Initial Problem

Start: start
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅
Temp_Vars: G, H
Locations: m1, start
Transitions:
t₁: m1(X₀, X₁, X₂, X₃, X₄, X₅) → m1(X₀, X₁, H, X₃, X₄, G) :|: G ≤ 1+X₁ ∧ G ≤ 1+X₅ ∧ H ≤ 1+X₂ ∧ 1+X₅ ≤ G ∧ 1+X₂ ≤ H ∧ 1+X₄ ≤ X₀ ∧ 1 ≤ X₁ ∧ 0 ≤ X₃
t₂: m1(X₀, X₁, X₂, X₃, X₄, X₅) → m1(H, X₁, X₂, X₃, X₄, G) :|: G ≤ 1+X₅ ∧ H ≤ 1+X₀ ∧ H ≤ 1+X₄ ∧ 1+X₅ ≤ G ∧ 1+X₀ ≤ H ∧ 1 ≤ X₁ ∧ 1+X₁ ≤ X₂ ∧ X₅ ≤ X₁ ∧ 0 ≤ X₃
t₃: m1(X₀, X₁, X₂, X₃, X₄, X₅) → m1(X₀, X₁, H, X₃, X₄, G) :|: G ≤ 1+X₅ ∧ H ≤ 1+X₁ ∧ H ≤ 1+X₂ ∧ 1+X₅ ≤ G ∧ 1+X₂ ≤ H ∧ 1 ≤ X₁ ∧ X₀ ≤ X₄ ∧ X₅ ≤ X₁ ∧ 0 ≤ X₃
t₄: m1(X₀, X₁, X₂, X₃, X₄, X₅) → m1(H, X₁, X₂, X₃, X₄, G) :|: G ≤ 1+X₅ ∧ H ≤ 1+X₀ ∧ H ≤ 1+X₄ ∧ 1+X₅ ≤ G ∧ 1+X₀ ≤ H ∧ 1 ≤ X₁ ∧ X₂ ≤ X₁ ∧ X₅ ≤ X₁ ∧ 0 ≤ X₃
t₀: start(X₀, X₁, X₂, X₃, X₄, X₅) → m1(X₀, X₁, X₂, X₃, X₄, X₅) :|: 2⋅X₂ ≤ 2+X₀+X₁ ∧ X₂ ≤ 1+X₄ ∧ 1+X₀ ≤ X₁ ∧ 1+X₄ ≤ X₂ ∧ 0 ≤ X₀ ∧ X₅ ≤ X₀ ∧ X₀+X₁ ≤ 2⋅X₂ ∧ X₀ ≤ X₅ ∧ 0 ≤ X₃

Preprocessing

Found invariant X₅ ≤ 1+X₁ ∧ 0 ≤ X₅ ∧ 0 ≤ X₄+X₅ ∧ 0 ≤ X₃+X₅ ∧ 1 ≤ X₂+X₅ ∧ 1 ≤ X₁+X₅ ∧ 0 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1+X₄ ≤ X₂ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ 1 ≤ X₂+X₄ ∧ 1 ≤ X₁+X₄ ∧ 0 ≤ X₀+X₄ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ X₀ ≤ 1+X₁ ∧ 0 ≤ X₀ for location m1

Problem after Preprocessing

Start: start
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅
Temp_Vars:
Locations: m1, start
Transitions:
t₁: m1(X₀, X₁, X₂, X₃, X₄, X₅) → m1(X₀, X₁, 1+X₂, X₃, X₄, 1+X₅) :|: X₅ ≤ X₁ ∧ 1+X₄ ≤ X₀ ∧ 1 ≤ X₁ ∧ 0 ≤ X₃ ∧ X₀ ≤ 1+X₁ ∧ X₅ ≤ 1+X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₁+X₄ ∧ 1 ≤ X₁+X₅ ∧ 1 ≤ X₂ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₂+X₄ ∧ 1+X₄ ≤ X₂ ∧ 1 ≤ X₂+X₅ ∧ 2 ≤ X₁+X₂ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₃ ∧ 0 ≤ X₀+X₄ ∧ 0 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 0 ≤ X₃+X₄ ∧ 0 ≤ X₃+X₅ ∧ 0 ≤ X₄ ∧ 0 ≤ X₄+X₅ ∧ 0 ≤ X₅
t₂: m1(X₀, X₁, X₂, X₃, X₄, X₅) → m1(1+X₀, X₁, X₂, X₃, X₄, 1+X₅) :|: X₀ ≤ X₄ ∧ 1 ≤ X₁ ∧ 1+X₁ ≤ X₂ ∧ X₅ ≤ X₁ ∧ 0 ≤ X₃ ∧ X₀ ≤ 1+X₁ ∧ X₅ ≤ 1+X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₁+X₄ ∧ 1 ≤ X₁+X₅ ∧ 1 ≤ X₂ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₂+X₄ ∧ 1+X₄ ≤ X₂ ∧ 1 ≤ X₂+X₅ ∧ 2 ≤ X₁+X₂ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₃ ∧ 0 ≤ X₀+X₄ ∧ 0 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 0 ≤ X₃+X₄ ∧ 0 ≤ X₃+X₅ ∧ 0 ≤ X₄ ∧ 0 ≤ X₄+X₅ ∧ 0 ≤ X₅
t₃: m1(X₀, X₁, X₂, X₃, X₄, X₅) → m1(X₀, X₁, 1+X₂, X₃, X₄, 1+X₅) :|: X₂ ≤ X₁ ∧ 1 ≤ X₁ ∧ X₀ ≤ X₄ ∧ X₅ ≤ X₁ ∧ 0 ≤ X₃ ∧ X₀ ≤ 1+X₁ ∧ X₅ ≤ 1+X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₁+X₄ ∧ 1 ≤ X₁+X₅ ∧ 1 ≤ X₂ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₂+X₄ ∧ 1+X₄ ≤ X₂ ∧ 1 ≤ X₂+X₅ ∧ 2 ≤ X₁+X₂ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₃ ∧ 0 ≤ X₀+X₄ ∧ 0 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 0 ≤ X₃+X₄ ∧ 0 ≤ X₃+X₅ ∧ 0 ≤ X₄ ∧ 0 ≤ X₄+X₅ ∧ 0 ≤ X₅
t₄: m1(X₀, X₁, X₂, X₃, X₄, X₅) → m1(1+X₀, X₁, X₂, X₃, X₄, 1+X₅) :|: X₀ ≤ X₄ ∧ 1 ≤ X₁ ∧ X₂ ≤ X₁ ∧ X₅ ≤ X₁ ∧ 0 ≤ X₃ ∧ X₀ ≤ 1+X₁ ∧ X₅ ≤ 1+X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₁+X₄ ∧ 1 ≤ X₁+X₅ ∧ 1 ≤ X₂ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₂+X₄ ∧ 1+X₄ ≤ X₂ ∧ 1 ≤ X₂+X₅ ∧ 2 ≤ X₁+X₂ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₃ ∧ 0 ≤ X₀+X₄ ∧ 0 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 0 ≤ X₃+X₄ ∧ 0 ≤ X₃+X₅ ∧ 0 ≤ X₄ ∧ 0 ≤ X₄+X₅ ∧ 0 ≤ X₅
t₀: start(X₀, X₁, X₂, X₃, X₄, X₅) → m1(X₀, X₁, X₂, X₃, X₄, X₅) :|: 2⋅X₂ ≤ 2+X₀+X₁ ∧ X₂ ≤ 1+X₄ ∧ 1+X₀ ≤ X₁ ∧ 1+X₄ ≤ X₂ ∧ 0 ≤ X₀ ∧ X₅ ≤ X₀ ∧ X₀+X₁ ≤ 2⋅X₂ ∧ X₀ ≤ X₅ ∧ 0 ≤ X₃

MPRF for transition t₁: m1(X₀, X₁, X₂, X₃, X₄, X₅) → m1(X₀, X₁, 1+X₂, X₃, X₄, 1+X₅) :|: X₅ ≤ X₁ ∧ 1+X₄ ≤ X₀ ∧ 1 ≤ X₁ ∧ 0 ≤ X₃ ∧ X₀ ≤ 1+X₁ ∧ X₅ ≤ 1+X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₁+X₄ ∧ 1 ≤ X₁+X₅ ∧ 1 ≤ X₂ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₂+X₄ ∧ 1+X₄ ≤ X₂ ∧ 1 ≤ X₂+X₅ ∧ 2 ≤ X₁+X₂ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₃ ∧ 0 ≤ X₀+X₄ ∧ 0 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 0 ≤ X₃+X₄ ∧ 0 ≤ X₃+X₅ ∧ 0 ≤ X₄ ∧ 0 ≤ X₄+X₅ ∧ 0 ≤ X₅ of depth 1:

new bound:

X₁+X₅+1 {O(n)}

MPRF:

• m1: [1+X₁-X₅]

MPRF for transition t₂: m1(X₀, X₁, X₂, X₃, X₄, X₅) → m1(1+X₀, X₁, X₂, X₃, X₄, 1+X₅) :|: X₀ ≤ X₄ ∧ 1 ≤ X₁ ∧ 1+X₁ ≤ X₂ ∧ X₅ ≤ X₁ ∧ 0 ≤ X₃ ∧ X₀ ≤ 1+X₁ ∧ X₅ ≤ 1+X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₁+X₄ ∧ 1 ≤ X₁+X₅ ∧ 1 ≤ X₂ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₂+X₄ ∧ 1+X₄ ≤ X₂ ∧ 1 ≤ X₂+X₅ ∧ 2 ≤ X₁+X₂ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₃ ∧ 0 ≤ X₀+X₄ ∧ 0 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 0 ≤ X₃+X₄ ∧ 0 ≤ X₃+X₅ ∧ 0 ≤ X₄ ∧ 0 ≤ X₄+X₅ ∧ 0 ≤ X₅ of depth 1:

new bound:

X₀+X₁+1 {O(n)}

MPRF:

• m1: [1+X₁-X₀]

MPRF for transition t₃: m1(X₀, X₁, X₂, X₃, X₄, X₅) → m1(X₀, X₁, 1+X₂, X₃, X₄, 1+X₅) :|: X₂ ≤ X₁ ∧ 1 ≤ X₁ ∧ X₀ ≤ X₄ ∧ X₅ ≤ X₁ ∧ 0 ≤ X₃ ∧ X₀ ≤ 1+X₁ ∧ X₅ ≤ 1+X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₁+X₄ ∧ 1 ≤ X₁+X₅ ∧ 1 ≤ X₂ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₂+X₄ ∧ 1+X₄ ≤ X₂ ∧ 1 ≤ X₂+X₅ ∧ 2 ≤ X₁+X₂ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₃ ∧ 0 ≤ X₀+X₄ ∧ 0 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 0 ≤ X₃+X₄ ∧ 0 ≤ X₃+X₅ ∧ 0 ≤ X₄ ∧ 0 ≤ X₄+X₅ ∧ 0 ≤ X₅ of depth 1:

new bound:

X₁+X₂+1 {O(n)}

MPRF:

• m1: [1+X₁-X₂]

MPRF for transition t₄: m1(X₀, X₁, X₂, X₃, X₄, X₅) → m1(1+X₀, X₁, X₂, X₃, X₄, 1+X₅) :|: X₀ ≤ X₄ ∧ 1 ≤ X₁ ∧ X₂ ≤ X₁ ∧ X₅ ≤ X₁ ∧ 0 ≤ X₃ ∧ X₀ ≤ 1+X₁ ∧ X₅ ≤ 1+X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₁+X₄ ∧ 1 ≤ X₁+X₅ ∧ 1 ≤ X₂ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₂+X₄ ∧ 1+X₄ ≤ X₂ ∧ 1 ≤ X₂+X₅ ∧ 2 ≤ X₁+X₂ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₃ ∧ 0 ≤ X₀+X₄ ∧ 0 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 0 ≤ X₃+X₄ ∧ 0 ≤ X₃+X₅ ∧ 0 ≤ X₄ ∧ 0 ≤ X₄+X₅ ∧ 0 ≤ X₅ of depth 1:

new bound:

X₀+X₁+1 {O(n)}

MPRF:

• m1: [1+X₁-X₀]

All Bounds

Timebounds

Overall timebound:2⋅X₀+4⋅X₁+X₂+X₅+5 {O(n)}
t₀: 1 {O(1)}
t₁: X₁+X₅+1 {O(n)}
t₂: X₀+X₁+1 {O(n)}
t₃: X₁+X₂+1 {O(n)}
t₄: X₀+X₁+1 {O(n)}

Costbounds

Overall costbound: 2⋅X₀+4⋅X₁+X₂+X₅+5 {O(n)}
t₀: 1 {O(1)}
t₁: X₁+X₅+1 {O(n)}
t₂: X₀+X₁+1 {O(n)}
t₃: X₁+X₂+1 {O(n)}
t₄: X₀+X₁+1 {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: 3⋅X₁+5⋅X₀+3 {O(n)}
t₁, X₁: X₁ {O(n)}
t₁, X₂: 3⋅X₁+4⋅X₂+X₅+3 {O(n)}
t₁, X₃: X₃ {O(n)}
t₁, X₄: X₄ {O(n)}
t₁, X₅: 2⋅X₂+3⋅X₀+3⋅X₅+6⋅X₁+6 {O(n)}
t₂, X₀: 2⋅X₁+3⋅X₀+2 {O(n)}
t₂, X₁: X₁ {O(n)}
t₂, X₂: 2⋅X₂+X₁+1 {O(n)}
t₂, X₃: X₃ {O(n)}
t₂, X₄: X₄ {O(n)}
t₂, X₅: 2⋅X₀+3⋅X₁+X₂+X₅+3 {O(n)}
t₃, X₀: 2⋅X₀+X₁+1 {O(n)}
t₃, X₁: X₁ {O(n)}
t₃, X₂: 2⋅X₂+X₁+1 {O(n)}
t₃, X₃: X₃ {O(n)}
t₃, X₄: X₄ {O(n)}
t₃, X₅: 2⋅X₁+X₀+X₂+X₅+2 {O(n)}
t₄, X₀: 2⋅X₀+X₁+1 {O(n)}
t₄, X₁: X₁ {O(n)}
t₄, X₂: 2⋅X₂+X₁+1 {O(n)}
t₄, X₃: X₃ {O(n)}
t₄, X₄: X₄ {O(n)}
t₄, X₅: 2⋅X₁+X₀+X₂+X₅+2 {O(n)}