Initial Problem

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

Preprocessing

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

Found invariant X₁ ≤ 0 for location l2

Found invariant 1 ≤ X₁ for location l1

Found invariant X₁ ≤ 1 ∧ X₀+X₁ ≤ 1 ∧ X₀ ≤ 0 for location l3

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1, l2, l3
Transitions:
t₁₃: l0(X₀, X₁) → l1(X₀, X₁) :|: 1 ≤ X₁
t₁₄: l0(X₀, X₁) → l2(X₀, X₁) :|: X₁ ≤ 0
t₁₅: l1(X₀, X₁) → l1(X₀, X₁) :|: 1 ≤ X₁
t₁₆: l2(X₀, X₁) → l2(X₀-1, X₁) :|: 1 ≤ X₀ ∧ X₁ ≤ 0
t₁₇: l2(X₀, X₁) → l3(X₀, X₁) :|: X₀ ≤ 0 ∧ X₁ ≤ 0
t₁₈: l3(X₀, X₁) → l3(X₀, 1) :|: X₁ ≤ 1 ∧ X₀+X₁ ≤ 1 ∧ X₀ ≤ 0

Analysing control-flow refined program

Found invariant X₁ ≤ 0 for location l2

Found invariant 1 ≤ X₁ for location l1

Found invariant X₁ ≤ 1 ∧ X₀+X₁ ≤ 1 ∧ X₀ ≤ 0 for location l3

CFR did not improve the program. Rolling back

CFR did not improve the program. Rolling back

MPRF for transition t₁₆: l2(X₀, X₁) → l2(X₀-1, X₁) :|: 1 ≤ X₀ ∧ X₁ ≤ 0 of depth 1:

new bound:

X₀ {O(n)}

Analysing control-flow refined program

Found invariant X₁ ≤ 0 for location l2

Found invariant 1 ≤ X₁ for location l1

Found invariant X₁ ≤ 1 ∧ X₀+X₁ ≤ 1 ∧ 1 ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 0 for location n_l3___1

Found invariant X₁ ≤ 0 ∧ X₀+X₁ ≤ 0 ∧ X₀ ≤ 0 for location l3

CFR did not improve the program. Rolling back

CFR did not improve the program. Rolling back

All Bounds

Timebounds

Overall timebound:inf {Infinity}
t₁₃: 1 {O(1)}
t₁₄: 1 {O(1)}
t₁₅: inf {Infinity}
t₁₆: X₀ {O(n)}
t₁₇: 1 {O(1)}
t₁₈: inf {Infinity}

Costbounds

Overall costbound: inf {Infinity}
t₁₃: 1 {O(1)}
t₁₄: 1 {O(1)}
t₁₅: inf {Infinity}
t₁₆: X₀ {O(n)}
t₁₇: 1 {O(1)}
t₁₈: inf {Infinity}

Sizebounds

t₁₃, X₀: X₀ {O(n)}
t₁₃, X₁: X₁ {O(n)}
t₁₄, X₀: X₀ {O(n)}
t₁₄, X₁: X₁ {O(n)}
t₁₅, X₀: X₀ {O(n)}
t₁₅, X₁: X₁ {O(n)}
t₁₆, X₀: X₀ {O(n)}
t₁₆, X₁: X₁ {O(n)}
t₁₇, X₀: 2⋅X₀ {O(n)}
t₁₇, X₁: 2⋅X₁ {O(n)}
t₁₈, X₀: 2⋅X₀ {O(n)}
t₁₈, X₁: 1 {O(1)}