Initial Problem
Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l6(X₀, X₁, X₂, X₃)
t₇: l1(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃+X₀)
t₈: l2(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃-X₀)
t₃: l3(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₃ ≤ X₁
t₄: l3(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₁+1 ≤ X₃
t₅: l4(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, X₃) :|: 1 ≤ X₂
t₆: l4(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₂ ≤ 0
t₉: l5(X₀, X₁, X₂, X₃) → l7(X₀, X₁, X₂, X₃)
t₁: l6(X₀, X₁, X₂, X₃) → l3(1, X₂, X₀, X₁) :|: 1 ≤ X₀
t₂: l6(X₀, X₁, X₂, X₃) → l3(-1, X₂, X₀, X₁) :|: X₀ ≤ 0
Preprocessing
Found invariant X₃ ≤ X₁ ∧ X₂ ≤ 0 ∧ X₂ ≤ 1+X₀ ∧ X₀+X₂ ≤ 1 ∧ X₀ ≤ 1 ∧ 0 ≤ 1+X₀ for location l2
Found invariant 1+X₁ ≤ X₃ ∧ X₀ ≤ 1 ∧ 0 ≤ 1+X₀ for location l7
Found invariant 1+X₁ ≤ X₃ ∧ X₀ ≤ 1 ∧ 0 ≤ 1+X₀ for location l5
Found invariant X₃ ≤ X₁ ∧ 1 ≤ X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₀ ≤ 1 ∧ 0 ≤ 1+X₀ for location l1
Found invariant X₃ ≤ X₁ ∧ X₀ ≤ 1 ∧ 0 ≤ 1+X₀ for location l4
Found invariant X₀ ≤ 1 ∧ 0 ≤ 1+X₀ for location l3
Problem after Preprocessing
Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l6(X₀, X₁, X₂, X₃)
t₇: l1(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃+X₀) :|: X₃ ≤ X₁ ∧ 1 ≤ X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₀ ≤ 1 ∧ 0 ≤ 1+X₀
t₈: l2(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃-X₀) :|: X₃ ≤ X₁ ∧ X₂ ≤ 0 ∧ X₂ ≤ 1+X₀ ∧ X₀+X₂ ≤ 1 ∧ X₀ ≤ 1 ∧ 0 ≤ 1+X₀
t₃: l3(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₃ ≤ X₁ ∧ X₀ ≤ 1 ∧ 0 ≤ 1+X₀
t₄: l3(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₁+1 ≤ X₃ ∧ X₀ ≤ 1 ∧ 0 ≤ 1+X₀
t₅: l4(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, X₃) :|: 1 ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₀ ≤ 1 ∧ 0 ≤ 1+X₀
t₆: l4(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₂ ≤ 0 ∧ X₃ ≤ X₁ ∧ X₀ ≤ 1 ∧ 0 ≤ 1+X₀
t₉: l5(X₀, X₁, X₂, X₃) → l7(X₀, X₁, X₂, X₃) :|: 1+X₁ ≤ X₃ ∧ X₀ ≤ 1 ∧ 0 ≤ 1+X₀
t₁: l6(X₀, X₁, X₂, X₃) → l3(1, X₂, X₀, X₁) :|: 1 ≤ X₀
t₂: l6(X₀, X₁, X₂, X₃) → l3(-1, X₂, X₀, X₁) :|: X₀ ≤ 0
Chain transitions t₅: l4→l1 and t₇: l1→l3 to t₈₉: l4→l3
Chain transitions t₆: l4→l2 and t₈: l2→l3 to t₉₀: l4→l3
Chain transitions t₂: l6→l3 and t₄: l3→l5 to t₉₁: l6→l5
Chain transitions t₁: l6→l3 and t₄: l3→l5 to t₉₂: l6→l5
Chain transitions t₁: l6→l3 and t₃: l3→l4 to t₉₃: l6→l4
Chain transitions t₂: l6→l3 and t₃: l3→l4 to t₉₄: l6→l4
Chain transitions t₉₀: l4→l3 and t₃: l3→l4 to t₉₅: l4→l4
Chain transitions t₉₀: l4→l3 and t₄: l3→l5 to t₉₆: l4→l5
Chain transitions t₈₉: l4→l3 and t₃: l3→l4 to t₉₇: l4→l4
Chain transitions t₈₉: l4→l3 and t₄: l3→l5 to t₉₈: l4→l5
Analysing control-flow refined program
Found invariant X₃ ≤ X₁ ∧ X₂ ≤ 0 ∧ X₂ ≤ 1+X₀ ∧ X₀+X₂ ≤ 1 ∧ X₀ ≤ 1 ∧ 0 ≤ 1+X₀ for location l2
Found invariant 1+X₁ ≤ X₃ ∧ X₀ ≤ 1 ∧ 0 ≤ 1+X₀ for location l7
Found invariant X₁ ≤ 1+X₃ ∧ X₀ ≤ 1 ∧ 0 ≤ 1+X₀ for location l5
Found invariant X₃ ≤ X₁ ∧ 1 ≤ X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₀ ≤ 1 ∧ 0 ≤ 1+X₀ for location l1
Found invariant X₃ ≤ 1+X₁ ∧ X₀ ≤ 1 ∧ 0 ≤ 1+X₀ for location l4
Found invariant X₀ ≤ 1 ∧ 0 ≤ 1+X₀ for location l3
CFR did not improve the program. Rolling back
CFR did not improve the program. Rolling back
Analysing control-flow refined program
Found invariant X₃ ≤ 1+X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ for location n_l3___4
Found invariant X₃ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ for location n_l4___6
Found invariant X₃ ≤ X₁ ∧ X₂ ≤ 0 ∧ X₂ ≤ 1+X₀ ∧ 1+X₀+X₂ ≤ 0 ∧ 1+X₀ ≤ 0 ∧ 0 ≤ 1+X₀ for location n_l4___3
Found invariant X₃ ≤ X₁ ∧ X₂ ≤ 0 ∧ X₂ ≤ 1+X₀ ∧ 1+X₀+X₂ ≤ 0 ∧ 1+X₀ ≤ 0 ∧ 0 ≤ 1+X₀ for location n_l2___2
Found invariant 1+X₁ ≤ X₃ ∧ X₀ ≤ 1 ∧ 0 ≤ 1+X₀ for location l7
Found invariant 1+X₁ ≤ X₃ ∧ X₀ ≤ 1 ∧ 0 ≤ 1+X₀ for location l5
Found invariant X₃ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ for location n_l1___5
Found invariant X₃ ≤ 1+X₁ ∧ X₂ ≤ 0 ∧ X₂ ≤ 1+X₀ ∧ 1+X₀+X₂ ≤ 0 ∧ 1+X₀ ≤ 0 ∧ 0 ≤ 1+X₀ for location n_l3___1
Found invariant X₀ ≤ 1 ∧ 0 ≤ 1+X₀ for location l3
MPRF for transition t₂₁₈: n_l2___2(X₀, X₁, X₂, X₃) → n_l3___1(X₀, X₁, X₂, X₃-X₀) :|: X₀+1 ≤ 0 ∧ X₂ ≤ 0 ∧ X₃ ≤ X₁ ∧ 0 ≤ 1+X₀ ∧ X₃ ≤ X₁ ∧ X₂ ≤ 0 ∧ X₀ ≤ 1 ∧ 0 ≤ 1+X₀ ∧ X₃ ≤ X₁ ∧ X₂ ≤ 0 ∧ X₂ ≤ 1+X₀ ∧ 1+X₀+X₂ ≤ 0 ∧ 1+X₀ ≤ 0 ∧ 0 ≤ 1+X₀ of depth 1:
new bound:
X₁+X₂+1 {O(n)}
MPRF for transition t₂₁₉: n_l3___1(X₀, X₁, X₂, X₃) → n_l4___3(X₀, X₁, X₂, X₃) :|: X₂ ≤ 0 ∧ 1+X₀ ≤ 0 ∧ X₂ ≤ 0 ∧ X₀+X₃ ≤ X₁ ∧ X₂ ≤ 0 ∧ X₃ ≤ X₁ ∧ X₀ ≤ 1 ∧ 0 ≤ 1+X₀ ∧ 0 ≤ 1+X₀ ∧ 0 ≤ 1+X₀ ∧ X₀ ≤ 1 ∧ 0 ≤ 1+X₀ ∧ X₀ ≤ 1 ∧ X₃ ≤ 1+X₁ ∧ X₂ ≤ 0 ∧ X₂ ≤ 1+X₀ ∧ 1+X₀+X₂ ≤ 0 ∧ 1+X₀ ≤ 0 ∧ 0 ≤ 1+X₀ of depth 1:
new bound:
X₁+X₂ {O(n)}
MPRF for transition t₂₂₃: n_l4___3(X₀, X₁, X₂, X₃) → n_l2___2(X₀, X₁, X₂, X₃) :|: X₂ ≤ 0 ∧ X₀+1 ≤ 0 ∧ X₂ ≤ 0 ∧ X₃ ≤ X₁ ∧ 0 ≤ 1+X₀ ∧ 0 ≤ 1+X₀ ∧ X₃ ≤ X₁ ∧ X₀ ≤ 1 ∧ X₃ ≤ X₁ ∧ X₂ ≤ 0 ∧ X₂ ≤ 1+X₀ ∧ 1+X₀+X₂ ≤ 0 ∧ 1+X₀ ≤ 0 ∧ 0 ≤ 1+X₀ of depth 1:
new bound:
X₁+X₂+1 {O(n)}
MPRF for transition t₂₁₇: n_l1___5(X₀, X₁, X₂, X₃) → n_l3___4(X₀, X₁, X₂, X₀+X₃) :|: X₀ ≤ 1 ∧ 1 ≤ X₀ ∧ 1 ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₃ ≤ X₁ ∧ 1 ≤ X₂ ∧ 0 ≤ 1+X₀ ∧ X₀ ≤ 1 ∧ X₃ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ of depth 1:
new bound:
X₁+X₂+1 {O(n)}
MPRF for transition t₂₂₀: n_l3___4(X₀, X₁, X₂, X₃) → n_l4___6(X₀, X₁, X₂, X₃) :|: 1 ≤ X₂ ∧ 1 ≤ X₀ ∧ 1 ≤ X₂ ∧ 1 ≤ X₂ ∧ X₃ ≤ X₀+X₁ ∧ X₃ ≤ X₁ ∧ X₀ ≤ 1 ∧ 0 ≤ 1+X₀ ∧ X₀ ≤ 1 ∧ 0 ≤ 1+X₀ ∧ X₀ ≤ 1 ∧ 0 ≤ 1+X₀ ∧ X₀ ≤ 1 ∧ X₃ ≤ 1+X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ of depth 1:
new bound:
X₁+X₂+1 {O(n)}
MPRF for transition t₂₂₄: n_l4___6(X₀, X₁, X₂, X₃) → n_l1___5(X₀, X₁, X₂, X₃) :|: 1 ≤ X₂ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ ∧ 1 ≤ X₂ ∧ X₃ ≤ X₁ ∧ 0 ≤ 1+X₀ ∧ X₃ ≤ X₁ ∧ X₀ ≤ 1 ∧ X₃ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ of depth 1:
new bound:
X₁+X₂+1 {O(n)}
CFR: Improvement to new bound with the following program:
new bound:
Infinite
cfr-program:
Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l3, l5, l6, l7, n_l1___5, n_l2___2, n_l3___1, n_l3___4, n_l4___3, n_l4___6
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l6(X₀, X₁, X₂, X₃)
t₄: l3(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₁+1 ≤ X₃ ∧ X₀ ≤ 1 ∧ 0 ≤ 1+X₀ ∧ X₀ ≤ 1 ∧ 0 ≤ 1+X₀
t₂₂₁: l3(X₀, X₁, X₂, X₃) → n_l4___3(X₀, X₁, X₂, X₃) :|: X₂ ≤ 0 ∧ 1+X₀ ≤ 0 ∧ X₂ ≤ 0 ∧ X₃ ≤ X₁ ∧ X₀ ≤ 1 ∧ 0 ≤ 1+X₀ ∧ 0 ≤ 1+X₀ ∧ 0 ≤ 1+X₀ ∧ X₀ ≤ 1 ∧ X₀ ≤ 1 ∧ 0 ≤ 1+X₀
t₂₂₂: l3(X₀, X₁, X₂, X₃) → n_l4___6(X₀, X₁, X₂, X₃) :|: 1 ≤ X₂ ∧ 1 ≤ X₀ ∧ 1 ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₀ ≤ 1 ∧ 0 ≤ 1+X₀ ∧ X₀ ≤ 1 ∧ 0 ≤ 1+X₀ ∧ X₀ ≤ 1 ∧ X₀ ≤ 1 ∧ 0 ≤ 1+X₀
t₉: l5(X₀, X₁, X₂, X₃) → l7(X₀, X₁, X₂, X₃) :|: 1+X₁ ≤ X₃ ∧ X₀ ≤ 1 ∧ 0 ≤ 1+X₀ ∧ 1+X₁ ≤ X₃ ∧ X₀ ≤ 1 ∧ 0 ≤ 1+X₀
t₁: l6(X₀, X₁, X₂, X₃) → l3(1, X₂, X₀, X₁) :|: 1 ≤ X₀
t₂: l6(X₀, X₁, X₂, X₃) → l3(-1, X₂, X₀, X₁) :|: X₀ ≤ 0
t₂₁₇: n_l1___5(X₀, X₁, X₂, X₃) → n_l3___4(X₀, X₁, X₂, X₀+X₃) :|: X₀ ≤ 1 ∧ 1 ≤ X₀ ∧ 1 ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₃ ≤ X₁ ∧ 1 ≤ X₂ ∧ 0 ≤ 1+X₀ ∧ X₀ ≤ 1 ∧ X₃ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀
t₂₁₈: n_l2___2(X₀, X₁, X₂, X₃) → n_l3___1(X₀, X₁, X₂, X₃-X₀) :|: X₀+1 ≤ 0 ∧ X₂ ≤ 0 ∧ X₃ ≤ X₁ ∧ 0 ≤ 1+X₀ ∧ X₃ ≤ X₁ ∧ X₂ ≤ 0 ∧ X₀ ≤ 1 ∧ 0 ≤ 1+X₀ ∧ X₃ ≤ X₁ ∧ X₂ ≤ 0 ∧ X₂ ≤ 1+X₀ ∧ 1+X₀+X₂ ≤ 0 ∧ 1+X₀ ≤ 0 ∧ 0 ≤ 1+X₀
t₂₃₃: n_l3___1(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₁+1 ≤ X₃ ∧ X₀ ≤ 1 ∧ 0 ≤ 1+X₀ ∧ X₃ ≤ 1+X₁ ∧ X₂ ≤ 0 ∧ X₂ ≤ 1+X₀ ∧ 1+X₀+X₂ ≤ 0 ∧ 1+X₀ ≤ 0 ∧ 0 ≤ 1+X₀
t₂₁₉: n_l3___1(X₀, X₁, X₂, X₃) → n_l4___3(X₀, X₁, X₂, X₃) :|: X₂ ≤ 0 ∧ 1+X₀ ≤ 0 ∧ X₂ ≤ 0 ∧ X₀+X₃ ≤ X₁ ∧ X₂ ≤ 0 ∧ X₃ ≤ X₁ ∧ X₀ ≤ 1 ∧ 0 ≤ 1+X₀ ∧ 0 ≤ 1+X₀ ∧ 0 ≤ 1+X₀ ∧ X₀ ≤ 1 ∧ 0 ≤ 1+X₀ ∧ X₀ ≤ 1 ∧ X₃ ≤ 1+X₁ ∧ X₂ ≤ 0 ∧ X₂ ≤ 1+X₀ ∧ 1+X₀+X₂ ≤ 0 ∧ 1+X₀ ≤ 0 ∧ 0 ≤ 1+X₀
t₂₃₄: n_l3___4(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₁+1 ≤ X₃ ∧ X₀ ≤ 1 ∧ 0 ≤ 1+X₀ ∧ X₃ ≤ 1+X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀
t₂₂₀: n_l3___4(X₀, X₁, X₂, X₃) → n_l4___6(X₀, X₁, X₂, X₃) :|: 1 ≤ X₂ ∧ 1 ≤ X₀ ∧ 1 ≤ X₂ ∧ 1 ≤ X₂ ∧ X₃ ≤ X₀+X₁ ∧ X₃ ≤ X₁ ∧ X₀ ≤ 1 ∧ 0 ≤ 1+X₀ ∧ X₀ ≤ 1 ∧ 0 ≤ 1+X₀ ∧ X₀ ≤ 1 ∧ 0 ≤ 1+X₀ ∧ X₀ ≤ 1 ∧ X₃ ≤ 1+X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀
t₂₂₃: n_l4___3(X₀, X₁, X₂, X₃) → n_l2___2(X₀, X₁, X₂, X₃) :|: X₂ ≤ 0 ∧ X₀+1 ≤ 0 ∧ X₂ ≤ 0 ∧ X₃ ≤ X₁ ∧ 0 ≤ 1+X₀ ∧ 0 ≤ 1+X₀ ∧ X₃ ≤ X₁ ∧ X₀ ≤ 1 ∧ X₃ ≤ X₁ ∧ X₂ ≤ 0 ∧ X₂ ≤ 1+X₀ ∧ 1+X₀+X₂ ≤ 0 ∧ 1+X₀ ≤ 0 ∧ 0 ≤ 1+X₀
t₂₂₄: n_l4___6(X₀, X₁, X₂, X₃) → n_l1___5(X₀, X₁, X₂, X₃) :|: 1 ≤ X₂ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ ∧ 1 ≤ X₂ ∧ X₃ ≤ X₁ ∧ 0 ≤ 1+X₀ ∧ X₃ ≤ X₁ ∧ X₀ ≤ 1 ∧ X₃ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀
CFR: Improvement to new bound with the following program:
new bound:
6⋅X₁+6⋅X₂+5 {O(n)}
cfr-program:
Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l3, l5, l6, l7, n_l1___5, n_l2___2, n_l3___1, n_l3___4, n_l4___3, n_l4___6
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l6(X₀, X₁, X₂, X₃)
t₄: l3(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₁+1 ≤ X₃ ∧ X₀ ≤ 1 ∧ 0 ≤ 1+X₀ ∧ X₀ ≤ 1 ∧ 0 ≤ 1+X₀
t₂₂₁: l3(X₀, X₁, X₂, X₃) → n_l4___3(X₀, X₁, X₂, X₃) :|: X₂ ≤ 0 ∧ 1+X₀ ≤ 0 ∧ X₂ ≤ 0 ∧ X₃ ≤ X₁ ∧ X₀ ≤ 1 ∧ 0 ≤ 1+X₀ ∧ 0 ≤ 1+X₀ ∧ 0 ≤ 1+X₀ ∧ X₀ ≤ 1 ∧ X₀ ≤ 1 ∧ 0 ≤ 1+X₀
t₂₂₂: l3(X₀, X₁, X₂, X₃) → n_l4___6(X₀, X₁, X₂, X₃) :|: 1 ≤ X₂ ∧ 1 ≤ X₀ ∧ 1 ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₀ ≤ 1 ∧ 0 ≤ 1+X₀ ∧ X₀ ≤ 1 ∧ 0 ≤ 1+X₀ ∧ X₀ ≤ 1 ∧ X₀ ≤ 1 ∧ 0 ≤ 1+X₀
t₉: l5(X₀, X₁, X₂, X₃) → l7(X₀, X₁, X₂, X₃) :|: 1+X₁ ≤ X₃ ∧ X₀ ≤ 1 ∧ 0 ≤ 1+X₀ ∧ 1+X₁ ≤ X₃ ∧ X₀ ≤ 1 ∧ 0 ≤ 1+X₀
t₁: l6(X₀, X₁, X₂, X₃) → l3(1, X₂, X₀, X₁) :|: 1 ≤ X₀
t₂: l6(X₀, X₁, X₂, X₃) → l3(-1, X₂, X₀, X₁) :|: X₀ ≤ 0
t₂₁₇: n_l1___5(X₀, X₁, X₂, X₃) → n_l3___4(X₀, X₁, X₂, X₀+X₃) :|: X₀ ≤ 1 ∧ 1 ≤ X₀ ∧ 1 ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₃ ≤ X₁ ∧ 1 ≤ X₂ ∧ 0 ≤ 1+X₀ ∧ X₀ ≤ 1 ∧ X₃ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀
t₂₁₈: n_l2___2(X₀, X₁, X₂, X₃) → n_l3___1(X₀, X₁, X₂, X₃-X₀) :|: X₀+1 ≤ 0 ∧ X₂ ≤ 0 ∧ X₃ ≤ X₁ ∧ 0 ≤ 1+X₀ ∧ X₃ ≤ X₁ ∧ X₂ ≤ 0 ∧ X₀ ≤ 1 ∧ 0 ≤ 1+X₀ ∧ X₃ ≤ X₁ ∧ X₂ ≤ 0 ∧ X₂ ≤ 1+X₀ ∧ 1+X₀+X₂ ≤ 0 ∧ 1+X₀ ≤ 0 ∧ 0 ≤ 1+X₀
t₂₃₃: n_l3___1(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₁+1 ≤ X₃ ∧ X₀ ≤ 1 ∧ 0 ≤ 1+X₀ ∧ X₃ ≤ 1+X₁ ∧ X₂ ≤ 0 ∧ X₂ ≤ 1+X₀ ∧ 1+X₀+X₂ ≤ 0 ∧ 1+X₀ ≤ 0 ∧ 0 ≤ 1+X₀
t₂₁₉: n_l3___1(X₀, X₁, X₂, X₃) → n_l4___3(X₀, X₁, X₂, X₃) :|: X₂ ≤ 0 ∧ 1+X₀ ≤ 0 ∧ X₂ ≤ 0 ∧ X₀+X₃ ≤ X₁ ∧ X₂ ≤ 0 ∧ X₃ ≤ X₁ ∧ X₀ ≤ 1 ∧ 0 ≤ 1+X₀ ∧ 0 ≤ 1+X₀ ∧ 0 ≤ 1+X₀ ∧ X₀ ≤ 1 ∧ 0 ≤ 1+X₀ ∧ X₀ ≤ 1 ∧ X₃ ≤ 1+X₁ ∧ X₂ ≤ 0 ∧ X₂ ≤ 1+X₀ ∧ 1+X₀+X₂ ≤ 0 ∧ 1+X₀ ≤ 0 ∧ 0 ≤ 1+X₀
t₂₃₄: n_l3___4(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₁+1 ≤ X₃ ∧ X₀ ≤ 1 ∧ 0 ≤ 1+X₀ ∧ X₃ ≤ 1+X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀
t₂₂₀: n_l3___4(X₀, X₁, X₂, X₃) → n_l4___6(X₀, X₁, X₂, X₃) :|: 1 ≤ X₂ ∧ 1 ≤ X₀ ∧ 1 ≤ X₂ ∧ 1 ≤ X₂ ∧ X₃ ≤ X₀+X₁ ∧ X₃ ≤ X₁ ∧ X₀ ≤ 1 ∧ 0 ≤ 1+X₀ ∧ X₀ ≤ 1 ∧ 0 ≤ 1+X₀ ∧ X₀ ≤ 1 ∧ 0 ≤ 1+X₀ ∧ X₀ ≤ 1 ∧ X₃ ≤ 1+X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀
t₂₂₃: n_l4___3(X₀, X₁, X₂, X₃) → n_l2___2(X₀, X₁, X₂, X₃) :|: X₂ ≤ 0 ∧ X₀+1 ≤ 0 ∧ X₂ ≤ 0 ∧ X₃ ≤ X₁ ∧ 0 ≤ 1+X₀ ∧ 0 ≤ 1+X₀ ∧ X₃ ≤ X₁ ∧ X₀ ≤ 1 ∧ X₃ ≤ X₁ ∧ X₂ ≤ 0 ∧ X₂ ≤ 1+X₀ ∧ 1+X₀+X₂ ≤ 0 ∧ 1+X₀ ≤ 0 ∧ 0 ≤ 1+X₀
t₂₂₄: n_l4___6(X₀, X₁, X₂, X₃) → n_l1___5(X₀, X₁, X₂, X₃) :|: 1 ≤ X₂ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ ∧ 1 ≤ X₂ ∧ X₃ ≤ X₁ ∧ 0 ≤ 1+X₀ ∧ X₃ ≤ X₁ ∧ X₀ ≤ 1 ∧ X₃ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀
All Bounds
Timebounds
Overall timebound:6⋅X₁+6⋅X₂+14 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₄: 1 {O(1)}
t₉: 1 {O(1)}
t₂₁₇: X₁+X₂+1 {O(n)}
t₂₁₈: X₁+X₂+1 {O(n)}
t₂₁₉: X₁+X₂ {O(n)}
t₂₂₀: X₁+X₂+1 {O(n)}
t₂₂₁: 1 {O(1)}
t₂₂₂: 1 {O(1)}
t₂₂₃: X₁+X₂+1 {O(n)}
t₂₂₄: X₁+X₂+1 {O(n)}
t₂₃₃: 1 {O(1)}
t₂₃₄: 1 {O(1)}
Costbounds
Overall costbound: 6⋅X₁+6⋅X₂+14 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₄: 1 {O(1)}
t₉: 1 {O(1)}
t₂₁₇: X₁+X₂+1 {O(n)}
t₂₁₈: X₁+X₂+1 {O(n)}
t₂₁₉: X₁+X₂ {O(n)}
t₂₂₀: X₁+X₂+1 {O(n)}
t₂₂₁: 1 {O(1)}
t₂₂₂: 1 {O(1)}
t₂₂₃: X₁+X₂+1 {O(n)}
t₂₂₄: X₁+X₂+1 {O(n)}
t₂₃₃: 1 {O(1)}
t₂₃₄: 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: 1 {O(1)}
t₁, X₁: X₂ {O(n)}
t₁, X₂: X₀ {O(n)}
t₁, X₃: X₁ {O(n)}
t₂, X₀: 1 {O(1)}
t₂, X₁: X₂ {O(n)}
t₂, X₂: X₀ {O(n)}
t₂, X₃: X₁ {O(n)}
t₄, X₀: 1 {O(1)}
t₄, X₁: 2⋅X₂ {O(n)}
t₄, X₂: 2⋅X₀ {O(n)}
t₄, X₃: 2⋅X₁ {O(n)}
t₉, X₀: 1 {O(1)}
t₉, X₁: 4⋅X₂ {O(n)}
t₉, X₂: 4⋅X₀ {O(n)}
t₉, X₃: 2⋅X₂+6⋅X₁+2 {O(n)}
t₂₁₇, X₀: 1 {O(1)}
t₂₁₇, X₁: X₂ {O(n)}
t₂₁₇, X₂: X₀ {O(n)}
t₂₁₇, X₃: 2⋅X₁+X₂+1 {O(n)}
t₂₁₈, X₀: 1 {O(1)}
t₂₁₈, X₁: X₂ {O(n)}
t₂₁₈, X₂: X₀ {O(n)}
t₂₁₈, X₃: 2⋅X₁+X₂+1 {O(n)}
t₂₁₉, X₀: 1 {O(1)}
t₂₁₉, X₁: X₂ {O(n)}
t₂₁₉, X₂: X₀ {O(n)}
t₂₁₉, X₃: 2⋅X₁+X₂+1 {O(n)}
t₂₂₀, X₀: 1 {O(1)}
t₂₂₀, X₁: X₂ {O(n)}
t₂₂₀, X₂: X₀ {O(n)}
t₂₂₀, X₃: 2⋅X₁+X₂+1 {O(n)}
t₂₂₁, X₀: 1 {O(1)}
t₂₂₁, X₁: X₂ {O(n)}
t₂₂₁, X₂: X₀ {O(n)}
t₂₂₁, X₃: X₁ {O(n)}
t₂₂₂, X₀: 1 {O(1)}
t₂₂₂, X₁: X₂ {O(n)}
t₂₂₂, X₂: X₀ {O(n)}
t₂₂₂, X₃: X₁ {O(n)}
t₂₂₃, X₀: 1 {O(1)}
t₂₂₃, X₁: X₂ {O(n)}
t₂₂₃, X₂: X₀ {O(n)}
t₂₂₃, X₃: 2⋅X₁+X₂+1 {O(n)}
t₂₂₄, X₀: 1 {O(1)}
t₂₂₄, X₁: X₂ {O(n)}
t₂₂₄, X₂: X₀ {O(n)}
t₂₂₄, X₃: 2⋅X₁+X₂+1 {O(n)}
t₂₃₃, X₀: 1 {O(1)}
t₂₃₃, X₁: X₂ {O(n)}
t₂₃₃, X₂: X₀ {O(n)}
t₂₃₃, X₃: 2⋅X₁+X₂+1 {O(n)}
t₂₃₄, X₀: 1 {O(1)}
t₂₃₄, X₁: X₂ {O(n)}
t₂₃₄, X₂: X₀ {O(n)}
t₂₃₄, X₃: 2⋅X₁+X₂+1 {O(n)}