WORST_CASE(?,O(n^1)) * Step 1: LocalSizeboundsProc WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. f0(A,B) -> f1(A,B) [A >= 1] (1,1) 1. f1(A,B) -> f1(A,-1*A + B) [A >= 1 && B >= 0] (?,1) Signature: {(f0,2);(f1,2)} Flow Graph: [0->{1},1->{1}] + Applied Processor: LocalSizeboundsProc + Details: LocalSizebounds generated; rvgraph (<0,0,A>, A, .= 0) (<0,0,B>, B, .= 0) (<1,0,A>, A, .= 0) (<1,0,B>, A + B, .* 0) * Step 2: SizeboundsProc WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. f0(A,B) -> f1(A,B) [A >= 1] (1,1) 1. f1(A,B) -> f1(A,-1*A + B) [A >= 1 && B >= 0] (?,1) Signature: {(f0,2);(f1,2)} Flow Graph: [0->{1},1->{1}] Sizebounds: (<0,0,A>, ?) (<0,0,B>, ?) (<1,0,A>, ?) (<1,0,B>, ?) + Applied Processor: SizeboundsProc + Details: Sizebounds computed: (<0,0,A>, A) (<0,0,B>, B) (<1,0,A>, A) (<1,0,B>, ?) * Step 3: PolyRank WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. f0(A,B) -> f1(A,B) [A >= 1] (1,1) 1. f1(A,B) -> f1(A,-1*A + B) [A >= 1 && B >= 0] (?,1) Signature: {(f0,2);(f1,2)} Flow Graph: [0->{1},1->{1}] Sizebounds: (<0,0,A>, A) (<0,0,B>, B) (<1,0,A>, A) (<1,0,B>, ?) + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(f0) = 1 + x2 p(f1) = 1 + x2 The following rules are strictly oriented: [A >= 1 && B >= 0] ==> f1(A,B) = 1 + B > 1 + -1*A + B = f1(A,-1*A + B) The following rules are weakly oriented: [A >= 1] ==> f0(A,B) = 1 + B >= 1 + B = f1(A,B) * Step 4: KnowledgePropagation WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. f0(A,B) -> f1(A,B) [A >= 1] (1,1) 1. f1(A,B) -> f1(A,-1*A + B) [A >= 1 && B >= 0] (1 + B,1) Signature: {(f0,2);(f1,2)} Flow Graph: [0->{1},1->{1}] Sizebounds: (<0,0,A>, A) (<0,0,B>, B) (<1,0,A>, A) (<1,0,B>, ?) + Applied Processor: KnowledgePropagation + Details: The problem is already solved. WORST_CASE(?,O(n^1))