MAYBE * Step 1: UnsatPaths MAYBE + Considered Problem: Rules: 0. f0(A,B,C,D) -> f6(B,B,D,D) True (1,1) 1. f6(A,B,C,D) -> f6(-1 + A,B,-1 + C,D) [-1*C + D >= 0 && -1*A + B >= 0 && 0 >= 1 + A] (?,1) 2. f6(A,B,C,D) -> f6(-1 + A,B,-1 + C,D) [-1*C + D >= 0 && -1*A + B >= 0 && A >= 1] (?,1) 3. f6(A,B,C,D) -> f14(0,B,C,D) [-1*C + D >= 0 && -1*A + B >= 0 && D >= 1 + B && A = 0] (?,1) 4. f6(A,B,C,D) -> f14(0,B,C,D) [-1*C + D >= 0 && -1*A + B >= 0 && B >= 1 + D && A = 0] (?,1) 5. f6(A,B,C,D) -> f14(0,B,C,B) [-1*C + D >= 0 && -1*A + B >= 0 && A = 0 && B = D] (?,1) Signature: {(f0,4);(f14,4);(f6,4)} Flow Graph: [0->{1,2,3,4,5},1->{1,2,3,4,5},2->{1,2,3,4,5},3->{},4->{},5->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(1,2),(1,3),(1,4),(1,5),(2,1)] * Step 2: FromIts MAYBE + Considered Problem: Rules: 0. f0(A,B,C,D) -> f6(B,B,D,D) True (1,1) 1. f6(A,B,C,D) -> f6(-1 + A,B,-1 + C,D) [-1*C + D >= 0 && -1*A + B >= 0 && 0 >= 1 + A] (?,1) 2. f6(A,B,C,D) -> f6(-1 + A,B,-1 + C,D) [-1*C + D >= 0 && -1*A + B >= 0 && A >= 1] (?,1) 3. f6(A,B,C,D) -> f14(0,B,C,D) [-1*C + D >= 0 && -1*A + B >= 0 && D >= 1 + B && A = 0] (?,1) 4. f6(A,B,C,D) -> f14(0,B,C,D) [-1*C + D >= 0 && -1*A + B >= 0 && B >= 1 + D && A = 0] (?,1) 5. f6(A,B,C,D) -> f14(0,B,C,B) [-1*C + D >= 0 && -1*A + B >= 0 && A = 0 && B = D] (?,1) Signature: {(f0,4);(f14,4);(f6,4)} Flow Graph: [0->{1,2,3,4,5},1->{1},2->{2,3,4,5},3->{},4->{},5->{}] + Applied Processor: FromIts + Details: () * Step 3: AddSinks MAYBE + Considered Problem: Rules: f0(A,B,C,D) -> f6(B,B,D,D) True f6(A,B,C,D) -> f6(-1 + A,B,-1 + C,D) [-1*C + D >= 0 && -1*A + B >= 0 && 0 >= 1 + A] f6(A,B,C,D) -> f6(-1 + A,B,-1 + C,D) [-1*C + D >= 0 && -1*A + B >= 0 && A >= 1] f6(A,B,C,D) -> f14(0,B,C,D) [-1*C + D >= 0 && -1*A + B >= 0 && D >= 1 + B && A = 0] f6(A,B,C,D) -> f14(0,B,C,D) [-1*C + D >= 0 && -1*A + B >= 0 && B >= 1 + D && A = 0] f6(A,B,C,D) -> f14(0,B,C,B) [-1*C + D >= 0 && -1*A + B >= 0 && A = 0 && B = D] Signature: {(f0,4);(f14,4);(f6,4)} Rule Graph: [0->{1,2,3,4,5},1->{1},2->{2,3,4,5},3->{},4->{},5->{}] + Applied Processor: AddSinks + Details: () * Step 4: Failure MAYBE + Considered Problem: Rules: f0(A,B,C,D) -> f6(B,B,D,D) True f6(A,B,C,D) -> f6(-1 + A,B,-1 + C,D) [-1*C + D >= 0 && -1*A + B >= 0 && 0 >= 1 + A] f6(A,B,C,D) -> f6(-1 + A,B,-1 + C,D) [-1*C + D >= 0 && -1*A + B >= 0 && A >= 1] f6(A,B,C,D) -> f14(0,B,C,D) [-1*C + D >= 0 && -1*A + B >= 0 && D >= 1 + B && A = 0] f6(A,B,C,D) -> f14(0,B,C,D) [-1*C + D >= 0 && -1*A + B >= 0 && B >= 1 + D && A = 0] f6(A,B,C,D) -> f14(0,B,C,B) [-1*C + D >= 0 && -1*A + B >= 0 && A = 0 && B = D] f14(A,B,C,D) -> exitus616(A,B,C,D) True f14(A,B,C,D) -> exitus616(A,B,C,D) True f14(A,B,C,D) -> exitus616(A,B,C,D) True f6(A,B,C,D) -> exitus616(A,B,C,D) True Signature: {(exitus616,4);(f0,4);(f14,4);(f6,4)} Rule Graph: [0->{1,2,3,4,5},1->{1,9},2->{2,3,4,5},3->{8},4->{7},5->{6}] + Applied Processor: Decompose Greedy + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9] | +- p:[2] c: [2] | `- p:[1] c: [] MAYBE