Initial Problem
Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅
Temp_Vars:
Locations: l0, l1, l2, l3, l4
Transitions:
t₇: l0(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₂, X₂, X₄, X₄, X₀)
t₆: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, X₁-1, X₂, X₃, X₄, X₅) :|: 1 ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₁+1 ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₃ ∧ X₅ ≤ X₀ ∧ X₀ ≤ X₅
t₅: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, X₁, X₂, X₃-1, X₄, X₅) :|: X₃ ≤ X₀ ∧ 1 ≤ X₀ ∧ 1 ≤ X₃ ∧ X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ X₅ ≤ X₀ ∧ X₀ ≤ X₅
t₄: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, X₅-1, X₂, X₃, X₄, X₅) :|: 1 ≤ X₀ ∧ 1 ≤ X₃ ∧ 0 ≤ X₃ ∧ X₃+1 ≤ X₀ ∧ X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ X₅ ≤ X₀ ∧ X₀ ≤ X₅
t₃: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, X₅, X₂, X₃-1, X₄, X₅) :|: 1 ≤ X₃ ∧ X₀ ≤ 0 ∧ 0 ≤ X₃ ∧ X₃+1 ≤ X₀ ∧ X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ X₅ ≤ X₀ ∧ X₀ ≤ X₅
t₂: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l4(X₀, X₁, X₂, X₃, X₄, X₅) :|: 1 ≤ X₀ ∧ X₃ ≤ 0 ∧ 0 ≤ X₃ ∧ X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ X₅ ≤ X₀ ∧ X₀ ≤ X₅
t₁: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, X₅-1, X₂, X₅, X₄, X₅) :|: 1 ≤ X₀ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₃ ≤ X₄ ∧ X₄ ≤ X₃ ∧ X₅ ≤ X₀ ∧ X₀ ≤ X₅
t₀: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l4(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: l2→l2
Found invariant X₅ ≤ X₀ ∧ 1 ≤ X₅ ∧ 1 ≤ X₃+X₅ ∧ 1+X₃ ≤ X₅ ∧ 1 ≤ X₁+X₅ ∧ 1+X₁ ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 1 ≤ X₀+X₃ ∧ X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l2
Found invariant X₅ ≤ X₀ ∧ 1 ≤ X₅ ∧ 2 ≤ X₃+X₅ ∧ X₃ ≤ X₅ ∧ 1 ≤ X₁+X₅ ∧ 1+X₁ ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l1
Found invariant X₅ ≤ X₀ ∧ X₃ ≤ X₅ ∧ X₀ ≤ X₅ ∧ X₃ ≤ 0 ∧ X₃ ≤ X₀ for location l4
Found invariant X₅ ≤ X₀ ∧ X₀ ≤ X₅ ∧ X₄ ≤ X₃ ∧ X₃ ≤ X₄ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂ 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:
t₇: l0(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₂, X₂, X₄, X₄, X₀)
t₆: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, X₁-1, X₂, X₃, X₄, X₅) :|: 1 ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₁+1 ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₃ ∧ X₅ ≤ X₀ ∧ X₀ ≤ X₅ ∧ X₅ ≤ X₀ ∧ 1 ≤ X₅ ∧ 2 ≤ X₃+X₅ ∧ X₃ ≤ X₅ ∧ 1 ≤ X₁+X₅ ∧ 1+X₁ ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₅: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, X₁, X₂, X₃-1, X₄, X₅) :|: X₃ ≤ X₀ ∧ 1 ≤ X₀ ∧ 1 ≤ X₃ ∧ X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ X₅ ≤ X₀ ∧ X₀ ≤ X₅ ∧ X₅ ≤ X₀ ∧ 1 ≤ X₅ ∧ 2 ≤ X₃+X₅ ∧ X₃ ≤ X₅ ∧ 1 ≤ X₁+X₅ ∧ 1+X₁ ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₄: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, X₅-1, X₂, X₃, X₄, X₅) :|: 1 ≤ X₀ ∧ 1 ≤ X₃ ∧ 0 ≤ X₃ ∧ X₃+1 ≤ X₀ ∧ X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ X₅ ≤ X₀ ∧ X₀ ≤ X₅ ∧ X₅ ≤ X₀ ∧ 1 ≤ X₅ ∧ 1 ≤ X₃+X₅ ∧ 1+X₃ ≤ X₅ ∧ 1 ≤ X₁+X₅ ∧ 1+X₁ ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 1 ≤ X₀+X₃ ∧ X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₂: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l4(X₀, X₁, X₂, X₃, X₄, X₅) :|: 1 ≤ X₀ ∧ X₃ ≤ 0 ∧ 0 ≤ X₃ ∧ X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ X₅ ≤ X₀ ∧ X₀ ≤ X₅ ∧ X₅ ≤ X₀ ∧ 1 ≤ X₅ ∧ 1 ≤ X₃+X₅ ∧ 1+X₃ ≤ X₅ ∧ 1 ≤ X₁+X₅ ∧ 1+X₁ ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 1 ≤ X₀+X₃ ∧ X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₁: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, X₅-1, X₂, X₅, X₄, X₅) :|: 1 ≤ X₀ ∧ 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: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l4(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, X₁, X₂, X₃-1, X₄, X₅) :|: X₃ ≤ X₀ ∧ 1 ≤ X₀ ∧ 1 ≤ X₃ ∧ X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ X₅ ≤ X₀ ∧ X₀ ≤ X₅ ∧ X₅ ≤ X₀ ∧ 1 ≤ X₅ ∧ 2 ≤ X₃+X₅ ∧ X₃ ≤ X₅ ∧ 1 ≤ X₁+X₅ ∧ 1+X₁ ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₀ {O(n)}
MPRF:
l2 [X₃ ]
l1 [X₃ ]
MPRF for transition t₄: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, X₅-1, X₂, X₃, X₄, X₅) :|: 1 ≤ X₀ ∧ 1 ≤ X₃ ∧ 0 ≤ X₃ ∧ X₃+1 ≤ X₀ ∧ X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ X₅ ≤ X₀ ∧ X₀ ≤ X₅ ∧ X₅ ≤ X₀ ∧ 1 ≤ X₅ ∧ 1 ≤ X₃+X₅ ∧ 1+X₃ ≤ X₅ ∧ 1 ≤ X₁+X₅ ∧ 1+X₁ ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 1 ≤ X₀+X₃ ∧ X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₀ {O(n)}
MPRF:
l2 [X₃+1 ]
l1 [X₃ ]
MPRF for transition t₆: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, X₁-1, X₂, X₃, X₄, X₅) :|: 1 ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₁+1 ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₃ ∧ X₅ ≤ X₀ ∧ X₀ ≤ X₅ ∧ X₅ ≤ X₀ ∧ 1 ≤ X₅ ∧ 2 ≤ X₃+X₅ ∧ X₃ ≤ X₅ ∧ 1 ≤ X₁+X₅ ∧ 1+X₁ ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
2⋅X₀⋅X₀+2⋅X₀+1 {O(n^2)}
MPRF:
l2 [0 ]
l1 [X₁+1 ]
Analysing control-flow refined program
Found invariant X₅ ≤ X₀ ∧ 1 ≤ X₅ ∧ 1 ≤ X₃+X₅ ∧ 1+X₃ ≤ X₅ ∧ 1 ≤ X₁+X₅ ∧ 1+X₁ ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 1 ≤ X₀+X₃ ∧ X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l2
Found invariant X₅ ≤ 1+X₁ ∧ X₅ ≤ X₀ ∧ 1 ≤ X₅ ∧ 2 ≤ X₃+X₅ ∧ X₃ ≤ X₅ ∧ 1 ≤ X₁+X₅ ∧ 1+X₁ ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ X₃ ≤ 1+X₁ ∧ X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ X₀ ≤ 1+X₁ ∧ 1 ≤ X₀ for location l1
Found invariant X₅ ≤ X₀ ∧ X₃ ≤ X₅ ∧ X₀ ≤ X₅ ∧ X₃ ≤ 0 ∧ X₃ ≤ X₀ for location l4
Found invariant X₅ ≤ X₀ ∧ X₀ ≤ X₅ ∧ X₄ ≤ X₃ ∧ X₃ ≤ X₄ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂ for location l3
Found invariant X₅ ≤ X₀ ∧ 2 ≤ X₅ ∧ 3 ≤ X₃+X₅ ∧ X₃ ≤ X₅ ∧ 2 ≤ X₁+X₅ ∧ 2+X₁ ≤ X₅ ∧ 4 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 3 ≤ X₀+X₃ ∧ 2+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ 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, X₁, X₂, X₃-1, X₄, X₅) :|: X₃ ≤ X₀ ∧ 1 ≤ X₀ ∧ 1 ≤ X₃ ∧ X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ X₅ ≤ X₀ ∧ X₀ ≤ X₅ ∧ X₅ ≤ X₀ ∧ 1 ≤ X₅ ∧ 2 ≤ X₃+X₅ ∧ X₃ ≤ X₅ ∧ 1 ≤ X₁+X₅ ∧ 1+X₁ ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ ∧ X₅ ≤ 1+X₁ ∧ X₅ ≤ X₀ ∧ 1 ≤ X₅ ∧ 2 ≤ X₃+X₅ ∧ X₃ ≤ X₅ ∧ 1 ≤ X₁+X₅ ∧ 1+X₁ ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ X₃ ≤ 1+X₁ ∧ X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ X₀ ≤ 1+X₁ ∧ 1 ≤ X₀
knowledge_propagation leads to new time bound X₀ {O(n)} for transition t₅₅: l1(X₀, X₁, X₂, X₃, X₄, X₅) → n_l1___1(X₀, X₁-1, X₂, X₃, X₄, X₀) :|: X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ X₀ ≤ X₅ ∧ X₅ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ X₅ ∧ X₅ ≤ X₀ ∧ 1 ≤ X₃ ∧ 1+X₃ ≤ X₀ ∧ X₀ ≤ X₅ ∧ X₅ ≤ X₀ ∧ 1 ≤ X₁ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₃ ∧ X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 1 ≤ X₁ ∧ X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ X₅ ∧ X₅ ≤ X₀ ∧ X₅ ≤ 1+X₁ ∧ X₅ ≤ X₀ ∧ 1 ≤ X₅ ∧ 2 ≤ X₃+X₅ ∧ X₃ ≤ X₅ ∧ 1 ≤ X₁+X₅ ∧ 1+X₁ ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ X₃ ≤ 1+X₁ ∧ X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ X₀ ≤ 1+X₁ ∧ 1 ≤ X₀
knowledge_propagation leads to new time bound 1 {O(1)} for transition t₅₆: l1(X₀, X₁, X₂, X₃, X₄, X₅) → n_l1___1(X₀, X₁-1, X₂, X₃, X₄, X₀) :|: X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ X₅ ∧ X₅ ≤ X₀ ∧ X₃ ≤ X₅ ∧ X₅ ≤ X₃ ∧ X₀ ≤ X₃ ∧ X₃ ≤ X₀ ∧ 1+X₁ ≤ X₃ ∧ X₃ ≤ 1+X₁ ∧ 1 ≤ X₃ ∧ 1 ≤ X₃ ∧ 1 ≤ X₁ ∧ X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ X₅ ∧ X₅ ≤ X₀ ∧ X₅ ≤ 1+X₁ ∧ X₅ ≤ X₀ ∧ 1 ≤ X₅ ∧ 2 ≤ X₃+X₅ ∧ X₃ ≤ X₅ ∧ 1 ≤ X₁+X₅ ∧ 1+X₁ ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ X₃ ≤ 1+X₁ ∧ X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ X₀ ≤ 1+X₁ ∧ 1 ≤ X₀
MPRF for transition t₅₄: n_l1___1(X₀, X₁, X₂, X₃, X₄, X₅) → n_l1___1(X₀, X₁-1, X₂, X₃, X₄, X₀) :|: X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ X₅ ∧ X₅ ≤ X₀ ∧ X₀ ≤ X₅ ∧ X₅ ≤ X₀ ∧ 0 ≤ X₁ ∧ 2+X₁ ≤ X₀ ∧ 1 ≤ X₃ ∧ X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 1 ≤ X₁ ∧ X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ X₅ ∧ X₅ ≤ X₀ ∧ X₅ ≤ X₀ ∧ 2 ≤ X₅ ∧ 3 ≤ X₃+X₅ ∧ X₃ ≤ X₅ ∧ 2 ≤ X₁+X₅ ∧ 2+X₁ ≤ X₅ ∧ 4 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 3 ≤ X₀+X₃ ∧ 2+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀ of depth 1:
new bound:
16⋅X₀⋅X₀+2⋅X₀ {O(n^2)}
MPRF:
l1 [2⋅X₁ ]
n_l1___1 [X₀+X₁-1 ]
l2 [X₀-1 ]
MPRF for transition t₅₉: n_l1___1(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, X₁, X₂, X₃-1, X₄, X₅) :|: X₃ ≤ X₀ ∧ 1 ≤ X₀ ∧ 1 ≤ X₃ ∧ X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ X₅ ≤ X₀ ∧ X₀ ≤ X₅ ∧ X₅ ≤ X₀ ∧ 1 ≤ X₅ ∧ 2 ≤ X₃+X₅ ∧ X₃ ≤ X₅ ∧ 1 ≤ X₁+X₅ ∧ 1+X₁ ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ ∧ X₅ ≤ X₀ ∧ 2 ≤ X₅ ∧ 3 ≤ X₃+X₅ ∧ X₃ ≤ X₅ ∧ 2 ≤ X₁+X₅ ∧ 2+X₁ ≤ X₅ ∧ 4 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 3 ≤ X₀+X₃ ∧ 2+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀ of depth 1:
new bound:
3⋅X₀ {O(n)}
MPRF:
l1 [X₀+X₃-X₁ ]
n_l1___1 [X₃+1 ]
l2 [X₀+X₃+1-X₅ ]
CFR did not improve the program. Rolling back
All Bounds
Timebounds
Overall timebound:2⋅X₀⋅X₀+4⋅X₀+5 {O(n^2)}
t₇: 1 {O(1)}
t₅: X₀ {O(n)}
t₆: 2⋅X₀⋅X₀+2⋅X₀+1 {O(n^2)}
t₂: 1 {O(1)}
t₄: X₀ {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
Costbounds
Overall costbound: 2⋅X₀⋅X₀+4⋅X₀+5 {O(n^2)}
t₇: 1 {O(1)}
t₅: X₀ {O(n)}
t₆: 2⋅X₀⋅X₀+2⋅X₀+1 {O(n^2)}
t₂: 1 {O(1)}
t₄: X₀ {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
Sizebounds
t₇, X₀: X₀ {O(n)}
t₇, X₁: X₂ {O(n)}
t₇, X₂: X₂ {O(n)}
t₇, X₃: X₄ {O(n)}
t₇, X₄: X₄ {O(n)}
t₇, X₅: X₀ {O(n)}
t₅, X₀: 2⋅X₀ {O(n)}
t₅, X₁: 0 {O(1)}
t₅, X₂: 2⋅X₂ {O(n)}
t₅, X₃: 2⋅X₀ {O(n)}
t₅, X₄: 2⋅X₄ {O(n)}
t₅, X₅: 2⋅X₀ {O(n)}
t₆, X₀: 2⋅X₀ {O(n)}
t₆, X₁: 3⋅X₀ {O(n)}
t₆, X₂: 2⋅X₂ {O(n)}
t₆, X₃: 2⋅X₀ {O(n)}
t₆, X₄: 2⋅X₄ {O(n)}
t₆, X₅: 2⋅X₀ {O(n)}
t₂, X₀: 2⋅X₀ {O(n)}
t₂, X₁: 0 {O(1)}
t₂, X₂: 2⋅X₂ {O(n)}
t₂, X₃: 0 {O(1)}
t₂, X₄: 2⋅X₄ {O(n)}
t₂, X₅: 2⋅X₀ {O(n)}
t₄, X₀: 2⋅X₀ {O(n)}
t₄, X₁: 2⋅X₀ {O(n)}
t₄, X₂: 2⋅X₂ {O(n)}
t₄, X₃: 2⋅X₀ {O(n)}
t₄, X₄: 2⋅X₄ {O(n)}
t₄, X₅: 2⋅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: X₀ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₀ {O(n)}
t₁, X₄: X₄ {O(n)}
t₁, X₅: X₀ {O(n)}