Initial Problem

Start: start
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: eval1, eval2, start
Transitions:
t₀: eval1(X₀, X₁, X₂) → eval2(X₀, X₁, X₂) :|: 1+X₁ ≤ X₀
t₁: eval2(X₀, X₁, X₂) → eval1(X₀, 1+X₁, X₂) :|: 1+X₂ ≤ X₀
t₂: eval2(X₀, X₁, X₂) → eval1(X₀, X₁, 1+X₂) :|: 1+X₂ ≤ X₀
t₃: eval2(X₀, X₁, X₂) → eval1(X₀-1, X₁, X₂) :|: X₀ ≤ X₂
t₄: start(X₀, X₁, X₂) → eval1(X₀, X₁, X₂)

Preprocessing

Found invariant 1+X₁ ≤ X₀ for location eval2

Problem after Preprocessing

Start: start
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: eval1, eval2, start
Transitions:
t₀: eval1(X₀, X₁, X₂) → eval2(X₀, X₁, X₂) :|: 1+X₁ ≤ X₀
t₁: eval2(X₀, X₁, X₂) → eval1(X₀, 1+X₁, X₂) :|: 1+X₂ ≤ X₀ ∧ 1+X₁ ≤ X₀
t₂: eval2(X₀, X₁, X₂) → eval1(X₀, X₁, 1+X₂) :|: 1+X₂ ≤ X₀ ∧ 1+X₁ ≤ X₀
t₃: eval2(X₀, X₁, X₂) → eval1(X₀-1, X₁, X₂) :|: X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀
t₄: start(X₀, X₁, X₂) → eval1(X₀, X₁, X₂)

MPRF for transition t₁: eval2(X₀, X₁, X₂) → eval1(X₀, 1+X₁, X₂) :|: 1+X₂ ≤ X₀ ∧ 1+X₁ ≤ X₀ of depth 1:

new bound:

X₀+X₁ {O(n)}

• eval1: [X₀-X₁]
• eval2: [X₀-X₁]

MPRF for transition t₂: eval2(X₀, X₁, X₂) → eval1(X₀, X₁, 1+X₂) :|: 1+X₂ ≤ X₀ ∧ 1+X₁ ≤ X₀ of depth 1:

new bound:

X₀+X₂ {O(n)}

• eval1: [X₀-X₂]
• eval2: [X₀-X₂]

MPRF for transition t₃: eval2(X₀, X₁, X₂) → eval1(X₀-1, X₁, X₂) :|: X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ of depth 1:

new bound:

X₀+X₁ {O(n)}

• eval1: [X₀-X₁]
• eval2: [X₀-X₁]

knowledge_propagation leads to new time bound 2⋅X₁+3⋅X₀+X₂+1 {O(n)} for transition t₀: eval1(X₀, X₁, X₂) → eval2(X₀, X₁, X₂) :|: 1+X₁ ≤ X₀

All Bounds

Timebounds

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

Costbounds

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

Sizebounds

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