YES * Step 1: TrivialSCCs YES + Considered Problem: Rules: 0. f(A,B,C) -> g(A,1,1) True (1,1) 1. g(A,B,C) -> g(-1 + A,2*B,C) [1 + -1*C >= 0 && B + -1*C >= 0 && -1 + C >= 0 && -2 + B + C >= 0 && -1 + B >= 0 && -1 + A >= 0] (?,1) 2. g(A,B,C) -> h(A,B,C) [1 + -1*C >= 0 && B + -1*C >= 0 && -1 + C >= 0 && -2 + B + C >= 0 && -1 + B >= 0 && 0 >= A] (?,1) 3. h(A,B,C) -> h(A,-1 + B,2*C) [-1 + C >= 0 && -2 + B + C >= 0 && -1 + -1*A + C >= 0 && -1*A >= 0 && -1 + B >= 0] (?,1) 4. h(A,B,C) -> i(A,B,C) [-1 + C >= 0 && -2 + B + C >= 0 && -1 + -1*A + C >= 0 && -1*A >= 0 && 0 >= B] (?,1) 5. i(A,B,C) -> i(A,B,-1 + C) [-1*B >= 0 && -1*A + -1*B >= 0 && -1*A >= 0 && -1 + C >= 0] (?,1) Signature: {(f,3);(g,3);(h,3);(i,3)} Flow Graph: [0->{1,2},1->{1,2},2->{3,4},3->{3,4},4->{5},5->{5}] + Applied Processor: TrivialSCCs + Details: All trivial SCCs of the transition graph admit timebound 1. * Step 2: UnsatPaths YES + Considered Problem: Rules: 0. f(A,B,C) -> g(A,1,1) True (1,1) 1. g(A,B,C) -> g(-1 + A,2*B,C) [1 + -1*C >= 0 && B + -1*C >= 0 && -1 + C >= 0 && -2 + B + C >= 0 && -1 + B >= 0 && -1 + A >= 0] (?,1) 2. g(A,B,C) -> h(A,B,C) [1 + -1*C >= 0 && B + -1*C >= 0 && -1 + C >= 0 && -2 + B + C >= 0 && -1 + B >= 0 && 0 >= A] (1,1) 3. h(A,B,C) -> h(A,-1 + B,2*C) [-1 + C >= 0 && -2 + B + C >= 0 && -1 + -1*A + C >= 0 && -1*A >= 0 && -1 + B >= 0] (?,1) 4. h(A,B,C) -> i(A,B,C) [-1 + C >= 0 && -2 + B + C >= 0 && -1 + -1*A + C >= 0 && -1*A >= 0 && 0 >= B] (1,1) 5. i(A,B,C) -> i(A,B,-1 + C) [-1*B >= 0 && -1*A + -1*B >= 0 && -1*A >= 0 && -1 + C >= 0] (?,1) Signature: {(f,3);(g,3);(h,3);(i,3)} Flow Graph: [0->{1,2},1->{1,2},2->{3,4},3->{3,4},4->{5},5->{5}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(2,4)] * Step 3: Looptree YES + Considered Problem: Rules: 0. f(A,B,C) -> g(A,1,1) True (1,1) 1. g(A,B,C) -> g(-1 + A,2*B,C) [1 + -1*C >= 0 && B + -1*C >= 0 && -1 + C >= 0 && -2 + B + C >= 0 && -1 + B >= 0 && -1 + A >= 0] (?,1) 2. g(A,B,C) -> h(A,B,C) [1 + -1*C >= 0 && B + -1*C >= 0 && -1 + C >= 0 && -2 + B + C >= 0 && -1 + B >= 0 && 0 >= A] (1,1) 3. h(A,B,C) -> h(A,-1 + B,2*C) [-1 + C >= 0 && -2 + B + C >= 0 && -1 + -1*A + C >= 0 && -1*A >= 0 && -1 + B >= 0] (?,1) 4. h(A,B,C) -> i(A,B,C) [-1 + C >= 0 && -2 + B + C >= 0 && -1 + -1*A + C >= 0 && -1*A >= 0 && 0 >= B] (1,1) 5. i(A,B,C) -> i(A,B,-1 + C) [-1*B >= 0 && -1*A + -1*B >= 0 && -1*A >= 0 && -1 + C >= 0] (?,1) Signature: {(f,3);(g,3);(h,3);(i,3)} Flow Graph: [0->{1,2},1->{1,2},2->{3},3->{3,4},4->{5},5->{5}] + Applied Processor: Looptree + Details: We construct a looptree: P: [0,1,2,3,4,5] | +- p:[1] c: [1] | +- p:[3] c: [3] | `- p:[5] c: [5] YES