Initial Problem
Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁, X₂, X₃, X₄, X₅)
t₅: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₅ ≤ X₀
t₄: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l4(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₀ < X₅
t₁₀: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l5(X₀, X₁, X₂, X₃, X₄, X₅)
t₁: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l1(0, 0, X₂, X₃, X₄, X₅) :|: 0 < X₄ ∧ X₄ < X₅
t₂: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₄ ≤ 0
t₃: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₅ ≤ X₄
t₆: l4(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, X₁+1, X₂, X₃, X₄, X₅) :|: X₁ < X₄ ∧ X₁ < X₄
t₇: l4(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀+1, X₁+1, X₂, X₃, X₄, X₅) :|: X₁ < X₄ ∧ X₄ ≤ X₁
t₈: l4(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, 0, X₂, X₃, X₄, X₅) :|: X₄ ≤ X₁ ∧ X₁ < X₄
t₉: l4(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀+1, 0, X₂, X₃, X₄, X₅) :|: X₄ ≤ X₁ ∧ X₄ ≤ X₁
Preprocessing
Cut unsatisfiable transition t₇: l4→l1
Cut unsatisfiable transition t₈: l4→l1
Eliminate variables {X₂,X₃} that do not contribute to the problem
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:
t₂₁: l0(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃)
t₂₂: 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
t₂₃: 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
t₂₄: l2(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃)
t₂₅: l3(X₀, X₁, X₂, X₃) → l1(0, 0, X₂, X₃) :|: 0 < X₂ ∧ X₂ < X₃
t₂₆: l3(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₂ ≤ 0
t₂₇: l3(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₃ ≤ X₂
t₂₈: 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
t₂₉: 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 t₂₉: 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)}
TWN: t₂₃: l1→l4
cycle: [t₂₃: l1→l4; t₂₈: l4→l1]
loop: (X₀ < X₃ ∧ X₁ < X₂ ∧ X₁ < X₂,(X₀,X₁,X₂,X₃) -> (X₀,X₁+1,X₂,X₃)
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)}
loop: (X₀ < X₃ ∧ X₁ < X₂ ∧ X₁ < X₂,(X₀,X₁,X₂,X₃) -> (X₀,X₁+1,X₂,X₃)
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)}
TWN - Lifting for t₂₃: l1→l4 of 2⋅X₁+2⋅X₂+5 {O(n)}
relevant size-bounds w.r.t. t₂₉:
X₁: 0 {O(1)}
X₂: X₂ {O(n)}
Runtime-bound of t₂₉: X₃ {O(n)}
Results in: 2⋅X₂⋅X₃+5⋅X₃ {O(n^2)}
TWN - Lifting for t₂₃: l1→l4 of 2⋅X₁+2⋅X₂+5 {O(n)}
relevant size-bounds w.r.t. t₂₅:
X₁: 0 {O(1)}
X₂: X₂ {O(n)}
Runtime-bound of t₂₅: 1 {O(1)}
Results in: 2⋅X₂+5 {O(n)}
TWN: t₂₈: l4→l1
TWN - Lifting for t₂₈: l4→l1 of 2⋅X₁+2⋅X₂+5 {O(n)}
relevant size-bounds w.r.t. t₂₉:
X₁: 0 {O(1)}
X₂: X₂ {O(n)}
Runtime-bound of t₂₉: X₃ {O(n)}
Results in: 2⋅X₂⋅X₃+5⋅X₃ {O(n^2)}
TWN - Lifting for t₂₈: l4→l1 of 2⋅X₁+2⋅X₂+5 {O(n)}
relevant size-bounds w.r.t. t₂₅:
X₁: 0 {O(1)}
X₂: X₂ {O(n)}
Runtime-bound of t₂₅: 1 {O(1)}
Results in: 2⋅X₂+5 {O(n)}
Chain transitions t₂₉: l4→l1 and t₂₃: l1→l4 to t₆₅: l4→l4
Chain transitions t₂₈: l4→l1 and t₂₃: l1→l4 to t₆₆: l4→l4
Chain transitions t₂₈: l4→l1 and t₂₂: l1→l2 to t₆₇: l4→l2
Chain transitions t₂₉: l4→l1 and t₂₂: l1→l2 to t₆₈: l4→l2
Chain transitions t₂₅: l3→l1 and t₂₂: l1→l2 to t₆₉: l3→l2
Chain transitions t₂₅: l3→l1 and t₂₃: l1→l4 to t₇₀: l3→l4
Analysing control-flow refined program
Cut unsatisfiable transition t₆₇: l4→l2
Cut unsatisfiable transition t₆₉: l3→l2
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
MPRF for transition t₆₅: l4(X₀, X₁, X₂, X₃) -{2}> l4(1+X₀, 0, X₂, X₃) :|: X₂ ≤ X₁ ∧ X₂ ≤ X₁ ∧ 1+X₀ < X₃ ∧ 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 ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₃ ∧ 1 ≤ X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₂ ∧ 0 ≤ X₂ ∧ 0 ≤ X₀+X₂ ∧ 0 ≤ 0 ∧ 0 ≤ 1+X₀ ∧ 0 ≤ 1+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 of depth 1:
new bound:
X₃ {O(n)}
TWN: t₆₆: l4→l4
cycle: [t₆₆: l4→l4]
loop: (X₁ < X₂ ∧ X₁ < X₂ ∧ X₀ < X₃,(X₀,X₁,X₂,X₃) -> (X₀,1+X₁,X₂,X₃)
order: [X₀; X₁; X₂; X₃]
closed-form:
X₀: X₀
X₁: X₁ + [[n != 0]] * n^1
X₂: X₂
X₃: X₃
Termination: true
Formula:
X₀ < X₃ ∧ 1 < 0
∨ X₀ < X₃ ∧ X₁ < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1
Stabilization-Threshold for: X₁ < X₂
alphas_abs: X₁+X₂
M: 0
N: 1
Bound: 2⋅X₁+2⋅X₂+2 {O(n)}
loop: (X₁ < X₂ ∧ X₁ < X₂ ∧ X₀ < X₃,(X₀,X₁,X₂,X₃) -> (X₀,1+X₁,X₂,X₃)
order: [X₀; X₁; X₂; X₃]
closed-form:
X₀: X₀
X₁: X₁ + [[n != 0]] * n^1
X₂: X₂
X₃: X₃
Termination: true
Formula:
X₀ < X₃ ∧ 1 < 0
∨ X₀ < X₃ ∧ X₁ < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1
Stabilization-Threshold for: X₁ < X₂
alphas_abs: X₁+X₂
M: 0
N: 1
Bound: 2⋅X₁+2⋅X₂+2 {O(n)}
TWN - Lifting for t₆₆: l4→l4 of 2⋅X₁+2⋅X₂+5 {O(n)}
relevant size-bounds w.r.t. t₆₅:
X₁: 0 {O(1)}
X₂: X₂ {O(n)}
Runtime-bound of t₆₅: X₃ {O(n)}
Results in: 2⋅X₂⋅X₃+5⋅X₃ {O(n^2)}
TWN - Lifting for t₆₆: l4→l4 of 2⋅X₁+2⋅X₂+5 {O(n)}
relevant size-bounds w.r.t. t₇₀:
X₁: 0 {O(1)}
X₂: X₂ {O(n)}
Runtime-bound of t₇₀: 1 {O(1)}
Results in: 2⋅X₂+5 {O(n)}
CFR did not improve the program. Rolling back
CFR did not improve the program. Rolling back
Analysing control-flow refined program
Cut unsatisfiable transition t₂₂: l1→l2
Cut unsatisfiable transition t₁₅₀: n_l1___1→l2
Cut unsatisfiable transition t₁₅₂: 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 t₁₃₆: n_l1___1(X₀, X₁, X₂, X₃) → n_l4___4(X₀, X₁, X₂, X₃) :|: X₀ < X₃ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₁ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₁ ∧ 1+X₀ ≤ X₃ ∧ X₀ < X₃ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₃ ∧ 1+X₁ ≤ X₃ ∧ X₁ ≤ X₂ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₂ ∧ 1+X₂ ≤ X₃ ∧ 0 ≤ X₀ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₃ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀ ∧ 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 for transition t₁₃₇: n_l1___3(X₀, X₁, X₂, X₃) → n_l4___2(X₀, X₁, X₂, X₃) :|: X₁ < X₂ ∧ X₁ ≤ 0 ∧ 1 ≤ X₀ ∧ X₀ < X₃ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₃ ∧ 1+X₁ ≤ X₃ ∧ 0 ≤ X₁ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₃ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀ ∧ 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 for transition t₁₄₀: n_l4___2(X₀, X₁, X₂, X₃) → n_l1___1(X₀, X₁+1, X₂, X₃) :|: X₀ < X₃ ∧ 1 ≤ X₀ ∧ X₁ ≤ 0 ∧ X₁ < X₂ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₂ ∧ 0 ≤ X₁ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₃ ∧ 0 ≤ X₁ ∧ 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 for transition t₁₄₁: n_l4___4(X₀, X₁, X₂, X₃) → n_l1___3(X₀+1, 0, X₁, X₃) :|: 1 ≤ X₁ ∧ 1 ≤ X₁ ∧ X₂ ≤ X₁ ∧ 1+X₀ ≤ X₃ ∧ 0 ≤ X₀ ∧ 1+X₂ ≤ X₃ ∧ X₁ ≤ X₂ ∧ 1+X₁ ≤ X₃ ∧ 1+X₀ ≤ X₃ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₂ ∧ 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 for transition t₁₃₈: n_l1___5(X₀, X₁, X₂, X₃) → n_l4___4(X₀, X₁, X₂, X₃) :|: X₀ < X₃ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₁ ∧ X₀ < X₃ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₃ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀ ∧ 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 for transition t₁₄₂: n_l4___4(X₀, X₁, X₂, X₃) → n_l1___5(X₀, X₁+1, X₂, X₃) :|: 1 ≤ X₁ ∧ X₁ < X₂ ∧ 1+X₀ ≤ X₃ ∧ 0 ≤ X₀ ∧ 1+X₂ ≤ X₃ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₃ ∧ 0 ≤ X₁ ∧ 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)}
CFR did not improve the program. Rolling back
CFR did not improve the program. Rolling back
All Bounds
Timebounds
Overall timebound:4⋅X₂⋅X₃+11⋅X₃+4⋅X₂+16 {O(n^2)}
t₂₁: 1 {O(1)}
t₂₂: 1 {O(1)}
t₂₃: 2⋅X₂⋅X₃+2⋅X₂+5⋅X₃+5 {O(n^2)}
t₂₄: 1 {O(1)}
t₂₅: 1 {O(1)}
t₂₆: 1 {O(1)}
t₂₇: 1 {O(1)}
t₂₈: 2⋅X₂⋅X₃+2⋅X₂+5⋅X₃+5 {O(n^2)}
t₂₉: X₃ {O(n)}
Costbounds
Overall costbound: 4⋅X₂⋅X₃+11⋅X₃+4⋅X₂+16 {O(n^2)}
t₂₁: 1 {O(1)}
t₂₂: 1 {O(1)}
t₂₃: 2⋅X₂⋅X₃+2⋅X₂+5⋅X₃+5 {O(n^2)}
t₂₄: 1 {O(1)}
t₂₅: 1 {O(1)}
t₂₆: 1 {O(1)}
t₂₇: 1 {O(1)}
t₂₈: 2⋅X₂⋅X₃+2⋅X₂+5⋅X₃+5 {O(n^2)}
t₂₉: X₃ {O(n)}
Sizebounds
t₂₁, X₀: X₀ {O(n)}
t₂₁, X₁: X₁ {O(n)}
t₂₁, X₂: X₂ {O(n)}
t₂₁, X₃: X₃ {O(n)}
t₂₂, X₀: X₃ {O(n)}
t₂₂, X₁: 0 {O(1)}
t₂₂, X₂: X₂ {O(n)}
t₂₂, X₃: X₃ {O(n)}
t₂₃, X₀: X₃ {O(n)}
t₂₃, X₁: 2⋅X₂⋅X₃+2⋅X₂+5⋅X₃+5 {O(n^2)}
t₂₃, X₂: X₂ {O(n)}
t₂₃, X₃: X₃ {O(n)}
t₂₄, X₀: 2⋅X₀+X₃ {O(n)}
t₂₄, X₁: 2⋅X₁ {O(n)}
t₂₄, X₂: 3⋅X₂ {O(n)}
t₂₄, X₃: 3⋅X₃ {O(n)}
t₂₅, X₀: 0 {O(1)}
t₂₅, X₁: 0 {O(1)}
t₂₅, X₂: X₂ {O(n)}
t₂₅, X₃: X₃ {O(n)}
t₂₆, X₀: X₀ {O(n)}
t₂₆, X₁: X₁ {O(n)}
t₂₆, X₂: X₂ {O(n)}
t₂₆, X₃: X₃ {O(n)}
t₂₇, X₀: X₀ {O(n)}
t₂₇, X₁: X₁ {O(n)}
t₂₇, X₂: X₂ {O(n)}
t₂₇, X₃: X₃ {O(n)}
t₂₈, X₀: X₃ {O(n)}
t₂₈, X₁: 2⋅X₂⋅X₃+2⋅X₂+5⋅X₃+5 {O(n^2)}
t₂₈, X₂: X₂ {O(n)}
t₂₈, X₃: X₃ {O(n)}
t₂₉, X₀: X₃ {O(n)}
t₂₉, X₁: 0 {O(1)}
t₂₉, X₂: X₂ {O(n)}
t₂₉, X₃: X₃ {O(n)}