Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₀: l0(X₀, X₁, X₂) → l2(X₀, X₁, X₂)
t₂: l1(X₀, X₁, X₂) → l3(X₀, X₁, X₂) :|: X₀ ≤ 10
t₃: l1(X₀, X₁, X₂) → l4(X₀, X₁, X₂) :|: 10 < X₀
t₁: l2(X₀, X₁, X₂) → l1(0, X₁, X₂)
t₄: l3(X₀, X₁, X₂) → l1(X₀+1, X₁, X₂)
t₅: l4(X₀, X₁, X₂) → l5(X₀, X₁, X₂)

Preprocessing

Eliminate variables {X₁,X₂} that do not contribute to the problem

Found invariant 11 ≤ X₀ for location l5

Found invariant 0 ≤ X₀ for location l1

Found invariant 11 ≤ X₀ for location l4

Found invariant X₀ ≤ 10 ∧ 0 ≤ X₀ for location l3

Problem after Preprocessing

Start: l0
Program_Vars: X₀
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₁₁: l0(X₀) → l2(X₀)
t₁₂: l1(X₀) → l3(X₀) :|: X₀ ≤ 10 ∧ 0 ≤ X₀
t₁₃: l1(X₀) → l4(X₀) :|: 10 < X₀ ∧ 0 ≤ X₀
t₁₄: l2(X₀) → l1(0)
t₁₅: l3(X₀) → l1(X₀+1) :|: X₀ ≤ 10 ∧ 0 ≤ X₀
t₁₆: l4(X₀) → l5(X₀) :|: 11 ≤ X₀

MPRF for transition t₁₂: l1(X₀) → l3(X₀) :|: X₀ ≤ 10 ∧ 0 ≤ X₀ of depth 1:

new bound:

11 {O(1)}

MPRF for transition t₁₅: l3(X₀) → l1(X₀+1) :|: X₀ ≤ 10 ∧ 0 ≤ X₀ of depth 1:

new bound:

11 {O(1)}

All Bounds

Timebounds

Overall timebound:26 {O(1)}
t₁₁: 1 {O(1)}
t₁₂: 11 {O(1)}
t₁₃: 1 {O(1)}
t₁₄: 1 {O(1)}
t₁₅: 11 {O(1)}
t₁₆: 1 {O(1)}

Costbounds

Overall costbound: 26 {O(1)}
t₁₁: 1 {O(1)}
t₁₂: 11 {O(1)}
t₁₃: 1 {O(1)}
t₁₄: 1 {O(1)}
t₁₅: 11 {O(1)}
t₁₆: 1 {O(1)}

Sizebounds

t₁₁, X₀: X₀ {O(n)}
t₁₂, X₀: 10 {O(1)}
t₁₃, X₀: 11 {O(1)}
t₁₄, X₀: 0 {O(1)}
t₁₅, X₀: 11 {O(1)}
t₁₆, X₀: 11 {O(1)}