Initial Problem
Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7
Transitions:
t₀: l0(X₀, X₁, X₂) → l2(X₀, X₁, X₂)
t₂: l1(X₀, X₁, X₂) → l3(X₀, X₁, X₂) :|: X₁ < X₀
t₃: l1(X₀, X₁, X₂) → l4(X₀, X₁, X₂) :|: X₀ ≤ X₁
t₁: l2(X₀, X₁, X₂) → l1(X₀, 0, 0)
t₄: l3(X₀, X₁, X₂) → l1(X₀, X₁+1, X₂+1)
t₅: l4(X₀, X₁, X₂) → l5(X₀, X₁, X₂) :|: 0 < X₂
t₆: l4(X₀, X₁, X₂) → l6(X₀, X₁, X₂) :|: X₂ ≤ 0
t₇: l5(X₀, X₁, X₂) → l1(X₀, X₁, X₂-1)
t₈: l6(X₀, X₁, X₂) → l7(X₀, X₁, X₂)
Preprocessing
Found invariant X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁ ∧ X₀ ≤ X₁ for location l6
Found invariant X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁ ∧ X₀ ≤ X₁ for location l7
Found invariant X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁ ∧ X₀ ≤ X₁ for location l5
Found invariant X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁ for location l1
Found invariant X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁ ∧ X₀ ≤ X₁ for location l4
Found invariant X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l3
Problem after Preprocessing
Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7
Transitions:
t₀: l0(X₀, X₁, X₂) → l2(X₀, X₁, X₂)
t₂: l1(X₀, X₁, X₂) → l3(X₀, X₁, X₂) :|: X₁ < X₀ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁
t₃: l1(X₀, X₁, X₂) → l4(X₀, X₁, X₂) :|: X₀ ≤ X₁ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁
t₁: l2(X₀, X₁, X₂) → l1(X₀, 0, 0)
t₄: l3(X₀, X₁, X₂) → l1(X₀, X₁+1, X₂+1) :|: X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₅: l4(X₀, X₁, X₂) → l5(X₀, X₁, X₂) :|: 0 < X₂ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁ ∧ X₀ ≤ X₁
t₆: l4(X₀, X₁, X₂) → l6(X₀, X₁, X₂) :|: X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁ ∧ X₀ ≤ X₁
t₇: l5(X₀, X₁, X₂) → l1(X₀, X₁, X₂-1) :|: X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁ ∧ X₀ ≤ X₁
t₈: l6(X₀, X₁, X₂) → l7(X₀, X₁, X₂) :|: X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁ ∧ X₀ ≤ X₁
MPRF for transition t₂: l1(X₀, X₁, X₂) → l3(X₀, X₁, X₂) :|: X₁ < X₀ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁ of depth 1:
new bound:
X₀ {O(n)}
MPRF for transition t₄: l3(X₀, X₁, X₂) → l1(X₀, X₁+1, X₂+1) :|: X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₀ {O(n)}
MPRF for transition t₃: l1(X₀, X₁, X₂) → l4(X₀, X₁, X₂) :|: X₀ ≤ X₁ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁ of depth 1:
new bound:
X₀⋅X₀+X₀+1 {O(n^2)}
MPRF for transition t₅: l4(X₀, X₁, X₂) → l5(X₀, X₁, X₂) :|: 0 < X₂ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁ ∧ X₀ ≤ X₁ of depth 1:
new bound:
X₀⋅X₀+X₀+1 {O(n^2)}
MPRF for transition t₇: l5(X₀, X₁, X₂) → l1(X₀, X₁, X₂-1) :|: X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁ ∧ X₀ ≤ X₁ of depth 1:
new bound:
X₀⋅X₀ {O(n^2)}
Chain transitions t₇: l5→l1 and t₃: l1→l4 to t₅₈: l5→l4
Chain transitions t₄: l3→l1 and t₃: l1→l4 to t₅₉: l3→l4
Chain transitions t₄: l3→l1 and t₂: l1→l3 to t₆₀: l3→l3
Chain transitions t₇: l5→l1 and t₂: l1→l3 to t₆₁: l5→l3
Chain transitions t₁: l2→l1 and t₂: l1→l3 to t₆₂: l2→l3
Chain transitions t₁: l2→l1 and t₃: l1→l4 to t₆₃: l2→l4
Chain transitions t₅₈: l5→l4 and t₆: l4→l6 to t₆₄: l5→l6
Chain transitions t₅₉: l3→l4 and t₆: l4→l6 to t₆₅: l3→l6
Chain transitions t₅₉: l3→l4 and t₅: l4→l5 to t₆₆: l3→l5
Chain transitions t₅₈: l5→l4 and t₅: l4→l5 to t₆₇: l5→l5
Chain transitions t₆₃: l2→l4 and t₅: l4→l5 to t₆₈: l2→l5
Chain transitions t₆₃: l2→l4 and t₆: l4→l6 to t₆₉: l2→l6
Analysing control-flow refined program
Cut unsatisfiable transition t₆₁: l5→l3
Cut unsatisfiable transition t₆₅: l3→l6
Cut unsatisfiable transition t₆₈: l2→l5
Found invariant X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁ ∧ X₀ ≤ X₁ for location l6
Found invariant X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁ ∧ X₀ ≤ X₁ for location l7
Found invariant X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ for location l5
Found invariant X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁ for location l1
Found invariant X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁ ∧ X₀ ≤ X₁ for location l4
Found invariant X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l3
MPRF for transition t₆₀: l3(X₀, X₁, X₂) -{2}> l3(X₀, 1+X₁, 1+X₂) :|: 1+X₁ < X₀ ∧ X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ ∧ X₂ ≤ X₁ ∧ 0 ≤ 1+X₂ ∧ 0 ≤ 2+X₁+X₂ ∧ 0 ≤ 1+X₁ ∧ X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₀ {O(n)}
MPRF for transition t₆₇: l5(X₀, X₁, X₂) -{3}> l5(X₀, X₁, X₂-1) :|: X₀ ≤ X₁ ∧ 1 < X₂ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁ ∧ X₀ ≤ X₁ ∧ X₂ ≤ X₁+1 ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 0 ≤ X₁ ∧ X₂ ≤ X₁+1 ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 0 ≤ X₁ ∧ X₀ ≤ X₁ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₀+2 {O(n)}
CFR did not improve the program. Rolling back
Analysing control-flow refined program
Cut unsatisfiable transition t₁₆₅: n_l4___5→l6
Found invariant 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 2 ≤ X₀ for location n_l5___1
Found invariant X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁ ∧ X₀ ≤ X₁ for location l6
Found invariant X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ X₁+X₂ ≤ 0 ∧ X₀+X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 0 ∧ X₀+X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 for location n_l4___6
Found invariant 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l4___2
Found invariant 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l1___3
Found invariant X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l4___5
Found invariant X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l5___4
Found invariant X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁ ∧ X₀ ≤ X₁ for location l7
Found invariant X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₁ for location l1
Found invariant X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l3
MPRF for transition t₁₅₂: n_l1___3(X₀, X₁, X₂) → n_l4___2(X₀, X₁, X₂) :|: X₀ ≤ X₁ ∧ X₀ ≤ X₁ ∧ 1+X₂ ≤ X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ X₁ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₀+1 {O(n)}
MPRF for transition t₁₅₅: n_l4___2(X₀, X₁, X₂) → n_l5___1(X₀, X₁, X₂) :|: 1+X₂ ≤ X₁ ∧ 0 < X₂ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₀ ≤ X₁ ∧ 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₀+1 {O(n)}
MPRF for transition t₁₅₇: n_l5___1(X₀, X₁, X₂) → n_l1___3(X₀, X₁, X₂-1) :|: 1+X₂ ≤ X₁ ∧ 0 < X₂ ∧ X₀ ≤ X₁ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ X₀ ≤ X₁ ∧ 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 2 ≤ X₀ of depth 1:
new bound:
X₀ {O(n)}
CFR did not improve the program. Rolling back
CFR: Improvement to new bound with the following program:
new bound:
5⋅X₀+2 {O(n)}
cfr-program:
Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1, l2, l3, l6, l7, n_l1___3, n_l4___2, n_l4___5, n_l4___6, n_l5___1, n_l5___4
Transitions:
t₀: l0(X₀, X₁, X₂) → l2(X₀, X₁, X₂)
t₂: l1(X₀, X₁, X₂) → l3(X₀, X₁, X₂) :|: X₁ < X₀ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₁
t₁₅₃: l1(X₀, X₁, X₂) → n_l4___5(X₀, X₁, X₂) :|: 0 < X₂ ∧ 1 ≤ X₂ ∧ 1 ≤ X₂ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₁
t₁₅₄: l1(X₀, X₁, X₂) → n_l4___6(X₀, X₁, X₂) :|: X₁ ≤ 0 ∧ X₂ ≤ 0 ∧ X₀ ≤ X₁ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₂ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₁
t₁: l2(X₀, X₁, X₂) → l1(X₀, 0, 0)
t₄: l3(X₀, X₁, X₂) → l1(X₀, X₁+1, X₂+1) :|: X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ ∧ X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₈: l6(X₀, X₁, X₂) → l7(X₀, X₁, X₂) :|: X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁ ∧ X₀ ≤ X₁ ∧ X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁ ∧ X₀ ≤ X₁
t₁₅₂: n_l1___3(X₀, X₁, X₂) → n_l4___2(X₀, X₁, X₂) :|: X₀ ≤ X₁ ∧ X₀ ≤ X₁ ∧ 1+X₂ ≤ X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ X₁ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀
t₁₆₄: n_l4___2(X₀, X₁, X₂) → l6(X₀, X₁, X₂) :|: X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁ ∧ X₀ ≤ X₁ ∧ 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀
t₁₅₅: n_l4___2(X₀, X₁, X₂) → n_l5___1(X₀, X₁, X₂) :|: 1+X₂ ≤ X₁ ∧ 0 < X₂ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₀ ≤ X₁ ∧ 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀
t₁₅₆: n_l4___5(X₀, X₁, X₂) → n_l5___4(X₀, X₁, X₂) :|: X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ X₁ ≤ X₀ ∧ 0 < X₂ ∧ X₀ ≤ X₁ ∧ X₂ ≤ X₁ ∧ X₀ ≤ X₁ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀
t₁₆₆: n_l4___6(X₀, X₁, X₂) → l6(X₀, X₁, X₂) :|: X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁ ∧ X₀ ≤ X₁ ∧ X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ X₁+X₂ ≤ 0 ∧ X₀+X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 0 ∧ X₀+X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0
t₁₅₇: n_l5___1(X₀, X₁, X₂) → n_l1___3(X₀, X₁, X₂-1) :|: 1+X₂ ≤ X₁ ∧ 0 < X₂ ∧ X₀ ≤ X₁ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ X₀ ≤ X₁ ∧ 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 2 ≤ X₀
t₁₅₈: n_l5___4(X₀, X₁, X₂) → n_l1___3(X₀, X₁, X₂-1) :|: X₂ ≤ X₀ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₂ ∧ X₀ ≤ X₁ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ X₀ ≤ X₁ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀
All Bounds
Timebounds
Overall timebound:5⋅X₀+11 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₀ {O(n)}
t₄: X₀ {O(n)}
t₈: 1 {O(1)}
t₁₅₂: X₀+1 {O(n)}
t₁₅₃: 1 {O(1)}
t₁₅₄: 1 {O(1)}
t₁₅₅: X₀+1 {O(n)}
t₁₅₆: 1 {O(1)}
t₁₅₇: X₀ {O(n)}
t₁₅₈: 1 {O(1)}
t₁₆₄: 1 {O(1)}
t₁₆₆: 1 {O(1)}
Costbounds
Overall costbound: 5⋅X₀+11 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₀ {O(n)}
t₄: X₀ {O(n)}
t₈: 1 {O(1)}
t₁₅₂: X₀+1 {O(n)}
t₁₅₃: 1 {O(1)}
t₁₅₄: 1 {O(1)}
t₁₅₅: X₀+1 {O(n)}
t₁₅₆: 1 {O(1)}
t₁₅₇: X₀ {O(n)}
t₁₅₈: 1 {O(1)}
t₁₆₄: 1 {O(1)}
t₁₆₆: 1 {O(1)}
Sizebounds
t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₁, X₀: X₀ {O(n)}
t₁, X₁: 0 {O(1)}
t₁, X₂: 0 {O(1)}
t₂, X₀: X₀ {O(n)}
t₂, X₁: X₀ {O(n)}
t₂, X₂: X₀ {O(n)}
t₄, X₀: X₀ {O(n)}
t₄, X₁: X₀ {O(n)}
t₄, X₂: X₀ {O(n)}
t₈, X₀: 2⋅X₀ {O(n)}
t₈, X₁: X₀ {O(n)}
t₈, X₂: 0 {O(1)}
t₁₅₂, X₀: X₀ {O(n)}
t₁₅₂, X₁: X₀ {O(n)}
t₁₅₂, X₂: X₀ {O(n)}
t₁₅₃, X₀: X₀ {O(n)}
t₁₅₃, X₁: X₀ {O(n)}
t₁₅₃, X₂: X₀ {O(n)}
t₁₅₄, X₀: X₀ {O(n)}
t₁₅₄, X₁: 0 {O(1)}
t₁₅₄, X₂: 0 {O(1)}
t₁₅₅, X₀: X₀ {O(n)}
t₁₅₅, X₁: X₀ {O(n)}
t₁₅₅, X₂: X₀ {O(n)}
t₁₅₆, X₀: X₀ {O(n)}
t₁₅₆, X₁: X₀ {O(n)}
t₁₅₆, X₂: X₀ {O(n)}
t₁₅₇, X₀: X₀ {O(n)}
t₁₅₇, X₁: X₀ {O(n)}
t₁₅₇, X₂: X₀ {O(n)}
t₁₅₈, X₀: X₀ {O(n)}
t₁₅₈, X₁: X₀ {O(n)}
t₁₅₈, X₂: X₀ {O(n)}
t₁₆₄, X₀: X₀ {O(n)}
t₁₆₄, X₁: X₀ {O(n)}
t₁₆₄, X₂: 0 {O(1)}
t₁₆₆, X₀: X₀ {O(n)}
t₁₆₆, X₁: 0 {O(1)}
t₁₆₆, X₂: 0 {O(1)}