Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆
Temp_Vars:
Locations: l0, l1, l2, l3, l5
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l1(X₀, X₁, X₂, X₃, X₀, 0, 0)
t₁: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l2(X₀, X₁, X₂, X₃, X₄-1, X₁+X₂, (X₄)²+X₆) :|: 1 ≤ X₄
t₄: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l1(X₀, X₁, X₂, X₁, X₄, X₅, X₆)
t₂: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l3(X₀, X₁, X₂, X₃, X₄, X₅-1, X₆) :|: 1 ≤ X₅
t₅: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₃: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l2(X₀, X₃, X₀, X₃, X₄, X₅, X₆)
t₆: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆-1) :|: 1 ≤ X₆

Preprocessing

Found invariant 1 ≤ X₆ ∧ 1 ≤ X₄+X₆ ∧ 1+X₄ ≤ X₆ ∧ 2 ≤ X₀+X₆ ∧ 1+X₄ ≤ X₀ ∧ 0 ≤ X₄ ∧ 1 ≤ X₀+X₄ ∧ 1 ≤ X₀ for location l2

Found invariant 0 ≤ X₆ ∧ 0 ≤ X₄+X₆ ∧ 1 ≤ X₀+X₆ ∧ 1+X₄ ≤ X₀ ∧ 0 ≤ X₄ ∧ 1 ≤ X₀+X₄ ∧ 1 ≤ X₀ for location l5

Found invariant 0 ≤ X₆ ∧ X₄ ≤ X₀ for location l1

Found invariant 1 ≤ X₆ ∧ 1 ≤ X₅+X₆ ∧ 1 ≤ X₄+X₆ ∧ 1+X₄ ≤ X₆ ∧ 2 ≤ X₀+X₆ ∧ 0 ≤ X₅ ∧ 0 ≤ X₄+X₅ ∧ 1 ≤ X₀+X₅ ∧ 1+X₄ ≤ X₀ ∧ 0 ≤ X₄ ∧ 1 ≤ X₀+X₄ ∧ 1 ≤ X₀ for location l3

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆
Temp_Vars:
Locations: l0, l1, l2, l3, l5
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l1(X₀, X₁, X₂, X₃, X₀, 0, 0)
t₁: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l2(X₀, X₁, X₂, X₃, X₄-1, X₁+X₂, (X₄)²+X₆) :|: 1 ≤ X₄ ∧ X₄ ≤ X₀ ∧ 0 ≤ X₆
t₄: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l1(X₀, X₁, X₂, X₁, X₄, X₅, X₆) :|: 1 ≤ X₀ ∧ 1 ≤ X₀+X₄ ∧ 1+X₄ ≤ X₀ ∧ 1 ≤ X₄+X₆ ∧ 1+X₄ ≤ X₆ ∧ 1 ≤ X₆ ∧ 2 ≤ X₀+X₆ ∧ 0 ≤ X₄
t₂: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l3(X₀, X₁, X₂, X₃, X₄, X₅-1, X₆) :|: 1 ≤ X₅ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₄ ∧ 1+X₄ ≤ X₀ ∧ 1 ≤ X₄+X₆ ∧ 1+X₄ ≤ X₆ ∧ 1 ≤ X₆ ∧ 2 ≤ X₀+X₆ ∧ 0 ≤ X₄
t₅: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 1 ≤ X₀ ∧ 1 ≤ X₀+X₄ ∧ 1+X₄ ≤ X₀ ∧ 1 ≤ X₄+X₆ ∧ 1+X₄ ≤ X₆ ∧ 1 ≤ X₆ ∧ 2 ≤ X₀+X₆ ∧ 0 ≤ X₄
t₃: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l2(X₀, X₃, X₀, X₃, X₄, X₅, X₆) :|: 1 ≤ X₀ ∧ 1 ≤ X₀+X₄ ∧ 1+X₄ ≤ X₀ ∧ 1 ≤ X₀+X₅ ∧ 1 ≤ X₄+X₆ ∧ 1+X₄ ≤ X₆ ∧ 1 ≤ X₅+X₆ ∧ 1 ≤ X₆ ∧ 2 ≤ X₀+X₆ ∧ 0 ≤ X₄ ∧ 0 ≤ X₄+X₅ ∧ 0 ≤ X₅
t₆: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆-1) :|: 1 ≤ X₆ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₄ ∧ 1+X₄ ≤ X₀ ∧ 1 ≤ X₀+X₆ ∧ 0 ≤ X₄ ∧ 0 ≤ X₄+X₆ ∧ 0 ≤ X₆

MPRF for transition t₁: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l2(X₀, X₁, X₂, X₃, X₄-1, X₁+X₂, Temp_Int₂₃₇+X₆) :|: 1 ≤ X₄ ∧ 1 ≤ Temp_Int₂₃₇ ∧ X₄ ≤ Temp_Int₂₃₇ ∧ X₄ ≤ X₀ ∧ 0 ≤ X₆ of depth 1:

new bound:

X₀ {O(n)}

MPRF:

• l1: [X₄]
• l2: [X₄]
• l3: [X₄]

MPRF for transition t₄: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l1(X₀, X₁, X₂, X₁, X₄, X₅, X₆) :|: 1 ≤ X₀ ∧ 1 ≤ X₀+X₄ ∧ 1+X₄ ≤ X₀ ∧ 1 ≤ X₄+X₆ ∧ 1+X₄ ≤ X₆ ∧ 1 ≤ X₆ ∧ 2 ≤ X₀+X₆ ∧ 0 ≤ X₄ of depth 1:

new bound:

X₀ {O(n)}

MPRF:

• l1: [X₄]
• l2: [1+X₄]
• l3: [1+X₄]

MPRF for transition t₂: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l3(X₀, X₁, X₂, X₃, X₄, X₅-1, X₆) :|: 1 ≤ X₅ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₄ ∧ 1+X₄ ≤ X₀ ∧ 1 ≤ X₄+X₆ ∧ 1+X₄ ≤ X₆ ∧ 1 ≤ X₆ ∧ 2 ≤ X₀+X₆ ∧ 0 ≤ X₄ of depth 1:

new bound:

X₀⋅X₀+X₀⋅X₁+X₀⋅X₂+X₀⋅X₃+X₁+X₂ {O(n^2)}

MPRF:

• l1: [X₁+X₂]
• l2: [X₅]
• l3: [X₅]

MPRF for transition t₃: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l2(X₀, X₃, X₀, X₃, X₄, X₅, X₆) :|: 1 ≤ X₀ ∧ 1 ≤ X₀+X₄ ∧ 1+X₄ ≤ X₀ ∧ 1 ≤ X₀+X₅ ∧ 1 ≤ X₄+X₆ ∧ 1+X₄ ≤ X₆ ∧ 1 ≤ X₅+X₆ ∧ 1 ≤ X₆ ∧ 2 ≤ X₀+X₆ ∧ 0 ≤ X₄ ∧ 0 ≤ X₄+X₅ ∧ 0 ≤ X₅ of depth 1:

new bound:

X₀⋅X₀+X₀⋅X₁+X₀⋅X₂+X₀⋅X₃+X₁+X₂ {O(n^2)}

MPRF:

• l1: [X₁+X₂]
• l2: [X₅]
• l3: [1+X₅]

Found invariant 1 ≤ X₆ ∧ 1 ≤ X₄+X₆ ∧ 1+X₄ ≤ X₆ ∧ 2 ≤ X₀+X₆ ∧ 1+X₄ ≤ X₀ ∧ 0 ≤ X₄ ∧ 1 ≤ X₀+X₄ ∧ 1 ≤ X₀ for location l2

Found invariant 1 ≤ X₆ ∧ 1 ≤ X₅+X₆ ∧ 1 ≤ X₄+X₆ ∧ 1+X₄ ≤ X₆ ∧ 2 ≤ X₂+X₆ ∧ 2 ≤ X₀+X₆ ∧ 0 ≤ X₅ ∧ 0 ≤ X₄+X₅ ∧ 1 ≤ X₂+X₅ ∧ 1 ≤ X₀+X₅ ∧ 1+X₄ ≤ X₂ ∧ 1+X₄ ≤ X₀ ∧ 0 ≤ X₄ ∧ 1 ≤ X₂+X₄ ∧ 1 ≤ X₀+X₄ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₃ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₀ for location l3_v2

Found invariant 0 ≤ X₆ ∧ 0 ≤ X₄+X₆ ∧ 1 ≤ X₀+X₆ ∧ 1+X₄ ≤ X₀ ∧ 0 ≤ X₄ ∧ 1 ≤ X₀+X₄ ∧ 1 ≤ X₀ for location l5

Found invariant 1 ≤ X₆ ∧ 1 ≤ X₅+X₆ ∧ 1 ≤ X₄+X₆ ∧ 1+X₄ ≤ X₆ ∧ 2 ≤ X₂+X₆ ∧ 2 ≤ X₀+X₆ ∧ 0 ≤ X₅ ∧ 0 ≤ X₄+X₅ ∧ 1 ≤ X₂+X₅ ∧ 1 ≤ X₀+X₅ ∧ 1+X₄ ≤ X₂ ∧ 1+X₄ ≤ X₀ ∧ 0 ≤ X₄ ∧ 1 ≤ X₂+X₄ ∧ 1 ≤ X₀+X₄ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₃ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₀ for location l2_v1

Found invariant 0 ≤ X₆ ∧ X₄ ≤ X₀ for location l1

Found invariant 1 ≤ X₆ ∧ 1 ≤ X₅+X₆ ∧ 1 ≤ X₄+X₆ ∧ 1+X₄ ≤ X₆ ∧ 2 ≤ X₀+X₆ ∧ 0 ≤ X₅ ∧ 0 ≤ X₄+X₅ ∧ 1 ≤ X₀+X₅ ∧ 1+X₄ ≤ X₀ ∧ 0 ≤ X₄ ∧ 1 ≤ X₀+X₄ ∧ 1 ≤ X₀ for location l3_v1

Found invariant 1 ≤ X₆ ∧ 1 ≤ X₄+X₆ ∧ 1+X₄ ≤ X₆ ∧ 2 ≤ X₀+X₆ ∧ 1+X₄ ≤ X₀ ∧ 0 ≤ X₄ ∧ 1 ≤ X₀+X₄ ∧ 1 ≤ X₀ for location l2

Found invariant 1 ≤ X₆ ∧ 1 ≤ X₄+X₆ ∧ 1+X₄ ≤ X₆ ∧ 2 ≤ X₀+X₆ ∧ 1+X₄ ≤ X₀ ∧ 0 ≤ X₄ ∧ 1 ≤ X₀+X₄ ∧ 1 ≤ X₀ for location l5

Found invariant 0 ≤ X₆ ∧ X₄ ≤ X₀ for location l1

Found invariant 1 ≤ X₆ ∧ 1 ≤ X₅+X₆ ∧ 1 ≤ X₄+X₆ ∧ 1+X₄ ≤ X₆ ∧ 2 ≤ X₀+X₆ ∧ 0 ≤ X₅ ∧ 0 ≤ X₄+X₅ ∧ 1 ≤ X₀+X₅ ∧ 1+X₄ ≤ X₀ ∧ 0 ≤ X₄ ∧ 1 ≤ X₀+X₄ ∧ 1 ≤ X₀ for location l3

Found invariant 0 ≤ X₆ ∧ 0 ≤ X₄+X₆ ∧ 1 ≤ X₀+X₆ ∧ 1+X₄ ≤ X₀ ∧ 0 ≤ X₄ ∧ 1 ≤ X₀+X₄ ∧ 1 ≤ X₀ for location l5_v1

All Bounds

Timebounds

Overall timebound:inf {Infinity}
t₀: 1 {O(1)}
t₁: X₀ {O(n)}
t₂: X₀⋅X₀+X₀⋅X₁+X₀⋅X₂+X₀⋅X₃+X₁+X₂ {O(n^2)}
t₃: X₀⋅X₀+X₀⋅X₁+X₀⋅X₂+X₀⋅X₃+X₁+X₂ {O(n^2)}
t₄: X₀ {O(n)}
t₅: 1 {O(1)}
t₆: inf {Infinity}

Costbounds

Overall costbound: inf {Infinity}
t₀: 1 {O(1)}
t₁: X₀ {O(n)}
t₂: X₀⋅X₀+X₀⋅X₁+X₀⋅X₂+X₀⋅X₃+X₁+X₂ {O(n^2)}
t₃: X₀⋅X₀+X₀⋅X₁+X₀⋅X₂+X₀⋅X₃+X₁+X₂ {O(n^2)}
t₄: X₀ {O(n)}
t₅: 1 {O(1)}
t₆: inf {Infinity}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₀, X₃: X₃ {O(n)}
t₀, X₄: X₀ {O(n)}
t₀, X₅: 0 {O(1)}
t₀, X₆: 0 {O(1)}
t₁, X₀: X₀ {O(n)}
t₁, X₁: X₁+X₃ {O(n)}
t₁, X₂: X₀+X₂ {O(n)}
t₁, X₃: X₁+X₃ {O(n)}
t₁, X₄: X₀ {O(n)}
t₁, X₅: 2⋅X₁+2⋅X₂+X₀+X₃ {O(n)}
t₂, X₀: X₀ {O(n)}
t₂, X₁: 2⋅X₁+2⋅X₃ {O(n)}
t₂, X₂: 2⋅X₀+X₂ {O(n)}
t₂, X₃: X₁+X₃ {O(n)}
t₂, X₄: X₀ {O(n)}
t₂, X₅: 2⋅X₁+2⋅X₂+X₀+X₃ {O(n)}
t₃, X₀: X₀ {O(n)}
t₃, X₁: X₁+X₃ {O(n)}
t₃, X₂: X₀ {O(n)}
t₃, X₃: X₁+X₃ {O(n)}
t₃, X₄: X₀ {O(n)}
t₃, X₅: 2⋅X₁+2⋅X₂+X₀+X₃ {O(n)}
t₄, X₀: X₀ {O(n)}
t₄, X₁: X₁+X₃ {O(n)}
t₄, X₂: X₀+X₂ {O(n)}
t₄, X₃: X₁+X₃ {O(n)}
t₄, X₄: X₀ {O(n)}
t₄, X₅: 2⋅X₀+2⋅X₃+4⋅X₁+4⋅X₂ {O(n)}
t₅, X₀: 2⋅X₀ {O(n)}
t₅, X₁: 2⋅X₁+2⋅X₃ {O(n)}
t₅, X₂: 2⋅X₀+X₂ {O(n)}
t₅, X₃: 2⋅X₁+2⋅X₃ {O(n)}
t₅, X₄: 2⋅X₀ {O(n)}
t₅, X₅: 2⋅X₀+2⋅X₃+4⋅X₁+4⋅X₂ {O(n)}
t₆, X₀: 2⋅X₀ {O(n)}
t₆, X₁: 2⋅X₁+2⋅X₃ {O(n)}
t₆, X₂: 2⋅X₀+X₂ {O(n)}
t₆, X₃: 2⋅X₁+2⋅X₃ {O(n)}
t₆, X₄: 2⋅X₀ {O(n)}
t₆, X₅: 2⋅X₀+2⋅X₃+4⋅X₁+4⋅X₂ {O(n)}