YES * Step 1: UnsatPaths YES + Considered Problem: Rules: 0. eval1(A,B) -> eval2(A,B) [A >= 1 && B >= 1 && A >= 1 + B] (?,1) 1. eval1(A,B) -> eval3(A,B) [A >= 1 && B >= 1 && B >= A] (?,1) 2. eval2(A,B) -> eval2(-1 + A,B) [A >= 1] (?,1) 3. eval2(A,B) -> eval1(A,B) [0 >= A] (?,1) 4. eval3(A,B) -> eval3(A,-1 + B) [B >= 1] (?,1) 5. eval3(A,B) -> eval1(A,B) [0 >= B] (?,1) 6. start(A,B) -> eval1(A,B) True (1,1) Signature: {(eval1,2);(eval2,2);(eval3,2);(start,2)} Flow Graph: [0->{2,3},1->{4,5},2->{2,3},3->{0,1},4->{4,5},5->{0,1},6->{0,1}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(0,3),(1,5),(3,0),(3,1),(5,0),(5,1)] * Step 2: FromIts YES + Considered Problem: Rules: 0. eval1(A,B) -> eval2(A,B) [A >= 1 && B >= 1 && A >= 1 + B] (?,1) 1. eval1(A,B) -> eval3(A,B) [A >= 1 && B >= 1 && B >= A] (?,1) 2. eval2(A,B) -> eval2(-1 + A,B) [A >= 1] (?,1) 3. eval2(A,B) -> eval1(A,B) [0 >= A] (?,1) 4. eval3(A,B) -> eval3(A,-1 + B) [B >= 1] (?,1) 5. eval3(A,B) -> eval1(A,B) [0 >= B] (?,1) 6. start(A,B) -> eval1(A,B) True (1,1) Signature: {(eval1,2);(eval2,2);(eval3,2);(start,2)} Flow Graph: [0->{2},1->{4},2->{2,3},3->{},4->{4,5},5->{},6->{0,1}] + Applied Processor: FromIts + Details: () * Step 3: Decompose YES + Considered Problem: Rules: eval1(A,B) -> eval2(A,B) [A >= 1 && B >= 1 && A >= 1 + B] eval1(A,B) -> eval3(A,B) [A >= 1 && B >= 1 && B >= A] eval2(A,B) -> eval2(-1 + A,B) [A >= 1] eval2(A,B) -> eval1(A,B) [0 >= A] eval3(A,B) -> eval3(A,-1 + B) [B >= 1] eval3(A,B) -> eval1(A,B) [0 >= B] start(A,B) -> eval1(A,B) True Signature: {(eval1,2);(eval2,2);(eval3,2);(start,2)} Rule Graph: [0->{2},1->{4},2->{2,3},3->{},4->{4,5},5->{},6->{0,1}] + Applied Processor: Decompose NoGreedy + Details: We construct a looptree: P: [0,1,2,3,4,5,6] | +- p:[4] c: [4] | `- p:[2] c: [2] * Step 4: CloseWith YES + Considered Problem: (Rules: eval1(A,B) -> eval2(A,B) [A >= 1 && B >= 1 && A >= 1 + B] eval1(A,B) -> eval3(A,B) [A >= 1 && B >= 1 && B >= A] eval2(A,B) -> eval2(-1 + A,B) [A >= 1] eval2(A,B) -> eval1(A,B) [0 >= A] eval3(A,B) -> eval3(A,-1 + B) [B >= 1] eval3(A,B) -> eval1(A,B) [0 >= B] start(A,B) -> eval1(A,B) True Signature: {(eval1,2);(eval2,2);(eval3,2);(start,2)} Rule Graph: [0->{2},1->{4},2->{2,3},3->{},4->{4,5},5->{},6->{0,1}] ,We construct a looptree: P: [0,1,2,3,4,5,6] | +- p:[4] c: [4] | `- p:[2] c: [2]) + Applied Processor: CloseWith True + Details: () YES