WORST_CASE(?,O(n^1)) * Step 1: LocalSizeboundsProc WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. eval0(A,B,C) -> eval1(A,B,C) [A >= 1] (1,1) 1. eval1(A,B,C) -> eval1(A,A + B,C) [A >= 1 + B && C >= 1 + A && A >= 1] (?,1) 2. eval1(A,B,C) -> eval1(A,B,-1*A + B) [A >= 1 + B && C >= 1 + A && A >= 1] (?,1) Signature: {(eval0,3);(eval1,3)} Flow Graph: [0->{1,2},1->{1,2},2->{1,2}] + Applied Processor: LocalSizeboundsProc + Details: LocalSizebounds generated; rvgraph (<0,0,A>, A, .= 0) (<0,0,B>, B, .= 0) (<0,0,C>, C, .= 0) (<1,0,A>, A, .= 0) (<1,0,B>, 1 + A + B, .* 1) (<1,0,C>, C, .= 0) (<2,0,A>, A, .= 0) (<2,0,B>, B, .= 0) (<2,0,C>, 1 + A + B, .* 1) * Step 2: SizeboundsProc WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. eval0(A,B,C) -> eval1(A,B,C) [A >= 1] (1,1) 1. eval1(A,B,C) -> eval1(A,A + B,C) [A >= 1 + B && C >= 1 + A && A >= 1] (?,1) 2. eval1(A,B,C) -> eval1(A,B,-1*A + B) [A >= 1 + B && C >= 1 + A && A >= 1] (?,1) Signature: {(eval0,3);(eval1,3)} Flow Graph: [0->{1,2},1->{1,2},2->{1,2}] Sizebounds: (<0,0,A>, ?) (<0,0,B>, ?) (<0,0,C>, ?) (<1,0,A>, ?) (<1,0,B>, ?) (<1,0,C>, ?) (<2,0,A>, ?) (<2,0,B>, ?) (<2,0,C>, ?) + Applied Processor: SizeboundsProc + Details: Sizebounds computed: (<0,0,A>, A) (<0,0,B>, B) (<0,0,C>, C) (<1,0,A>, A) (<1,0,B>, A) (<1,0,C>, 1 + 2*A + B + C) (<2,0,A>, A) (<2,0,B>, A) (<2,0,C>, 1 + 2*A + B) * Step 3: UnsatPaths WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. eval0(A,B,C) -> eval1(A,B,C) [A >= 1] (1,1) 1. eval1(A,B,C) -> eval1(A,A + B,C) [A >= 1 + B && C >= 1 + A && A >= 1] (?,1) 2. eval1(A,B,C) -> eval1(A,B,-1*A + B) [A >= 1 + B && C >= 1 + A && A >= 1] (?,1) Signature: {(eval0,3);(eval1,3)} Flow Graph: [0->{1,2},1->{1,2},2->{1,2}] Sizebounds: (<0,0,A>, A) (<0,0,B>, B) (<0,0,C>, C) (<1,0,A>, A) (<1,0,B>, A) (<1,0,C>, 1 + 2*A + B + C) (<2,0,A>, A) (<2,0,B>, A) (<2,0,C>, 1 + 2*A + B) + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(2,1),(2,2)] * Step 4: LeafRules WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. eval0(A,B,C) -> eval1(A,B,C) [A >= 1] (1,1) 1. eval1(A,B,C) -> eval1(A,A + B,C) [A >= 1 + B && C >= 1 + A && A >= 1] (?,1) 2. eval1(A,B,C) -> eval1(A,B,-1*A + B) [A >= 1 + B && C >= 1 + A && A >= 1] (?,1) Signature: {(eval0,3);(eval1,3)} Flow Graph: [0->{1,2},1->{1,2},2->{}] Sizebounds: (<0,0,A>, A) (<0,0,B>, B) (<0,0,C>, C) (<1,0,A>, A) (<1,0,B>, A) (<1,0,C>, 1 + 2*A + B + C) (<2,0,A>, A) (<2,0,B>, A) (<2,0,C>, 1 + 2*A + B) + Applied Processor: LeafRules + Details: The following transitions are estimated by its predecessors and are removed [2] * Step 5: PolyRank WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. eval0(A,B,C) -> eval1(A,B,C) [A >= 1] (1,1) 1. eval1(A,B,C) -> eval1(A,A + B,C) [A >= 1 + B && C >= 1 + A && A >= 1] (?,1) Signature: {(eval0,3);(eval1,3)} Flow Graph: [0->{1},1->{1}] Sizebounds: (<0,0,A>, A) (<0,0,B>, B) (<0,0,C>, C) (<1,0,A>, A) (<1,0,B>, A) (<1,0,C>, 1 + 2*A + B + C) + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(eval0) = x1 + -1*x2 p(eval1) = x1 + -1*x2 The following rules are strictly oriented: [A >= 1 + B && C >= 1 + A && A >= 1] ==> eval1(A,B,C) = A + -1*B > -1*B = eval1(A,A + B,C) The following rules are weakly oriented: [A >= 1] ==> eval0(A,B,C) = A + -1*B >= A + -1*B = eval1(A,B,C) * Step 6: KnowledgePropagation WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. eval0(A,B,C) -> eval1(A,B,C) [A >= 1] (1,1) 1. eval1(A,B,C) -> eval1(A,A + B,C) [A >= 1 + B && C >= 1 + A && A >= 1] (A + B,1) Signature: {(eval0,3);(eval1,3)} Flow Graph: [0->{1},1->{1}] Sizebounds: (<0,0,A>, A) (<0,0,B>, B) (<0,0,C>, C) (<1,0,A>, A) (<1,0,B>, A) (<1,0,C>, 1 + 2*A + B + C) + Applied Processor: KnowledgePropagation + Details: The problem is already solved. WORST_CASE(?,O(n^1))