Initial Problem
Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars:
Locations: l0, l1, l10, l11, l12, l13, l2, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂, X₃, X₄)
t₃: l1(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄)
t₈: l10(X₀, X₁, X₂, X₃, X₄) → l12(X₁-X₃-1, X₁, X₂, X₃, 2⋅X₃+100)
t₁₂: l11(X₀, X₁, X₂, X₃, X₄) → l8(X₀, X₁, X₂, X₃, X₄)
t₉: l12(X₀, X₁, X₂, X₃, X₄) → l13(X₀, X₁, X₂, X₃, X₄) :|: 0 < X₄
t₁₀: l12(X₀, X₁, X₂, X₃, X₄) → l9(X₀, X₀, X₂, X₃, X₄) :|: X₄ ≤ 0
t₁₁: l13(X₀, X₁, X₂, X₃, X₄) → l12(X₀, X₁, X₂, X₃, X₄-1)
t₁: l2(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₃, X₄)
t₂: l3(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁, X₂, X₃, X₄)
t₅: l4(X₀, X₁, X₂, X₃, X₄) → l6(X₀, X₁, X₂, X₃, X₄) :|: X₃ < 0
t₄: l4(X₀, X₁, X₂, X₃, X₄) → l9(X₀, X₂, X₂, X₃, X₄) :|: 0 ≤ X₃
t₁₅: l5(X₀, X₁, X₂, X₃, X₄) → l8(X₀, X₁, X₂, X₃, X₄)
t₁₃: l6(X₀, X₁, X₂, X₃, X₄) → l7(X₀, X₁, X₂, X₃, X₄)
t₁₄: l7(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁, X₂, X₃, X₄)
t₆: l9(X₀, X₁, X₂, X₃, X₄) → l10(X₀, X₁, X₂, X₃, X₄) :|: X₃ < X₁
t₇: l9(X₀, X₁, X₂, X₃, X₄) → l11(X₀, X₁, X₂, X₃, X₄) :|: X₁ ≤ X₃
Preprocessing
Found invariant 0 ≤ X₃ ∧ X₁ ≤ X₃ ∧ X₁ ≤ X₂ for location l11
Found invariant 1+X₃ ≤ 0 for location l6
Found invariant 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ for location l12
Found invariant 1+X₃ ≤ 0 for location l7
Found invariant 1+X₃ ≤ 0 for location l5
Found invariant 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₁+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ for location l13
Found invariant 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₁ for location l10
Found invariant 0 ≤ X₃ ∧ X₁ ≤ X₂ for location l9
Problem after Preprocessing
Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars:
Locations: l0, l1, l10, l11, l12, l13, l2, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂, X₃, X₄)
t₃: l1(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄)
t₈: l10(X₀, X₁, X₂, X₃, X₄) → l12(X₁-X₃-1, X₁, X₂, X₃, 2⋅X₃+100) :|: 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₁
t₁₂: l11(X₀, X₁, X₂, X₃, X₄) → l8(X₀, X₁, X₂, X₃, X₄) :|: 0 ≤ X₃ ∧ X₁ ≤ X₃ ∧ X₁ ≤ X₂
t₉: l12(X₀, X₁, X₂, X₃, X₄) → l13(X₀, X₁, X₂, X₃, X₄) :|: 0 < X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁
t₁₀: l12(X₀, X₁, X₂, X₃, X₄) → l9(X₀, X₀, X₂, X₃, X₄) :|: X₄ ≤ 0 ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁
t₁₁: l13(X₀, X₁, X₂, X₃, X₄) → l12(X₀, X₁, X₂, X₃, X₄-1) :|: 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₁+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁
t₁: l2(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₃, X₄)
t₂: l3(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁, X₂, X₃, X₄)
t₅: l4(X₀, X₁, X₂, X₃, X₄) → l6(X₀, X₁, X₂, X₃, X₄) :|: X₃ < 0
t₄: l4(X₀, X₁, X₂, X₃, X₄) → l9(X₀, X₂, X₂, X₃, X₄) :|: 0 ≤ X₃
t₁₅: l5(X₀, X₁, X₂, X₃, X₄) → l8(X₀, X₁, X₂, X₃, X₄) :|: 1+X₃ ≤ 0
t₁₃: l6(X₀, X₁, X₂, X₃, X₄) → l7(X₀, X₁, X₂, X₃, X₄) :|: 1+X₃ ≤ 0
t₁₄: l7(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁, X₂, X₃, X₄) :|: 1+X₃ ≤ 0
t₆: l9(X₀, X₁, X₂, X₃, X₄) → l10(X₀, X₁, X₂, X₃, X₄) :|: X₃ < X₁ ∧ 0 ≤ X₃ ∧ X₁ ≤ X₂
t₇: l9(X₀, X₁, X₂, X₃, X₄) → l11(X₀, X₁, X₂, X₃, X₄) :|: X₁ ≤ X₃ ∧ 0 ≤ X₃ ∧ X₁ ≤ X₂
MPRF for transition t₈: l10(X₀, X₁, X₂, X₃, X₄) → l12(X₁-X₃-1, X₁, X₂, X₃, 2⋅X₃+100) :|: 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₁ of depth 1:
new bound:
X₂ {O(n)}
MPRF:
l13 [X₁-1 ]
l12 [X₁-1 ]
l9 [X₁ ]
l10 [X₁ ]
MPRF for transition t₁₀: l12(X₀, X₁, X₂, X₃, X₄) → l9(X₀, X₀, X₂, X₃, X₄) :|: X₄ ≤ 0 ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ of depth 1:
new bound:
X₂+1 {O(n)}
MPRF:
l13 [X₁+1 ]
l12 [X₁+1 ]
l9 [X₁+1 ]
l10 [X₁+1 ]
MPRF for transition t₆: l9(X₀, X₁, X₂, X₃, X₄) → l10(X₀, X₁, X₂, X₃, X₄) :|: X₃ < X₁ ∧ 0 ≤ X₃ ∧ X₁ ≤ X₂ of depth 1:
new bound:
X₂+1 {O(n)}
MPRF:
l13 [X₁ ]
l12 [X₁ ]
l9 [X₁+1 ]
l10 [X₁ ]
MPRF for transition t₉: l12(X₀, X₁, X₂, X₃, X₄) → l13(X₀, X₁, X₂, X₃, X₄) :|: 0 < X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ of depth 1:
new bound:
2⋅X₂⋅X₃+100⋅X₂+2⋅X₃+100 {O(n^2)}
MPRF:
l10 [2⋅X₃+100 ]
l9 [X₄ ]
l13 [X₄-1 ]
l12 [X₄ ]
MPRF for transition t₁₁: l13(X₀, X₁, X₂, X₃, X₄) → l12(X₀, X₁, X₂, X₃, X₄-1) :|: 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₁+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ of depth 1:
new bound:
2⋅X₂⋅X₃+100⋅X₂+2⋅X₃+100 {O(n^2)}
MPRF:
l10 [2⋅X₃+100 ]
l9 [X₄ ]
l13 [X₄ ]
l12 [X₄ ]
Analysing control-flow refined program
Cut unsatisfiable transition t₁₀: l12→l9
Cut unsatisfiable transition t₁₀₅: n_l12___4→l9
Found invariant 0 ≤ X₃ ∧ X₁ ≤ X₃ ∧ X₁ ≤ X₂ for location l11
Found invariant 99 ≤ X₄ ∧ 99 ≤ X₃+X₄ ∧ 99+X₃ ≤ X₄ ∧ 100 ≤ X₂+X₄ ∧ 100 ≤ X₁+X₄ ∧ 99 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location n_l13___3
Found invariant 1+X₃ ≤ 0 for location l6
Found invariant 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₁+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location n_l13___1
Found invariant 100 ≤ X₄ ∧ 100 ≤ X₃+X₄ ∧ 100+X₃ ≤ X₄ ∧ 101 ≤ X₂+X₄ ∧ 101 ≤ X₁+X₄ ∧ 100 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location n_l13___5
Found invariant 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ 1 ≤ X₂+X₄ ∧ 1 ≤ X₁+X₄ ∧ 0 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location n_l12___2
Found invariant 100 ≤ X₄ ∧ 100 ≤ X₃+X₄ ∧ 100+X₃ ≤ X₄ ∧ 101 ≤ X₂+X₄ ∧ 101 ≤ X₁+X₄ ∧ 100 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ for location l12
Found invariant 1+X₃ ≤ 0 for location l7
Found invariant 1+X₃ ≤ 0 for location l5
Found invariant 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₁ for location l10
Found invariant 0 ≤ X₃ ∧ X₁ ≤ X₂ for location l9
Found invariant 99 ≤ X₄ ∧ 99 ≤ X₃+X₄ ∧ 99+X₃ ≤ X₄ ∧ 100 ≤ X₂+X₄ ∧ 100 ≤ X₁+X₄ ∧ 99 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location n_l12___4
knowledge_propagation leads to new time bound X₂ {O(n)} for transition t₉₇: l12(X₀, X₁, X₂, X₃, X₄) → n_l13___5(X₀, X₁, X₂, X₃, X₄) :|: 1+X₃ ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ X₀+X₃ ∧ 0 < X₄ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₄ ∧ 100+2⋅X₃ ≤ X₄ ∧ X₄ ≤ 100+2⋅X₃ ∧ 1+X₀+X₃ ≤ X₁ ∧ X₁ ≤ 1+X₀+X₃ ∧ 0 ≤ X₀ ∧ 0 ≤ X₃ ∧ 1+X₀+X₃ ≤ X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₄ ∧ 0 ≤ X₀+X₃ ∧ 0 ≤ X₃ ∧ 1+X₀ ≤ X₁ ∧ 1+X₃ ≤ X₁ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₄ ∧ 0 ≤ X₀+X₃ ∧ 0 ≤ X₃ ∧ 1+X₀ ≤ X₁ ∧ 1+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 0 < X₄ ∧ X₁ ≤ X₂ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀+X₃ ∧ 100 ≤ X₄ ∧ 100 ≤ X₃+X₄ ∧ 100+X₃ ≤ X₄ ∧ 101 ≤ X₂+X₄ ∧ 101 ≤ X₁+X₄ ∧ 100 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁
knowledge_propagation leads to new time bound X₂ {O(n)} for transition t₁₀₀: n_l13___5(X₀, X₁, X₂, X₃, X₄) → n_l12___4(X₀, X₁, X₂, X₃, X₄-1) :|: 2⋅X₀+X₄ ≤ 98+2⋅X₂ ∧ 100 ≤ X₄ ∧ 0 ≤ X₀ ∧ 2⋅X₀+X₄ ≤ 2⋅X₁+98 ∧ 98+2⋅X₁ ≤ 2⋅X₀+X₄ ∧ 2⋅X₃+100 ≤ X₄ ∧ X₄ ≤ 100+2⋅X₃ ∧ 1+X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 1 ≤ X₄ ∧ X₁ ≤ X₂ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀+X₃ ∧ 100 ≤ X₄ ∧ 100 ≤ X₃+X₄ ∧ 100+X₃ ≤ X₄ ∧ 101 ≤ X₂+X₄ ∧ 101 ≤ X₁+X₄ ∧ 100 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀
knowledge_propagation leads to new time bound X₂ {O(n)} for transition t₉₆: n_l12___4(X₀, X₁, X₂, X₃, X₄) → n_l13___3(X₀, X₁, X₂, X₃, X₄) :|: 1+X₃ ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ X₀+X₃ ∧ 0 < X₄ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₄ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₄ ∧ 0 ≤ X₀+X₃ ∧ 0 ≤ X₃ ∧ 1+X₀ ≤ X₁ ∧ 1+X₃ ≤ X₁ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₄ ∧ 0 ≤ X₀+X₃ ∧ 0 ≤ X₃ ∧ 1+X₀ ≤ X₁ ∧ 1+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 0 < X₄ ∧ X₁ ≤ X₂ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀+X₃ ∧ 99 ≤ X₄ ∧ 99 ≤ X₃+X₄ ∧ 99+X₃ ≤ X₄ ∧ 100 ≤ X₂+X₄ ∧ 100 ≤ X₁+X₄ ∧ 99 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀
knowledge_propagation leads to new time bound X₂ {O(n)} for transition t₉₉: n_l13___3(X₀, X₁, X₂, X₃, X₄) → n_l12___2(X₀, X₁, X₂, X₃, X₄-1) :|: 1+X₃ ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ X₀+X₃ ∧ 1 ≤ X₄ ∧ X₁ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 1 ≤ X₄ ∧ X₁ ≤ X₂ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀+X₃ ∧ 99 ≤ X₄ ∧ 99 ≤ X₃+X₄ ∧ 99+X₃ ≤ X₄ ∧ 100 ≤ X₂+X₄ ∧ 100 ≤ X₁+X₄ ∧ 99 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀
MPRF for transition t₉₅: n_l12___2(X₀, X₁, X₂, X₃, X₄) → n_l13___1(X₀, X₁, X₂, X₃, X₄) :|: 1+X₃ ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ X₀+X₃ ∧ X₁ ≤ X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₄ ∧ 0 ≤ X₀+X₃ ∧ 0 ≤ X₃ ∧ 1+X₀ ≤ X₁ ∧ 1+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 0 < X₄ ∧ X₁ ≤ X₂ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀+X₃ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ 1 ≤ X₂+X₄ ∧ 1 ≤ X₁+X₄ ∧ 0 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:
new bound:
98⋅X₂+1 {O(n)}
MPRF:
l12 [98⋅X₁+1 ]
l10 [98⋅X₁+1 ]
l9 [98⋅X₁+1 ]
n_l13___1 [98⋅X₀+X₄ ]
n_l13___3 [98⋅X₀+X₄ ]
n_l12___2 [98⋅X₀+X₄+1 ]
n_l13___5 [98⋅X₀+X₄-1 ]
n_l12___4 [98⋅X₀+X₄ ]
MPRF for transition t₁₀₄: n_l12___2(X₀, X₁, X₂, X₃, X₄) → l9(X₀, X₀, X₂, X₃, X₄) :|: X₄ ≤ 0 ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ 1 ≤ X₂+X₄ ∧ 1 ≤ X₁+X₄ ∧ 0 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:
new bound:
X₂ {O(n)}
MPRF:
l12 [X₁ ]
l10 [X₁ ]
l9 [X₁ ]
n_l13___1 [X₁ ]
n_l13___3 [X₁ ]
n_l12___2 [X₁ ]
n_l13___5 [X₁ ]
n_l12___4 [X₁ ]
MPRF for transition t₉₈: n_l13___1(X₀, X₁, X₂, X₃, X₄) → n_l12___2(X₀, X₁, X₂, X₃, X₄-1) :|: 1+X₃ ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ X₀+X₃ ∧ 0 < X₄ ∧ X₁ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 1 ≤ X₄ ∧ X₁ ≤ X₂ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀+X₃ ∧ 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₁+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:
new bound:
98⋅X₂+97 {O(n)}
MPRF:
l12 [2⋅X₀+96⋅X₁+X₄-1 ]
l10 [98⋅X₁+97 ]
l9 [98⋅X₁+97 ]
n_l13___1 [98⋅X₀+X₄+97 ]
n_l13___3 [2⋅X₀+96⋅X₁+X₄ ]
n_l12___2 [98⋅X₀+X₄+97 ]
n_l13___5 [2⋅X₀+96⋅X₁+X₄-1 ]
n_l12___4 [2⋅X₀+96⋅X₁+X₄ ]
CFR: Improvement to new bound with the following program:
new bound:
203⋅X₂+99 {O(n)}
cfr-program:
Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars:
Locations: l0, l1, l10, l11, l12, l2, l3, l4, l5, l6, l7, l8, l9, n_l12___2, n_l12___4, n_l13___1, n_l13___3, n_l13___5
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂, X₃, X₄)
t₃: l1(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄)
t₈: l10(X₀, X₁, X₂, X₃, X₄) → l12(X₁-X₃-1, X₁, X₂, X₃, 2⋅X₃+100) :|: 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₁
t₁₂: l11(X₀, X₁, X₂, X₃, X₄) → l8(X₀, X₁, X₂, X₃, X₄) :|: 0 ≤ X₃ ∧ X₁ ≤ X₃ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₃ ∧ X₁ ≤ X₃ ∧ X₁ ≤ X₂
t₉₇: l12(X₀, X₁, X₂, X₃, X₄) → n_l13___5(X₀, X₁, X₂, X₃, X₄) :|: 1+X₃ ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ X₀+X₃ ∧ 0 < X₄ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₄ ∧ 100+2⋅X₃ ≤ X₄ ∧ X₄ ≤ 100+2⋅X₃ ∧ 1+X₀+X₃ ≤ X₁ ∧ X₁ ≤ 1+X₀+X₃ ∧ 0 ≤ X₀ ∧ 0 ≤ X₃ ∧ 1+X₀+X₃ ≤ X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₄ ∧ 0 ≤ X₀+X₃ ∧ 0 ≤ X₃ ∧ 1+X₀ ≤ X₁ ∧ 1+X₃ ≤ X₁ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₄ ∧ 0 ≤ X₀+X₃ ∧ 0 ≤ X₃ ∧ 1+X₀ ≤ X₁ ∧ 1+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 0 < X₄ ∧ X₁ ≤ X₂ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀+X₃ ∧ 100 ≤ X₄ ∧ 100 ≤ X₃+X₄ ∧ 100+X₃ ≤ X₄ ∧ 101 ≤ X₂+X₄ ∧ 101 ≤ X₁+X₄ ∧ 100 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁
t₁: l2(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₃, X₄)
t₂: l3(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁, X₂, X₃, X₄)
t₅: l4(X₀, X₁, X₂, X₃, X₄) → l6(X₀, X₁, X₂, X₃, X₄) :|: X₃ < 0
t₄: l4(X₀, X₁, X₂, X₃, X₄) → l9(X₀, X₂, X₂, X₃, X₄) :|: 0 ≤ X₃
t₁₅: l5(X₀, X₁, X₂, X₃, X₄) → l8(X₀, X₁, X₂, X₃, X₄) :|: 1+X₃ ≤ 0 ∧ 1+X₃ ≤ 0
t₁₃: l6(X₀, X₁, X₂, X₃, X₄) → l7(X₀, X₁, X₂, X₃, X₄) :|: 1+X₃ ≤ 0 ∧ 1+X₃ ≤ 0
t₁₄: l7(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁, X₂, X₃, X₄) :|: 1+X₃ ≤ 0 ∧ 1+X₃ ≤ 0
t₆: l9(X₀, X₁, X₂, X₃, X₄) → l10(X₀, X₁, X₂, X₃, X₄) :|: X₃ < X₁ ∧ 0 ≤ X₃ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₃ ∧ X₁ ≤ X₂
t₇: l9(X₀, X₁, X₂, X₃, X₄) → l11(X₀, X₁, X₂, X₃, X₄) :|: X₁ ≤ X₃ ∧ 0 ≤ X₃ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₃ ∧ X₁ ≤ X₂
t₁₀₄: n_l12___2(X₀, X₁, X₂, X₃, X₄) → l9(X₀, X₀, X₂, X₃, X₄) :|: X₄ ≤ 0 ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ 1 ≤ X₂+X₄ ∧ 1 ≤ X₁+X₄ ∧ 0 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀
t₉₅: n_l12___2(X₀, X₁, X₂, X₃, X₄) → n_l13___1(X₀, X₁, X₂, X₃, X₄) :|: 1+X₃ ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ X₀+X₃ ∧ X₁ ≤ X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₄ ∧ 0 ≤ X₀+X₃ ∧ 0 ≤ X₃ ∧ 1+X₀ ≤ X₁ ∧ 1+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 0 < X₄ ∧ X₁ ≤ X₂ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀+X₃ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ 1 ≤ X₂+X₄ ∧ 1 ≤ X₁+X₄ ∧ 0 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀
t₉₆: n_l12___4(X₀, X₁, X₂, X₃, X₄) → n_l13___3(X₀, X₁, X₂, X₃, X₄) :|: 1+X₃ ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ X₀+X₃ ∧ 0 < X₄ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₄ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₄ ∧ 0 ≤ X₀+X₃ ∧ 0 ≤ X₃ ∧ 1+X₀ ≤ X₁ ∧ 1+X₃ ≤ X₁ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₄ ∧ 0 ≤ X₀+X₃ ∧ 0 ≤ X₃ ∧ 1+X₀ ≤ X₁ ∧ 1+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 0 < X₄ ∧ X₁ ≤ X₂ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀+X₃ ∧ 99 ≤ X₄ ∧ 99 ≤ X₃+X₄ ∧ 99+X₃ ≤ X₄ ∧ 100 ≤ X₂+X₄ ∧ 100 ≤ X₁+X₄ ∧ 99 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀
t₉₈: n_l13___1(X₀, X₁, X₂, X₃, X₄) → n_l12___2(X₀, X₁, X₂, X₃, X₄-1) :|: 1+X₃ ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ X₀+X₃ ∧ 0 < X₄ ∧ X₁ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 1 ≤ X₄ ∧ X₁ ≤ X₂ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀+X₃ ∧ 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₁+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀
t₉₉: n_l13___3(X₀, X₁, X₂, X₃, X₄) → n_l12___2(X₀, X₁, X₂, X₃, X₄-1) :|: 1+X₃ ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ X₀+X₃ ∧ 1 ≤ X₄ ∧ X₁ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 1 ≤ X₄ ∧ X₁ ≤ X₂ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀+X₃ ∧ 99 ≤ X₄ ∧ 99 ≤ X₃+X₄ ∧ 99+X₃ ≤ X₄ ∧ 100 ≤ X₂+X₄ ∧ 100 ≤ X₁+X₄ ∧ 99 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀
t₁₀₀: n_l13___5(X₀, X₁, X₂, X₃, X₄) → n_l12___4(X₀, X₁, X₂, X₃, X₄-1) :|: 2⋅X₀+X₄ ≤ 98+2⋅X₂ ∧ 100 ≤ X₄ ∧ 0 ≤ X₀ ∧ 2⋅X₀+X₄ ≤ 2⋅X₁+98 ∧ 98+2⋅X₁ ≤ 2⋅X₀+X₄ ∧ 2⋅X₃+100 ≤ X₄ ∧ X₄ ≤ 100+2⋅X₃ ∧ 1+X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 1 ≤ X₄ ∧ X₁ ≤ X₂ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀+X₃ ∧ 100 ≤ X₄ ∧ 100 ≤ X₃+X₄ ∧ 100+X₃ ≤ X₄ ∧ 101 ≤ X₂+X₄ ∧ 101 ≤ X₁+X₄ ∧ 100 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀
All Bounds
Timebounds
Overall timebound:203⋅X₂+110 {O(n)}
t₀: 1 {O(1)}
t₃: 1 {O(1)}
t₈: X₂ {O(n)}
t₁₂: 1 {O(1)}
t₉₇: X₂ {O(n)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₄: 1 {O(1)}
t₅: 1 {O(1)}
t₁₅: 1 {O(1)}
t₁₃: 1 {O(1)}
t₁₄: 1 {O(1)}
t₆: X₂+1 {O(n)}
t₇: 1 {O(1)}
t₉₅: 98⋅X₂+1 {O(n)}
t₁₀₄: X₂ {O(n)}
t₉₆: X₂ {O(n)}
t₉₈: 98⋅X₂+97 {O(n)}
t₉₉: X₂ {O(n)}
t₁₀₀: X₂ {O(n)}
Costbounds
Overall costbound: 203⋅X₂+110 {O(n)}
t₀: 1 {O(1)}
t₃: 1 {O(1)}
t₈: X₂ {O(n)}
t₁₂: 1 {O(1)}
t₉₇: X₂ {O(n)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₄: 1 {O(1)}
t₅: 1 {O(1)}
t₁₅: 1 {O(1)}
t₁₃: 1 {O(1)}
t₁₄: 1 {O(1)}
t₆: X₂+1 {O(n)}
t₇: 1 {O(1)}
t₉₅: 98⋅X₂+1 {O(n)}
t₁₀₄: X₂ {O(n)}
t₉₆: X₂ {O(n)}
t₉₈: 98⋅X₂+97 {O(n)}
t₉₉: X₂ {O(n)}
t₁₀₀: X₂ {O(n)}
Sizebounds
t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₀, X₃: X₃ {O(n)}
t₀, X₄: X₄ {O(n)}
t₃, X₀: X₀ {O(n)}
t₃, X₁: X₁ {O(n)}
t₃, X₂: X₂ {O(n)}
t₃, X₃: X₃ {O(n)}
t₃, X₄: X₄ {O(n)}
t₈, X₀: X₂ {O(n)}
t₈, X₁: X₂ {O(n)}
t₈, X₂: X₂ {O(n)}
t₈, X₃: X₃ {O(n)}
t₈, X₄: 2⋅X₃+100 {O(n)}
t₁₂, X₀: X₀+X₂ {O(n)}
t₁₂, X₁: 2⋅X₂ {O(n)}
t₁₂, X₂: 2⋅X₂ {O(n)}
t₁₂, X₃: 2⋅X₃ {O(n)}
t₁₂, X₄: X₄ {O(n)}
t₉₇, X₀: X₂ {O(n)}
t₉₇, X₁: X₂ {O(n)}
t₉₇, X₂: X₂ {O(n)}
t₉₇, X₃: X₃ {O(n)}
t₉₇, X₄: 2⋅X₃+100 {O(n)}
t₁, X₀: X₀ {O(n)}
t₁, X₁: X₁ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₃ {O(n)}
t₁, X₄: X₄ {O(n)}
t₂, X₀: X₀ {O(n)}
t₂, X₁: X₁ {O(n)}
t₂, X₂: X₂ {O(n)}
t₂, X₃: X₃ {O(n)}
t₂, X₄: X₄ {O(n)}
t₄, X₀: X₀ {O(n)}
t₄, X₁: X₂ {O(n)}
t₄, X₂: X₂ {O(n)}
t₄, X₃: X₃ {O(n)}
t₄, X₄: X₄ {O(n)}
t₅, X₀: X₀ {O(n)}
t₅, X₁: X₁ {O(n)}
t₅, X₂: X₂ {O(n)}
t₅, X₃: X₃ {O(n)}
t₅, X₄: X₄ {O(n)}
t₁₅, X₀: X₀ {O(n)}
t₁₅, X₁: X₁ {O(n)}
t₁₅, X₂: X₂ {O(n)}
t₁₅, X₃: X₃ {O(n)}
t₁₅, X₄: X₄ {O(n)}
t₁₃, X₀: X₀ {O(n)}
t₁₃, X₁: X₁ {O(n)}
t₁₃, X₂: X₂ {O(n)}
t₁₃, X₃: X₃ {O(n)}
t₁₃, X₄: X₄ {O(n)}
t₁₄, X₀: X₀ {O(n)}
t₁₄, X₁: X₁ {O(n)}
t₁₄, X₂: X₂ {O(n)}
t₁₄, X₃: X₃ {O(n)}
t₁₄, X₄: X₄ {O(n)}
t₆, X₀: X₀+X₂ {O(n)}
t₆, X₁: X₂ {O(n)}
t₆, X₂: X₂ {O(n)}
t₆, X₃: X₃ {O(n)}
t₆, X₄: X₄ {O(n)}
t₇, X₀: X₀+X₂ {O(n)}
t₇, X₁: 2⋅X₂ {O(n)}
t₇, X₂: 2⋅X₂ {O(n)}
t₇, X₃: 2⋅X₃ {O(n)}
t₇, X₄: X₄ {O(n)}
t₉₅, X₀: X₂ {O(n)}
t₉₅, X₁: X₂ {O(n)}
t₉₅, X₂: X₂ {O(n)}
t₉₅, X₃: X₃ {O(n)}
t₉₅, X₄: 2⋅X₃+100 {O(n)}
t₁₀₄, X₀: X₂ {O(n)}
t₁₀₄, X₁: X₂ {O(n)}
t₁₀₄, X₂: X₂ {O(n)}
t₁₀₄, X₃: X₃ {O(n)}
t₁₀₄, X₄: 0 {O(1)}
t₉₆, X₀: X₂ {O(n)}
t₉₆, X₁: X₂ {O(n)}
t₉₆, X₂: X₂ {O(n)}
t₉₆, X₃: X₃ {O(n)}
t₉₆, X₄: 2⋅X₃+100 {O(n)}
t₉₈, X₀: X₂ {O(n)}
t₉₈, X₁: X₂ {O(n)}
t₉₈, X₂: X₂ {O(n)}
t₉₈, X₃: X₃ {O(n)}
t₉₈, X₄: 2⋅X₃+100 {O(n)}
t₉₉, X₀: X₂ {O(n)}
t₉₉, X₁: X₂ {O(n)}
t₉₉, X₂: X₂ {O(n)}
t₉₉, X₃: X₃ {O(n)}
t₉₉, X₄: 2⋅X₃+100 {O(n)}
t₁₀₀, X₀: X₂ {O(n)}
t₁₀₀, X₁: X₂ {O(n)}
t₁₀₀, X₂: X₂ {O(n)}
t₁₀₀, X₃: X₃ {O(n)}
t₁₀₀, X₄: 2⋅X₃+100 {O(n)}