Initial Problem

Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1, l2
Transitions:
t₀: l0(X₀, X₁) → l1(X₀, 2)
t₁: l1(X₀, X₁) → l1(X₀-1, (X₁)²) :|: 1 ≤ X₀
t₂: l1(X₀, X₁) → l2(X₀, X₁) :|: X₀ ≤ 0
t₃: l2(X₀, X₁) → l2(X₀, X₁-1) :|: 1 ≤ X₁

Preprocessing

Found invariant 0 ≤ X₁ for location l1

Found invariant 0 ≤ X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 for location l2

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1, l2
Transitions:
t₀: l0(X₀, X₁) → l1(X₀, 2)
t₁: l1(X₀, X₁) → l1(X₀-1, (X₁)²) :|: 1 ≤ X₀ ∧ 0 ≤ X₁
t₂: l1(X₀, X₁) → l2(X₀, X₁) :|: X₀ ≤ 0 ∧ 0 ≤ X₁
t₃: l2(X₀, X₁) → l2(X₀, X₁-1) :|: 1 ≤ X₁ ∧ X₀ ≤ 0 ∧ X₀ ≤ X₁ ∧ 0 ≤ X₁

MPRF for transition t₁: l1(X₀, X₁) → l1(X₀-1, Temp_Int₃₄) :|: 1 ≤ X₀ ∧ 0 ≤ Temp_Int₃₄ ∧ 0 ≤ X₁ of depth 1:

new bound:

X₀ {O(n)}

• l1: [X₀]

Found invariant 0 ≤ X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 for location l2_v1

Found invariant 0 ≤ X₁ for location l1

Found invariant 0 ≤ X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 for location l2

All Bounds

Timebounds

Overall timebound:inf {Infinity}
t₀: 1 {O(1)}
t₁: X₀ {O(n)}
t₂: 1 {O(1)}
t₃: inf {Infinity}

Costbounds

Overall costbound: inf {Infinity}
t₀: 1 {O(1)}
t₁: X₀ {O(n)}
t₂: 1 {O(1)}
t₃: inf {Infinity}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: 2 {O(1)}
t₁, X₀: X₀ {O(n)}
t₂, X₀: 2⋅X₀ {O(n)}
t₃, X₀: 2⋅X₀ {O(n)}