Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅
Temp_Vars:
Locations: l0, l1, l2
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₃, X₄, X₅, X₃, X₄, X₅)
t₁: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀+X₂, X₁, X₂-1, X₃, X₄, X₅) :|: 1 ≤ X₂
t₂: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, X₁, X₅, X₃, X₄, X₅) :|: X₂ ≤ 0
t₄: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₃, X₄, X₅, X₃, X₄, X₅-1) :|: 1 ≤ X₅
t₃: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, 3⋅X₁-4⋅X₂, 4⋅X₁-3⋅X₂, 5⋅X₃, 5⋅X₄-(X₀)², X₅) :|: 1 ≤ 2⋅X₀+X₀*X₂ ∧ 2 ≤ (X₁)²

Preprocessing

Found invariant X₂ ≤ 1+X₅ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ for location l1

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅
Temp_Vars:
Locations: l0, l1, l2
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₃, X₄, X₅, X₃, X₄, X₅)
t₁: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀+X₂, X₁, X₂-1, X₃, X₄, X₅) :|: 1 ≤ X₂ ∧ X₂ ≤ 1+X₅ ∧ X₃ ≤ X₀ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄
t₂: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, X₁, X₅, X₃, X₄, X₅) :|: X₂ ≤ 0 ∧ X₂ ≤ 1+X₅ ∧ X₃ ≤ X₀ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄
t₄: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₃, X₄, X₅, X₃, X₄, X₅-1) :|: 1 ≤ X₅
t₃: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, 3⋅X₁-4⋅X₂, 4⋅X₁-3⋅X₂, 5⋅X₃, 5⋅X₄-(X₀)², X₅) :|: 1 ≤ 2⋅X₀+X₀*X₂ ∧ 2 ≤ (X₁)²

MPRF for transition t₄: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₃, X₄, X₅, X₃, X₄, X₅-1) :|: 1 ≤ X₅ of depth 1:

new bound:

X₅ {O(n)}

• l1: [X₅]
• l2: [X₅]

MPRF for transition t₁: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀+X₂, X₁, X₂-1, X₃, X₄, X₅) :|: 1 ≤ X₂ ∧ X₂ ≤ 1+X₅ ∧ X₃ ≤ X₀ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ of depth 1:

new bound:

2⋅X₅⋅X₅+X₅ {O(n^2)}

• l1: [X₂]

MPRF for transition t₂: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, X₁, X₅, X₃, X₄, X₅) :|: X₂ ≤ 0 ∧ X₂ ≤ 1+X₅ ∧ X₃ ≤ X₀ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ of depth 1:

new bound:

X₅+1 {O(n)}

• l1: [1]
• l2: [0]

Found invariant 1 ≤ X₅ ∧ 1 ≤ X₂+X₅ ∧ 1+X₂ ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ 3+X₃ ≤ X₀ ∧ 0 ≤ X₂ for location l1_v2

Found invariant X₅ ≤ 1+X₂ ∧ 0 ≤ X₅ ∧ 0 ≤ X₂+X₅ ∧ X₂ ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₂ for location l1_v1

Found invariant X₅ ≤ X₂ ∧ X₂ ≤ 1+X₅ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ for location l1

All Bounds

Timebounds

Overall timebound:inf {Infinity}
t₀: 1 {O(1)}
t₁: 2⋅X₅⋅X₅+X₅ {O(n^2)}
t₂: X₅+1 {O(n)}
t₃: inf {Infinity}
t₄: X₅ {O(n)}

Costbounds

Overall costbound: inf {Infinity}
t₀: 1 {O(1)}
t₁: 2⋅X₅⋅X₅+X₅ {O(n^2)}
t₂: X₅+1 {O(n)}
t₃: inf {Infinity}
t₄: X₅ {O(n)}

Sizebounds

t₀, X₀: X₃ {O(n)}
t₀, X₁: X₄ {O(n)}
t₀, X₂: X₅ {O(n)}
t₀, X₃: X₃ {O(n)}
t₀, X₄: X₄ {O(n)}
t₀, X₅: X₅ {O(n)}
t₁, X₂: 3⋅X₅ {O(n)}
t₁, X₅: X₅ {O(n)}
t₂, X₂: 2⋅X₅ {O(n)}
t₂, X₅: X₅ {O(n)}
t₃, X₅: X₅ {O(n)}
t₄, X₂: 2⋅X₅ {O(n)}
t₄, X₅: X₅ {O(n)}