Initial Problem
Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₃, X₄)
t₄: l1(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂, X₃, X₄) :|: X₀ ≤ X₃
t₃: l1(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄) :|: X₃ < X₀
t₉: l2(X₀, X₁, X₂, X₃, X₄) → l7(X₀, X₁, X₂, X₃, X₄)
t₂: l3(X₀, X₁, X₂, X₃, X₄) → l1(X₂, X₁, X₂, X₃, X₄) :|: 0 ≤ X₃
t₁: l3(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂, X₃, X₄) :|: X₃ < 0
t₅: l4(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₀-X₃-1, X₂, X₃, 2⋅X₃+100)
t₇: l5(X₀, X₁, X₂, X₃, X₄) → l1(X₁, X₁, X₂, X₃, X₄) :|: X₄ ≤ 0
t₆: l5(X₀, X₁, X₂, X₃, X₄) → l6(X₀, X₁, X₂, X₃, X₄) :|: 0 < X₄
t₈: l6(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁, X₂, X₃, X₄-1)
Preprocessing
Found invariant 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l6
Found invariant 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l5
Found invariant 0 ≤ X₃ ∧ X₀ ≤ X₂ for location l1
Found invariant 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₀ for location l4
Problem after Preprocessing
Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₃, X₄)
t₄: l1(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂, X₃, X₄) :|: X₀ ≤ X₃ ∧ 0 ≤ X₃ ∧ X₀ ≤ X₂
t₃: l1(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄) :|: X₃ < X₀ ∧ 0 ≤ X₃ ∧ X₀ ≤ X₂
t₉: l2(X₀, X₁, X₂, X₃, X₄) → l7(X₀, X₁, X₂, X₃, X₄)
t₂: l3(X₀, X₁, X₂, X₃, X₄) → l1(X₂, X₁, X₂, X₃, X₄) :|: 0 ≤ X₃
t₁: l3(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂, X₃, X₄) :|: X₃ < 0
t₅: l4(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₀-X₃-1, X₂, X₃, 2⋅X₃+100) :|: 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₀
t₇: l5(X₀, X₁, X₂, X₃, X₄) → l1(X₁, X₁, X₂, X₃, X₄) :|: X₄ ≤ 0 ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₆: l5(X₀, X₁, X₂, X₃, X₄) → l6(X₀, X₁, X₂, X₃, X₄) :|: 0 < X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₈: l6(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁, X₂, X₃, X₄-1) :|: 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀
MPRF for transition t₃: l1(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄) :|: X₃ < X₀ ∧ 0 ≤ X₃ ∧ X₀ ≤ X₂ of depth 1:
new bound:
X₂+1 {O(n)}
MPRF:
l4 [X₀ ]
l1 [X₀+1 ]
l6 [X₀ ]
l5 [X₀ ]
MPRF for transition t₅: l4(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₀-X₃-1, X₂, X₃, 2⋅X₃+100) :|: 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₂ {O(n)}
MPRF:
l4 [X₀ ]
l1 [X₀ ]
l6 [X₀-1 ]
l5 [X₀-1 ]
MPRF for transition t₇: l5(X₀, X₁, X₂, X₃, X₄) → l1(X₁, X₁, X₂, X₃, X₄) :|: X₄ ≤ 0 ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₂ {O(n)}
MPRF:
l4 [X₀ ]
l1 [X₀ ]
l6 [X₀ ]
l5 [X₀ ]
Found invariant 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l6
Found invariant 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ 1 ≤ X₂+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l5
Found invariant 0 ≤ X₃ ∧ X₀ ≤ X₂ for location l1
Found invariant 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₀ for location l4
Time-Bound by TWN-Loops:
TWN-Loops: t₆ 4⋅X₂⋅X₃+204⋅X₂ {O(n^2)}
TWN-Loops:
entry: t₅: l4(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₀-X₃-1, X₂, X₃, 2⋅X₃+100) :|: 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₀
results in twn-loop: twn:Inv: [1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀] , (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. t₅:
X₄: 2⋅X₃+100 {O(n)}
Runtime-bound of t₅: 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: t₈ 4⋅X₂⋅X₃+204⋅X₂ {O(n^2)}
relevant size-bounds w.r.t. t₅:
X₄: 2⋅X₃+100 {O(n)}
Runtime-bound of t₅: 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 t₇: l5→l1
Cut unsatisfiable transition t₈₈: n_l5___4→l1
Found invariant 99 ≤ X₄ ∧ 99 ≤ X₃+X₄ ∧ 99+X₃ ≤ X₄ ∧ 100 ≤ X₂+X₄ ∧ 99 ≤ X₁+X₄ ∧ 100 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l6___3
Found invariant 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l6___1
Found invariant 100 ≤ X₄ ∧ 100 ≤ X₃+X₄ ∧ 100+X₃ ≤ X₄ ∧ 101 ≤ X₂+X₄ ∧ 100 ≤ X₁+X₄ ∧ 101 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l6___5
Found invariant 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ 1 ≤ X₂+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l5___2
Found invariant 99 ≤ X₄ ∧ 99 ≤ X₃+X₄ ∧ 99+X₃ ≤ X₄ ∧ 100 ≤ X₂+X₄ ∧ 99 ≤ X₁+X₄ ∧ 100 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l5___4
Found invariant 100 ≤ X₄ ∧ 100 ≤ X₃+X₄ ∧ 100+X₃ ≤ X₄ ∧ 101 ≤ X₂+X₄ ∧ 100 ≤ X₁+X₄ ∧ 101 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l5
Found invariant 0 ≤ X₃ ∧ X₀ ≤ X₂ for location l1
Found invariant 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₀ for location l4
knowledge_propagation leads to new time bound X₂ {O(n)} for transition t₈₀: l5(X₀, X₁, X₂, X₃, X₄) → n_l6___5(X₀, X₁, X₂, X₃, X₄) :|: 1+X₁ ≤ X₀ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₃ ∧ X₀ ≤ X₂ ∧ 0 < X₄ ∧ 1 ≤ X₄ ∧ 100+2⋅X₃ ≤ X₄ ∧ X₄ ≤ 100+2⋅X₃ ∧ X₀ ≤ 1+X₁+X₃ ∧ 1+X₁+X₃ ≤ X₀ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₄ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₁+X₃ ∧ 1+X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₄ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₁+X₃ ∧ 1+X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 < X₄ ∧ 1+X₃ ≤ X₀ ∧ X₀ ≤ X₂ ∧ 100 ≤ X₄ ∧ 100 ≤ X₃+X₄ ∧ 100+X₃ ≤ X₄ ∧ 101 ≤ X₂+X₄ ∧ 100 ≤ X₁+X₄ ∧ 101 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀
knowledge_propagation leads to new time bound X₂ {O(n)} for transition t₈₃: n_l6___5(X₀, X₁, X₂, X₃, X₄) → n_l5___4(X₀, X₁, X₂, X₃, X₄-1) :|: X₀ ≤ X₂ ∧ 100 ≤ X₄ ∧ X₄ ≤ 98+2⋅X₀ ∧ 2⋅X₀+98 ≤ 2⋅X₁+X₄ ∧ 2⋅X₁+X₄ ≤ 98+2⋅X₀ ∧ 2⋅X₃+100 ≤ X₄ ∧ X₄ ≤ 100+2⋅X₃ ∧ 0 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₄ ∧ 1+X₃ ≤ X₀ ∧ X₀ ≤ X₂ ∧ 100 ≤ X₄ ∧ 100 ≤ X₃+X₄ ∧ 100+X₃ ≤ X₄ ∧ 101 ≤ X₂+X₄ ∧ 100 ≤ X₁+X₄ ∧ 101 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀
knowledge_propagation leads to new time bound X₂ {O(n)} for transition t₇₉: n_l5___4(X₀, X₁, X₂, X₃, X₄) → n_l6___3(X₀, X₁, X₂, X₃, X₄) :|: 1+X₁ ≤ X₀ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₃ ∧ X₀ ≤ X₂ ∧ 0 < X₄ ∧ 1 ≤ X₄ ∧ 1 ≤ X₄ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₁+X₃ ∧ 1+X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₄ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₁+X₃ ∧ 1+X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 < X₄ ∧ 1+X₃ ≤ X₀ ∧ X₀ ≤ X₂ ∧ 99 ≤ X₄ ∧ 99 ≤ X₃+X₄ ∧ 99+X₃ ≤ X₄ ∧ 100 ≤ X₂+X₄ ∧ 99 ≤ X₁+X₄ ∧ 100 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀
knowledge_propagation leads to new time bound X₂ {O(n)} for transition t₈₂: n_l6___3(X₀, X₁, X₂, X₃, X₄) → n_l5___2(X₀, X₁, X₂, X₃, X₄-1) :|: 1+X₁ ≤ X₀ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₃ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₄ ∧ 0 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₄ ∧ 1+X₃ ≤ X₀ ∧ X₀ ≤ X₂ ∧ 99 ≤ X₄ ∧ 99 ≤ X₃+X₄ ∧ 99+X₃ ≤ X₄ ∧ 100 ≤ X₂+X₄ ∧ 99 ≤ X₁+X₄ ∧ 100 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀
MPRF for transition t₇₈: n_l5___2(X₀, X₁, X₂, X₃, X₄) → n_l6___1(X₀, X₁, X₂, X₃, X₄) :|: 1+X₁ ≤ X₀ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₃ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₄ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₁+X₃ ∧ 1+X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 < X₄ ∧ 1+X₃ ≤ X₀ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ 1 ≤ X₂+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
99⋅X₂+99⋅X₃ {O(n)}
MPRF:
l4 [99⋅X₀+99⋅X₃ ]
l5 [99⋅X₀+97⋅X₃+X₄-100 ]
l1 [99⋅X₀+99⋅X₃ ]
n_l6___1 [99⋅X₁+99⋅X₃+X₄ ]
n_l6___3 [97⋅X₀+2⋅X₁+99⋅X₃+X₄-97 ]
n_l5___2 [99⋅X₁+99⋅X₃+X₄+1 ]
n_l6___5 [97⋅X₀+2⋅X₁+99⋅X₃+X₄-98 ]
n_l5___4 [97⋅X₀+2⋅X₁+99⋅X₃+X₄-97 ]
MPRF for transition t₈₇: n_l5___2(X₀, X₁, X₂, X₃, X₄) → l1(X₁, X₁, X₂, X₃, X₄) :|: X₄ ≤ 0 ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ 1 ≤ X₂+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
99⋅X₂+99⋅X₃ {O(n)}
MPRF:
l4 [99⋅X₀+99⋅X₃ ]
l5 [99⋅X₀+99⋅X₃ ]
l1 [99⋅X₀+99⋅X₃ ]
n_l6___1 [99⋅X₁+99⋅X₃+1 ]
n_l6___3 [99⋅X₁+99⋅X₃+X₄ ]
n_l5___2 [99⋅X₁+99⋅X₃+1 ]
n_l6___5 [97⋅X₀+2⋅X₁+99⋅X₃+X₄-98 ]
n_l5___4 [97⋅X₀+2⋅X₁+99⋅X₃+X₄-97 ]
MPRF for transition t₈₁: n_l6___1(X₀, X₁, X₂, X₃, X₄) → n_l5___2(X₀, X₁, X₂, X₃, X₄-1) :|: 1+X₁ ≤ X₀ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₃ ∧ X₀ ≤ X₂ ∧ 0 < X₄ ∧ 0 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₄ ∧ 1+X₃ ≤ X₀ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
98⋅X₂+98⋅X₃ {O(n)}
MPRF:
l4 [98⋅X₀+98⋅X₃ ]
l5 [98⋅X₀+98⋅X₃ ]
l1 [98⋅X₀+98⋅X₃ ]
n_l6___1 [98⋅X₁+98⋅X₃+X₄ ]
n_l6___3 [98⋅X₁+98⋅X₃+X₄-1 ]
n_l5___2 [98⋅X₁+98⋅X₃+X₄ ]
n_l6___5 [98⋅X₁+98⋅X₃+X₄-2 ]
n_l5___4 [98⋅X₁+98⋅X₃+X₄-1 ]
CFR: Improvement to new bound with the following program:
new bound:
296⋅X₃+302⋅X₂+1 {O(n)}
cfr-program:
Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l7, n_l5___2, n_l5___4, n_l6___1, n_l6___3, n_l6___5
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₃, X₄)
t₄: l1(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂, X₃, X₄) :|: X₀ ≤ X₃ ∧ 0 ≤ X₃ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₃ ∧ X₀ ≤ X₂
t₃: l1(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄) :|: X₃ < X₀ ∧ 0 ≤ X₃ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₃ ∧ X₀ ≤ X₂
t₉: l2(X₀, X₁, X₂, X₃, X₄) → l7(X₀, X₁, X₂, X₃, X₄)
t₂: l3(X₀, X₁, X₂, X₃, X₄) → l1(X₂, X₁, X₂, X₃, X₄) :|: 0 ≤ X₃
t₁: l3(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂, X₃, X₄) :|: X₃ < 0
t₅: l4(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₀-X₃-1, X₂, X₃, 2⋅X₃+100) :|: 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₀ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₀
t₈₀: l5(X₀, X₁, X₂, X₃, X₄) → n_l6___5(X₀, X₁, X₂, X₃, X₄) :|: 1+X₁ ≤ X₀ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₃ ∧ X₀ ≤ X₂ ∧ 0 < X₄ ∧ 1 ≤ X₄ ∧ 100+2⋅X₃ ≤ X₄ ∧ X₄ ≤ 100+2⋅X₃ ∧ X₀ ≤ 1+X₁+X₃ ∧ 1+X₁+X₃ ≤ X₀ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₄ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₁+X₃ ∧ 1+X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₄ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₁+X₃ ∧ 1+X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 < X₄ ∧ 1+X₃ ≤ X₀ ∧ X₀ ≤ X₂ ∧ 100 ≤ X₄ ∧ 100 ≤ X₃+X₄ ∧ 100+X₃ ≤ X₄ ∧ 101 ≤ X₂+X₄ ∧ 100 ≤ X₁+X₄ ∧ 101 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₈₇: n_l5___2(X₀, X₁, X₂, X₃, X₄) → l1(X₁, X₁, X₂, X₃, X₄) :|: X₄ ≤ 0 ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ 1 ≤ X₂+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₇₈: n_l5___2(X₀, X₁, X₂, X₃, X₄) → n_l6___1(X₀, X₁, X₂, X₃, X₄) :|: 1+X₁ ≤ X₀ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₃ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₄ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₁+X₃ ∧ 1+X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 < X₄ ∧ 1+X₃ ≤ X₀ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ 1 ≤ X₂+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₇₉: n_l5___4(X₀, X₁, X₂, X₃, X₄) → n_l6___3(X₀, X₁, X₂, X₃, X₄) :|: 1+X₁ ≤ X₀ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₃ ∧ X₀ ≤ X₂ ∧ 0 < X₄ ∧ 1 ≤ X₄ ∧ 1 ≤ X₄ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₁+X₃ ∧ 1+X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₄ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₁+X₃ ∧ 1+X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 < X₄ ∧ 1+X₃ ≤ X₀ ∧ X₀ ≤ X₂ ∧ 99 ≤ X₄ ∧ 99 ≤ X₃+X₄ ∧ 99+X₃ ≤ X₄ ∧ 100 ≤ X₂+X₄ ∧ 99 ≤ X₁+X₄ ∧ 100 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₈₁: n_l6___1(X₀, X₁, X₂, X₃, X₄) → n_l5___2(X₀, X₁, X₂, X₃, X₄-1) :|: 1+X₁ ≤ X₀ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₃ ∧ X₀ ≤ X₂ ∧ 0 < X₄ ∧ 0 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₄ ∧ 1+X₃ ≤ X₀ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₈₂: n_l6___3(X₀, X₁, X₂, X₃, X₄) → n_l5___2(X₀, X₁, X₂, X₃, X₄-1) :|: 1+X₁ ≤ X₀ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₃ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₄ ∧ 0 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₄ ∧ 1+X₃ ≤ X₀ ∧ X₀ ≤ X₂ ∧ 99 ≤ X₄ ∧ 99 ≤ X₃+X₄ ∧ 99+X₃ ≤ X₄ ∧ 100 ≤ X₂+X₄ ∧ 99 ≤ X₁+X₄ ∧ 100 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₈₃: n_l6___5(X₀, X₁, X₂, X₃, X₄) → n_l5___4(X₀, X₁, X₂, X₃, X₄-1) :|: X₀ ≤ X₂ ∧ 100 ≤ X₄ ∧ X₄ ≤ 98+2⋅X₀ ∧ 2⋅X₀+98 ≤ 2⋅X₁+X₄ ∧ 2⋅X₁+X₄ ≤ 98+2⋅X₀ ∧ 2⋅X₃+100 ≤ X₄ ∧ X₄ ≤ 100+2⋅X₃ ∧ 0 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₄ ∧ 1+X₃ ≤ X₀ ∧ X₀ ≤ X₂ ∧ 100 ≤ X₄ ∧ 100 ≤ X₃+X₄ ∧ 100+X₃ ≤ X₄ ∧ 101 ≤ X₂+X₄ ∧ 100 ≤ X₁+X₄ ∧ 101 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀
All Bounds
Timebounds
Overall timebound:296⋅X₃+302⋅X₂+6 {O(n)}
t₀: 1 {O(1)}
t₃: X₂+1 {O(n)}
t₄: 1 {O(1)}
t₉: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₅: X₂ {O(n)}
t₈₀: X₂ {O(n)}
t₇₈: 99⋅X₂+99⋅X₃ {O(n)}
t₈₇: 99⋅X₂+99⋅X₃ {O(n)}
t₇₉: X₂ {O(n)}
t₈₁: 98⋅X₂+98⋅X₃ {O(n)}
t₈₂: X₂ {O(n)}
t₈₃: X₂ {O(n)}
Costbounds
Overall costbound: 296⋅X₃+302⋅X₂+6 {O(n)}
t₀: 1 {O(1)}
t₃: X₂+1 {O(n)}
t₄: 1 {O(1)}
t₉: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₅: X₂ {O(n)}
t₈₀: X₂ {O(n)}
t₇₈: 99⋅X₂+99⋅X₃ {O(n)}
t₈₇: 99⋅X₂+99⋅X₃ {O(n)}
t₇₉: X₂ {O(n)}
t₈₁: 98⋅X₂+98⋅X₃ {O(n)}
t₈₂: X₂ {O(n)}
t₈₃: 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: X₂ {O(n)}
t₃, X₁: X₁+X₂ {O(n)}
t₃, X₂: X₂ {O(n)}
t₃, X₃: X₃ {O(n)}
t₃, X₄: X₄ {O(n)}
t₄, X₀: 2⋅X₂ {O(n)}
t₄, X₁: X₁+X₂ {O(n)}
t₄, X₂: 2⋅X₂ {O(n)}
t₄, X₃: 2⋅X₃ {O(n)}
t₄, X₄: X₄ {O(n)}
t₉, X₀: 2⋅X₂+X₀ {O(n)}
t₉, X₁: 2⋅X₁+X₂ {O(n)}
t₉, X₂: 3⋅X₂ {O(n)}
t₉, X₃: 3⋅X₃ {O(n)}
t₉, X₄: 2⋅X₄ {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: X₂ {O(n)}
t₂, X₁: X₁ {O(n)}
t₂, X₂: X₂ {O(n)}
t₂, X₃: X₃ {O(n)}
t₂, X₄: X₄ {O(n)}
t₅, X₀: X₂ {O(n)}
t₅, X₁: X₂ {O(n)}
t₅, X₂: X₂ {O(n)}
t₅, X₃: X₃ {O(n)}
t₅, X₄: 2⋅X₃+100 {O(n)}
t₈₀, X₀: X₂ {O(n)}
t₈₀, X₁: X₂ {O(n)}
t₈₀, X₂: X₂ {O(n)}
t₈₀, X₃: X₃ {O(n)}
t₈₀, X₄: 2⋅X₃+100 {O(n)}
t₇₈, X₀: X₂ {O(n)}
t₇₈, X₁: X₂ {O(n)}
t₇₈, X₂: X₂ {O(n)}
t₇₈, X₃: X₃ {O(n)}
t₇₈, X₄: 2⋅X₃+100 {O(n)}
t₈₇, X₀: X₂ {O(n)}
t₈₇, X₁: X₂ {O(n)}
t₈₇, X₂: X₂ {O(n)}
t₈₇, X₃: X₃ {O(n)}
t₈₇, X₄: 0 {O(1)}
t₇₉, X₀: X₂ {O(n)}
t₇₉, X₁: X₂ {O(n)}
t₇₉, X₂: X₂ {O(n)}
t₇₉, X₃: X₃ {O(n)}
t₇₉, X₄: 2⋅X₃+100 {O(n)}
t₈₁, X₀: X₂ {O(n)}
t₈₁, X₁: X₂ {O(n)}
t₈₁, X₂: X₂ {O(n)}
t₈₁, X₃: X₃ {O(n)}
t₈₁, X₄: 2⋅X₃+100 {O(n)}
t₈₂, X₀: X₂ {O(n)}
t₈₂, X₁: X₂ {O(n)}
t₈₂, X₂: X₂ {O(n)}
t₈₂, X₃: X₃ {O(n)}
t₈₂, X₄: 2⋅X₃+100 {O(n)}
t₈₃, X₀: X₂ {O(n)}
t₈₃, X₁: X₂ {O(n)}
t₈₃, X₂: X₂ {O(n)}
t₈₃, X₃: X₃ {O(n)}
t₈₃, X₄: 2⋅X₃+100 {O(n)}