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