WORST_CASE(?,O(n^2)) * Step 1: LocalSizeboundsProc WORST_CASE(?,O(n^2)) + Considered Problem: Rules: 0. evalfstart(A,B,C,D) -> evalfentryin(A,B,C,D) True (1,1) 1. evalfentryin(A,B,C,D) -> evalfbb4in(1,B,C,D) True (?,1) 2. evalfbb4in(A,B,C,D) -> evalfbb2in(A,B,1,D) [B >= A] (?,1) 3. evalfbb4in(A,B,C,D) -> evalfreturnin(A,B,C,D) [A >= 1 + B] (?,1) 4. evalfbb2in(A,B,C,D) -> evalfbb1in(A,B,C,D) [D >= C] (?,1) 5. evalfbb2in(A,B,C,D) -> evalfbb3in(A,B,C,D) [C >= 1 + D] (?,1) 6. evalfbb1in(A,B,C,D) -> evalfbb2in(A,B,1 + C,D) True (?,1) 7. evalfbb3in(A,B,C,D) -> evalfbb4in(1 + A,B,C,D) True (?,1) 8. evalfreturnin(A,B,C,D) -> evalfstop(A,B,C,D) True (?,1) Signature: {(evalfbb1in,4) ;(evalfbb2in,4) ;(evalfbb3in,4) ;(evalfbb4in,4) ;(evalfentryin,4) ;(evalfreturnin,4) ;(evalfstart,4) ;(evalfstop,4)} Flow Graph: [0->{1},1->{2,3},2->{4,5},3->{8},4->{6},5->{7},6->{4,5},7->{2,3},8->{}] + Applied Processor: LocalSizeboundsProc + Details: LocalSizebounds generated; rvgraph (<0,0,A>, A, .= 0) (<0,0,B>, B, .= 0) (<0,0,C>, C, .= 0) (<0,0,D>, D, .= 0) (<1,0,A>, 1, .= 1) (<1,0,B>, B, .= 0) (<1,0,C>, C, .= 0) (<1,0,D>, D, .= 0) (<2,0,A>, A, .= 0) (<2,0,B>, B, .= 0) (<2,0,C>, 1, .= 1) (<2,0,D>, D, .= 0) (<3,0,A>, A, .= 0) (<3,0,B>, B, .= 0) (<3,0,C>, C, .= 0) (<3,0,D>, D, .= 0) (<4,0,A>, A, .= 0) (<4,0,B>, B, .= 0) (<4,0,C>, C, .= 0) (<4,0,D>, D, .= 0) (<5,0,A>, A, .= 0) (<5,0,B>, B, .= 0) (<5,0,C>, C, .= 0) (<5,0,D>, D, .= 0) (<6,0,A>, A, .= 0) (<6,0,B>, B, .= 0) (<6,0,C>, 1 + C, .+ 1) (<6,0,D>, D, .= 0) (<7,0,A>, 1 + A, .+ 1) (<7,0,B>, B, .= 0) (<7,0,C>, C, .= 0) (<7,0,D>, D, .= 0) (<8,0,A>, A, .= 0) (<8,0,B>, B, .= 0) (<8,0,C>, C, .= 0) (<8,0,D>, D, .= 0) * Step 2: SizeboundsProc WORST_CASE(?,O(n^2)) + Considered Problem: Rules: 0. evalfstart(A,B,C,D) -> evalfentryin(A,B,C,D) True (1,1) 1. evalfentryin(A,B,C,D) -> evalfbb4in(1,B,C,D) True (?,1) 2. evalfbb4in(A,B,C,D) -> evalfbb2in(A,B,1,D) [B >= A] (?,1) 3. evalfbb4in(A,B,C,D) -> evalfreturnin(A,B,C,D) [A >= 1 + B] (?,1) 4. evalfbb2in(A,B,C,D) -> evalfbb1in(A,B,C,D) [D >= C] (?,1) 5. evalfbb2in(A,B,C,D) -> evalfbb3in(A,B,C,D) [C >= 1 + D] (?,1) 6. evalfbb1in(A,B,C,D) -> evalfbb2in(A,B,1 + C,D) True (?,1) 7. evalfbb3in(A,B,C,D) -> evalfbb4in(1 + A,B,C,D) True (?,1) 8. evalfreturnin(A,B,C,D) -> evalfstop(A,B,C,D) True (?,1) Signature: {(evalfbb1in,4) ;(evalfbb2in,4) ;(evalfbb3in,4) ;(evalfbb4in,4) ;(evalfentryin,4) ;(evalfreturnin,4) ;(evalfstart,4) ;(evalfstop,4)} Flow Graph: [0->{1},1->{2,3},2->{4,5},3->{8},4->{6},5->{7},6->{4,5},7->{2,3},8->{}] Sizebounds: (<0,0,A>, ?) (<0,0,B>, ?) (<0,0,C>, ?) (<0,0,D>, ?) (<1,0,A>, ?) (<1,0,B>, ?) (<1,0,C>, ?) (<1,0,D>, ?) (<2,0,A>, ?) (<2,0,B>, ?) (<2,0,C>, ?) (<2,0,D>, ?) (<3,0,A>, ?) (<3,0,B>, ?) (<3,0,C>, ?) (<3,0,D>, ?) (<4,0,A>, ?) (<4,0,B>, ?) (<4,0,C>, ?) (<4,0,D>, ?) (<5,0,A>, ?) (<5,0,B>, ?) (<5,0,C>, ?) (<5,0,D>, ?) (<6,0,A>, ?) (<6,0,B>, ?) (<6,0,C>, ?) (<6,0,D>, ?) (<7,0,A>, ?) (<7,0,B>, ?) (<7,0,C>, ?) (<7,0,D>, ?) (<8,0,A>, ?) (<8,0,B>, ?) (<8,0,C>, ?) (<8,0,D>, ?) + Applied Processor: SizeboundsProc + Details: Sizebounds computed: (<0,0,A>, A) (<0,0,B>, B) (<0,0,C>, C) (<0,0,D>, D) (<1,0,A>, 1) (<1,0,B>, B) (<1,0,C>, C) (<1,0,D>, D) (<2,0,A>, B) (<2,0,B>, B) (<2,0,C>, 1) (<2,0,D>, D) (<3,0,A>, ?) (<3,0,B>, B) (<3,0,C>, 1 + C + D) (<3,0,D>, D) (<4,0,A>, ?) (<4,0,B>, B) (<4,0,C>, D) (<4,0,D>, D) (<5,0,A>, ?) (<5,0,B>, B) (<5,0,C>, 1 + D) (<5,0,D>, D) (<6,0,A>, ?) (<6,0,B>, B) (<6,0,C>, D) (<6,0,D>, D) (<7,0,A>, ?) (<7,0,B>, B) (<7,0,C>, 1 + D) (<7,0,D>, D) (<8,0,A>, ?) (<8,0,B>, B) (<8,0,C>, 1 + C + D) (<8,0,D>, D) * Step 3: LeafRules WORST_CASE(?,O(n^2)) + Considered Problem: Rules: 0. evalfstart(A,B,C,D) -> evalfentryin(A,B,C,D) True (1,1) 1. evalfentryin(A,B,C,D) -> evalfbb4in(1,B,C,D) True (?,1) 2. evalfbb4in(A,B,C,D) -> evalfbb2in(A,B,1,D) [B >= A] (?,1) 3. evalfbb4in(A,B,C,D) -> evalfreturnin(A,B,C,D) [A >= 1 + B] (?,1) 4. evalfbb2in(A,B,C,D) -> evalfbb1in(A,B,C,D) [D >= C] (?,1) 5. evalfbb2in(A,B,C,D) -> evalfbb3in(A,B,C,D) [C >= 1 + D] (?,1) 6. evalfbb1in(A,B,C,D) -> evalfbb2in(A,B,1 + C,D) True (?,1) 7. evalfbb3in(A,B,C,D) -> evalfbb4in(1 + A,B,C,D) True (?,1) 8. evalfreturnin(A,B,C,D) -> evalfstop(A,B,C,D) True (?,1) Signature: {(evalfbb1in,4) ;(evalfbb2in,4) ;(evalfbb3in,4) ;(evalfbb4in,4) ;(evalfentryin,4) ;(evalfreturnin,4) ;(evalfstart,4) ;(evalfstop,4)} Flow Graph: [0->{1},1->{2,3},2->{4,5},3->{8},4->{6},5->{7},6->{4,5},7->{2,3},8->{}] Sizebounds: (<0,0,A>, A) (<0,0,B>, B) (<0,0,C>, C) (<0,0,D>, D) (<1,0,A>, 1) (<1,0,B>, B) (<1,0,C>, C) (<1,0,D>, D) (<2,0,A>, B) (<2,0,B>, B) (<2,0,C>, 1) (<2,0,D>, D) (<3,0,A>, ?) (<3,0,B>, B) (<3,0,C>, 1 + C + D) (<3,0,D>, D) (<4,0,A>, ?) (<4,0,B>, B) (<4,0,C>, D) (<4,0,D>, D) (<5,0,A>, ?) (<5,0,B>, B) (<5,0,C>, 1 + D) (<5,0,D>, D) (<6,0,A>, ?) (<6,0,B>, B) (<6,0,C>, D) (<6,0,D>, D) (<7,0,A>, ?) (<7,0,B>, B) (<7,0,C>, 1 + D) (<7,0,D>, D) (<8,0,A>, ?) (<8,0,B>, B) (<8,0,C>, 1 + C + D) (<8,0,D>, D) + Applied Processor: LeafRules + Details: The following transitions are estimated by its predecessors and are removed [3,8] * Step 4: PolyRank WORST_CASE(?,O(n^2)) + Considered Problem: Rules: 0. evalfstart(A,B,C,D) -> evalfentryin(A,B,C,D) True (1,1) 1. evalfentryin(A,B,C,D) -> evalfbb4in(1,B,C,D) True (?,1) 2. evalfbb4in(A,B,C,D) -> evalfbb2in(A,B,1,D) [B >= A] (?,1) 4. evalfbb2in(A,B,C,D) -> evalfbb1in(A,B,C,D) [D >= C] (?,1) 5. evalfbb2in(A,B,C,D) -> evalfbb3in(A,B,C,D) [C >= 1 + D] (?,1) 6. evalfbb1in(A,B,C,D) -> evalfbb2in(A,B,1 + C,D) True (?,1) 7. evalfbb3in(A,B,C,D) -> evalfbb4in(1 + A,B,C,D) True (?,1) Signature: {(evalfbb1in,4) ;(evalfbb2in,4) ;(evalfbb3in,4) ;(evalfbb4in,4) ;(evalfentryin,4) ;(evalfreturnin,4) ;(evalfstart,4) ;(evalfstop,4)} Flow Graph: [0->{1},1->{2},2->{4,5},4->{6},5->{7},6->{4,5},7->{2}] Sizebounds: (<0,0,A>, A) (<0,0,B>, B) (<0,0,C>, C) (<0,0,D>, D) (<1,0,A>, 1) (<1,0,B>, B) (<1,0,C>, C) (<1,0,D>, D) (<2,0,A>, B) (<2,0,B>, B) (<2,0,C>, 1) (<2,0,D>, D) (<4,0,A>, ?) (<4,0,B>, B) (<4,0,C>, D) (<4,0,D>, D) (<5,0,A>, ?) (<5,0,B>, B) (<5,0,C>, 1 + D) (<5,0,D>, D) (<6,0,A>, ?) (<6,0,B>, B) (<6,0,C>, D) (<6,0,D>, D) (<7,0,A>, ?) (<7,0,B>, B) (<7,0,C>, 1 + D) (<7,0,D>, D) + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(evalfbb1in) = 1 p(evalfbb2in) = 1 p(evalfbb3in) = 1 p(evalfbb4in) = 1 p(evalfentryin) = 2 p(evalfstart) = 2 The following rules are strictly oriented: True ==> evalfentryin(A,B,C,D) = 2 > 1 = evalfbb4in(1,B,C,D) The following rules are weakly oriented: True ==> evalfstart(A,B,C,D) = 2 >= 2 = evalfentryin(A,B,C,D) [B >= A] ==> evalfbb4in(A,B,C,D) = 1 >= 1 = evalfbb2in(A,B,1,D) [D >= C] ==> evalfbb2in(A,B,C,D) = 1 >= 1 = evalfbb1in(A,B,C,D) [C >= 1 + D] ==> evalfbb2in(A,B,C,D) = 1 >= 1 = evalfbb3in(A,B,C,D) True ==> evalfbb1in(A,B,C,D) = 1 >= 1 = evalfbb2in(A,B,1 + C,D) True ==> evalfbb3in(A,B,C,D) = 1 >= 1 = evalfbb4in(1 + A,B,C,D) * Step 5: PolyRank WORST_CASE(?,O(n^2)) + Considered Problem: Rules: 0. evalfstart(A,B,C,D) -> evalfentryin(A,B,C,D) True (1,1) 1. evalfentryin(A,B,C,D) -> evalfbb4in(1,B,C,D) True (2,1) 2. evalfbb4in(A,B,C,D) -> evalfbb2in(A,B,1,D) [B >= A] (?,1) 4. evalfbb2in(A,B,C,D) -> evalfbb1in(A,B,C,D) [D >= C] (?,1) 5. evalfbb2in(A,B,C,D) -> evalfbb3in(A,B,C,D) [C >= 1 + D] (?,1) 6. evalfbb1in(A,B,C,D) -> evalfbb2in(A,B,1 + C,D) True (?,1) 7. evalfbb3in(A,B,C,D) -> evalfbb4in(1 + A,B,C,D) True (?,1) Signature: {(evalfbb1in,4) ;(evalfbb2in,4) ;(evalfbb3in,4) ;(evalfbb4in,4) ;(evalfentryin,4) ;(evalfreturnin,4) ;(evalfstart,4) ;(evalfstop,4)} Flow Graph: [0->{1},1->{2},2->{4,5},4->{6},5->{7},6->{4,5},7->{2}] Sizebounds: (<0,0,A>, A) (<0,0,B>, B) (<0,0,C>, C) (<0,0,D>, D) (<1,0,A>, 1) (<1,0,B>, B) (<1,0,C>, C) (<1,0,D>, D) (<2,0,A>, B) (<2,0,B>, B) (<2,0,C>, 1) (<2,0,D>, D) (<4,0,A>, ?) (<4,0,B>, B) (<4,0,C>, D) (<4,0,D>, D) (<5,0,A>, ?) (<5,0,B>, B) (<5,0,C>, 1 + D) (<5,0,D>, D) (<6,0,A>, ?) (<6,0,B>, B) (<6,0,C>, D) (<6,0,D>, D) (<7,0,A>, ?) (<7,0,B>, B) (<7,0,C>, 1 + D) (<7,0,D>, D) + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(evalfbb1in) = -1*x1 + x2 p(evalfbb2in) = -1*x1 + x2 p(evalfbb3in) = -1*x1 + x2 p(evalfbb4in) = 1 + -1*x1 + x2 p(evalfentryin) = x2 p(evalfstart) = x2 The following rules are strictly oriented: [B >= A] ==> evalfbb4in(A,B,C,D) = 1 + -1*A + B > -1*A + B = evalfbb2in(A,B,1,D) The following rules are weakly oriented: True ==> evalfstart(A,B,C,D) = B >= B = evalfentryin(A,B,C,D) True ==> evalfentryin(A,B,C,D) = B >= B = evalfbb4in(1,B,C,D) [D >= C] ==> evalfbb2in(A,B,C,D) = -1*A + B >= -1*A + B = evalfbb1in(A,B,C,D) [C >= 1 + D] ==> evalfbb2in(A,B,C,D) = -1*A + B >= -1*A + B = evalfbb3in(A,B,C,D) True ==> evalfbb1in(A,B,C,D) = -1*A + B >= -1*A + B = evalfbb2in(A,B,1 + C,D) True ==> evalfbb3in(A,B,C,D) = -1*A + B >= -1*A + B = evalfbb4in(1 + A,B,C,D) * Step 6: PolyRank WORST_CASE(?,O(n^2)) + Considered Problem: Rules: 0. evalfstart(A,B,C,D) -> evalfentryin(A,B,C,D) True (1,1) 1. evalfentryin(A,B,C,D) -> evalfbb4in(1,B,C,D) True (2,1) 2. evalfbb4in(A,B,C,D) -> evalfbb2in(A,B,1,D) [B >= A] (B,1) 4. evalfbb2in(A,B,C,D) -> evalfbb1in(A,B,C,D) [D >= C] (?,1) 5. evalfbb2in(A,B,C,D) -> evalfbb3in(A,B,C,D) [C >= 1 + D] (?,1) 6. evalfbb1in(A,B,C,D) -> evalfbb2in(A,B,1 + C,D) True (?,1) 7. evalfbb3in(A,B,C,D) -> evalfbb4in(1 + A,B,C,D) True (?,1) Signature: {(evalfbb1in,4) ;(evalfbb2in,4) ;(evalfbb3in,4) ;(evalfbb4in,4) ;(evalfentryin,4) ;(evalfreturnin,4) ;(evalfstart,4) ;(evalfstop,4)} Flow Graph: [0->{1},1->{2},2->{4,5},4->{6},5->{7},6->{4,5},7->{2}] Sizebounds: (<0,0,A>, A) (<0,0,B>, B) (<0,0,C>, C) (<0,0,D>, D) (<1,0,A>, 1) (<1,0,B>, B) (<1,0,C>, C) (<1,0,D>, D) (<2,0,A>, B) (<2,0,B>, B) (<2,0,C>, 1) (<2,0,D>, D) (<4,0,A>, ?) (<4,0,B>, B) (<4,0,C>, D) (<4,0,D>, D) (<5,0,A>, ?) (<5,0,B>, B) (<5,0,C>, 1 + D) (<5,0,D>, D) (<6,0,A>, ?) (<6,0,B>, B) (<6,0,C>, D) (<6,0,D>, D) (<7,0,A>, ?) (<7,0,B>, B) (<7,0,C>, 1 + D) (<7,0,D>, D) + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [7,5,6,4], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(evalfbb1in) = 1 p(evalfbb2in) = 1 p(evalfbb3in) = 1 p(evalfbb4in) = 0 The following rules are strictly oriented: True ==> evalfbb3in(A,B,C,D) = 1 > 0 = evalfbb4in(1 + A,B,C,D) The following rules are weakly oriented: [D >= C] ==> evalfbb2in(A,B,C,D) = 1 >= 1 = evalfbb1in(A,B,C,D) [C >= 1 + D] ==> evalfbb2in(A,B,C,D) = 1 >= 1 = evalfbb3in(A,B,C,D) True ==> evalfbb1in(A,B,C,D) = 1 >= 1 = evalfbb2in(A,B,1 + C,D) We use the following global sizebounds: (<0,0,A>, A) (<0,0,B>, B) (<0,0,C>, C) (<0,0,D>, D) (<1,0,A>, 1) (<1,0,B>, B) (<1,0,C>, C) (<1,0,D>, D) (<2,0,A>, B) (<2,0,B>, B) (<2,0,C>, 1) (<2,0,D>, D) (<4,0,A>, ?) (<4,0,B>, B) (<4,0,C>, D) (<4,0,D>, D) (<5,0,A>, ?) (<5,0,B>, B) (<5,0,C>, 1 + D) (<5,0,D>, D) (<6,0,A>, ?) (<6,0,B>, B) (<6,0,C>, D) (<6,0,D>, D) (<7,0,A>, ?) (<7,0,B>, B) (<7,0,C>, 1 + D) (<7,0,D>, D) * Step 7: PolyRank WORST_CASE(?,O(n^2)) + Considered Problem: Rules: 0. evalfstart(A,B,C,D) -> evalfentryin(A,B,C,D) True (1,1) 1. evalfentryin(A,B,C,D) -> evalfbb4in(1,B,C,D) True (2,1) 2. evalfbb4in(A,B,C,D) -> evalfbb2in(A,B,1,D) [B >= A] (B,1) 4. evalfbb2in(A,B,C,D) -> evalfbb1in(A,B,C,D) [D >= C] (?,1) 5. evalfbb2in(A,B,C,D) -> evalfbb3in(A,B,C,D) [C >= 1 + D] (?,1) 6. evalfbb1in(A,B,C,D) -> evalfbb2in(A,B,1 + C,D) True (?,1) 7. evalfbb3in(A,B,C,D) -> evalfbb4in(1 + A,B,C,D) True (B,1) Signature: {(evalfbb1in,4) ;(evalfbb2in,4) ;(evalfbb3in,4) ;(evalfbb4in,4) ;(evalfentryin,4) ;(evalfreturnin,4) ;(evalfstart,4) ;(evalfstop,4)} Flow Graph: [0->{1},1->{2},2->{4,5},4->{6},5->{7},6->{4,5},7->{2}] Sizebounds: (<0,0,A>, A) (<0,0,B>, B) (<0,0,C>, C) (<0,0,D>, D) (<1,0,A>, 1) (<1,0,B>, B) (<1,0,C>, C) (<1,0,D>, D) (<2,0,A>, B) (<2,0,B>, B) (<2,0,C>, 1) (<2,0,D>, D) (<4,0,A>, ?) (<4,0,B>, B) (<4,0,C>, D) (<4,0,D>, D) (<5,0,A>, ?) (<5,0,B>, B) (<5,0,C>, 1 + D) (<5,0,D>, D) (<6,0,A>, ?) (<6,0,B>, B) (<6,0,C>, D) (<6,0,D>, D) (<7,0,A>, ?) (<7,0,B>, B) (<7,0,C>, 1 + D) (<7,0,D>, D) + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [7,5,6,4], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(evalfbb1in) = 1 p(evalfbb2in) = 1 p(evalfbb3in) = 0 p(evalfbb4in) = 0 The following rules are strictly oriented: [C >= 1 + D] ==> evalfbb2in(A,B,C,D) = 1 > 0 = evalfbb3in(A,B,C,D) The following rules are weakly oriented: [D >= C] ==> evalfbb2in(A,B,C,D) = 1 >= 1 = evalfbb1in(A,B,C,D) True ==> evalfbb1in(A,B,C,D) = 1 >= 1 = evalfbb2in(A,B,1 + C,D) True ==> evalfbb3in(A,B,C,D) = 0 >= 0 = evalfbb4in(1 + A,B,C,D) We use the following global sizebounds: (<0,0,A>, A) (<0,0,B>, B) (<0,0,C>, C) (<0,0,D>, D) (<1,0,A>, 1) (<1,0,B>, B) (<1,0,C>, C) (<1,0,D>, D) (<2,0,A>, B) (<2,0,B>, B) (<2,0,C>, 1) (<2,0,D>, D) (<4,0,A>, ?) (<4,0,B>, B) (<4,0,C>, D) (<4,0,D>, D) (<5,0,A>, ?) (<5,0,B>, B) (<5,0,C>, 1 + D) (<5,0,D>, D) (<6,0,A>, ?) (<6,0,B>, B) (<6,0,C>, D) (<6,0,D>, D) (<7,0,A>, ?) (<7,0,B>, B) (<7,0,C>, 1 + D) (<7,0,D>, D) * Step 8: PolyRank WORST_CASE(?,O(n^2)) + Considered Problem: Rules: 0. evalfstart(A,B,C,D) -> evalfentryin(A,B,C,D) True (1,1) 1. evalfentryin(A,B,C,D) -> evalfbb4in(1,B,C,D) True (2,1) 2. evalfbb4in(A,B,C,D) -> evalfbb2in(A,B,1,D) [B >= A] (B,1) 4. evalfbb2in(A,B,C,D) -> evalfbb1in(A,B,C,D) [D >= C] (?,1) 5. evalfbb2in(A,B,C,D) -> evalfbb3in(A,B,C,D) [C >= 1 + D] (B,1) 6. evalfbb1in(A,B,C,D) -> evalfbb2in(A,B,1 + C,D) True (?,1) 7. evalfbb3in(A,B,C,D) -> evalfbb4in(1 + A,B,C,D) True (B,1) Signature: {(evalfbb1in,4) ;(evalfbb2in,4) ;(evalfbb3in,4) ;(evalfbb4in,4) ;(evalfentryin,4) ;(evalfreturnin,4) ;(evalfstart,4) ;(evalfstop,4)} Flow Graph: [0->{1},1->{2},2->{4,5},4->{6},5->{7},6->{4,5},7->{2}] Sizebounds: (<0,0,A>, A) (<0,0,B>, B) (<0,0,C>, C) (<0,0,D>, D) (<1,0,A>, 1) (<1,0,B>, B) (<1,0,C>, C) (<1,0,D>, D) (<2,0,A>, B) (<2,0,B>, B) (<2,0,C>, 1) (<2,0,D>, D) (<4,0,A>, ?) (<4,0,B>, B) (<4,0,C>, D) (<4,0,D>, D) (<5,0,A>, ?) (<5,0,B>, B) (<5,0,C>, 1 + D) (<5,0,D>, D) (<6,0,A>, ?) (<6,0,B>, B) (<6,0,C>, D) (<6,0,D>, D) (<7,0,A>, ?) (<7,0,B>, B) (<7,0,C>, 1 + D) (<7,0,D>, D) + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [7,5,6,4], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(evalfbb1in) = 1 + -1*x3 + x4 p(evalfbb2in) = 2 + -1*x3 + x4 p(evalfbb3in) = 2 + -1*x3 + x4 p(evalfbb4in) = 2 + -1*x3 + x4 The following rules are strictly oriented: [D >= C] ==> evalfbb2in(A,B,C,D) = 2 + -1*C + D > 1 + -1*C + D = evalfbb1in(A,B,C,D) The following rules are weakly oriented: [C >= 1 + D] ==> evalfbb2in(A,B,C,D) = 2 + -1*C + D >= 2 + -1*C + D = evalfbb3in(A,B,C,D) True ==> evalfbb1in(A,B,C,D) = 1 + -1*C + D >= 1 + -1*C + D = evalfbb2in(A,B,1 + C,D) True ==> evalfbb3in(A,B,C,D) = 2 + -1*C + D >= 2 + -1*C + D = evalfbb4in(1 + A,B,C,D) We use the following global sizebounds: (<0,0,A>, A) (<0,0,B>, B) (<0,0,C>, C) (<0,0,D>, D) (<1,0,A>, 1) (<1,0,B>, B) (<1,0,C>, C) (<1,0,D>, D) (<2,0,A>, B) (<2,0,B>, B) (<2,0,C>, 1) (<2,0,D>, D) (<4,0,A>, ?) (<4,0,B>, B) (<4,0,C>, D) (<4,0,D>, D) (<5,0,A>, ?) (<5,0,B>, B) (<5,0,C>, 1 + D) (<5,0,D>, D) (<6,0,A>, ?) (<6,0,B>, B) (<6,0,C>, D) (<6,0,D>, D) (<7,0,A>, ?) (<7,0,B>, B) (<7,0,C>, 1 + D) (<7,0,D>, D) * Step 9: KnowledgePropagation WORST_CASE(?,O(n^2)) + Considered Problem: Rules: 0. evalfstart(A,B,C,D) -> evalfentryin(A,B,C,D) True (1,1) 1. evalfentryin(A,B,C,D) -> evalfbb4in(1,B,C,D) True (2,1) 2. evalfbb4in(A,B,C,D) -> evalfbb2in(A,B,1,D) [B >= A] (B,1) 4. evalfbb2in(A,B,C,D) -> evalfbb1in(A,B,C,D) [D >= C] (3*B + B*D,1) 5. evalfbb2in(A,B,C,D) -> evalfbb3in(A,B,C,D) [C >= 1 + D] (B,1) 6. evalfbb1in(A,B,C,D) -> evalfbb2in(A,B,1 + C,D) True (?,1) 7. evalfbb3in(A,B,C,D) -> evalfbb4in(1 + A,B,C,D) True (B,1) Signature: {(evalfbb1in,4) ;(evalfbb2in,4) ;(evalfbb3in,4) ;(evalfbb4in,4) ;(evalfentryin,4) ;(evalfreturnin,4) ;(evalfstart,4) ;(evalfstop,4)} Flow Graph: [0->{1},1->{2},2->{4,5},4->{6},5->{7},6->{4,5},7->{2}] Sizebounds: (<0,0,A>, A) (<0,0,B>, B) (<0,0,C>, C) (<0,0,D>, D) (<1,0,A>, 1) (<1,0,B>, B) (<1,0,C>, C) (<1,0,D>, D) (<2,0,A>, B) (<2,0,B>, B) (<2,0,C>, 1) (<2,0,D>, D) (<4,0,A>, ?) (<4,0,B>, B) (<4,0,C>, D) (<4,0,D>, D) (<5,0,A>, ?) (<5,0,B>, B) (<5,0,C>, 1 + D) (<5,0,D>, D) (<6,0,A>, ?) (<6,0,B>, B) (<6,0,C>, D) (<6,0,D>, D) (<7,0,A>, ?) (<7,0,B>, B) (<7,0,C>, 1 + D) (<7,0,D>, D) + Applied Processor: KnowledgePropagation + Details: We propagate bounds from predecessors. * Step 10: LocalSizeboundsProc WORST_CASE(?,O(n^2)) + Considered Problem: Rules: 0. evalfstart(A,B,C,D) -> evalfentryin(A,B,C,D) True (1,1) 1. evalfentryin(A,B,C,D) -> evalfbb4in(1,B,C,D) True (2,1) 2. evalfbb4in(A,B,C,D) -> evalfbb2in(A,B,1,D) [B >= A] (B,1) 4. evalfbb2in(A,B,C,D) -> evalfbb1in(A,B,C,D) [D >= C] (3*B + B*D,1) 5. evalfbb2in(A,B,C,D) -> evalfbb3in(A,B,C,D) [C >= 1 + D] (B,1) 6. evalfbb1in(A,B,C,D) -> evalfbb2in(A,B,1 + C,D) True (3*B + B*D,1) 7. evalfbb3in(A,B,C,D) -> evalfbb4in(1 + A,B,C,D) True (B,1) Signature: {(evalfbb1in,4) ;(evalfbb2in,4) ;(evalfbb3in,4) ;(evalfbb4in,4) ;(evalfentryin,4) ;(evalfreturnin,4) ;(evalfstart,4) ;(evalfstop,4)} Flow Graph: [0->{1},1->{2},2->{4,5},4->{6},5->{7},6->{4,5},7->{2}] Sizebounds: (<0,0,A>, A) (<0,0,B>, B) (<0,0,C>, C) (<0,0,D>, D) (<1,0,A>, 1) (<1,0,B>, B) (<1,0,C>, C) (<1,0,D>, D) (<2,0,A>, B) (<2,0,B>, B) (<2,0,C>, 1) (<2,0,D>, D) (<4,0,A>, ?) (<4,0,B>, B) (<4,0,C>, D) (<4,0,D>, D) (<5,0,A>, ?) (<5,0,B>, B) (<5,0,C>, 1 + D) (<5,0,D>, D) (<6,0,A>, ?) (<6,0,B>, B) (<6,0,C>, D) (<6,0,D>, D) (<7,0,A>, ?) (<7,0,B>, B) (<7,0,C>, 1 + D) (<7,0,D>, D) + Applied Processor: LocalSizeboundsProc + Details: The problem is already solved. WORST_CASE(?,O(n^2))