Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l2
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l1(0, 1, 1, X₃)
t₁: l1(X₀, X₁, X₂, X₃) → l1(X₀+1, X₁+2, X₂+X₁+2, X₃) :|: X₂ ≤ X₃ ∧ 0 ≤ X₁
t₂: l1(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₃+1 ≤ X₂

Preprocessing

Eliminate variables {X₀} that do not contribute to the problem

Found invariant 1+X₂ ≤ X₁ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ for location l2

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

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1, l2
Transitions:
t₆: l0(X₀, X₁, X₂) → l1(1, 1, X₂)
t₇: l1(X₀, X₁, X₂) → l1(X₀+2, X₁+X₀+2, X₂) :|: X₁ ≤ X₂ ∧ 0 ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀
t₈: l1(X₀, X₁, X₂) → l2(X₀, X₁, X₂) :|: X₂+1 ≤ X₁ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀

MPRF for transition t₇: l1(X₀, X₁, X₂) → l1(X₀+2, X₁+X₀+2, X₂) :|: X₁ ≤ X₂ ∧ 0 ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₂+2 {O(n)}

All Bounds

Timebounds

Overall timebound:X₂+4 {O(n)}
t₆: 1 {O(1)}
t₇: X₂+2 {O(n)}
t₈: 1 {O(1)}

Costbounds

Overall costbound: X₂+4 {O(n)}
t₆: 1 {O(1)}
t₇: X₂+2 {O(n)}
t₈: 1 {O(1)}

Sizebounds

t₆, X₀: 1 {O(1)}
t₆, X₁: 1 {O(1)}
t₆, X₂: X₂ {O(n)}
t₇, X₀: 2⋅X₂+5 {O(n)}
t₇, X₁: 2^(X₂+2)⋅3+2^(X₂+2)⋅X₂ {O(EXP)}
t₇, X₂: X₂ {O(n)}
t₈, X₀: 2⋅X₂+6 {O(n)}
t₈, X₁: 2^(X₂+2)⋅3+2^(X₂+2)⋅X₂+1 {O(EXP)}
t₈, X₂: 2⋅X₂ {O(n)}