Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃)
t₂: l1(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: 0 < X₀+X₁
t₃: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₀+X₁ ≤ 0
t₁: l2(X₀, X₁, X₂, X₃) → l1(X₂, X₃, X₂, X₃)
t₄: l3(X₀, X₁, X₂, X₃) → l1(X₀-1, -2⋅X₁, X₂, X₃)
t₅: l4(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃)

Preprocessing

Found invariant X₀ ≤ X₂ ∧ X₀+X₁ ≤ 0 for location l5

Found invariant X₀ ≤ X₂ for location l1

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

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

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃)
t₂: l1(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: 0 < X₀+X₁ ∧ X₀ ≤ X₂
t₃: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₀+X₁ ≤ 0 ∧ X₀ ≤ X₂
t₁: l2(X₀, X₁, X₂, X₃) → l1(X₂, X₃, X₂, X₃)
t₄: l3(X₀, X₁, X₂, X₃) → l1(X₀-1, -2⋅X₁, X₂, X₃) :|: 1 ≤ X₁+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₀+X₁
t₅: l4(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₀ ≤ X₂ ∧ X₀+X₁ ≤ 0

MPRF for transition t₂: l1(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: 0 < X₀+X₁ ∧ X₀ ≤ X₂ of depth 2:

new bound:

32⋅X₂+8⋅X₃+25 {O(n)}

MPRF for transition t₄: l3(X₀, X₁, X₂, X₃) → l1(X₀-1, -2⋅X₁, X₂, X₃) :|: 1 ≤ X₁+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₀+X₁ of depth 2:

new bound:

32⋅X₂+8⋅X₃+17 {O(n)}

All Bounds

Timebounds

Overall timebound:16⋅X₃+64⋅X₂+46 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 32⋅X₂+8⋅X₃+25 {O(n)}
t₃: 1 {O(1)}
t₄: 32⋅X₂+8⋅X₃+17 {O(n)}
t₅: 1 {O(1)}

Costbounds

Overall costbound: 16⋅X₃+64⋅X₂+46 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 32⋅X₂+8⋅X₃+25 {O(n)}
t₃: 1 {O(1)}
t₄: 32⋅X₂+8⋅X₃+17 {O(n)}
t₅: 1 {O(1)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₀, X₃: X₃ {O(n)}
t₁, X₀: X₂ {O(n)}
t₁, X₁: X₃ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₃ {O(n)}
t₂, X₀: 33⋅X₂+8⋅X₃+17 {O(n)}
t₂, X₁: 2^(32⋅X₂+8⋅X₃+17)⋅X₃ {O(EXP)}
t₂, X₂: X₂ {O(n)}
t₂, X₃: X₃ {O(n)}
t₃, X₀: 34⋅X₂+8⋅X₃+17 {O(n)}
t₃, X₁: 2^(32⋅X₂+8⋅X₃+17)⋅X₃+X₃ {O(EXP)}
t₃, X₂: 2⋅X₂ {O(n)}
t₃, X₃: 2⋅X₃ {O(n)}
t₄, X₀: 33⋅X₂+8⋅X₃+17 {O(n)}
t₄, X₁: 2^(32⋅X₂+8⋅X₃+17)⋅X₃ {O(EXP)}
t₄, X₂: X₂ {O(n)}
t₄, X₃: X₃ {O(n)}
t₅, X₀: 34⋅X₂+8⋅X₃+17 {O(n)}
t₅, X₁: 2^(32⋅X₂+8⋅X₃+17)⋅X₃+X₃ {O(EXP)}
t₅, X₂: 2⋅X₂ {O(n)}
t₅, X₃: 2⋅X₃ {O(n)}