YES * Step 1: UnsatPaths YES + Considered Problem: Rules: 0. div(A,B) -> end(A,B) [0 >= A] (?,1) 1. div(A,B) -> end(A,B) [A >= B] (?,1) 2. div(A,B) -> div(A,-1*A + B) [B >= 1 + A && A >= 1] (?,1) 3. start(A,B) -> div(A,B) True (1,1) Signature: {(div,2);(end,2);(start,2)} Flow Graph: [0->{},1->{},2->{0,1,2},3->{0,1,2}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(2,0)] * Step 2: FromIts YES + Considered Problem: Rules: 0. div(A,B) -> end(A,B) [0 >= A] (?,1) 1. div(A,B) -> end(A,B) [A >= B] (?,1) 2. div(A,B) -> div(A,-1*A + B) [B >= 1 + A && A >= 1] (?,1) 3. start(A,B) -> div(A,B) True (1,1) Signature: {(div,2);(end,2);(start,2)} Flow Graph: [0->{},1->{},2->{1,2},3->{0,1,2}] + Applied Processor: FromIts + Details: () * Step 3: Decompose YES + Considered Problem: Rules: div(A,B) -> end(A,B) [0 >= A] div(A,B) -> end(A,B) [A >= B] div(A,B) -> div(A,-1*A + B) [B >= 1 + A && A >= 1] start(A,B) -> div(A,B) True Signature: {(div,2);(end,2);(start,2)} Rule Graph: [0->{},1->{},2->{1,2},3->{0,1,2}] + Applied Processor: Decompose NoGreedy + Details: We construct a looptree: P: [0,1,2,3] | `- p:[2] c: [2] * Step 4: CloseWith YES + Considered Problem: (Rules: div(A,B) -> end(A,B) [0 >= A] div(A,B) -> end(A,B) [A >= B] div(A,B) -> div(A,-1*A + B) [B >= 1 + A && A >= 1] start(A,B) -> div(A,B) True Signature: {(div,2);(end,2);(start,2)} Rule Graph: [0->{},1->{},2->{1,2},3->{0,1,2}] ,We construct a looptree: P: [0,1,2,3] | `- p:[2] c: [2]) + Applied Processor: CloseWith True + Details: () YES