Initial Problem

Start: eval_twn01_start
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: eval_twn01_bb0_in, eval_twn01_bb1_in, eval_twn01_bb2_in, eval_twn01_bb3_in, eval_twn01_start, eval_twn01_stop
Transitions:
t₁: eval_twn01_bb0_in(X₀, X₁, X₂, X₃) → eval_twn01_bb1_in(X₂, X₃, X₂, X₃)
t₂: eval_twn01_bb1_in(X₀, X₁, X₂, X₃) → eval_twn01_bb2_in(X₀, X₁, X₂, X₃) :|: 1 ≤ X₀ ∧ 1+X₀ ≤ X₁
t₃: eval_twn01_bb1_in(X₀, X₁, X₂, X₃) → eval_twn01_bb3_in(X₀, X₁, X₂, X₃) :|: X₁ ≤ X₀
t₄: eval_twn01_bb1_in(X₀, X₁, X₂, X₃) → eval_twn01_bb3_in(X₀, X₁, X₂, X₃) :|: X₀ ≤ 0
t₅: eval_twn01_bb2_in(X₀, X₁, X₂, X₃) → eval_twn01_bb1_in(3⋅X₀, 2⋅X₁, X₂, X₃)
t₆: eval_twn01_bb3_in(X₀, X₁, X₂, X₃) → eval_twn01_stop(X₀, X₁, X₂, X₃)
t₀: eval_twn01_start(X₀, X₁, X₂, X₃) → eval_twn01_bb0_in(X₀, X₁, X₂, X₃)

Preprocessing

Found invariant X₃ ≤ X₁ ∧ X₂ ≤ X₀ for location eval_twn01_bb1_in

Found invariant X₃ ≤ X₁ ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location eval_twn01_bb2_in

Found invariant X₃ ≤ X₁ ∧ X₂ ≤ X₀ for location eval_twn01_bb3_in

Found invariant X₃ ≤ X₁ ∧ X₂ ≤ X₀ for location eval_twn01_stop

Problem after Preprocessing

Start: eval_twn01_start
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: eval_twn01_bb0_in, eval_twn01_bb1_in, eval_twn01_bb2_in, eval_twn01_bb3_in, eval_twn01_start, eval_twn01_stop
Transitions:
t₁: eval_twn01_bb0_in(X₀, X₁, X₂, X₃) → eval_twn01_bb1_in(X₂, X₃, X₂, X₃)
t₂: eval_twn01_bb1_in(X₀, X₁, X₂, X₃) → eval_twn01_bb2_in(X₀, X₁, X₂, X₃) :|: 1 ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₃ ≤ X₁
t₃: eval_twn01_bb1_in(X₀, X₁, X₂, X₃) → eval_twn01_bb3_in(X₀, X₁, X₂, X₃) :|: X₁ ≤ X₀ ∧ X₂ ≤ X₀ ∧ X₃ ≤ X₁
t₄: eval_twn01_bb1_in(X₀, X₁, X₂, X₃) → eval_twn01_bb3_in(X₀, X₁, X₂, X₃) :|: X₀ ≤ 0 ∧ X₂ ≤ X₀ ∧ X₃ ≤ X₁
t₅: eval_twn01_bb2_in(X₀, X₁, X₂, X₃) → eval_twn01_bb1_in(3⋅X₀, 2⋅X₁, X₂, X₃) :|: 1 ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ 1+X₂ ≤ X₁ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ X₂ ≤ X₀ ∧ X₃ ≤ X₁
t₆: eval_twn01_bb3_in(X₀, X₁, X₂, X₃) → eval_twn01_stop(X₀, X₁, X₂, X₃) :|: X₂ ≤ X₀ ∧ X₃ ≤ X₁
t₀: eval_twn01_start(X₀, X₁, X₂, X₃) → eval_twn01_bb0_in(X₀, X₁, X₂, X₃)

TWN: t₂: eval_twn01_bb1_in→eval_twn01_bb2_in

Show Graph

Termination: true
Formula:

TWN - Lifting for [2: eval_twn01_bb1_in->eval_twn01_bb2_in; 5: eval_twn01_bb2_in->eval_twn01_bb1_in] of 2⋅log(X₁)+2⋅log(X₂)+log(X₃)+16 {O(log(n))}

All Bounds

Timebounds

Overall timebound:4⋅log(X₂)+6⋅log(X₃)+37 {O(log(n))}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 2⋅log(X₂)+3⋅log(X₃)+16 {O(log(n))}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₅: 2⋅log(X₂)+3⋅log(X₃)+16 {O(log(n))}
t₆: 1 {O(1)}

Costbounds

Overall costbound: 4⋅log(X₂)+6⋅log(X₃)+37 {O(log(n))}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 2⋅log(X₂)+3⋅log(X₃)+16 {O(log(n))}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₅: 2⋅log(X₂)+3⋅log(X₃)+16 {O(log(n))}
t₆: 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: X₂ {O(n)}
t₁, X₁: X₃ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₃ {O(n)}
t₂, X₀: 3^(2⋅log(X₂))⋅3^(3⋅log(X₃))⋅43046721⋅X₂ {O(EXP)}
t₂, X₁: 2^(2⋅log(X₂))⋅2^(3⋅log(X₃))⋅65536⋅X₃ {O(EXP)}
t₂, X₂: X₂ {O(n)}
t₂, X₃: X₃ {O(n)}
t₃, X₀: 3^(2⋅log(X₂))⋅3^(3⋅log(X₃))⋅43046721⋅X₂+X₂ {O(EXP)}
t₃, X₁: 2^(2⋅log(X₂))⋅2^(3⋅log(X₃))⋅65536⋅X₃+X₃ {O(EXP)}
t₃, X₂: 2⋅X₂ {O(n)}
t₃, X₃: 2⋅X₃ {O(n)}
t₄, X₀: X₂ {O(n)}
t₄, X₁: X₃ {O(n)}
t₄, X₂: X₂ {O(n)}
t₄, X₃: X₃ {O(n)}
t₅, X₀: 3^(2⋅log(X₂))⋅3^(3⋅log(X₃))⋅43046721⋅X₂ {O(EXP)}
t₅, X₁: 2^(2⋅log(X₂))⋅2^(3⋅log(X₃))⋅65536⋅X₃ {O(EXP)}
t₅, X₂: X₂ {O(n)}
t₅, X₃: X₃ {O(n)}
t₆, X₀: 3^(2⋅log(X₂))⋅3^(3⋅log(X₃))⋅43046721⋅X₂+2⋅X₂ {O(EXP)}
t₆, X₁: 2^(2⋅log(X₂))⋅2^(3⋅log(X₃))⋅65536⋅X₃+2⋅X₃ {O(EXP)}
t₆, X₂: 3⋅X₂ {O(n)}
t₆, X₃: 3⋅X₃ {O(n)}