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) → l2(X₀, X₁, X₂, X₃, X₄)
t₂: l1(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₃, X₄) :|: X₃ < X₂
t₃: l1(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄) :|: X₂ ≤ X₃
t₁: l2(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁, X₂, 0, X₄)
t₄: l3(X₀, X₁, X₂, X₃, X₄) → l5(X₃+1, X₁, X₂, X₃, 0)
t₈: l4(X₀, X₁, X₂, X₃, X₄) → l7(X₀, X₁, X₂, X₃, X₄)
t₆: l5(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁, X₂, X₀, X₄) :|: X₁ ≤ X₄
t₅: l5(X₀, X₁, X₂, X₃, X₄) → l6(X₀, X₁, X₂, X₃, X₄) :|: X₄ < X₁
t₇: l6(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁, X₂, X₃, X₄+1)
Preprocessing
Found invariant 1+X₄ ≤ X₁ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ 1 ≤ X₂+X₄ ∧ 1 ≤ X₁+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l6
Found invariant 0 ≤ X₃ ∧ X₂ ≤ X₃ for location l7
Found invariant 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ 1 ≤ X₂+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₀ for location l5
Found invariant 0 ≤ X₃ for location l1
Found invariant 0 ≤ X₃ ∧ X₂ ≤ X₃ for location l4
Found invariant 1+X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₂ for location l3
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) → l2(X₀, X₁, X₂, X₃, X₄)
t₂: l1(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₃, X₄) :|: X₃ < X₂ ∧ 0 ≤ X₃
t₃: l1(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄) :|: X₂ ≤ X₃ ∧ 0 ≤ X₃
t₁: l2(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁, X₂, 0, X₄)
t₄: l3(X₀, X₁, X₂, X₃, X₄) → l5(X₃+1, X₁, X₂, X₃, 0) :|: 1+X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₂
t₈: l4(X₀, X₁, X₂, X₃, X₄) → l7(X₀, X₁, X₂, X₃, X₄) :|: 0 ≤ X₃ ∧ X₂ ≤ X₃
t₆: l5(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁, X₂, X₀, X₄) :|: X₁ ≤ X₄ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ 1 ≤ X₂+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₀
t₅: l5(X₀, X₁, X₂, X₃, X₄) → l6(X₀, X₁, X₂, X₃, X₄) :|: X₄ < X₁ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ 1 ≤ X₂+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₀
t₇: l6(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁, X₂, X₃, X₄+1) :|: 1+X₄ ≤ X₁ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ 1 ≤ X₂+X₄ ∧ 1 ≤ X₁+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀
MPRF for transition t₂: l1(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₃, X₄) :|: X₃ < X₂ ∧ 0 ≤ X₃ of depth 1:
new bound:
X₂ {O(n)}
MPRF:
l3 [X₂-X₃-1 ]
l1 [X₂-X₃ ]
l6 [X₂-X₀ ]
l5 [X₂-X₀ ]
MPRF for transition t₄: l3(X₀, X₁, X₂, X₃, X₄) → l5(X₃+1, X₁, X₂, X₃, 0) :|: 1+X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₂ of depth 1:
new bound:
X₂ {O(n)}
MPRF:
l3 [X₂-X₃ ]
l1 [X₂-X₃ ]
l6 [X₂-X₃-1 ]
l5 [X₂-X₃-1 ]
MPRF for transition t₆: l5(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁, X₂, X₀, X₄) :|: X₁ ≤ X₄ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ 1 ≤ X₂+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₂ {O(n)}
MPRF:
l3 [X₂-X₃ ]
l1 [X₂-X₃ ]
l6 [X₂-X₃ ]
l5 [X₂-X₃ ]
Found invariant 1+X₄ ≤ X₁ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ 1 ≤ X₂+X₄ ∧ 1 ≤ X₁+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l6
Found invariant 0 ≤ X₃ ∧ X₂ ≤ X₃ for location l7
Found invariant 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ 1 ≤ X₂+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₀ for location l5
Found invariant 0 ≤ X₃ for location l1
Found invariant 0 ≤ X₃ ∧ X₂ ≤ X₃ for location l4
Found invariant 1+X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₂ for location l3
Time-Bound by TWN-Loops:
TWN-Loops: t₅ 2⋅X₁⋅X₂+4⋅X₂ {O(n^2)}
TWN-Loops:
entry: t₄: l3(X₀, X₁, X₂, X₃, X₄) → l5(X₃+1, X₁, X₂, X₃, 0) :|: 1+X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₂
results in twn-loop: twn:Inv: [0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ 1 ≤ X₂+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₀ ∧ 1+X₄ ≤ X₁ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ 1 ≤ X₂+X₄ ∧ 1 ≤ X₁+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀] , (X₀,X₁,X₂,X₃,X₄) -> (X₀,X₁,X₂,X₃,X₄+1) :|: X₄ < X₁
order: [X₀; X₁; X₂; X₃; X₄]
closed-form:
X₀: X₀
X₁: X₁
X₂: X₂
X₃: X₃
X₄: X₄ + [[n != 0]] * n^1
Termination: true
Formula:
1 < 0
∨ X₄ < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1
Stabilization-Threshold for: X₄ < X₁
alphas_abs: X₄+X₁
M: 0
N: 1
Bound: 2⋅X₁+2⋅X₄+2 {O(n)}
relevant size-bounds w.r.t. t₄:
X₁: X₁ {O(n)}
X₄: 0 {O(1)}
Runtime-bound of t₄: X₂ {O(n)}
Results in: 2⋅X₁⋅X₂+4⋅X₂ {O(n^2)}
2⋅X₁⋅X₂+4⋅X₂ {O(n^2)}
Time-Bound by TWN-Loops:
TWN-Loops: t₇ 2⋅X₁⋅X₂+4⋅X₂ {O(n^2)}
relevant size-bounds w.r.t. t₄:
X₁: X₁ {O(n)}
X₄: 0 {O(1)}
Runtime-bound of t₄: X₂ {O(n)}
Results in: 2⋅X₁⋅X₂+4⋅X₂ {O(n^2)}
2⋅X₁⋅X₂+4⋅X₂ {O(n^2)}
Analysing control-flow refined program
Found invariant X₄ ≤ 0 ∧ X₄ ≤ X₃ ∧ 1+X₄ ≤ X₂ ∧ 1+X₄ ≤ X₁ ∧ 1+X₄ ≤ X₀ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ 1 ≤ X₂+X₄ ∧ 1 ≤ X₁+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l6___3
Found invariant 1+X₄ ≤ X₁ ∧ 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 2 ≤ X₂+X₄ ∧ 3 ≤ X₁+X₄ ∧ 2 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l6___1
Found invariant X₄ ≤ X₁ ∧ 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l5___2
Found invariant 0 ≤ X₃ ∧ X₂ ≤ X₃ for location l7
Found invariant X₄ ≤ 0 ∧ X₄ ≤ X₃ ∧ 1+X₄ ≤ X₂ ∧ 1+X₄ ≤ X₀ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ 1 ≤ X₂+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₀ for location l5
Found invariant 0 ≤ X₃ for location l1
Found invariant 0 ≤ X₃ ∧ X₂ ≤ X₃ for location l4
Found invariant 1+X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₂ for location l3
knowledge_propagation leads to new time bound X₂ {O(n)} for transition t₇₃: l5(X₀, X₁, X₂, X₃, X₄) → n_l6___3(X₀, X₁, X₂, X₀-1, X₄) :|: X₀ ≤ X₂ ∧ 0 ≤ X₄ ∧ 1 ≤ X₀ ∧ X₀ ≤ X₃+1 ∧ 1+X₃ ≤ X₀ ∧ X₄ ≤ 0 ∧ 0 ≤ X₄ ∧ X₀ ≤ 1+X₃ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1+X₃ ≤ X₂ ∧ X₄ < X₁ ∧ 1 ≤ X₀ ∧ 0 ≤ X₄ ∧ X₀ ≤ X₂ ∧ X₀ ≤ X₃+1 ∧ 1+X₃ ≤ X₀ ∧ X₄ ≤ 0 ∧ X₄ ≤ X₃ ∧ 1+X₄ ≤ X₂ ∧ 1+X₄ ≤ X₀ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ 1 ≤ X₂+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₀
knowledge_propagation leads to new time bound X₂ {O(n)} for transition t₇₅: n_l6___3(X₀, X₁, X₂, X₃, X₄) → n_l5___2(X₀, X₁, X₂, X₀-1, X₄+1) :|: 1+X₃ ≤ X₂ ∧ 0 < X₁ ∧ 0 ≤ X₃ ∧ X₀ ≤ X₃+1 ∧ 1+X₃ ≤ X₀ ∧ X₄ ≤ 0 ∧ 0 ≤ X₄ ∧ 1+X₄ ≤ X₁ ∧ 1 ≤ X₀ ∧ 0 ≤ X₄ ∧ X₀ ≤ X₂ ∧ X₀ ≤ X₃+1 ∧ 1+X₃ ≤ X₀ ∧ X₄ ≤ 0 ∧ X₄ ≤ X₃ ∧ 1+X₄ ≤ X₂ ∧ 1+X₄ ≤ X₁ ∧ 1+X₄ ≤ X₀ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ 1 ≤ X₂+X₄ ∧ 1 ≤ X₁+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀
MPRF for transition t₇₂: n_l5___2(X₀, X₁, X₂, X₃, X₄) → n_l6___1(X₀, X₁, X₂, X₀-1, X₄) :|: X₀ ≤ X₂ ∧ 0 ≤ X₄ ∧ 1 ≤ X₀ ∧ X₀ ≤ X₃+1 ∧ 1+X₃ ≤ X₀ ∧ X₀ ≤ 1+X₃ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₀ ∧ 1 ≤ X₄ ∧ X₄ ≤ X₁ ∧ X₀ ≤ X₂ ∧ X₄ < X₁ ∧ 1 ≤ X₀ ∧ 0 ≤ X₄ ∧ X₀ ≤ X₂ ∧ X₀ ≤ X₃+1 ∧ 1+X₃ ≤ X₀ ∧ X₄ ≤ X₁ ∧ 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₁⋅X₂+2⋅X₂ {O(n^2)}
MPRF:
l3 [0 ]
l5 [0 ]
n_l6___3 [0 ]
l1 [0 ]
n_l6___1 [X₁-X₄ ]
n_l5___2 [X₁+1-X₄ ]
MPRF for transition t₇₉: n_l5___2(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁, X₂, X₀, X₄) :|: X₁ ≤ X₄ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ 1 ≤ X₂+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₀ ∧ X₄ ≤ X₁ ∧ 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₂ {O(n)}
MPRF:
l3 [X₂-X₃ ]
l5 [X₂-X₃ ]
l1 [X₂-X₃ ]
n_l6___1 [X₂+1-X₀ ]
n_l6___3 [X₂-X₃ ]
n_l5___2 [X₂+1-X₀ ]
MPRF for transition t₇₄: n_l6___1(X₀, X₁, X₂, X₃, X₄) → n_l5___2(X₀, X₁, X₂, X₀-1, X₄+1) :|: X₀ ≤ X₂ ∧ X₄ < X₁ ∧ 1 ≤ X₄ ∧ 1 ≤ X₀ ∧ X₀ ≤ X₃+1 ∧ 1+X₃ ≤ X₀ ∧ 1+X₄ ≤ X₁ ∧ 1 ≤ X₀ ∧ 0 ≤ X₄ ∧ X₀ ≤ X₂ ∧ X₀ ≤ X₃+1 ∧ 1+X₃ ≤ X₀ ∧ 1+X₄ ≤ X₁ ∧ 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 2 ≤ X₂+X₄ ∧ 3 ≤ X₁+X₄ ∧ 2 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
2⋅X₁⋅X₂+3⋅X₂+X₁+2 {O(n^2)}
MPRF:
l3 [X₁-2 ]
l5 [X₁-2 ]
n_l6___3 [X₁-2⋅X₂ ]
l1 [X₁-2 ]
n_l6___1 [2⋅X₁-X₄-2 ]
n_l5___2 [2⋅X₁-X₄-2 ]
CFR did not improve the program. Rolling back
All Bounds
Timebounds
Overall timebound:4⋅X₁⋅X₂+11⋅X₂+4 {O(n^2)}
t₀: 1 {O(1)}
t₂: X₂ {O(n)}
t₃: 1 {O(1)}
t₁: 1 {O(1)}
t₄: X₂ {O(n)}
t₈: 1 {O(1)}
t₅: 2⋅X₁⋅X₂+4⋅X₂ {O(n^2)}
t₆: X₂ {O(n)}
t₇: 2⋅X₁⋅X₂+4⋅X₂ {O(n^2)}
Costbounds
Overall costbound: 4⋅X₁⋅X₂+11⋅X₂+4 {O(n^2)}
t₀: 1 {O(1)}
t₂: X₂ {O(n)}
t₃: 1 {O(1)}
t₁: 1 {O(1)}
t₄: X₂ {O(n)}
t₈: 1 {O(1)}
t₅: 2⋅X₁⋅X₂+4⋅X₂ {O(n^2)}
t₆: X₂ {O(n)}
t₇: 2⋅X₁⋅X₂+4⋅X₂ {O(n^2)}
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)}
t₂, X₀: 2⋅X₂+X₀ {O(n)}
t₂, X₁: X₁ {O(n)}
t₂, X₂: X₂ {O(n)}
t₂, X₃: X₂ {O(n)}
t₂, X₄: 2⋅X₁⋅X₂+4⋅X₂+X₄ {O(n^2)}
t₃, X₀: 2⋅X₂+X₀ {O(n)}
t₃, X₁: 2⋅X₁ {O(n)}
t₃, X₂: 2⋅X₂ {O(n)}
t₃, X₃: X₂ {O(n)}
t₃, X₄: 2⋅X₁⋅X₂+4⋅X₂+X₄ {O(n^2)}
t₁, X₀: X₀ {O(n)}
t₁, X₁: X₁ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: 0 {O(1)}
t₁, X₄: X₄ {O(n)}
t₄, X₀: X₂ {O(n)}
t₄, X₁: X₁ {O(n)}
t₄, X₂: X₂ {O(n)}
t₄, X₃: X₂ {O(n)}
t₄, X₄: 0 {O(1)}
t₈, X₀: 2⋅X₂+X₀ {O(n)}
t₈, X₁: 2⋅X₁ {O(n)}
t₈, X₂: 2⋅X₂ {O(n)}
t₈, X₃: X₂ {O(n)}
t₈, X₄: 2⋅X₁⋅X₂+4⋅X₂+X₄ {O(n^2)}
t₅, X₀: X₂ {O(n)}
t₅, X₁: X₁ {O(n)}
t₅, X₂: X₂ {O(n)}
t₅, X₃: X₂ {O(n)}
t₅, X₄: 2⋅X₁⋅X₂+4⋅X₂ {O(n^2)}
t₆, X₀: 2⋅X₂ {O(n)}
t₆, X₁: X₁ {O(n)}
t₆, X₂: X₂ {O(n)}
t₆, X₃: X₂ {O(n)}
t₆, X₄: 2⋅X₁⋅X₂+4⋅X₂ {O(n^2)}
t₇, X₀: X₂ {O(n)}
t₇, X₁: X₁ {O(n)}
t₇, X₂: X₂ {O(n)}
t₇, X₃: X₂ {O(n)}
t₇, X₄: 2⋅X₁⋅X₂+4⋅X₂ {O(n^2)}