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