Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars: D
Locations: l0, l1, l2
Transitions:
t₃: l0(X₀, X₁, X₂) → l1(X₀, X₁, X₂)
t₀: l1(X₀, X₁, X₂) → l1(1+X₀, 1+X₁, X₂) :|: X₀ ≤ 1
t₁: l1(X₀, X₁, X₂) → l1(1+X₀, 1+X₁, X₂) :|: X₁ ≤ 2 ∧ 2 ≤ X₀
t₂: l1(X₀, X₁, X₂) → l2(X₀, X₁, D) :|: 3 ≤ X₁ ∧ 2 ≤ X₀

Preprocessing

Eliminate variables {D,X₂} that do not contribute to the problem

Found invariant 3 ≤ X₁ ∧ 5 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location l2

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1, l2
Transitions:
t₁₁: l0(X₀, X₁) → l1(X₀, X₁)
t₁₂: l1(X₀, X₁) → l1(1+X₀, 1+X₁) :|: X₀ ≤ 1
t₁₃: l1(X₀, X₁) → l1(1+X₀, 1+X₁) :|: X₁ ≤ 2 ∧ 2 ≤ X₀
t₁₄: l1(X₀, X₁) → l2(X₀, X₁) :|: 3 ≤ X₁ ∧ 2 ≤ X₀

MPRF for transition t₁₂: l1(X₀, X₁) → l1(1+X₀, 1+X₁) :|: X₀ ≤ 1 of depth 1:

new bound:

X₀+2 {O(n)}

MPRF:

l1 [2-X₀ ]

MPRF for transition t₁₃: l1(X₀, X₁) → l1(1+X₀, 1+X₁) :|: X₁ ≤ 2 ∧ 2 ≤ X₀ of depth 1:

new bound:

X₁+3 {O(n)}

MPRF:

l1 [3-X₁ ]

All Bounds

Timebounds

Overall timebound:X₀+X₁+7 {O(n)}
t₁₁: 1 {O(1)}
t₁₂: X₀+2 {O(n)}
t₁₃: X₁+3 {O(n)}
t₁₄: 1 {O(1)}

Costbounds

Overall costbound: X₀+X₁+7 {O(n)}
t₁₁: 1 {O(1)}
t₁₂: X₀+2 {O(n)}
t₁₃: X₁+3 {O(n)}
t₁₄: 1 {O(1)}

Sizebounds

t₁₁, X₀: X₀ {O(n)}
t₁₁, X₁: X₁ {O(n)}
t₁₂, X₀: 2⋅X₀+2 {O(n)}
t₁₂, X₁: X₀+X₁+2 {O(n)}
t₁₃, X₀: 3⋅X₀+X₁+5 {O(n)}
t₁₃, X₁: 3⋅X₁+X₀+5 {O(n)}
t₁₄, X₀: 6⋅X₀+X₁+7 {O(n)}
t₁₄, X₁: 2⋅X₀+5⋅X₁+7 {O(n)}