Initial Problem
Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars: nondef.0
Locations: l0, l1, l2, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄) → l7(X₀, X₁, X₂, X₃, X₄)
t₆: l1(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄) :|: 0 < X₀
t₇: l1(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁, X₂, X₃, X₄) :|: X₀ ≤ 0
t₃: l2(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₃, X₄)
t₅: l3(X₀, X₁, X₂, X₃, X₄) → l1(nondef.0, X₁, X₂, X₃, X₄)
t₈: l4(X₀, X₁, X₂, X₃, X₄) → l8(X₀, X₁, X₂, 0, X₄) :|: X₄ ≤ X₂+1
t₉: l4(X₀, X₁, X₂, X₃, X₄) → l8(X₀, X₁, X₂, X₂+1, X₄) :|: X₂+1 < X₄
t₁₀: l5(X₀, X₁, X₂, X₃, X₄) → l8(X₀, X₁, X₂, 0, X₄) :|: X₂+X₄ ≤ 1
t₁₁: l5(X₀, X₁, X₂, X₃, X₄) → l8(X₀, X₁, X₂, X₂-1, X₄) :|: 1 < X₄+X₂
t₁₄: l6(X₀, X₁, X₂, X₃, X₄) → l9(X₀, X₁, X₂, X₃, X₄)
t₁: l7(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₄, 0, X₃, X₄) :|: 1 ≤ X₄
t₂: l7(X₀, X₁, X₂, X₃, X₄) → l6(X₀, X₁, X₂, X₃, X₄) :|: X₄ < 1
t₁₂: l8(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁-1, X₃, X₃, X₄) :|: 1 < X₁
t₁₃: l8(X₀, X₁, X₂, X₃, X₄) → l6(X₀, X₁, X₂, X₃, X₄) :|: X₁ ≤ 1
Preprocessing
Found invariant 1 ≤ X₄ ∧ 1 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 1 ≤ X₁ for location l2
Found invariant 1 ≤ X₄ ∧ 1 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 1+X₀ ≤ X₄ ∧ 1 ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 0 for location l5
Found invariant 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 1+X₃ ≤ X₄ ∧ 1 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 1 ≤ X₁ for location l8
Found invariant 1 ≤ X₄ ∧ 1 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 1 ≤ X₁ for location l1
Found invariant 1 ≤ X₄ ∧ 1 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 2 ≤ X₀+X₄ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l4
Found invariant 1 ≤ X₄ ∧ 1 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 1 ≤ X₁ for location l3
Problem after Preprocessing
Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars: nondef.0
Locations: l0, l1, l2, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄) → l7(X₀, X₁, X₂, X₃, X₄)
t₆: l1(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄) :|: 0 < X₀ ∧ 1 ≤ X₄ ∧ 1 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 1 ≤ X₁
t₇: l1(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁, X₂, X₃, X₄) :|: X₀ ≤ 0 ∧ 1 ≤ X₄ ∧ 1 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 1 ≤ X₁
t₃: l2(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₃, X₄) :|: 1 ≤ X₄ ∧ 1 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 1 ≤ X₁
t₅: l3(X₀, X₁, X₂, X₃, X₄) → l1(nondef.0, X₁, X₂, X₃, X₄) :|: 1 ≤ X₄ ∧ 1 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 1 ≤ X₁
t₈: l4(X₀, X₁, X₂, X₃, X₄) → l8(X₀, X₁, X₂, 0, X₄) :|: X₄ ≤ X₂+1 ∧ 1 ≤ X₄ ∧ 1 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 2 ≤ X₀+X₄ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₉: l4(X₀, X₁, X₂, X₃, X₄) → l8(X₀, X₁, X₂, X₂+1, X₄) :|: X₂+1 < X₄ ∧ 1 ≤ X₄ ∧ 1 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 2 ≤ X₀+X₄ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₁₀: l5(X₀, X₁, X₂, X₃, X₄) → l8(X₀, X₁, X₂, 0, X₄) :|: X₂+X₄ ≤ 1 ∧ 1 ≤ X₄ ∧ 1 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 1+X₀ ≤ X₄ ∧ 1 ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 0
t₁₁: l5(X₀, X₁, X₂, X₃, X₄) → l8(X₀, X₁, X₂, X₂-1, X₄) :|: 1 < X₄+X₂ ∧ 1 ≤ X₄ ∧ 1 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 1+X₀ ≤ X₄ ∧ 1 ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 0
t₁₄: l6(X₀, X₁, X₂, X₃, X₄) → l9(X₀, X₁, X₂, X₃, X₄)
t₁: l7(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₄, 0, X₃, X₄) :|: 1 ≤ X₄
t₂: l7(X₀, X₁, X₂, X₃, X₄) → l6(X₀, X₁, X₂, X₃, X₄) :|: X₄ < 1
t₁₂: l8(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁-1, X₃, X₃, X₄) :|: 1 < X₁ ∧ 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 1+X₃ ≤ X₄ ∧ 1 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 1 ≤ X₁
t₁₃: l8(X₀, X₁, X₂, X₃, X₄) → l6(X₀, X₁, X₂, X₃, X₄) :|: X₁ ≤ 1 ∧ 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 1+X₃ ≤ X₄ ∧ 1 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 1 ≤ X₁
MPRF for transition t₃: l2(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₃, X₄) :|: 1 ≤ X₄ ∧ 1 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 1 ≤ X₁ of depth 1:
new bound:
X₄+1 {O(n)}
MPRF for transition t₅: l3(X₀, X₁, X₂, X₃, X₄) → l1(nondef.0, X₁, X₂, X₃, X₄) :|: 1 ≤ X₄ ∧ 1 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 1 ≤ X₁ of depth 1:
new bound:
X₄+1 {O(n)}
MPRF for transition t₆: l1(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄) :|: 0 < X₀ ∧ 1 ≤ X₄ ∧ 1 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 1 ≤ X₁ of depth 1:
new bound:
X₄ {O(n)}
MPRF for transition t₇: l1(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁, X₂, X₃, X₄) :|: X₀ ≤ 0 ∧ 1 ≤ X₄ ∧ 1 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 1 ≤ X₁ of depth 1:
new bound:
X₄ {O(n)}
MPRF for transition t₈: l4(X₀, X₁, X₂, X₃, X₄) → l8(X₀, X₁, X₂, 0, X₄) :|: X₄ ≤ X₂+1 ∧ 1 ≤ X₄ ∧ 1 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 2 ≤ X₀+X₄ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₄ {O(n)}
MPRF for transition t₉: l4(X₀, X₁, X₂, X₃, X₄) → l8(X₀, X₁, X₂, X₂+1, X₄) :|: X₂+1 < X₄ ∧ 1 ≤ X₄ ∧ 1 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 2 ≤ X₀+X₄ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₄ {O(n)}
MPRF for transition t₁₀: l5(X₀, X₁, X₂, X₃, X₄) → l8(X₀, X₁, X₂, 0, X₄) :|: X₂+X₄ ≤ 1 ∧ 1 ≤ X₄ ∧ 1 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 1+X₀ ≤ X₄ ∧ 1 ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 0 of depth 1:
new bound:
X₄ {O(n)}
MPRF for transition t₁₁: l5(X₀, X₁, X₂, X₃, X₄) → l8(X₀, X₁, X₂, X₂-1, X₄) :|: 1 < X₄+X₂ ∧ 1 ≤ X₄ ∧ 1 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 1+X₀ ≤ X₄ ∧ 1 ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 0 of depth 1:
new bound:
X₄ {O(n)}
MPRF for transition t₁₂: l8(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁-1, X₃, X₃, X₄) :|: 1 < X₁ ∧ 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 1+X₃ ≤ X₄ ∧ 1 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 1 ≤ X₁ of depth 1:
new bound:
X₄+1 {O(n)}
All Bounds
Timebounds
Overall timebound:9⋅X₄+8 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: X₄+1 {O(n)}
t₅: X₄+1 {O(n)}
t₆: X₄ {O(n)}
t₇: X₄ {O(n)}
t₈: X₄ {O(n)}
t₉: X₄ {O(n)}
t₁₀: X₄ {O(n)}
t₁₁: X₄ {O(n)}
t₁₂: X₄+1 {O(n)}
t₁₃: 1 {O(1)}
t₁₄: 1 {O(1)}
Costbounds
Overall costbound: 9⋅X₄+8 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: X₄+1 {O(n)}
t₅: X₄+1 {O(n)}
t₆: X₄ {O(n)}
t₇: X₄ {O(n)}
t₈: X₄ {O(n)}
t₉: X₄ {O(n)}
t₁₀: X₄ {O(n)}
t₁₁: X₄ {O(n)}
t₁₂: X₄+1 {O(n)}
t₁₃: 1 {O(1)}
t₁₄: 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)}
t₁, X₀: X₀ {O(n)}
t₁, X₁: X₄ {O(n)}
t₁, X₂: 0 {O(1)}
t₁, X₃: X₃ {O(n)}
t₁, X₄: X₄ {O(n)}
t₂, X₀: X₀ {O(n)}
t₂, X₁: X₁ {O(n)}
t₂, X₂: X₂ {O(n)}
t₂, X₃: X₃ {O(n)}
t₂, X₄: X₄ {O(n)}
t₃, X₁: X₄ {O(n)}
t₃, X₂: 2⋅X₄ {O(n)}
t₃, X₃: 4⋅X₄+X₃ {O(n)}
t₃, X₄: X₄ {O(n)}
t₅, X₁: X₄ {O(n)}
t₅, X₂: 2⋅X₄ {O(n)}
t₅, X₃: 4⋅X₄+X₃ {O(n)}
t₅, X₄: X₄ {O(n)}
t₆, X₁: X₄ {O(n)}
t₆, X₂: 2⋅X₄ {O(n)}
t₆, X₃: 4⋅X₄+X₃ {O(n)}
t₆, X₄: X₄ {O(n)}
t₇, X₁: X₄ {O(n)}
t₇, X₂: 2⋅X₄ {O(n)}
t₇, X₃: 4⋅X₄+X₃ {O(n)}
t₇, X₄: X₄ {O(n)}
t₈, X₁: X₄ {O(n)}
t₈, X₂: 2⋅X₄ {O(n)}
t₈, X₃: 0 {O(1)}
t₈, X₄: X₄ {O(n)}
t₉, X₁: X₄ {O(n)}
t₉, X₂: 2⋅X₄ {O(n)}
t₉, X₃: 2⋅X₄ {O(n)}
t₉, X₄: X₄ {O(n)}
t₁₀, X₁: X₄ {O(n)}
t₁₀, X₂: 2⋅X₄ {O(n)}
t₁₀, X₃: 0 {O(1)}
t₁₀, X₄: X₄ {O(n)}
t₁₁, X₁: X₄ {O(n)}
t₁₁, X₂: 2⋅X₄ {O(n)}
t₁₁, X₃: 2⋅X₄ {O(n)}
t₁₁, X₄: X₄ {O(n)}
t₁₂, X₁: X₄ {O(n)}
t₁₂, X₂: 2⋅X₄ {O(n)}
t₁₂, X₃: 4⋅X₄ {O(n)}
t₁₂, X₄: X₄ {O(n)}
t₁₃, X₁: 1 {O(1)}
t₁₃, X₂: 8⋅X₄ {O(n)}
t₁₃, X₃: 4⋅X₄ {O(n)}
t₁₃, X₄: 4⋅X₄ {O(n)}
t₁₄, X₁: X₁+1 {O(n)}
t₁₄, X₂: 8⋅X₄+X₂ {O(n)}
t₁₄, X₃: 4⋅X₄+X₃ {O(n)}
t₁₄, X₄: 5⋅X₄ {O(n)}