Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7, l8
Transitions:
t₀: l0(X₀, X₁, X₂) → l2(X₀, X₁, X₂)
t₃: l1(X₀, X₁, X₂) → l4(X₀, X₁, X₂)
t₁: l2(X₀, X₁, X₂) → l3(X₀, X₁, X₂)
t₂: l3(X₀, X₁, X₂) → l1(X₀, X₁, X₂)
t₆: l4(X₀, X₁, X₂) → l5(X₂, X₁, X₂) :|: 0 < X₁ ∧ X₁ < X₂
t₄: l4(X₀, X₁, X₂) → l6(X₀, X₁, X₂) :|: X₁ ≤ 0
t₅: l4(X₀, X₁, X₂) → l6(X₀, X₁, X₂) :|: X₂ ≤ X₁
t₈: l5(X₀, X₁, X₂) → l6(X₀, X₁, X₂) :|: X₀ ≤ 0
t₇: l5(X₀, X₁, X₂) → l7(X₀, X₁, X₂) :|: 0 < X₀
t₁₁: l6(X₀, X₁, X₂) → l8(X₀, X₁, X₂)
t₉: l7(X₀, X₁, X₂) → l5(X₀-1, X₁, X₂) :|: X₀ < X₁
t₁₀: l7(X₀, X₁, X₂) → l5(X₀-X₁, X₁, X₂) :|: X₁ ≤ X₀

Preprocessing

Found invariant 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l7

Found invariant 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ for location l5

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7, l8
Transitions:
t₀: l0(X₀, X₁, X₂) → l2(X₀, X₁, X₂)
t₃: l1(X₀, X₁, X₂) → l4(X₀, X₁, X₂)
t₁: l2(X₀, X₁, X₂) → l3(X₀, X₁, X₂)
t₂: l3(X₀, X₁, X₂) → l1(X₀, X₁, X₂)
t₆: l4(X₀, X₁, X₂) → l5(X₂, X₁, X₂) :|: 0 < X₁ ∧ X₁ < X₂
t₄: l4(X₀, X₁, X₂) → l6(X₀, X₁, X₂) :|: X₁ ≤ 0
t₅: l4(X₀, X₁, X₂) → l6(X₀, X₁, X₂) :|: X₂ ≤ X₁
t₈: l5(X₀, X₁, X₂) → l6(X₀, X₁, X₂) :|: X₀ ≤ 0 ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁
t₇: l5(X₀, X₁, X₂) → l7(X₀, X₁, X₂) :|: 0 < X₀ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁
t₁₁: l6(X₀, X₁, X₂) → l8(X₀, X₁, X₂)
t₉: l7(X₀, X₁, X₂) → l5(X₀-1, X₁, X₂) :|: X₀ < X₁ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₁₀: l7(X₀, X₁, X₂) → l5(X₀-X₁, X₁, X₂) :|: X₁ ≤ X₀ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀

MPRF for transition t₇: l5(X₀, X₁, X₂) → l7(X₀, X₁, X₂) :|: 0 < X₀ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ of depth 1:

new bound:

X₂ {O(n)}

MPRF:

l7 [X₀-1 ]
l5 [X₀ ]

MPRF for transition t₉: l7(X₀, X₁, X₂) → l5(X₀-1, X₁, X₂) :|: X₀ < X₁ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₂ {O(n)}

MPRF:

l7 [X₀ ]
l5 [X₀ ]

MPRF for transition t₁₀: l7(X₀, X₁, X₂) → l5(X₀-X₁, X₁, X₂) :|: X₁ ≤ X₀ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₂ {O(n)}

MPRF:

l7 [X₀ ]
l5 [X₀ ]

All Bounds

Timebounds

Overall timebound:3⋅X₂+9 {O(n)}
t₀: 1 {O(1)}
t₃: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₄: 1 {O(1)}
t₅: 1 {O(1)}
t₆: 1 {O(1)}
t₇: X₂ {O(n)}
t₈: 1 {O(1)}
t₁₁: 1 {O(1)}
t₉: X₂ {O(n)}
t₁₀: X₂ {O(n)}

Costbounds

Overall costbound: 3⋅X₂+9 {O(n)}
t₀: 1 {O(1)}
t₃: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₄: 1 {O(1)}
t₅: 1 {O(1)}
t₆: 1 {O(1)}
t₇: X₂ {O(n)}
t₈: 1 {O(1)}
t₁₁: 1 {O(1)}
t₉: X₂ {O(n)}
t₁₀: X₂ {O(n)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₃, X₀: X₀ {O(n)}
t₃, X₁: X₁ {O(n)}
t₃, X₂: X₂ {O(n)}
t₁, X₀: X₀ {O(n)}
t₁, X₁: X₁ {O(n)}
t₁, X₂: X₂ {O(n)}
t₂, X₀: X₀ {O(n)}
t₂, X₁: X₁ {O(n)}
t₂, X₂: X₂ {O(n)}
t₄, X₀: X₀ {O(n)}
t₄, X₁: X₁ {O(n)}
t₄, X₂: X₂ {O(n)}
t₅, X₀: X₀ {O(n)}
t₅, X₁: X₁ {O(n)}
t₅, X₂: X₂ {O(n)}
t₆, X₀: X₂ {O(n)}
t₆, X₁: X₁ {O(n)}
t₆, X₂: X₂ {O(n)}
t₇, X₀: X₂ {O(n)}
t₇, X₁: X₁ {O(n)}
t₇, X₂: X₂ {O(n)}
t₈, X₀: 2⋅X₂ {O(n)}
t₈, X₁: 2⋅X₁ {O(n)}
t₈, X₂: 2⋅X₂ {O(n)}
t₁₁, X₀: 2⋅X₀+2⋅X₂ {O(n)}
t₁₁, X₁: 4⋅X₁ {O(n)}
t₁₁, X₂: 4⋅X₂ {O(n)}
t₉, X₀: X₂ {O(n)}
t₉, X₁: X₁ {O(n)}
t₉, X₂: X₂ {O(n)}
t₁₀, X₀: X₂ {O(n)}
t₁₀, X₁: X₁ {O(n)}
t₁₀, X₂: X₂ {O(n)}