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 ∧ X₀ < X₁
t₃: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₀ ≤ 0
t₄: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₁ ≤ X₀
t₁: l2(X₀, X₁, X₂, X₃) → l1(X₂, X₃, X₂, X₃)
t₅: l3(X₀, X₁, X₂, X₃) → l1(2⋅X₀, X₁+1, X₂, X₃)
t₆: l4(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃)

Preprocessing

Found invariant X₃ ≤ X₁ ∧ X₂ ≤ X₀ for location l5

Found invariant X₃ ≤ X₁ ∧ X₂ ≤ X₀ for location l1

Found invariant X₃ ≤ X₁ ∧ X₂ ≤ X₀ for location l4

Found invariant X₃ ≤ X₁ ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ 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 ∧ X₀ < X₁ ∧ X₃ ≤ X₁ ∧ X₂ ≤ X₀
t₃: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₀ ≤ 0 ∧ X₃ ≤ X₁ ∧ X₂ ≤ X₀
t₄: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₁ ≤ X₀ ∧ X₃ ≤ X₁ ∧ X₂ ≤ X₀
t₁: l2(X₀, X₁, X₂, X₃) → l1(X₂, X₃, X₂, X₃)
t₅: l3(X₀, X₁, X₂, X₃) → l1(2⋅X₀, X₁+1, X₂, X₃) :|: X₃ ≤ X₁ ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀
t₆: l4(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₃ ≤ X₁ ∧ X₂ ≤ X₀

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

new bound:

16⋅X₂+8⋅X₃+17 {O(n)}

MPRF:

l3 [1-X₀ ; X₁+1-2⋅X₀ ]
l1 [2-X₀ ; X₁-X₀ ]

MPRF for transition t₅: l3(X₀, X₁, X₂, X₃) → l1(2⋅X₀, X₁+1, X₂, X₃) :|: X₃ ≤ X₁ ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 2:

new bound:

16⋅X₃+24⋅X₂+17 {O(n)}

MPRF:

l3 [X₁+1-2⋅X₀ ; 0 ]
l1 [X₁+1-2⋅X₀ ; X₁-X₀-1 ]

All Bounds

Timebounds

Overall timebound:24⋅X₃+40⋅X₂+39 {O(n)}
t₀: 1 {O(1)}
t₂: 16⋅X₂+8⋅X₃+17 {O(n)}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₁: 1 {O(1)}
t₅: 16⋅X₃+24⋅X₂+17 {O(n)}
t₆: 1 {O(1)}

Costbounds

Overall costbound: 24⋅X₃+40⋅X₂+39 {O(n)}
t₀: 1 {O(1)}
t₂: 16⋅X₂+8⋅X₃+17 {O(n)}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₁: 1 {O(1)}
t₅: 16⋅X₃+24⋅X₂+17 {O(n)}
t₆: 1 {O(1)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₀, X₃: X₃ {O(n)}
t₂, X₀: 2^(16⋅X₃+24⋅X₂+17)⋅X₂ {O(EXP)}
t₂, X₁: 17⋅X₃+24⋅X₂+17 {O(n)}
t₂, X₂: X₂ {O(n)}
t₂, X₃: X₃ {O(n)}
t₃, X₀: X₂ {O(n)}
t₃, X₁: X₃ {O(n)}
t₃, X₂: X₂ {O(n)}
t₃, X₃: X₃ {O(n)}
t₄, X₀: 2^(16⋅X₃+24⋅X₂+17)⋅X₂+X₂ {O(EXP)}
t₄, X₁: 18⋅X₃+24⋅X₂+17 {O(n)}
t₄, X₂: 2⋅X₂ {O(n)}
t₄, X₃: 2⋅X₃ {O(n)}
t₁, X₀: X₂ {O(n)}
t₁, X₁: X₃ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₃ {O(n)}
t₅, X₀: 2^(16⋅X₃+24⋅X₂+17)⋅X₂ {O(EXP)}
t₅, X₁: 17⋅X₃+24⋅X₂+17 {O(n)}
t₅, X₂: X₂ {O(n)}
t₅, X₃: X₃ {O(n)}
t₆, X₀: 2^(16⋅X₃+24⋅X₂+17)⋅X₂+2⋅X₂ {O(EXP)}
t₆, X₁: 19⋅X₃+24⋅X₂+17 {O(n)}
t₆, X₂: 3⋅X₂ {O(n)}
t₆, X₃: 3⋅X₃ {O(n)}