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) → l6(X₀, X₁, X₂)
t₂: l1(X₀, X₁, X₂) → l2(X₀, X₁, X₂) :|: 1 ≤ X₂ ∧ X₂+1 ≤ X₁
t₃: l1(X₀, X₁, X₂) → l5(X₀, X₁, X₂) :|: X₂ ≤ 0
t₄: l1(X₀, X₁, X₂) → l5(X₀, X₁, X₂) :|: X₁ ≤ X₂
t₅: l2(X₀, X₁, X₂) → l3(X₀, X₁, X₂) :|: 1 ≤ X₀
t₆: l2(X₀, X₁, X₂) → l4(X₀, X₁, X₂) :|: X₀ ≤ 0
t₇: l3(X₀, X₁, X₂) → l1(X₀, X₁, X₂+1)
t₈: l4(X₀, X₁, X₂) → l1(X₀, X₁, X₂-1)
t₉: l5(X₀, X₁, X₂) → l7(X₀, X₁, X₂)
t₁: l6(X₀, X₁, X₂) → l1(X₂, X₁, X₀) :|: 1 ≤ X₀ ∧ X₀+1 ≤ X₁
Preprocessing
Found invariant 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₁ for location l2
Found invariant X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₁ for location l7
Found invariant X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₁ for location l5
Found invariant X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₁ for location l1
Found invariant 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 2+X₀ ≤ X₁ ∧ X₀ ≤ 0 for location l4
Found invariant 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ 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) → l6(X₀, X₁, X₂)
t₂: l1(X₀, X₁, X₂) → l2(X₀, X₁, X₂) :|: 1 ≤ X₂ ∧ X₂+1 ≤ X₁ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₁
t₃: l1(X₀, X₁, X₂) → l5(X₀, X₁, X₂) :|: X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₁
t₄: l1(X₀, X₁, X₂) → l5(X₀, X₁, X₂) :|: X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₁
t₅: l2(X₀, X₁, X₂) → l3(X₀, X₁, X₂) :|: 1 ≤ X₀ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₁
t₆: l2(X₀, X₁, X₂) → l4(X₀, X₁, X₂) :|: X₀ ≤ 0 ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₁
t₇: l3(X₀, X₁, X₂) → l1(X₀, X₁, X₂+1) :|: 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₈: l4(X₀, X₁, X₂) → l1(X₀, X₁, X₂-1) :|: 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 2+X₀ ≤ X₁ ∧ X₀ ≤ 0
t₉: l5(X₀, X₁, X₂) → l7(X₀, X₁, X₂) :|: X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₁
t₁: l6(X₀, X₁, X₂) → l1(X₂, X₁, X₀) :|: 1 ≤ X₀ ∧ X₀+1 ≤ X₁
Chain transitions t₁: l6→l1 and t₄: l1→l5 to t₈₉: l6→l5
Chain transitions t₈: l4→l1 and t₄: l1→l5 to t₉₀: l4→l5
Chain transitions t₈: l4→l1 and t₃: l1→l5 to t₉₁: l4→l5
Chain transitions t₁: l6→l1 and t₃: l1→l5 to t₉₂: l6→l5
Chain transitions t₇: l3→l1 and t₃: l1→l5 to t₉₃: l3→l5
Chain transitions t₇: l3→l1 and t₄: l1→l5 to t₉₄: l3→l5
Chain transitions t₇: l3→l1 and t₂: l1→l2 to t₉₅: l3→l2
Chain transitions t₈: l4→l1 and t₂: l1→l2 to t₉₆: l4→l2
Chain transitions t₁: l6→l1 and t₂: l1→l2 to t₉₇: l6→l2
Chain transitions t₉₇: l6→l2 and t₆: l2→l4 to t₉₈: l6→l4
Chain transitions t₉₆: l4→l2 and t₆: l2→l4 to t₉₉: l4→l4
Chain transitions t₉₆: l4→l2 and t₅: l2→l3 to t₁₀₀: l4→l3
Chain transitions t₉₇: l6→l2 and t₅: l2→l3 to t₁₀₁: l6→l3
Chain transitions t₉₅: l3→l2 and t₅: l2→l3 to t₁₀₂: l3→l3
Chain transitions t₉₅: l3→l2 and t₆: l2→l4 to t₁₀₃: l3→l4
Analysing control-flow refined program
Cut unsatisfiable transition t₈₉: l6→l5
Cut unsatisfiable transition t₉₀: l4→l5
Cut unsatisfiable transition t₉₂: l6→l5
Cut unsatisfiable transition t₉₃: l3→l5
Cut unsatisfiable transition t₁₀₀: l4→l3
Cut unsatisfiable transition t₁₀₃: l3→l4
Found invariant 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₁ for location l2
Found invariant X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₁ for location l7
Found invariant X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₁ for location l5
Found invariant X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₁ for location l1
Found invariant 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 2+X₀ ≤ X₁ ∧ X₀ ≤ 0 for location l4
Found invariant 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l3
MPRF for transition t₁₀₂: l3(X₀, X₁, X₂) -{3}> l3(X₀, X₁, 1+X₂) :|: 0 ≤ X₂ ∧ 2+X₂ ≤ X₁ ∧ 1 ≤ X₀ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1 ≤ X₀ ∧ X₂+1 ≤ X₁ ∧ 0 ≤ 1+X₂ ∧ 1 ≤ X₁+X₂ ∧ 2 ≤ X₁ ∧ 2+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₁ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₀+X₁ {O(n)}
MPRF for transition t₉₉: l4(X₀, X₁, X₂) -{3}> l4(X₀, X₁, X₂-1) :|: 2 ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₀ ≤ 0 ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 2+X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ X₂ ≤ X₁+1 ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₁ ∧ X₂ ≤ X₁ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 2 ≤ X₁ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 2+X₀ ≤ X₁ ∧ X₀ ≤ 0 of depth 1:
new bound:
X₀ {O(n)}
Analysing control-flow refined program
Cut unsatisfiable transition t₃: l1→l5
Cut unsatisfiable transition t₄: l1→l5
Cut unsatisfiable transition t₂₁₂: n_l1___6→l5
Cut unsatisfiable transition t₂₁₃: n_l1___3→l5
Found invariant X₂ ≤ X₁ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l1___6
Found invariant 1+X₂ ≤ X₁ ∧ 2 ≤ X₂ ∧ 5 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l3___4
Found invariant 1+X₂ ≤ X₁ ∧ 2 ≤ X₂ ∧ 5 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l2___5
Found invariant 2+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 2+X₀ ≤ X₁ ∧ X₀ ≤ 0 for location n_l1___3
Found invariant 2+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 1+X₀ ≤ X₂ ∧ 3 ≤ X₁ ∧ 3+X₀ ≤ X₁ ∧ X₀ ≤ 0 for location n_l2___2
Found invariant X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₁ for location l7
Found invariant 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₁ for location n_l2___9
Found invariant 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l3___8
Found invariant 2+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 1+X₀ ≤ X₂ ∧ 3 ≤ X₁ ∧ 3+X₀ ≤ X₁ ∧ X₀ ≤ 0 for location n_l4___1
Found invariant X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₁ for location l5
Found invariant 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₁ for location l1
Found invariant 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 2+X₀ ≤ X₁ ∧ X₀ ≤ 0 for location n_l4___7
MPRF for transition t₁₉₂: n_l1___6(X₀, X₁, X₂) → n_l2___5(X₀, X₁, X₂) :|: 1 ≤ X₂ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ 2 ≤ X₂ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₁ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₀+X₁+2 {O(n)}
MPRF for transition t₁₉₄: n_l2___5(X₀, X₁, X₂) → n_l3___4(X₀, X₁, X₂) :|: 2 ≤ X₂ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₁ ∧ 2 ≤ X₂ ∧ 5 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₀+X₁+1 {O(n)}
MPRF for transition t₁₉₇: n_l3___4(X₀, X₁, X₂) → n_l1___6(X₀, X₁, X₂+1) :|: 2 ≤ X₂ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₁ ∧ 2 ≤ X₂ ∧ 5 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₀+X₁+1 {O(n)}
MPRF for transition t₁₉₁: n_l1___3(X₀, X₁, X₂) → n_l2___2(X₀, X₁, X₂) :|: 1+X₂ ≤ X₁ ∧ X₀ ≤ 0 ∧ 2+X₂ ≤ X₁ ∧ X₀ ≤ 0 ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 0 ≤ X₂ ∧ 2+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 2+X₀ ≤ X₁ ∧ X₀ ≤ 0 of depth 1:
new bound:
X₀+1 {O(n)}
MPRF for transition t₁₉₃: n_l2___2(X₀, X₁, X₂) → n_l4___1(X₀, X₁, X₂) :|: X₀ ≤ 0 ∧ 2+X₂ ≤ X₁ ∧ X₀ ≤ 0 ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 1+X₀ ≤ X₂ ∧ 3 ≤ X₁ ∧ 3+X₀ ≤ X₁ ∧ X₀ ≤ 0 of depth 1:
new bound:
X₀ {O(n)}
MPRF for transition t₁₉₉: n_l4___1(X₀, X₁, X₂) → n_l1___3(X₀, X₁, X₂-1) :|: 2+X₂ ≤ X₁ ∧ X₀ ≤ 0 ∧ 1 ≤ X₂ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₁ ∧ X₀ ≤ 0 ∧ 2+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 1+X₀ ≤ X₂ ∧ 3 ≤ X₁ ∧ 3+X₀ ≤ X₁ ∧ X₀ ≤ 0 of depth 1:
new bound:
X₀ {O(n)}
CFR: Improvement to new bound with the following program:
new bound:
Infinite
cfr-program:
Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1, l5, l6, l7, n_l1___3, n_l1___6, n_l2___2, n_l2___5, n_l2___9, n_l3___4, n_l3___8, n_l4___1, n_l4___7
Transitions:
t₀: l0(X₀, X₁, X₂) → l6(X₀, X₁, X₂)
t₁₉₀: l1(X₀, X₁, X₂) → n_l2___9(X₀, X₁, X₂) :|: 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₁
t₉: l5(X₀, X₁, X₂) → l7(X₀, X₁, X₂) :|: X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₁ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₁
t₁: l6(X₀, X₁, X₂) → l1(X₂, X₁, X₀) :|: 1 ≤ X₀ ∧ X₀+1 ≤ X₁
t₂₁₁: n_l1___3(X₀, X₁, X₂) → l5(X₀, X₁, X₂) :|: X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₁ ∧ 2+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 2+X₀ ≤ X₁ ∧ X₀ ≤ 0
t₁₉₁: n_l1___3(X₀, X₁, X₂) → n_l2___2(X₀, X₁, X₂) :|: 1+X₂ ≤ X₁ ∧ X₀ ≤ 0 ∧ 2+X₂ ≤ X₁ ∧ X₀ ≤ 0 ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 0 ≤ X₂ ∧ 2+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 2+X₀ ≤ X₁ ∧ X₀ ≤ 0
t₂₁₄: n_l1___6(X₀, X₁, X₂) → l5(X₀, X₁, X₂) :|: X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₁ ∧ X₂ ≤ X₁ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₁₉₂: n_l1___6(X₀, X₁, X₂) → n_l2___5(X₀, X₁, X₂) :|: 1 ≤ X₂ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ 2 ≤ X₂ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₁ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₁₉₃: n_l2___2(X₀, X₁, X₂) → n_l4___1(X₀, X₁, X₂) :|: X₀ ≤ 0 ∧ 2+X₂ ≤ X₁ ∧ X₀ ≤ 0 ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 1+X₀ ≤ X₂ ∧ 3 ≤ X₁ ∧ 3+X₀ ≤ X₁ ∧ X₀ ≤ 0
t₁₉₄: n_l2___5(X₀, X₁, X₂) → n_l3___4(X₀, X₁, X₂) :|: 2 ≤ X₂ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₁ ∧ 2 ≤ X₂ ∧ 5 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₁₉₅: n_l2___9(X₀, X₁, X₂) → n_l3___8(X₀, X₁, X₂) :|: 1 ≤ X₀ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₁
t₁₉₆: n_l2___9(X₀, X₁, X₂) → n_l4___7(X₀, X₁, X₂) :|: X₀ ≤ 0 ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₁
t₁₉₇: n_l3___4(X₀, X₁, X₂) → n_l1___6(X₀, X₁, X₂+1) :|: 2 ≤ X₂ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₁ ∧ 2 ≤ X₂ ∧ 5 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₁₉₈: n_l3___8(X₀, X₁, X₂) → n_l1___6(X₀, X₁, X₂+1) :|: 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₁₉₉: n_l4___1(X₀, X₁, X₂) → n_l1___3(X₀, X₁, X₂-1) :|: 2+X₂ ≤ X₁ ∧ X₀ ≤ 0 ∧ 1 ≤ X₂ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₁ ∧ X₀ ≤ 0 ∧ 2+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 1+X₀ ≤ X₂ ∧ 3 ≤ X₁ ∧ 3+X₀ ≤ X₁ ∧ X₀ ≤ 0
t₂₀₀: n_l4___7(X₀, X₁, X₂) → n_l1___3(X₀, X₁, X₂-1) :|: X₀ ≤ 0 ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₁ ∧ X₀ ≤ 0 ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 2+X₀ ≤ X₁ ∧ X₀ ≤ 0
CFR: Improvement to new bound with the following program:
new bound:
3⋅X₁+6⋅X₀+5 {O(n)}
cfr-program:
Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1, l5, l6, l7, n_l1___3, n_l1___6, n_l2___2, n_l2___5, n_l2___9, n_l3___4, n_l3___8, n_l4___1, n_l4___7
Transitions:
t₀: l0(X₀, X₁, X₂) → l6(X₀, X₁, X₂)
t₁₉₀: l1(X₀, X₁, X₂) → n_l2___9(X₀, X₁, X₂) :|: 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₁
t₉: l5(X₀, X₁, X₂) → l7(X₀, X₁, X₂) :|: X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₁ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₁
t₁: l6(X₀, X₁, X₂) → l1(X₂, X₁, X₀) :|: 1 ≤ X₀ ∧ X₀+1 ≤ X₁
t₂₁₁: n_l1___3(X₀, X₁, X₂) → l5(X₀, X₁, X₂) :|: X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₁ ∧ 2+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 2+X₀ ≤ X₁ ∧ X₀ ≤ 0
t₁₉₁: n_l1___3(X₀, X₁, X₂) → n_l2___2(X₀, X₁, X₂) :|: 1+X₂ ≤ X₁ ∧ X₀ ≤ 0 ∧ 2+X₂ ≤ X₁ ∧ X₀ ≤ 0 ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 0 ≤ X₂ ∧ 2+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 2+X₀ ≤ X₁ ∧ X₀ ≤ 0
t₂₁₄: n_l1___6(X₀, X₁, X₂) → l5(X₀, X₁, X₂) :|: X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₁ ∧ X₂ ≤ X₁ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₁₉₂: n_l1___6(X₀, X₁, X₂) → n_l2___5(X₀, X₁, X₂) :|: 1 ≤ X₂ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ 2 ≤ X₂ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₁ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₁₉₃: n_l2___2(X₀, X₁, X₂) → n_l4___1(X₀, X₁, X₂) :|: X₀ ≤ 0 ∧ 2+X₂ ≤ X₁ ∧ X₀ ≤ 0 ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 1+X₀ ≤ X₂ ∧ 3 ≤ X₁ ∧ 3+X₀ ≤ X₁ ∧ X₀ ≤ 0
t₁₉₄: n_l2___5(X₀, X₁, X₂) → n_l3___4(X₀, X₁, X₂) :|: 2 ≤ X₂ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₁ ∧ 2 ≤ X₂ ∧ 5 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₁₉₅: n_l2___9(X₀, X₁, X₂) → n_l3___8(X₀, X₁, X₂) :|: 1 ≤ X₀ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₁
t₁₉₆: n_l2___9(X₀, X₁, X₂) → n_l4___7(X₀, X₁, X₂) :|: X₀ ≤ 0 ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₁
t₁₉₇: n_l3___4(X₀, X₁, X₂) → n_l1___6(X₀, X₁, X₂+1) :|: 2 ≤ X₂ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₁ ∧ 2 ≤ X₂ ∧ 5 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₁₉₈: n_l3___8(X₀, X₁, X₂) → n_l1___6(X₀, X₁, X₂+1) :|: 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₁₉₉: n_l4___1(X₀, X₁, X₂) → n_l1___3(X₀, X₁, X₂-1) :|: 2+X₂ ≤ X₁ ∧ X₀ ≤ 0 ∧ 1 ≤ X₂ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₁ ∧ X₀ ≤ 0 ∧ 2+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 1+X₀ ≤ X₂ ∧ 3 ≤ X₁ ∧ 3+X₀ ≤ X₁ ∧ X₀ ≤ 0
t₂₀₀: n_l4___7(X₀, X₁, X₂) → n_l1___3(X₀, X₁, X₂-1) :|: X₀ ≤ 0 ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₁ ∧ X₀ ≤ 0 ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 2+X₀ ≤ X₁ ∧ X₀ ≤ 0
All Bounds
Timebounds
Overall timebound:3⋅X₁+6⋅X₀+15 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₉: 1 {O(1)}
t₁₉₀: 1 {O(1)}
t₁₉₁: X₀+1 {O(n)}
t₁₉₂: X₀+X₁+2 {O(n)}
t₁₉₃: X₀ {O(n)}
t₁₉₄: X₀+X₁+1 {O(n)}
t₁₉₅: 1 {O(1)}
t₁₉₆: 1 {O(1)}
t₁₉₇: X₀+X₁+1 {O(n)}
t₁₉₈: 1 {O(1)}
t₁₉₉: X₀ {O(n)}
t₂₀₀: 1 {O(1)}
t₂₁₁: 1 {O(1)}
t₂₁₄: 1 {O(1)}
Costbounds
Overall costbound: 3⋅X₁+6⋅X₀+15 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₉: 1 {O(1)}
t₁₉₀: 1 {O(1)}
t₁₉₁: X₀+1 {O(n)}
t₁₉₂: X₀+X₁+2 {O(n)}
t₁₉₃: X₀ {O(n)}
t₁₉₄: X₀+X₁+1 {O(n)}
t₁₉₅: 1 {O(1)}
t₁₉₆: 1 {O(1)}
t₁₉₇: X₀+X₁+1 {O(n)}
t₁₉₈: 1 {O(1)}
t₁₉₉: X₀ {O(n)}
t₂₀₀: 1 {O(1)}
t₂₁₁: 1 {O(1)}
t₂₁₄: 1 {O(1)}
Sizebounds
t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₁, X₀: X₂ {O(n)}
t₁, X₁: X₁ {O(n)}
t₁, X₂: X₀ {O(n)}
t₉, X₀: 4⋅X₂ {O(n)}
t₉, X₁: 4⋅X₁ {O(n)}
t₉, X₂: 3⋅X₀+X₁+3 {O(n)}
t₁₉₀, X₀: X₂ {O(n)}
t₁₉₀, X₁: X₁ {O(n)}
t₁₉₀, X₂: X₀ {O(n)}
t₁₉₁, X₀: X₂ {O(n)}
t₁₉₁, X₁: X₁ {O(n)}
t₁₉₁, X₂: X₀ {O(n)}
t₁₉₂, X₀: X₂ {O(n)}
t₁₉₂, X₁: X₁ {O(n)}
t₁₉₂, X₂: 2⋅X₀+X₁+2 {O(n)}
t₁₉₃, X₀: X₂ {O(n)}
t₁₉₃, X₁: X₁ {O(n)}
t₁₉₃, X₂: X₀ {O(n)}
t₁₉₄, X₀: X₂ {O(n)}
t₁₉₄, X₁: X₁ {O(n)}
t₁₉₄, X₂: 2⋅X₀+X₁+2 {O(n)}
t₁₉₅, X₀: X₂ {O(n)}
t₁₉₅, X₁: X₁ {O(n)}
t₁₉₅, X₂: X₀ {O(n)}
t₁₉₆, X₀: X₂ {O(n)}
t₁₉₆, X₁: X₁ {O(n)}
t₁₉₆, X₂: X₀ {O(n)}
t₁₉₇, X₀: X₂ {O(n)}
t₁₉₇, X₁: X₁ {O(n)}
t₁₉₇, X₂: 2⋅X₀+X₁+2 {O(n)}
t₁₉₈, X₀: X₂ {O(n)}
t₁₉₈, X₁: X₁ {O(n)}
t₁₉₈, X₂: X₀+1 {O(n)}
t₁₉₉, X₀: X₂ {O(n)}
t₁₉₉, X₁: X₁ {O(n)}
t₁₉₉, X₂: X₀ {O(n)}
t₂₀₀, X₀: X₂ {O(n)}
t₂₀₀, X₁: X₁ {O(n)}
t₂₀₀, X₂: X₀ {O(n)}
t₂₁₁, X₀: 2⋅X₂ {O(n)}
t₂₁₁, X₁: 2⋅X₁ {O(n)}
t₂₁₁, X₂: 0 {O(1)}
t₂₁₄, X₀: 2⋅X₂ {O(n)}
t₂₁₄, X₁: 2⋅X₁ {O(n)}
t₂₁₄, X₂: 3⋅X₀+X₁+3 {O(n)}