YES * Step 1: UnsatPaths YES + Considered Problem: Rules: 0. f300(A,B,C,D,E) -> f300(1 + A,B,C,D,E) [-1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && 100 >= A && B >= 1] (?,1) 1. f300(A,B,C,D,E) -> f3(A,B,0,0,0) [-1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && A >= 101] (?,1) 2. f2(A,B,C,D,E) -> f300(1,B,C,D,E) [B >= 1] (1,1) 3. f2(A,B,C,D,E) -> f3(0,B,0,0,0) [0 >= B] (1,1) Signature: {(f2,5);(f3,5);(f300,5)} Flow Graph: [0->{0,1},1->{},2->{0,1},3->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(2,1)] * Step 2: FromIts YES + Considered Problem: Rules: 0. f300(A,B,C,D,E) -> f300(1 + A,B,C,D,E) [-1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && 100 >= A && B >= 1] (?,1) 1. f300(A,B,C,D,E) -> f3(A,B,0,0,0) [-1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && A >= 101] (?,1) 2. f2(A,B,C,D,E) -> f300(1,B,C,D,E) [B >= 1] (1,1) 3. f2(A,B,C,D,E) -> f3(0,B,0,0,0) [0 >= B] (1,1) Signature: {(f2,5);(f3,5);(f300,5)} Flow Graph: [0->{0,1},1->{},2->{0},3->{}] + Applied Processor: FromIts + Details: () * Step 3: Decompose YES + Considered Problem: Rules: f300(A,B,C,D,E) -> f300(1 + A,B,C,D,E) [-1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && 100 >= A && B >= 1] f300(A,B,C,D,E) -> f3(A,B,0,0,0) [-1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && A >= 101] f2(A,B,C,D,E) -> f300(1,B,C,D,E) [B >= 1] f2(A,B,C,D,E) -> f3(0,B,0,0,0) [0 >= B] Signature: {(f2,5);(f3,5);(f300,5)} Rule Graph: [0->{0,1},1->{},2->{0},3->{}] + Applied Processor: Decompose NoGreedy + Details: We construct a looptree: P: [0,1,2,3] | `- p:[0] c: [0] * Step 4: CloseWith YES + Considered Problem: (Rules: f300(A,B,C,D,E) -> f300(1 + A,B,C,D,E) [-1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && 100 >= A && B >= 1] f300(A,B,C,D,E) -> f3(A,B,0,0,0) [-1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && A >= 101] f2(A,B,C,D,E) -> f300(1,B,C,D,E) [B >= 1] f2(A,B,C,D,E) -> f3(0,B,0,0,0) [0 >= B] Signature: {(f2,5);(f3,5);(f300,5)} Rule Graph: [0->{0,1},1->{},2->{0},3->{}] ,We construct a looptree: P: [0,1,2,3] | `- p:[0] c: [0]) + Applied Processor: CloseWith True + Details: () YES