WORST_CASE(?,O(n^1)) * Step 1: RestrictVarsProcessor WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. eval(A,B,C,D,E) -> eval(A,1 + B,C,D,1 + E) [A >= 1 + B && C >= 1 + D] (?,1) 1. eval(A,B,C,D,E) -> eval(A,B,C,1 + D,1 + E) [A >= 1 + B && C >= 1 + D] (?,1) 2. eval(A,B,C,D,E) -> eval(A,B,C,1 + D,1 + E) [B >= A && C >= 1 + D] (?,1) 3. eval(A,B,C,D,E) -> eval(A,1 + B,C,D,1 + E) [A >= 1 + B && D >= C] (?,1) 4. start(A,B,C,D,E) -> eval(A,B,C,D,E) True (1,1) Signature: {(eval,5);(start,5)} Flow Graph: [0->{0,1,2,3},1->{0,1,2,3},2->{0,1,2,3},3->{0,1,2,3},4->{0,1,2,3}] + Applied Processor: RestrictVarsProcessor + Details: We removed the arguments [E] . * Step 2: LocalSizeboundsProc WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. eval(A,B,C,D) -> eval(A,1 + B,C,D) [A >= 1 + B && C >= 1 + D] (?,1) 1. eval(A,B,C,D) -> eval(A,B,C,1 + D) [A >= 1 + B && C >= 1 + D] (?,1) 2. eval(A,B,C,D) -> eval(A,B,C,1 + D) [B >= A && C >= 1 + D] (?,1) 3. eval(A,B,C,D) -> eval(A,1 + B,C,D) [A >= 1 + B && D >= C] (?,1) 4. start(A,B,C,D) -> eval(A,B,C,D) True (1,1) Signature: {(eval,4);(start,4)} Flow Graph: [0->{0,1,2,3},1->{0,1,2,3},2->{0,1,2,3},3->{0,1,2,3},4->{0,1,2,3}] + Applied Processor: LocalSizeboundsProc + Details: LocalSizebounds generated; rvgraph (<0,0,A>, A, .= 0) (<0,0,B>, 1 + B, .+ 1) (<0,0,C>, C, .= 0) (<0,0,D>, D, .= 0) (<1,0,A>, A, .= 0) (<1,0,B>, B, .= 0) (<1,0,C>, C, .= 0) (<1,0,D>, 1 + D, .+ 1) (<2,0,A>, A, .= 0) (<2,0,B>, B, .= 0) (<2,0,C>, C, .= 0) (<2,0,D>, 1 + D, .+ 1) (<3,0,A>, A, .= 0) (<3,0,B>, 1 + B, .+ 1) (<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) * Step 3: SizeboundsProc WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. eval(A,B,C,D) -> eval(A,1 + B,C,D) [A >= 1 + B && C >= 1 + D] (?,1) 1. eval(A,B,C,D) -> eval(A,B,C,1 + D) [A >= 1 + B && C >= 1 + D] (?,1) 2. eval(A,B,C,D) -> eval(A,B,C,1 + D) [B >= A && C >= 1 + D] (?,1) 3. eval(A,B,C,D) -> eval(A,1 + B,C,D) [A >= 1 + B && D >= C] (?,1) 4. start(A,B,C,D) -> eval(A,B,C,D) True (1,1) Signature: {(eval,4);(start,4)} Flow Graph: [0->{0,1,2,3},1->{0,1,2,3},2->{0,1,2,3},3->{0,1,2,3},4->{0,1,2,3}] 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>, ?) + Applied Processor: SizeboundsProc + Details: Sizebounds computed: (<0,0,A>, A) (<0,0,B>, A) (<0,0,C>, C) (<0,0,D>, C) (<1,0,A>, A) (<1,0,B>, A) (<1,0,C>, C) (<1,0,D>, C) (<2,0,A>, A) (<2,0,B>, A + B) (<2,0,C>, C) (<2,0,D>, C) (<3,0,A>, A) (<3,0,B>, A) (<3,0,C>, C) (<3,0,D>, C + D) (<4,0,A>, A) (<4,0,B>, B) (<4,0,C>, C) (<4,0,D>, D) * Step 4: UnsatPaths WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. eval(A,B,C,D) -> eval(A,1 + B,C,D) [A >= 1 + B && C >= 1 + D] (?,1) 1. eval(A,B,C,D) -> eval(A,B,C,1 + D) [A >= 1 + B && C >= 1 + D] (?,1) 2. eval(A,B,C,D) -> eval(A,B,C,1 + D) [B >= A && C >= 1 + D] (?,1) 3. eval(A,B,C,D) -> eval(A,1 + B,C,D) [A >= 1 + B && D >= C] (?,1) 4. start(A,B,C,D) -> eval(A,B,C,D) True (1,1) Signature: {(eval,4);(start,4)} Flow Graph: [0->{0,1,2,3},1->{0,1,2,3},2->{0,1,2,3},3->{0,1,2,3},4->{0,1,2,3}] Sizebounds: (<0,0,A>, A) (<0,0,B>, A) (<0,0,C>, C) (<0,0,D>, C) (<1,0,A>, A) (<1,0,B>, A) (<1,0,C>, C) (<1,0,D>, C) (<2,0,A>, A) (<2,0,B>, A + B) (<2,0,C>, C) (<2,0,D>, C) (<3,0,A>, A) (<3,0,B>, A) (<3,0,C>, C) (<3,0,D>, C + D) (<4,0,A>, A) (<4,0,B>, B) (<4,0,C>, C) (<4,0,D>, D) + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(0,3),(1,2),(2,0),(2,1),(2,3),(3,0),(3,1),(3,2)] * Step 5: PolyRank WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. eval(A,B,C,D) -> eval(A,1 + B,C,D) [A >= 1 + B && C >= 1 + D] (?,1) 1. eval(A,B,C,D) -> eval(A,B,C,1 + D) [A >= 1 + B && C >= 1 + D] (?,1) 2. eval(A,B,C,D) -> eval(A,B,C,1 + D) [B >= A && C >= 1 + D] (?,1) 3. eval(A,B,C,D) -> eval(A,1 + B,C,D) [A >= 1 + B && D >= C] (?,1) 4. start(A,B,C,D) -> eval(A,B,C,D) True (1,1) Signature: {(eval,4);(start,4)} Flow Graph: [0->{0,1,2},1->{0,1,3},2->{2},3->{3},4->{0,1,2,3}] Sizebounds: (<0,0,A>, A) (<0,0,B>, A) (<0,0,C>, C) (<0,0,D>, C) (<1,0,A>, A) (<1,0,B>, A) (<1,0,C>, C) (<1,0,D>, C) (<2,0,A>, A) (<2,0,B>, A + B) (<2,0,C>, C) (<2,0,D>, C) (<3,0,A>, A) (<3,0,B>, A) (<3,0,C>, C) (<3,0,D>, C + D) (<4,0,A>, A) (<4,0,B>, B) (<4,0,C>, C) (<4,0,D>, D) + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(eval) = x1 + -1*x2 p(start) = x1 + -1*x2 The following rules are strictly oriented: [A >= 1 + B && D >= C] ==> eval(A,B,C,D) = A + -1*B > -1 + A + -1*B = eval(A,1 + B,C,D) The following rules are weakly oriented: [A >= 1 + B && C >= 1 + D] ==> eval(A,B,C,D) = A + -1*B >= -1 + A + -1*B = eval(A,1 + B,C,D) [A >= 1 + B && C >= 1 + D] ==> eval(A,B,C,D) = A + -1*B >= A + -1*B = eval(A,B,C,1 + D) [B >= A && C >= 1 + D] ==> eval(A,B,C,D) = A + -1*B >= A + -1*B = eval(A,B,C,1 + D) True ==> start(A,B,C,D) = A + -1*B >= A + -1*B = eval(A,B,C,D) * Step 6: PolyRank WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. eval(A,B,C,D) -> eval(A,1 + B,C,D) [A >= 1 + B && C >= 1 + D] (?,1) 1. eval(A,B,C,D) -> eval(A,B,C,1 + D) [A >= 1 + B && C >= 1 + D] (?,1) 2. eval(A,B,C,D) -> eval(A,B,C,1 + D) [B >= A && C >= 1 + D] (?,1) 3. eval(A,B,C,D) -> eval(A,1 + B,C,D) [A >= 1 + B && D >= C] (A + B,1) 4. start(A,B,C,D) -> eval(A,B,C,D) True (1,1) Signature: {(eval,4);(start,4)} Flow Graph: [0->{0,1,2},1->{0,1,3},2->{2},3->{3},4->{0,1,2,3}] Sizebounds: (<0,0,A>, A) (<0,0,B>, A) (<0,0,C>, C) (<0,0,D>, C) (<1,0,A>, A) (<1,0,B>, A) (<1,0,C>, C) (<1,0,D>, C) (<2,0,A>, A) (<2,0,B>, A + B) (<2,0,C>, C) (<2,0,D>, C) (<3,0,A>, A) (<3,0,B>, A) (<3,0,C>, C) (<3,0,D>, C + D) (<4,0,A>, A) (<4,0,B>, B) (<4,0,C>, C) (<4,0,D>, D) + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(eval) = x3 + -1*x4 p(start) = x3 + -1*x4 The following rules are strictly oriented: [B >= A && C >= 1 + D] ==> eval(A,B,C,D) = C + -1*D > -1 + C + -1*D = eval(A,B,C,1 + D) The following rules are weakly oriented: [A >= 1 + B && C >= 1 + D] ==> eval(A,B,C,D) = C + -1*D >= C + -1*D = eval(A,1 + B,C,D) [A >= 1 + B && C >= 1 + D] ==> eval(A,B,C,D) = C + -1*D >= -1 + C + -1*D = eval(A,B,C,1 + D) [A >= 1 + B && D >= C] ==> eval(A,B,C,D) = C + -1*D >= C + -1*D = eval(A,1 + B,C,D) True ==> start(A,B,C,D) = C + -1*D >= C + -1*D = eval(A,B,C,D) * Step 7: PolyRank WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. eval(A,B,C,D) -> eval(A,1 + B,C,D) [A >= 1 + B && C >= 1 + D] (?,1) 1. eval(A,B,C,D) -> eval(A,B,C,1 + D) [A >= 1 + B && C >= 1 + D] (?,1) 2. eval(A,B,C,D) -> eval(A,B,C,1 + D) [B >= A && C >= 1 + D] (C + D,1) 3. eval(A,B,C,D) -> eval(A,1 + B,C,D) [A >= 1 + B && D >= C] (A + B,1) 4. start(A,B,C,D) -> eval(A,B,C,D) True (1,1) Signature: {(eval,4);(start,4)} Flow Graph: [0->{0,1,2},1->{0,1,3},2->{2},3->{3},4->{0,1,2,3}] Sizebounds: (<0,0,A>, A) (<0,0,B>, A) (<0,0,C>, C) (<0,0,D>, C) (<1,0,A>, A) (<1,0,B>, A) (<1,0,C>, C) (<1,0,D>, C) (<2,0,A>, A) (<2,0,B>, A + B) (<2,0,C>, C) (<2,0,D>, C) (<3,0,A>, A) (<3,0,B>, A) (<3,0,C>, C) (<3,0,D>, C + D) (<4,0,A>, A) (<4,0,B>, B) (<4,0,C>, C) (<4,0,D>, D) + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(eval) = x3 + -1*x4 p(start) = x3 + -1*x4 The following rules are strictly oriented: [A >= 1 + B && C >= 1 + D] ==> eval(A,B,C,D) = C + -1*D > -1 + C + -1*D = eval(A,B,C,1 + D) [B >= A && C >= 1 + D] ==> eval(A,B,C,D) = C + -1*D > -1 + C + -1*D = eval(A,B,C,1 + D) The following rules are weakly oriented: [A >= 1 + B && C >= 1 + D] ==> eval(A,B,C,D) = C + -1*D >= C + -1*D = eval(A,1 + B,C,D) [A >= 1 + B && D >= C] ==> eval(A,B,C,D) = C + -1*D >= C + -1*D = eval(A,1 + B,C,D) True ==> start(A,B,C,D) = C + -1*D >= C + -1*D = eval(A,B,C,D) * Step 8: PolyRank WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. eval(A,B,C,D) -> eval(A,1 + B,C,D) [A >= 1 + B && C >= 1 + D] (?,1) 1. eval(A,B,C,D) -> eval(A,B,C,1 + D) [A >= 1 + B && C >= 1 + D] (C + D,1) 2. eval(A,B,C,D) -> eval(A,B,C,1 + D) [B >= A && C >= 1 + D] (C + D,1) 3. eval(A,B,C,D) -> eval(A,1 + B,C,D) [A >= 1 + B && D >= C] (A + B,1) 4. start(A,B,C,D) -> eval(A,B,C,D) True (1,1) Signature: {(eval,4);(start,4)} Flow Graph: [0->{0,1,2},1->{0,1,3},2->{2},3->{3},4->{0,1,2,3}] Sizebounds: (<0,0,A>, A) (<0,0,B>, A) (<0,0,C>, C) (<0,0,D>, C) (<1,0,A>, A) (<1,0,B>, A) (<1,0,C>, C) (<1,0,D>, C) (<2,0,A>, A) (<2,0,B>, A + B) (<2,0,C>, C) (<2,0,D>, C) (<3,0,A>, A) (<3,0,B>, A) (<3,0,C>, C) (<3,0,D>, C + D) (<4,0,A>, A) (<4,0,B>, B) (<4,0,C>, C) (<4,0,D>, D) + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(eval) = x1 + -1*x2 p(start) = x1 + -1*x2 The following rules are strictly oriented: [A >= 1 + B && C >= 1 + D] ==> eval(A,B,C,D) = A + -1*B > -1 + A + -1*B = eval(A,1 + B,C,D) [A >= 1 + B && D >= C] ==> eval(A,B,C,D) = A + -1*B > -1 + A + -1*B = eval(A,1 + B,C,D) The following rules are weakly oriented: [A >= 1 + B && C >= 1 + D] ==> eval(A,B,C,D) = A + -1*B >= A + -1*B = eval(A,B,C,1 + D) [B >= A && C >= 1 + D] ==> eval(A,B,C,D) = A + -1*B >= A + -1*B = eval(A,B,C,1 + D) True ==> start(A,B,C,D) = A + -1*B >= A + -1*B = eval(A,B,C,D) * Step 9: KnowledgePropagation WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. eval(A,B,C,D) -> eval(A,1 + B,C,D) [A >= 1 + B && C >= 1 + D] (A + B,1) 1. eval(A,B,C,D) -> eval(A,B,C,1 + D) [A >= 1 + B && C >= 1 + D] (C + D,1) 2. eval(A,B,C,D) -> eval(A,B,C,1 + D) [B >= A && C >= 1 + D] (C + D,1) 3. eval(A,B,C,D) -> eval(A,1 + B,C,D) [A >= 1 + B && D >= C] (A + B,1) 4. start(A,B,C,D) -> eval(A,B,C,D) True (1,1) Signature: {(eval,4);(start,4)} Flow Graph: [0->{0,1,2},1->{0,1,3},2->{2},3->{3},4->{0,1,2,3}] Sizebounds: (<0,0,A>, A) (<0,0,B>, A) (<0,0,C>, C) (<0,0,D>, C) (<1,0,A>, A) (<1,0,B>, A) (<1,0,C>, C) (<1,0,D>, C) (<2,0,A>, A) (<2,0,B>, A + B) (<2,0,C>, C) (<2,0,D>, C) (<3,0,A>, A) (<3,0,B>, A) (<3,0,C>, C) (<3,0,D>, C + D) (<4,0,A>, A) (<4,0,B>, B) (<4,0,C>, C) (<4,0,D>, D) + Applied Processor: KnowledgePropagation + Details: The problem is already solved. WORST_CASE(?,O(n^1))