Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅
Temp_Vars: Y
Locations: l0, l1, l2, l3
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, X₁, X₂, X₃, X₄, X₅)
t₁: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₅, X₅, 2, X₂, X₅, X₅-Y) :|: 1 ≤ Y ∧ Y ≤ X₅
t₅: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁, X₂, X₃, X₄, X₀) :|: X₅ ≤ 0
t₂: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, X₁, X₂, X₃, X₄, X₅)
t₃: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l2(3⋅X₀+2⋅X₁, -5⋅X₀-3⋅X₁, X₂, -2⋅X₃, (X₂)²+3⋅X₄, X₅) :|: 1+(X₃)² ≤ (X₂)⁵+X₄ ∧ 1+X₃ ≤ 0
t₄: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l2(3⋅X₀+2⋅X₁, -5⋅X₀-3⋅X₁, X₂, -2⋅X₃, (X₂)²+3⋅X₄, X₅) :|: 1+(X₃)² ≤ (X₂)⁵+X₄ ∧ 1 ≤ X₃
t₆: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁, X₂, X₃, X₄, X₅-1) :|: 1 ≤ X₅

Preprocessing

Found invariant 1+X₅ ≤ X₄ ∧ 1 ≤ X₄+X₅ ∧ 1 ≤ X₄ ∧ 3 ≤ X₂+X₄ ∧ X₂ ≤ 1+X₄ ∧ X₂ ≤ 2 ∧ 2 ≤ X₂ for location l2

Found invariant X₅ ≤ X₀ for location l3

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅
Temp_Vars: Y
Locations: l0, l1, l2, l3
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, X₁, X₂, X₃, X₄, X₅)
t₁: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₅, X₅, 2, X₂, X₅, X₅-Y) :|: 1 ≤ Y ∧ Y ≤ X₅
t₅: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁, X₂, X₃, X₄, X₀) :|: X₅ ≤ 0
t₂: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₂ ≤ 2 ∧ X₂ ≤ 1+X₄ ∧ 1 ≤ X₄ ∧ 1 ≤ X₄+X₅ ∧ 1+X₅ ≤ X₄ ∧ 2 ≤ X₂ ∧ 3 ≤ X₂+X₄
t₃: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l2(3⋅X₀+2⋅X₁, -5⋅X₀-3⋅X₁, X₂, -2⋅X₃, (X₂)²+3⋅X₄, X₅) :|: 1+(X₃)² ≤ (X₂)⁵+X₄ ∧ 1+X₃ ≤ 0 ∧ X₂ ≤ 2 ∧ X₂ ≤ 1+X₄ ∧ 1 ≤ X₄ ∧ 1 ≤ X₄+X₅ ∧ 1+X₅ ≤ X₄ ∧ 2 ≤ X₂ ∧ 3 ≤ X₂+X₄
t₄: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l2(3⋅X₀+2⋅X₁, -5⋅X₀-3⋅X₁, X₂, -2⋅X₃, (X₂)²+3⋅X₄, X₅) :|: 1+(X₃)² ≤ (X₂)⁵+X₄ ∧ 1 ≤ X₃ ∧ X₂ ≤ 2 ∧ X₂ ≤ 1+X₄ ∧ 1 ≤ X₄ ∧ 1 ≤ X₄+X₅ ∧ 1+X₅ ≤ X₄ ∧ 2 ≤ X₂ ∧ 3 ≤ X₂+X₄
t₆: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁, X₂, X₃, X₄, X₅-1) :|: 1 ≤ X₅ ∧ X₅ ≤ X₀

MPRF for transition t₁: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₅, X₅, 2, X₂, X₅, X₅-Y) :|: 1 ≤ Y ∧ Y ≤ X₅ of depth 1:

new bound:

X₅ {O(n)}

• l1: [X₅]
• l2: [X₅]

TWN: t₃: l2→l2

Show Graph

Termination: true
Formula:

TWN - Lifting for [3: l2->l2; 4: l2->l2] of 4⋅log(X₄)+56⋅log(X₂)+8⋅log(X₅)+97 {O(log(n))}

knowledge_propagation leads to new time bound 24⋅X₅⋅log(X₅)+315⋅X₅ {O(log(n)*n)} for transition t₂: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₂ ≤ 2 ∧ X₂ ≤ 1+X₄ ∧ 1 ≤ X₄ ∧ 1 ≤ X₄+X₅ ∧ 1+X₅ ≤ X₄ ∧ 2 ≤ X₂ ∧ 3 ≤ X₂+X₄

MPRF for transition t₆: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁, X₂, X₃, X₄, X₅-1) :|: 1 ≤ X₅ ∧ X₅ ≤ X₀ of depth 1:

new bound:

146⋅X₅+X₀ {O(n)}

• l3: [X₅]

All Bounds

Timebounds

Overall timebound:48⋅X₅⋅log(X₅)+776⋅X₅+X₀+2 {O(log(n)*n)}
t₀: 1 {O(1)}
t₁: X₅ {O(n)}
t₂: 24⋅X₅⋅log(X₅)+315⋅X₅ {O(log(n)*n)}
t₃: 12⋅X₅⋅log(X₅)+157⋅X₅ {O(log(n)*n)}
t₄: 12⋅X₅⋅log(X₅)+157⋅X₅ {O(log(n)*n)}
t₅: 1 {O(1)}
t₆: 146⋅X₅+X₀ {O(n)}

Costbounds

Overall costbound: 48⋅X₅⋅log(X₅)+776⋅X₅+X₀+2 {O(log(n)*n)}
t₀: 1 {O(1)}
t₁: X₅ {O(n)}
t₂: 24⋅X₅⋅log(X₅)+315⋅X₅ {O(log(n)*n)}
t₃: 12⋅X₅⋅log(X₅)+157⋅X₅ {O(log(n)*n)}
t₄: 12⋅X₅⋅log(X₅)+157⋅X₅ {O(log(n)*n)}
t₅: 1 {O(1)}
t₆: 146⋅X₅+X₀ {O(n)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₀, X₃: X₃ {O(n)}
t₀, X₄: X₄ {O(n)}
t₀, X₅: X₅ {O(n)}
t₁, X₀: 2⋅X₅ {O(n)}
t₁, X₁: 2⋅X₅ {O(n)}
t₁, X₂: 2 {O(1)}
t₁, X₃: X₂+2 {O(n)}
t₁, X₄: 2⋅X₅ {O(n)}
t₁, X₅: X₅ {O(n)}
t₂, X₀: 146⋅X₅ {O(n)}
t₂, X₁: 250⋅X₅ {O(n)}
t₂, X₂: 2 {O(1)}
t₂, X₃: 2⋅2^(12⋅X₅⋅log(X₅))⋅2^(12⋅X₅⋅log(X₅))⋅2^(157⋅X₅)⋅2^(157⋅X₅)⋅X₂+2^(12⋅X₅⋅log(X₅))⋅2^(12⋅X₅⋅log(X₅))⋅2^(157⋅X₅)⋅2^(157⋅X₅)⋅4+X₂+2 {O(EXP)}
t₂, X₅: X₅ {O(n)}
t₃, X₀: 72⋅X₅ {O(n)}
t₃, X₁: 124⋅X₅ {O(n)}
t₃, X₂: 2 {O(1)}
t₃, X₃: 2⋅2^(24⋅X₅⋅log(X₅))⋅2^(314⋅X₅)⋅X₂+2^(24⋅X₅⋅log(X₅))⋅2^(314⋅X₅)⋅4 {O(EXP)}
t₃, X₄: 3^(24⋅X₅⋅log(X₅))⋅3^(314⋅X₅)⋅6⋅X₅+3^(24⋅X₅⋅log(X₅))⋅3^(314⋅X₅)⋅8+4 {O(EXP)}
t₃, X₅: X₅ {O(n)}
t₄, X₀: 72⋅X₅ {O(n)}
t₄, X₁: 124⋅X₅ {O(n)}
t₄, X₂: 2 {O(1)}
t₄, X₃: 2⋅2^(24⋅X₅⋅log(X₅))⋅2^(314⋅X₅)⋅X₂+2^(24⋅X₅⋅log(X₅))⋅2^(314⋅X₅)⋅4 {O(EXP)}
t₄, X₄: 3^(24⋅X₅⋅log(X₅))⋅3^(314⋅X₅)⋅6⋅X₅+3^(24⋅X₅⋅log(X₅))⋅3^(314⋅X₅)⋅8+4 {O(EXP)}
t₄, X₅: X₅ {O(n)}
t₅, X₀: 146⋅X₅+X₀ {O(n)}
t₅, X₁: 250⋅X₅+X₁ {O(n)}
t₅, X₂: X₂+2 {O(n)}
t₅, X₃: 2⋅2^(12⋅X₅⋅log(X₅))⋅2^(12⋅X₅⋅log(X₅))⋅2^(157⋅X₅)⋅2^(157⋅X₅)⋅X₂+2^(12⋅X₅⋅log(X₅))⋅2^(12⋅X₅⋅log(X₅))⋅2^(157⋅X₅)⋅2^(157⋅X₅)⋅4+X₂+X₃+2 {O(EXP)}
t₅, X₅: 146⋅X₅+X₀ {O(n)}
t₆, X₀: 146⋅X₅+X₀ {O(n)}
t₆, X₁: 250⋅X₅+X₁ {O(n)}
t₆, X₂: X₂+2 {O(n)}
t₆, X₃: 2⋅2^(12⋅X₅⋅log(X₅))⋅2^(12⋅X₅⋅log(X₅))⋅2^(157⋅X₅)⋅2^(157⋅X₅)⋅X₂+2^(12⋅X₅⋅log(X₅))⋅2^(12⋅X₅⋅log(X₅))⋅2^(157⋅X₅)⋅2^(157⋅X₅)⋅4+X₂+X₃+2 {O(EXP)}
t₆, X₅: 146⋅X₅+X₀ {O(n)}