WORST_CASE(?,O(n^1)) * Step 1: LocalSizeboundsProc WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. eval(A,B) -> eval(A,A + B) [A >= 1 && A >= 1 + B] (?,1) 1. start(A,B) -> eval(A,B) True (1,1) Signature: {(eval,2);(start,2)} Flow Graph: [0->{0},1->{0}] + Applied Processor: LocalSizeboundsProc + Details: LocalSizebounds generated; rvgraph (<0,0,A>, A, .= 0) (<0,0,B>, 1 + A + B, .* 1) (<1,0,A>, A, .= 0) (<1,0,B>, B, .= 0) * Step 2: SizeboundsProc WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. eval(A,B) -> eval(A,A + B) [A >= 1 && A >= 1 + B] (?,1) 1. start(A,B) -> eval(A,B) True (1,1) Signature: {(eval,2);(start,2)} Flow Graph: [0->{0},1->{0}] Sizebounds: (<0,0,A>, ?) (<0,0,B>, ?) (<1,0,A>, ?) (<1,0,B>, ?) + Applied Processor: SizeboundsProc + Details: Sizebounds computed: (<0,0,A>, A) (<0,0,B>, A) (<1,0,A>, A) (<1,0,B>, B) * Step 3: PolyRank WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. eval(A,B) -> eval(A,A + B) [A >= 1 && A >= 1 + B] (?,1) 1. start(A,B) -> eval(A,B) True (1,1) Signature: {(eval,2);(start,2)} Flow Graph: [0->{0},1->{0}] Sizebounds: (<0,0,A>, A) (<0,0,B>, A) (<1,0,A>, A) (<1,0,B>, B) + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(eval) = x1 + -1*x2 p(start) = x1 + -1*x2 The following rules are strictly oriented: [A >= 1 && A >= 1 + B] ==> eval(A,B) = A + -1*B > -1*B = eval(A,A + B) The following rules are weakly oriented: True ==> start(A,B) = A + -1*B >= A + -1*B = eval(A,B) * Step 4: KnowledgePropagation WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. eval(A,B) -> eval(A,A + B) [A >= 1 && A >= 1 + B] (A + B,1) 1. start(A,B) -> eval(A,B) True (1,1) Signature: {(eval,2);(start,2)} Flow Graph: [0->{0},1->{0}] Sizebounds: (<0,0,A>, A) (<0,0,B>, A) (<1,0,A>, A) (<1,0,B>, B) + Applied Processor: KnowledgePropagation + Details: The problem is already solved. WORST_CASE(?,O(n^1))