Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₀: l0(X₀, X₁, X₂) → l3(X₀, X₁, X₂)
t₄: l1(X₀, X₁, X₂) → l2(X₀, X₁, X₂) :|: X₀ < 0
t₃: l1(X₀, X₁, X₂) → l4(X₀, X₁, X₂) :|: 0 ≤ X₀
t₆: l2(X₀, X₁, X₂) → l5(X₀, X₁, X₂)
t₁: l3(X₀, X₁, X₂) → l1(X₁, X₁, X₂) :|: 1 ≤ 2⋅X₂
t₂: l3(X₀, X₁, X₂) → l2(X₀, X₁, X₂) :|: 2⋅X₂ < 1
t₅: l4(X₀, X₁, X₂) → l1(X₀+1-2⋅X₂, X₁, X₂)

Preprocessing

Found invariant 1 ≤ X₂ ∧ X₀ ≤ X₁ for location l1

Found invariant 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀ for location l4

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₀: l0(X₀, X₁, X₂) → l3(X₀, X₁, X₂)
t₄: l1(X₀, X₁, X₂) → l2(X₀, X₁, X₂) :|: X₀ < 0 ∧ 1 ≤ X₂ ∧ X₀ ≤ X₁
t₃: l1(X₀, X₁, X₂) → l4(X₀, X₁, X₂) :|: 0 ≤ X₀ ∧ 1 ≤ X₂ ∧ X₀ ≤ X₁
t₆: l2(X₀, X₁, X₂) → l5(X₀, X₁, X₂)
t₁: l3(X₀, X₁, X₂) → l1(X₁, X₁, X₂) :|: 1 ≤ 2⋅X₂
t₂: l3(X₀, X₁, X₂) → l2(X₀, X₁, X₂) :|: 2⋅X₂ < 1
t₅: l4(X₀, X₁, X₂) → l1(X₀+1-2⋅X₂, X₁, X₂) :|: 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀

MPRF for transition t₃: l1(X₀, X₁, X₂) → l4(X₀, X₁, X₂) :|: 0 ≤ X₀ ∧ 1 ≤ X₂ ∧ X₀ ≤ X₁ of depth 1:

new bound:

X₁+1 {O(n)}

MPRF:

l4 [X₀ ]
l1 [X₀+1 ]

MPRF for transition t₅: l4(X₀, X₁, X₂) → l1(X₀+1-2⋅X₂, X₁, X₂) :|: 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

2⋅X₂+X₁+1 {O(n)}

MPRF:

l4 [X₀+1 ]
l1 [X₀+2⋅X₂-1 ]

All Bounds

Timebounds

Overall timebound:2⋅X₁+2⋅X₂+7 {O(n)}
t₀: 1 {O(1)}
t₃: X₁+1 {O(n)}
t₄: 1 {O(1)}
t₆: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₅: 2⋅X₂+X₁+1 {O(n)}

Costbounds

Overall costbound: 2⋅X₁+2⋅X₂+7 {O(n)}
t₀: 1 {O(1)}
t₃: X₁+1 {O(n)}
t₄: 1 {O(1)}
t₆: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₅: 2⋅X₂+X₁+1 {O(n)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₃, X₀: 2⋅2^(2⋅X₂+X₁+1)⋅X₂+2⋅2^(2⋅X₂+X₁+1)⋅X₂⋅X₂+2^(2⋅X₂+X₁+1)⋅X₁+2^(2⋅X₂+X₁+1)⋅X₁⋅X₂ {O(EXP)}
t₃, X₁: X₁ {O(n)}
t₃, X₂: X₂ {O(n)}
t₄, X₀: 2⋅2^(2⋅X₂+X₁+1)⋅X₂+2⋅2^(2⋅X₂+X₁+1)⋅X₂⋅X₂+2^(2⋅X₂+X₁+1)⋅X₁+2^(2⋅X₂+X₁+1)⋅X₁⋅X₂+X₁ {O(EXP)}
t₄, X₁: 2⋅X₁ {O(n)}
t₄, X₂: 2⋅X₂ {O(n)}
t₆, X₀: 2⋅2^(2⋅X₂+X₁+1)⋅X₂+2⋅2^(2⋅X₂+X₁+1)⋅X₂⋅X₂+2^(2⋅X₂+X₁+1)⋅X₁+2^(2⋅X₂+X₁+1)⋅X₁⋅X₂+X₀+X₁ {O(EXP)}
t₆, X₁: 3⋅X₁ {O(n)}
t₆, X₂: 3⋅X₂ {O(n)}
t₁, X₀: X₁ {O(n)}
t₁, X₁: X₁ {O(n)}
t₁, X₂: X₂ {O(n)}
t₂, X₀: X₀ {O(n)}
t₂, X₁: X₁ {O(n)}
t₂, X₂: X₂ {O(n)}
t₅, X₀: 2⋅2^(2⋅X₂+X₁+1)⋅X₂+2⋅2^(2⋅X₂+X₁+1)⋅X₂⋅X₂+2^(2⋅X₂+X₁+1)⋅X₁+2^(2⋅X₂+X₁+1)⋅X₁⋅X₂ {O(EXP)}
t₅, X₁: X₁ {O(n)}
t₅, X₂: X₂ {O(n)}