NO * Step 1: UnsatPaths NO + Considered Problem: Rules: 0. f1(A,B,C,D,E,F) -> f0(G,H,K,I,J,G + H + I + J + K) [G + H + I + J + K >= 1] (1,1) 1. f0(A,B,C,D,E,F) -> f0(A + C,B,-1*C,D,C + E,F) [0 >= 1 + C] (?,1) 2. f0(A,B,C,D,E,F) -> f0(A,B,C + E,D + E,-1*E,F) [0 >= 1 + E] (?,1) 3. f0(A,B,C,D,E,F) -> f0(A,B + D,C,-1*D,D + E,F) [0 >= 1 + D] (?,1) 4. f0(A,B,C,D,E,F) -> f0(A + B,-1*B,C,B + D,E,F) [0 >= 1 + B] (?,1) 5. f0(A,B,C,D,E,F) -> f0(-1*A,A + B,A + C,D,E,F) [0 >= 1 + A] (?,1) Signature: {(f0,6);(f1,6)} Flow Graph: [0->{1,2,3,4,5},1->{1,2,3,4,5},2->{1,2,3,4,5},3->{1,2,3,4,5},4->{1,2,3,4,5},5->{1,2,3,4,5}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(1,1),(2,2),(3,3),(4,4),(5,5)] * Step 2: Looptree NO + Considered Problem: Rules: 0. f1(A,B,C,D,E,F) -> f0(G,H,K,I,J,G + H + I + J + K) [G + H + I + J + K >= 1] (1,1) 1. f0(A,B,C,D,E,F) -> f0(A + C,B,-1*C,D,C + E,F) [0 >= 1 + C] (?,1) 2. f0(A,B,C,D,E,F) -> f0(A,B,C + E,D + E,-1*E,F) [0 >= 1 + E] (?,1) 3. f0(A,B,C,D,E,F) -> f0(A,B + D,C,-1*D,D + E,F) [0 >= 1 + D] (?,1) 4. f0(A,B,C,D,E,F) -> f0(A + B,-1*B,C,B + D,E,F) [0 >= 1 + B] (?,1) 5. f0(A,B,C,D,E,F) -> f0(-1*A,A + B,A + C,D,E,F) [0 >= 1 + A] (?,1) Signature: {(f0,6);(f1,6)} Flow Graph: [0->{1,2,3,4,5},1->{2,3,4,5},2->{1,3,4,5},3->{1,2,4,5},4->{1,2,3,5},5->{1,2,3,4}] + Applied Processor: Looptree + Details: We construct a looptree: P: [0,1,2,3,4,5] | `- p:[1,2,3,4,5] c: [] NO