ X₁ ≤ 1+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁+X₂ ∧ X₀ ≤ 1+X₂ ∧ 1 ≤ X₀+X₁ of depth 1:
new bound:
X₄+X₅ {O(n)}
MPRF for transition t₄₃: l6(X₀, X₁, X₂, X₃, X₄, X₅) → l5(X₀, X₁, X₀-1, X₁, X₄, X₅) :|: 1 ≤ X₄+X₅ ∧ X₁ ≤ X₅ ∧ 1 ≤ X₀+X₅ ∧ 1 ≤ X₄ ∧ 1 ≤ X₁+X₄ ∧ 1+X₁ ≤ X₄ ∧ 2 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
2⋅X₄ {O(n)}
MPRF for transition t₄₄: l7(X₀, X₁, X₂, X₃, X₄, X₅) → l5(X₀, X₁, X₀-1, X₁, X₄, X₅) :|: X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₅ ∧ 1 ≤ X₄+X₅ ∧ 2 ≤ X₁+X₅ ∧ X₁ ≤ X₅ ∧ 1 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₁+X₄ ∧ X₀ ≤ X₄ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ X₀ ≤ X₁ of depth 1:
new bound:
X₄ {O(n)}
MPRF for transition t₄₅: l7(X₀, X₁, X₂, X₃, X₄, X₅) → l5(X₀, X₁, X₀, X₁-1, X₄, X₅) :|: X₀ < X₁ ∧ X₀ < X₁ ∧ 1 ≤ X₅ ∧ 1 ≤ X₄+X₅ ∧ 2 ≤ X₁+X₅ ∧ X₁ ≤ X₅ ∧ 1 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₁+X₄ ∧ X₀ ≤ X₄ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ X₀ ≤ X₁ of depth 1:
new bound:
X₅ {O(n)}
All Bounds
Timebounds
Overall timebound:5⋅X₅+9⋅X₄+6 {O(n)}
t₃₅: 1 {O(1)}
t₃₆: 2⋅X₄+2⋅X₅+1 {O(n)}
t₃₇: 1 {O(1)}
t₃₈: 1 {O(1)}
t₃₉: 2⋅X₄ {O(n)}
t₄₀: X₄+X₅+1 {O(n)}
t₄₁: 1 {O(1)}
t₄₂: X₄+X₅ {O(n)}
t₄₃: 2⋅X₄ {O(n)}
t₄₄: X₄ {O(n)}
t₄₅: X₅ {O(n)}
Costbounds
Overall costbound: 5⋅X₅+9⋅X₄+6 {O(n)}
t₃₅: 1 {O(1)}
t₃₆: 2⋅X₄+2⋅X₅+1 {O(n)}
t₃₇: 1 {O(1)}
t₃₈: 1 {O(1)}
t₃₉: 2⋅X₄ {O(n)}
t₄₀: X₄+X₅+1 {O(n)}
t₄₁: 1 {O(1)}
t₄₂: X₄+X₅ {O(n)}
t₄₃: 2⋅X₄ {O(n)}
t₄₄: X₄ {O(n)}
t₄₅: X₅ {O(n)}
Sizebounds
t₃₅, X₀: X₀ {O(n)}
t₃₅, X₁: X₁ {O(n)}
t₃₅, X₂: X₂ {O(n)}
t₃₅, X₃: X₃ {O(n)}
t₃₅, X₄: X₄ {O(n)}
t₃₅, X₅: X₅ {O(n)}
t₃₆, X₀: 2⋅X₄+X₅ {O(n)}
t₃₆, X₁: 2⋅X₅+X₄ {O(n)}
t₃₆, X₂: 3⋅X₅+6⋅X₄+X₂ {O(n)}
t₃₆, X₃: 3⋅X₄+6⋅X₅+X₃ {O(n)}
t₃₆, X₄: X₄ {O(n)}
t₃₆, X₅: X₅ {O(n)}
t₃₇, X₀: 3⋅X₄+X₅ {O(n)}
t₃₇, X₁: 3⋅X₅+X₄ {O(n)}
t₃₇, X₂: 3⋅X₅+6⋅X₄+X₂ {O(n)}
t₃₇, X₃: 3⋅X₄+6⋅X₅+X₃ {O(n)}
t₃₇, X₄: 2⋅X₄ {O(n)}
t₃₇, X₅: 2⋅X₅ {O(n)}
t₃₈, X₀: X₄ {O(n)}
t₃₈, X₁: X₅ {O(n)}
t₃₈, X₂: X₂ {O(n)}
t₃₈, X₃: X₃ {O(n)}
t₃₈, X₄: X₄ {O(n)}
t₃₈, X₅: X₅ {O(n)}
t₃₉, X₀: 2⋅X₄+X₅ {O(n)}
t₃₉, X₁: 2⋅X₅+X₄ {O(n)}
t₃₉, X₂: 3⋅X₅+6⋅X₄+X₂ {O(n)}
t₃₉, X₃: 3⋅X₄+6⋅X₅+X₃ {O(n)}
t₃₉, X₄: X₄ {O(n)}
t₃₉, X₅: X₅ {O(n)}
t₄₀, X₀: 2⋅X₄+X₅ {O(n)}
t₄₀, X₁: 2⋅X₅+X₄ {O(n)}
t₄₀, X₂: 3⋅X₅+6⋅X₄+X₂ {O(n)}
t₄₀, X₃: 3⋅X₄+6⋅X₅+X₃ {O(n)}
t₄₀, X₄: X₄ {O(n)}
t₄₀, X₅: X₅ {O(n)}
t₄₁, X₀: 3⋅X₄+X₅ {O(n)}
t₄₁, X₁: 3⋅X₅+X₄ {O(n)}
t₄₁, X₂: 3⋅X₅+6⋅X₄+X₂ {O(n)}
t₄₁, X₃: 3⋅X₄+6⋅X₅+X₃ {O(n)}
t₄₁, X₄: 2⋅X₄ {O(n)}
t₄₁, X₅: 2⋅X₅ {O(n)}
t₄₂, X₀: 2⋅X₄+X₅ {O(n)}
t₄₂, X₁: 2⋅X₅+X₄ {O(n)}
t₄₂, X₂: 3⋅X₅+6⋅X₄ {O(n)}
t₄₂, X₃: 3⋅X₄+6⋅X₅ {O(n)}
t₄₂, X₄: X₄ {O(n)}
t₄₂, X₅: X₅ {O(n)}
t₄₃, X₀: 2⋅X₄+X₅ {O(n)}
t₄₃, X₁: 2⋅X₅+X₄ {O(n)}
t₄₃, X₂: 2⋅X₄+X₅ {O(n)}
t₄₃, X₃: 2⋅X₅+X₄ {O(n)}
t₄₃, X₄: X₄ {O(n)}
t₄₃, X₅: X₅ {O(n)}
t₄₄, X₀: 2⋅X₄+X₅ {O(n)}
t₄₄, X₁: 2⋅X₅+X₄ {O(n)}
t₄₄, X₂: 2⋅X₄+X₅ {O(n)}
t₄₄, X₃: 2⋅X₅+X₄ {O(n)}
t₄₄, X₄: X₄ {O(n)}
t₄₄, X₅: X₅ {O(n)}
t₄₅, X₀: 2⋅X₄+X₅ {O(n)}
t₄₅, X₁: 2⋅X₅+X₄ {O(n)}
t₄₅, X₂: 2⋅X₄+X₅ {O(n)}
t₄₅, X₃: 2⋅X₅+X₄ {O(n)}
t₄₅, X₄: X₄ {O(n)}
t₄₅, X₅: X₅ {O(n)}