WORST_CASE(?,O(n^1)) * Step 1: LocalSizeboundsProc WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. eval(A,B,C) -> eval(C,-1 + B,1 + A) [100 >= A && B >= C] (?,1) 1. start(A,B,C) -> eval(A,B,C) True (1,1) Signature: {(eval,3);(start,3)} Flow Graph: [0->{0},1->{0}] + Applied Processor: LocalSizeboundsProc + Details: LocalSizebounds generated; rvgraph (<0,0,A>, C, .= 0) (<0,0,B>, 1 + B, .+ 1) (<0,0,C>, 1 + A, .+ 1) (<1,0,A>, A, .= 0) (<1,0,B>, B, .= 0) (<1,0,C>, C, .= 0) * Step 2: SizeboundsProc WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. eval(A,B,C) -> eval(C,-1 + B,1 + A) [100 >= A && B >= C] (?,1) 1. start(A,B,C) -> eval(A,B,C) True (1,1) Signature: {(eval,3);(start,3)} Flow Graph: [0->{0},1->{0}] Sizebounds: (<0,0,A>, ?) (<0,0,B>, ?) (<0,0,C>, ?) (<1,0,A>, ?) (<1,0,B>, ?) (<1,0,C>, ?) + Applied Processor: SizeboundsProc + Details: Sizebounds computed: (<0,0,A>, 1) (<0,0,B>, ?) (<0,0,C>, 2) (<1,0,A>, A) (<1,0,B>, B) (<1,0,C>, C) * Step 3: PolyRank WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. eval(A,B,C) -> eval(C,-1 + B,1 + A) [100 >= A && B >= C] (?,1) 1. start(A,B,C) -> eval(A,B,C) True (1,1) Signature: {(eval,3);(start,3)} Flow Graph: [0->{0},1->{0}] Sizebounds: (<0,0,A>, 1) (<0,0,B>, ?) (<0,0,C>, 2) (<1,0,A>, A) (<1,0,B>, B) (<1,0,C>, C) + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(eval) = 101 + -1*x1 + x2 + -1*x3 p(start) = 101 + -1*x1 + x2 + -1*x3 The following rules are strictly oriented: [100 >= A && B >= C] ==> eval(A,B,C) = 101 + -1*A + B + -1*C > 99 + -1*A + B + -1*C = eval(C,-1 + B,1 + A) The following rules are weakly oriented: True ==> start(A,B,C) = 101 + -1*A + B + -1*C >= 101 + -1*A + B + -1*C = eval(A,B,C) * Step 4: KnowledgePropagation WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. eval(A,B,C) -> eval(C,-1 + B,1 + A) [100 >= A && B >= C] (101 + A + B + C,1) 1. start(A,B,C) -> eval(A,B,C) True (1,1) Signature: {(eval,3);(start,3)} Flow Graph: [0->{0},1->{0}] Sizebounds: (<0,0,A>, 1) (<0,0,B>, ?) (<0,0,C>, 2) (<1,0,A>, A) (<1,0,B>, B) (<1,0,C>, C) + Applied Processor: KnowledgePropagation + Details: The problem is already solved. WORST_CASE(?,O(n^1))