WORST_CASE(?,O(n^1)) * Step 1: LocalSizeboundsProc WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. f1(A) -> f0(A) True (1,1) 1. f0(A) -> f0(-1 + A) [A >= 0] (?,1) Signature: {(f0,1);(f1,1)} Flow Graph: [0->{1},1->{1}] + Applied Processor: LocalSizeboundsProc + Details: LocalSizebounds generated; rvgraph (<0,0,A>, A, .= 0) (<1,0,A>, 1 + A, .+ 1) * Step 2: SizeboundsProc WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. f1(A) -> f0(A) True (1,1) 1. f0(A) -> f0(-1 + A) [A >= 0] (?,1) Signature: {(f0,1);(f1,1)} Flow Graph: [0->{1},1->{1}] Sizebounds: (<0,0,A>, ?) (<1,0,A>, ?) + Applied Processor: SizeboundsProc + Details: Sizebounds computed: (<0,0,A>, A) (<1,0,A>, ?) * Step 3: PolyRank WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. f1(A) -> f0(A) True (1,1) 1. f0(A) -> f0(-1 + A) [A >= 0] (?,1) Signature: {(f0,1);(f1,1)} Flow Graph: [0->{1},1->{1}] Sizebounds: (<0,0,A>, A) (<1,0,A>, ?) + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(f0) = 1 + x1 p(f1) = 1 + x1 The following rules are strictly oriented: [A >= 0] ==> f0(A) = 1 + A > A = f0(-1 + A) The following rules are weakly oriented: True ==> f1(A) = 1 + A >= 1 + A = f0(A) * Step 4: KnowledgePropagation WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. f1(A) -> f0(A) True (1,1) 1. f0(A) -> f0(-1 + A) [A >= 0] (1 + A,1) Signature: {(f0,1);(f1,1)} Flow Graph: [0->{1},1->{1}] Sizebounds: (<0,0,A>, A) (<1,0,A>, ?) + Applied Processor: KnowledgePropagation + Details: The problem is already solved. WORST_CASE(?,O(n^1))