Initial Problem

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

Preprocessing

Cut unsatisfiable transition t₃: l1→l3

Cut unsatisfiable transition t₈: l2→l2

Found invariant X₅ ≤ X₁ ∧ X₅ ≤ X₀ ∧ 1 ≤ X₅ ∧ 1 ≤ X₃+X₅ ∧ 1+X₃ ≤ X₅ ∧ 2 ≤ X₁+X₅ ∧ X₁ ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ for location l2

Found invariant X₅ ≤ X₀ ∧ 1 ≤ X₅ ∧ 2 ≤ X₃+X₅ ∧ X₃ ≤ X₅ ∧ 1 ≤ X₁+X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ 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 ∧ X₃ ≤ X₅ ∧ X₀ ≤ X₅ ∧ X₃ ≤ 0 ∧ X₃ ≤ X₀ 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:
t₉: l0(X₀, X₁, X₂, X₃, X₄, X₅) → l4(X₀, X₂, X₂, X₄, X₄, X₀)
t₄: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, X₁-1, X₂, X₃, X₄, X₅) :|: 1 ≤ X₃ ∧ 1 ≤ X₁ ∧ 0 ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₅ ≤ X₀ ∧ X₀ ≤ X₅ ∧ X₅ ≤ X₀ ∧ 1 ≤ X₅ ∧ 2 ≤ X₃+X₅ ∧ X₃ ≤ X₅ ∧ 1 ≤ X₁+X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₅: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, X₅, X₂, X₃-1, X₄, X₅) :|: 1 ≤ X₃ ∧ X₃ ≤ X₀ ∧ X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ X₅ ≤ X₀ ∧ X₀ ≤ X₅ ∧ X₅ ≤ X₀ ∧ 1 ≤ X₅ ∧ 2 ≤ X₃+X₅ ∧ X₃ ≤ X₅ ∧ 1 ≤ X₁+X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₇: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, X₁-1, X₂, X₃, X₄, X₅) :|: 1 ≤ X₃ ∧ 1 ≤ X₀ ∧ 0 ≤ X₃ ∧ X₃+1 ≤ X₀ ∧ X₅ ≤ X₀ ∧ X₀ ≤ X₅ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₅ ≤ X₁ ∧ X₅ ≤ X₀ ∧ 1 ≤ X₅ ∧ 1 ≤ X₃+X₅ ∧ 1+X₃ ≤ X₅ ∧ 2 ≤ X₁+X₅ ∧ X₁ ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀
t₆: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁, X₂, X₃, X₄, X₅) :|: 1 ≤ X₀ ∧ X₃ ≤ 0 ∧ 0 ≤ X₃ ∧ X₅ ≤ X₀ ∧ X₀ ≤ X₅ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₅ ≤ X₁ ∧ X₅ ≤ X₀ ∧ 1 ≤ X₅ ∧ 1 ≤ X₃+X₅ ∧ 1+X₃ ≤ X₅ ∧ 2 ≤ X₁+X₅ ∧ X₁ ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀
t₁: l4(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, X₁-1, X₂, X₅, X₄, X₅) :|: 1 ≤ X₀ ∧ 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
t₂: l4(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, X₅, X₂, X₅-1, X₄, X₅) :|: 1 ≤ X₀ ∧ X₂ ≤ 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
t₀: l4(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁, X₂, X₅, X₄, X₅) :|: X₀ ≤ 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

MPRF for transition t₅: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, X₅, X₂, X₃-1, X₄, X₅) :|: 1 ≤ X₃ ∧ X₃ ≤ X₀ ∧ X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ X₅ ≤ X₀ ∧ X₀ ≤ X₅ ∧ X₅ ≤ X₀ ∧ 1 ≤ X₅ ∧ 2 ≤ X₃+X₅ ∧ X₃ ≤ X₅ ∧ 1 ≤ X₁+X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

2⋅X₀ {O(n)}

MPRF:

l2 [X₃ ]
l1 [X₃ ]

MPRF for transition t₇: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, X₁-1, X₂, X₃, X₄, X₅) :|: 1 ≤ X₃ ∧ 1 ≤ X₀ ∧ 0 ≤ X₃ ∧ X₃+1 ≤ X₀ ∧ X₅ ≤ X₀ ∧ X₀ ≤ X₅ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₅ ≤ X₁ ∧ X₅ ≤ X₀ ∧ 1 ≤ X₅ ∧ 1 ≤ X₃+X₅ ∧ 1+X₃ ≤ X₅ ∧ 2 ≤ X₁+X₅ ∧ X₁ ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

2⋅X₀+1 {O(n)}

MPRF:

l2 [X₃+1 ]
l1 [X₃ ]

MPRF for transition t₄: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, X₁-1, X₂, X₃, X₄, X₅) :|: 1 ≤ X₃ ∧ 1 ≤ X₁ ∧ 0 ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₅ ≤ X₀ ∧ X₀ ≤ X₅ ∧ X₅ ≤ X₀ ∧ 1 ≤ X₅ ∧ 2 ≤ X₃+X₅ ∧ X₃ ≤ X₅ ∧ 1 ≤ X₁+X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

10⋅X₀⋅X₀+7⋅X₀+X₂+2 {O(n^2)}

MPRF:

l1 [X₁+1 ]
l2 [0 ]

Analysing control-flow refined program

Found invariant X₅ ≤ X₁ ∧ X₅ ≤ X₀ ∧ 1 ≤ X₅ ∧ 1 ≤ X₃+X₅ ∧ 1+X₃ ≤ X₅ ∧ 2 ≤ X₁+X₅ ∧ X₁ ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ for location l2

Found invariant X₅ ≤ X₀ ∧ 1 ≤ X₅ ∧ 2 ≤ X₃+X₅ ∧ X₃ ≤ X₅ ∧ 1 ≤ X₁+X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ 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 ∧ X₃ ≤ X₅ ∧ X₀ ≤ X₅ ∧ X₃ ≤ 0 ∧ X₃ ≤ X₀ for location l3

Found invariant X₅ ≤ X₀ ∧ 1 ≤ X₅ ∧ 2 ≤ X₃+X₅ ∧ X₃ ≤ X₅ ∧ 1 ≤ X₁+X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l1___1

knowledge_propagation leads to new time bound 1 {O(1)} for transition t₅: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, X₅, X₂, X₃-1, X₄, X₅) :|: 1 ≤ X₃ ∧ X₃ ≤ X₀ ∧ X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ X₅ ≤ X₀ ∧ X₀ ≤ X₅ ∧ X₅ ≤ X₀ ∧ 1 ≤ X₅ ∧ 2 ≤ X₃+X₅ ∧ X₃ ≤ X₅ ∧ 1 ≤ X₁+X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ ∧ X₅ ≤ X₀ ∧ 1 ≤ X₅ ∧ 2 ≤ X₃+X₅ ∧ X₃ ≤ X₅ ∧ 1 ≤ X₁+X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀

knowledge_propagation leads to new time bound 2⋅X₀+1 {O(n)} for transition t₆₅: l1(X₀, X₁, X₂, X₃, X₄, X₅) → n_l1___1(X₀, X₁-1, X₂, X₃, X₄, X₀) :|: 1 ≤ X₁ ∧ X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ X₀ ≤ X₅ ∧ X₅ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ X₅ ∧ X₅ ≤ X₀ ∧ 1 ≤ X₃ ∧ 1+X₃ ≤ X₀ ∧ X₀ ≤ X₅ ∧ X₅ ≤ X₀ ∧ 1 ≤ X₃ ∧ X₃ ≤ X₀ ∧ 1 ≤ X₁ ∧ X₀ ≤ X₅ ∧ X₅ ≤ X₀ ∧ 1 ≤ X₃ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₃ ∧ 1 ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₅ ∧ X₅ ≤ X₀ ∧ X₅ ≤ X₀ ∧ 1 ≤ X₅ ∧ 2 ≤ X₃+X₅ ∧ X₃ ≤ X₅ ∧ 1 ≤ X₁+X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀

knowledge_propagation leads to new time bound 1 {O(1)} for transition t₆₆: l1(X₀, X₁, X₂, X₃, X₄, X₅) → n_l1___1(X₀, X₁-1, X₂, X₃, X₄, X₀) :|: X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ X₀ ≤ X₅ ∧ X₅ ≤ X₀ ∧ 1+X₁ ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ X₀ ≤ X₃ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₅ ∧ X₅ ≤ X₀ ∧ 1 ≤ X₀ ∧ 0 ≤ X₁ ∧ X₀ ≤ X₅ ∧ X₅ ≤ X₀ ∧ 1 ≤ X₃ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₃ ∧ 1 ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₅ ∧ X₅ ≤ X₀ ∧ X₅ ≤ X₀ ∧ 1 ≤ X₅ ∧ 2 ≤ X₃+X₅ ∧ X₃ ≤ X₅ ∧ 1 ≤ X₁+X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀

MPRF for transition t₆₄: n_l1___1(X₀, X₁, X₂, X₃, X₄, X₅) → n_l1___1(X₀, X₁-1, X₂, X₃, X₄, X₀) :|: X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ X₀ ≤ X₅ ∧ X₅ ≤ X₀ ∧ X₀ ≤ X₅ ∧ X₅ ≤ X₀ ∧ 1 ≤ X₃ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₃ ∧ 1 ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₅ ∧ X₅ ≤ X₀ ∧ X₅ ≤ X₀ ∧ 1 ≤ X₅ ∧ 2 ≤ X₃+X₅ ∧ X₃ ≤ X₅ ∧ 1 ≤ X₁+X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

10⋅X₀⋅X₀+5⋅X₀+X₂ {O(n^2)}

MPRF:

l1 [X₁ ]
n_l1___1 [X₁+1 ]
l2 [0 ]

MPRF for transition t₆₉: n_l1___1(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, X₅, X₂, X₃-1, X₄, X₅) :|: 1 ≤ X₃ ∧ X₃ ≤ X₀ ∧ X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ X₅ ≤ X₀ ∧ X₀ ≤ X₅ ∧ X₅ ≤ X₀ ∧ 1 ≤ X₅ ∧ 2 ≤ X₃+X₅ ∧ X₃ ≤ X₅ ∧ 1 ≤ X₁+X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ ∧ X₅ ≤ X₀ ∧ 1 ≤ X₅ ∧ 2 ≤ X₃+X₅ ∧ X₃ ≤ X₅ ∧ 1 ≤ X₁+X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

6⋅X₀ {O(n)}

MPRF:

l1 [X₃+X₅-X₀ ]
n_l1___1 [X₃ ]
l2 [X₃+X₅-X₀ ]

CFR did not improve the program. Rolling back

All Bounds

Timebounds

Overall timebound:10⋅X₀⋅X₀+11⋅X₀+X₂+8 {O(n^2)}
t₉: 1 {O(1)}
t₄: 10⋅X₀⋅X₀+7⋅X₀+X₂+2 {O(n^2)}
t₅: 2⋅X₀ {O(n)}
t₆: 1 {O(1)}
t₇: 2⋅X₀+1 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}

Costbounds

Overall costbound: 10⋅X₀⋅X₀+11⋅X₀+X₂+8 {O(n^2)}
t₉: 1 {O(1)}
t₄: 10⋅X₀⋅X₀+7⋅X₀+X₂+2 {O(n^2)}
t₅: 2⋅X₀ {O(n)}
t₆: 1 {O(1)}
t₇: 2⋅X₀+1 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}

Sizebounds

t₉, X₀: X₀ {O(n)}
t₉, X₁: X₂ {O(n)}
t₉, X₂: X₂ {O(n)}
t₉, X₃: X₄ {O(n)}
t₉, X₄: X₄ {O(n)}
t₉, X₅: X₀ {O(n)}
t₄, X₀: 3⋅X₀ {O(n)}
t₄, X₁: 5⋅X₀+X₂ {O(n)}
t₄, X₂: 3⋅X₂ {O(n)}
t₄, X₃: 3⋅X₀ {O(n)}
t₄, X₄: 3⋅X₄ {O(n)}
t₄, X₅: 3⋅X₀ {O(n)}
t₅, X₀: 3⋅X₀ {O(n)}
t₅, X₁: 4⋅X₀ {O(n)}
t₅, X₂: 3⋅X₂ {O(n)}
t₅, X₃: 3⋅X₀ {O(n)}
t₅, X₄: 3⋅X₄ {O(n)}
t₅, X₅: 3⋅X₀ {O(n)}
t₆, X₀: 4⋅X₀ {O(n)}
t₆, X₁: 5⋅X₀ {O(n)}
t₆, X₂: 4⋅X₂ {O(n)}
t₆, X₃: 0 {O(1)}
t₆, X₄: 4⋅X₄ {O(n)}
t₆, X₅: 4⋅X₀ {O(n)}
t₇, X₀: 3⋅X₀ {O(n)}
t₇, X₁: 5⋅X₀ {O(n)}
t₇, X₂: 3⋅X₂ {O(n)}
t₇, X₃: 3⋅X₀ {O(n)}
t₇, X₄: 3⋅X₄ {O(n)}
t₇, X₅: 3⋅X₀ {O(n)}
t₀, X₀: X₀ {O(n)}
t₀, X₁: X₂ {O(n)}
t₀, X₂: X₂ {O(n)}
t₀, X₃: X₀ {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: X₀ {O(n)}
t₁, X₄: X₄ {O(n)}
t₁, X₅: X₀ {O(n)}
t₂, X₀: X₀ {O(n)}
t₂, X₁: X₀ {O(n)}
t₂, X₂: X₂ {O(n)}
t₂, X₃: X₀ {O(n)}
t₂, X₄: X₄ {O(n)}
t₂, X₅: X₀ {O(n)}