WORST_CASE(?,O(n^1)) * Step 1: LocalSizeboundsProc WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. evalfstart(A,B) -> evalfentryin(A,B) True (1,1) 1. evalfentryin(A,B) -> evalfbb1in(B,A) True (?,1) 2. evalfbb1in(A,B) -> evalfbbin(A,B) [A >= B] (?,1) 3. evalfbb1in(A,B) -> evalfreturnin(A,B) [B >= 1 + A] (?,1) 4. evalfbbin(A,B) -> evalfbb1in(A,1 + B) True (?,1) 5. evalfreturnin(A,B) -> evalfstop(A,B) True (?,1) Signature: {(evalfbb1in,2);(evalfbbin,2);(evalfentryin,2);(evalfreturnin,2);(evalfstart,2);(evalfstop,2)} Flow Graph: [0->{1},1->{2,3},2->{4},3->{5},4->{2,3},5->{}] + Applied Processor: LocalSizeboundsProc + Details: LocalSizebounds generated; rvgraph (<0,0,A>, A, .= 0) (<0,0,B>, B, .= 0) (<1,0,A>, B, .= 0) (<1,0,B>, A, .= 0) (<2,0,A>, A, .= 0) (<2,0,B>, B, .= 0) (<3,0,A>, A, .= 0) (<3,0,B>, B, .= 0) (<4,0,A>, A, .= 0) (<4,0,B>, 1 + B, .+ 1) (<5,0,A>, A, .= 0) (<5,0,B>, B, .= 0) * Step 2: SizeboundsProc WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. evalfstart(A,B) -> evalfentryin(A,B) True (1,1) 1. evalfentryin(A,B) -> evalfbb1in(B,A) True (?,1) 2. evalfbb1in(A,B) -> evalfbbin(A,B) [A >= B] (?,1) 3. evalfbb1in(A,B) -> evalfreturnin(A,B) [B >= 1 + A] (?,1) 4. evalfbbin(A,B) -> evalfbb1in(A,1 + B) True (?,1) 5. evalfreturnin(A,B) -> evalfstop(A,B) True (?,1) Signature: {(evalfbb1in,2);(evalfbbin,2);(evalfentryin,2);(evalfreturnin,2);(evalfstart,2);(evalfstop,2)} Flow Graph: [0->{1},1->{2,3},2->{4},3->{5},4->{2,3},5->{}] Sizebounds: (<0,0,A>, ?) (<0,0,B>, ?) (<1,0,A>, ?) (<1,0,B>, ?) (<2,0,A>, ?) (<2,0,B>, ?) (<3,0,A>, ?) (<3,0,B>, ?) (<4,0,A>, ?) (<4,0,B>, ?) (<5,0,A>, ?) (<5,0,B>, ?) + Applied Processor: SizeboundsProc + Details: Sizebounds computed: (<0,0,A>, A) (<0,0,B>, B) (<1,0,A>, B) (<1,0,B>, A) (<2,0,A>, B) (<2,0,B>, B) (<3,0,A>, B) (<3,0,B>, A + B) (<4,0,A>, B) (<4,0,B>, B) (<5,0,A>, B) (<5,0,B>, A + B) * Step 3: LeafRules WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. evalfstart(A,B) -> evalfentryin(A,B) True (1,1) 1. evalfentryin(A,B) -> evalfbb1in(B,A) True (?,1) 2. evalfbb1in(A,B) -> evalfbbin(A,B) [A >= B] (?,1) 3. evalfbb1in(A,B) -> evalfreturnin(A,B) [B >= 1 + A] (?,1) 4. evalfbbin(A,B) -> evalfbb1in(A,1 + B) True (?,1) 5. evalfreturnin(A,B) -> evalfstop(A,B) True (?,1) Signature: {(evalfbb1in,2);(evalfbbin,2);(evalfentryin,2);(evalfreturnin,2);(evalfstart,2);(evalfstop,2)} Flow Graph: [0->{1},1->{2,3},2->{4},3->{5},4->{2,3},5->{}] Sizebounds: (<0,0,A>, A) (<0,0,B>, B) (<1,0,A>, B) (<1,0,B>, A) (<2,0,A>, B) (<2,0,B>, B) (<3,0,A>, B) (<3,0,B>, A + B) (<4,0,A>, B) (<4,0,B>, B) (<5,0,A>, B) (<5,0,B>, A + B) + Applied Processor: LeafRules + Details: The following transitions are estimated by its predecessors and are removed [3,5] * Step 4: PolyRank WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. evalfstart(A,B) -> evalfentryin(A,B) True (1,1) 1. evalfentryin(A,B) -> evalfbb1in(B,A) True (?,1) 2. evalfbb1in(A,B) -> evalfbbin(A,B) [A >= B] (?,1) 4. evalfbbin(A,B) -> evalfbb1in(A,1 + B) True (?,1) Signature: {(evalfbb1in,2);(evalfbbin,2);(evalfentryin,2);(evalfreturnin,2);(evalfstart,2);(evalfstop,2)} Flow Graph: [0->{1},1->{2},2->{4},4->{2}] Sizebounds: (<0,0,A>, A) (<0,0,B>, B) (<1,0,A>, B) (<1,0,B>, A) (<2,0,A>, B) (<2,0,B>, B) (<4,0,A>, B) (<4,0,B>, B) + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(evalfbb1in) = 2 + x1 + -1*x2 p(evalfbbin) = 1 + x1 + -1*x2 p(evalfentryin) = 2 + -1*x1 + x2 p(evalfstart) = 2 + -1*x1 + x2 The following rules are strictly oriented: [A >= B] ==> evalfbb1in(A,B) = 2 + A + -1*B > 1 + A + -1*B = evalfbbin(A,B) The following rules are weakly oriented: True ==> evalfstart(A,B) = 2 + -1*A + B >= 2 + -1*A + B = evalfentryin(A,B) True ==> evalfentryin(A,B) = 2 + -1*A + B >= 2 + -1*A + B = evalfbb1in(B,A) True ==> evalfbbin(A,B) = 1 + A + -1*B >= 1 + A + -1*B = evalfbb1in(A,1 + B) * Step 5: KnowledgePropagation WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. evalfstart(A,B) -> evalfentryin(A,B) True (1,1) 1. evalfentryin(A,B) -> evalfbb1in(B,A) True (?,1) 2. evalfbb1in(A,B) -> evalfbbin(A,B) [A >= B] (2 + A + B,1) 4. evalfbbin(A,B) -> evalfbb1in(A,1 + B) True (?,1) Signature: {(evalfbb1in,2);(evalfbbin,2);(evalfentryin,2);(evalfreturnin,2);(evalfstart,2);(evalfstop,2)} Flow Graph: [0->{1},1->{2},2->{4},4->{2}] Sizebounds: (<0,0,A>, A) (<0,0,B>, B) (<1,0,A>, B) (<1,0,B>, A) (<2,0,A>, B) (<2,0,B>, B) (<4,0,A>, B) (<4,0,B>, B) + Applied Processor: KnowledgePropagation + Details: We propagate bounds from predecessors. * Step 6: LocalSizeboundsProc WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. evalfstart(A,B) -> evalfentryin(A,B) True (1,1) 1. evalfentryin(A,B) -> evalfbb1in(B,A) True (1,1) 2. evalfbb1in(A,B) -> evalfbbin(A,B) [A >= B] (2 + A + B,1) 4. evalfbbin(A,B) -> evalfbb1in(A,1 + B) True (2 + A + B,1) Signature: {(evalfbb1in,2);(evalfbbin,2);(evalfentryin,2);(evalfreturnin,2);(evalfstart,2);(evalfstop,2)} Flow Graph: [0->{1},1->{2},2->{4},4->{2}] Sizebounds: (<0,0,A>, A) (<0,0,B>, B) (<1,0,A>, B) (<1,0,B>, A) (<2,0,A>, B) (<2,0,B>, B) (<4,0,A>, B) (<4,0,B>, B) + Applied Processor: LocalSizeboundsProc + Details: The problem is already solved. WORST_CASE(?,O(n^1))