Initial Problem

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

Preprocessing

Found invariant 0 ≤ X₀ for location l1

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

Found invariant X₃ ≤ X₂ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ X₁ ≤ X₃ ∧ 1 ≤ X₀+X₃ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀ for location l3

Problem after Preprocessing

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

MPRF for transition t₁: l1(X₀, X₁, X₂, X₃) → l1(1+X₀, X₁-1, X₂, X₃) :|: 1 ≤ X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₁ {O(n)}

• l1: [X₁]

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

new bound:

X₁+1 {O(n)}

• l2: [1+X₂]
• l3: [X₂]

MPRF for transition t₅: l3(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂-1, X₃) :|: 1 ≤ X₂ ∧ X₃ ≤ 0 ∧ 1 ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀+X₃ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₂+X₃ ∧ 2 ≤ X₀+X₂ ∧ X₂ ≤ X₀ ∧ X₃ ≤ X₀ ∧ X₁ ≤ 0 ∧ X₁ ≤ X₃ ∧ X₃ ≤ X₂ ∧ 0 ≤ X₃ of depth 1:

new bound:

X₁ {O(n)}

• l2: [X₂]
• l3: [X₂]

TWN: t₄: l3→l3

Show Graph

Termination: true
Formula:

TWN - Lifting for [4: l3->l3] of 10⋅X₃+2⋅X₀+2⋅X₁+2⋅X₂+16 {O(n)}

Cut unsatisfiable transition [t₅: l3→l2; t₃₇: l3→l2]

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

Found invariant 0 ≤ X₀ for location l1

Found invariant X₃ ≤ X₂ ∧ X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 1+X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀ for location l3

Found invariant 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ X₁ ≤ X₃ ∧ 1 ≤ X₀+X₃ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀ for location l3_v1

All Bounds

Timebounds

Overall timebound:28⋅X₁⋅X₁+47⋅X₁+19 {O(n^2)}
t₀: 1 {O(1)}
t₁: X₁ {O(n)}
t₂: 1 {O(1)}
t₃: X₁+1 {O(n)}
t₄: 28⋅X₁⋅X₁+44⋅X₁+16 {O(n^2)}
t₅: X₁ {O(n)}

Costbounds

Overall costbound: 28⋅X₁⋅X₁+47⋅X₁+19 {O(n^2)}
t₀: 1 {O(1)}
t₁: X₁ {O(n)}
t₂: 1 {O(1)}
t₃: X₁+1 {O(n)}
t₄: 28⋅X₁⋅X₁+44⋅X₁+16 {O(n^2)}
t₅: X₁ {O(n)}

Sizebounds

t₀, X₀: 0 {O(1)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₀, X₃: X₃ {O(n)}
t₁, X₀: X₁ {O(n)}
t₁, X₁: X₁ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₃ {O(n)}
t₂, X₀: X₁ {O(n)}
t₂, X₁: 2⋅X₁ {O(n)}
t₂, X₂: X₁ {O(n)}
t₂, X₃: 2⋅X₃ {O(n)}
t₃, X₀: X₁ {O(n)}
t₃, X₁: 2⋅X₁ {O(n)}
t₃, X₂: X₁ {O(n)}
t₃, X₃: 2⋅X₁ {O(n)}
t₄, X₀: X₁ {O(n)}
t₄, X₁: 2⋅X₁ {O(n)}
t₄, X₂: X₁ {O(n)}
t₄, X₃: 2⋅X₁ {O(n)}
t₅, X₀: X₁ {O(n)}
t₅, X₁: 2⋅X₁ {O(n)}
t₅, X₂: X₁ {O(n)}
t₅, X₃: 0 {O(1)}