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) :|: 0 < X₀
t₅: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₀ ≤ 0
t₁₀: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l8(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₉: 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, X₁-1, X₄, X₅, X₆) :|: 0 < X₁
t₈: l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l5(X₀, X₁, X₀, X₁, X₄, X₅, X₆) :|: X₁ ≤ 0
Preprocessing
Eliminate variables {X₄} that do not contribute to the problem
Found invariant 1 ≤ X₅+X₆ ∧ X₁ ≤ X₆ ∧ 1 ≤ X₀+X₆ ∧ 1 ≤ X₅ ∧ 1 ≤ X₁+X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l6
Found invariant 1 ≤ X₆ ∧ 1 ≤ X₅+X₆ ∧ 2 ≤ X₁+X₆ ∧ X₁ ≤ X₆ ∧ 1 ≤ X₀+X₆ ∧ 1+X₀ ≤ X₆ ∧ 1 ≤ X₁+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 0 for location l7
Found invariant 1 ≤ X₅+X₆ ∧ X₃ ≤ X₆ ∧ 0 ≤ X₂+X₆ ∧ X₁ ≤ X₆ ∧ 1 ≤ X₀+X₆ ∧ 0 ≤ X₃+X₅ ∧ X₂ ≤ X₅ ∧ 1 ≤ X₁+X₅ ∧ X₀ ≤ X₅ ∧ 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 ≤ X₆ ∧ X₀ ≤ X₅ ∧ X₀+X₁ ≤ 0 for location l8
Found invariant X₁ ≤ X₆ ∧ X₀ ≤ X₅ for location l1
Found invariant X₁ ≤ X₆ ∧ X₀ ≤ X₅ ∧ X₀+X₁ ≤ 0 for location l4
Found invariant 1 ≤ X₅+X₆ ∧ X₁ ≤ X₆ ∧ 1 ≤ X₀+X₆ ∧ 1 ≤ X₁+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₀+X₁ for location l3
Cut unsatisfiable transition t₃₂: l7→l5
Problem after Preprocessing
Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₅, X₆
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7, l8
Transitions:
t₂₂: l0(X₀, X₁, X₂, X₃, X₅, X₆) → l2(X₀, X₁, X₂, X₃, X₅, X₆)
t₂₃: l1(X₀, X₁, X₂, X₃, X₅, X₆) → l3(X₀, X₁, X₂, X₃, X₅, X₆) :|: 0 < X₀+X₁ ∧ X₁ ≤ X₆ ∧ X₀ ≤ X₅
t₂₄: l1(X₀, X₁, X₂, X₃, X₅, X₆) → l4(X₀, X₁, X₂, X₃, X₅, X₆) :|: X₀+X₁ ≤ 0 ∧ X₁ ≤ X₆ ∧ X₀ ≤ X₅
t₂₅: l2(X₀, X₁, X₂, X₃, X₅, X₆) → l1(X₅, X₆, X₂, X₃, X₅, X₆)
t₂₆: l3(X₀, X₁, X₂, X₃, X₅, X₆) → l6(X₀, X₁, X₂, X₃, X₅, X₆) :|: 0 < X₀ ∧ 1 ≤ X₅+X₆ ∧ X₁ ≤ X₆ ∧ 1 ≤ X₀+X₆ ∧ 1 ≤ X₁+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₀+X₁
t₂₇: l3(X₀, X₁, X₂, X₃, X₅, X₆) → l7(X₀, X₁, X₂, X₃, X₅, X₆) :|: X₀ ≤ 0 ∧ 1 ≤ X₅+X₆ ∧ X₁ ≤ X₆ ∧ 1 ≤ X₀+X₆ ∧ 1 ≤ X₁+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₀+X₁
t₂₈: l4(X₀, X₁, X₂, X₃, X₅, X₆) → l8(X₀, X₁, X₂, X₃, X₅, X₆) :|: X₁ ≤ X₆ ∧ X₀ ≤ X₅ ∧ X₀+X₁ ≤ 0
t₂₉: l5(X₀, X₁, X₂, X₃, X₅, X₆) → l1(X₂, X₃, X₂, X₃, X₅, X₆) :|: 1 ≤ X₅+X₆ ∧ X₃ ≤ X₆ ∧ 0 ≤ X₂+X₆ ∧ X₁ ≤ X₆ ∧ 1 ≤ X₀+X₆ ∧ 0 ≤ X₃+X₅ ∧ X₂ ≤ X₅ ∧ 1 ≤ X₁+X₅ ∧ X₀ ≤ X₅ ∧ X₃ ≤ X₁ ∧ 0 ≤ X₂+X₃ ∧ X₁ ≤ 1+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁+X₂ ∧ X₀ ≤ 1+X₂ ∧ 1 ≤ X₀+X₁
t₃₀: l6(X₀, X₁, X₂, X₃, X₅, X₆) → l5(X₀, X₁, X₀-1, X₁, X₅, X₆) :|: 1 ≤ X₅+X₆ ∧ X₁ ≤ X₆ ∧ 1 ≤ X₀+X₆ ∧ 1 ≤ X₅ ∧ 1 ≤ X₁+X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₃₁: l7(X₀, X₁, X₂, X₃, X₅, X₆) → l5(X₀, X₁, X₀, X₁-1, X₅, X₆) :|: 0 < X₁ ∧ 1 ≤ X₆ ∧ 1 ≤ X₅+X₆ ∧ 2 ≤ X₁+X₆ ∧ X₁ ≤ X₆ ∧ 1 ≤ X₀+X₆ ∧ 1+X₀ ≤ X₆ ∧ 1 ≤ X₁+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 0
MPRF for transition t₂₃: l1(X₀, X₁, X₂, X₃, X₅, X₆) → l3(X₀, X₁, X₂, X₃, X₅, X₆) :|: 0 < X₀+X₁ ∧ X₁ ≤ X₆ ∧ X₀ ≤ X₅ of depth 1:
new bound:
2⋅X₅+2⋅X₆+1 {O(n)}
MPRF:
l3 [2⋅X₀+X₁+X₆-2 ]
l1 [2⋅X₀+X₁+X₆-1 ]
l6 [2⋅X₀+X₁+X₆-2 ]
l7 [2⋅X₀+X₁+X₆-2 ]
l5 [2⋅X₂+X₃+X₆-1 ]
MPRF for transition t₂₆: l3(X₀, X₁, X₂, X₃, X₅, X₆) → l6(X₀, X₁, X₂, X₃, X₅, X₆) :|: 0 < X₀ ∧ 1 ≤ X₅+X₆ ∧ X₁ ≤ X₆ ∧ 1 ≤ X₀+X₆ ∧ 1 ≤ X₁+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₀+X₁ of depth 1:
new bound:
X₅ {O(n)}
MPRF:
l3 [X₀ ]
l1 [X₀ ]
l6 [X₀-1 ]
l7 [X₀ ]
l5 [X₂ ]
MPRF for transition t₂₇: l3(X₀, X₁, X₂, X₃, X₅, X₆) → l7(X₀, X₁, X₂, X₃, X₅, X₆) :|: X₀ ≤ 0 ∧ 1 ≤ X₅+X₆ ∧ X₁ ≤ X₆ ∧ 1 ≤ X₀+X₆ ∧ 1 ≤ X₁+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₀+X₁ of depth 1:
new bound:
X₆ {O(n)}
MPRF:
l3 [X₁ ]
l1 [X₁ ]
l6 [X₁ ]
l7 [X₁-1 ]
l5 [X₃ ]
MPRF for transition t₂₉: l5(X₀, X₁, X₂, X₃, X₅, X₆) → l1(X₂, X₃, X₂, X₃, X₅, X₆) :|: 1 ≤ X₅+X₆ ∧ X₃ ≤ X₆ ∧ 0 ≤ X₂+X₆ ∧ X₁ ≤ X₆ ∧ 1 ≤ X₀+X₆ ∧ 0 ≤ X₃+X₅ ∧ X₂ ≤ X₅ ∧ 1 ≤ X₁+X₅ ∧ X₀ ≤ X₅ ∧ 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:
X₅+X₆ {O(n)}
MPRF:
l3 [X₀+X₁ ]
l1 [X₀+X₁ ]
l6 [X₀+X₁ ]
l7 [X₀+X₁ ]
l5 [X₂+X₃+1 ]
MPRF for transition t₃₀: l6(X₀, X₁, X₂, X₃, X₅, X₆) → l5(X₀, X₁, X₀-1, X₁, X₅, X₆) :|: 1 ≤ X₅+X₆ ∧ X₁ ≤ X₆ ∧ 1 ≤ X₀+X₆ ∧ 1 ≤ X₅ ∧ 1 ≤ X₁+X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₅ {O(n)}
MPRF:
l3 [X₀ ]
l1 [X₀ ]
l6 [X₀ ]
l7 [X₀ ]
l5 [X₂ ]
MPRF for transition t₃₁: l7(X₀, X₁, X₂, X₃, X₅, X₆) → l5(X₀, X₁, X₀, X₁-1, X₅, X₆) :|: 0 < X₁ ∧ 1 ≤ X₆ ∧ 1 ≤ X₅+X₆ ∧ 2 ≤ X₁+X₆ ∧ X₁ ≤ X₆ ∧ 1 ≤ X₀+X₆ ∧ 1+X₀ ≤ X₆ ∧ 1 ≤ X₁+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 0 of depth 1:
new bound:
X₆ {O(n)}
MPRF:
l3 [X₁ ]
l1 [X₁ ]
l6 [X₁ ]
l7 [X₁ ]
l5 [X₃ ]
All Bounds
Timebounds
Overall timebound:5⋅X₅+5⋅X₆+5 {O(n)}
t₂₂: 1 {O(1)}
t₂₃: 2⋅X₅+2⋅X₆+1 {O(n)}
t₂₄: 1 {O(1)}
t₂₅: 1 {O(1)}
t₂₆: X₅ {O(n)}
t₂₇: X₆ {O(n)}
t₂₈: 1 {O(1)}
t₂₉: X₅+X₆ {O(n)}
t₃₀: X₅ {O(n)}
t₃₁: X₆ {O(n)}
Costbounds
Overall costbound: 5⋅X₅+5⋅X₆+5 {O(n)}
t₂₂: 1 {O(1)}
t₂₃: 2⋅X₅+2⋅X₆+1 {O(n)}
t₂₄: 1 {O(1)}
t₂₅: 1 {O(1)}
t₂₆: X₅ {O(n)}
t₂₇: X₆ {O(n)}
t₂₈: 1 {O(1)}
t₂₉: X₅+X₆ {O(n)}
t₃₀: X₅ {O(n)}
t₃₁: X₆ {O(n)}
Sizebounds
t₂₂, X₀: X₀ {O(n)}
t₂₂, X₁: X₁ {O(n)}
t₂₂, X₂: X₂ {O(n)}
t₂₂, X₃: X₃ {O(n)}
t₂₂, X₅: X₅ {O(n)}
t₂₂, X₆: X₆ {O(n)}
t₂₃, X₀: 2⋅X₅+X₆ {O(n)}
t₂₃, X₁: 2⋅X₆+X₅ {O(n)}
t₂₃, X₂: 2⋅X₆+4⋅X₅+X₂ {O(n)}
t₂₃, X₃: 2⋅X₅+4⋅X₆+X₃ {O(n)}
t₂₃, X₅: X₅ {O(n)}
t₂₃, X₆: X₆ {O(n)}
t₂₄, X₀: 3⋅X₅+X₆ {O(n)}
t₂₄, X₁: 3⋅X₆+X₅ {O(n)}
t₂₄, X₂: 2⋅X₆+4⋅X₅+X₂ {O(n)}
t₂₄, X₃: 2⋅X₅+4⋅X₆+X₃ {O(n)}
t₂₄, X₅: 2⋅X₅ {O(n)}
t₂₄, X₆: 2⋅X₆ {O(n)}
t₂₅, X₀: X₅ {O(n)}
t₂₅, X₁: X₆ {O(n)}
t₂₅, X₂: X₂ {O(n)}
t₂₅, X₃: X₃ {O(n)}
t₂₅, X₅: X₅ {O(n)}
t₂₅, X₆: X₆ {O(n)}
t₂₆, X₀: 2⋅X₅+X₆ {O(n)}
t₂₆, X₁: 2⋅X₆+X₅ {O(n)}
t₂₆, X₂: 2⋅X₆+4⋅X₅+X₂ {O(n)}
t₂₆, X₃: 2⋅X₅+4⋅X₆+X₃ {O(n)}
t₂₆, X₅: X₅ {O(n)}
t₂₆, X₆: X₆ {O(n)}
t₂₇, X₀: 2⋅X₅+X₆ {O(n)}
t₂₇, X₁: 2⋅X₆+X₅ {O(n)}
t₂₇, X₂: 2⋅X₆+4⋅X₅+X₂ {O(n)}
t₂₇, X₃: 2⋅X₅+4⋅X₆+X₃ {O(n)}
t₂₇, X₅: X₅ {O(n)}
t₂₇, X₆: X₆ {O(n)}
t₂₈, X₀: 3⋅X₅+X₆ {O(n)}
t₂₈, X₁: 3⋅X₆+X₅ {O(n)}
t₂₈, X₂: 2⋅X₆+4⋅X₅+X₂ {O(n)}
t₂₈, X₃: 2⋅X₅+4⋅X₆+X₃ {O(n)}
t₂₈, X₅: 2⋅X₅ {O(n)}
t₂₈, X₆: 2⋅X₆ {O(n)}
t₂₉, X₀: 2⋅X₅+X₆ {O(n)}
t₂₉, X₁: 2⋅X₆+X₅ {O(n)}
t₂₉, X₂: 2⋅X₆+4⋅X₅ {O(n)}
t₂₉, X₃: 2⋅X₅+4⋅X₆ {O(n)}
t₂₉, X₅: X₅ {O(n)}
t₂₉, X₆: X₆ {O(n)}
t₃₀, X₀: 2⋅X₅+X₆ {O(n)}
t₃₀, X₁: 2⋅X₆+X₅ {O(n)}
t₃₀, X₂: 2⋅X₅+X₆ {O(n)}
t₃₀, X₃: 2⋅X₆+X₅ {O(n)}
t₃₀, X₅: X₅ {O(n)}
t₃₀, X₆: X₆ {O(n)}
t₃₁, X₀: 2⋅X₅+X₆ {O(n)}
t₃₁, X₁: 2⋅X₆+X₅ {O(n)}
t₃₁, X₂: 2⋅X₅+X₆ {O(n)}
t₃₁, X₃: 2⋅X₆+X₅ {O(n)}
t₃₁, X₅: X₅ {O(n)}
t₃₁, X₆: X₆ {O(n)}