Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1, l2
Transitions:
t₄: l0(X₀, X₁, X₂) → l2(X₀, X₁, X₂)
t₁: l1(X₀, X₁, X₂) → l2(X₀, X₁+1, X₂) :|: X₂+1 ≤ X₀
t₂: l1(X₀, X₁, X₂) → l2(X₀, X₁, X₂+1) :|: X₂+1 ≤ X₀
t₃: l1(X₀, X₁, X₂) → l2(X₀-1, X₁, X₂) :|: X₀ ≤ X₂
t₀: l2(X₀, X₁, X₂) → l1(X₀, X₁, X₂) :|: X₁+1 ≤ X₀

Preprocessing

Found invariant 1+X₁ ≤ X₀ for location l1

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1, l2
Transitions:
t₄: l0(X₀, X₁, X₂) → l2(X₀, X₁, X₂)
t₁: l1(X₀, X₁, X₂) → l2(X₀, X₁+1, X₂) :|: X₂+1 ≤ X₀ ∧ 1+X₁ ≤ X₀
t₂: l1(X₀, X₁, X₂) → l2(X₀, X₁, X₂+1) :|: X₂+1 ≤ X₀ ∧ 1+X₁ ≤ X₀
t₃: l1(X₀, X₁, X₂) → l2(X₀-1, X₁, X₂) :|: X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀
t₀: l2(X₀, X₁, X₂) → l1(X₀, X₁, X₂) :|: X₁+1 ≤ X₀

MPRF for transition t₁: l1(X₀, X₁, X₂) → l2(X₀, X₁+1, X₂) :|: X₂+1 ≤ X₀ ∧ 1+X₁ ≤ X₀ of depth 1:

new bound:

X₀+X₁ {O(n)}

MPRF:

l2 [X₀-X₁ ]
l1 [X₀-X₁ ]

MPRF for transition t₂: l1(X₀, X₁, X₂) → l2(X₀, X₁, X₂+1) :|: X₂+1 ≤ X₀ ∧ 1+X₁ ≤ X₀ of depth 1:

new bound:

X₀+X₂ {O(n)}

MPRF:

l2 [X₀-X₂ ]
l1 [X₀-X₂ ]

MPRF for transition t₃: l1(X₀, X₁, X₂) → l2(X₀-1, X₁, X₂) :|: X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ of depth 1:

new bound:

X₀+X₁ {O(n)}

MPRF:

l2 [X₀-X₁ ]
l1 [X₀-X₁ ]

knowledge_propagation leads to new time bound 2⋅X₁+3⋅X₀+X₂+1 {O(n)} for transition t₀: l2(X₀, X₁, X₂) → l1(X₀, X₁, X₂) :|: X₁+1 ≤ X₀

All Bounds

Timebounds

Overall timebound:2⋅X₂+4⋅X₁+6⋅X₀+2 {O(n)}
t₄: 1 {O(1)}
t₁: X₀+X₁ {O(n)}
t₂: X₀+X₂ {O(n)}
t₃: X₀+X₁ {O(n)}
t₀: 2⋅X₁+3⋅X₀+X₂+1 {O(n)}

Costbounds

Overall costbound: 2⋅X₂+4⋅X₁+6⋅X₀+2 {O(n)}
t₄: 1 {O(1)}
t₁: X₀+X₁ {O(n)}
t₂: X₀+X₂ {O(n)}
t₃: X₀+X₁ {O(n)}
t₀: 2⋅X₁+3⋅X₀+X₂+1 {O(n)}

Sizebounds

t₄, X₀: X₀ {O(n)}
t₄, X₁: X₁ {O(n)}
t₄, X₂: X₂ {O(n)}
t₁, X₀: 2⋅X₀+X₁ {O(n)}
t₁, X₁: 2⋅X₁+X₀ {O(n)}
t₁, X₂: 2⋅X₂+X₀ {O(n)}
t₂, X₀: 2⋅X₀+X₁ {O(n)}
t₂, X₁: 2⋅X₁+X₀ {O(n)}
t₂, X₂: 2⋅X₂+X₀ {O(n)}
t₃, X₀: 2⋅X₀+X₁ {O(n)}
t₃, X₁: 2⋅X₁+X₀ {O(n)}
t₃, X₂: 2⋅X₂+X₀ {O(n)}
t₀, X₀: 2⋅X₀+X₁ {O(n)}
t₀, X₁: 2⋅X₁+X₀ {O(n)}
t₀, X₂: 2⋅X₂+X₀ {O(n)}