Initial Problem
Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7
Transitions:
t₀: l0(X₀, X₁) → l6(X₀, X₁)
t₉: l1(X₀, X₁) → l3(X₀-X₁, X₁)
t₁₀: l2(X₀, X₁) → l3(X₀, X₁-X₀)
t₄: l3(X₀, X₁) → l4(X₀, X₁) :|: X₁+1 ≤ X₀
t₅: l3(X₀, X₁) → l4(X₀, X₁) :|: X₀+1 ≤ X₁
t₆: l3(X₀, X₁) → l5(X₀, X₁) :|: X₁ ≤ X₀ ∧ X₀ ≤ X₁
t₇: l4(X₀, X₁) → l1(X₀, X₁) :|: X₁+1 ≤ X₀
t₈: l4(X₀, X₁) → l2(X₀, X₁) :|: X₀ ≤ X₁
t₁₁: l5(X₀, X₁) → l7(X₀, X₁)
t₃: l6(X₀, X₁) → l3(X₁, X₀) :|: 1 ≤ X₀ ∧ 1 ≤ X₁
t₁: l6(X₀, X₁) → l5(X₀, X₁) :|: X₀ ≤ 0
t₂: l6(X₀, X₁) → l5(X₀, X₁) :|: X₁ ≤ 0
Preprocessing
Found invariant 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ X₀ ≤ X₁ for location l2
Found invariant 1+X₁ ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l1
Found invariant 1 ≤ X₀+X₁ for location l4
Found invariant 1 ≤ X₀+X₁ for location l3
Problem after Preprocessing
Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7
Transitions:
t₀: l0(X₀, X₁) → l6(X₀, X₁)
t₉: l1(X₀, X₁) → l3(X₀-X₁, X₁) :|: 1+X₁ ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₁₀: l2(X₀, X₁) → l3(X₀, X₁-X₀) :|: 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ X₀ ≤ X₁
t₄: l3(X₀, X₁) → l4(X₀, X₁) :|: X₁+1 ≤ X₀ ∧ 1 ≤ X₀+X₁
t₅: l3(X₀, X₁) → l4(X₀, X₁) :|: X₀+1 ≤ X₁ ∧ 1 ≤ X₀+X₁
t₆: l3(X₀, X₁) → l5(X₀, X₁) :|: X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀+X₁
t₇: l4(X₀, X₁) → l1(X₀, X₁) :|: X₁+1 ≤ X₀ ∧ 1 ≤ X₀+X₁
t₈: l4(X₀, X₁) → l2(X₀, X₁) :|: X₀ ≤ X₁ ∧ 1 ≤ X₀+X₁
t₁₁: l5(X₀, X₁) → l7(X₀, X₁)
t₃: l6(X₀, X₁) → l3(X₁, X₀) :|: 1 ≤ X₀ ∧ 1 ≤ X₁
t₁: l6(X₀, X₁) → l5(X₀, X₁) :|: X₀ ≤ 0
t₂: l6(X₀, X₁) → l5(X₀, X₁) :|: X₁ ≤ 0
Solv. Size Bound: t₄: l3→l4 for X₀
cycle: [t₄: l3→l4; t₅: l3→l4; t₇: l4→l1; t₉: l1→l3]
loop: (X₁+1 ≤ X₀ ∧ X₁+1 ≤ X₀ ∨ X₀+1 ≤ X₁ ∧ X₁+1 ≤ X₀,(X₀,X₁) -> (X₀-X₁,X₁)
overappr. closed-form: X₁⋅n+X₀ {O(n^2)}
runtime bound: inf {Infinity}
Solv. Size Bound - Lifting for t₄: l3→l4 and X₀: inf {Infinity}
Solv. Size Bound: t₄: l3→l4 for X₁
cycle: [t₄: l3→l4; t₅: l3→l4; t₈: l4→l2; t₁₀: l2→l3]
loop: (X₁+1 ≤ X₀ ∧ X₀ ≤ X₁ ∨ X₀+1 ≤ X₁ ∧ X₀ ≤ X₁,(X₀,X₁) -> (X₀,X₁-X₀)
overappr. closed-form: X₀⋅n+X₁ {O(n^2)}
runtime bound: inf {Infinity}
Solv. Size Bound - Lifting for t₄: l3→l4 and X₁: inf {Infinity}
Solv. Size Bound: t₅: l3→l4 for X₀
cycle: [t₄: l3→l4; t₅: l3→l4; t₇: l4→l1; t₉: l1→l3]
loop: (X₁+1 ≤ X₀ ∧ X₁+1 ≤ X₀ ∨ X₀+1 ≤ X₁ ∧ X₁+1 ≤ X₀,(X₀,X₁) -> (X₀-X₁,X₁)
overappr. closed-form: X₁⋅n+X₀ {O(n^2)}
runtime bound: inf {Infinity}
Solv. Size Bound - Lifting for t₅: l3→l4 and X₀: inf {Infinity}
Solv. Size Bound: t₅: l3→l4 for X₁
cycle: [t₄: l3→l4; t₅: l3→l4; t₈: l4→l2; t₁₀: l2→l3]
loop: (X₁+1 ≤ X₀ ∧ X₀ ≤ X₁ ∨ X₀+1 ≤ X₁ ∧ X₀ ≤ X₁,(X₀,X₁) -> (X₀,X₁-X₀)
overappr. closed-form: X₀⋅n+X₁ {O(n^2)}
runtime bound: inf {Infinity}
Solv. Size Bound - Lifting for t₅: l3→l4 and X₁: inf {Infinity}
Solv. Size Bound: t₇: l4→l1 for X₀
cycle: [t₇: l4→l1; t₉: l1→l3; t₄: l3→l4; t₅: l3→l4]
loop: (X₁+1 ≤ X₀ ∧ 2⋅X₁+1 ≤ X₀ ∨ X₁+1 ≤ X₀ ∧ X₀+1 ≤ 2⋅X₁,(X₀,X₁) -> (X₀-X₁,X₁)
overappr. closed-form: X₁⋅n+X₀ {O(n^2)}
runtime bound: inf {Infinity}
Solv. Size Bound - Lifting for t₇: l4→l1 and X₀: inf {Infinity}
Solv. Size Bound: t₈: l4→l2 for X₀
Solv. Size Bound: t₈: l4→l2 for X₁
cycle: [t₈: l4→l2; t₁₀: l2→l3; t₄: l3→l4; t₅: l3→l4]
loop: (X₀ ≤ X₁ ∧ X₁+1 ≤ 2⋅X₀ ∨ X₀ ≤ X₁ ∧ 2⋅X₀+1 ≤ X₁,(X₀,X₁) -> (X₀,X₁-X₀)
overappr. closed-form: X₀⋅n+X₁ {O(n^2)}
runtime bound: inf {Infinity}
Solv. Size Bound - Lifting for t₈: l4→l2 and X₁: inf {Infinity}
Solv. Size Bound: t₉: l1→l3 for X₀
cycle: [t₇: l4→l1; t₄: l3→l4; t₅: l3→l4; t₉: l1→l3]
loop: (2⋅X₁+1 ≤ X₀ ∧ 2⋅X₁+1 ≤ X₀ ∨ 2⋅X₁+1 ≤ X₀ ∧ X₀+1 ≤ 2⋅X₁,(X₀,X₁) -> (X₀-X₁,X₁)
overappr. closed-form: X₁⋅n+X₀ {O(n^2)}
runtime bound: inf {Infinity}
Solv. Size Bound - Lifting for t₉: l1→l3 and X₀: inf {Infinity}
Solv. Size Bound: t₁₀: l2→l3 for X₀
Solv. Size Bound: t₁₀: l2→l3 for X₁
cycle: [t₈: l4→l2; t₄: l3→l4; t₅: l3→l4; t₁₀: l2→l3]
loop: (2⋅X₀ ≤ X₁ ∧ X₁+1 ≤ 2⋅X₀ ∨ 2⋅X₀ ≤ X₁ ∧ 2⋅X₀+1 ≤ X₁,(X₀,X₁) -> (X₀,X₁-X₀)
overappr. closed-form: X₀⋅n+X₁ {O(n^2)}
runtime bound: inf {Infinity}
Solv. Size Bound - Lifting for t₁₀: l2→l3 and X₁: inf {Infinity}
Solv. Size Bound - Lifting for t₄: l3→l4 and X₀: inf {Infinity}
Solv. Size Bound - Lifting for t₄: l3→l4 and X₁: inf {Infinity}
Solv. Size Bound - Lifting for t₅: l3→l4 and X₀: inf {Infinity}
Solv. Size Bound - Lifting for t₅: l3→l4 and X₁: inf {Infinity}
Solv. Size Bound - Lifting for t₇: l4→l1 and X₀: inf {Infinity}
Solv. Size Bound: t₈: l4→l2 for X₀
Solv. Size Bound - Lifting for t₈: l4→l2 and X₁: inf {Infinity}
Solv. Size Bound - Lifting for t₉: l1→l3 and X₀: inf {Infinity}
Solv. Size Bound: t₁₀: l2→l3 for X₀
Solv. Size Bound - Lifting for t₁₀: l2→l3 and X₁: inf {Infinity}
Chain transitions t₇: l4→l1 and t₉: l1→l3 to t₂₉₃: l4→l3
Chain transitions t₈: l4→l2 and t₁₀: l2→l3 to t₂₉₄: l4→l3
Chain transitions t₃: l6→l3 and t₆: l3→l5 to t₂₉₅: l6→l5
Chain transitions t₂₉₄: l4→l3 and t₆: l3→l5 to t₂₉₆: l4→l5
Chain transitions t₂₉₄: l4→l3 and t₅: l3→l4 to t₂₉₇: l4→l4
Chain transitions t₃: l6→l3 and t₅: l3→l4 to t₂₉₈: l6→l4
Chain transitions t₂₉₃: l4→l3 and t₅: l3→l4 to t₂₉₉: l4→l4
Chain transitions t₂₉₃: l4→l3 and t₆: l3→l5 to t₃₀₀: l4→l5
Chain transitions t₂₉₃: l4→l3 and t₄: l3→l4 to t₃₀₁: l4→l4
Chain transitions t₂₉₄: l4→l3 and t₄: l3→l4 to t₃₀₂: l4→l4
Chain transitions t₃: l6→l3 and t₄: l3→l4 to t₃₀₃: l6→l4
Analysing control-flow refined program
Found invariant 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ X₀ ≤ X₁ for location l2
Found invariant 1+X₁ ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l1
Found invariant 1 ≤ X₀+X₁ for location l4
Found invariant 1 ≤ X₀+X₁ for location l3
Solv. Size Bound: t₂₉₇: l4→l4 for X₀
Solv. Size Bound: t₂₉₇: l4→l4 for X₁
cycle: [t₂₉₇: l4→l4; t₃₀₂: l4→l4]
loop: (X₀ ≤ X₁ ∧ 2⋅X₀+1 ≤ X₁ ∨ X₀ ≤ X₁ ∧ X₁+1 ≤ 2⋅X₀,(X₀,X₁) -> (X₀,X₁-X₀)
overappr. closed-form: X₀⋅n+X₁ {O(n^2)}
runtime bound: inf {Infinity}
Solv. Size Bound - Lifting for t₂₉₇: l4→l4 and X₁: inf {Infinity}
Solv. Size Bound: t₂₉₉: l4→l4 for X₀
cycle: [t₂₉₉: l4→l4; t₃₀₁: l4→l4]
loop: (X₁+1 ≤ X₀ ∧ X₀+1 ≤ 2⋅X₁ ∨ X₁+1 ≤ X₀ ∧ 2⋅X₁+1 ≤ X₀,(X₀,X₁) -> (X₀-X₁,X₁)
overappr. closed-form: X₁⋅n+X₀ {O(n^2)}
runtime bound: inf {Infinity}
Solv. Size Bound - Lifting for t₂₉₉: l4→l4 and X₀: inf {Infinity}
Solv. Size Bound: t₃₀₁: l4→l4 for X₀
cycle: [t₂₉₉: l4→l4; t₃₀₁: l4→l4]
loop: (X₁+1 ≤ X₀ ∧ X₀+1 ≤ 2⋅X₁ ∨ X₁+1 ≤ X₀ ∧ 2⋅X₁+1 ≤ X₀,(X₀,X₁) -> (X₀-X₁,X₁)
overappr. closed-form: X₁⋅n+X₀ {O(n^2)}
runtime bound: inf {Infinity}
Solv. Size Bound - Lifting for t₃₀₁: l4→l4 and X₀: inf {Infinity}
Solv. Size Bound: t₃₀₂: l4→l4 for X₀
Solv. Size Bound: t₃₀₂: l4→l4 for X₁
cycle: [t₂₉₇: l4→l4; t₃₀₂: l4→l4]
loop: (X₀ ≤ X₁ ∧ 2⋅X₀+1 ≤ X₁ ∨ X₀ ≤ X₁ ∧ X₁+1 ≤ 2⋅X₀,(X₀,X₁) -> (X₀,X₁-X₀)
overappr. closed-form: X₀⋅n+X₁ {O(n^2)}
runtime bound: inf {Infinity}
Solv. Size Bound - Lifting for t₃₀₂: l4→l4 and X₁: inf {Infinity}
Solv. Size Bound: t₂₉₇: l4→l4 for X₀
Solv. Size Bound - Lifting for t₂₉₇: l4→l4 and X₁: inf {Infinity}
Solv. Size Bound - Lifting for t₂₉₉: l4→l4 and X₀: inf {Infinity}
Solv. Size Bound - Lifting for t₃₀₁: l4→l4 and X₀: inf {Infinity}
Solv. Size Bound: t₃₀₂: l4→l4 for X₀
Solv. Size Bound - Lifting for t₃₀₂: l4→l4 and X₁: inf {Infinity}
CFR did not improve the program. Rolling back
CFR did not improve the program. Rolling back
Analysing control-flow refined program
Found invariant 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l4___3
Found invariant 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location n_l4___4
Found invariant 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location n_l1___2
Found invariant 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l2___1
Found invariant 2 ≤ X₀+X₁ for location l3
MPRF for transition t₅₉₀: n_l1___2(X₀, X₁) → l3(X₀-X₁, X₁) :|: 1 ≤ X₁ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1+X₁ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ of depth 1:
new bound:
X₁+1 {O(n)}
MPRF for transition t₅₉₁: n_l2___1(X₀, X₁) → l3(X₀, X₁-X₀) :|: 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₁ ∧ X₀ ≤ X₁ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₀ {O(n)}
MPRF for transition t₅₉₂: l3(X₀, X₁) → n_l4___3(X₀, X₁) :|: 1 ≤ X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+2⋅X₁ ∧ 1 ≤ 2⋅X₀+X₁ ∧ 0 ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₁ of depth 1:
new bound:
X₀+1 {O(n)}
MPRF for transition t₅₉₃: l3(X₀, X₁) → n_l4___4(X₀, X₁) :|: 1 ≤ X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+2⋅X₁ ∧ 1 ≤ 2⋅X₀+X₁ ∧ 0 ≤ X₁ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₁ of depth 1:
new bound:
X₁ {O(n)}
MPRF for transition t₅₉₄: n_l4___3(X₀, X₁) → n_l2___1(X₀, X₁) :|: 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
2⋅X₀ {O(n)}
MPRF for transition t₅₉₅: n_l4___4(X₀, X₁) → n_l1___2(X₀, X₁) :|: 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ of depth 1:
new bound:
X₀+X₁ {O(n)}
CFR: Improvement to new bound with the following program:
new bound:
Infinite
cfr-program:
Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l3, l5, l6, l7, n_l1___2, n_l2___1, n_l4___3, n_l4___4
Transitions:
t₀: l0(X₀, X₁) → l6(X₀, X₁)
t₆: l3(X₀, X₁) → l5(X₀, X₁) :|: X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₁
t₅₉₂: l3(X₀, X₁) → n_l4___3(X₀, X₁) :|: 1 ≤ X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+2⋅X₁ ∧ 1 ≤ 2⋅X₀+X₁ ∧ 0 ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₁
t₅₉₃: l3(X₀, X₁) → n_l4___4(X₀, X₁) :|: 1 ≤ X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+2⋅X₁ ∧ 1 ≤ 2⋅X₀+X₁ ∧ 0 ≤ X₁ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₁
t₁₁: l5(X₀, X₁) → l7(X₀, X₁)
t₃: l6(X₀, X₁) → l3(X₁, X₀) :|: 1 ≤ X₀ ∧ 1 ≤ X₁
t₁: l6(X₀, X₁) → l5(X₀, X₁) :|: X₀ ≤ 0
t₂: l6(X₀, X₁) → l5(X₀, X₁) :|: X₁ ≤ 0
t₅₉₀: n_l1___2(X₀, X₁) → l3(X₀-X₁, X₁) :|: 1 ≤ X₁ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1+X₁ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀
t₅₉₁: n_l2___1(X₀, X₁) → l3(X₀, X₁-X₀) :|: 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₁ ∧ X₀ ≤ X₁ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀
t₅₉₄: n_l4___3(X₀, X₁) → n_l2___1(X₀, X₁) :|: 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀
t₅₉₅: n_l4___4(X₀, X₁) → n_l1___2(X₀, X₁) :|: 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀
CFR: Improvement to new bound with the following program:
new bound:
3⋅X₁+5⋅X₀+2 {O(n)}
cfr-program:
Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l3, l5, l6, l7, n_l1___2, n_l2___1, n_l4___3, n_l4___4
Transitions:
t₀: l0(X₀, X₁) → l6(X₀, X₁)
t₆: l3(X₀, X₁) → l5(X₀, X₁) :|: X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₁
t₅₉₂: l3(X₀, X₁) → n_l4___3(X₀, X₁) :|: 1 ≤ X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+2⋅X₁ ∧ 1 ≤ 2⋅X₀+X₁ ∧ 0 ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₁
t₅₉₃: l3(X₀, X₁) → n_l4___4(X₀, X₁) :|: 1 ≤ X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+2⋅X₁ ∧ 1 ≤ 2⋅X₀+X₁ ∧ 0 ≤ X₁ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₁
t₁₁: l5(X₀, X₁) → l7(X₀, X₁)
t₃: l6(X₀, X₁) → l3(X₁, X₀) :|: 1 ≤ X₀ ∧ 1 ≤ X₁
t₁: l6(X₀, X₁) → l5(X₀, X₁) :|: X₀ ≤ 0
t₂: l6(X₀, X₁) → l5(X₀, X₁) :|: X₁ ≤ 0
t₅₉₀: n_l1___2(X₀, X₁) → l3(X₀-X₁, X₁) :|: 1 ≤ X₁ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1+X₁ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀
t₅₉₁: n_l2___1(X₀, X₁) → l3(X₀, X₁-X₀) :|: 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₁ ∧ X₀ ≤ X₁ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀
t₅₉₄: n_l4___3(X₀, X₁) → n_l2___1(X₀, X₁) :|: 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀
t₅₉₅: n_l4___4(X₀, X₁) → n_l1___2(X₀, X₁) :|: 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀
All Bounds
Timebounds
Overall timebound:3⋅X₁+5⋅X₀+8 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 1 {O(1)}
t₆: 1 {O(1)}
t₁₁: 1 {O(1)}
t₅₉₀: X₁+1 {O(n)}
t₅₉₁: X₀ {O(n)}
t₅₉₂: X₀+1 {O(n)}
t₅₉₃: X₁ {O(n)}
t₅₉₄: 2⋅X₀ {O(n)}
t₅₉₅: X₀+X₁ {O(n)}
Costbounds
Overall costbound: 3⋅X₁+5⋅X₀+8 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 1 {O(1)}
t₆: 1 {O(1)}
t₁₁: 1 {O(1)}
t₅₉₀: X₁+1 {O(n)}
t₅₉₁: X₀ {O(n)}
t₅₉₂: X₀+1 {O(n)}
t₅₉₃: X₁ {O(n)}
t₅₉₄: 2⋅X₀ {O(n)}
t₅₉₅: X₀+X₁ {O(n)}
Sizebounds
t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₁, X₀: X₀ {O(n)}
t₁, X₁: X₁ {O(n)}
t₂, X₀: X₀ {O(n)}
t₂, X₁: X₁ {O(n)}
t₃, X₀: X₁ {O(n)}
t₃, X₁: X₀ {O(n)}
t₆, X₀: 3⋅X₁ {O(n)}
t₆, X₁: 3⋅X₀ {O(n)}
t₁₁, X₀: 2⋅X₀+3⋅X₁ {O(n)}
t₁₁, X₁: 2⋅X₁+3⋅X₀ {O(n)}
t₅₉₀, X₀: X₁ {O(n)}
t₅₉₀, X₁: X₀ {O(n)}
t₅₉₁, X₀: X₁ {O(n)}
t₅₉₁, X₁: X₀ {O(n)}
t₅₉₂, X₀: X₁ {O(n)}
t₅₉₂, X₁: X₀ {O(n)}
t₅₉₃, X₀: X₁ {O(n)}
t₅₉₃, X₁: X₀ {O(n)}
t₅₉₄, X₀: X₁ {O(n)}
t₅₉₄, X₁: X₀ {O(n)}
t₅₉₅, X₀: X₁ {O(n)}
t₅₉₅, X₁: X₀ {O(n)}