WORST_CASE(?,O(n^1)) * Step 1: LocalSizeboundsProc WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. merge(A,B) -> merge(-1 + A,B) [A >= 1 && B >= 1] (?,1) 1. merge(A,B) -> merge(A,-1 + B) [A >= 1 && B >= 1] (?,1) 2. start(A,B) -> merge(A,B) True (1,1) Signature: {(merge,2);(start,2)} Flow Graph: [0->{0,1},1->{0,1},2->{0,1}] + Applied Processor: LocalSizeboundsProc + Details: LocalSizebounds generated; rvgraph (<0,0,A>, 1 + A, .+ 1) (<0,0,B>, B, .= 0) (<1,0,A>, A, .= 0) (<1,0,B>, 1 + B, .+ 1) (<2,0,A>, A, .= 0) (<2,0,B>, B, .= 0) * Step 2: SizeboundsProc WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. merge(A,B) -> merge(-1 + A,B) [A >= 1 && B >= 1] (?,1) 1. merge(A,B) -> merge(A,-1 + B) [A >= 1 && B >= 1] (?,1) 2. start(A,B) -> merge(A,B) True (1,1) Signature: {(merge,2);(start,2)} Flow Graph: [0->{0,1},1->{0,1},2->{0,1}] Sizebounds: (<0,0,A>, ?) (<0,0,B>, ?) (<1,0,A>, ?) (<1,0,B>, ?) (<2,0,A>, ?) (<2,0,B>, ?) + Applied Processor: SizeboundsProc + Details: Sizebounds computed: (<0,0,A>, ?) (<0,0,B>, ?) (<1,0,A>, ?) (<1,0,B>, ?) (<2,0,A>, A) (<2,0,B>, B) * Step 3: PolyRank WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. merge(A,B) -> merge(-1 + A,B) [A >= 1 && B >= 1] (?,1) 1. merge(A,B) -> merge(A,-1 + B) [A >= 1 && B >= 1] (?,1) 2. start(A,B) -> merge(A,B) True (1,1) Signature: {(merge,2);(start,2)} Flow Graph: [0->{0,1},1->{0,1},2->{0,1}] Sizebounds: (<0,0,A>, ?) (<0,0,B>, ?) (<1,0,A>, ?) (<1,0,B>, ?) (<2,0,A>, A) (<2,0,B>, B) + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(merge) = x2 p(start) = x2 The following rules are strictly oriented: [A >= 1 && B >= 1] ==> merge(A,B) = B > -1 + B = merge(A,-1 + B) The following rules are weakly oriented: [A >= 1 && B >= 1] ==> merge(A,B) = B >= B = merge(-1 + A,B) True ==> start(A,B) = B >= B = merge(A,B) * Step 4: PolyRank WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. merge(A,B) -> merge(-1 + A,B) [A >= 1 && B >= 1] (?,1) 1. merge(A,B) -> merge(A,-1 + B) [A >= 1 && B >= 1] (B,1) 2. start(A,B) -> merge(A,B) True (1,1) Signature: {(merge,2);(start,2)} Flow Graph: [0->{0,1},1->{0,1},2->{0,1}] Sizebounds: (<0,0,A>, ?) (<0,0,B>, ?) (<1,0,A>, ?) (<1,0,B>, ?) (<2,0,A>, A) (<2,0,B>, B) + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(merge) = x1 p(start) = x1 The following rules are strictly oriented: [A >= 1 && B >= 1] ==> merge(A,B) = A > -1 + A = merge(-1 + A,B) The following rules are weakly oriented: [A >= 1 && B >= 1] ==> merge(A,B) = A >= A = merge(A,-1 + B) True ==> start(A,B) = A >= A = merge(A,B) * Step 5: KnowledgePropagation WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. merge(A,B) -> merge(-1 + A,B) [A >= 1 && B >= 1] (A,1) 1. merge(A,B) -> merge(A,-1 + B) [A >= 1 && B >= 1] (B,1) 2. start(A,B) -> merge(A,B) True (1,1) Signature: {(merge,2);(start,2)} Flow Graph: [0->{0,1},1->{0,1},2->{0,1}] Sizebounds: (<0,0,A>, ?) (<0,0,B>, ?) (<1,0,A>, ?) (<1,0,B>, ?) (<2,0,A>, A) (<2,0,B>, B) + Applied Processor: KnowledgePropagation + Details: The problem is already solved. WORST_CASE(?,O(n^1))