Initial Problem
Start: eval_loops_start
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: eval_loops_bb0_in, eval_loops_bb1_in, eval_loops_bb2_in, eval_loops_bb3_in, eval_loops_bb4_in, eval_loops_bb5_in, eval_loops_bb6_in, eval_loops_start, eval_loops_stop
Transitions:
t₁: eval_loops_bb0_in(X₀, X₁, X₂) → eval_loops_bb1_in(X₀, X₀, X₂) :|: 0 ≤ X₀
t₂: eval_loops_bb0_in(X₀, X₁, X₂) → eval_loops_bb6_in(X₀, X₁, X₂) :|: 1+X₀ ≤ 0
t₃: eval_loops_bb1_in(X₀, X₁, X₂) → eval_loops_bb2_in(X₀, X₁, X₂) :|: 0 ≤ X₁
t₄: eval_loops_bb1_in(X₀, X₁, X₂) → eval_loops_bb6_in(X₀, X₁, X₂) :|: 1+X₁ ≤ 0
t₅: eval_loops_bb2_in(X₀, X₁, X₂) → eval_loops_bb3_in(X₀, X₁, 1) :|: 2 ≤ X₁
t₆: eval_loops_bb2_in(X₀, X₁, X₂) → eval_loops_bb5_in(X₀, X₁, X₂) :|: X₁ ≤ 1
t₇: eval_loops_bb3_in(X₀, X₁, X₂) → eval_loops_bb4_in(X₀, X₁, X₂) :|: 1+X₂ ≤ X₁
t₈: eval_loops_bb3_in(X₀, X₁, X₂) → eval_loops_bb5_in(X₀, X₁, X₂) :|: X₁ ≤ X₂
t₉: eval_loops_bb4_in(X₀, X₁, X₂) → eval_loops_bb3_in(X₀, X₁, 2⋅X₂)
t₁₀: eval_loops_bb5_in(X₀, X₁, X₂) → eval_loops_bb1_in(X₀, X₁-1, X₂)
t₁₁: eval_loops_bb6_in(X₀, X₁, X₂) → eval_loops_stop(X₀, X₁, X₂)
t₀: eval_loops_start(X₀, X₁, X₂) → eval_loops_bb0_in(X₀, X₁, X₂)
Preprocessing
Found invariant X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location eval_loops_bb2_in
Found invariant X₁ ≤ X₀ ∧ 0 ≤ 1+X₁ ∧ 0 ≤ 1+X₀+X₁ ∧ 0 ≤ X₀ for location eval_loops_bb1_in
Found invariant X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location eval_loops_bb5_in
Found invariant 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location eval_loops_bb3_in
Found invariant 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location eval_loops_bb4_in
Problem after Preprocessing
Start: eval_loops_start
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: eval_loops_bb0_in, eval_loops_bb1_in, eval_loops_bb2_in, eval_loops_bb3_in, eval_loops_bb4_in, eval_loops_bb5_in, eval_loops_bb6_in, eval_loops_start, eval_loops_stop
Transitions:
t₁: eval_loops_bb0_in(X₀, X₁, X₂) → eval_loops_bb1_in(X₀, X₀, X₂) :|: 0 ≤ X₀
t₂: eval_loops_bb0_in(X₀, X₁, X₂) → eval_loops_bb6_in(X₀, X₁, X₂) :|: 1+X₀ ≤ 0
t₃: eval_loops_bb1_in(X₀, X₁, X₂) → eval_loops_bb2_in(X₀, X₁, X₂) :|: 0 ≤ X₁ ∧ 0 ≤ 1+X₀+X₁ ∧ 0 ≤ 1+X₁ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₀
t₄: eval_loops_bb1_in(X₀, X₁, X₂) → eval_loops_bb6_in(X₀, X₁, X₂) :|: 1+X₁ ≤ 0 ∧ 0 ≤ 1+X₀+X₁ ∧ 0 ≤ 1+X₁ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₀
t₅: eval_loops_bb2_in(X₀, X₁, X₂) → eval_loops_bb3_in(X₀, X₁, 1) :|: 2 ≤ X₁ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₁ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁
t₆: eval_loops_bb2_in(X₀, X₁, X₂) → eval_loops_bb5_in(X₀, X₁, X₂) :|: X₁ ≤ 1 ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₁ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁
t₇: eval_loops_bb3_in(X₀, X₁, X₂) → eval_loops_bb4_in(X₀, X₁, X₂) :|: 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₁+X₂ ∧ 4 ≤ X₀+X₁ ∧ X₁ ≤ X₀
t₈: eval_loops_bb3_in(X₀, X₁, X₂) → eval_loops_bb5_in(X₀, X₁, X₂) :|: X₁ ≤ X₂ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₁+X₂ ∧ 4 ≤ X₀+X₁ ∧ X₁ ≤ X₀
t₉: eval_loops_bb4_in(X₀, X₁, X₂) → eval_loops_bb3_in(X₀, X₁, 2⋅X₂) :|: 1+X₂ ≤ X₀ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₁+X₂ ∧ 4 ≤ X₀+X₁ ∧ X₁ ≤ X₀
t₁₀: eval_loops_bb5_in(X₀, X₁, X₂) → eval_loops_bb1_in(X₀, X₁-1, X₂) :|: 0 ≤ X₀ ∧ 0 ≤ X₀+X₁ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁
t₁₁: eval_loops_bb6_in(X₀, X₁, X₂) → eval_loops_stop(X₀, X₁, X₂)
t₀: eval_loops_start(X₀, X₁, X₂) → eval_loops_bb0_in(X₀, X₁, X₂)
MPRF for transition t₃: eval_loops_bb1_in(X₀, X₁, X₂) → eval_loops_bb2_in(X₀, X₁, X₂) :|: 0 ≤ X₁ ∧ 0 ≤ 1+X₀+X₁ ∧ 0 ≤ 1+X₁ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₀ of depth 1:
new bound:
X₀+2 {O(n)}
MPRF:
• eval_loops_bb1_in: [2+X₁]
• eval_loops_bb2_in: [1+X₁]
• eval_loops_bb3_in: [1+X₁]
• eval_loops_bb4_in: [1+X₁]
• eval_loops_bb5_in: [1+X₁]
MPRF for transition t₅: eval_loops_bb2_in(X₀, X₁, X₂) → eval_loops_bb3_in(X₀, X₁, 1) :|: 2 ≤ X₁ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₁ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ of depth 1:
new bound:
X₀+1 {O(n)}
MPRF:
• eval_loops_bb1_in: [1+X₁]
• eval_loops_bb2_in: [1+X₁]
• eval_loops_bb3_in: [X₁]
• eval_loops_bb4_in: [X₁]
• eval_loops_bb5_in: [X₁]
MPRF for transition t₆: eval_loops_bb2_in(X₀, X₁, X₂) → eval_loops_bb5_in(X₀, X₁, X₂) :|: X₁ ≤ 1 ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₁ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ of depth 1:
new bound:
X₀+1 {O(n)}
MPRF:
• eval_loops_bb1_in: [1+X₁]
• eval_loops_bb2_in: [1+X₁]
• eval_loops_bb3_in: [X₁]
• eval_loops_bb4_in: [X₁]
• eval_loops_bb5_in: [X₁]
MPRF for transition t₈: eval_loops_bb3_in(X₀, X₁, X₂) → eval_loops_bb5_in(X₀, X₁, X₂) :|: X₁ ≤ X₂ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₁+X₂ ∧ 4 ≤ X₀+X₁ ∧ X₁ ≤ X₀ of depth 1:
new bound:
2⋅X₀+3 {O(n)}
MPRF:
• eval_loops_bb1_in: [X₀+X₁-3]
• eval_loops_bb2_in: [X₀+X₁-3]
• eval_loops_bb3_in: [X₀+X₁-3]
• eval_loops_bb4_in: [X₀+X₁-3]
• eval_loops_bb5_in: [X₀+X₁-4]
MPRF for transition t₁₀: eval_loops_bb5_in(X₀, X₁, X₂) → eval_loops_bb1_in(X₀, X₁-1, X₂) :|: 0 ≤ X₀ ∧ 0 ≤ X₀+X₁ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ of depth 1:
new bound:
X₀+1 {O(n)}
MPRF:
• eval_loops_bb1_in: [1+X₁]
• eval_loops_bb2_in: [1+X₁]
• eval_loops_bb3_in: [1+X₁]
• eval_loops_bb4_in: [1+X₁]
• eval_loops_bb5_in: [1+X₁]
TWN: t₉: eval_loops_bb4_in→eval_loops_bb3_in
cycle: [t₉: eval_loops_bb4_in→eval_loops_bb3_in; t₇: eval_loops_bb3_in→eval_loops_bb4_in]
original loop: (1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₁+X₂ ∧ 4 ≤ X₀+X₁ ∧ X₁ ≤ X₀ ∧ 1+X₂ ≤ X₀ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₁+X₂ ∧ 4 ≤ X₀+X₁ ∧ X₁ ≤ X₀,(X₀,X₁,X₂) -> (X₀,X₁,2⋅X₂))
transformed loop: (1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₁+X₂ ∧ 4 ≤ X₀+X₁ ∧ X₁ ≤ X₀ ∧ 1+X₂ ≤ X₀ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₁+X₂ ∧ 4 ≤ X₀+X₁ ∧ X₁ ≤ X₀,(X₀,X₁,X₂) -> (X₀,X₁,2⋅X₂))
loop: (1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₁+X₂ ∧ 4 ≤ X₀+X₁ ∧ X₁ ≤ X₀ ∧ 1+X₂ ≤ X₀ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₁+X₂ ∧ 4 ≤ X₀+X₁ ∧ X₁ ≤ X₀,(X₀,X₁,X₂) -> (X₀,X₁,2⋅X₂))
order: [X₂; X₁; X₀]
closed-form:X₂: X₂⋅(2)^n
X₁: X₁
X₀: X₀
Termination: true
Formula:
X₀ ≤ 3 ∧ X₁ ≤ 3 ∧ X₀ ≤ 1 ∧ X₁ ≤ 1 ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀ ∧ 3 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0
∨ X₀ ≤ 3 ∧ X₁ ≤ 3 ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ 0 ∧ 2 ≤ X₀ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀ ∧ 3 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0
∨ X₀ ≤ 3 ∧ X₁ ≤ 3 ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀ ∧ 3 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0
∨ X₀ ≤ 3 ∧ X₁ ≤ 3 ∧ X₁ ≤ 1 ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ 0 ∧ 2 ≤ X₀ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀ ∧ 3 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0
∨ X₀ ≤ 3 ∧ X₁ ≤ 3 ∧ X₁ ≤ 1 ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀ ∧ 3 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0
∨ X₀ ≤ 3 ∧ X₁ ≤ 3 ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ 0 ∧ 2 ≤ X₀ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀ ∧ 3 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0
∨ X₀ ≤ 3 ∧ X₁ ≤ 3 ∧ 1 ≤ X₂ ∧ 2 ≤ X₀ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀ ∧ 3 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0
∨ X₀ ≤ 3 ∧ X₀ ≤ 1 ∧ X₁ ≤ 1 ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀ ∧ 4 ≤ X₀+X₁ ∧ 4 ≤ X₁ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0
∨ X₀ ≤ 3 ∧ X₀ ≤ 1 ∧ X₁ ≤ 1 ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀ ∧ 4 ≤ X₀+X₁ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0
∨ X₀ ≤ 3 ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ 0 ∧ 2 ≤ X₀ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀ ∧ 4 ≤ X₀+X₁ ∧ 4 ≤ X₁ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0
∨ X₀ ≤ 3 ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ 0 ∧ 2 ≤ X₀ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀ ∧ 4 ≤ X₀+X₁ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0
∨ X₀ ≤ 3 ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀ ∧ 4 ≤ X₀+X₁ ∧ 4 ≤ X₁ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0
∨ X₀ ≤ 3 ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀ ∧ 4 ≤ X₀+X₁ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0
∨ X₀ ≤ 3 ∧ X₁ ≤ 1 ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ 0 ∧ 2 ≤ X₀ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀ ∧ 4 ≤ X₀+X₁ ∧ 4 ≤ X₁ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0
∨ X₀ ≤ 3 ∧ X₁ ≤ 1 ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ 0 ∧ 2 ≤ X₀ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀ ∧ 4 ≤ X₀+X₁ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0
∨ X₀ ≤ 3 ∧ X₁ ≤ 1 ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀ ∧ 4 ≤ X₀+X₁ ∧ 4 ≤ X₁ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0
∨ X₀ ≤ 3 ∧ X₁ ≤ 1 ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀ ∧ 4 ≤ X₀+X₁ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0
∨ X₀ ≤ 3 ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ 0 ∧ 2 ≤ X₀ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀ ∧ 4 ≤ X₀+X₁ ∧ 4 ≤ X₁ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0
∨ X₀ ≤ 3 ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ 0 ∧ 2 ≤ X₀ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀ ∧ 4 ≤ X₀+X₁ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0
∨ X₀ ≤ 3 ∧ 1 ≤ X₂ ∧ 2 ≤ X₀ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀ ∧ 4 ≤ X₀+X₁ ∧ 4 ≤ X₁ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0
∨ X₀ ≤ 3 ∧ 1 ≤ X₂ ∧ 2 ≤ X₀ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀ ∧ 4 ≤ X₀+X₁ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0
∨ X₁ ≤ 3 ∧ X₀ ≤ 1 ∧ X₁ ≤ 1 ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀ ∧ 2 ≤ X₁ ∧ 3 ≤ X₁ ∧ 4 ≤ X₀ ∧ 4 ≤ X₀+X₁ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0
∨ X₁ ≤ 3 ∧ X₀ ≤ 1 ∧ X₁ ≤ 1 ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀ ∧ 2 ≤ X₁ ∧ 3 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0
∨ X₁ ≤ 3 ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ 0 ∧ 2 ≤ X₀ ∧ 2 ≤ X₁ ∧ 3 ≤ X₁ ∧ 4 ≤ X₀ ∧ 4 ≤ X₀+X₁ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0
∨ X₁ ≤ 3 ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ 0 ∧ 2 ≤ X₀ ∧ 2 ≤ X₁ ∧ 3 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0
∨ X₁ ≤ 3 ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀ ∧ 2 ≤ X₁ ∧ 3 ≤ X₁ ∧ 4 ≤ X₀ ∧ 4 ≤ X₀+X₁ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0
∨ X₁ ≤ 3 ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀ ∧ 2 ≤ X₁ ∧ 3 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0
∨ X₁ ≤ 3 ∧ X₁ ≤ 1 ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ 0 ∧ 2 ≤ X₀ ∧ 2 ≤ X₁ ∧ 3 ≤ X₁ ∧ 4 ≤ X₀ ∧ 4 ≤ X₀+X₁ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0
∨ X₁ ≤ 3 ∧ X₁ ≤ 1 ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ 0 ∧ 2 ≤ X₀ ∧ 2 ≤ X₁ ∧ 3 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0
∨ X₁ ≤ 3 ∧ X₁ ≤ 1 ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀ ∧ 2 ≤ X₁ ∧ 3 ≤ X₁ ∧ 4 ≤ X₀ ∧ 4 ≤ X₀+X₁ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0
∨ X₁ ≤ 3 ∧ X₁ ≤ 1 ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀ ∧ 2 ≤ X₁ ∧ 3 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0
∨ X₁ ≤ 3 ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ 0 ∧ 2 ≤ X₀ ∧ 2 ≤ X₁ ∧ 3 ≤ X₁ ∧ 4 ≤ X₀ ∧ 4 ≤ X₀+X₁ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0
∨ X₁ ≤ 3 ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ 0 ∧ 2 ≤ X₀ ∧ 2 ≤ X₁ ∧ 3 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0
∨ X₁ ≤ 3 ∧ 1 ≤ X₂ ∧ 2 ≤ X₀ ∧ 2 ≤ X₁ ∧ 3 ≤ X₁ ∧ 4 ≤ X₀ ∧ 4 ≤ X₀+X₁ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0
∨ X₁ ≤ 3 ∧ 1 ≤ X₂ ∧ 2 ≤ X₀ ∧ 2 ≤ X₁ ∧ 3 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0
∨ X₀ ≤ 1 ∧ X₁ ≤ 1 ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀ ∧ 4 ≤ X₀+X₁ ∧ 4 ≤ X₁ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0
∨ X₀ ≤ 1 ∧ X₁ ≤ 1 ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀ ∧ 4 ≤ X₀+X₁ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0
∨ X₀ ≤ 1 ∧ X₁ ≤ 1 ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 4 ≤ X₁ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0
∨ X₀ ≤ 1 ∧ X₁ ≤ 1 ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0
∨ X₀ ≤ 1 ∧ 1 ≤ X₀ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ 0 ∧ 2 ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀ ∧ 4 ≤ X₀+X₁ ∧ 4 ≤ X₁ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0
∨ X₀ ≤ 1 ∧ 1 ≤ X₀ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ 0 ∧ 2 ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀ ∧ 4 ≤ X₀+X₁ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0
∨ X₀ ≤ 1 ∧ 1 ≤ X₀ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ 0 ∧ 2 ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 4 ≤ X₁ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0
∨ X₀ ≤ 1 ∧ 1 ≤ X₀ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ 0 ∧ 2 ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0
∨ X₀ ≤ 1 ∧ 1 ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀ ∧ 4 ≤ X₀+X₁ ∧ 4 ≤ X₁ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0
∨ X₀ ≤ 1 ∧ 1 ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀ ∧ 4 ≤ X₀+X₁ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0
∨ X₀ ≤ 1 ∧ 1 ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 4 ≤ X₁ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0
∨ X₀ ≤ 1 ∧ 1 ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0
∨ X₁ ≤ 1 ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ 0 ∧ 2 ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀ ∧ 4 ≤ X₀+X₁ ∧ 4 ≤ X₁ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0
∨ X₁ ≤ 1 ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ 0 ∧ 2 ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀ ∧ 4 ≤ X₀+X₁ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0
∨ X₁ ≤ 1 ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ 0 ∧ 2 ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 4 ≤ X₁ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0
∨ X₁ ≤ 1 ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ 0 ∧ 2 ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0
∨ X₁ ≤ 1 ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀ ∧ 4 ≤ X₀+X₁ ∧ 4 ≤ X₁ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0
∨ X₁ ≤ 1 ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀ ∧ 4 ≤ X₀+X₁ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0
∨ X₁ ≤ 1 ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 4 ≤ X₁ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0
∨ X₁ ≤ 1 ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0
∨ 1 ≤ X₂ ∧ 1+X₂ ≤ 0 ∧ 2 ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀ ∧ 4 ≤ X₀+X₁ ∧ 4 ≤ X₁ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0
∨ 1 ≤ X₂ ∧ 1+X₂ ≤ 0 ∧ 2 ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀ ∧ 4 ≤ X₀+X₁ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0
∨ 1 ≤ X₂ ∧ 1+X₂ ≤ 0 ∧ 2 ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 4 ≤ X₁ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0
∨ 1 ≤ X₂ ∧ 1+X₂ ≤ 0 ∧ 2 ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₁ ≤ X₀
∨ 1 ≤ X₂ ∧ 1+X₂ ≤ 0 ∧ 2 ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0
∨ 1 ≤ X₂ ∧ 2 ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀ ∧ 4 ≤ X₀+X₁ ∧ 4 ≤ X₁ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0
∨ 1 ≤ X₂ ∧ 2 ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀ ∧ 4 ≤ X₀+X₁ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0
∨ 1 ≤ X₂ ∧ 2 ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 4 ≤ X₁ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0
∨ 1 ≤ X₂ ∧ 2 ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0
Stabilization-Threshold for: 3 ≤ X₁+X₂
alphas_abs: 2+X₁
M': 1
N: 1
Bound: log(X₁)+4 {O(log(n))}
Stabilization-Threshold for: 3 ≤ X₀+X₂
alphas_abs: 2+X₀
M': 1
N: 1
Bound: log(X₀)+4 {O(log(n))}
Stabilization-Threshold for: 1+X₂ ≤ X₁
alphas_abs: X₁
M': 1
N: 1
Bound: log(X₁)+2 {O(log(n))}
Stabilization-Threshold for: 1+X₂ ≤ X₀
alphas_abs: X₀
M': 1
N: 1
Bound: log(X₀)+2 {O(log(n))}
TWN - Lifting for [7: eval_loops_bb3_in->eval_loops_bb4_in; 9: eval_loops_bb4_in->eval_loops_bb3_in] of 2⋅log(X₀)+2⋅log(X₁)+14 {O(log(n))}
relevant size-bounds w.r.t. t₅: eval_loops_bb2_in→eval_loops_bb3_in:
X₀: X₀ {O(n)}
X₁: X₀+2 {O(n)}
Runtime-bound of t₅: X₀+1 {O(n)}
Results in: 4⋅X₀⋅log(X₀)+16⋅X₀+4⋅log(X₀)+16 {O(log(n)*n)}
All Bounds
Timebounds
Overall timebound:8⋅X₀⋅log(X₀)+38⋅X₀+8⋅log(X₀)+45 {O(log(n)*n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: X₀+2 {O(n)}
t₄: 1 {O(1)}
t₅: X₀+1 {O(n)}
t₆: X₀+1 {O(n)}
t₇: 4⋅X₀⋅log(X₀)+16⋅X₀+4⋅log(X₀)+16 {O(log(n)*n)}
t₈: 2⋅X₀+3 {O(n)}
t₉: 4⋅X₀⋅log(X₀)+16⋅X₀+4⋅log(X₀)+16 {O(log(n)*n)}
t₁₀: X₀+1 {O(n)}
t₁₁: 1 {O(1)}
Costbounds
Overall costbound: 8⋅X₀⋅log(X₀)+38⋅X₀+8⋅log(X₀)+45 {O(log(n)*n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: X₀+2 {O(n)}
t₄: 1 {O(1)}
t₅: X₀+1 {O(n)}
t₆: X₀+1 {O(n)}
t₇: 4⋅X₀⋅log(X₀)+16⋅X₀+4⋅log(X₀)+16 {O(log(n)*n)}
t₈: 2⋅X₀+3 {O(n)}
t₉: 4⋅X₀⋅log(X₀)+16⋅X₀+4⋅log(X₀)+16 {O(log(n)*n)}
t₁₀: X₀+1 {O(n)}
t₁₁: 1 {O(1)}
Sizebounds
t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₁, X₀: X₀ {O(n)}
t₁, X₁: X₀ {O(n)}
t₁, X₂: X₂ {O(n)}
t₂, X₀: X₀ {O(n)}
t₂, X₁: X₁ {O(n)}
t₂, X₂: X₂ {O(n)}
t₃, X₀: X₀ {O(n)}
t₃, X₁: X₀+2 {O(n)}
t₃, X₂: 2^(16⋅X₀)⋅2^(4⋅X₀⋅log(X₀))⋅2^(4⋅log(X₀))⋅65536+X₂ {O(EXP)}
t₄, X₀: X₀ {O(n)}
t₄, X₁: 1 {O(1)}
t₄, X₂: 2^(16⋅X₀)⋅2^(4⋅X₀⋅log(X₀))⋅2^(4⋅log(X₀))⋅65536+X₂ {O(EXP)}
t₅, X₀: X₀ {O(n)}
t₅, X₁: X₀+2 {O(n)}
t₅, X₂: 1 {O(1)}
t₆, X₀: X₀ {O(n)}
t₆, X₁: 1 {O(1)}
t₆, X₂: 2^(16⋅X₀)⋅2^(4⋅X₀⋅log(X₀))⋅2^(4⋅log(X₀))⋅65536+X₂ {O(EXP)}
t₇, X₀: X₀ {O(n)}
t₇, X₁: X₀+2 {O(n)}
t₇, X₂: 2^(16⋅X₀)⋅2^(4⋅X₀⋅log(X₀))⋅2^(4⋅log(X₀))⋅65536 {O(EXP)}
t₈, X₀: X₀ {O(n)}
t₈, X₁: X₀+2 {O(n)}
t₈, X₂: 2^(16⋅X₀)⋅2^(4⋅X₀⋅log(X₀))⋅2^(4⋅log(X₀))⋅65536 {O(EXP)}
t₉, X₀: X₀ {O(n)}
t₉, X₁: X₀+2 {O(n)}
t₉, X₂: 2^(16⋅X₀)⋅2^(4⋅X₀⋅log(X₀))⋅2^(4⋅log(X₀))⋅65536 {O(EXP)}
t₁₀, X₀: X₀ {O(n)}
t₁₀, X₁: X₀+2 {O(n)}
t₁₀, X₂: 2^(16⋅X₀)⋅2^(4⋅X₀⋅log(X₀))⋅2^(4⋅log(X₀))⋅65536+X₂ {O(EXP)}
t₁₁, X₀: 2⋅X₀ {O(n)}
t₁₁, X₁: X₁+1 {O(n)}
t₁₁, X₂: 2^(16⋅X₀)⋅2^(4⋅X₀⋅log(X₀))⋅2^(4⋅log(X₀))⋅65536+2⋅X₂ {O(EXP)}