Initial Problem

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

Preprocessing

Found invariant X₄ ≤ X₂ ∧ X₂ ≤ X₄ ∧ X₃ ≤ 5 ∧ 0 ≤ 5+X₃ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ for location l2

Found invariant 0 ≤ 5+X₃ ∧ 0 ≤ 4+X₀+X₃ ∧ 1 ≤ X₀ for location l3

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars:
Locations: l0, l1, l2, l3
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁, X₂, X₃, X₄)
t₂: l1(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₀, X₄, X₃, X₄) :|: 0 ≤ 5+X₃ ∧ X₃ ≤ 5
t₁: l1(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₀, X₄, X₃, X₄) :|: 1 ≤ X₀ ∧ 1 ≤ X₃
t₃: l2(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₀, X₄, X₃, X₄) :|: 1 ≤ X₀ ∧ 0 ≤ 5+X₃ ∧ X₃ ≤ 5 ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₄ ≤ X₂ ∧ X₂ ≤ X₄
t₆: l3(X₀, X₁, X₂, X₃, X₄) → l1(X₀-1, X₁, X₂, X₃, X₄) :|: 0 ≤ 5+X₃ ∧ 0 ≤ 4+X₀+X₃ ∧ 1 ≤ X₀
t₄: l3(X₀, X₁, X₂, X₃, X₄) → l3(X₀, -2⋅X₁, 3⋅X₂-2⋅(X₃)³, X₃, X₄) :|: 1+X₁ ≤ 0 ∧ 1+(X₁)²+(X₃)⁵ ≤ X₂ ∧ 0 ≤ 5+X₃ ∧ 0 ≤ 4+X₀+X₃ ∧ 1 ≤ X₀
t₅: l3(X₀, X₁, X₂, X₃, X₄) → l3(X₀, -2⋅X₁, 3⋅X₂-2⋅(X₃)³, X₃, X₄) :|: 1 ≤ X₁ ∧ 1+(X₁)²+(X₃)⁵ ≤ X₂ ∧ 0 ≤ 5+X₃ ∧ 0 ≤ 4+X₀+X₃ ∧ 1 ≤ X₀

MPRF for transition t₁: l1(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₀, X₄, X₃, X₄) :|: 1 ≤ X₀ ∧ 1 ≤ X₃ of depth 1:

new bound:

X₀ {O(n)}

• l1: [X₀]
• l2: [X₀-1]
• l3: [X₀-1]

MPRF for transition t₃: l2(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₀, X₄, X₃, X₄) :|: 1 ≤ X₀ ∧ 0 ≤ 5+X₃ ∧ X₃ ≤ 5 ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₄ ≤ X₂ ∧ X₂ ≤ X₄ of depth 1:

new bound:

X₀ {O(n)}

• l1: [X₀]
• l2: [X₀]
• l3: [X₀-1]

MPRF for transition t₆: l3(X₀, X₁, X₂, X₃, X₄) → l1(X₀-1, X₁, X₂, X₃, X₄) :|: 0 ≤ 5+X₃ ∧ 0 ≤ 4+X₀+X₃ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₀ {O(n)}

• l1: [X₀]
• l2: [X₀]
• l3: [X₀]

TWN: t₄: l3→l3

Show Graph

Termination: true
Formula:

Termination: true
Formula:

TWN - Lifting for [4: l3->l3; 5: l3->l3] of 32⋅log(X₃)+4⋅log(X₂)+29 {O(log(n))}

TWN - Lifting for [4: l3->l3; 5: l3->l3] of 32⋅log(X₃)+4⋅log(X₂)+29 {O(log(n))}

knowledge_propagation leads to new time bound X₀+1 {O(n)} for transition t₂: l1(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₀, X₄, X₃, X₄) :|: 0 ≤ 5+X₃ ∧ X₃ ≤ 5

All Bounds

Timebounds

Overall timebound:16⋅X₀⋅log(X₄)+64⋅X₀⋅log(X₃)+512⋅X₀+2 {O(log(n)*n)}
t₀: 1 {O(1)}
t₁: X₀ {O(n)}
t₂: X₀+1 {O(n)}
t₃: X₀ {O(n)}
t₄: 32⋅X₀⋅log(X₃)+8⋅X₀⋅log(X₄)+254⋅X₀ {O(log(n)*n)}
t₅: 32⋅X₀⋅log(X₃)+8⋅X₀⋅log(X₄)+254⋅X₀ {O(log(n)*n)}
t₆: X₀ {O(n)}

Costbounds

Overall costbound: 16⋅X₀⋅log(X₄)+64⋅X₀⋅log(X₃)+512⋅X₀+2 {O(log(n)*n)}
t₀: 1 {O(1)}
t₁: X₀ {O(n)}
t₂: X₀+1 {O(n)}
t₃: X₀ {O(n)}
t₄: 32⋅X₀⋅log(X₃)+8⋅X₀⋅log(X₄)+254⋅X₀ {O(log(n)*n)}
t₅: 32⋅X₀⋅log(X₃)+8⋅X₀⋅log(X₄)+254⋅X₀ {O(log(n)*n)}
t₆: 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)}
t₁, X₀: X₀ {O(n)}
t₁, X₁: 2⋅X₀ {O(n)}
t₁, X₂: 2⋅X₄ {O(n)}
t₁, X₃: X₃+5 {O(n)}
t₁, X₄: X₄ {O(n)}
t₂, X₀: X₀ {O(n)}
t₂, X₁: 2⋅X₀ {O(n)}
t₂, X₂: 2⋅X₄ {O(n)}
t₂, X₃: 5 {O(1)}
t₂, X₄: X₄ {O(n)}
t₃, X₀: X₀ {O(n)}
t₃, X₁: X₀ {O(n)}
t₃, X₂: X₄ {O(n)}
t₃, X₃: 5 {O(1)}
t₃, X₄: X₄ {O(n)}
t₄, X₀: X₀ {O(n)}
t₄, X₁: 2^(254⋅X₀)⋅2^(254⋅X₀)⋅2^(32⋅X₀⋅log(X₃))⋅2^(32⋅X₀⋅log(X₃))⋅2^(8⋅X₀⋅log(X₄))⋅2^(8⋅X₀⋅log(X₄))⋅3⋅X₀ {O(EXP)}
t₄, X₂: 225⋅3^(16⋅X₀⋅log(X₄))⋅3^(192⋅X₀)⋅3^(508⋅X₀)⋅3^(64⋅X₀⋅log(X₃))⋅X₃+3⋅3^(16⋅X₀⋅log(X₄))⋅3^(192⋅X₀)⋅3^(508⋅X₀)⋅3^(64⋅X₀⋅log(X₃))⋅X₃⋅X₃⋅X₃+3⋅3^(16⋅X₀⋅log(X₄))⋅3^(192⋅X₀)⋅3^(508⋅X₀)⋅X₄+375⋅3^(16⋅X₀⋅log(X₄))⋅3^(192⋅X₀)⋅3^(508⋅X₀)+375⋅3^(16⋅X₀⋅log(X₄))⋅3^(192⋅X₀)⋅3^(508⋅X₀)⋅3^(64⋅X₀⋅log(X₃))+3^(16⋅X₀⋅log(X₄))⋅3^(192⋅X₀)⋅3^(508⋅X₀)⋅3^(64⋅X₀⋅log(X₃))⋅45⋅X₃⋅X₃+3^(16⋅X₀⋅log(X₄))⋅3^(192⋅X₀)⋅3^(508⋅X₀)⋅3^(64⋅X₀⋅log(X₃))⋅6⋅X₄+X₃⋅X₃⋅X₃+15⋅X₃⋅X₃+75⋅X₃+250 {O(EXP)}
t₄, X₃: X₃+5 {O(n)}
t₄, X₄: X₄ {O(n)}
t₅, X₀: X₀ {O(n)}
t₅, X₁: 2^(254⋅X₀)⋅2^(254⋅X₀)⋅2^(32⋅X₀⋅log(X₃))⋅2^(32⋅X₀⋅log(X₃))⋅2^(8⋅X₀⋅log(X₄))⋅2^(8⋅X₀⋅log(X₄))⋅3⋅X₀ {O(EXP)}
t₅, X₂: 225⋅3^(16⋅X₀⋅log(X₄))⋅3^(192⋅X₀)⋅3^(508⋅X₀)⋅3^(64⋅X₀⋅log(X₃))⋅X₃+3⋅3^(16⋅X₀⋅log(X₄))⋅3^(192⋅X₀)⋅3^(508⋅X₀)⋅3^(64⋅X₀⋅log(X₃))⋅X₃⋅X₃⋅X₃+3⋅3^(16⋅X₀⋅log(X₄))⋅3^(192⋅X₀)⋅3^(508⋅X₀)⋅X₄+375⋅3^(16⋅X₀⋅log(X₄))⋅3^(192⋅X₀)⋅3^(508⋅X₀)+375⋅3^(16⋅X₀⋅log(X₄))⋅3^(192⋅X₀)⋅3^(508⋅X₀)⋅3^(64⋅X₀⋅log(X₃))+3^(16⋅X₀⋅log(X₄))⋅3^(192⋅X₀)⋅3^(508⋅X₀)⋅3^(64⋅X₀⋅log(X₃))⋅45⋅X₃⋅X₃+3^(16⋅X₀⋅log(X₄))⋅3^(192⋅X₀)⋅3^(508⋅X₀)⋅3^(64⋅X₀⋅log(X₃))⋅6⋅X₄+X₃⋅X₃⋅X₃+15⋅X₃⋅X₃+75⋅X₃+250 {O(EXP)}
t₅, X₃: X₃+5 {O(n)}
t₅, X₄: X₄ {O(n)}
t₆, X₀: X₀ {O(n)}
t₆, X₁: 2^(254⋅X₀)⋅2^(254⋅X₀)⋅2^(32⋅X₀⋅log(X₃))⋅2^(32⋅X₀⋅log(X₃))⋅2^(8⋅X₀⋅log(X₄))⋅2^(8⋅X₀⋅log(X₄))⋅6⋅X₀+3⋅X₀ {O(EXP)}
t₆, X₃: X₃+5 {O(n)}
t₆, X₄: X₄ {O(n)}