Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅
Temp_Vars: G, H
Locations: l0, l1
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, X₁, X₂, X₃, X₄, X₅) :|: 0 ≤ X₀ ∧ 2⋅X₂ ≤ X₁+X₀+2 ∧ X₀+1 ≤ X₁ ∧ X₁+X₀ ≤ 2⋅X₂ ∧ 0 ≤ X₃ ∧ X₄+1 ≤ X₂ ∧ X₂ ≤ X₄+1 ∧ X₅ ≤ X₀ ∧ X₀ ≤ X₅
t₁: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, X₁, H, X₃, X₄, G) :|: 1 ≤ X₁ ∧ 0 ≤ X₃ ∧ X₄+1 ≤ X₀ ∧ G ≤ X₁+1 ∧ H ≤ X₂+1 ∧ 1+X₂ ≤ H ∧ G ≤ X₅+1 ∧ 1+X₅ ≤ G
t₂: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l1(H, X₁, X₂, X₃, X₄, G) :|: 1 ≤ X₁ ∧ 0 ≤ X₃ ∧ X₅ ≤ X₁ ∧ H ≤ X₄+1 ∧ X₁+1 ≤ X₂ ∧ G ≤ X₅+1 ∧ 1+X₅ ≤ G ∧ H ≤ X₀+1 ∧ 1+X₀ ≤ H
t₃: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, X₁, H, X₃, X₄, G) :|: 1 ≤ X₁ ∧ 0 ≤ X₃ ∧ X₅ ≤ X₁ ∧ H ≤ X₁+1 ∧ X₀ ≤ X₄ ∧ G ≤ X₅+1 ∧ 1+X₅ ≤ G ∧ H ≤ X₂+1 ∧ 1+X₂ ≤ H
t₄: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l1(H, X₁, X₂, X₃, X₄, G) :|: 1 ≤ X₁ ∧ 0 ≤ X₃ ∧ X₅ ≤ X₁ ∧ X₂ ≤ X₁ ∧ H ≤ X₄+1 ∧ H ≤ X₀+1 ∧ 1+X₀ ≤ H ∧ G ≤ X₅+1 ∧ 1+X₅ ≤ G

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 l1

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅
Temp_Vars: G, H
Locations: l0, l1
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, X₁, X₂, X₃, X₄, X₅) :|: 0 ≤ X₀ ∧ 2⋅X₂ ≤ X₁+X₀+2 ∧ X₀+1 ≤ X₁ ∧ X₁+X₀ ≤ 2⋅X₂ ∧ 0 ≤ X₃ ∧ X₄+1 ≤ X₂ ∧ X₂ ≤ X₄+1 ∧ X₅ ≤ X₀ ∧ X₀ ≤ X₅
t₁: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, X₁, H, X₃, X₄, G) :|: 1 ≤ X₁ ∧ 0 ≤ X₃ ∧ X₄+1 ≤ X₀ ∧ G ≤ X₁+1 ∧ H ≤ X₂+1 ∧ 1+X₂ ≤ H ∧ G ≤ X₅+1 ∧ 1+X₅ ≤ G ∧ 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
t₂: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l1(H, X₁, X₂, X₃, X₄, G) :|: 1 ≤ X₁ ∧ 0 ≤ X₃ ∧ X₅ ≤ X₁ ∧ H ≤ X₄+1 ∧ X₁+1 ≤ X₂ ∧ G ≤ X₅+1 ∧ 1+X₅ ≤ G ∧ H ≤ X₀+1 ∧ 1+X₀ ≤ H ∧ 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
t₃: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, X₁, H, X₃, X₄, G) :|: 1 ≤ X₁ ∧ 0 ≤ X₃ ∧ X₅ ≤ X₁ ∧ H ≤ X₁+1 ∧ X₀ ≤ X₄ ∧ G ≤ X₅+1 ∧ 1+X₅ ≤ G ∧ H ≤ X₂+1 ∧ 1+X₂ ≤ H ∧ 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
t₄: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l1(H, X₁, X₂, X₃, X₄, G) :|: 1 ≤ X₁ ∧ 0 ≤ X₃ ∧ X₅ ≤ X₁ ∧ X₂ ≤ X₁ ∧ H ≤ X₄+1 ∧ H ≤ X₀+1 ∧ 1+X₀ ≤ H ∧ G ≤ X₅+1 ∧ 1+X₅ ≤ G ∧ 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

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

new bound:

X₁+X₅+2 {O(n)}

MPRF:

l1 [X₁+2-X₅ ]

MPRF for transition t₂: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l1(H, X₁, X₂, X₃, X₄, G) :|: 1 ≤ X₁ ∧ 0 ≤ X₃ ∧ X₅ ≤ X₁ ∧ H ≤ X₄+1 ∧ X₁+1 ≤ X₂ ∧ G ≤ X₅+1 ∧ 1+X₅ ≤ G ∧ H ≤ X₀+1 ∧ 1+X₀ ≤ H ∧ 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 of depth 1:

new bound:

X₀+X₁+1 {O(n)}

MPRF:

l1 [X₁+1-X₀ ]

MPRF for transition t₃: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, X₁, H, X₃, X₄, G) :|: 1 ≤ X₁ ∧ 0 ≤ X₃ ∧ X₅ ≤ X₁ ∧ H ≤ X₁+1 ∧ X₀ ≤ X₄ ∧ G ≤ X₅+1 ∧ 1+X₅ ≤ G ∧ H ≤ X₂+1 ∧ 1+X₂ ≤ H ∧ 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 of depth 1:

new bound:

X₁+X₂+1 {O(n)}

MPRF:

l1 [X₁+1-X₂ ]

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

new bound:

X₀+X₁+1 {O(n)}

MPRF:

l1 [X₁+1-X₀ ]

All Bounds

Timebounds

Overall timebound:2⋅X₀+4⋅X₁+X₂+X₅+6 {O(n)}
t₀: 1 {O(1)}
t₁: X₁+X₅+2 {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+6 {O(n)}
t₀: 1 {O(1)}
t₁: X₁+X₅+2 {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+7⋅X₀+3 {O(n)}
t₁, X₁: 4⋅X₁ {O(n)}
t₁, X₂: 3⋅X₁+6⋅X₂+X₅+4 {O(n)}
t₁, X₃: 4⋅X₃ {O(n)}
t₁, X₄: 4⋅X₄ {O(n)}
t₁, X₅: 2⋅X₂+3⋅X₀+5⋅X₅+6⋅X₁+7 {O(n)}
t₂, X₀: 2⋅X₁+4⋅X₀+2 {O(n)}
t₂, X₁: 2⋅X₁ {O(n)}
t₂, X₂: 3⋅X₂+X₁+1 {O(n)}
t₂, X₃: 2⋅X₃ {O(n)}
t₂, X₄: 2⋅X₄ {O(n)}
t₂, X₅: 2⋅X₀+2⋅X₅+3⋅X₁+X₂+3 {O(n)}
t₃, X₀: 3⋅X₀+X₁+1 {O(n)}
t₃, X₁: 2⋅X₁ {O(n)}
t₃, X₂: 3⋅X₂+X₁+1 {O(n)}
t₃, X₃: 2⋅X₃ {O(n)}
t₃, X₄: 2⋅X₄ {O(n)}
t₃, X₅: 2⋅X₁+2⋅X₅+X₀+X₂+2 {O(n)}
t₄, X₀: 3⋅X₀+X₁+1 {O(n)}
t₄, X₁: 2⋅X₁ {O(n)}
t₄, X₂: 3⋅X₂+X₁+1 {O(n)}
t₄, X₃: 2⋅X₃ {O(n)}
t₄, X₄: 2⋅X₄ {O(n)}
t₄, X₅: 2⋅X₁+2⋅X₅+X₀+X₂+2 {O(n)}