Initial Problem
Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃)
t₅: l1(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₃ ≤ X₀
t₄: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₀ < X₃
t₁₀: l2(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃)
t₃: l3(X₀, X₁, X₂, X₃) → l1(0, 0, X₂, X₃) :|: 0 < X₂ ∧ X₂ < X₃
t₁: l3(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₂ ≤ 0
t₂: l3(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₃ ≤ X₂
t₆: l4(X₀, X₁, X₂, X₃) → l1(X₀, X₁+1, X₂, X₃) :|: X₁ < X₂ ∧ X₁ < X₂
t₇: l4(X₀, X₁, X₂, X₃) → l1(X₀+1, X₁+1, X₂, X₃) :|: X₁ < X₂ ∧ X₂ ≤ X₁
t₈: l4(X₀, X₁, X₂, X₃) → l1(X₀, 0, X₂, X₃) :|: X₂ ≤ X₁ ∧ X₁ < X₂
t₉: l4(X₀, X₁, X₂, X₃) → l1(X₀+1, 0, X₂, X₃) :|: X₂ ≤ X₁ ∧ X₂ ≤ X₁
Preprocessing
Cut unsatisfiable transition t₇: l4→l1
Cut unsatisfiable transition t₈: l4→l1
Found invariant 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location l1
Found invariant 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location l4
Problem after Preprocessing
Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃)
t₅: l1(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₃ ≤ X₀ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀
t₄: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₀ < X₃ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀
t₁₀: l2(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃)
t₃: l3(X₀, X₁, X₂, X₃) → l1(0, 0, X₂, X₃) :|: 0 < X₂ ∧ X₂ < X₃
t₁: l3(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₂ ≤ 0
t₂: l3(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₃ ≤ X₂
t₆: l4(X₀, X₁, X₂, X₃) → l1(X₀, X₁+1, X₂, X₃) :|: X₁ < X₂ ∧ X₁ < X₂ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀
t₉: l4(X₀, X₁, X₂, X₃) → l1(X₀+1, 0, X₂, X₃) :|: X₂ ≤ X₁ ∧ X₂ ≤ X₁ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀
MPRF for transition t₉: l4(X₀, X₁, X₂, X₃) → l1(X₀+1, 0, X₂, X₃) :|: X₂ ≤ X₁ ∧ X₂ ≤ X₁ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ of depth 1:
new bound:
X₃ {O(n)}
MPRF:
l4 [X₃-X₀ ]
l1 [X₃-X₀ ]
Found invariant 1 ≤ 0 for location l1
Found invariant 1 ≤ 0 for location l4
Found invariant 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ 2+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location l1
Found invariant 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ 2+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location l4
Time-Bound by TWN-Loops:
TWN-Loops: t₄ 2⋅X₂⋅X₃+2⋅X₂+5⋅X₃+5 {O(n^2)}
TWN-Loops:
entry: t₉: l4(X₀, X₁, X₂, X₃) → l1(X₀+1, 0, X₂, X₃) :|: X₂ ≤ X₁ ∧ X₂ ≤ X₁ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀
results in twn-loop: twn:Inv: [2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀] , (X₀,X₁,X₂,X₃) -> (X₀,X₁+1,X₂,X₃) :|: X₀ < X₃ ∧ X₁ < X₂ ∧ X₁ < X₂
entry: t₃: l3(X₀, X₁, X₂, X₃) → l1(0, 0, X₂, X₃) :|: 0 < X₂ ∧ X₂ < X₃
results in twn-loop: twn:Inv: [2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀] , (X₀,X₁,X₂,X₃) -> (X₀,X₁+1,X₂,X₃) :|: X₀ < X₃ ∧ X₁ < X₂ ∧ X₁ < X₂
order: [X₀; X₁; X₂; X₃]
closed-form:
X₀: X₀
X₁: X₁ + [[n != 0]] * n^1
X₂: X₂
X₃: X₃
Termination: true
Formula:
1 < 0 ∧ X₀ < X₃
∨ X₁ < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₀ < X₃
Stabilization-Threshold for: X₁ < X₂
alphas_abs: X₁+X₂
M: 0
N: 1
Bound: 2⋅X₁+2⋅X₂+2 {O(n)}
relevant size-bounds w.r.t. t₉:
X₁: 0 {O(1)}
X₂: X₂ {O(n)}
Runtime-bound of t₉: X₃ {O(n)}
Results in: 2⋅X₂⋅X₃+5⋅X₃ {O(n^2)}
order: [X₀; X₁; X₂; X₃]
closed-form:
X₀: X₀
X₁: X₁ + [[n != 0]] * n^1
X₂: X₂
X₃: X₃
Termination: true
Formula:
1 < 0 ∧ X₀ < X₃
∨ X₁ < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₀ < X₃
Stabilization-Threshold for: X₁ < X₂
alphas_abs: X₁+X₂
M: 0
N: 1
Bound: 2⋅X₁+2⋅X₂+2 {O(n)}
relevant size-bounds w.r.t. t₃:
X₁: 0 {O(1)}
X₂: X₂ {O(n)}
Runtime-bound of t₃: 1 {O(1)}
Results in: 2⋅X₂+5 {O(n)}
2⋅X₂⋅X₃+2⋅X₂+5⋅X₃+5 {O(n^2)}
Time-Bound by TWN-Loops:
TWN-Loops: t₆ 2⋅X₂⋅X₃+2⋅X₂+5⋅X₃+5 {O(n^2)}
relevant size-bounds w.r.t. t₉:
X₁: 0 {O(1)}
X₂: X₂ {O(n)}
Runtime-bound of t₉: X₃ {O(n)}
Results in: 2⋅X₂⋅X₃+5⋅X₃ {O(n^2)}
relevant size-bounds w.r.t. t₃:
X₁: 0 {O(1)}
X₂: X₂ {O(n)}
Runtime-bound of t₃: 1 {O(1)}
Results in: 2⋅X₂+5 {O(n)}
2⋅X₂⋅X₃+2⋅X₂+5⋅X₃+5 {O(n^2)}
Analysing control-flow refined program
Cut unsatisfiable transition t₅: l1→l2
Cut unsatisfiable transition t₉₆: n_l1___1→l2
Cut unsatisfiable transition t₉₈: n_l1___5→l2
Found invariant 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 2+X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ 2+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ 0 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location n_l4___6
Found invariant 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 2+X₁ ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l4___2
Found invariant 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location n_l4___4
Found invariant 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 2+X₁ ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l1___3
Found invariant 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location n_l1___5
Found invariant 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 2+X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ 2+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ 0 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location l1
Found invariant 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₁ ≤ 1 ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l1___1
MPRF for transition t₈₂: n_l1___1(X₀, X₁, X₂, X₃) → n_l4___4(X₀, X₁, X₂, X₃) :|: 0 ≤ X₁ ∧ 0 ≤ X₀ ∧ X₀ < X₃ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₃ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₁ ∧ 1+X₁ ≤ X₃ ∧ X₁ ≤ X₂ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1+X₀ ≤ X₃ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₂ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₃ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀ ∧ X₀ < X₃ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₁ ≤ 1 ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₃+1 {O(n)}
MPRF:
n_l4___2 [X₃-X₀ ]
n_l1___1 [X₃-X₀ ]
n_l1___3 [X₃-X₀ ]
n_l4___4 [X₃-X₀-1 ]
n_l1___5 [X₃-X₀-1 ]
MPRF for transition t₈₃: n_l1___3(X₀, X₁, X₂, X₃) → n_l4___2(X₀, X₁, X₂, X₃) :|: 0 ≤ X₁ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₃ ∧ X₁ < X₂ ∧ 1+X₁ ≤ X₃ ∧ X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₀ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₃ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀ ∧ X₀ < X₃ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 2+X₁ ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₃ {O(n)}
MPRF:
n_l4___2 [X₃-X₀ ]
n_l1___1 [X₃-X₀ ]
n_l1___3 [X₃+1-X₀ ]
n_l4___4 [X₃-X₀ ]
n_l1___5 [X₃-X₀ ]
MPRF for transition t₈₆: n_l4___2(X₀, X₁, X₂, X₃) → n_l1___1(X₀, X₁+1, X₂, X₃) :|: X₀ < X₃ ∧ 1 ≤ X₀ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₂ ∧ X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₃ ∧ 0 ≤ X₁ ∧ X₁ < X₂ ∧ 0 ≤ X₀ ∧ 1+X₀ ≤ X₃ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 2+X₁ ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₃+1 {O(n)}
MPRF:
n_l4___2 [X₃-X₀ ]
n_l1___1 [X₃-X₀-1 ]
n_l1___3 [X₃-X₀ ]
n_l4___4 [X₃-X₀-1 ]
n_l1___5 [X₃-X₀-1 ]
MPRF for transition t₈₇: n_l4___4(X₀, X₁, X₂, X₃) → n_l1___3(X₀+1, 0, X₁, X₃) :|: 1+X₀ ≤ X₃ ∧ 0 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1+X₂ ≤ X₃ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1+X₁ ≤ X₃ ∧ 1+X₀ ≤ X₃ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀ of depth 1:
new bound:
X₃ {O(n)}
MPRF:
n_l4___2 [X₃-X₀ ]
n_l1___1 [X₃-X₀ ]
n_l1___3 [X₃-X₀ ]
n_l4___4 [X₃-X₀ ]
n_l1___5 [X₃-X₀ ]
Found invariant 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 2+X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ 2+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ 0 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location n_l4___6
Found invariant 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 2+X₁ ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ X₀+X₁ ≤ 1 ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ X₀ ≤ 1+X₁ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ for location n_l4___2
Found invariant 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ 2+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location n_l4___4
Found invariant 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 2+X₁ ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ X₀+X₁ ≤ 1 ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ X₀ ≤ 1+X₁ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ for location n_l1___3
Found invariant 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ 2+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location n_l1___5
Found invariant 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 2+X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ 2+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ 0 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location l1
Found invariant 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 1 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 2 ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ for location n_l1___1
Found invariant 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 2+X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ 2+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ 0 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location n_l4___6
Found invariant 1 ≤ 0 for location n_l4___2
Found invariant 1 ≤ 0 for location n_l4___4
Found invariant 1 ≤ 0 for location n_l1___3
Found invariant 1 ≤ 0 for location n_l1___5
Found invariant 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 2+X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ 2+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ 0 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location l1
Found invariant 1 ≤ 0 for location n_l1___1
Found invariant 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 2+X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ 2+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ 0 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location n_l4___6
Found invariant 1 ≤ 0 for location n_l4___2
Found invariant 1 ≤ 0 for location n_l4___4
Found invariant 1 ≤ 0 for location n_l1___3
Found invariant 1 ≤ 0 for location n_l1___5
Found invariant 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 2+X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ 2+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ 0 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location l1
Found invariant 1 ≤ 0 for location n_l1___1
MPRF for transition t₈₄: n_l1___5(X₀, X₁, X₂, X₃) → n_l4___4(X₀, X₁, X₂, X₃) :|: 0 ≤ X₁ ∧ 0 ≤ X₀ ∧ X₀ < X₃ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₃ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₃ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀ ∧ X₀ < X₃ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀ of depth 1:
new bound:
X₃⋅X₃+X₂+2 {O(n^2)}
MPRF:
n_l1___3 [X₃ ]
n_l4___2 [X₂ ]
n_l1___1 [X₂ ]
n_l4___4 [X₂-X₁ ]
n_l1___5 [X₂+1-X₁ ]
MPRF for transition t₈₈: n_l4___4(X₀, X₁, X₂, X₃) → n_l1___5(X₀, X₁+1, X₂, X₃) :|: 1+X₀ ≤ X₃ ∧ 0 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1+X₂ ≤ X₃ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₃ ∧ 0 ≤ X₁ ∧ X₁ < X₂ ∧ 0 ≤ X₀ ∧ 1+X₀ ≤ X₃ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀ of depth 1:
new bound:
X₃⋅X₃+X₂+2 {O(n^2)}
MPRF:
n_l1___3 [X₃ ]
n_l4___2 [X₃ ]
n_l1___1 [X₂+1 ]
n_l4___4 [X₂+1-X₁ ]
n_l1___5 [X₂+1-X₁ ]
CFR did not improve the program. Rolling back
All Bounds
Timebounds
Overall timebound:4⋅X₂⋅X₃+11⋅X₃+4⋅X₂+16 {O(n^2)}
t₀: 1 {O(1)}
t₄: 2⋅X₂⋅X₃+2⋅X₂+5⋅X₃+5 {O(n^2)}
t₅: 1 {O(1)}
t₁₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 1 {O(1)}
t₆: 2⋅X₂⋅X₃+2⋅X₂+5⋅X₃+5 {O(n^2)}
t₉: X₃ {O(n)}
Costbounds
Overall costbound: 4⋅X₂⋅X₃+11⋅X₃+4⋅X₂+16 {O(n^2)}
t₀: 1 {O(1)}
t₄: 2⋅X₂⋅X₃+2⋅X₂+5⋅X₃+5 {O(n^2)}
t₅: 1 {O(1)}
t₁₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 1 {O(1)}
t₆: 2⋅X₂⋅X₃+2⋅X₂+5⋅X₃+5 {O(n^2)}
t₉: X₃ {O(n)}
Sizebounds
t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₀, X₃: X₃ {O(n)}
t₄, X₀: X₃ {O(n)}
t₄, X₁: 2⋅X₂⋅X₃+2⋅X₂+5⋅X₃+5 {O(n^2)}
t₄, X₂: X₂ {O(n)}
t₄, X₃: X₃ {O(n)}
t₅, X₀: X₃ {O(n)}
t₅, X₁: 0 {O(1)}
t₅, X₂: X₂ {O(n)}
t₅, X₃: X₃ {O(n)}
t₁₀, X₀: 2⋅X₀+X₃ {O(n)}
t₁₀, X₁: 2⋅X₁ {O(n)}
t₁₀, X₂: 3⋅X₂ {O(n)}
t₁₀, X₃: 3⋅X₃ {O(n)}
t₁, X₀: X₀ {O(n)}
t₁, X₁: X₁ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₃ {O(n)}
t₂, X₀: X₀ {O(n)}
t₂, X₁: X₁ {O(n)}
t₂, X₂: X₂ {O(n)}
t₂, X₃: X₃ {O(n)}
t₃, X₀: 0 {O(1)}
t₃, X₁: 0 {O(1)}
t₃, X₂: X₂ {O(n)}
t₃, X₃: X₃ {O(n)}
t₆, X₀: X₃ {O(n)}
t₆, X₁: 2⋅X₂⋅X₃+2⋅X₂+5⋅X₃+5 {O(n^2)}
t₆, X₂: X₂ {O(n)}
t₆, X₃: X₃ {O(n)}
t₉, X₀: X₃ {O(n)}
t₉, X₁: 0 {O(1)}
t₉, X₂: X₂ {O(n)}
t₉, X₃: X₃ {O(n)}