WORST_CASE(?,O(n^1)) * Step 1: UnreachableRules WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. zip3(A,B,C) -> zip3(-1 + A,-1 + B,-1 + C) [A >= 1 && B >= 1 && C >= 1] (?,1) 1. group3(A,B,C) -> group3(-3 + A,B,C) [A >= 4] (?,1) 2. start(A,B,C) -> zip3(A,B,C) True (1,1) Signature: {(group3,3);(start,3);(zip3,3)} Flow Graph: [0->{0},1->{1},2->{0}] + Applied Processor: UnreachableRules + Details: The following transitions are not reachable from the starting states and are removed: [1] * Step 2: LocalSizeboundsProc WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. zip3(A,B,C) -> zip3(-1 + A,-1 + B,-1 + C) [A >= 1 && B >= 1 && C >= 1] (?,1) 2. start(A,B,C) -> zip3(A,B,C) True (1,1) Signature: {(group3,3);(start,3);(zip3,3)} Flow Graph: [0->{0},2->{0}] + Applied Processor: LocalSizeboundsProc + Details: LocalSizebounds generated; rvgraph (<0,0,A>, 1 + A, .+ 1) (<0,0,B>, 1 + B, .+ 1) (<0,0,C>, 1 + C, .+ 1) (<2,0,A>, A, .= 0) (<2,0,B>, B, .= 0) (<2,0,C>, C, .= 0) * Step 3: SizeboundsProc WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. zip3(A,B,C) -> zip3(-1 + A,-1 + B,-1 + C) [A >= 1 && B >= 1 && C >= 1] (?,1) 2. start(A,B,C) -> zip3(A,B,C) True (1,1) Signature: {(group3,3);(start,3);(zip3,3)} Flow Graph: [0->{0},2->{0}] Sizebounds: (<0,0,A>, ?) (<0,0,B>, ?) (<0,0,C>, ?) (<2,0,A>, ?) (<2,0,B>, ?) (<2,0,C>, ?) + Applied Processor: SizeboundsProc + Details: Sizebounds computed: (<0,0,A>, ?) (<0,0,B>, ?) (<0,0,C>, ?) (<2,0,A>, A) (<2,0,B>, B) (<2,0,C>, C) * Step 4: PolyRank WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. zip3(A,B,C) -> zip3(-1 + A,-1 + B,-1 + C) [A >= 1 && B >= 1 && C >= 1] (?,1) 2. start(A,B,C) -> zip3(A,B,C) True (1,1) Signature: {(group3,3);(start,3);(zip3,3)} Flow Graph: [0->{0},2->{0}] Sizebounds: (<0,0,A>, ?) (<0,0,B>, ?) (<0,0,C>, ?) (<2,0,A>, A) (<2,0,B>, B) (<2,0,C>, C) + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(start) = x1 p(zip3) = x1 The following rules are strictly oriented: [A >= 1 && B >= 1 && C >= 1] ==> zip3(A,B,C) = A > -1 + A = zip3(-1 + A,-1 + B,-1 + C) The following rules are weakly oriented: True ==> start(A,B,C) = A >= A = zip3(A,B,C) * Step 5: KnowledgePropagation WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. zip3(A,B,C) -> zip3(-1 + A,-1 + B,-1 + C) [A >= 1 && B >= 1 && C >= 1] (A,1) 2. start(A,B,C) -> zip3(A,B,C) True (1,1) Signature: {(group3,3);(start,3);(zip3,3)} Flow Graph: [0->{0},2->{0}] Sizebounds: (<0,0,A>, ?) (<0,0,B>, ?) (<0,0,C>, ?) (<2,0,A>, A) (<2,0,B>, B) (<2,0,C>, C) + Applied Processor: KnowledgePropagation + Details: The problem is already solved. WORST_CASE(?,O(n^1))