WORST_CASE(?,O(n^1)) * Step 1: RestrictVarsProcessor WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. l0(A,B) -> l1(0,B) True (1,1) 1. l1(A,B) -> l1(1 + A,-1 + B) [B >= 1] (?,1) 2. l1(A,B) -> l2(A,B) [0 >= B] (?,1) Signature: {(l0,2);(l1,2);(l2,2)} Flow Graph: [0->{1,2},1->{1,2},2->{}] + Applied Processor: RestrictVarsProcessor + Details: We removed the arguments [A] . * Step 2: LocalSizeboundsProc WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. l0(B) -> l1(B) True (1,1) 1. l1(B) -> l1(-1 + B) [B >= 1] (?,1) 2. l1(B) -> l2(B) [0 >= B] (?,1) Signature: {(l0,1);(l1,1);(l2,1)} Flow Graph: [0->{1,2},1->{1,2},2->{}] + Applied Processor: LocalSizeboundsProc + Details: LocalSizebounds generated; rvgraph (<0,0,B>, B, .= 0) (<1,0,B>, 1 + B, .+ 1) (<2,0,B>, B, .= 0) * Step 3: SizeboundsProc WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. l0(B) -> l1(B) True (1,1) 1. l1(B) -> l1(-1 + B) [B >= 1] (?,1) 2. l1(B) -> l2(B) [0 >= B] (?,1) Signature: {(l0,1);(l1,1);(l2,1)} Flow Graph: [0->{1,2},1->{1,2},2->{}] Sizebounds: (<0,0,B>, ?) (<1,0,B>, ?) (<2,0,B>, ?) + Applied Processor: SizeboundsProc + Details: Sizebounds computed: (<0,0,B>, B) (<1,0,B>, ?) (<2,0,B>, ?) * Step 4: LeafRules WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. l0(B) -> l1(B) True (1,1) 1. l1(B) -> l1(-1 + B) [B >= 1] (?,1) 2. l1(B) -> l2(B) [0 >= B] (?,1) Signature: {(l0,1);(l1,1);(l2,1)} Flow Graph: [0->{1,2},1->{1,2},2->{}] Sizebounds: (<0,0,B>, B) (<1,0,B>, ?) (<2,0,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. l0(B) -> l1(B) True (1,1) 1. l1(B) -> l1(-1 + B) [B >= 1] (?,1) Signature: {(l0,1);(l1,1);(l2,1)} Flow Graph: [0->{1},1->{1}] Sizebounds: (<0,0,B>, B) (<1,0,B>, ?) + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(l0) = x1 p(l1) = x1 The following rules are strictly oriented: [B >= 1] ==> l1(B) = B > -1 + B = l1(-1 + B) The following rules are weakly oriented: True ==> l0(B) = B >= B = l1(B) * Step 6: KnowledgePropagation WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. l0(B) -> l1(B) True (1,1) 1. l1(B) -> l1(-1 + B) [B >= 1] (B,1) Signature: {(l0,1);(l1,1);(l2,1)} Flow Graph: [0->{1},1->{1}] Sizebounds: (<0,0,B>, B) (<1,0,B>, ?) + Applied Processor: KnowledgePropagation + Details: The problem is already solved. WORST_CASE(?,O(n^1))