Initial Problem
Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇
Temp_Vars: I, J, K
Locations: l0, l1, l2, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₂₂: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇)
t₁: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l1(X₀, X₁, X₂, X₃, X₄+1, J, I, X₇) :|: X₄ ≤ X₀ ∧ J ≤ I
t₂: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l1(X₀, X₁, J, X₄, X₄+1, I, K, X₇) :|: X₄ ≤ X₀ ∧ 1+K ≤ I
t₁₈: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l3(X₀, X₁, X₂, X₁, X₄, X₅, X₆, X₇) :|: 1+X₀ ≤ X₄ ∧ X₁ ≤ X₃ ∧ X₃ ≤ X₁
t₁₉: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₃+1 ≤ X₁ ∧ 1+X₀ ≤ X₄
t₂₀: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 1+X₁ ≤ X₃ ∧ 1+X₀ ≤ X₄
t₅: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₂+1 ≤ 0
t₆: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 1 ≤ X₂
t₁₂: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l5(X₀, X₁+1, 0, X₃, X₄, X₅, X₆, X₇) :|: X₂ ≤ 0 ∧ 0 ≤ X₂
t₁₁: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l4(X₀, X₁, X₂, X₃+1, X₄, X₅, X₆, 0) :|: X₃ ≤ X₀
t₁₅: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l5(X₀, X₁+1, X₂, X₃, X₄, X₅, X₆, X₇) :|: 1+X₀ ≤ X₃
t₇: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l8(X₀, X₁, X₂, X₃, X₄, X₅, X₆, J) :|: X₃ ≤ X₀ ∧ I+1 ≤ 0
t₈: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l8(X₀, X₁, X₂, X₃, X₄, X₅, X₆, J) :|: X₃ ≤ X₀ ∧ 1 ≤ I
t₀: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l1(X₀, X₁, 0, X₁, X₄, X₅, X₆, X₇) :|: X₁+1 ≤ X₀
t₂₁: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₀ ≤ X₁
t₃: l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l6(X₀, X₁, X₂, X₃, X₄+1, X₅, X₆, J) :|: X₄ ≤ X₀
t₁₇: l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 1+X₀ ≤ X₄
t₁₆: l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 1+X₀ ≤ X₄
t₄: l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l7(X₀, X₁, X₂, X₃, X₄+1, X₅, X₆, J) :|: X₄ ≤ X₀
t₉: l8(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l8(X₀, X₁, X₂, X₃, X₄+1, X₅, X₆, X₇) :|: X₄ ≤ X₀
t₁₄: l8(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l9(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 1+X₀ ≤ X₄
t₁₃: l9(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l4(X₀, X₁, X₂, X₃+1, X₄, X₅, X₆, X₇) :|: 1+X₀ ≤ X₄
t₁₀: l9(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l9(X₀, X₁, X₂, X₃, X₄+1, X₅, X₆, X₇) :|: X₄ ≤ X₀
Preprocessing
Cut unsatisfiable transition t₃: l6→l6
Cut unsatisfiable transition t₄: l7→l7
Cut unsatisfiable transition t₁₀: l9→l9
Eliminate variables {X₅,X₆,X₇} that do not contribute to the problem
Found invariant X₀ ≤ X₁ for location l2
Found invariant 1+X₃ ≤ X₄ ∧ 2+X₁ ≤ X₄ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀ for location l6
Found invariant 1+X₃ ≤ X₄ ∧ 2+X₁ ≤ X₄ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀ for location l7
Found invariant 1+X₃ ≤ X₄ ∧ 2+X₁ ≤ X₄ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀ for location l8
Found invariant X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀ for location l1
Found invariant X₃ ≤ X₄ ∧ 2+X₁ ≤ X₄ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ 1+X₀ ∧ 1+X₁ ≤ X₀ for location l4
Found invariant 1+X₃ ≤ X₄ ∧ 2+X₁ ≤ X₄ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀ for location l9
Found invariant 1+X₃ ≤ X₄ ∧ 2+X₁ ≤ X₄ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀ for location l3
Cut unsatisfiable transition t₇₀: l8→l8
Problem after Preprocessing
Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars: I, J, K
Locations: l0, l1, l2, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₅₃: l0(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁, X₂, X₃, X₄)
t₅₄: l1(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁, X₂, X₃, X₄+1) :|: X₄ ≤ X₀ ∧ J ≤ I ∧ X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀
t₅₅: l1(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁, J, X₄, X₄+1) :|: X₄ ≤ X₀ ∧ 1+K ≤ I ∧ X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀
t₅₆: l1(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₁, X₄) :|: 1+X₀ ≤ X₄ ∧ X₁ ≤ X₃ ∧ X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀
t₅₇: l1(X₀, X₁, X₂, X₃, X₄) → l6(X₀, X₁, X₂, X₃, X₄) :|: X₃+1 ≤ X₁ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀
t₅₈: l1(X₀, X₁, X₂, X₃, X₄) → l6(X₀, X₁, X₂, X₃, X₄) :|: 1+X₁ ≤ X₃ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀
t₅₉: l3(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄) :|: X₂+1 ≤ 0 ∧ 1+X₃ ≤ X₄ ∧ 2+X₁ ≤ X₄ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀
t₆₀: l3(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄) :|: 1 ≤ X₂ ∧ 1+X₃ ≤ X₄ ∧ 2+X₁ ≤ X₄ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀
t₆₁: l3(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁+1, 0, X₃, X₄) :|: X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1+X₃ ≤ X₄ ∧ 2+X₁ ≤ X₄ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀
t₆₄: l4(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃+1, X₄) :|: X₃ ≤ X₀ ∧ X₃ ≤ X₄ ∧ 2+X₁ ≤ X₄ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ 1+X₀ ∧ 1+X₁ ≤ X₀
t₆₅: l4(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁+1, X₂, X₃, X₄) :|: 1+X₀ ≤ X₃ ∧ X₃ ≤ X₄ ∧ 2+X₁ ≤ X₄ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ 1+X₀ ∧ 1+X₁ ≤ X₀
t₆₂: l4(X₀, X₁, X₂, X₃, X₄) → l8(X₀, X₁, X₂, X₃, X₄) :|: X₃ ≤ X₀ ∧ I+1 ≤ 0 ∧ X₃ ≤ X₄ ∧ 2+X₁ ≤ X₄ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ 1+X₀ ∧ 1+X₁ ≤ X₀
t₆₃: l4(X₀, X₁, X₂, X₃, X₄) → l8(X₀, X₁, X₂, X₃, X₄) :|: X₃ ≤ X₀ ∧ 1 ≤ I ∧ X₃ ≤ X₄ ∧ 2+X₁ ≤ X₄ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ 1+X₀ ∧ 1+X₁ ≤ X₀
t₆₆: l5(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁, 0, X₁, X₄) :|: X₁+1 ≤ X₀
t₆₇: l5(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂, X₃, X₄) :|: X₀ ≤ X₁
t₆₈: l6(X₀, X₁, X₂, X₃, X₄) → l7(X₀, X₁, X₂, X₃, X₄) :|: 1+X₀ ≤ X₄ ∧ 1+X₃ ≤ X₄ ∧ 2+X₁ ≤ X₄ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀
t₆₉: l7(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₃, X₄) :|: 1+X₀ ≤ X₄ ∧ 1+X₃ ≤ X₄ ∧ 2+X₁ ≤ X₄ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀
t₇₁: l8(X₀, X₁, X₂, X₃, X₄) → l9(X₀, X₁, X₂, X₃, X₄) :|: 1+X₀ ≤ X₄ ∧ 1+X₃ ≤ X₄ ∧ 2+X₁ ≤ X₄ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀
t₇₂: l9(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃+1, X₄) :|: 1+X₀ ≤ X₄ ∧ 1+X₃ ≤ X₄ ∧ 2+X₁ ≤ X₄ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀
MPRF for transition t₅₄: l1(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁, X₂, X₃, X₄+1) :|: X₄ ≤ X₀ ∧ J ≤ I ∧ X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀ of depth 1:
new bound:
X₀+X₄+1 {O(n)}
MPRF:
l5 [X₀+1-X₄ ]
l1 [X₀+1-X₄ ]
l6 [X₀+1-X₄ ]
l7 [X₀+1-X₄ ]
l3 [X₀+1-X₄ ]
l8 [X₀+1-X₄ ]
l9 [X₀+1-X₄ ]
l4 [X₀+1-X₄ ]
MPRF for transition t₅₅: l1(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁, J, X₄, X₄+1) :|: X₄ ≤ X₀ ∧ 1+K ≤ I ∧ X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀ of depth 1:
new bound:
X₀+X₄+1 {O(n)}
MPRF:
l5 [X₀+1-X₄ ]
l1 [X₀+1-X₄ ]
l6 [X₀+1-X₄ ]
l7 [X₀+1-X₄ ]
l3 [X₀+1-X₄ ]
l8 [X₀+1-X₄ ]
l9 [X₀+1-X₄ ]
l4 [X₀+1-X₄ ]
MPRF for transition t₅₆: l1(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₁, X₄) :|: 1+X₀ ≤ X₄ ∧ X₁ ≤ X₃ ∧ X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀ of depth 1:
new bound:
X₀+X₁+1 {O(n)}
MPRF:
l5 [X₀+1-X₁ ]
l1 [X₀+1-X₁ ]
l6 [X₀-X₁ ]
l7 [X₀-X₁ ]
l3 [X₀-X₁ ]
l8 [X₀-X₁ ]
l9 [X₀-X₁ ]
l4 [X₀-X₁ ]
MPRF for transition t₅₇: l1(X₀, X₁, X₂, X₃, X₄) → l6(X₀, X₁, X₂, X₃, X₄) :|: X₃+1 ≤ X₁ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀ of depth 1:
new bound:
X₀+X₁+2 {O(n)}
MPRF:
l5 [X₀+2-X₁ ]
l1 [X₀+2-X₁ ]
l6 [X₀+1-X₁ ]
l7 [X₀+1-X₁ ]
l3 [X₀+1-X₁ ]
l8 [X₀+1-X₁ ]
l9 [X₀+1-X₁ ]
l4 [X₀+1-X₁ ]
MPRF for transition t₅₈: l1(X₀, X₁, X₂, X₃, X₄) → l6(X₀, X₁, X₂, X₃, X₄) :|: 1+X₁ ≤ X₃ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀ of depth 1:
new bound:
X₀+X₁+1 {O(n)}
MPRF:
l5 [X₀+1-X₁ ]
l1 [X₀+1-X₁ ]
l6 [X₀-X₁ ]
l7 [X₀-X₁ ]
l3 [X₀-X₁ ]
l8 [X₀-X₁ ]
l9 [X₀-X₁ ]
l4 [X₀-X₁ ]
MPRF for transition t₅₉: l3(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄) :|: X₂+1 ≤ 0 ∧ 1+X₃ ≤ X₄ ∧ 2+X₁ ≤ X₄ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀ of depth 1:
new bound:
X₀+X₁ {O(n)}
MPRF:
l5 [X₀-X₁ ]
l1 [X₀-X₁ ]
l6 [X₀-X₁ ]
l7 [X₀-X₁ ]
l3 [X₀-X₁ ]
l8 [X₀-X₁-1 ]
l9 [X₀-X₁-1 ]
l4 [X₀-X₁-1 ]
MPRF for transition t₆₀: l3(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄) :|: 1 ≤ X₂ ∧ 1+X₃ ≤ X₄ ∧ 2+X₁ ≤ X₄ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀ of depth 1:
new bound:
X₀+X₁ {O(n)}
MPRF:
l5 [X₀-X₁ ]
l1 [X₀-X₁ ]
l6 [X₀-X₁ ]
l7 [X₀-X₁ ]
l3 [X₀-X₁ ]
l8 [X₀-X₁-1 ]
l9 [X₀-X₁-1 ]
l4 [X₀-X₁-1 ]
MPRF for transition t₆₁: l3(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁+1, 0, X₃, X₄) :|: X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1+X₃ ≤ X₄ ∧ 2+X₁ ≤ X₄ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀ of depth 1:
new bound:
X₀+X₁ {O(n)}
MPRF:
l5 [X₀-X₁ ]
l1 [X₀-X₁ ]
l6 [X₀-X₁ ]
l7 [X₀-X₁ ]
l3 [X₀-X₁ ]
l8 [X₀-X₁ ]
l9 [X₀-X₁ ]
l4 [X₀-X₁ ]
MPRF for transition t₆₅: l4(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁+1, X₂, X₃, X₄) :|: 1+X₀ ≤ X₃ ∧ X₃ ≤ X₄ ∧ 2+X₁ ≤ X₄ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ 1+X₀ ∧ 1+X₁ ≤ X₀ of depth 1:
new bound:
X₀+X₁ {O(n)}
MPRF:
l5 [X₀-X₁ ]
l1 [X₀-X₁ ]
l6 [X₀-X₁ ]
l7 [X₀-X₁ ]
l3 [X₀-X₁ ]
l8 [X₀-X₁ ]
l9 [X₀-X₁ ]
l4 [X₀-X₁ ]
MPRF for transition t₆₆: l5(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁, 0, X₁, X₄) :|: X₁+1 ≤ X₀ of depth 1:
new bound:
X₀+X₁ {O(n)}
MPRF:
l5 [X₀-X₁ ]
l1 [X₀-X₁-1 ]
l6 [X₀-X₁-1 ]
l7 [X₀-X₁-1 ]
l3 [X₀-X₁-1 ]
l8 [X₀-X₁-1 ]
l9 [X₀-X₁-1 ]
l4 [X₀-X₁-1 ]
MPRF for transition t₆₈: l6(X₀, X₁, X₂, X₃, X₄) → l7(X₀, X₁, X₂, X₃, X₄) :|: 1+X₀ ≤ X₄ ∧ 1+X₃ ≤ X₄ ∧ 2+X₁ ≤ X₄ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀ of depth 1:
new bound:
X₀+X₁+1 {O(n)}
MPRF:
l5 [X₀+1-X₁ ]
l1 [X₀+1-X₁ ]
l6 [X₀+1-X₁ ]
l7 [X₀-X₁ ]
l3 [X₀-X₁ ]
l8 [X₀-X₁ ]
l9 [X₀-X₁ ]
l4 [X₀-X₁ ]
MPRF for transition t₆₉: l7(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₃, X₄) :|: 1+X₀ ≤ X₄ ∧ 1+X₃ ≤ X₄ ∧ 2+X₁ ≤ X₄ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀ of depth 1:
new bound:
X₀+X₁+1 {O(n)}
MPRF:
l5 [X₀+1-X₁ ]
l1 [X₀+1-X₁ ]
l6 [X₀+1-X₁ ]
l7 [X₀+1-X₁ ]
l3 [X₀-X₁ ]
l8 [X₀-X₁ ]
l9 [X₀-X₁ ]
l4 [X₀-X₁ ]
MPRF for transition t₆₂: l4(X₀, X₁, X₂, X₃, X₄) → l8(X₀, X₁, X₂, X₃, X₄) :|: X₃ ≤ X₀ ∧ I+1 ≤ 0 ∧ X₃ ≤ X₄ ∧ 2+X₁ ≤ X₄ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ 1+X₀ ∧ 1+X₁ ≤ X₀ of depth 1:
new bound:
17⋅X₁⋅X₁+27⋅X₀⋅X₄+27⋅X₁⋅X₄+30⋅X₀⋅X₀+47⋅X₀⋅X₁+27⋅X₄+34⋅X₁+47⋅X₀+19 {O(n^2)}
MPRF:
l1 [X₀+1-X₁ ]
l3 [X₀+1-X₃ ]
l5 [0 ]
l6 [X₀-X₁ ]
l7 [X₀-X₁ ]
l8 [X₀-X₃ ]
l9 [X₀-X₃ ]
l4 [X₀+1-X₃ ]
MPRF for transition t₆₃: l4(X₀, X₁, X₂, X₃, X₄) → l8(X₀, X₁, X₂, X₃, X₄) :|: X₃ ≤ X₀ ∧ 1 ≤ I ∧ X₃ ≤ X₄ ∧ 2+X₁ ≤ X₄ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ 1+X₀ ∧ 1+X₁ ≤ X₀ of depth 1:
new bound:
27⋅X₀⋅X₄+27⋅X₁⋅X₄+29⋅X₁⋅X₁+42⋅X₀⋅X₀+71⋅X₀⋅X₁+27⋅X₄+38⋅X₁+51⋅X₀+18 {O(n^2)}
MPRF:
l1 [3⋅X₀-3⋅X₁ ]
l3 [3⋅X₀-2⋅X₁-X₃ ]
l5 [3⋅X₀-2⋅X₁-X₄ ]
l6 [3⋅X₀-3⋅X₁ ]
l7 [3⋅X₀-3⋅X₁ ]
l8 [3⋅X₀-2⋅X₁-X₃-1 ]
l9 [3⋅X₀-2⋅X₁-X₃-1 ]
l4 [3⋅X₀-2⋅X₁-X₃ ]
MPRF for transition t₆₄: l4(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃+1, X₄) :|: X₃ ≤ X₀ ∧ X₃ ≤ X₄ ∧ 2+X₁ ≤ X₄ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ 1+X₀ ∧ 1+X₁ ≤ X₀ of depth 1:
new bound:
17⋅X₁⋅X₁+27⋅X₀⋅X₄+27⋅X₁⋅X₄+30⋅X₀⋅X₀+47⋅X₀⋅X₁+27⋅X₄+34⋅X₁+47⋅X₀+19 {O(n^2)}
MPRF:
l1 [X₀+1-X₁ ]
l3 [X₀+1-X₃ ]
l5 [X₀-X₄ ]
l6 [X₀-X₁ ]
l7 [X₀-X₁ ]
l8 [X₀-X₃ ]
l9 [X₀-X₃ ]
l4 [X₀+1-X₃ ]
MPRF for transition t₇₁: l8(X₀, X₁, X₂, X₃, X₄) → l9(X₀, X₁, X₂, X₃, X₄) :|: 1+X₀ ≤ X₄ ∧ 1+X₃ ≤ X₄ ∧ 2+X₁ ≤ X₄ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀ of depth 1:
new bound:
17⋅X₁⋅X₁+27⋅X₀⋅X₄+27⋅X₁⋅X₄+30⋅X₀⋅X₀+47⋅X₀⋅X₁+27⋅X₄+34⋅X₁+47⋅X₀+19 {O(n^2)}
MPRF:
l1 [X₀+1-X₁ ]
l3 [X₀+1-X₃ ]
l5 [0 ]
l6 [X₀-X₁ ]
l7 [X₀-X₁ ]
l8 [X₀+1-X₃ ]
l9 [X₀-X₃ ]
l4 [X₀+1-X₃ ]
MPRF for transition t₇₂: l9(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃+1, X₄) :|: 1+X₀ ≤ X₄ ∧ 1+X₃ ≤ X₄ ∧ 2+X₁ ≤ X₄ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀ of depth 1:
new bound:
17⋅X₁⋅X₁+27⋅X₀⋅X₄+27⋅X₁⋅X₄+30⋅X₀⋅X₀+47⋅X₀⋅X₁+27⋅X₄+34⋅X₁+47⋅X₀+19 {O(n^2)}
MPRF:
l1 [X₀+1-X₁ ]
l3 [X₀+1-X₃ ]
l5 [0 ]
l6 [X₀-X₁ ]
l7 [X₀-X₁ ]
l8 [X₀+1-X₃ ]
l9 [X₀+1-X₃ ]
l4 [X₀+1-X₃ ]
Analysing control-flow refined program
Cut unsatisfiable transition t₆₅: l4→l5
Found invariant X₀ ≤ X₁ for location l2
Found invariant 1+X₃ ≤ X₄ ∧ 2+X₁ ≤ X₄ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ X₀ ∧ 1 ≤ X₂ ∧ 1+X₁ ≤ X₀ for location n_l8___2
Found invariant 1+X₃ ≤ X₄ ∧ 2+X₁ ≤ X₄ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀ for location l6
Found invariant 1+X₃ ≤ X₄ ∧ 2+X₁ ≤ X₄ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀ for location n_l9___4
Found invariant 1+X₃ ≤ X₄ ∧ 2+X₁ ≤ X₄ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ X₀ ∧ 1 ≤ X₂ ∧ 1+X₁ ≤ X₀ for location n_l9___1
Found invariant 1+X₃ ≤ X₄ ∧ 2+X₁ ≤ X₄ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀ for location n_l8___5
Found invariant 1+X₃ ≤ X₄ ∧ 2+X₁ ≤ X₄ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ X₀ ∧ 1+X₂ ≤ 0 ∧ 1+X₁ ≤ X₀ for location n_l8___6
Found invariant 1+X₃ ≤ X₄ ∧ 2+X₁ ≤ X₄ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ X₀ ∧ 1+X₂ ≤ 0 ∧ 1+X₁ ≤ X₀ for location n_l9___3
Found invariant 1+X₃ ≤ X₄ ∧ 2+X₁ ≤ X₄ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀ for location l7
Found invariant X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀ for location l1
Found invariant 1+X₃ ≤ X₄ ∧ 2+X₁ ≤ X₄ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀ for location l4
Found invariant 1+X₃ ≤ X₄ ∧ 2+X₁ ≤ X₄ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀ for location l3
Found invariant X₃ ≤ X₄ ∧ 2+X₁ ≤ X₄ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ 1+X₀ ∧ 1+X₁ ≤ X₀ for location n_l4___7
knowledge_propagation leads to new time bound X₀+X₁ {O(n)} for transition t₂₁₉: l4(X₀, X₁, X₂, X₃, X₄) → n_l4___7(X₀, X₁, X₂, X₃+1, X₄) :|: 1+X₁ ≤ X₀ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₂ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ 1+X₀ ∧ 1+X₁ ≤ X₀ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ X₀ ∧ X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 1+X₀ ≤ X₄ ∧ 1+X₁ ≤ X₀ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ 1+X₀ ∧ 1+X₁ ≤ X₀ ∧ X₃ ≤ X₀ ∧ 1+X₀ ≤ X₄ ∧ 1+X₃ ≤ X₄ ∧ 2+X₁ ≤ X₄ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀
knowledge_propagation leads to new time bound X₀+X₁ {O(n)} for transition t₂₂₀: l4(X₀, X₁, X₂, X₃, X₄) → n_l8___2(X₀, Arg1_P, X₂, Arg3_P, Arg4_P) :|: 1+X₁ ≤ X₀ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₂ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ 1+X₀ ∧ 1+X₁ ≤ X₀ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ X₀ ∧ X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 1+X₀ ≤ X₄ ∧ 1+X₁ ≤ X₀ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ 1+X₀ ∧ 1+X₀ ≤ Arg4_P ∧ 1+Arg1_P ≤ X₀ ∧ Arg3_P ≤ X₀ ∧ X₃ ≤ Arg3_P ∧ Arg3_P ≤ X₃ ∧ X₁ ≤ Arg1_P ∧ Arg1_P ≤ X₁ ∧ X₄ ≤ Arg4_P ∧ Arg4_P ≤ X₄ ∧ 1+X₃ ≤ X₄ ∧ 2+X₁ ≤ X₄ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀
knowledge_propagation leads to new time bound X₀+X₁ {O(n)} for transition t₂₂₁: l4(X₀, X₁, X₂, X₃, X₄) → n_l8___2(X₀, Arg1_P, X₂, Arg3_P, Arg4_P) :|: 1+X₁ ≤ X₀ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₂ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ 1+X₀ ∧ 1+X₁ ≤ X₀ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ X₀ ∧ X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 1+X₀ ≤ X₄ ∧ 1+X₁ ≤ X₀ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ 1+X₀ ∧ 1+X₀ ≤ Arg4_P ∧ 1+Arg1_P ≤ X₀ ∧ Arg3_P ≤ X₀ ∧ X₃ ≤ Arg3_P ∧ Arg3_P ≤ X₃ ∧ X₁ ≤ Arg1_P ∧ Arg1_P ≤ X₁ ∧ X₄ ≤ Arg4_P ∧ Arg4_P ≤ X₄ ∧ 1+X₃ ≤ X₄ ∧ 2+X₁ ≤ X₄ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀
knowledge_propagation leads to new time bound X₀+X₁ {O(n)} for transition t₂₂₂: l4(X₀, X₁, X₂, X₃, X₄) → n_l4___7(X₀, X₁, X₂, X₃+1, X₄) :|: 1+X₁ ≤ X₀ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ X₀ ∧ 1+X₂ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ 1+X₀ ∧ 1+X₁ ≤ X₀ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ X₀ ∧ X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 1+X₀ ≤ X₄ ∧ 1+X₁ ≤ X₀ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ 1+X₀ ∧ 1+X₁ ≤ X₀ ∧ X₃ ≤ X₀ ∧ 1+X₀ ≤ X₄ ∧ 1+X₃ ≤ X₄ ∧ 2+X₁ ≤ X₄ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀
knowledge_propagation leads to new time bound X₀+X₁ {O(n)} for transition t₂₂₃: l4(X₀, X₁, X₂, X₃, X₄) → n_l8___6(X₀, Arg1_P, X₂, Arg3_P, Arg4_P) :|: 1+X₁ ≤ X₀ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ X₀ ∧ 1+X₂ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ 1+X₀ ∧ 1+X₁ ≤ X₀ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ X₀ ∧ X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 1+X₀ ≤ X₄ ∧ 1+X₁ ≤ X₀ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ 1+X₀ ∧ 1+X₀ ≤ Arg4_P ∧ 1+Arg1_P ≤ X₀ ∧ Arg3_P ≤ X₀ ∧ X₃ ≤ Arg3_P ∧ Arg3_P ≤ X₃ ∧ X₁ ≤ Arg1_P ∧ Arg1_P ≤ X₁ ∧ X₄ ≤ Arg4_P ∧ Arg4_P ≤ X₄ ∧ 1+X₃ ≤ X₄ ∧ 2+X₁ ≤ X₄ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀
knowledge_propagation leads to new time bound X₀+X₁ {O(n)} for transition t₂₂₄: l4(X₀, X₁, X₂, X₃, X₄) → n_l8___6(X₀, Arg1_P, X₂, Arg3_P, Arg4_P) :|: 1+X₁ ≤ X₀ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ X₀ ∧ 1+X₂ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ 1+X₀ ∧ 1+X₁ ≤ X₀ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ X₀ ∧ X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 1+X₀ ≤ X₄ ∧ 1+X₁ ≤ X₀ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ 1+X₀ ∧ 1+X₀ ≤ Arg4_P ∧ 1+Arg1_P ≤ X₀ ∧ Arg3_P ≤ X₀ ∧ X₃ ≤ Arg3_P ∧ Arg3_P ≤ X₃ ∧ X₁ ≤ Arg1_P ∧ Arg1_P ≤ X₁ ∧ X₄ ≤ Arg4_P ∧ Arg4_P ≤ X₄ ∧ 1+X₃ ≤ X₄ ∧ 2+X₁ ≤ X₄ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀
knowledge_propagation leads to new time bound 2⋅X₀+2⋅X₁ {O(n)} for transition t₂₂₅: n_l8___2(X₀, X₁, X₂, X₃, X₄) → n_l9___1(X₀, X₁, X₂, X₃, X₄) :|: 1+X₁ ≤ X₀ ∧ 1+X₀ ≤ X₄ ∧ 1 ≤ X₂ ∧ X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ X₃ ≤ X₀ ∧ 1+X₀ ≤ X₄ ∧ 1+X₃ ≤ X₄ ∧ 2+X₁ ≤ X₄ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ X₀ ∧ 1 ≤ X₂ ∧ 1+X₁ ≤ X₀
knowledge_propagation leads to new time bound 2⋅X₀+2⋅X₁ {O(n)} for transition t₂₂₇: n_l8___6(X₀, X₁, X₂, X₃, X₄) → n_l9___3(X₀, X₁, X₂, X₃, X₄) :|: 1+X₁ ≤ X₀ ∧ 1+X₂ ≤ 0 ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ X₃ ≤ X₀ ∧ 1+X₀ ≤ X₄ ∧ 1+X₃ ≤ X₄ ∧ 2+X₁ ≤ X₄ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ X₀ ∧ 1+X₂ ≤ 0 ∧ 1+X₁ ≤ X₀
knowledge_propagation leads to new time bound 2⋅X₀+2⋅X₁ {O(n)} for transition t₂₂₈: n_l9___1(X₀, X₁, X₂, X₃, X₄) → n_l4___7(X₀, X₁, X₂, X₃+1, X₄) :|: 1+X₁ ≤ X₀ ∧ 1+X₀ ≤ X₄ ∧ 1 ≤ X₂ ∧ X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ X₃ ≤ X₀ ∧ 1+X₀ ≤ X₄ ∧ 1+X₃ ≤ X₄ ∧ 2+X₁ ≤ X₄ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ X₀ ∧ 1 ≤ X₂ ∧ 1+X₁ ≤ X₀
knowledge_propagation leads to new time bound 2⋅X₀+2⋅X₁ {O(n)} for transition t₂₂₉: n_l9___3(X₀, X₁, X₂, X₃, X₄) → n_l4___7(X₀, X₁, X₂, X₃+1, X₄) :|: 1+X₁ ≤ X₀ ∧ 1+X₂ ≤ 0 ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ X₃ ≤ X₀ ∧ 1+X₀ ≤ X₄ ∧ 1+X₃ ≤ X₄ ∧ 2+X₁ ≤ X₄ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ X₀ ∧ 1+X₂ ≤ 0 ∧ 1+X₁ ≤ X₀
MPRF for transition t₂₁₆: n_l4___7(X₀, X₁, X₂, X₃, X₄) → n_l4___7(X₀, X₁, X₂, X₃+1, X₄) :|: 1+X₁ ≤ X₀ ∧ 1+X₀ ≤ X₄ ∧ 1+X₁ ≤ X₀ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ 1+X₀ ∧ 1+X₁ ≤ X₀ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ 1+X₀ ∧ 1+X₁ ≤ X₀ ∧ X₃ ≤ X₀ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ X₄ ∧ 2+X₁ ≤ X₄ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ 1+X₀ ∧ 1+X₁ ≤ X₀ of depth 1:
new bound:
17⋅X₁⋅X₁+27⋅X₀⋅X₄+27⋅X₁⋅X₄+30⋅X₀⋅X₀+47⋅X₀⋅X₁+27⋅X₄+32⋅X₁+45⋅X₀+18 {O(n^2)}
MPRF:
l1 [X₀-X₁ ]
l3 [X₀-X₃ ]
l4 [X₀-X₃ ]
l6 [X₀-X₁ ]
l7 [X₀-X₁ ]
l5 [X₀-X₄ ]
n_l8___2 [X₀-X₃ ]
n_l8___5 [X₀-X₃ ]
n_l8___6 [X₀-X₃ ]
n_l9___1 [X₀-X₃ ]
n_l9___3 [X₀-X₃ ]
n_l9___4 [X₀-X₃ ]
n_l4___7 [X₀+1-X₃ ]
MPRF for transition t₂₁₇: n_l4___7(X₀, X₁, X₂, X₃, X₄) → n_l8___5(X₀, Arg1_P, X₂, Arg3_P, Arg4_P) :|: 1+X₁ ≤ X₀ ∧ 1+X₀ ≤ X₄ ∧ 1+X₁ ≤ X₀ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ 1+X₀ ∧ 1+X₁ ≤ X₀ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ 1+X₀ ∧ 1+X₀ ≤ Arg4_P ∧ 1+Arg1_P ≤ X₀ ∧ Arg3_P ≤ X₀ ∧ X₃ ≤ Arg3_P ∧ Arg3_P ≤ X₃ ∧ X₁ ≤ Arg1_P ∧ Arg1_P ≤ X₁ ∧ X₄ ≤ Arg4_P ∧ Arg4_P ≤ X₄ ∧ X₃ ≤ X₄ ∧ 2+X₁ ≤ X₄ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ 1+X₀ ∧ 1+X₁ ≤ X₀ of depth 1:
new bound:
17⋅X₁⋅X₁+27⋅X₀⋅X₄+27⋅X₁⋅X₄+30⋅X₀⋅X₀+47⋅X₀⋅X₁+27⋅X₄+32⋅X₁+45⋅X₀+18 {O(n^2)}
MPRF:
l1 [X₀-X₁ ]
l3 [X₀-X₃ ]
l4 [X₀-X₃ ]
l6 [X₀-X₁ ]
l7 [X₀-X₁ ]
l5 [X₀-X₄ ]
n_l8___2 [X₀-X₃ ]
n_l8___5 [X₀-X₃ ]
n_l8___6 [X₀-X₃ ]
n_l9___1 [X₀-X₃ ]
n_l9___3 [X₀-X₃ ]
n_l9___4 [X₀-X₃ ]
n_l4___7 [X₀+1-X₃ ]
MPRF for transition t₂₁₈: n_l4___7(X₀, X₁, X₂, X₃, X₄) → n_l8___5(X₀, Arg1_P, X₂, Arg3_P, Arg4_P) :|: 1+X₁ ≤ X₀ ∧ 1+X₀ ≤ X₄ ∧ 1+X₁ ≤ X₀ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ 1+X₀ ∧ 1+X₁ ≤ X₀ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ 1+X₀ ∧ 1+X₀ ≤ Arg4_P ∧ 1+Arg1_P ≤ X₀ ∧ Arg3_P ≤ X₀ ∧ X₃ ≤ Arg3_P ∧ Arg3_P ≤ X₃ ∧ X₁ ≤ Arg1_P ∧ Arg1_P ≤ X₁ ∧ X₄ ≤ Arg4_P ∧ Arg4_P ≤ X₄ ∧ X₃ ≤ X₄ ∧ 2+X₁ ≤ X₄ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ 1+X₀ ∧ 1+X₁ ≤ X₀ of depth 1:
new bound:
17⋅X₁⋅X₁+27⋅X₀⋅X₄+27⋅X₁⋅X₄+30⋅X₀⋅X₀+47⋅X₀⋅X₁+27⋅X₄+32⋅X₁+45⋅X₀+18 {O(n^2)}
MPRF:
l1 [X₀-X₁ ]
l3 [X₀-X₃ ]
l4 [X₀-X₃ ]
l6 [X₀-X₁ ]
l7 [2⋅X₀-X₁-X₄ ]
l5 [0 ]
n_l8___2 [X₀-X₃ ]
n_l8___5 [X₀-X₃ ]
n_l8___6 [X₀-X₃ ]
n_l9___1 [X₀-X₃ ]
n_l9___3 [X₀-X₃ ]
n_l9___4 [X₀-X₃ ]
n_l4___7 [X₀+1-X₃ ]
MPRF for transition t₂₄₂: n_l4___7(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁+1, X₂, X₃, X₄) :|: 1+X₀ ≤ X₃ ∧ X₃ ≤ X₄ ∧ 2+X₁ ≤ X₄ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ 1+X₀ ∧ 1+X₁ ≤ X₀ ∧ X₃ ≤ X₄ ∧ 2+X₁ ≤ X₄ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ 1+X₀ ∧ 1+X₁ ≤ X₀ of depth 1:
new bound:
X₀+X₁ {O(n)}
MPRF:
l4 [X₀-X₁ ]
l1 [X₀-X₁ ]
l6 [X₀-X₁ ]
l7 [X₀-X₁ ]
l3 [X₀-X₁ ]
l5 [X₀-X₁ ]
n_l8___2 [X₀-X₁ ]
n_l8___5 [X₀-X₁ ]
n_l8___6 [X₀-X₁ ]
n_l9___1 [X₀-X₁ ]
n_l9___3 [X₀-X₁ ]
n_l9___4 [X₀-X₁ ]
n_l4___7 [X₀-X₁ ]
MPRF for transition t₂₂₆: n_l8___5(X₀, X₁, X₂, X₃, X₄) → n_l9___4(X₀, X₁, X₂, X₃, X₄) :|: 1+X₁ ≤ X₀ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ X₃ ≤ X₀ ∧ 1+X₀ ≤ X₄ ∧ 1+X₃ ≤ X₄ ∧ 2+X₁ ≤ X₄ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀ of depth 1:
new bound:
17⋅X₁⋅X₁+27⋅X₀⋅X₄+27⋅X₁⋅X₄+30⋅X₀⋅X₀+47⋅X₀⋅X₁+27⋅X₄+32⋅X₁+45⋅X₀+18 {O(n^2)}
MPRF:
l1 [X₀-X₁ ]
l3 [X₀-X₃ ]
l4 [X₀-X₃ ]
l6 [X₀-X₁ ]
l7 [X₀-X₁ ]
l5 [X₀-X₄ ]
n_l8___2 [X₀-X₃ ]
n_l8___5 [X₀+1-X₃ ]
n_l8___6 [X₀-X₃ ]
n_l9___1 [X₀-X₃ ]
n_l9___3 [X₀-X₃ ]
n_l9___4 [X₀-X₃ ]
n_l4___7 [X₀+1-X₃ ]
MPRF for transition t₂₃₀: n_l9___4(X₀, X₁, X₂, X₃, X₄) → n_l4___7(X₀, X₁, X₂, X₃+1, X₄) :|: 1+X₁ ≤ X₀ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ X₃ ≤ X₀ ∧ 1+X₀ ≤ X₄ ∧ 1+X₃ ≤ X₄ ∧ 2+X₁ ≤ X₄ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀ of depth 1:
new bound:
17⋅X₁⋅X₁+27⋅X₀⋅X₄+27⋅X₁⋅X₄+30⋅X₀⋅X₀+47⋅X₀⋅X₁+27⋅X₄+32⋅X₁+45⋅X₀+18 {O(n^2)}
MPRF:
l1 [X₀-X₁ ]
l3 [X₀-X₃ ]
l4 [X₀-X₃ ]
l6 [X₀-X₁ ]
l7 [X₀-X₁ ]
l5 [X₀-X₄ ]
n_l8___2 [X₀-X₃ ]
n_l8___5 [X₀+1-X₃ ]
n_l8___6 [X₀-X₃ ]
n_l9___1 [X₀-X₃ ]
n_l9___3 [X₀-X₃ ]
n_l9___4 [X₀+1-X₃ ]
n_l4___7 [X₀+1-X₃ ]
CFR did not improve the program. Rolling back
All Bounds
Timebounds
Overall timebound:135⋅X₀⋅X₄+135⋅X₁⋅X₄+162⋅X₀⋅X₀+259⋅X₀⋅X₁+97⋅X₁⋅X₁+137⋅X₄+184⋅X₁+251⋅X₀+104 {O(n^2)}
t₅₃: 1 {O(1)}
t₅₄: X₀+X₄+1 {O(n)}
t₅₅: X₀+X₄+1 {O(n)}
t₅₆: X₀+X₁+1 {O(n)}
t₅₇: X₀+X₁+2 {O(n)}
t₅₈: X₀+X₁+1 {O(n)}
t₅₉: X₀+X₁ {O(n)}
t₆₀: X₀+X₁ {O(n)}
t₆₁: X₀+X₁ {O(n)}
t₆₂: 17⋅X₁⋅X₁+27⋅X₀⋅X₄+27⋅X₁⋅X₄+30⋅X₀⋅X₀+47⋅X₀⋅X₁+27⋅X₄+34⋅X₁+47⋅X₀+19 {O(n^2)}
t₆₃: 27⋅X₀⋅X₄+27⋅X₁⋅X₄+29⋅X₁⋅X₁+42⋅X₀⋅X₀+71⋅X₀⋅X₁+27⋅X₄+38⋅X₁+51⋅X₀+18 {O(n^2)}
t₆₄: 17⋅X₁⋅X₁+27⋅X₀⋅X₄+27⋅X₁⋅X₄+30⋅X₀⋅X₀+47⋅X₀⋅X₁+27⋅X₄+34⋅X₁+47⋅X₀+19 {O(n^2)}
t₆₅: X₀+X₁ {O(n)}
t₆₆: X₀+X₁ {O(n)}
t₆₇: 1 {O(1)}
t₆₈: X₀+X₁+1 {O(n)}
t₆₉: X₀+X₁+1 {O(n)}
t₇₁: 17⋅X₁⋅X₁+27⋅X₀⋅X₄+27⋅X₁⋅X₄+30⋅X₀⋅X₀+47⋅X₀⋅X₁+27⋅X₄+34⋅X₁+47⋅X₀+19 {O(n^2)}
t₇₂: 17⋅X₁⋅X₁+27⋅X₀⋅X₄+27⋅X₁⋅X₄+30⋅X₀⋅X₀+47⋅X₀⋅X₁+27⋅X₄+34⋅X₁+47⋅X₀+19 {O(n^2)}
Costbounds
Overall costbound: 135⋅X₀⋅X₄+135⋅X₁⋅X₄+162⋅X₀⋅X₀+259⋅X₀⋅X₁+97⋅X₁⋅X₁+137⋅X₄+184⋅X₁+251⋅X₀+104 {O(n^2)}
t₅₃: 1 {O(1)}
t₅₄: X₀+X₄+1 {O(n)}
t₅₅: X₀+X₄+1 {O(n)}
t₅₆: X₀+X₁+1 {O(n)}
t₅₇: X₀+X₁+2 {O(n)}
t₅₈: X₀+X₁+1 {O(n)}
t₅₉: X₀+X₁ {O(n)}
t₆₀: X₀+X₁ {O(n)}
t₆₁: X₀+X₁ {O(n)}
t₆₂: 17⋅X₁⋅X₁+27⋅X₀⋅X₄+27⋅X₁⋅X₄+30⋅X₀⋅X₀+47⋅X₀⋅X₁+27⋅X₄+34⋅X₁+47⋅X₀+19 {O(n^2)}
t₆₃: 27⋅X₀⋅X₄+27⋅X₁⋅X₄+29⋅X₁⋅X₁+42⋅X₀⋅X₀+71⋅X₀⋅X₁+27⋅X₄+38⋅X₁+51⋅X₀+18 {O(n^2)}
t₆₄: 17⋅X₁⋅X₁+27⋅X₀⋅X₄+27⋅X₁⋅X₄+30⋅X₀⋅X₀+47⋅X₀⋅X₁+27⋅X₄+34⋅X₁+47⋅X₀+19 {O(n^2)}
t₆₅: X₀+X₁ {O(n)}
t₆₆: X₀+X₁ {O(n)}
t₆₇: 1 {O(1)}
t₆₈: X₀+X₁+1 {O(n)}
t₆₉: X₀+X₁+1 {O(n)}
t₇₁: 17⋅X₁⋅X₁+27⋅X₀⋅X₄+27⋅X₁⋅X₄+30⋅X₀⋅X₀+47⋅X₀⋅X₁+27⋅X₄+34⋅X₁+47⋅X₀+19 {O(n^2)}
t₇₂: 17⋅X₁⋅X₁+27⋅X₀⋅X₄+27⋅X₁⋅X₄+30⋅X₀⋅X₀+47⋅X₀⋅X₁+27⋅X₄+34⋅X₁+47⋅X₀+19 {O(n^2)}
Sizebounds
t₅₃, X₀: X₀ {O(n)}
t₅₃, X₁: X₁ {O(n)}
t₅₃, X₂: X₂ {O(n)}
t₅₃, X₃: X₃ {O(n)}
t₅₃, X₄: X₄ {O(n)}
t₅₄, X₀: X₀ {O(n)}
t₅₄, X₁: 2⋅X₀+3⋅X₁ {O(n)}
t₅₄, X₃: 10⋅X₀+7⋅X₁+9⋅X₄+6 {O(n)}
t₅₄, X₄: 2⋅X₀+3⋅X₄+2 {O(n)}
t₅₅, X₀: X₀ {O(n)}
t₅₅, X₁: 2⋅X₀+3⋅X₁ {O(n)}
t₅₅, X₃: 6⋅X₀+9⋅X₄+6 {O(n)}
t₅₅, X₄: 2⋅X₀+3⋅X₄+2 {O(n)}
t₅₆, X₀: X₀ {O(n)}
t₅₆, X₁: 2⋅X₀+3⋅X₁ {O(n)}
t₅₆, X₃: 4⋅X₀+6⋅X₁ {O(n)}
t₅₆, X₄: 2⋅X₀+3⋅X₄+2 {O(n)}
t₅₇, X₀: X₀ {O(n)}
t₅₇, X₁: 2⋅X₀+3⋅X₁ {O(n)}
t₅₇, X₃: 10⋅X₀+7⋅X₁+9⋅X₄+6 {O(n)}
t₅₇, X₄: 2⋅X₀+3⋅X₄+2 {O(n)}
t₅₈, X₀: X₀ {O(n)}
t₅₈, X₁: 2⋅X₀+3⋅X₁ {O(n)}
t₅₈, X₃: 16⋅X₀+18⋅X₄+7⋅X₁+12 {O(n)}
t₅₈, X₄: 2⋅X₀+3⋅X₄+2 {O(n)}
t₅₉, X₀: X₀ {O(n)}
t₅₉, X₁: 2⋅X₀+3⋅X₁ {O(n)}
t₅₉, X₃: 20⋅X₁+27⋅X₄+30⋅X₀+18 {O(n)}
t₅₉, X₄: 2⋅X₀+3⋅X₄+2 {O(n)}
t₆₀, X₀: X₀ {O(n)}
t₆₀, X₁: 2⋅X₀+3⋅X₁ {O(n)}
t₆₀, X₃: 20⋅X₁+27⋅X₄+30⋅X₀+18 {O(n)}
t₆₀, X₄: 2⋅X₀+3⋅X₄+2 {O(n)}
t₆₁, X₀: X₀ {O(n)}
t₆₁, X₁: 2⋅X₀+3⋅X₁ {O(n)}
t₆₁, X₂: 0 {O(1)}
t₆₁, X₃: 20⋅X₁+27⋅X₄+30⋅X₀+18 {O(n)}
t₆₁, X₄: 2⋅X₀+3⋅X₄+2 {O(n)}
t₆₂, X₀: X₀ {O(n)}
t₆₂, X₁: 2⋅X₀+3⋅X₁ {O(n)}
t₆₂, X₃: 34⋅X₁⋅X₁+54⋅X₀⋅X₄+54⋅X₁⋅X₄+60⋅X₀⋅X₀+94⋅X₀⋅X₁+188⋅X₁+216⋅X₄+274⋅X₀+146 {O(n^2)}
t₆₂, X₄: 2⋅X₀+3⋅X₄+2 {O(n)}
t₆₃, X₀: X₀ {O(n)}
t₆₃, X₁: 2⋅X₀+3⋅X₁ {O(n)}
t₆₃, X₃: 34⋅X₁⋅X₁+54⋅X₀⋅X₄+54⋅X₁⋅X₄+60⋅X₀⋅X₀+94⋅X₀⋅X₁+188⋅X₁+216⋅X₄+274⋅X₀+146 {O(n^2)}
t₆₃, X₄: 2⋅X₀+3⋅X₄+2 {O(n)}
t₆₄, X₀: X₀ {O(n)}
t₆₄, X₁: 2⋅X₀+3⋅X₁ {O(n)}
t₆₄, X₃: 34⋅X₁⋅X₁+54⋅X₀⋅X₄+54⋅X₁⋅X₄+60⋅X₀⋅X₀+94⋅X₀⋅X₁+188⋅X₁+216⋅X₄+274⋅X₀+146 {O(n^2)}
t₆₄, X₄: 2⋅X₀+3⋅X₄+2 {O(n)}
t₆₅, X₀: X₀ {O(n)}
t₆₅, X₁: 2⋅X₀+3⋅X₁ {O(n)}
t₆₅, X₃: 108⋅X₀⋅X₄+108⋅X₁⋅X₄+120⋅X₀⋅X₀+188⋅X₀⋅X₁+68⋅X₁⋅X₁+376⋅X₁+432⋅X₄+548⋅X₀+292 {O(n^2)}
t₆₅, X₄: 2⋅X₀+3⋅X₄+2 {O(n)}
t₆₆, X₀: X₀ {O(n)}
t₆₆, X₁: 2⋅X₀+3⋅X₁ {O(n)}
t₆₆, X₂: 0 {O(1)}
t₆₆, X₃: 4⋅X₀+7⋅X₁ {O(n)}
t₆₆, X₄: 2⋅X₀+3⋅X₄+2 {O(n)}
t₆₇, X₀: 3⋅X₀ {O(n)}
t₆₇, X₁: 4⋅X₀+7⋅X₁ {O(n)}
t₆₇, X₃: 108⋅X₀⋅X₄+108⋅X₁⋅X₄+120⋅X₀⋅X₀+188⋅X₀⋅X₁+68⋅X₁⋅X₁+396⋅X₁+459⋅X₄+578⋅X₀+X₃+310 {O(n^2)}
t₆₇, X₄: 4⋅X₀+7⋅X₄+4 {O(n)}
t₆₈, X₀: X₀ {O(n)}
t₆₈, X₁: 2⋅X₀+3⋅X₁ {O(n)}
t₆₈, X₃: 14⋅X₁+26⋅X₀+27⋅X₄+18 {O(n)}
t₆₈, X₄: 2⋅X₀+3⋅X₄+2 {O(n)}
t₆₉, X₀: X₀ {O(n)}
t₆₉, X₁: 2⋅X₀+3⋅X₁ {O(n)}
t₆₉, X₃: 14⋅X₁+26⋅X₀+27⋅X₄+18 {O(n)}
t₆₉, X₄: 2⋅X₀+3⋅X₄+2 {O(n)}
t₇₁, X₀: X₀ {O(n)}
t₇₁, X₁: 2⋅X₀+3⋅X₁ {O(n)}
t₇₁, X₃: 34⋅X₁⋅X₁+54⋅X₀⋅X₄+54⋅X₁⋅X₄+60⋅X₀⋅X₀+94⋅X₀⋅X₁+188⋅X₁+216⋅X₄+274⋅X₀+146 {O(n^2)}
t₇₁, X₄: 2⋅X₀+3⋅X₄+2 {O(n)}
t₇₂, X₀: X₀ {O(n)}
t₇₂, X₁: 2⋅X₀+3⋅X₁ {O(n)}
t₇₂, X₃: 34⋅X₁⋅X₁+54⋅X₀⋅X₄+54⋅X₁⋅X₄+60⋅X₀⋅X₀+94⋅X₀⋅X₁+188⋅X₁+216⋅X₄+274⋅X₀+146 {O(n^2)}
t₇₂, X₄: 2⋅X₀+3⋅X₄+2 {O(n)}