KoAT2 Proof Output

Initial Problem

Start: start0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅
Temp_Vars:
Locations: lbl71, start, start0, stop
Transitions:
t₃: lbl71(X₀, X₁, X₂, X₃, X₄, X₅) → lbl71(X₀, X₁-1, X₂-1, X₃, 1+X₄, X₅) :|: 1+X₃ ≤ X₀+X₂ ∧ 1+X₂ ≤ X₃ ∧ X₁+X₃ ≤ X₀+X₂ ∧ X₃ ≤ X₀+X₂ ∧ X₀+X₂ ≤ X₁+X₃ ∧ X₃+X₅ ≤ X₂+X₄ ∧ X₂+X₄ ≤ X₃+X₅
t₂: lbl71(X₀, X₁, X₂, X₃, X₄, X₅) → stop(X₀, X₁, X₂, X₃, X₄, X₅) :|: 1+X₂ ≤ X₃ ∧ X₃ ≤ X₀+X₂ ∧ X₀+X₂ ≤ X₃ ∧ 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ X₃+X₅ ≤ X₂+X₄ ∧ X₂+X₄ ≤ X₃+X₅
t₁: start(X₀, X₁, X₂, X₃, X₄, X₅) → lbl71(X₀, X₁-1, X₂-1, X₃, 1+X₄, X₅) :|: 1 ≤ X₀ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₃ ≤ X₂ ∧ X₂ ≤ X₃ ∧ X₅ ≤ X₄ ∧ X₄ ≤ X₅
t₀: start(X₀, X₁, X₂, X₃, X₄, X₅) → stop(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₁ ≤ X₀ ∧ X₀ ≤ 0 ∧ X₀ ≤ X₁ ∧ X₃ ≤ X₂ ∧ X₂ ≤ X₃ ∧ X₅ ≤ X₄ ∧ X₄ ≤ X₅
t₄: start0(X₀, X₁, X₂, X₃, X₄, X₅) → start(X₀, X₀, X₃, X₃, X₅, X₅)

Preprocessing

Found invariant X₅ ≤ X₄ ∧ X₄ ≤ X₅ ∧ X₃ ≤ X₂ ∧ X₂ ≤ X₃ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ for location start

Found invariant 1+X₅ ≤ X₄ ∧ 1+X₂ ≤ X₃ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀ for location lbl71

Found invariant X₅ ≤ X₄ ∧ X₂ ≤ X₃ ∧ X₁ ≤ 0 ∧ X₁ ≤ X₀ for location stop

Problem after Preprocessing

Start: start0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅
Temp_Vars:
Locations: lbl71, start, start0, stop
Transitions:
t₃: lbl71(X₀, X₁, X₂, X₃, X₄, X₅) → lbl71(X₀, X₁-1, X₂-1, X₃, 1+X₄, X₅) :|: 1+X₃ ≤ X₀+X₂ ∧ 1+X₂ ≤ X₃ ∧ X₁+X₃ ≤ X₀+X₂ ∧ X₃ ≤ X₀+X₂ ∧ X₀+X₂ ≤ X₁+X₃ ∧ X₃+X₅ ≤ X₂+X₄ ∧ X₂+X₄ ≤ X₃+X₅ ∧ 1 ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 1+X₅ ≤ X₄
t₂: lbl71(X₀, X₁, X₂, X₃, X₄, X₅) → stop(X₀, X₁, X₂, X₃, X₄, X₅) :|: 1+X₂ ≤ X₃ ∧ X₃ ≤ X₀+X₂ ∧ X₀+X₂ ≤ X₃ ∧ 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ X₃+X₅ ≤ X₂+X₄ ∧ X₂+X₄ ≤ X₃+X₅ ∧ 1 ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 1+X₅ ≤ X₄
t₁: start(X₀, X₁, X₂, X₃, X₄, X₅) → lbl71(X₀, X₁-1, X₂-1, X₃, 1+X₄, X₅) :|: 1 ≤ X₀ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₃ ≤ X₂ ∧ X₂ ≤ X₃ ∧ X₅ ≤ X₄ ∧ X₄ ≤ X₅
t₀: start(X₀, X₁, X₂, X₃, X₄, X₅) → stop(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₁ ≤ X₀ ∧ X₀ ≤ 0 ∧ X₀ ≤ X₁ ∧ X₃ ≤ X₂ ∧ X₂ ≤ X₃ ∧ X₅ ≤ X₄ ∧ X₄ ≤ X₅
t₄: start0(X₀, X₁, X₂, X₃, X₄, X₅) → start(X₀, X₀, X₃, X₃, X₅, X₅)

MPRF for transition t₃: lbl71(X₀, X₁, X₂, X₃, X₄, X₅) → lbl71(X₀, X₁-1, X₂-1, X₃, 1+X₄, X₅) :|: 1+X₃ ≤ X₀+X₂ ∧ 1+X₂ ≤ X₃ ∧ X₁+X₃ ≤ X₀+X₂ ∧ X₃ ≤ X₀+X₂ ∧ X₀+X₂ ≤ X₁+X₃ ∧ X₃+X₅ ≤ X₂+X₄ ∧ X₂+X₄ ≤ X₃+X₅ ∧ 1 ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 1+X₅ ≤ X₄ of depth 1:

new bound:

2⋅X₃+X₀+2 {O(n)}

MPRF:

• lbl71: [1+X₀+X₂-X₃]

All Bounds

Timebounds

Overall timebound:2⋅X₃+X₀+6 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 2⋅X₃+X₀+2 {O(n)}
t₄: 1 {O(1)}

Costbounds

Overall costbound: 2⋅X₃+X₀+6 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 2⋅X₃+X₀+2 {O(n)}
t₄: 1 {O(1)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₀ {O(n)}
t₀, X₂: X₃ {O(n)}
t₀, X₃: X₃ {O(n)}
t₀, X₄: X₅ {O(n)}
t₀, X₅: X₅ {O(n)}
t₁, X₀: X₀ {O(n)}
t₁, X₁: X₀ {O(n)}
t₁, X₂: X₃+1 {O(n)}
t₁, X₃: X₃ {O(n)}
t₁, X₄: X₅+1 {O(n)}
t₁, X₅: X₅ {O(n)}
t₂, X₀: 2⋅X₀ {O(n)}
t₂, X₁: 0 {O(1)}
t₂, X₂: 4⋅X₃+X₀+4 {O(n)}
t₂, X₃: 2⋅X₃ {O(n)}
t₂, X₄: 2⋅X₃+2⋅X₅+X₀+4 {O(n)}
t₂, X₅: 2⋅X₅ {O(n)}
t₃, X₀: X₀ {O(n)}
t₃, X₁: X₀ {O(n)}
t₃, X₂: 3⋅X₃+X₀+3 {O(n)}
t₃, X₃: X₃ {O(n)}
t₃, X₄: 2⋅X₃+X₀+X₅+3 {O(n)}
t₃, X₅: X₅ {O(n)}
t₄, X₀: X₀ {O(n)}
t₄, X₁: X₀ {O(n)}
t₄, X₂: X₃ {O(n)}
t₄, X₃: X₃ {O(n)}
t₄, X₄: X₅ {O(n)}
t₄, X₅: X₅ {O(n)}