Initial Problem
Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅
Temp_Vars:
Locations: l0, l1, l10, l2, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅) → l9(X₀, X₁, X₂, X₃, X₄, X₅)
t₇: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l4(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₅ ≤ X₃+X₄
t₈: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l5(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₃+X₄+1 ≤ X₅
t₄: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₄ ≤ X₂
t₅: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l6(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₂+1 ≤ X₄
t₆: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, X₁, X₂, X₃, X₄, X₃-X₄)
t₉: l4(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, X₁, X₂, X₃, X₄, X₅+1)
t₁₀: l5(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, X₁, X₂, X₃, X₄+1, X₅)
t₁₁: l6(X₀, X₁, X₂, X₃, X₄, X₅) → l7(X₀, X₁, X₂, X₃+1, X₄, X₅)
t₂: l7(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, X₁, X₂, X₃, X₁, X₅) :|: X₃ ≤ X₀
t₃: l7(X₀, X₁, X₂, X₃, X₄, X₅) → l8(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₀+1 ≤ X₃
t₁₂: l8(X₀, X₁, X₂, X₃, X₄, X₅) → l10(X₀, X₁, X₂, X₃, X₄, X₅)
t₁: l9(X₀, X₁, X₂, X₃, X₄, X₅) → l7(X₁, X₂, X₃, X₀, X₄, X₅)
Preprocessing
Found invariant X₁ ≤ X₄ ∧ X₃ ≤ X₀ for location l2
Found invariant 1+X₂ ≤ X₄ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ for location l6
Found invariant X₄ ≤ X₂ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₂ for location l5
Found invariant 1+X₀ ≤ X₃ for location l8
Found invariant X₄ ≤ X₂ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₂ for location l1
Found invariant 1+X₀ ≤ X₃ for location l10
Found invariant X₄ ≤ X₂ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₂ for location l4
Found invariant X₄ ≤ X₂ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₂ for location l3
Problem after Preprocessing
Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅
Temp_Vars:
Locations: l0, l1, l10, l2, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅) → l9(X₀, X₁, X₂, X₃, X₄, X₅)
t₇: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l4(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₅ ≤ X₃+X₄ ∧ X₄ ≤ X₂ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₂
t₈: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l5(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₃+X₄+1 ≤ X₅ ∧ X₄ ≤ X₂ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₂
t₄: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₄ ≤ X₂ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀
t₅: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l6(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₂+1 ≤ X₄ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀
t₆: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, X₁, X₂, X₃, X₄, X₃-X₄) :|: X₄ ≤ X₂ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₂
t₉: l4(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, X₁, X₂, X₃, X₄, X₅+1) :|: X₄ ≤ X₂ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₂
t₁₀: l5(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, X₁, X₂, X₃, X₄+1, X₅) :|: X₄ ≤ X₂ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₂
t₁₁: l6(X₀, X₁, X₂, X₃, X₄, X₅) → l7(X₀, X₁, X₂, X₃+1, X₄, X₅) :|: 1+X₂ ≤ X₄ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀
t₂: l7(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, X₁, X₂, X₃, X₁, X₅) :|: X₃ ≤ X₀
t₃: l7(X₀, X₁, X₂, X₃, X₄, X₅) → l8(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₀+1 ≤ X₃
t₁₂: l8(X₀, X₁, X₂, X₃, X₄, X₅) → l10(X₀, X₁, X₂, X₃, X₄, X₅) :|: 1+X₀ ≤ X₃
t₁: l9(X₀, X₁, X₂, X₃, X₄, X₅) → l7(X₁, X₂, X₃, X₀, X₄, X₅)
Solv. Size Bound: t₅: l2→l6 for X₃
Solv. Size Bound: t₅: l2→l6 for X₄
cycle: [t₅: l2→l6; t₁₁: l6→l7; t₂: l7→l2]
loop: (X₂+1 ≤ X₄ ∧ 1+X₃ ≤ X₀,(X₁,X₄) -> (X₁,X₁)
overappr. closed-form: 2⋅X₁ {O(n)}
runtime bound: X₀+X₃+1 {O(n)}
Solv. Size Bound - Lifting for t₅: l2→l6 and X₄: 4⋅X₂ {O(n)}
Solv. Size Bound: t₁₁: l6→l7 for X₃
Solv. Size Bound: t₁₁: l6→l7 for X₄
cycle: [t₅: l2→l6; t₂: l7→l2; t₁₁: l6→l7]
loop: (X₂+1 ≤ X₄ ∧ 1+X₃ ≤ X₀,(X₁,X₄) -> (X₁,X₁)
overappr. closed-form: 2⋅X₁ {O(n)}
runtime bound: X₀+X₃+1 {O(n)}
Solv. Size Bound - Lifting for t₁₁: l6→l7 and X₄: 4⋅X₂ {O(n)}
MPRF for transition t₂: l7(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, X₁, X₂, X₃, X₁, X₅) :|: X₃ ≤ X₀ of depth 1:
new bound:
X₀+X₁+1 {O(n)}
MPRF for transition t₅: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l6(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₂+1 ≤ X₄ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ of depth 1:
new bound:
X₀+X₁+1 {O(n)}
MPRF for transition t₁₁: l6(X₀, X₁, X₂, X₃, X₄, X₅) → l7(X₀, X₁, X₂, X₃+1, X₄, X₅) :|: 1+X₂ ≤ X₄ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ of depth 1:
new bound:
X₀+X₁+1 {O(n)}
MPRF for transition t₄: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₄ ≤ X₂ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ of depth 1:
new bound:
X₀⋅X₂+X₀⋅X₃+X₁⋅X₂+X₁⋅X₃+2⋅X₂+2⋅X₃+X₀+X₁+2 {O(n^2)}
MPRF for transition t₆: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, X₁, X₂, X₃, X₄, X₃-X₄) :|: X₄ ≤ X₂ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₂ of depth 1:
new bound:
X₀⋅X₂+X₀⋅X₃+X₁⋅X₂+X₁⋅X₃+2⋅X₂+2⋅X₃+X₀+X₁+2 {O(n^2)}
MPRF for transition t₈: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l5(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₃+X₄+1 ≤ X₅ ∧ X₄ ≤ X₂ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₂ of depth 1:
new bound:
4⋅X₀⋅X₂+4⋅X₀⋅X₃+4⋅X₁⋅X₂+4⋅X₁⋅X₃+8⋅X₂+8⋅X₃+X₀+X₁+2 {O(n^2)}
MPRF for transition t₁₀: l5(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, X₁, X₂, X₃, X₄+1, X₅) :|: X₄ ≤ X₂ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₂ of depth 1:
new bound:
X₀⋅X₂+X₀⋅X₃+X₁⋅X₂+X₁⋅X₃+2⋅X₂+2⋅X₃+X₀+X₁+2 {O(n^2)}
MPRF for transition t₇: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l4(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₅ ≤ X₃+X₄ ∧ X₄ ≤ X₂ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₂ of depth 1:
new bound:
2⋅X₀⋅X₂⋅X₃+2⋅X₀⋅X₃⋅X₃+2⋅X₁⋅X₂⋅X₃+2⋅X₁⋅X₃⋅X₃+3⋅X₀⋅X₃+3⋅X₁⋅X₃+4⋅X₂⋅X₃+4⋅X₃⋅X₃+X₀⋅X₂+X₁⋅X₂+2⋅X₂+8⋅X₃+X₀+X₁+3 {O(n^3)}
knowledge_propagation leads to new time bound 2⋅X₀⋅X₂⋅X₃+2⋅X₀⋅X₃⋅X₃+2⋅X₁⋅X₂⋅X₃+2⋅X₁⋅X₃⋅X₃+3⋅X₀⋅X₃+3⋅X₁⋅X₃+4⋅X₂⋅X₃+4⋅X₃⋅X₃+X₀⋅X₂+X₁⋅X₂+2⋅X₂+8⋅X₃+X₀+X₁+3 {O(n^3)} for transition t₉: l4(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, X₁, X₂, X₃, X₄, X₅+1) :|: X₄ ≤ X₂ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₂
Chain transitions t₉: l4→l1 and t₈: l1→l5 to t₁₂₀: l4→l5
Chain transitions t₆: l3→l1 and t₈: l1→l5 to t₁₂₁: l3→l5
Chain transitions t₆: l3→l1 and t₇: l1→l4 to t₁₂₂: l3→l4
Chain transitions t₉: l4→l1 and t₇: l1→l4 to t₁₂₃: l4→l4
Chain transitions t₂: l7→l2 and t₅: l2→l6 to t₁₂₄: l7→l6
Chain transitions t₁₀: l5→l2 and t₅: l2→l6 to t₁₂₅: l5→l6
Chain transitions t₁₀: l5→l2 and t₄: l2→l3 to t₁₂₆: l5→l3
Chain transitions t₂: l7→l2 and t₄: l2→l3 to t₁₂₇: l7→l3
Chain transitions t₁₂₇: l7→l3 and t₁₂₁: l3→l5 to t₁₂₈: l7→l5
Chain transitions t₁₂₆: l5→l3 and t₁₂₁: l3→l5 to t₁₂₉: l5→l5
Chain transitions t₁₂₆: l5→l3 and t₁₂₂: l3→l4 to t₁₃₀: l5→l4
Chain transitions t₁₂₇: l7→l3 and t₁₂₂: l3→l4 to t₁₃₁: l7→l4
Chain transitions t₁₂₆: l5→l3 and t₆: l3→l1 to t₁₃₂: l5→l1
Chain transitions t₁₂₇: l7→l3 and t₆: l3→l1 to t₁₃₃: l7→l1
Chain transitions t₁₂₄: l7→l6 and t₁₁: l6→l7 to t₁₃₄: l7→l7
Chain transitions t₁₂₅: l5→l6 and t₁₁: l6→l7 to t₁₃₅: l5→l7
Analysing control-flow refined program
Found invariant X₁ ≤ X₄ ∧ X₃ ≤ X₀ for location l2
Found invariant 1+X₂ ≤ X₄ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ for location l6
Found invariant 1+X₃ ≤ X₅ ∧ X₄ ≤ X₂ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₂ for location l5
Found invariant 1+X₀ ≤ X₃ for location l8
Found invariant X₄ ≤ X₂ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₂ for location l1
Found invariant 1+X₀ ≤ X₃ for location l10
Found invariant X₄ ≤ X₂ ∧ 0 ≤ X₄ ∧ 0 ≤ X₂+X₄ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₁ ≤ X₂ for location l4
Found invariant X₄ ≤ X₂ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₂ for location l3
Solv. Size Bound: t₁₂₀: l4→l5 for X₃
Solv. Size Bound: t₁₂₀: l4→l5 for X₄
cycle: [t₁₂₀: l4→l5; t₁₃₅: l5→l7; t₁₃₁: l7→l4]
loop: (X₃+X₄ ≤ X₅ ∧ X₂ ≤ X₄ ∧ 1+X₃ ≤ X₀ ∧ X₁ ≤ X₂ ∧ 0 ≤ 2⋅X₁,(X₁,X₄) -> (X₁,X₁)
overappr. closed-form: 2⋅X₁ {O(n)}
runtime bound: X₀+X₃+1 {O(n)}
Solv. Size Bound - Lifting for t₁₂₀: l4→l5 and X₄: 8⋅X₂ {O(n)}
Solv. Size Bound: t₁₃₅: l5→l7 for X₃
Solv. Size Bound: t₁₃₅: l5→l7 for X₄
cycle: [t₁₃₅: l5→l7; t₁₃₁: l7→l4; t₁₂₀: l4→l5]
loop: (X₂ ≤ X₄ ∧ 1+X₃ ≤ X₀ ∧ X₁ ≤ X₂ ∧ 0 ≤ 2⋅X₁ ∧ 2⋅X₁ ≤ 0,(X₁,X₄) -> (X₁,X₁)
overappr. closed-form: 2⋅X₁ {O(n)}
runtime bound: X₀+X₃+1 {O(n)}
Solv. Size Bound - Lifting for t₁₃₅: l5→l7 and X₄: 8⋅X₂ {O(n)}
MPRF for transition t₁₂₈: l7(X₀, X₁, X₂, X₃, X₄, X₅) -{4}> l5(X₀, X₁, X₂, X₃, X₁, X₃-X₁) :|: X₃ ≤ X₀ ∧ X₁ ≤ X₂ ∧ 2⋅X₁+1 ≤ 0 ∧ 0 ≤ 0 ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₂ ∧ 0 ≤ 0 ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ 0 ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₂ of depth 1:
new bound:
X₀+X₁+1 {O(n)}
MPRF for transition t₁₃₁: l7(X₀, X₁, X₂, X₃, X₄, X₅) -{4}> l4(X₀, X₁, X₂, X₃, X₁, X₃-X₁) :|: X₃ ≤ X₀ ∧ X₁ ≤ X₂ ∧ 0 ≤ 2⋅X₁ ∧ 0 ≤ 0 ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₂ ∧ 0 ≤ 0 ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ 0 ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₂ of depth 1:
new bound:
X₀+X₁+1 {O(n)}
MPRF for transition t₁₃₄: l7(X₀, X₁, X₂, X₃, X₄, X₅) -{3}> l7(X₀, X₁, X₂, X₃+1, X₁, X₅) :|: X₃ ≤ X₀ ∧ X₂+1 ≤ X₁ ∧ 0 ≤ 0 ∧ X₃ ≤ X₀ ∧ 1+X₂ ≤ X₁ ∧ 0 ≤ 0 ∧ X₃ ≤ X₀ of depth 1:
new bound:
X₀+X₁+1 {O(n)}
MPRF for transition t₁₃₅: l5(X₀, X₁, X₂, X₃, X₄, X₅) -{3}> l7(X₀, X₁, X₂, X₃+1, 1+X₄, X₅) :|: X₂ ≤ X₄ ∧ X₄ ≤ X₂ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₂ ∧ X₁ ≤ X₄+1 ∧ X₃ ≤ X₀ ∧ X₂ ≤ X₄ ∧ X₁ ≤ 1+X₄ ∧ X₃ ≤ X₀ ∧ 1+X₃ ≤ X₅ ∧ X₄ ≤ X₂ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₂ of depth 1:
new bound:
X₀+X₁+1 {O(n)}
TWN: t₁₂₉: l5→l5
cycle: [t₁₂₉: l5→l5]
loop: (1+X₄ ≤ X₂ ∧ 3+2⋅X₄ ≤ 0,(X₂,X₄) -> (X₂,1+X₄)
order: [X₂; X₄]
closed-form:
X₂: X₂
X₄: X₄ + [[n != 0]] * n^1
Termination: true
Formula:
2 < 0 ∧ 1 < 0
∨ 2 < 0 ∧ 1+X₄ < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 2 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₄ ≤ X₂ ∧ X₂ ≤ 1+X₄
∨ 3+2⋅X₄ < 0 ∧ 2 ≤ 0 ∧ 0 ≤ 2 ∧ 1 < 0
∨ 3+2⋅X₄ < 0 ∧ 2 ≤ 0 ∧ 0 ≤ 2 ∧ 1+X₄ < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 3+2⋅X₄ < 0 ∧ 2 ≤ 0 ∧ 0 ≤ 2 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₄ ≤ X₂ ∧ X₂ ≤ 1+X₄
∨ 2 ≤ 0 ∧ 0 ≤ 2 ∧ 3+2⋅X₄ ≤ 0 ∧ 0 ≤ 3+2⋅X₄ ∧ 1 < 0
∨ 2 ≤ 0 ∧ 0 ≤ 2 ∧ 3+2⋅X₄ ≤ 0 ∧ 0 ≤ 3+2⋅X₄ ∧ 1+X₄ < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 2 ≤ 0 ∧ 0 ≤ 2 ∧ 3+2⋅X₄ ≤ 0 ∧ 0 ≤ 3+2⋅X₄ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₄ ≤ X₂ ∧ X₂ ≤ 1+X₄
Stabilization-Threshold for: 3+2⋅X₄ ≤ 0
alphas_abs: 3+2⋅X₄
M: 0
N: 1
Bound: 4⋅X₄+8 {O(n)}
Stabilization-Threshold for: 1+X₄ ≤ X₂
alphas_abs: 1+X₄+X₂
M: 0
N: 1
Bound: 2⋅X₂+2⋅X₄+4 {O(n)}
TWN - Lifting for t₁₂₉: l5→l5 of 2⋅X₂+6⋅X₄+14 {O(n)}
relevant size-bounds w.r.t. t₁₂₈:
X₂: X₃ {O(n)}
X₄: 2⋅X₂ {O(n)}
Runtime-bound of t₁₂₈: X₀+X₁+1 {O(n)}
Results in: 12⋅X₀⋅X₂+12⋅X₁⋅X₂+2⋅X₀⋅X₃+2⋅X₁⋅X₃+12⋅X₂+14⋅X₀+14⋅X₁+2⋅X₃+14 {O(n^2)}
MPRF for transition t₁₂₀: l4(X₀, X₁, X₂, X₃, X₄, X₅) -{2}> l5(X₀, X₁, X₂, X₃, X₄, 1+X₅) :|: X₃+X₄ ≤ X₅ ∧ X₄ ≤ X₂ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₂ ∧ X₄ ≤ X₂ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₂ ∧ X₄ ≤ X₂ ∧ 0 ≤ X₄ ∧ 0 ≤ X₂+X₄ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₁ ≤ X₂ of depth 1:
new bound:
X₀⋅X₂+X₀⋅X₃+X₁⋅X₂+X₁⋅X₃+2⋅X₂+2⋅X₃+X₀+X₁+2 {O(n^2)}
MPRF for transition t₁₃₀: l5(X₀, X₁, X₂, X₃, X₄, X₅) -{4}> l4(X₀, X₁, X₂, X₃, 1+X₄, X₃-1-X₄) :|: 1+X₄ ≤ X₂ ∧ 0 ≤ 2+2⋅X₄ ∧ X₄ ≤ X₂ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₂ ∧ X₁ ≤ X₄+1 ∧ X₃ ≤ X₀ ∧ 1+X₄ ≤ X₂ ∧ X₁ ≤ 1+X₄ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₂ ∧ 1+X₄ ≤ X₂ ∧ X₁ ≤ 1+X₄ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₂ ∧ 1+X₃ ≤ X₅ ∧ X₄ ≤ X₂ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₂ of depth 1:
new bound:
X₀⋅X₂+X₀⋅X₃+X₁⋅X₂+X₁⋅X₃+2⋅X₂+2⋅X₃+X₀+X₁+2 {O(n^2)}
MPRF for transition t₁₂₃: l4(X₀, X₁, X₂, X₃, X₄, X₅) -{2}> l4(X₀, X₁, X₂, X₃, X₄, 1+X₅) :|: 1+X₅ ≤ X₃+X₄ ∧ X₄ ≤ X₂ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₂ ∧ X₄ ≤ X₂ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₂ ∧ X₄ ≤ X₂ ∧ 0 ≤ X₄ ∧ 0 ≤ X₂+X₄ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₁ ≤ X₂ of depth 1:
new bound:
2⋅X₀⋅X₀⋅X₂⋅X₃+2⋅X₀⋅X₁⋅X₂⋅X₂+2⋅X₀⋅X₁⋅X₃⋅X₃+2⋅X₁⋅X₁⋅X₂⋅X₃+4⋅X₀⋅X₁⋅X₂⋅X₃+X₀⋅X₀⋅X₂⋅X₂+X₀⋅X₀⋅X₃⋅X₃+X₁⋅X₁⋅X₂⋅X₂+X₁⋅X₁⋅X₃⋅X₃+10⋅X₀⋅X₀⋅X₂+10⋅X₀⋅X₀⋅X₃+16⋅X₀⋅X₁⋅X₂+16⋅X₀⋅X₁⋅X₃+22⋅X₀⋅X₂⋅X₂+22⋅X₁⋅X₂⋅X₂+26⋅X₀⋅X₂⋅X₃+26⋅X₁⋅X₂⋅X₃+4⋅X₀⋅X₃⋅X₃+4⋅X₁⋅X₃⋅X₃+6⋅X₁⋅X₁⋅X₂+6⋅X₁⋅X₁⋅X₃+14⋅X₀⋅X₁+23⋅X₁⋅X₃+31⋅X₀⋅X₃+4⋅X₃⋅X₃+40⋅X₂⋅X₂+43⋅X₁⋅X₂+44⋅X₂⋅X₃+5⋅X₁⋅X₁+51⋅X₀⋅X₂+9⋅X₀⋅X₀+19⋅X₁+22⋅X₃+27⋅X₀+62⋅X₂+18 {O(n^4)}
CFR did not improve the program. Rolling back
CFR did not improve the program. Rolling back
Analysing control-flow refined program
Found invariant X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ for location l2
Found invariant 1+X₂ ≤ X₄ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ for location l6
Found invariant X₄ ≤ X₂ ∧ 0 ≤ X₄ ∧ 0 ≤ X₂+X₄ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₁ ≤ X₂ for location n_l4___4
Found invariant X₄ ≤ X₂ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₂ for location n_l5___6
Found invariant X₄ ≤ X₂ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₂ for location n_l1___8
Found invariant X₄ ≤ 1+X₂ ∧ 1+X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₂ for location n_l2___2
Found invariant 1+X₀ ≤ X₃ for location l8
Found invariant X₄ ≤ X₂ ∧ 0 ≤ X₄ ∧ 0 ≤ X₂+X₄ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₁ ≤ X₂ for location n_l1___5
Found invariant X₄ ≤ X₂ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₂ for location n_l3___9
Found invariant 1+X₀ ≤ X₃ for location l10
Found invariant X₄ ≤ X₂ ∧ 1+X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ 1+X₁ ≤ X₂ for location n_l3___1
Found invariant X₄ ≤ X₂ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₂ for location n_l4___7
Found invariant 1+X₃ ≤ X₅ ∧ X₄ ≤ X₂ ∧ 0 ≤ X₄ ∧ 0 ≤ X₂+X₄ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₁ ≤ X₂ for location n_l5___3
Solv. Size Bound: t₃₃₄: n_l1___5→n_l5___3 for X₄
cycle: [t₃₃₄: n_l1___5→n_l5___3; t₃₄₃: n_l5___3→n_l2___2; t₃₅₄: n_l2___2→l6; t₁₁: l6→l7; t₂: l7→l2; t₃₃₇: l2→n_l3___9; t₃₄₀: n_l3___9→n_l1___8; t₃₃₅: n_l1___8→n_l4___7; t₃₄₂: n_l4___7→n_l1___5]
loop: (1+X₃+X₄ ≤ X₅ ∧ 1+X₃+X₄ ≤ X₅ ∧ X₂ ≤ X₄ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ 0 ∧ X₁ ≤ X₂ ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ 2⋅X₁ ∧ 0 ≤ X₁ ∧ 0 ≤ 0 ∧ 0 ≤ 0,(X₁,X₄) -> (X₁,X₁)
overappr. closed-form: 2⋅X₁ {O(n)}
runtime bound: X₀+X₃+1 {O(n)}
Solv. Size Bound - Lifting for t₃₃₄: n_l1___5→n_l5___3 and X₄: 8⋅X₂ {O(n)}
Solv. Size Bound: t₃₃₅: n_l1___8→n_l4___7 for X₄
cycle: [t₃₃₅: n_l1___8→n_l4___7; t₃₄₂: n_l4___7→n_l1___5; t₃₃₄: n_l1___5→n_l5___3; t₃₄₃: n_l5___3→n_l2___2; t₃₅₄: n_l2___2→l6; t₁₁: l6→l7; t₂: l7→l2; t₃₃₇: l2→n_l3___9; t₃₄₀: n_l3___9→n_l1___8]
loop: (X₃ ≤ X₄+X₅ ∧ X₄+X₅ ≤ X₃ ∧ X₄+X₅ ≤ X₀ ∧ X₅ ≤ X₃+X₄ ∧ 0 ≤ X₄ ∧ X₃ ≤ X₄+X₅ ∧ X₄+X₅ ≤ X₃ ∧ X₃+X₄ ≤ X₅ ∧ X₃+X₄ ≤ X₅ ∧ X₂ ≤ X₄ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ 0 ∧ X₁ ≤ X₂ ∧ 0 ≤ 0,(X₁,X₄) -> (X₁,X₁)
overappr. closed-form: 2⋅X₁ {O(n)}
runtime bound: X₀+X₃+1 {O(n)}
Solv. Size Bound - Lifting for t₃₃₅: n_l1___8→n_l4___7 and X₄: 8⋅X₂ {O(n)}
Solv. Size Bound: t₃₃₆: n_l1___8→n_l5___6 for X₄
cycle: [t₃₃₆: n_l1___8→n_l5___6; t₃₄₄: n_l5___6→n_l2___2; t₃₅₄: n_l2___2→l6; t₁₁: l6→l7; t₂: l7→l2; t₃₃₇: l2→n_l3___9; t₃₄₀: n_l3___9→n_l1___8]
loop: (X₃ ≤ X₄+X₅ ∧ X₄+X₅ ≤ X₃ ∧ X₄+X₅ ≤ X₀ ∧ 1+X₃+X₄ ≤ X₅ ∧ 1+2⋅X₄ ≤ 0 ∧ X₄+X₅ ≤ X₀ ∧ X₃ ≤ X₄+X₅ ∧ X₄+X₅ ≤ X₃ ∧ X₂ ≤ X₄ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ 0 ∧ X₁ ≤ X₂ ∧ 0 ≤ 0,(X₁,X₄) -> (X₁,X₁)
overappr. closed-form: 2⋅X₁ {O(n)}
runtime bound: X₀+X₃+2 {O(n)}
Solv. Size Bound - Lifting for t₃₃₆: n_l1___8→n_l5___6 and X₄: 8⋅X₂ {O(n)}
Solv. Size Bound: t₃₄₃: n_l5___3→n_l2___2 for X₄
cycle: [t₃₃₄: n_l1___5→n_l5___3; t₃₄₂: n_l4___7→n_l1___5; t₃₃₅: n_l1___8→n_l4___7; t₃₄₀: n_l3___9→n_l1___8; t₃₃₇: l2→n_l3___9; t₂: l7→l2; t₁₁: l6→l7; t₃₅₄: n_l2___2→l6; t₃₄₃: n_l5___3→n_l2___2]
loop: (1+X₃+X₄ ≤ X₅ ∧ 2+X₃+X₄ ≤ X₅ ∧ 0 ≤ 1+X₄ ∧ X₃ ≤ 1+X₄+X₅ ∧ 1+X₄+X₅ ≤ X₃ ∧ X₃ ≤ 2+X₄+X₅ ∧ 2+X₄+X₅ ≤ X₃ ∧ 2+X₄+X₅ ≤ X₀ ∧ X₅ ≤ X₃+X₄ ∧ 1+X₄ ≤ X₁ ∧ 1+X₄ ≤ X₁ ∧ 1+X₄ ≤ X₂ ∧ X₃ ≤ X₀ ∧ X₂+1 ≤ X₁,(X₁,X₄) -> (X₁,X₁)
overappr. closed-form: 2⋅X₁ {O(n)}
runtime bound: X₀+X₃+2 {O(n)}
Solv. Size Bound - Lifting for t₃₄₃: n_l5___3→n_l2___2 and X₄: 8⋅X₂ {O(n)}
Solv. Size Bound: t₃₄₄: n_l5___6→n_l2___2 for X₄
cycle: [t₃₃₆: n_l1___8→n_l5___6; t₃₄₀: n_l3___9→n_l1___8; t₃₃₇: l2→n_l3___9; t₂: l7→l2; t₁₁: l6→l7; t₃₅₄: n_l2___2→l6; t₃₄₄: n_l5___6→n_l2___2]
loop: (1+2⋅X₄ ≤ 0 ∧ X₄+X₅ ≤ X₀ ∧ X₃ ≤ X₄+X₅ ∧ X₄+X₅ ≤ X₃ ∧ X₃ ≤ X₄+1+X₅ ∧ X₄+1+X₅ ≤ X₃ ∧ X₄+1+X₅ ≤ X₀ ∧ 2+X₃+X₄ ≤ X₅ ∧ 1+X₄ ≤ X₁ ∧ 1+X₄ ≤ X₁ ∧ 1+X₄ ≤ X₂ ∧ X₃ ≤ X₀ ∧ X₂+1 ≤ X₁,(X₁,X₄) -> (X₁,X₁)
overappr. closed-form: 2⋅X₁ {O(n)}
runtime bound: X₀+X₃+2 {O(n)}
Solv. Size Bound - Lifting for t₃₄₄: n_l5___6→n_l2___2 and X₄: 8⋅X₂ {O(n)}
Solv. Size Bound: t₃₅₄: n_l2___2→l6 for X₄
cycle: [t₃₄₄: n_l5___6→n_l2___2; t₃₃₆: n_l1___8→n_l5___6; t₃₄₀: n_l3___9→n_l1___8; t₃₃₇: l2→n_l3___9; t₂: l7→l2; t₁₁: l6→l7; t₃₅₄: n_l2___2→l6]
loop: (X₂+1 ≤ X₄ ∧ 1+2⋅X₄ ≤ 0 ∧ X₄+X₅ ≤ X₀ ∧ X₃ ≤ X₄+X₅ ∧ X₄+X₅ ≤ X₃ ∧ X₃ ≤ X₄+1+X₅ ∧ X₄+1+X₅ ≤ X₃ ∧ X₄+1+X₅ ≤ X₀ ∧ 2+X₃+X₄ ≤ X₅ ∧ 1+X₄ ≤ X₁ ∧ 1+X₄ ≤ X₁ ∧ 1+X₄ ≤ X₂ ∧ X₃ ≤ X₀,(X₁,X₄) -> (X₁,X₁)
overappr. closed-form: 2⋅X₁ {O(n)}
runtime bound: X₀+X₃+2 {O(n)}
Solv. Size Bound - Lifting for t₃₅₄: n_l2___2→l6 and X₄: 8⋅X₂ {O(n)}
knowledge_propagation leads to new time bound X₀+X₁+1 {O(n)} for transition t₃₃₇: l2(X₀, X₁, X₂, X₃, X₄, X₅) → n_l3___9(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₄ ≤ X₁ ∧ X₄ ≤ X₂ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₄ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀
knowledge_propagation leads to new time bound X₀+X₁+1 {O(n)} for transition t₃₄₀: n_l3___9(X₀, X₁, X₂, X₃, X₄, X₅) → n_l1___8(X₀, X₁, X₂, X₃, X₄, X₃-X₄) :|: X₄ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₄ ∧ X₄ ≤ X₂ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₄ ∧ X₄ ≤ X₂ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₂
MPRF for transition t₃₃₄: n_l1___5(X₀, X₁, X₂, X₃, X₄, X₅) → n_l5___3(X₀, X₁, X₂, X₃, X₄, X₅) :|: 1+X₃+X₄ ≤ X₅ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ X₄ ≤ X₂ ∧ X₄ ≤ X₂ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₄ ∧ X₄ ≤ X₂ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₄ ∧ X₄ ≤ X₂ ∧ 0 ≤ X₄ ∧ 0 ≤ X₂+X₄ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₁ ≤ X₂ of depth 1:
new bound:
2⋅X₀⋅X₂+2⋅X₁⋅X₂+X₀⋅X₃+X₁⋅X₃+2⋅X₂+X₀+X₁+X₃+1 {O(n^2)}
MPRF for transition t₃₃₅: n_l1___8(X₀, X₁, X₂, X₃, X₄, X₅) → n_l4___7(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₃ ≤ X₄+X₅ ∧ X₄+X₅ ≤ X₃ ∧ X₄+X₅ ≤ X₀ ∧ X₅ ≤ X₃+X₄ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ X₄ ≤ X₂ ∧ X₄ ≤ X₂ ∧ X₁ ≤ X₄ ∧ X₄ ≤ X₂ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₄ ∧ X₄ ≤ X₂ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₄ ∧ X₄ ≤ X₂ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₂ of depth 1:
new bound:
2⋅X₀⋅X₂+2⋅X₁⋅X₂+X₀⋅X₃+X₁⋅X₃+2⋅X₂+X₀+X₁+X₃+1 {O(n^2)}
MPRF for transition t₃₃₆: n_l1___8(X₀, X₁, X₂, X₃, X₄, X₅) → n_l5___6(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₃ ≤ X₄+X₅ ∧ X₄+X₅ ≤ X₃ ∧ X₄+X₅ ≤ X₀ ∧ 1+X₃+X₄ ≤ X₅ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ X₄ ≤ X₂ ∧ X₄ ≤ X₂ ∧ X₁ ≤ X₄ ∧ X₄ ≤ X₂ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₄ ∧ X₄ ≤ X₂ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₄ ∧ X₄ ≤ X₂ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₂ of depth 1:
new bound:
4⋅X₀⋅X₂+4⋅X₁⋅X₂+2⋅X₃+4⋅X₂+2 {O(n^2)}
MPRF for transition t₃₃₈: n_l2___2(X₀, X₁, X₂, X₃, X₄, X₅) → n_l3___1(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₄ ≤ 1+X₂ ∧ 1+X₁ ≤ X₄ ∧ X₄ ≤ X₂ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ X₃ ≤ X₀ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₄ ∧ X₄ ≤ 1+X₂ ∧ 1+X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₂ of depth 1:
new bound:
2⋅X₀⋅X₂+2⋅X₁⋅X₂+X₀⋅X₃+X₁⋅X₃+2⋅X₂+X₃ {O(n^2)}
MPRF for transition t₃₃₉: n_l3___1(X₀, X₁, X₂, X₃, X₄, X₅) → n_l1___8(X₀, X₁, X₂, X₃, X₄, X₃-X₄) :|: 1+X₁ ≤ X₄ ∧ X₄ ≤ X₂ ∧ X₃ ≤ X₀ ∧ X₄ ≤ X₂ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₄ ∧ X₄ ≤ X₂ ∧ 1+X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ 1+X₁ ≤ X₂ of depth 1:
new bound:
2⋅X₀⋅X₂+2⋅X₁⋅X₂+X₀⋅X₃+X₁⋅X₃+2⋅X₂+X₃ {O(n^2)}
MPRF for transition t₃₄₂: n_l4___7(X₀, X₁, X₂, X₃, X₄, X₅) → n_l1___5(X₀, X₁, X₂, X₃, X₄, X₅+1) :|: 0 ≤ X₄ ∧ X₃ ≤ X₄+X₅ ∧ X₄+X₅ ≤ X₃ ∧ X₁ ≤ X₄ ∧ X₄ ≤ X₂ ∧ X₃ ≤ X₀ ∧ X₄ ≤ X₂ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₄ ∧ X₄ ≤ X₂ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₂ of depth 1:
new bound:
2⋅X₀⋅X₂+2⋅X₁⋅X₂+X₀⋅X₃+X₁⋅X₃+2⋅X₂+X₀+X₁+X₃+1 {O(n^2)}
MPRF for transition t₃₄₃: n_l5___3(X₀, X₁, X₂, X₃, X₄, X₅) → n_l2___2(X₀, X₁, X₂, X₃, X₄+1, X₅) :|: 1+X₃+X₄ ≤ X₅ ∧ X₁ ≤ X₄ ∧ X₄ ≤ X₂ ∧ X₃ ≤ X₀ ∧ X₄ ≤ X₂ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₄ ∧ 1+X₃ ≤ X₅ ∧ X₄ ≤ X₂ ∧ 0 ≤ X₄ ∧ 0 ≤ X₂+X₄ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₁ ≤ X₂ of depth 1:
new bound:
2⋅X₀⋅X₂+2⋅X₁⋅X₂+X₀⋅X₃+X₁⋅X₃+2⋅X₂+X₀+X₁+X₃+1 {O(n^2)}
MPRF for transition t₃₄₄: n_l5___6(X₀, X₁, X₂, X₃, X₄, X₅) → n_l2___2(X₀, X₁, X₂, X₃, X₄+1, X₅) :|: 1+2⋅X₄ ≤ 0 ∧ X₄+X₅ ≤ X₀ ∧ X₃ ≤ X₄+X₅ ∧ X₄+X₅ ≤ X₃ ∧ X₁ ≤ X₄ ∧ X₄ ≤ X₂ ∧ X₄ ≤ X₂ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₄ ∧ X₄ ≤ X₂ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₂ of depth 1:
new bound:
4⋅X₀⋅X₂+4⋅X₁⋅X₂+2⋅X₃+4⋅X₂+X₀+X₁+2 {O(n^2)}
MPRF for transition t₃₅₄: n_l2___2(X₀, X₁, X₂, X₃, X₄, X₅) → l6(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₂+1 ≤ X₄ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ X₄ ≤ 1+X₂ ∧ 1+X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₂ of depth 1:
new bound:
X₀+X₁+1 {O(n)}
MPRF for transition t₃₃₃: n_l1___5(X₀, X₁, X₂, X₃, X₄, X₅) → n_l4___4(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₅ ≤ X₃+X₄ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ X₄ ≤ X₂ ∧ X₄ ≤ X₂ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₄ ∧ X₄ ≤ X₂ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₄ ∧ X₄ ≤ X₂ ∧ 0 ≤ X₄ ∧ 0 ≤ X₂+X₄ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₁ ≤ X₂ of depth 1:
new bound:
2⋅X₀⋅X₃⋅X₃+2⋅X₁⋅X₃⋅X₃+4⋅X₀⋅X₂⋅X₃+4⋅X₁⋅X₂⋅X₃+2⋅X₀⋅X₃+2⋅X₁⋅X₃+2⋅X₃⋅X₃+4⋅X₂⋅X₃+4⋅X₃ {O(n^3)}
MPRF for transition t₃₄₁: n_l4___4(X₀, X₁, X₂, X₃, X₄, X₅) → n_l1___5(X₀, X₁, X₂, X₃, X₄, X₅+1) :|: X₅ ≤ X₃+X₄ ∧ X₁ ≤ X₄ ∧ X₄ ≤ X₂ ∧ X₃ ≤ X₀ ∧ X₄ ≤ X₂ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₄ ∧ X₄ ≤ X₂ ∧ 0 ≤ X₄ ∧ 0 ≤ X₂+X₄ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₁ ≤ X₂ of depth 1:
new bound:
2⋅X₀⋅X₀⋅X₃+2⋅X₀⋅X₃⋅X₃+2⋅X₁⋅X₁⋅X₃+2⋅X₁⋅X₃⋅X₃+4⋅X₀⋅X₀⋅X₂+4⋅X₀⋅X₁⋅X₃+4⋅X₀⋅X₂⋅X₃+4⋅X₁⋅X₁⋅X₂+4⋅X₁⋅X₂⋅X₃+8⋅X₀⋅X₁⋅X₂+2⋅X₀⋅X₀+2⋅X₁⋅X₁+2⋅X₃⋅X₃+4⋅X₀⋅X₁+4⋅X₂⋅X₃+5⋅X₀⋅X₃+5⋅X₁⋅X₃+6⋅X₀⋅X₂+6⋅X₁⋅X₂+2⋅X₂+4⋅X₀+4⋅X₁+5⋅X₃+1 {O(n^3)}
CFR did not improve the program. Rolling back
CFR did not improve the program. Rolling back
All Bounds
Timebounds
Overall timebound:4⋅X₀⋅X₂⋅X₃+4⋅X₀⋅X₃⋅X₃+4⋅X₁⋅X₂⋅X₃+4⋅X₁⋅X₃⋅X₃+13⋅X₀⋅X₃+13⋅X₁⋅X₃+8⋅X₂⋅X₃+8⋅X₃⋅X₃+9⋅X₀⋅X₂+9⋅X₁⋅X₂+18⋅X₂+30⋅X₃+9⋅X₀+9⋅X₁+21 {O(n^3)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₀+X₁+1 {O(n)}
t₃: 1 {O(1)}
t₄: X₀⋅X₂+X₀⋅X₃+X₁⋅X₂+X₁⋅X₃+2⋅X₂+2⋅X₃+X₀+X₁+2 {O(n^2)}
t₅: X₀+X₁+1 {O(n)}
t₆: X₀⋅X₂+X₀⋅X₃+X₁⋅X₂+X₁⋅X₃+2⋅X₂+2⋅X₃+X₀+X₁+2 {O(n^2)}
t₇: 2⋅X₀⋅X₂⋅X₃+2⋅X₀⋅X₃⋅X₃+2⋅X₁⋅X₂⋅X₃+2⋅X₁⋅X₃⋅X₃+3⋅X₀⋅X₃+3⋅X₁⋅X₃+4⋅X₂⋅X₃+4⋅X₃⋅X₃+X₀⋅X₂+X₁⋅X₂+2⋅X₂+8⋅X₃+X₀+X₁+3 {O(n^3)}
t₈: 4⋅X₀⋅X₂+4⋅X₀⋅X₃+4⋅X₁⋅X₂+4⋅X₁⋅X₃+8⋅X₂+8⋅X₃+X₀+X₁+2 {O(n^2)}
t₉: 2⋅X₀⋅X₂⋅X₃+2⋅X₀⋅X₃⋅X₃+2⋅X₁⋅X₂⋅X₃+2⋅X₁⋅X₃⋅X₃+3⋅X₀⋅X₃+3⋅X₁⋅X₃+4⋅X₂⋅X₃+4⋅X₃⋅X₃+X₀⋅X₂+X₁⋅X₂+2⋅X₂+8⋅X₃+X₀+X₁+3 {O(n^3)}
t₁₀: X₀⋅X₂+X₀⋅X₃+X₁⋅X₂+X₁⋅X₃+2⋅X₂+2⋅X₃+X₀+X₁+2 {O(n^2)}
t₁₁: X₀+X₁+1 {O(n)}
t₁₂: 1 {O(1)}
Costbounds
Overall costbound: 4⋅X₀⋅X₂⋅X₃+4⋅X₀⋅X₃⋅X₃+4⋅X₁⋅X₂⋅X₃+4⋅X₁⋅X₃⋅X₃+13⋅X₀⋅X₃+13⋅X₁⋅X₃+8⋅X₂⋅X₃+8⋅X₃⋅X₃+9⋅X₀⋅X₂+9⋅X₁⋅X₂+18⋅X₂+30⋅X₃+9⋅X₀+9⋅X₁+21 {O(n^3)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₀+X₁+1 {O(n)}
t₃: 1 {O(1)}
t₄: X₀⋅X₂+X₀⋅X₃+X₁⋅X₂+X₁⋅X₃+2⋅X₂+2⋅X₃+X₀+X₁+2 {O(n^2)}
t₅: X₀+X₁+1 {O(n)}
t₆: X₀⋅X₂+X₀⋅X₃+X₁⋅X₂+X₁⋅X₃+2⋅X₂+2⋅X₃+X₀+X₁+2 {O(n^2)}
t₇: 2⋅X₀⋅X₂⋅X₃+2⋅X₀⋅X₃⋅X₃+2⋅X₁⋅X₂⋅X₃+2⋅X₁⋅X₃⋅X₃+3⋅X₀⋅X₃+3⋅X₁⋅X₃+4⋅X₂⋅X₃+4⋅X₃⋅X₃+X₀⋅X₂+X₁⋅X₂+2⋅X₂+8⋅X₃+X₀+X₁+3 {O(n^3)}
t₈: 4⋅X₀⋅X₂+4⋅X₀⋅X₃+4⋅X₁⋅X₂+4⋅X₁⋅X₃+8⋅X₂+8⋅X₃+X₀+X₁+2 {O(n^2)}
t₉: 2⋅X₀⋅X₂⋅X₃+2⋅X₀⋅X₃⋅X₃+2⋅X₁⋅X₂⋅X₃+2⋅X₁⋅X₃⋅X₃+3⋅X₀⋅X₃+3⋅X₁⋅X₃+4⋅X₂⋅X₃+4⋅X₃⋅X₃+X₀⋅X₂+X₁⋅X₂+2⋅X₂+8⋅X₃+X₀+X₁+3 {O(n^3)}
t₁₀: X₀⋅X₂+X₀⋅X₃+X₁⋅X₂+X₁⋅X₃+2⋅X₂+2⋅X₃+X₀+X₁+2 {O(n^2)}
t₁₁: X₀+X₁+1 {O(n)}
t₁₂: 1 {O(1)}
Sizebounds
t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₀, X₃: X₃ {O(n)}
t₀, X₄: X₄ {O(n)}
t₀, X₅: X₅ {O(n)}
t₁, X₀: X₁ {O(n)}
t₁, X₁: X₂ {O(n)}
t₁, X₂: X₃ {O(n)}
t₁, X₃: X₀ {O(n)}
t₁, X₄: X₄ {O(n)}
t₁, X₅: X₅ {O(n)}
t₂, X₀: X₁ {O(n)}
t₂, X₁: X₂ {O(n)}
t₂, X₂: X₃ {O(n)}
t₂, X₃: 2⋅X₀+X₁+1 {O(n)}
t₂, X₄: 2⋅X₂ {O(n)}
t₂, X₅: 2⋅X₀⋅X₂⋅X₃+2⋅X₀⋅X₃⋅X₃+2⋅X₁⋅X₂⋅X₃+2⋅X₁⋅X₃⋅X₃+3⋅X₀⋅X₂+3⋅X₁⋅X₂+4⋅X₂⋅X₃+4⋅X₃⋅X₃+5⋅X₀⋅X₃+5⋅X₁⋅X₃+10⋅X₂+12⋅X₃+5⋅X₁+7⋅X₀+X₅+9 {O(n^3)}
t₃, X₀: 2⋅X₁ {O(n)}
t₃, X₁: 2⋅X₂ {O(n)}
t₃, X₂: 2⋅X₃ {O(n)}
t₃, X₃: 3⋅X₀+X₁+1 {O(n)}
t₃, X₄: 4⋅X₂+X₄ {O(n)}
t₃, X₅: 2⋅X₀⋅X₂⋅X₃+2⋅X₀⋅X₃⋅X₃+2⋅X₁⋅X₂⋅X₃+2⋅X₁⋅X₃⋅X₃+3⋅X₀⋅X₂+3⋅X₁⋅X₂+4⋅X₂⋅X₃+4⋅X₃⋅X₃+5⋅X₀⋅X₃+5⋅X₁⋅X₃+10⋅X₂+12⋅X₃+2⋅X₅+5⋅X₁+7⋅X₀+9 {O(n^3)}
t₄, X₀: X₁ {O(n)}
t₄, X₁: X₂ {O(n)}
t₄, X₂: X₃ {O(n)}
t₄, X₃: 2⋅X₀+X₁+1 {O(n)}
t₄, X₄: X₀⋅X₂+X₀⋅X₃+X₁⋅X₂+X₁⋅X₃+2⋅X₃+4⋅X₂+X₀+X₁+2 {O(n^2)}
t₄, X₅: 4⋅X₀⋅X₂⋅X₃+4⋅X₀⋅X₃⋅X₃+4⋅X₁⋅X₂⋅X₃+4⋅X₁⋅X₃⋅X₃+10⋅X₀⋅X₃+10⋅X₁⋅X₃+6⋅X₀⋅X₂+6⋅X₁⋅X₂+8⋅X₂⋅X₃+8⋅X₃⋅X₃+10⋅X₁+14⋅X₀+20⋅X₂+24⋅X₃+X₅+18 {O(n^3)}
t₅, X₀: X₁ {O(n)}
t₅, X₁: X₂ {O(n)}
t₅, X₂: X₃ {O(n)}
t₅, X₃: 2⋅X₀+X₁+1 {O(n)}
t₅, X₄: 4⋅X₂ {O(n)}
t₅, X₅: 2⋅X₀⋅X₂⋅X₃+2⋅X₀⋅X₃⋅X₃+2⋅X₁⋅X₂⋅X₃+2⋅X₁⋅X₃⋅X₃+3⋅X₀⋅X₂+3⋅X₁⋅X₂+4⋅X₂⋅X₃+4⋅X₃⋅X₃+5⋅X₀⋅X₃+5⋅X₁⋅X₃+10⋅X₂+12⋅X₃+5⋅X₁+7⋅X₀+X₅+9 {O(n^3)}
t₆, X₀: X₁ {O(n)}
t₆, X₁: X₂ {O(n)}
t₆, X₂: X₃ {O(n)}
t₆, X₃: 2⋅X₀+X₁+1 {O(n)}
t₆, X₄: X₀⋅X₂+X₀⋅X₃+X₁⋅X₂+X₁⋅X₃+2⋅X₃+4⋅X₂+X₀+X₁+2 {O(n^2)}
t₆, X₅: X₀⋅X₂+X₀⋅X₃+X₁⋅X₂+X₁⋅X₃+2⋅X₁+2⋅X₃+3⋅X₀+4⋅X₂+3 {O(n^2)}
t₇, X₀: X₁ {O(n)}
t₇, X₁: X₂ {O(n)}
t₇, X₂: X₃ {O(n)}
t₇, X₃: 2⋅X₀+X₁+1 {O(n)}
t₇, X₄: X₀⋅X₂+X₀⋅X₃+X₁⋅X₂+X₁⋅X₃+2⋅X₃+4⋅X₂+X₀+X₁+2 {O(n^2)}
t₇, X₅: 2⋅X₀⋅X₂⋅X₃+2⋅X₀⋅X₃⋅X₃+2⋅X₁⋅X₂⋅X₃+2⋅X₁⋅X₃⋅X₃+2⋅X₀⋅X₂+2⋅X₁⋅X₂+4⋅X₀⋅X₃+4⋅X₁⋅X₃+4⋅X₂⋅X₃+4⋅X₃⋅X₃+10⋅X₃+3⋅X₁+4⋅X₀+6⋅X₂+6 {O(n^3)}
t₈, X₀: X₁ {O(n)}
t₈, X₁: X₂ {O(n)}
t₈, X₂: X₃ {O(n)}
t₈, X₃: 2⋅X₀+X₁+1 {O(n)}
t₈, X₄: X₀⋅X₂+X₀⋅X₃+X₁⋅X₂+X₁⋅X₃+2⋅X₃+4⋅X₂+X₀+X₁+2 {O(n^2)}
t₈, X₅: 2⋅X₀⋅X₂⋅X₃+2⋅X₀⋅X₃⋅X₃+2⋅X₁⋅X₂⋅X₃+2⋅X₁⋅X₃⋅X₃+3⋅X₀⋅X₂+3⋅X₁⋅X₂+4⋅X₂⋅X₃+4⋅X₃⋅X₃+5⋅X₀⋅X₃+5⋅X₁⋅X₃+10⋅X₂+12⋅X₃+5⋅X₁+7⋅X₀+9 {O(n^3)}
t₉, X₀: X₁ {O(n)}
t₉, X₁: X₂ {O(n)}
t₉, X₂: X₃ {O(n)}
t₉, X₃: 2⋅X₀+X₁+1 {O(n)}
t₉, X₄: X₀⋅X₂+X₀⋅X₃+X₁⋅X₂+X₁⋅X₃+2⋅X₃+4⋅X₂+X₀+X₁+2 {O(n^2)}
t₉, X₅: 2⋅X₀⋅X₂⋅X₃+2⋅X₀⋅X₃⋅X₃+2⋅X₁⋅X₂⋅X₃+2⋅X₁⋅X₃⋅X₃+2⋅X₀⋅X₂+2⋅X₁⋅X₂+4⋅X₀⋅X₃+4⋅X₁⋅X₃+4⋅X₂⋅X₃+4⋅X₃⋅X₃+10⋅X₃+3⋅X₁+4⋅X₀+6⋅X₂+6 {O(n^3)}
t₁₀, X₀: X₁ {O(n)}
t₁₀, X₁: X₂ {O(n)}
t₁₀, X₂: X₃ {O(n)}
t₁₀, X₃: 2⋅X₀+X₁+1 {O(n)}
t₁₀, X₄: X₀⋅X₂+X₀⋅X₃+X₁⋅X₂+X₁⋅X₃+2⋅X₃+4⋅X₂+X₀+X₁+2 {O(n^2)}
t₁₀, X₅: 2⋅X₀⋅X₂⋅X₃+2⋅X₀⋅X₃⋅X₃+2⋅X₁⋅X₂⋅X₃+2⋅X₁⋅X₃⋅X₃+3⋅X₀⋅X₂+3⋅X₁⋅X₂+4⋅X₂⋅X₃+4⋅X₃⋅X₃+5⋅X₀⋅X₃+5⋅X₁⋅X₃+10⋅X₂+12⋅X₃+5⋅X₁+7⋅X₀+9 {O(n^3)}
t₁₁, X₀: X₁ {O(n)}
t₁₁, X₁: X₂ {O(n)}
t₁₁, X₂: X₃ {O(n)}
t₁₁, X₃: 2⋅X₀+X₁+1 {O(n)}
t₁₁, X₄: 4⋅X₂ {O(n)}
t₁₁, X₅: 2⋅X₀⋅X₂⋅X₃+2⋅X₀⋅X₃⋅X₃+2⋅X₁⋅X₂⋅X₃+2⋅X₁⋅X₃⋅X₃+3⋅X₀⋅X₂+3⋅X₁⋅X₂+4⋅X₂⋅X₃+4⋅X₃⋅X₃+5⋅X₀⋅X₃+5⋅X₁⋅X₃+10⋅X₂+12⋅X₃+5⋅X₁+7⋅X₀+X₅+9 {O(n^3)}
t₁₂, X₀: 2⋅X₁ {O(n)}
t₁₂, X₁: 2⋅X₂ {O(n)}
t₁₂, X₂: 2⋅X₃ {O(n)}
t₁₂, X₃: 3⋅X₀+X₁+1 {O(n)}
t₁₂, X₄: 4⋅X₂+X₄ {O(n)}
t₁₂, X₅: 2⋅X₀⋅X₂⋅X₃+2⋅X₀⋅X₃⋅X₃+2⋅X₁⋅X₂⋅X₃+2⋅X₁⋅X₃⋅X₃+3⋅X₀⋅X₂+3⋅X₁⋅X₂+4⋅X₂⋅X₃+4⋅X₃⋅X₃+5⋅X₀⋅X₃+5⋅X₁⋅X₃+10⋅X₂+12⋅X₃+2⋅X₅+5⋅X₁+7⋅X₀+9 {O(n^3)}