KoAT2 Proof Output

Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅
Temp_Vars:
Locations: l0, l1, l2, l3, l4
Transitions:
t₁₂: l0(X₀, X₁, X₂, X₃, X₄, X₅) → l4(X₀, X₂, X₂, X₄, X₄, X₀)
t₁₁: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, 1+X₅+X₁, X₂, X₃, X₄, X₅) :|: 0 ≤ X₀ ∧ X₁ ≤ X₃ ∧ X₃ ≤ X₄ ∧ X₀+X₂+1 ≤ X₁ ∧ X₁ ≤ X₀+X₃+1 ∧ X₅ ≤ X₀ ∧ X₀ ≤ X₅
t₁₀: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, X₁, X₂, X₃-1-X₅, X₄, X₅) :|: 0 ≤ X₀ ∧ X₁ ≤ X₃ ∧ X₃ ≤ X₄ ∧ X₀+X₂+1 ≤ X₁ ∧ X₁ ≤ X₀+X₃+1 ∧ X₅ ≤ X₀ ∧ X₀ ≤ X₅
t₈: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₃+1 ≤ X₁ ∧ X₃ ≤ X₄ ∧ 0 ≤ X₀ ∧ X₀+X₂+1 ≤ X₁ ∧ X₁ ≤ X₀+X₃+1 ∧ X₅ ≤ X₀ ∧ X₀ ≤ X₅
t₉: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₁ ≤ X₃ ∧ X₀+1 ≤ 0 ∧ X₃ ≤ X₄ ∧ 0 ≤ X₀ ∧ X₀+X₂+1 ≤ X₁ ∧ X₁ ≤ X₀+X₃+1 ∧ X₅ ≤ X₀ ∧ X₀ ≤ X₅
t₇: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, 1+X₅+X₁, X₂, X₃, X₄, X₅) :|: 0 ≤ X₀ ∧ X₁ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₀+X₃+1 ∧ X₀+X₃+1 ≤ X₄ ∧ X₅ ≤ X₀ ∧ X₀ ≤ X₅
t₆: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, X₁, X₂, X₃-1-X₅, X₄, X₅) :|: 0 ≤ X₀ ∧ X₁ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₀+X₃+1 ∧ X₀+X₃+1 ≤ X₄ ∧ X₅ ≤ X₀ ∧ X₀ ≤ X₅
t₄: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₃+1 ≤ X₁ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₀+X₃+1 ∧ X₀+X₃+1 ≤ X₄ ∧ X₅ ≤ X₀ ∧ X₀ ≤ X₅
t₅: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₁ ≤ X₃ ∧ X₀+1 ≤ 0 ∧ X₂ ≤ X₁ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₀+X₃+1 ∧ X₀+X₃+1 ≤ X₄ ∧ X₅ ≤ X₀ ∧ X₀ ≤ X₅
t₃: l4(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, 1+X₅+X₁, X₂, X₃, X₄, X₅) :|: 0 ≤ X₀ ∧ X₂ ≤ X₄ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₃ ≤ X₄ ∧ X₄ ≤ X₃ ∧ X₅ ≤ X₀ ∧ X₀ ≤ X₅
t₂: l4(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, X₁, X₂, X₃-1-X₅, X₄, X₅) :|: 0 ≤ X₀ ∧ X₂ ≤ X₄ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₃ ≤ X₄ ∧ X₄ ≤ X₃ ∧ X₅ ≤ X₀ ∧ X₀ ≤ X₅
t₀: l4(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₀+1 ≤ 0 ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₃ ≤ X₄ ∧ X₄ ≤ X₃ ∧ X₅ ≤ X₀ ∧ X₀ ≤ X₅
t₁: l4(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁, X₂, X₃, X₄, X₅) :|: 0 ≤ X₀ ∧ X₄+1 ≤ X₂ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₃ ≤ X₄ ∧ X₄ ≤ X₃ ∧ X₅ ≤ X₀ ∧ X₀ ≤ X₅

Preprocessing

Cut unsatisfiable transition t₉: l1→l3

Cut unsatisfiable transition t₅: l2→l3

Found invariant X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ 0 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1+X₃ ≤ X₄ ∧ X₂ ≤ X₄ ∧ X₁ ≤ X₄ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₀ for location l2

Found invariant X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ 0 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ X₃ ≤ X₄ ∧ X₂ ≤ X₄ ∧ X₂ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ 0 ≤ X₀ for location l1

Found invariant X₅ ≤ X₀ ∧ X₀ ≤ X₅ ∧ X₄ ≤ X₃ ∧ X₃ ≤ X₄ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂ for location l4

Found invariant X₅ ≤ X₀ ∧ X₀ ≤ X₅ ∧ X₃ ≤ X₄ ∧ X₂ ≤ X₁ for location l3

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅
Temp_Vars:
Locations: l0, l1, l2, l3, l4
Transitions:
t₁₂: l0(X₀, X₁, X₂, X₃, X₄, X₅) → l4(X₀, X₂, X₂, X₄, X₄, X₀)
t₁₁: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, 1+X₅+X₁, X₂, X₃, X₄, X₅) :|: 0 ≤ X₀ ∧ X₁ ≤ X₃ ∧ X₃ ≤ X₄ ∧ X₀+X₂+1 ≤ X₁ ∧ X₁ ≤ X₀+X₃+1 ∧ X₅ ≤ X₀ ∧ X₀ ≤ X₅ ∧ X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ 0 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ X₃ ≤ X₄ ∧ X₂ ≤ X₄ ∧ X₂ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ 0 ≤ X₀
t₁₀: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, X₁, X₂, X₃-1-X₅, X₄, X₅) :|: 0 ≤ X₀ ∧ X₁ ≤ X₃ ∧ X₃ ≤ X₄ ∧ X₀+X₂+1 ≤ X₁ ∧ X₁ ≤ X₀+X₃+1 ∧ X₅ ≤ X₀ ∧ X₀ ≤ X₅ ∧ X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ 0 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ X₃ ≤ X₄ ∧ X₂ ≤ X₄ ∧ X₂ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ 0 ≤ X₀
t₈: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₃+1 ≤ X₁ ∧ X₃ ≤ X₄ ∧ 0 ≤ X₀ ∧ X₀+X₂+1 ≤ X₁ ∧ X₁ ≤ X₀+X₃+1 ∧ X₅ ≤ X₀ ∧ X₀ ≤ X₅ ∧ X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ 0 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ X₃ ≤ X₄ ∧ X₂ ≤ X₄ ∧ X₂ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ 0 ≤ X₀
t₇: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, 1+X₅+X₁, X₂, X₃, X₄, X₅) :|: 0 ≤ X₀ ∧ X₁ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₀+X₃+1 ∧ X₀+X₃+1 ≤ X₄ ∧ X₅ ≤ X₀ ∧ X₀ ≤ X₅ ∧ X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ 0 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1+X₃ ≤ X₄ ∧ X₂ ≤ X₄ ∧ X₁ ≤ X₄ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₀
t₆: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, X₁, X₂, X₃-1-X₅, X₄, X₅) :|: 0 ≤ X₀ ∧ X₁ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₀+X₃+1 ∧ X₀+X₃+1 ≤ X₄ ∧ X₅ ≤ X₀ ∧ X₀ ≤ X₅ ∧ X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ 0 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1+X₃ ≤ X₄ ∧ X₂ ≤ X₄ ∧ X₁ ≤ X₄ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₀
t₄: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₃+1 ≤ X₁ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₀+X₃+1 ∧ X₀+X₃+1 ≤ X₄ ∧ X₅ ≤ X₀ ∧ X₀ ≤ X₅ ∧ X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ 0 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1+X₃ ≤ X₄ ∧ X₂ ≤ X₄ ∧ X₁ ≤ X₄ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₀
t₃: l4(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, 1+X₅+X₁, X₂, X₃, X₄, X₅) :|: 0 ≤ X₀ ∧ X₂ ≤ X₄ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₃ ≤ X₄ ∧ X₄ ≤ X₃ ∧ X₅ ≤ X₀ ∧ X₀ ≤ X₅ ∧ X₅ ≤ X₀ ∧ X₀ ≤ X₅ ∧ X₄ ≤ X₃ ∧ X₃ ≤ X₄ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂
t₂: l4(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, X₁, X₂, X₃-1-X₅, X₄, X₅) :|: 0 ≤ X₀ ∧ X₂ ≤ X₄ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₃ ≤ X₄ ∧ X₄ ≤ X₃ ∧ X₅ ≤ X₀ ∧ X₀ ≤ X₅ ∧ X₅ ≤ X₀ ∧ X₀ ≤ X₅ ∧ X₄ ≤ X₃ ∧ X₃ ≤ X₄ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂
t₀: l4(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₀+1 ≤ 0 ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₃ ≤ X₄ ∧ X₄ ≤ X₃ ∧ X₅ ≤ X₀ ∧ X₀ ≤ X₅ ∧ X₅ ≤ X₀ ∧ X₀ ≤ X₅ ∧ X₄ ≤ X₃ ∧ X₃ ≤ X₄ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂
t₁: l4(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁, X₂, X₃, X₄, X₅) :|: 0 ≤ X₀ ∧ X₄+1 ≤ X₂ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₃ ≤ X₄ ∧ X₄ ≤ X₃ ∧ X₅ ≤ X₀ ∧ X₀ ≤ X₅ ∧ X₅ ≤ X₀ ∧ X₀ ≤ X₅ ∧ X₄ ≤ X₃ ∧ X₃ ≤ X₄ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂

MPRF for transition t₁₀: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, X₁, X₂, X₃-1-X₅, X₄, X₅) :|: 0 ≤ X₀ ∧ X₁ ≤ X₃ ∧ X₃ ≤ X₄ ∧ X₀+X₂+1 ≤ X₁ ∧ X₁ ≤ X₀+X₃+1 ∧ X₅ ≤ X₀ ∧ X₀ ≤ X₅ ∧ X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ 0 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ X₃ ≤ X₄ ∧ X₂ ≤ X₄ ∧ X₂ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

2⋅X₂+2⋅X₄+X₀+3 {O(n)}

MPRF:

l2 [X₃+1-X₂ ]
l1 [X₃+1-X₂ ]

MPRF for transition t₁₁: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, 1+X₅+X₁, X₂, X₃, X₄, X₅) :|: 0 ≤ X₀ ∧ X₁ ≤ X₃ ∧ X₃ ≤ X₄ ∧ X₀+X₂+1 ≤ X₁ ∧ X₁ ≤ X₀+X₃+1 ∧ X₅ ≤ X₀ ∧ X₀ ≤ X₅ ∧ X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ 0 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ X₃ ≤ X₄ ∧ X₂ ≤ X₄ ∧ X₂ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

2⋅X₂+2⋅X₄+X₀+2 {O(n)}

MPRF:

l2 [X₄-X₁ ]
l1 [X₄+1-X₁ ]

MPRF for transition t₆: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, X₁, X₂, X₃-1-X₅, X₄, X₅) :|: 0 ≤ X₀ ∧ X₁ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₀+X₃+1 ∧ X₀+X₃+1 ≤ X₄ ∧ X₅ ≤ X₀ ∧ X₀ ≤ X₅ ∧ X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ 0 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1+X₃ ≤ X₄ ∧ X₂ ≤ X₄ ∧ X₁ ≤ X₄ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

2⋅X₀+2⋅X₂+2⋅X₄+3 {O(n)}

MPRF:

l2 [X₃+1-X₁ ]
l1 [X₃-X₁ ]

MPRF for transition t₇: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, 1+X₅+X₁, X₂, X₃, X₄, X₅) :|: 0 ≤ X₀ ∧ X₁ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₀+X₃+1 ∧ X₀+X₃+1 ≤ X₄ ∧ X₅ ≤ X₀ ∧ X₀ ≤ X₅ ∧ X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ 0 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1+X₃ ≤ X₄ ∧ X₂ ≤ X₄ ∧ X₁ ≤ X₄ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

2⋅X₂+2⋅X₄+X₀+1 {O(n)}

MPRF:

l2 [X₄-X₁ ]
l1 [X₄-X₁ ]

All Bounds

Timebounds

Overall timebound:5⋅X₀+8⋅X₂+8⋅X₄+16 {O(n)}
t₁₂: 1 {O(1)}
t₈: 1 {O(1)}
t₁₀: 2⋅X₂+2⋅X₄+X₀+3 {O(n)}
t₁₁: 2⋅X₂+2⋅X₄+X₀+2 {O(n)}
t₄: 1 {O(1)}
t₆: 2⋅X₀+2⋅X₂+2⋅X₄+3 {O(n)}
t₇: 2⋅X₂+2⋅X₄+X₀+1 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 1 {O(1)}

Costbounds

Overall costbound: 5⋅X₀+8⋅X₂+8⋅X₄+16 {O(n)}
t₁₂: 1 {O(1)}
t₈: 1 {O(1)}
t₁₀: 2⋅X₂+2⋅X₄+X₀+3 {O(n)}
t₁₁: 2⋅X₂+2⋅X₄+X₀+2 {O(n)}
t₄: 1 {O(1)}
t₆: 2⋅X₀+2⋅X₂+2⋅X₄+3 {O(n)}
t₇: 2⋅X₂+2⋅X₄+X₀+1 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 1 {O(1)}

Sizebounds

t₁₂, X₀: X₀ {O(n)}
t₁₂, X₁: X₂ {O(n)}
t₁₂, X₂: X₂ {O(n)}
t₁₂, X₃: X₄ {O(n)}
t₁₂, X₄: X₄ {O(n)}
t₁₂, X₅: X₀ {O(n)}
t₈, X₀: 9⋅X₀ {O(n)}
t₈, X₁: 36⋅X₀⋅X₀+72⋅X₀⋅X₂+72⋅X₀⋅X₄+17⋅X₂+8⋅X₄+99⋅X₀+11 {O(n^2)}
t₈, X₂: 9⋅X₂ {O(n)}
t₈, X₃: 54⋅X₀⋅X₀+72⋅X₀⋅X₂+72⋅X₀⋅X₄+154⋅X₀+17⋅X₄+8⋅X₂+16 {O(n^2)}
t₈, X₄: 9⋅X₄ {O(n)}
t₈, X₅: 9⋅X₀ {O(n)}
t₁₀, X₀: 4⋅X₀ {O(n)}
t₁₀, X₁: 18⋅X₀⋅X₀+36⋅X₀⋅X₂+36⋅X₀⋅X₄+4⋅X₄+49⋅X₀+8⋅X₂+5 {O(n^2)}
t₁₀, X₂: 4⋅X₂ {O(n)}
t₁₀, X₃: 27⋅X₀⋅X₀+36⋅X₀⋅X₂+36⋅X₀⋅X₄+4⋅X₂+77⋅X₀+8⋅X₄+8 {O(n^2)}
t₁₀, X₄: 4⋅X₄ {O(n)}
t₁₀, X₅: 4⋅X₀ {O(n)}
t₁₁, X₀: 4⋅X₀ {O(n)}
t₁₁, X₁: 18⋅X₀⋅X₀+36⋅X₀⋅X₂+36⋅X₀⋅X₄+4⋅X₄+49⋅X₀+8⋅X₂+5 {O(n^2)}
t₁₁, X₂: 4⋅X₂ {O(n)}
t₁₁, X₃: 27⋅X₀⋅X₀+36⋅X₀⋅X₂+36⋅X₀⋅X₄+4⋅X₂+77⋅X₀+8⋅X₄+8 {O(n^2)}
t₁₁, X₄: 4⋅X₄ {O(n)}
t₁₁, X₅: 4⋅X₀ {O(n)}
t₄, X₀: 9⋅X₀ {O(n)}
t₄, X₁: 36⋅X₀⋅X₀+72⋅X₀⋅X₂+72⋅X₀⋅X₄+17⋅X₂+8⋅X₄+98⋅X₀+10 {O(n^2)}
t₄, X₂: 9⋅X₂ {O(n)}
t₄, X₃: 54⋅X₀⋅X₀+72⋅X₀⋅X₂+72⋅X₀⋅X₄+155⋅X₀+17⋅X₄+8⋅X₂+17 {O(n^2)}
t₄, X₄: 9⋅X₄ {O(n)}
t₄, X₅: 9⋅X₀ {O(n)}
t₆, X₀: 4⋅X₀ {O(n)}
t₆, X₁: 18⋅X₀⋅X₀+36⋅X₀⋅X₂+36⋅X₀⋅X₄+4⋅X₄+49⋅X₀+8⋅X₂+5 {O(n^2)}
t₆, X₂: 4⋅X₂ {O(n)}
t₆, X₃: 27⋅X₀⋅X₀+36⋅X₀⋅X₂+36⋅X₀⋅X₄+4⋅X₂+77⋅X₀+8⋅X₄+8 {O(n^2)}
t₆, X₄: 4⋅X₄ {O(n)}
t₆, X₅: 4⋅X₀ {O(n)}
t₇, X₀: 4⋅X₀ {O(n)}
t₇, X₁: 18⋅X₀⋅X₀+36⋅X₀⋅X₂+36⋅X₀⋅X₄+4⋅X₄+49⋅X₀+8⋅X₂+5 {O(n^2)}
t₇, X₂: 4⋅X₂ {O(n)}
t₇, X₃: 27⋅X₀⋅X₀+36⋅X₀⋅X₂+36⋅X₀⋅X₄+4⋅X₂+77⋅X₀+8⋅X₄+8 {O(n^2)}
t₇, X₄: 4⋅X₄ {O(n)}
t₇, X₅: 4⋅X₀ {O(n)}
t₀, X₀: X₀ {O(n)}
t₀, X₁: X₂ {O(n)}
t₀, X₂: X₂ {O(n)}
t₀, X₃: X₄ {O(n)}
t₀, X₄: X₄ {O(n)}
t₀, X₅: X₀ {O(n)}
t₁, X₀: X₀ {O(n)}
t₁, X₁: X₂ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₄ {O(n)}
t₁, X₄: X₄ {O(n)}
t₁, X₅: X₀ {O(n)}
t₂, X₀: X₀ {O(n)}
t₂, X₁: X₂ {O(n)}
t₂, X₂: X₂ {O(n)}
t₂, X₃: X₀+X₄+1 {O(n)}
t₂, X₄: X₄ {O(n)}
t₂, X₅: X₀ {O(n)}
t₃, X₀: X₀ {O(n)}
t₃, X₁: X₀+X₂+1 {O(n)}
t₃, X₂: X₂ {O(n)}
t₃, X₃: X₄ {O(n)}
t₃, X₄: X₄ {O(n)}
t₃, X₅: X₀ {O(n)}