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 ]
Found invariant 0 ≤ X₃ ∧ X₁ ≤ X₃ ∧ X₁ ≤ X₂ for location l11
Found invariant 1+X₃ ≤ 0 for location l6
Found invariant 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ 1 ≤ X₂+X₄ ∧ 1 ≤ 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 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
Time-Bound by TWN-Loops:
TWN-Loops: t₉ 4⋅X₂⋅X₃+204⋅X₂ {O(n^2)}
TWN-Loops:
entry: 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
results in twn-loop: twn:Inv: [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 ∧ 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] , (X₀,X₁,X₂,X₃,X₄) -> (X₀,X₁,X₂,X₃,X₄-1) :|: 0 < X₄
order: [X₀; X₁; X₂; X₃; X₄]
closed-form:
X₀: X₀
X₁: X₁
X₂: X₂
X₃: X₃
X₄: X₄ + [[n != 0]] * -1 * n^1
Termination: true
Formula:
1 < 0
∨ 0 < X₄ ∧ 1 ≤ 0 ∧ 0 ≤ 1
Stabilization-Threshold for: 0 < X₄
alphas_abs: X₄
M: 0
N: 1
Bound: 2⋅X₄+2 {O(n)}
relevant size-bounds w.r.t. t₈:
X₄: 2⋅X₃+100 {O(n)}
Runtime-bound of t₈: X₂ {O(n)}
Results in: 4⋅X₂⋅X₃+204⋅X₂ {O(n^2)}
4⋅X₂⋅X₃+204⋅X₂ {O(n^2)}
Time-Bound by TWN-Loops:
TWN-Loops: t₁₁ 4⋅X₂⋅X₃+204⋅X₂ {O(n^2)}
relevant size-bounds w.r.t. t₈:
X₄: 2⋅X₃+100 {O(n)}
Runtime-bound of t₈: X₂ {O(n)}
Results in: 4⋅X₂⋅X₃+204⋅X₂ {O(n^2)}
4⋅X₂⋅X₃+204⋅X₂ {O(n^2)}
Analysing control-flow refined program
Cut unsatisfiable transition t₁₀: l12→l9
Cut unsatisfiable transition t₁₁₇: 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 t₁₀₉: 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 t₁₁₂: 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 t₁₀₈: 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 t₁₁₁: 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 t₁₀₇: 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+97 {O(n)}
MPRF:
l12 [195⋅X₁-97⋅X₀-97⋅X₃ ]
l10 [98⋅X₁+97 ]
l9 [98⋅X₁+97 ]
n_l13___1 [98⋅X₀+X₄+96 ]
n_l13___3 [98⋅X₀+X₄+96 ]
n_l12___2 [98⋅X₀+X₄+97 ]
n_l13___5 [2⋅X₀+96⋅X₁+X₄-1 ]
n_l12___4 [2⋅X₀+96⋅X₁+X₄ ]
MPRF for transition t₁₁₆: 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 t₁₁₀: 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 {O(n)}
MPRF:
l12 [98⋅X₁+2⋅X₃+100-X₄ ]
l10 [98⋅X₁ ]
l9 [98⋅X₁ ]
n_l13___1 [98⋅X₀+X₄ ]
n_l13___3 [2⋅X₀+96⋅X₁+X₄-97 ]
n_l12___2 [98⋅X₀+X₄ ]
n_l13___5 [2⋅X₀+96⋅X₁+2⋅X₃+2 ]
n_l12___4 [2⋅X₀+96⋅X₁+X₄-97 ]
CFR: Improvement to new bound with the following program:
new bound:
203⋅X₂+98 {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
t₁₀₉: 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
t₁₁₆: 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
t₁₀₇: 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
t₁₀₈: 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
t₁₁₀: 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
t₁₁₁: 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
t₁₁₂: 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+109 {O(n)}
t₀: 1 {O(1)}
t₃: 1 {O(1)}
t₈: X₂ {O(n)}
t₁₂: 1 {O(1)}
t₁₀₉: 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)}
t₁₀₇: 98⋅X₂+97 {O(n)}
t₁₁₆: X₂ {O(n)}
t₁₀₈: X₂ {O(n)}
t₁₁₀: 98⋅X₂ {O(n)}
t₁₁₁: X₂ {O(n)}
t₁₁₂: X₂ {O(n)}
Costbounds
Overall costbound: 203⋅X₂+109 {O(n)}
t₀: 1 {O(1)}
t₃: 1 {O(1)}
t₈: X₂ {O(n)}
t₁₂: 1 {O(1)}
t₁₀₉: 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)}
t₁₀₇: 98⋅X₂+97 {O(n)}
t₁₁₆: X₂ {O(n)}
t₁₀₈: X₂ {O(n)}
t₁₁₀: 98⋅X₂ {O(n)}
t₁₁₁: X₂ {O(n)}
t₁₁₂: 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)}
t₁₀₉, X₀: X₂ {O(n)}
t₁₀₉, X₁: X₂ {O(n)}
t₁₀₉, X₂: X₂ {O(n)}
t₁₀₉, X₃: X₃ {O(n)}
t₁₀₉, 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)}
t₁₀₇, X₀: X₂ {O(n)}
t₁₀₇, X₁: X₂ {O(n)}
t₁₀₇, X₂: X₂ {O(n)}
t₁₀₇, X₃: X₃ {O(n)}
t₁₀₇, X₄: 2⋅X₃+100 {O(n)}
t₁₁₆, X₀: X₂ {O(n)}
t₁₁₆, X₁: X₂ {O(n)}
t₁₁₆, X₂: X₂ {O(n)}
t₁₁₆, X₃: X₃ {O(n)}
t₁₁₆, X₄: 0 {O(1)}
t₁₀₈, X₀: X₂ {O(n)}
t₁₀₈, X₁: X₂ {O(n)}
t₁₀₈, X₂: X₂ {O(n)}
t₁₀₈, X₃: X₃ {O(n)}
t₁₀₈, X₄: 2⋅X₃+100 {O(n)}
t₁₁₀, X₀: X₂ {O(n)}
t₁₁₀, X₁: X₂ {O(n)}
t₁₁₀, X₂: X₂ {O(n)}
t₁₁₀, X₃: X₃ {O(n)}
t₁₁₀, X₄: 2⋅X₃+100 {O(n)}
t₁₁₁, X₀: X₂ {O(n)}
t₁₁₁, X₁: X₂ {O(n)}
t₁₁₁, X₂: X₂ {O(n)}
t₁₁₁, X₃: X₃ {O(n)}
t₁₁₁, X₄: 2⋅X₃+100 {O(n)}
t₁₁₂, X₀: X₂ {O(n)}
t₁₁₂, X₁: X₂ {O(n)}
t₁₁₂, X₂: X₂ {O(n)}
t₁₁₂, X₃: X₃ {O(n)}
t₁₁₂, X₄: 2⋅X₃+100 {O(n)}