Initial Problem
Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7, l8
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃)
t₃: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃)
t₁: l2(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃)
t₂: l3(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, X₃)
t₆: l4(X₀, X₁, X₂, X₃) → l5(0, 0, X₂, X₃) :|: 0 < X₂ ∧ X₂ < X₃
t₄: l4(X₀, X₁, X₂, X₃) → l6(X₀, X₁, X₂, X₃) :|: X₂ ≤ 0
t₅: l4(X₀, X₁, X₂, X₃) → l6(X₀, X₁, X₂, X₃) :|: X₃ ≤ X₂
t₈: l5(X₀, X₁, X₂, X₃) → l6(X₀, X₁, X₂, X₃) :|: X₃ ≤ X₀
t₇: l5(X₀, X₁, X₂, X₃) → l7(X₀, X₁, X₂, X₃) :|: X₀ < X₃
t₁₃: l6(X₀, X₁, X₂, X₃) → l8(X₀, X₁, X₂, X₃)
t₉: l7(X₀, X₁, X₂, X₃) → l5(X₀, X₁+1, X₂, X₃) :|: X₁ < X₂ ∧ X₁ < X₂
t₁₀: l7(X₀, X₁, X₂, X₃) → l5(X₀+1, X₁+1, X₂, X₃) :|: X₁ < X₂ ∧ X₂ ≤ X₁
t₁₁: l7(X₀, X₁, X₂, X₃) → l5(X₀, 0, X₂, X₃) :|: X₂ ≤ X₁ ∧ X₁ < X₂
t₁₂: l7(X₀, X₁, X₂, X₃) → l5(X₀+1, 0, X₂, X₃) :|: X₂ ≤ X₁ ∧ X₂ ≤ X₁
Preprocessing
Cut unsatisfiable transition t₁₀: l7→l5
Cut unsatisfiable transition t₁₁: l7→l5
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 l7
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 l5
Problem after Preprocessing
Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7, l8
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃)
t₃: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃)
t₁: l2(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃)
t₂: l3(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, X₃)
t₆: l4(X₀, X₁, X₂, X₃) → l5(0, 0, X₂, X₃) :|: 0 < X₂ ∧ X₂ < X₃
t₄: l4(X₀, X₁, X₂, X₃) → l6(X₀, X₁, X₂, X₃) :|: X₂ ≤ 0
t₅: l4(X₀, X₁, X₂, X₃) → l6(X₀, X₁, X₂, X₃) :|: X₃ ≤ X₂
t₈: l5(X₀, X₁, X₂, X₃) → l6(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
t₇: l5(X₀, X₁, X₂, X₃) → l7(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
t₁₃: l6(X₀, X₁, X₂, X₃) → l8(X₀, X₁, X₂, X₃)
t₉: l7(X₀, X₁, X₂, X₃) → l5(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
t₁₂: l7(X₀, X₁, X₂, X₃) → l5(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 t₁₂: l7(X₀, X₁, X₂, X₃) → l5(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: t₇: l5→l7
cycle: [t₇: l5→l7; t₉: l7→l5]
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 t₇: l5→l7 of 2⋅X₁+2⋅X₂+5 {O(n)}
relevant size-bounds w.r.t. t₁₂:
X₁: 0 {O(1)}
X₂: X₂ {O(n)}
Runtime-bound of t₁₂: X₃ {O(n)}
Results in: 2⋅X₂⋅X₃+5⋅X₃ {O(n^2)}
TWN - Lifting for t₇: l5→l7 of 2⋅X₁+2⋅X₂+5 {O(n)}
relevant size-bounds w.r.t. t₆:
X₁: 0 {O(1)}
X₂: X₂ {O(n)}
Runtime-bound of t₆: 1 {O(1)}
Results in: 2⋅X₂+5 {O(n)}
TWN: t₉: l7→l5
TWN - Lifting for t₉: l7→l5 of 2⋅X₁+2⋅X₂+5 {O(n)}
relevant size-bounds w.r.t. t₁₂:
X₁: 0 {O(1)}
X₂: X₂ {O(n)}
Runtime-bound of t₁₂: X₃ {O(n)}
Results in: 2⋅X₂⋅X₃+5⋅X₃ {O(n^2)}
TWN - Lifting for t₉: l7→l5 of 2⋅X₁+2⋅X₂+5 {O(n)}
relevant size-bounds w.r.t. t₆:
X₁: 0 {O(1)}
X₂: X₂ {O(n)}
Runtime-bound of t₆: 1 {O(1)}
Results in: 2⋅X₂+5 {O(n)}
Chain transitions t₁₂: l7→l5 and t₇: l5→l7 to t₈₀: l7→l7
Chain transitions t₉: l7→l5 and t₇: l5→l7 to t₈₁: l7→l7
Chain transitions t₉: l7→l5 and t₈: l5→l6 to t₈₂: l7→l6
Chain transitions t₁₂: l7→l5 and t₈: l5→l6 to t₈₃: l7→l6
Chain transitions t₆: l4→l5 and t₈: l5→l6 to t₈₄: l4→l6
Chain transitions t₆: l4→l5 and t₇: l5→l7 to t₈₅: l4→l7
Analysing control-flow refined program
Cut unsatisfiable transition t₈₂: l7→l6
Cut unsatisfiable transition t₈₄: l4→l6
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 l7
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 l5
MPRF for transition t₈₀: l7(X₀, X₁, X₂, X₃) -{2}> l7(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: t₈₁: l7→l7
cycle: [t₈₁: l7→l7]
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 t₈₁: l7→l7 of 2⋅X₁+2⋅X₂+5 {O(n)}
relevant size-bounds w.r.t. t₈₀:
X₁: 0 {O(1)}
X₂: X₂ {O(n)}
Runtime-bound of t₈₀: X₃ {O(n)}
Results in: 2⋅X₂⋅X₃+5⋅X₃ {O(n^2)}
TWN - Lifting for t₈₁: l7→l7 of 2⋅X₁+2⋅X₂+5 {O(n)}
relevant size-bounds w.r.t. t₈₅:
X₁: 0 {O(1)}
X₂: X₂ {O(n)}
Runtime-bound of t₈₅: 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 t₈: l5→l6
Cut unsatisfiable transition t₁₇₄: n_l5___1→l6
Cut unsatisfiable transition t₁₇₆: n_l5___5→l6
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_l5___1
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_l5___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 n_l7___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_l7___2
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 l5
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_l7___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_l5___3
MPRF for transition t₁₆₀: n_l5___1(X₀, X₁, X₂, X₃) → n_l7___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 t₁₆₁: n_l5___3(X₀, X₁, X₂, X₃) → n_l7___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 t₁₆₄: n_l7___2(X₀, X₁, X₂, X₃) → n_l5___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 t₁₆₅: n_l7___4(X₀, X₁, X₂, X₃) → n_l5___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 t₁₆₂: n_l5___5(X₀, X₁, X₂, X₃) → n_l7___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 t₁₆₆: n_l7___4(X₀, X₁, X₂, X₃) → n_l5___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+2⋅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+19 {O(n^2)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₅: 1 {O(1)}
t₆: 1 {O(1)}
t₇: 2⋅X₂⋅X₃+2⋅X₂+5⋅X₃+5 {O(n^2)}
t₈: 1 {O(1)}
t₉: 2⋅X₂⋅X₃+2⋅X₂+5⋅X₃+5 {O(n^2)}
t₁₂: X₃ {O(n)}
t₁₃: 1 {O(1)}
Costbounds
Overall costbound: 4⋅X₂⋅X₃+11⋅X₃+4⋅X₂+19 {O(n^2)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₅: 1 {O(1)}
t₆: 1 {O(1)}
t₇: 2⋅X₂⋅X₃+2⋅X₂+5⋅X₃+5 {O(n^2)}
t₈: 1 {O(1)}
t₉: 2⋅X₂⋅X₃+2⋅X₂+5⋅X₃+5 {O(n^2)}
t₁₂: X₃ {O(n)}
t₁₃: 1 {O(1)}
Sizebounds
t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₀, X₃: 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: X₀ {O(n)}
t₃, X₁: X₁ {O(n)}
t₃, X₂: X₂ {O(n)}
t₃, X₃: X₃ {O(n)}
t₄, X₀: X₀ {O(n)}
t₄, X₁: X₁ {O(n)}
t₄, X₂: X₂ {O(n)}
t₄, X₃: X₃ {O(n)}
t₅, X₀: X₀ {O(n)}
t₅, X₁: X₁ {O(n)}
t₅, X₂: X₂ {O(n)}
t₅, X₃: X₃ {O(n)}
t₆, X₀: 0 {O(1)}
t₆, X₁: 0 {O(1)}
t₆, X₂: X₂ {O(n)}
t₆, X₃: X₃ {O(n)}
t₇, X₀: X₃ {O(n)}
t₇, X₁: 2⋅X₂⋅X₃+2⋅X₂+5⋅X₃+5 {O(n^2)}
t₇, X₂: X₂ {O(n)}
t₇, X₃: X₃ {O(n)}
t₈, X₀: X₃ {O(n)}
t₈, X₁: 0 {O(1)}
t₈, X₂: X₂ {O(n)}
t₈, X₃: X₃ {O(n)}
t₉, X₀: X₃ {O(n)}
t₉, X₁: 2⋅X₂⋅X₃+2⋅X₂+5⋅X₃+5 {O(n^2)}
t₉, X₂: X₂ {O(n)}
t₉, X₃: X₃ {O(n)}
t₁₂, X₀: X₃ {O(n)}
t₁₂, X₁: 0 {O(1)}
t₁₂, X₂: X₂ {O(n)}
t₁₂, X₃: X₃ {O(n)}
t₁₃, X₀: 2⋅X₀+X₃ {O(n)}
t₁₃, X₁: 2⋅X₁ {O(n)}
t₁₃, X₂: 3⋅X₂ {O(n)}
t₁₃, X₃: 3⋅X₃ {O(n)}