Initial Problem
Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆
Temp_Vars: H
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l1(H, 0, X₂, X₃, X₄, X₅, X₆)
t₁: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l1(X₀, X₁+1, X₂, X₃, X₄, X₅, X₆) :|: X₁+1 ≤ X₂
t₉: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l2(X₀, X₁, X₂, X₂, 0, X₅, X₆) :|: X₂ ≤ X₁
t₂: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l3(X₀, X₁, X₂, X₃, X₄, 0, X₆) :|: 2+X₄ ≤ X₃
t₈: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l4(X₀, X₁, X₂, X₃, 0, X₅, X₆) :|: X₃ ≤ X₄+1
t₇: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l2(X₀, X₁, X₂, X₃, X₄+1, X₅, X₆) :|: X₃ ≤ X₅+X₄+1
t₃: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l3(X₀, X₁, X₂, X₃, X₄, X₅+1, X₆) :|: X₄+2+X₅ ≤ X₃
t₄: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l3(X₀, X₁, X₂, X₃, X₄, X₅+1, H) :|: X₄+2+X₅ ≤ X₃
t₅: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l4(X₀, X₁, X₂, X₃, X₄+1, X₅, X₆) :|: 2+X₄ ≤ X₃
t₆: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₃ ≤ X₄+1
Preprocessing
Eliminate variables {H,X₀,X₆} that do not contribute to the problem
Found invariant X₄ ≤ X₁ ∧ 0 ≤ X₄ ∧ 0 ≤ X₁+X₄ ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₂ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₁ for location l2
Found invariant X₄ ≤ X₁ ∧ 0 ≤ X₄ ∧ X₃ ≤ 1+X₄ ∧ X₂ ≤ 1+X₄ ∧ 0 ≤ X₁+X₄ ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₂ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₁ for location l5
Found invariant 0 ≤ X₁ for location l1
Found invariant X₄ ≤ X₁ ∧ 0 ≤ X₄ ∧ 0 ≤ X₁+X₄ ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₂ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₁ for location l4
Found invariant 1+X₅ ≤ X₃ ∧ 1+X₅ ≤ X₂ ∧ 1+X₅ ≤ X₁ ∧ 0 ≤ X₅ ∧ 0 ≤ X₄+X₅ ∧ 2 ≤ X₃+X₅ ∧ 2 ≤ X₂+X₅ ∧ 2 ≤ X₁+X₅ ∧ 2+X₄ ≤ X₃ ∧ 2+X₄ ≤ X₂ ∧ 2+X₄ ≤ X₁ ∧ 0 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₁+X₄ ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 2 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 4 ≤ X₁+X₃ ∧ X₂ ≤ X₁ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 2 ≤ X₁ for location l3
Problem after Preprocessing
Start: l0
Program_Vars: X₁, X₂, X₃, X₄, X₅
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₂₃: l0(X₁, X₂, X₃, X₄, X₅) → l1(0, X₂, X₃, X₄, X₅)
t₂₄: l1(X₁, X₂, X₃, X₄, X₅) → l1(X₁+1, X₂, X₃, X₄, X₅) :|: X₁+1 ≤ X₂ ∧ 0 ≤ X₁
t₂₅: l1(X₁, X₂, X₃, X₄, X₅) → l2(X₁, X₂, X₂, 0, X₅) :|: X₂ ≤ X₁ ∧ 0 ≤ X₁
t₂₆: l2(X₁, X₂, X₃, X₄, X₅) → l3(X₁, X₂, X₃, X₄, 0) :|: 2+X₄ ≤ X₃ ∧ X₄ ≤ X₁ ∧ 0 ≤ X₄ ∧ 0 ≤ X₁+X₄ ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₂ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₁
t₂₇: l2(X₁, X₂, X₃, X₄, X₅) → l4(X₁, X₂, X₃, 0, X₅) :|: X₃ ≤ X₄+1 ∧ X₄ ≤ X₁ ∧ 0 ≤ X₄ ∧ 0 ≤ X₁+X₄ ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₂ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₁
t₃₀: l3(X₁, X₂, X₃, X₄, X₅) → l2(X₁, X₂, X₃, X₄+1, X₅) :|: X₃ ≤ X₅+X₄+1 ∧ 1+X₅ ≤ X₃ ∧ 1+X₅ ≤ X₂ ∧ 1+X₅ ≤ X₁ ∧ 0 ≤ X₅ ∧ 0 ≤ X₄+X₅ ∧ 2 ≤ X₃+X₅ ∧ 2 ≤ X₂+X₅ ∧ 2 ≤ X₁+X₅ ∧ 2+X₄ ≤ X₃ ∧ 2+X₄ ≤ X₂ ∧ 2+X₄ ≤ X₁ ∧ 0 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₁+X₄ ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 2 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 4 ≤ X₁+X₃ ∧ X₂ ≤ X₁ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 2 ≤ X₁
t₂₈: l3(X₁, X₂, X₃, X₄, X₅) → l3(X₁, X₂, X₃, X₄, X₅+1) :|: X₄+2+X₅ ≤ X₃ ∧ 1+X₅ ≤ X₃ ∧ 1+X₅ ≤ X₂ ∧ 1+X₅ ≤ X₁ ∧ 0 ≤ X₅ ∧ 0 ≤ X₄+X₅ ∧ 2 ≤ X₃+X₅ ∧ 2 ≤ X₂+X₅ ∧ 2 ≤ X₁+X₅ ∧ 2+X₄ ≤ X₃ ∧ 2+X₄ ≤ X₂ ∧ 2+X₄ ≤ X₁ ∧ 0 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₁+X₄ ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 2 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 4 ≤ X₁+X₃ ∧ X₂ ≤ X₁ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 2 ≤ X₁
t₂₉: l3(X₁, X₂, X₃, X₄, X₅) → l3(X₁, X₂, X₃, X₄, X₅+1) :|: X₄+2+X₅ ≤ X₃ ∧ 1+X₅ ≤ X₃ ∧ 1+X₅ ≤ X₂ ∧ 1+X₅ ≤ X₁ ∧ 0 ≤ X₅ ∧ 0 ≤ X₄+X₅ ∧ 2 ≤ X₃+X₅ ∧ 2 ≤ X₂+X₅ ∧ 2 ≤ X₁+X₅ ∧ 2+X₄ ≤ X₃ ∧ 2+X₄ ≤ X₂ ∧ 2+X₄ ≤ X₁ ∧ 0 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₁+X₄ ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 2 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 4 ≤ X₁+X₃ ∧ X₂ ≤ X₁ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 2 ≤ X₁
t₃₁: l4(X₁, X₂, X₃, X₄, X₅) → l4(X₁, X₂, X₃, X₄+1, X₅) :|: 2+X₄ ≤ X₃ ∧ X₄ ≤ X₁ ∧ 0 ≤ X₄ ∧ 0 ≤ X₁+X₄ ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₂ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₁
t₃₂: l4(X₁, X₂, X₃, X₄, X₅) → l5(X₁, X₂, X₃, X₄, X₅) :|: X₃ ≤ X₄+1 ∧ X₄ ≤ X₁ ∧ 0 ≤ X₄ ∧ 0 ≤ X₁+X₄ ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₂ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₁
MPRF for transition t₂₄: l1(X₁, X₂, X₃, X₄, X₅) → l1(X₁+1, X₂, X₃, X₄, X₅) :|: X₁+1 ≤ X₂ ∧ 0 ≤ X₁ of depth 1:
new bound:
X₂ {O(n)}
MPRF:
l1 [X₂-X₁ ]
MPRF for transition t₂₆: l2(X₁, X₂, X₃, X₄, X₅) → l3(X₁, X₂, X₃, X₄, 0) :|: 2+X₄ ≤ X₃ ∧ X₄ ≤ X₁ ∧ 0 ≤ X₄ ∧ 0 ≤ X₁+X₄ ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₂ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₁ of depth 1:
new bound:
X₂+1 {O(n)}
MPRF:
l3 [X₁-X₄ ]
l2 [X₁+1-X₄ ]
MPRF for transition t₃₀: l3(X₁, X₂, X₃, X₄, X₅) → l2(X₁, X₂, X₃, X₄+1, X₅) :|: X₃ ≤ X₅+X₄+1 ∧ 1+X₅ ≤ X₃ ∧ 1+X₅ ≤ X₂ ∧ 1+X₅ ≤ X₁ ∧ 0 ≤ X₅ ∧ 0 ≤ X₄+X₅ ∧ 2 ≤ X₃+X₅ ∧ 2 ≤ X₂+X₅ ∧ 2 ≤ X₁+X₅ ∧ 2+X₄ ≤ X₃ ∧ 2+X₄ ≤ X₂ ∧ 2+X₄ ≤ X₁ ∧ 0 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₁+X₄ ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 2 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 4 ≤ X₁+X₃ ∧ X₂ ≤ X₁ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 2 ≤ X₁ of depth 1:
new bound:
X₂+1 {O(n)}
MPRF:
l3 [X₁-X₄-1 ]
l2 [X₁-X₄-1 ]
Found invariant X₄ ≤ X₁ ∧ 0 ≤ X₄ ∧ 0 ≤ X₁+X₄ ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₂ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₁ for location l2
Found invariant X₄ ≤ X₁ ∧ 0 ≤ X₄ ∧ X₃ ≤ 1+X₄ ∧ X₂ ≤ 1+X₄ ∧ 0 ≤ X₁+X₄ ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₂ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₁ for location l5
Found invariant 0 ≤ X₁ for location l1
Found invariant X₄ ≤ X₁ ∧ 0 ≤ X₄ ∧ 0 ≤ X₁+X₄ ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₂ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₁ for location l4
Found invariant 1+X₅ ≤ X₃ ∧ 1+X₅ ≤ X₂ ∧ 1+X₅ ≤ X₁ ∧ 0 ≤ X₅ ∧ 0 ≤ X₄+X₅ ∧ 2 ≤ X₃+X₅ ∧ 2 ≤ X₂+X₅ ∧ 2 ≤ X₁+X₅ ∧ 2+X₄ ≤ X₃ ∧ 2+X₄ ≤ X₂ ∧ 2+X₄ ≤ X₁ ∧ 0 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₁+X₄ ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 2 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 4 ≤ X₁+X₃ ∧ X₂ ≤ X₁ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 2 ≤ X₁ for location l3
MPRF for transition t₂₈: l3(X₁, X₂, X₃, X₄, X₅) → l3(X₁, X₂, X₃, X₄, X₅+1) :|: X₄+2+X₅ ≤ X₃ ∧ 1+X₅ ≤ X₃ ∧ 1+X₅ ≤ X₂ ∧ 1+X₅ ≤ X₁ ∧ 0 ≤ X₅ ∧ 0 ≤ X₄+X₅ ∧ 2 ≤ X₃+X₅ ∧ 2 ≤ X₂+X₅ ∧ 2 ≤ X₁+X₅ ∧ 2+X₄ ≤ X₃ ∧ 2+X₄ ≤ X₂ ∧ 2+X₄ ≤ X₁ ∧ 0 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₁+X₄ ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 2 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 4 ≤ X₁+X₃ ∧ X₂ ≤ X₁ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 2 ≤ X₁ of depth 1:
new bound:
2⋅X₂⋅X₂+4⋅X₂ {O(n^2)}
MPRF:
l2 [X₃ ]
l3 [X₃-X₅ ]
MPRF for transition t₂₉: l3(X₁, X₂, X₃, X₄, X₅) → l3(X₁, X₂, X₃, X₄, X₅+1) :|: X₄+2+X₅ ≤ X₃ ∧ 1+X₅ ≤ X₃ ∧ 1+X₅ ≤ X₂ ∧ 1+X₅ ≤ X₁ ∧ 0 ≤ X₅ ∧ 0 ≤ X₄+X₅ ∧ 2 ≤ X₃+X₅ ∧ 2 ≤ X₂+X₅ ∧ 2 ≤ X₁+X₅ ∧ 2+X₄ ≤ X₃ ∧ 2+X₄ ≤ X₂ ∧ 2+X₄ ≤ X₁ ∧ 0 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₁+X₄ ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 2 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 4 ≤ X₁+X₃ ∧ X₂ ≤ X₁ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 2 ≤ X₁ of depth 1:
new bound:
2⋅X₂⋅X₂+4⋅X₂ {O(n^2)}
MPRF:
l2 [X₃ ]
l3 [X₃-X₅ ]
Analysing control-flow refined program
Cut unsatisfiable transition t₃₀: l3→l2
Found invariant X₄ ≤ X₁ ∧ 0 ≤ X₄ ∧ 0 ≤ X₁+X₄ ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₂ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₁ for location l2
Found invariant X₄ ≤ X₁ ∧ 0 ≤ X₄ ∧ X₃ ≤ 1+X₄ ∧ X₂ ≤ 1+X₄ ∧ 0 ≤ X₁+X₄ ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₂ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₁ for location l5
Found invariant 0 ≤ X₁ for location l1
Found invariant X₄ ≤ X₁ ∧ 0 ≤ X₄ ∧ 0 ≤ X₁+X₄ ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₂ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₁ for location l4
Found invariant 1+X₅ ≤ X₃ ∧ 1+X₅ ≤ X₂ ∧ 1+X₅ ≤ X₁ ∧ 1 ≤ X₅ ∧ 1 ≤ X₄+X₅ ∧ 3 ≤ X₃+X₅ ∧ 3 ≤ X₂+X₅ ∧ 3 ≤ X₁+X₅ ∧ 2+X₄ ≤ X₃ ∧ 2+X₄ ≤ X₂ ∧ 2+X₄ ≤ X₁ ∧ 0 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₁+X₄ ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 2 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 4 ≤ X₁+X₃ ∧ X₂ ≤ X₁ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 2 ≤ X₁ for location n_l3___1
Found invariant X₅ ≤ 0 ∧ X₅ ≤ X₄ ∧ 2+X₅ ≤ X₃ ∧ 2+X₅ ≤ X₂ ∧ 2+X₅ ≤ X₁ ∧ 0 ≤ X₅ ∧ 0 ≤ X₄+X₅ ∧ 2 ≤ X₃+X₅ ∧ 2 ≤ X₂+X₅ ∧ 2 ≤ X₁+X₅ ∧ 2+X₄ ≤ X₃ ∧ 2+X₄ ≤ X₂ ∧ 2+X₄ ≤ X₁ ∧ 0 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₁+X₄ ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 2 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 4 ≤ X₁+X₃ ∧ X₂ ≤ X₁ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 2 ≤ X₁ for location l3
knowledge_propagation leads to new time bound X₂+1 {O(n)} for transition t₁₀₂: l3(X₁, X₂, X₃, X₄, X₅) → n_l3___1(X₁, X₂, X₂, X₄, X₅+1) :|: X₂ ≤ X₁ ∧ 2+X₄+X₅ ≤ X₂ ∧ 0 ≤ X₅ ∧ 0 ≤ X₄ ∧ X₂ ≤ X₃ ∧ X₃ ≤ X₂ ∧ X₂ ≤ X₃ ∧ X₃ ≤ X₂ ∧ X₅ ≤ 0 ∧ 0 ≤ X₅ ∧ 0 ≤ X₄ ∧ 2+X₄ ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₃ ∧ X₃ ≤ X₂ ∧ 0 ≤ X₄ ∧ 0 ≤ X₅ ∧ 2+X₄+X₅ ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₃ ∧ X₃ ≤ X₂ ∧ 0 ≤ X₄ ∧ 0 ≤ X₅ ∧ 2+X₄+X₅ ≤ X₂ ∧ X₂ ≤ X₁ ∧ 2+X₄+X₅ ≤ X₂ ∧ 0 ≤ X₄ ∧ 0 ≤ X₅ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₃ ∧ X₃ ≤ X₂ ∧ X₅ ≤ 0 ∧ X₅ ≤ X₄ ∧ 2+X₅ ≤ X₃ ∧ 2+X₅ ≤ X₂ ∧ 2+X₅ ≤ X₁ ∧ 0 ≤ X₅ ∧ 0 ≤ X₄+X₅ ∧ 2 ≤ X₃+X₅ ∧ 2 ≤ X₂+X₅ ∧ 2 ≤ X₁+X₅ ∧ 2+X₄ ≤ X₃ ∧ 2+X₄ ≤ X₂ ∧ 2+X₄ ≤ X₁ ∧ 0 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₁+X₄ ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 2 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 4 ≤ X₁+X₃ ∧ X₂ ≤ X₁ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 2 ≤ X₁
knowledge_propagation leads to new time bound X₂+1 {O(n)} for transition t₁₀₃: l3(X₁, X₂, X₃, X₄, X₅) → n_l3___1(X₁, X₂, X₂, X₄, X₅+1) :|: X₂ ≤ X₁ ∧ 2+X₄+X₅ ≤ X₂ ∧ 0 ≤ X₅ ∧ 0 ≤ X₄ ∧ X₂ ≤ X₃ ∧ X₃ ≤ X₂ ∧ X₂ ≤ X₃ ∧ X₃ ≤ X₂ ∧ X₅ ≤ 0 ∧ 0 ≤ X₅ ∧ 0 ≤ X₄ ∧ 2+X₄ ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₃ ∧ X₃ ≤ X₂ ∧ 0 ≤ X₄ ∧ 0 ≤ X₅ ∧ 2+X₄+X₅ ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₃ ∧ X₃ ≤ X₂ ∧ 0 ≤ X₄ ∧ 0 ≤ X₅ ∧ 2+X₄+X₅ ≤ X₂ ∧ X₂ ≤ X₁ ∧ 2+X₄+X₅ ≤ X₂ ∧ 0 ≤ X₄ ∧ 0 ≤ X₅ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₃ ∧ X₃ ≤ X₂ ∧ X₅ ≤ 0 ∧ X₅ ≤ X₄ ∧ 2+X₅ ≤ X₃ ∧ 2+X₅ ≤ X₂ ∧ 2+X₅ ≤ X₁ ∧ 0 ≤ X₅ ∧ 0 ≤ X₄+X₅ ∧ 2 ≤ X₃+X₅ ∧ 2 ≤ X₂+X₅ ∧ 2 ≤ X₁+X₅ ∧ 2+X₄ ≤ X₃ ∧ 2+X₄ ≤ X₂ ∧ 2+X₄ ≤ X₁ ∧ 0 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₁+X₄ ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 2 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 4 ≤ X₁+X₃ ∧ X₂ ≤ X₁ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 2 ≤ X₁
MPRF for transition t₁₀₀: n_l3___1(X₁, X₂, X₃, X₄, X₅) → n_l3___1(X₁, X₂, X₂, X₄, X₅+1) :|: X₂ ≤ X₁ ∧ 0 ≤ X₅ ∧ 0 ≤ X₄ ∧ X₂ ≤ X₃ ∧ X₃ ≤ X₂ ∧ X₂ ≤ X₃ ∧ X₃ ≤ X₂ ∧ 0 ≤ X₄ ∧ 1 ≤ X₅ ∧ 1+X₄+X₅ ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₃ ∧ X₃ ≤ X₂ ∧ 0 ≤ X₄ ∧ 1 ≤ X₅ ∧ 1+X₄+X₅ ≤ X₂ ∧ X₂ ≤ X₁ ∧ 2+X₄+X₅ ≤ X₂ ∧ 0 ≤ X₄ ∧ 0 ≤ X₅ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₃ ∧ X₃ ≤ X₂ ∧ 1+X₅ ≤ X₃ ∧ 1+X₅ ≤ X₂ ∧ 1+X₅ ≤ X₁ ∧ 1 ≤ X₅ ∧ 1 ≤ X₄+X₅ ∧ 3 ≤ X₃+X₅ ∧ 3 ≤ X₂+X₅ ∧ 3 ≤ X₁+X₅ ∧ 2+X₄ ≤ X₃ ∧ 2+X₄ ≤ X₂ ∧ 2+X₄ ≤ X₁ ∧ 0 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₁+X₄ ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 2 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 4 ≤ X₁+X₃ ∧ X₂ ≤ X₁ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 2 ≤ X₁ of depth 1:
new bound:
2⋅X₂⋅X₂+4⋅X₂+2 {O(n^2)}
MPRF:
l3 [X₂-X₃ ]
n_l3___1 [X₁-X₅ ]
l2 [0 ]
MPRF for transition t₁₀₁: n_l3___1(X₁, X₂, X₃, X₄, X₅) → n_l3___1(X₁, X₂, X₂, X₄, X₅+1) :|: X₂ ≤ X₁ ∧ 0 ≤ X₅ ∧ 0 ≤ X₄ ∧ X₂ ≤ X₃ ∧ X₃ ≤ X₂ ∧ X₂ ≤ X₃ ∧ X₃ ≤ X₂ ∧ 0 ≤ X₄ ∧ 1 ≤ X₅ ∧ 1+X₄+X₅ ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₃ ∧ X₃ ≤ X₂ ∧ 0 ≤ X₄ ∧ 1 ≤ X₅ ∧ 1+X₄+X₅ ≤ X₂ ∧ X₂ ≤ X₁ ∧ 2+X₄+X₅ ≤ X₂ ∧ 0 ≤ X₄ ∧ 0 ≤ X₅ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₃ ∧ X₃ ≤ X₂ ∧ 1+X₅ ≤ X₃ ∧ 1+X₅ ≤ X₂ ∧ 1+X₅ ≤ X₁ ∧ 1 ≤ X₅ ∧ 1 ≤ X₄+X₅ ∧ 3 ≤ X₃+X₅ ∧ 3 ≤ X₂+X₅ ∧ 3 ≤ X₁+X₅ ∧ 2+X₄ ≤ X₃ ∧ 2+X₄ ≤ X₂ ∧ 2+X₄ ≤ X₁ ∧ 0 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₁+X₄ ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 2 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 4 ≤ X₁+X₃ ∧ X₂ ≤ X₁ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 2 ≤ X₁ of depth 1:
new bound:
2⋅X₂⋅X₂+4⋅X₂+2 {O(n^2)}
MPRF:
l3 [X₂-X₃ ]
n_l3___1 [X₁-X₅ ]
l2 [0 ]
MPRF for transition t₁₁₀: n_l3___1(X₁, X₂, X₃, X₄, X₅) → l2(X₁, X₂, X₃, X₄+1, X₅) :|: X₃ ≤ X₅+X₄+1 ∧ 1+X₅ ≤ X₃ ∧ 1+X₅ ≤ X₂ ∧ 1+X₅ ≤ X₁ ∧ 0 ≤ X₅ ∧ 0 ≤ X₄+X₅ ∧ 2 ≤ X₃+X₅ ∧ 2 ≤ X₂+X₅ ∧ 2 ≤ X₁+X₅ ∧ 2+X₄ ≤ X₃ ∧ 2+X₄ ≤ X₂ ∧ 2+X₄ ≤ X₁ ∧ 0 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₁+X₄ ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 2 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 4 ≤ X₁+X₃ ∧ X₂ ≤ X₁ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 2 ≤ X₁ ∧ 1+X₅ ≤ X₃ ∧ 1+X₅ ≤ X₂ ∧ 1+X₅ ≤ X₁ ∧ 1 ≤ X₅ ∧ 1 ≤ X₄+X₅ ∧ 3 ≤ X₃+X₅ ∧ 3 ≤ X₂+X₅ ∧ 3 ≤ X₁+X₅ ∧ 2+X₄ ≤ X₃ ∧ 2+X₄ ≤ X₂ ∧ 2+X₄ ≤ X₁ ∧ 0 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₁+X₄ ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 2 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 4 ≤ X₁+X₃ ∧ X₂ ≤ X₁ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 2 ≤ X₁ of depth 1:
new bound:
X₂+1 {O(n)}
MPRF:
l3 [X₁-X₄-1 ]
n_l3___1 [X₁-X₄-1 ]
l2 [X₁-X₄-1 ]
CFR did not improve the program. Rolling back
MPRF for transition t₃₁: l4(X₁, X₂, X₃, X₄, X₅) → l4(X₁, X₂, X₃, X₄+1, X₅) :|: 2+X₄ ≤ X₃ ∧ X₄ ≤ X₁ ∧ 0 ≤ X₄ ∧ 0 ≤ X₁+X₄ ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₂ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₁ of depth 1:
new bound:
2⋅X₂+1 {O(n)}
MPRF:
l4 [X₁+1-X₄ ]
All Bounds
Timebounds
Overall timebound:4⋅X₂⋅X₂+13⋅X₂+7 {O(n^2)}
t₂₃: 1 {O(1)}
t₂₄: X₂ {O(n)}
t₂₅: 1 {O(1)}
t₂₆: X₂+1 {O(n)}
t₂₇: 1 {O(1)}
t₂₈: 2⋅X₂⋅X₂+4⋅X₂ {O(n^2)}
t₂₉: 2⋅X₂⋅X₂+4⋅X₂ {O(n^2)}
t₃₀: X₂+1 {O(n)}
t₃₁: 2⋅X₂+1 {O(n)}
t₃₂: 1 {O(1)}
Costbounds
Overall costbound: 4⋅X₂⋅X₂+13⋅X₂+7 {O(n^2)}
t₂₃: 1 {O(1)}
t₂₄: X₂ {O(n)}
t₂₅: 1 {O(1)}
t₂₆: X₂+1 {O(n)}
t₂₇: 1 {O(1)}
t₂₈: 2⋅X₂⋅X₂+4⋅X₂ {O(n^2)}
t₂₉: 2⋅X₂⋅X₂+4⋅X₂ {O(n^2)}
t₃₀: X₂+1 {O(n)}
t₃₁: 2⋅X₂+1 {O(n)}
t₃₂: 1 {O(1)}
Sizebounds
t₂₃, X₁: 0 {O(1)}
t₂₃, X₂: X₂ {O(n)}
t₂₃, X₃: X₃ {O(n)}
t₂₃, X₄: X₄ {O(n)}
t₂₃, X₅: X₅ {O(n)}
t₂₄, X₁: X₂ {O(n)}
t₂₄, X₂: X₂ {O(n)}
t₂₄, X₃: X₃ {O(n)}
t₂₄, X₄: X₄ {O(n)}
t₂₄, X₅: X₅ {O(n)}
t₂₅, X₁: X₂ {O(n)}
t₂₅, X₂: 2⋅X₂ {O(n)}
t₂₅, X₃: 2⋅X₂ {O(n)}
t₂₅, X₄: 0 {O(1)}
t₂₅, X₅: 2⋅X₅ {O(n)}
t₂₆, X₁: X₂ {O(n)}
t₂₆, X₂: 2⋅X₂ {O(n)}
t₂₆, X₃: 2⋅X₂ {O(n)}
t₂₆, X₄: X₂+1 {O(n)}
t₂₆, X₅: 0 {O(1)}
t₂₇, X₁: 2⋅X₂ {O(n)}
t₂₇, X₂: 4⋅X₂ {O(n)}
t₂₇, X₃: 4⋅X₂ {O(n)}
t₂₇, X₄: 0 {O(1)}
t₂₇, X₅: 8⋅X₂⋅X₂+16⋅X₂+2⋅X₅ {O(n^2)}
t₂₈, X₁: X₂ {O(n)}
t₂₈, X₂: 2⋅X₂ {O(n)}
t₂₈, X₃: 2⋅X₂ {O(n)}
t₂₈, X₄: X₂+1 {O(n)}
t₂₈, X₅: 4⋅X₂⋅X₂+8⋅X₂ {O(n^2)}
t₂₉, X₁: X₂ {O(n)}
t₂₉, X₂: 2⋅X₂ {O(n)}
t₂₉, X₃: 2⋅X₂ {O(n)}
t₂₉, X₄: X₂+1 {O(n)}
t₂₉, X₅: 4⋅X₂⋅X₂+8⋅X₂ {O(n^2)}
t₃₀, X₁: X₂ {O(n)}
t₃₀, X₂: 2⋅X₂ {O(n)}
t₃₀, X₃: 2⋅X₂ {O(n)}
t₃₀, X₄: X₂+1 {O(n)}
t₃₀, X₅: 8⋅X₂⋅X₂+16⋅X₂ {O(n^2)}
t₃₁, X₁: 2⋅X₂ {O(n)}
t₃₁, X₂: 4⋅X₂ {O(n)}
t₃₁, X₃: 4⋅X₂ {O(n)}
t₃₁, X₄: 2⋅X₂+1 {O(n)}
t₃₁, X₅: 8⋅X₂⋅X₂+16⋅X₂+2⋅X₅ {O(n^2)}
t₃₂, X₁: 4⋅X₂ {O(n)}
t₃₂, X₂: 8⋅X₂ {O(n)}
t₃₂, X₃: 8⋅X₂ {O(n)}
t₃₂, X₄: 2⋅X₂+1 {O(n)}
t₃₂, X₅: 16⋅X₂⋅X₂+32⋅X₂+4⋅X₅ {O(n^2)}