Initial Problem

Start: eval_twn19_start
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars:
Locations: eval_twn19_bb0_in, eval_twn19_bb1_in, eval_twn19_bb2_in, eval_twn19_bb3_in, eval_twn19_start, eval_twn19_stop
Transitions:
t₁: eval_twn19_bb0_in(X₀, X₁, X₂, X₃, X₄) → eval_twn19_bb1_in(X₂, X₃, X₂, X₃, X₄) :|: 1 ≤ X₄
t₂: eval_twn19_bb0_in(X₀, X₁, X₂, X₃, X₄) → eval_twn19_bb3_in(X₀, X₁, X₂, X₃, X₄) :|: X₄ ≤ 0
t₃: eval_twn19_bb1_in(X₀, X₁, X₂, X₃, X₄) → eval_twn19_bb2_in(X₀, X₁, X₂, X₃, X₄) :|: 1+X₀ ≤ 0 ∧ 1+(X₀)²+(X₄)⁵ ≤ X₁
t₄: eval_twn19_bb1_in(X₀, X₁, X₂, X₃, X₄) → eval_twn19_bb2_in(X₀, X₁, X₂, X₃, X₄) :|: 1 ≤ X₀ ∧ 1+(X₀)²+(X₄)⁵ ≤ X₁
t₅: eval_twn19_bb1_in(X₀, X₁, X₂, X₃, X₄) → eval_twn19_bb3_in(X₀, X₁, X₂, X₃, X₄) :|: X₁ ≤ (X₀)²+(X₄)⁵
t₆: eval_twn19_bb1_in(X₀, X₁, X₂, X₃, X₄) → eval_twn19_bb3_in(X₀, X₁, X₂, X₃, X₄) :|: 0 ≤ X₀ ∧ X₀ ≤ 0
t₇: eval_twn19_bb2_in(X₀, X₁, X₂, X₃, X₄) → eval_twn19_bb1_in(-2⋅X₀, 3⋅X₁-2⋅(X₄)³, X₂, X₃, X₄)
t₈: eval_twn19_bb3_in(X₀, X₁, X₂, X₃, X₄) → eval_twn19_stop(X₀, X₁, X₂, X₃, X₄)
t₀: eval_twn19_start(X₀, X₁, X₂, X₃, X₄) → eval_twn19_bb0_in(X₀, X₁, X₂, X₃, X₄)

Preprocessing

Found invariant 1 ≤ X₄ for location eval_twn19_bb2_in

Found invariant 1 ≤ X₄ for location eval_twn19_bb1_in

Problem after Preprocessing

Start: eval_twn19_start
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars:
Locations: eval_twn19_bb0_in, eval_twn19_bb1_in, eval_twn19_bb2_in, eval_twn19_bb3_in, eval_twn19_start, eval_twn19_stop
Transitions:
t₁: eval_twn19_bb0_in(X₀, X₁, X₂, X₃, X₄) → eval_twn19_bb1_in(X₂, X₃, X₂, X₃, X₄) :|: 1 ≤ X₄
t₂: eval_twn19_bb0_in(X₀, X₁, X₂, X₃, X₄) → eval_twn19_bb3_in(X₀, X₁, X₂, X₃, X₄) :|: X₄ ≤ 0
t₃: eval_twn19_bb1_in(X₀, X₁, X₂, X₃, X₄) → eval_twn19_bb2_in(X₀, X₁, X₂, X₃, X₄) :|: 1+X₀ ≤ 0 ∧ 1+(X₀)²+(X₄)⁵ ≤ X₁ ∧ 1 ≤ X₄
t₄: eval_twn19_bb1_in(X₀, X₁, X₂, X₃, X₄) → eval_twn19_bb2_in(X₀, X₁, X₂, X₃, X₄) :|: 1 ≤ X₀ ∧ 1+(X₀)²+(X₄)⁵ ≤ X₁ ∧ 1 ≤ X₄
t₅: eval_twn19_bb1_in(X₀, X₁, X₂, X₃, X₄) → eval_twn19_bb3_in(X₀, X₁, X₂, X₃, X₄) :|: X₁ ≤ (X₀)²+(X₄)⁵ ∧ 1 ≤ X₄
t₆: eval_twn19_bb1_in(X₀, X₁, X₂, X₃, X₄) → eval_twn19_bb3_in(X₀, X₁, X₂, X₃, X₄) :|: 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 1 ≤ X₄
t₇: eval_twn19_bb2_in(X₀, X₁, X₂, X₃, X₄) → eval_twn19_bb1_in(-2⋅X₀, 3⋅X₁-2⋅(X₄)³, X₂, X₃, X₄) :|: 1 ≤ X₄
t₈: eval_twn19_bb3_in(X₀, X₁, X₂, X₃, X₄) → eval_twn19_stop(X₀, X₁, X₂, X₃, X₄)
t₀: eval_twn19_start(X₀, X₁, X₂, X₃, X₄) → eval_twn19_bb0_in(X₀, X₁, X₂, X₃, X₄)

TWN: t₄: eval_twn19_bb1_in→eval_twn19_bb2_in

Show Graph

Termination: true
Formula:

TWN - Lifting for [3: eval_twn19_bb1_in->eval_twn19_bb2_in; 4: eval_twn19_bb1_in->eval_twn19_bb2_in; 7: eval_twn19_bb2_in->eval_twn19_bb1_in] of 32⋅log(X₄)+4⋅log(X₁)+29 {O(log(n))}

All Bounds

Timebounds

Overall timebound:12⋅log(X₃)+96⋅log(X₄)+93 {O(log(n))}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 32⋅log(X₄)+4⋅log(X₃)+29 {O(log(n))}
t₄: 32⋅log(X₄)+4⋅log(X₃)+29 {O(log(n))}
t₅: 1 {O(1)}
t₆: 1 {O(1)}
t₇: 32⋅log(X₄)+4⋅log(X₃)+29 {O(log(n))}
t₈: 1 {O(1)}

Costbounds

Overall costbound: 12⋅log(X₃)+96⋅log(X₄)+93 {O(log(n))}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 32⋅log(X₄)+4⋅log(X₃)+29 {O(log(n))}
t₄: 32⋅log(X₄)+4⋅log(X₃)+29 {O(log(n))}
t₅: 1 {O(1)}
t₆: 1 {O(1)}
t₇: 32⋅log(X₄)+4⋅log(X₃)+29 {O(log(n))}
t₈: 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)}
t₁, X₀: X₂ {O(n)}
t₁, X₁: X₃ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₃ {O(n)}
t₁, X₄: X₄ {O(n)}
t₂, X₀: X₀ {O(n)}
t₂, X₁: X₁ {O(n)}
t₂, X₂: X₂ {O(n)}
t₂, X₃: X₃ {O(n)}
t₂, X₄: X₄ {O(n)}
t₃, X₀: 2^(32⋅log(X₄))⋅2^(4⋅log(X₃))⋅536870912⋅X₂ {O(EXP)}
t₃, X₁: 323257909929174534292273980721360271853387⋅3^(12⋅log(X₃))⋅3^(96⋅log(X₄))⋅X₃+323257909929174534292273980721360271853387⋅3^(12⋅log(X₃))⋅3^(96⋅log(X₄))⋅X₄⋅X₄⋅X₄+X₄⋅X₄⋅X₄ {O(EXP)}
t₃, X₂: X₂ {O(n)}
t₃, X₃: X₃ {O(n)}
t₃, X₄: X₄ {O(n)}
t₄, X₀: 2^(32⋅log(X₄))⋅2^(4⋅log(X₃))⋅536870912⋅X₂ {O(EXP)}
t₄, X₁: 323257909929174534292273980721360271853387⋅3^(12⋅log(X₃))⋅3^(96⋅log(X₄))⋅X₃+323257909929174534292273980721360271853387⋅3^(12⋅log(X₃))⋅3^(96⋅log(X₄))⋅X₄⋅X₄⋅X₄+X₄⋅X₄⋅X₄ {O(EXP)}
t₄, X₂: X₂ {O(n)}
t₄, X₃: X₃ {O(n)}
t₄, X₄: X₄ {O(n)}
t₅, X₀: 2^(32⋅log(X₄))⋅2^(4⋅log(X₃))⋅536870912⋅X₂+X₂ {O(EXP)}
t₅, X₁: 323257909929174534292273980721360271853387⋅3^(12⋅log(X₃))⋅3^(96⋅log(X₄))⋅X₃+323257909929174534292273980721360271853387⋅3^(12⋅log(X₃))⋅3^(96⋅log(X₄))⋅X₄⋅X₄⋅X₄+X₄⋅X₄⋅X₄+X₃ {O(EXP)}
t₅, X₂: 2⋅X₂ {O(n)}
t₅, X₃: 2⋅X₃ {O(n)}
t₅, X₄: 2⋅X₄ {O(n)}
t₆, X₀: 0 {O(1)}
t₆, X₁: 323257909929174534292273980721360271853387⋅3^(12⋅log(X₃))⋅3^(96⋅log(X₄))⋅X₃+323257909929174534292273980721360271853387⋅3^(12⋅log(X₃))⋅3^(96⋅log(X₄))⋅X₄⋅X₄⋅X₄+X₄⋅X₄⋅X₄+X₃ {O(EXP)}
t₆, X₂: 2⋅X₂ {O(n)}
t₆, X₃: 2⋅X₃ {O(n)}
t₆, X₄: 2⋅X₄ {O(n)}
t₇, X₀: 2^(32⋅log(X₄))⋅2^(4⋅log(X₃))⋅536870912⋅X₂ {O(EXP)}
t₇, X₁: 323257909929174534292273980721360271853387⋅3^(12⋅log(X₃))⋅3^(96⋅log(X₄))⋅X₃+323257909929174534292273980721360271853387⋅3^(12⋅log(X₃))⋅3^(96⋅log(X₄))⋅X₄⋅X₄⋅X₄+X₄⋅X₄⋅X₄ {O(EXP)}
t₇, X₂: X₂ {O(n)}
t₇, X₃: X₃ {O(n)}
t₇, X₄: X₄ {O(n)}
t₈, X₀: 2^(32⋅log(X₄))⋅2^(4⋅log(X₃))⋅536870912⋅X₂+X₀+X₂ {O(EXP)}
t₈, X₁: 3^(12⋅log(X₃))⋅3^(96⋅log(X₄))⋅646515819858349068584547961442720543706774⋅X₃+3^(12⋅log(X₃))⋅3^(96⋅log(X₄))⋅646515819858349068584547961442720543706774⋅X₄⋅X₄⋅X₄+2⋅X₄⋅X₄⋅X₄+2⋅X₃+X₁ {O(EXP)}
t₈, X₂: 5⋅X₂ {O(n)}
t₈, X₃: 5⋅X₃ {O(n)}
t₈, X₄: 5⋅X₄ {O(n)}