Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅
Temp_Vars:
Locations: l0, l1, l2, l3, l4
Transitions:
t₈: l0(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₂, X₂, X₄, X₄, X₀)
t₆: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, 2⋅X₁, X₂, X₃, X₄, X₅) :|: X₁+1 ≤ X₃ ∧ 2 ≤ X₁ ∧ X₁+2 ≤ 2⋅X₃ ∧ X₃ ≤ X₀ ∧ X₅ ≤ X₀ ∧ X₀ ≤ X₅
t₇: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, X₁, X₂, X₃-1, X₄, X₅) :|: X₃ ≤ X₁ ∧ 2 ≤ X₁ ∧ X₁+2 ≤ 2⋅X₃ ∧ X₃ ≤ X₀ ∧ X₅ ≤ X₀ ∧ X₀ ≤ X₅
t₅: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, 2, X₂, X₃, X₄, X₅) :|: 2 ≤ X₃ ∧ X₃+1 ≤ X₀ ∧ X₃+1 ≤ X₁ ∧ 1 ≤ X₁ ∧ 0 ≤ 1+X₃ ∧ X₅ ≤ X₀ ∧ X₀ ≤ X₅
t₄: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, 1, X₂, X₃-1, X₄, X₅) :|: 0 ≤ X₃ ∧ X₃ ≤ 1 ∧ X₃+1 ≤ X₀ ∧ X₃+1 ≤ X₁ ∧ 1 ≤ X₁ ∧ 0 ≤ 1+X₃ ∧ X₅ ≤ X₀ ∧ X₀ ≤ X₅
t₃: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l4(X₀, X₁, X₂, X₃, X₄, X₅) :|: 0 ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₁ ∧ X₃+1 ≤ 0 ∧ 0 ≤ 1+X₃ ∧ X₅ ≤ X₀ ∧ X₀ ≤ X₅
t₂: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, 2, X₂, X₅, X₄, X₅) :|: 2 ≤ X₀ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₃ ≤ X₄ ∧ X₄ ≤ X₃ ∧ X₅ ≤ X₀ ∧ X₀ ≤ X₅
t₁: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, 1, X₂, X₅-1, X₄, X₅) :|: 0 ≤ X₀ ∧ X₀ ≤ 1 ∧ 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+1 ≤ 0 ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₃ ≤ X₄ ∧ X₄ ≤ X₃ ∧ X₅ ≤ X₀ ∧ X₀ ≤ X₅

Preprocessing

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

Found invariant X₅ ≤ X₀ ∧ 2 ≤ X₅ ∧ 4 ≤ X₃+X₅ ∧ X₃ ≤ X₅ ∧ 4 ≤ X₁+X₅ ∧ 4 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ X₃ ≤ X₀ ∧ 2 ≤ X₃ ∧ 4 ≤ X₁+X₃ ∧ 4 ≤ X₀+X₃ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location l1

Found invariant X₅ ≤ X₀ ∧ X₃ ≤ X₅ ∧ X₀ ≤ X₅ ∧ 1+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:
t₈: l0(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₂, X₂, X₄, X₄, X₀)
t₆: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, 2⋅X₁, X₂, X₃, X₄, X₅) :|: X₁+1 ≤ X₃ ∧ 2 ≤ X₁ ∧ X₁+2 ≤ 2⋅X₃ ∧ X₃ ≤ X₀ ∧ X₅ ≤ X₀ ∧ X₀ ≤ X₅ ∧ X₅ ≤ X₀ ∧ 2 ≤ X₅ ∧ 4 ≤ X₃+X₅ ∧ X₃ ≤ X₅ ∧ 4 ≤ X₁+X₅ ∧ 4 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ X₃ ≤ X₀ ∧ 2 ≤ X₃ ∧ 4 ≤ X₁+X₃ ∧ 4 ≤ X₀+X₃ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 2 ≤ X₀
t₇: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, X₁, X₂, X₃-1, X₄, X₅) :|: X₃ ≤ X₁ ∧ 2 ≤ X₁ ∧ X₁+2 ≤ 2⋅X₃ ∧ X₃ ≤ X₀ ∧ X₅ ≤ X₀ ∧ X₀ ≤ X₅ ∧ X₅ ≤ X₀ ∧ 2 ≤ X₅ ∧ 4 ≤ X₃+X₅ ∧ X₃ ≤ X₅ ∧ 4 ≤ X₁+X₅ ∧ 4 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ X₃ ≤ X₀ ∧ 2 ≤ X₃ ∧ 4 ≤ X₁+X₃ ∧ 4 ≤ X₀+X₃ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 2 ≤ X₀
t₅: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, 2, X₂, X₃, X₄, X₅) :|: 2 ≤ X₃ ∧ X₃+1 ≤ X₀ ∧ X₃+1 ≤ X₁ ∧ 1 ≤ X₁ ∧ 0 ≤ 1+X₃ ∧ X₅ ≤ X₀ ∧ X₀ ≤ X₅ ∧ X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ 0 ≤ 1+X₃+X₅ ∧ 1+X₃ ≤ X₅ ∧ 1 ≤ X₁+X₅ ∧ 0 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ 1+X₃ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ 1+X₀+X₃ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀
t₄: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, 1, X₂, X₃-1, X₄, X₅) :|: 0 ≤ X₃ ∧ X₃ ≤ 1 ∧ X₃+1 ≤ X₀ ∧ X₃+1 ≤ X₁ ∧ 1 ≤ X₁ ∧ 0 ≤ 1+X₃ ∧ X₅ ≤ X₀ ∧ X₀ ≤ X₅ ∧ X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ 0 ≤ 1+X₃+X₅ ∧ 1+X₃ ≤ X₅ ∧ 1 ≤ X₁+X₅ ∧ 0 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ 1+X₃ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ 1+X₀+X₃ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀
t₃: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l4(X₀, X₁, X₂, X₃, X₄, X₅) :|: 0 ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₁ ∧ X₃+1 ≤ 0 ∧ 0 ≤ 1+X₃ ∧ X₅ ≤ X₀ ∧ X₀ ≤ X₅ ∧ X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ 0 ≤ 1+X₃+X₅ ∧ 1+X₃ ≤ X₅ ∧ 1 ≤ X₁+X₅ ∧ 0 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ 1+X₃ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ 1+X₀+X₃ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀
t₂: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, 2, X₂, X₅, X₄, X₅) :|: 2 ≤ 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
t₁: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, 1, X₂, X₅-1, X₄, X₅) :|: 0 ≤ X₀ ∧ X₀ ≤ 1 ∧ 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+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

MPRF for transition t₇: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, X₁, X₂, X₃-1, X₄, X₅) :|: X₃ ≤ X₁ ∧ 2 ≤ X₁ ∧ X₁+2 ≤ 2⋅X₃ ∧ X₃ ≤ X₀ ∧ X₅ ≤ X₀ ∧ X₀ ≤ X₅ ∧ X₅ ≤ X₀ ∧ 2 ≤ X₅ ∧ 4 ≤ X₃+X₅ ∧ X₃ ≤ X₅ ∧ 4 ≤ X₁+X₅ ∧ 4 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ X₃ ≤ X₀ ∧ 2 ≤ X₃ ∧ 4 ≤ X₁+X₃ ∧ 4 ≤ X₀+X₃ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 2 ≤ X₀ of depth 1:

new bound:

X₀+3 {O(n)}

MPRF:

l2 [X₃-1 ]
l1 [X₃-1 ]

MPRF for transition t₄: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, 1, X₂, X₃-1, X₄, X₅) :|: 0 ≤ X₃ ∧ X₃ ≤ 1 ∧ X₃+1 ≤ X₀ ∧ X₃+1 ≤ X₁ ∧ 1 ≤ X₁ ∧ 0 ≤ 1+X₃ ∧ X₅ ≤ X₀ ∧ X₀ ≤ X₅ ∧ X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ 0 ≤ 1+X₃+X₅ ∧ 1+X₃ ≤ X₅ ∧ 1 ≤ X₁+X₅ ∧ 0 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ 1+X₃ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ 1+X₀+X₃ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₀+2 {O(n)}

MPRF:

l2 [X₃+1 ]
l1 [X₃ ]

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

new bound:

X₀+4 {O(n)}

MPRF:

l2 [X₃+2 ]
l1 [X₃+1 ]

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

Found invariant X₅ ≤ X₃ ∧ X₅ ≤ X₀ ∧ 2 ≤ X₅ ∧ 4 ≤ X₃+X₅ ∧ X₃ ≤ X₅ ∧ 4 ≤ X₁+X₅ ∧ 4 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ X₃ ≤ X₀ ∧ 2 ≤ X₃ ∧ 4 ≤ X₁+X₃ ∧ 4 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location l1

Found invariant X₅ ≤ X₀ ∧ X₃ ≤ X₅ ∧ X₀ ≤ X₅ ∧ 1+X₃ ≤ 0 ∧ X₃ ≤ X₀ for location l4

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

MPRF for transition t₆: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, 2⋅X₁, X₂, X₃, X₄, X₅) :|: X₁+1 ≤ X₃ ∧ 2 ≤ X₁ ∧ X₁+2 ≤ 2⋅X₃ ∧ X₃ ≤ X₀ ∧ X₅ ≤ X₀ ∧ X₀ ≤ X₅ ∧ X₅ ≤ X₀ ∧ 2 ≤ X₅ ∧ 4 ≤ X₃+X₅ ∧ X₃ ≤ X₅ ∧ 4 ≤ X₁+X₅ ∧ 4 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ X₃ ≤ X₀ ∧ 2 ≤ X₃ ∧ 4 ≤ X₁+X₃ ∧ 4 ≤ X₀+X₃ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 2 ≤ X₀ of depth 1:

new bound:

4⋅X₀⋅X₀+20⋅X₀+10 {O(n^2)}

MPRF:

l1 [2⋅X₃-X₁ ]
l2 [0 ]

Analysing control-flow refined program

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

Found invariant X₅ ≤ X₀ ∧ 2 ≤ X₅ ∧ 4 ≤ X₃+X₅ ∧ X₃ ≤ X₅ ∧ 4 ≤ X₁+X₅ ∧ X₁ ≤ X₅ ∧ 4 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ X₃ ≤ X₀ ∧ 2 ≤ X₃ ∧ 4 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 4 ≤ X₀+X₃ ∧ X₁ ≤ 2 ∧ X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location l1

Found invariant X₅ ≤ X₀ ∧ X₃ ≤ X₅ ∧ X₀ ≤ X₅ ∧ 1+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 ∧ 3 ≤ X₅ ∧ 6 ≤ X₃+X₅ ∧ X₃ ≤ X₅ ∧ 7 ≤ X₁+X₅ ∧ 6 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ X₃ ≤ X₀ ∧ 3 ≤ X₃ ∧ 7 ≤ X₁+X₃ ∧ 6 ≤ X₀+X₃ ∧ 4 ≤ X₁ ∧ 7 ≤ X₀+X₁ ∧ 3 ≤ X₀ for location n_l1___1

knowledge_propagation leads to new time bound X₀+4 {O(n)} for transition t₈₁: l1(X₀, X₁, X₂, X₃, X₄, X₅) → n_l1___1(X₀, 2⋅X₁, X₂, X₃, X₄, X₀) :|: X₃ ≤ X₀ ∧ 2 ≤ X₁ ∧ X₀ ≤ X₅ ∧ X₅ ≤ X₀ ∧ X₁ ≤ 2 ∧ 2 ≤ X₁ ∧ X₀ ≤ X₅ ∧ X₅ ≤ X₀ ∧ 2 ≤ X₃ ∧ 1+X₃ ≤ X₀ ∧ 2 ≤ X₁ ∧ X₃ ≤ X₀ ∧ 1+X₁ ≤ X₃ ∧ X₀ ≤ X₅ ∧ X₅ ≤ X₀ ∧ X₅ ≤ X₀ ∧ 2 ≤ X₅ ∧ 4 ≤ X₃+X₅ ∧ X₃ ≤ X₅ ∧ 4 ≤ X₁+X₅ ∧ X₁ ≤ X₅ ∧ 4 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ X₃ ≤ X₀ ∧ 2 ≤ X₃ ∧ 4 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 4 ≤ X₀+X₃ ∧ X₁ ≤ 2 ∧ X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 2 ≤ X₀

knowledge_propagation leads to new time bound 1 {O(1)} for transition t₈₂: l1(X₀, X₁, X₂, X₃, X₄, X₅) → n_l1___1(X₀, 2⋅X₁, X₂, X₃, X₄, X₀) :|: X₃ ≤ X₀ ∧ 2 ≤ X₁ ∧ X₀ ≤ X₅ ∧ X₅ ≤ X₀ ∧ X₀ ≤ X₅ ∧ X₅ ≤ X₀ ∧ X₀ ≤ X₃ ∧ X₃ ≤ X₀ ∧ X₁ ≤ 2 ∧ 2 ≤ X₁ ∧ 2 ≤ X₀ ∧ 2 ≤ X₁ ∧ X₃ ≤ X₀ ∧ 1+X₁ ≤ X₃ ∧ X₀ ≤ X₅ ∧ X₅ ≤ X₀ ∧ X₅ ≤ X₀ ∧ 2 ≤ X₅ ∧ 4 ≤ X₃+X₅ ∧ X₃ ≤ X₅ ∧ 4 ≤ X₁+X₅ ∧ X₁ ≤ X₅ ∧ 4 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ X₃ ≤ X₀ ∧ 2 ≤ X₃ ∧ 4 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 4 ≤ X₀+X₃ ∧ X₁ ≤ 2 ∧ X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 2 ≤ X₀

MPRF for transition t₈₀: n_l1___1(X₀, X₁, X₂, X₃, X₄, X₅) → n_l1___1(X₀, 2⋅X₁, X₂, X₃, X₄, X₀) :|: X₃ ≤ X₀ ∧ 2 ≤ X₁ ∧ X₀ ≤ X₅ ∧ X₅ ≤ X₀ ∧ X₀ ≤ X₅ ∧ X₅ ≤ X₀ ∧ 4 ≤ X₁ ∧ 2+X₁ ≤ 2⋅X₃ ∧ X₃ ≤ X₀ ∧ 2 ≤ X₁ ∧ X₃ ≤ X₀ ∧ 1+X₁ ≤ X₃ ∧ X₀ ≤ X₅ ∧ X₅ ≤ X₀ ∧ X₅ ≤ X₀ ∧ 3 ≤ X₅ ∧ 6 ≤ X₃+X₅ ∧ X₃ ≤ X₅ ∧ 7 ≤ X₁+X₅ ∧ 6 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ X₃ ≤ X₀ ∧ 3 ≤ X₃ ∧ 7 ≤ X₁+X₃ ∧ 6 ≤ X₀+X₃ ∧ 4 ≤ X₁ ∧ 7 ≤ X₀+X₁ ∧ 3 ≤ X₀ of depth 1:

new bound:

2⋅X₀⋅X₀+9⋅X₀+3 {O(n^2)}

MPRF:

l1 [X₀ ]
n_l1___1 [X₃-X₁ ]
l2 [X₀-2⋅X₅ ]

MPRF for transition t₈₅: n_l1___1(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, X₁, X₂, X₃-1, X₄, X₅) :|: X₃ ≤ X₁ ∧ 2 ≤ X₁ ∧ X₁+2 ≤ 2⋅X₃ ∧ X₃ ≤ X₀ ∧ X₅ ≤ X₀ ∧ X₀ ≤ X₅ ∧ X₅ ≤ X₀ ∧ 2 ≤ X₅ ∧ 4 ≤ X₃+X₅ ∧ X₃ ≤ X₅ ∧ 4 ≤ X₁+X₅ ∧ 4 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ X₃ ≤ X₀ ∧ 2 ≤ X₃ ∧ 4 ≤ X₁+X₃ ∧ 4 ≤ X₀+X₃ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 2 ≤ X₀ ∧ X₅ ≤ X₀ ∧ 3 ≤ X₅ ∧ 6 ≤ X₃+X₅ ∧ X₃ ≤ X₅ ∧ 7 ≤ X₁+X₅ ∧ 6 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ X₃ ≤ X₀ ∧ 3 ≤ X₃ ∧ 7 ≤ X₁+X₃ ∧ 6 ≤ X₀+X₃ ∧ 4 ≤ X₁ ∧ 7 ≤ X₀+X₁ ∧ 3 ≤ X₀ of depth 1:

new bound:

3⋅X₀+3 {O(n)}

MPRF:

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

CFR did not improve the program. Rolling back

All Bounds

Timebounds

Overall timebound:4⋅X₀⋅X₀+23⋅X₀+24 {O(n^2)}
t₈: 1 {O(1)}
t₆: 4⋅X₀⋅X₀+20⋅X₀+10 {O(n^2)}
t₇: X₀+3 {O(n)}
t₃: 1 {O(1)}
t₄: X₀+2 {O(n)}
t₅: X₀+4 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}

Costbounds

Overall costbound: 4⋅X₀⋅X₀+23⋅X₀+24 {O(n^2)}
t₈: 1 {O(1)}
t₆: 4⋅X₀⋅X₀+20⋅X₀+10 {O(n^2)}
t₇: X₀+3 {O(n)}
t₃: 1 {O(1)}
t₄: X₀+2 {O(n)}
t₅: X₀+4 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}

Sizebounds

t₈, X₀: X₀ {O(n)}
t₈, X₁: X₂ {O(n)}
t₈, X₂: X₂ {O(n)}
t₈, X₃: X₄ {O(n)}
t₈, X₄: X₄ {O(n)}
t₈, X₅: X₀ {O(n)}
t₆, X₀: 2⋅X₀ {O(n)}
t₆, X₁: 2^(4⋅X₀⋅X₀+20⋅X₀+10)⋅4 {O(EXP)}
t₆, X₂: 2⋅X₂ {O(n)}
t₆, X₃: 2⋅X₀ {O(n)}
t₆, X₄: 2⋅X₄ {O(n)}
t₆, X₅: 2⋅X₀ {O(n)}
t₇, X₀: 2⋅X₀ {O(n)}
t₇, X₁: 2^(4⋅X₀⋅X₀+20⋅X₀+10)⋅4+4 {O(EXP)}
t₇, X₂: 2⋅X₂ {O(n)}
t₇, X₃: 2⋅X₀ {O(n)}
t₇, X₄: 2⋅X₄ {O(n)}
t₇, X₅: 2⋅X₀ {O(n)}
t₃, X₀: 2⋅X₀+2 {O(n)}
t₃, X₁: 2 {O(1)}
t₃, X₂: 4⋅X₂ {O(n)}
t₃, X₃: 1 {O(1)}
t₃, X₄: 4⋅X₄ {O(n)}
t₃, X₅: 2⋅X₀+2 {O(n)}
t₄, X₀: 2⋅X₀+1 {O(n)}
t₄, X₁: 1 {O(1)}
t₄, X₂: 3⋅X₂ {O(n)}
t₄, X₃: 1 {O(1)}
t₄, X₄: 3⋅X₄ {O(n)}
t₄, X₅: 2⋅X₀+1 {O(n)}
t₅, X₀: 2⋅X₀ {O(n)}
t₅, X₁: 2 {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)}
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: 1 {O(1)}
t₁, X₁: 1 {O(1)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: 1 {O(1)}
t₁, X₄: X₄ {O(n)}
t₁, X₅: 1 {O(1)}
t₂, X₀: X₀ {O(n)}
t₂, X₁: 2 {O(1)}
t₂, X₂: X₂ {O(n)}
t₂, X₃: X₀ {O(n)}
t₂, X₄: X₄ {O(n)}
t₂, X₅: X₀ {O(n)}