Initial Problem

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

Preprocessing

Found invariant 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l2

Found invariant 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l1

Found invariant 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l3

Problem after Preprocessing

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

MPRF for transition t₈: l1(X₀, X₁, X₂) → l2(X₀, X₁+1, X₂-1) :|: 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₀ {O(n)}

MPRF:

l1 [X₂ ]
l3 [X₂ ]
l2 [X₂ ]

MPRF for transition t₄: l2(X₀, X₁, X₂) → l3(X₀, X₁, X₂) :|: 1 ≤ X₂ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

2⋅X₀+1 {O(n)}

MPRF:

l1 [X₁+2⋅X₂ ]
l3 [X₁+2⋅X₂ ]
l2 [X₁+2⋅X₂+1 ]

MPRF for transition t₆: l3(X₀, X₁, X₂) → l1(X₀, X₁, X₂) :|: X₁+1 ≤ X₀ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₀ {O(n)}

MPRF:

l1 [X₂-1 ]
l3 [X₂ ]
l2 [X₂ ]

MPRF for transition t₇: l3(X₀, X₁, X₂) → l2(X₀, 0, X₂) :|: X₀ ≤ X₁ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₀ {O(n)}

MPRF:

l1 [X₁+X₂ ]
l3 [X₁+X₂ ]
l2 [X₁+X₂ ]

All Bounds

Timebounds

Overall timebound:5⋅X₀+7 {O(n)}
t₀: 1 {O(1)}
t₈: X₀ {O(n)}
t₄: 2⋅X₀+1 {O(n)}
t₅: 1 {O(1)}
t₆: X₀ {O(n)}
t₇: X₀ {O(n)}
t₉: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 1 {O(1)}

Costbounds

Overall costbound: 5⋅X₀+7 {O(n)}
t₀: 1 {O(1)}
t₈: X₀ {O(n)}
t₄: 2⋅X₀+1 {O(n)}
t₅: 1 {O(1)}
t₆: X₀ {O(n)}
t₇: X₀ {O(n)}
t₉: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 1 {O(1)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₈, X₀: X₁ {O(n)}
t₈, X₁: X₀ {O(n)}
t₈, X₂: X₀ {O(n)}
t₄, X₀: X₁ {O(n)}
t₄, X₁: X₀ {O(n)}
t₄, X₂: X₀ {O(n)}
t₅, X₀: 2⋅X₁ {O(n)}
t₅, X₁: X₀ {O(n)}
t₅, X₂: 0 {O(1)}
t₆, X₀: X₁ {O(n)}
t₆, X₁: X₀ {O(n)}
t₆, X₂: X₀ {O(n)}
t₇, X₀: X₁ {O(n)}
t₇, X₁: 0 {O(1)}
t₇, X₂: X₀ {O(n)}
t₉, X₀: 2⋅X₀+2⋅X₁ {O(n)}
t₉, X₁: 2⋅X₁+X₀ {O(n)}
t₉, X₂: 2⋅X₂ {O(n)}
t₁, X₀: X₁ {O(n)}
t₁, X₁: 0 {O(1)}
t₁, X₂: X₀ {O(n)}
t₂, X₀: X₀ {O(n)}
t₂, X₁: X₁ {O(n)}
t₂, X₂: X₂ {O(n)}
t₃, X₀: X₀ {O(n)}
t₃, X₁: X₁ {O(n)}
t₃, X₂: X₂ {O(n)}