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) [0 >= 1 + A] (?,1) 2. f6(A,B,C,D) -> f6(-1 + A,B,-1 + C,D) [A >= 1] (?,1) 3. f6(A,B,C,D) -> f14(0,B,C,D) [D >= 1 + B && A = 0] (?,1) 4. f6(A,B,C,D) -> f14(0,B,C,D) [B >= 1 + D && A = 0] (?,1) 5. f6(A,B,C,D) -> f14(0,B,C,B) [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) [0 >= 1 + A] (?,1) 2. f6(A,B,C,D) -> f6(-1 + A,B,-1 + C,D) [A >= 1] (?,1) 3. f6(A,B,C,D) -> f14(0,B,C,D) [D >= 1 + B && A = 0] (?,1) 4. f6(A,B,C,D) -> f14(0,B,C,D) [B >= 1 + D && A = 0] (?,1) 5. f6(A,B,C,D) -> f14(0,B,C,B) [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: Unfold 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) [0 >= 1 + A] f6(A,B,C,D) -> f6(-1 + A,B,-1 + C,D) [A >= 1] f6(A,B,C,D) -> f14(0,B,C,D) [D >= 1 + B && A = 0] f6(A,B,C,D) -> f14(0,B,C,D) [B >= 1 + D && A = 0] f6(A,B,C,D) -> f14(0,B,C,B) [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: Unfold + Details: () * Step 4: AddSinks MAYBE + Considered Problem: Rules: f0.0(A,B,C,D) -> f6.1(B,B,D,D) True f0.0(A,B,C,D) -> f6.2(B,B,D,D) True f0.0(A,B,C,D) -> f6.3(B,B,D,D) True f0.0(A,B,C,D) -> f6.4(B,B,D,D) True f0.0(A,B,C,D) -> f6.5(B,B,D,D) True f6.1(A,B,C,D) -> f6.1(-1 + A,B,-1 + C,D) [0 >= 1 + A] f6.2(A,B,C,D) -> f6.2(-1 + A,B,-1 + C,D) [A >= 1] f6.2(A,B,C,D) -> f6.3(-1 + A,B,-1 + C,D) [A >= 1] f6.2(A,B,C,D) -> f6.4(-1 + A,B,-1 + C,D) [A >= 1] f6.2(A,B,C,D) -> f6.5(-1 + A,B,-1 + C,D) [A >= 1] f6.3(A,B,C,D) -> f14.6(0,B,C,D) [D >= 1 + B && A = 0] f6.4(A,B,C,D) -> f14.6(0,B,C,D) [B >= 1 + D && A = 0] f6.5(A,B,C,D) -> f14.6(0,B,C,B) [A = 0 && B = D] Signature: {(f0.0,4);(f14.6,4);(f6.1,4);(f6.2,4);(f6.3,4);(f6.4,4);(f6.5,4)} Rule Graph: [0->{5},1->{6,7,8,9},2->{10},3->{11},4->{12},5->{5},6->{6,7,8,9},7->{10},8->{11},9->{12},10->{},11->{} ,12->{}] + Applied Processor: AddSinks + Details: () * Step 5: Failure MAYBE + Considered Problem: Rules: f0.0(A,B,C,D) -> f6.1(B,B,D,D) True f0.0(A,B,C,D) -> f6.2(B,B,D,D) True f0.0(A,B,C,D) -> f6.3(B,B,D,D) True f0.0(A,B,C,D) -> f6.4(B,B,D,D) True f0.0(A,B,C,D) -> f6.5(B,B,D,D) True f6.1(A,B,C,D) -> f6.1(-1 + A,B,-1 + C,D) [0 >= 1 + A] f6.2(A,B,C,D) -> f6.2(-1 + A,B,-1 + C,D) [A >= 1] f6.2(A,B,C,D) -> f6.3(-1 + A,B,-1 + C,D) [A >= 1] f6.2(A,B,C,D) -> f6.4(-1 + A,B,-1 + C,D) [A >= 1] f6.2(A,B,C,D) -> f6.5(-1 + A,B,-1 + C,D) [A >= 1] f6.3(A,B,C,D) -> f14.6(0,B,C,D) [D >= 1 + B && A = 0] f6.4(A,B,C,D) -> f14.6(0,B,C,D) [B >= 1 + D && A = 0] f6.5(A,B,C,D) -> f14.6(0,B,C,B) [A = 0 && B = D] f14.6(A,B,C,D) -> exitus616(A,B,C,D) True f14.6(A,B,C,D) -> exitus616(A,B,C,D) True f14.6(A,B,C,D) -> exitus616(A,B,C,D) True f14.6(A,B,C,D) -> exitus616(A,B,C,D) True f14.6(A,B,C,D) -> exitus616(A,B,C,D) True f14.6(A,B,C,D) -> exitus616(A,B,C,D) True f6.1(A,B,C,D) -> exitus616(A,B,C,D) True Signature: {(exitus616,4);(f0.0,4);(f14.6,4);(f6.1,4);(f6.2,4);(f6.3,4);(f6.4,4);(f6.5,4)} Rule Graph: [0->{5},1->{6,7,8,9},2->{10},3->{11},4->{12},5->{5,19},6->{6,7,8,9},7->{10},8->{11},9->{12},10->{15,18} ,11->{14,17},12->{13,16}] + Applied Processor: Decompose Greedy + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19] | +- p:[6] c: [6] | `- p:[5] c: [] MAYBE