YES(?,O(1)) * Step 1: UnsatPaths WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A,B,C,D,E) -> f7(F,F,10,0,E) True (1,1) 1. f7(A,B,C,D,E) -> f7(A,B,C,1 + D,F) [C >= 1 + D] (?,1) 2. f7(A,B,C,D,E) -> f19(A,B,C,D,E) [D >= C] (?,1) Signature: {(f0,5);(f19,5);(f7,5)} Flow Graph: [0->{1,2},1->{1,2},2->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(0,2)] * Step 2: TrivialSCCs WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A,B,C,D,E) -> f7(F,F,10,0,E) True (1,1) 1. f7(A,B,C,D,E) -> f7(A,B,C,1 + D,F) [C >= 1 + D] (?,1) 2. f7(A,B,C,D,E) -> f19(A,B,C,D,E) [D >= C] (?,1) Signature: {(f0,5);(f19,5);(f7,5)} Flow Graph: [0->{1},1->{1,2},2->{}] + Applied Processor: TrivialSCCs + Details: All trivial SCCs of the transition graph admit timebound 1. * Step 3: PolyRank WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A,B,C,D,E) -> f7(F,F,10,0,E) True (1,1) 1. f7(A,B,C,D,E) -> f7(A,B,C,1 + D,F) [C >= 1 + D] (?,1) 2. f7(A,B,C,D,E) -> f19(A,B,C,D,E) [D >= C] (1,1) Signature: {(f0,5);(f19,5);(f7,5)} Flow Graph: [0->{1},1->{1,2},2->{}] + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(f0) = 10 p(f19) = x3 + -1*x4 p(f7) = x3 + -1*x4 Following rules are strictly oriented: [C >= 1 + D] ==> f7(A,B,C,D,E) = C + -1*D > -1 + C + -1*D = f7(A,B,C,1 + D,F) Following rules are weakly oriented: True ==> f0(A,B,C,D,E) = 10 >= 10 = f7(F,F,10,0,E) [D >= C] ==> f7(A,B,C,D,E) = C + -1*D >= C + -1*D = f19(A,B,C,D,E) * Step 4: KnowledgePropagation WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A,B,C,D,E) -> f7(F,F,10,0,E) True (1,1) 1. f7(A,B,C,D,E) -> f7(A,B,C,1 + D,F) [C >= 1 + D] (10,1) 2. f7(A,B,C,D,E) -> f19(A,B,C,D,E) [D >= C] (1,1) Signature: {(f0,5);(f19,5);(f7,5)} Flow Graph: [0->{1},1->{1,2},2->{}] + Applied Processor: KnowledgePropagation + Details: The problem is already solved. YES(?,O(1))