MAYBE * Step 1: UnsatPaths MAYBE + Considered Problem: Rules: 0. f3(A,B,C) -> f2(A,B,C) True (1,1) 1. f2(A,B,C) -> f2(-1 + A,D,C) [D >= 1 && A >= 0] (?,1) 2. f2(A,B,C) -> f2(-1 + A,D,C) [0 >= 1 + D && A >= 0] (?,1) 3. f2(A,B,C) -> f2(A,0,C) [A >= 0] (?,1) 4. f2(A,B,C) -> f300(A,B,D) [0 >= 1 + A] (?,1) Signature: {(f2,3);(f3,3);(f300,3)} Flow Graph: [0->{1,2,3,4},1->{1,2,3,4},2->{1,2,3,4},3->{1,2,3,4},4->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(3,4)] * Step 2: FromIts MAYBE + Considered Problem: Rules: 0. f3(A,B,C) -> f2(A,B,C) True (1,1) 1. f2(A,B,C) -> f2(-1 + A,D,C) [D >= 1 && A >= 0] (?,1) 2. f2(A,B,C) -> f2(-1 + A,D,C) [0 >= 1 + D && A >= 0] (?,1) 3. f2(A,B,C) -> f2(A,0,C) [A >= 0] (?,1) 4. f2(A,B,C) -> f300(A,B,D) [0 >= 1 + A] (?,1) Signature: {(f2,3);(f3,3);(f300,3)} Flow Graph: [0->{1,2,3,4},1->{1,2,3,4},2->{1,2,3,4},3->{1,2,3},4->{}] + Applied Processor: FromIts + Details: () * Step 3: Unfold MAYBE + Considered Problem: Rules: f3(A,B,C) -> f2(A,B,C) True f2(A,B,C) -> f2(-1 + A,D,C) [D >= 1 && A >= 0] f2(A,B,C) -> f2(-1 + A,D,C) [0 >= 1 + D && A >= 0] f2(A,B,C) -> f2(A,0,C) [A >= 0] f2(A,B,C) -> f300(A,B,D) [0 >= 1 + A] Signature: {(f2,3);(f3,3);(f300,3)} Rule Graph: [0->{1,2,3,4},1->{1,2,3,4},2->{1,2,3,4},3->{1,2,3},4->{}] + Applied Processor: Unfold + Details: () * Step 4: AddSinks MAYBE + Considered Problem: Rules: f3.0(A,B,C) -> f2.1(A,B,C) True f3.0(A,B,C) -> f2.2(A,B,C) True f3.0(A,B,C) -> f2.3(A,B,C) True f3.0(A,B,C) -> f2.4(A,B,C) True f2.1(A,B,C) -> f2.1(-1 + A,D,C) [D >= 1 && A >= 0] f2.1(A,B,C) -> f2.2(-1 + A,D,C) [D >= 1 && A >= 0] f2.1(A,B,C) -> f2.3(-1 + A,D,C) [D >= 1 && A >= 0] f2.1(A,B,C) -> f2.4(-1 + A,D,C) [D >= 1 && A >= 0] f2.2(A,B,C) -> f2.1(-1 + A,D,C) [0 >= 1 + D && A >= 0] f2.2(A,B,C) -> f2.2(-1 + A,D,C) [0 >= 1 + D && A >= 0] f2.2(A,B,C) -> f2.3(-1 + A,D,C) [0 >= 1 + D && A >= 0] f2.2(A,B,C) -> f2.4(-1 + A,D,C) [0 >= 1 + D && A >= 0] f2.3(A,B,C) -> f2.1(A,0,C) [A >= 0] f2.3(A,B,C) -> f2.2(A,0,C) [A >= 0] f2.3(A,B,C) -> f2.3(A,0,C) [A >= 0] f2.4(A,B,C) -> f300.5(A,B,D) [0 >= 1 + A] Signature: {(f2.1,3);(f2.2,3);(f2.3,3);(f2.4,3);(f3.0,3);(f300.5,3)} Rule Graph: [0->{4,5,6,7},1->{8,9,10,11},2->{12,13,14},3->{15},4->{4,5,6,7},5->{8,9,10,11},6->{12,13,14},7->{15},8->{4 ,5,6,7},9->{8,9,10,11},10->{12,13,14},11->{15},12->{4,5,6,7},13->{8,9,10,11},14->{12,13,14},15->{}] + Applied Processor: AddSinks + Details: () * Step 5: Failure MAYBE + Considered Problem: Rules: f3.0(A,B,C) -> f2.1(A,B,C) True f3.0(A,B,C) -> f2.2(A,B,C) True f3.0(A,B,C) -> f2.3(A,B,C) True f3.0(A,B,C) -> f2.4(A,B,C) True f2.1(A,B,C) -> f2.1(-1 + A,D,C) [D >= 1 && A >= 0] f2.1(A,B,C) -> f2.2(-1 + A,D,C) [D >= 1 && A >= 0] f2.1(A,B,C) -> f2.3(-1 + A,D,C) [D >= 1 && A >= 0] f2.1(A,B,C) -> f2.4(-1 + A,D,C) [D >= 1 && A >= 0] f2.2(A,B,C) -> f2.1(-1 + A,D,C) [0 >= 1 + D && A >= 0] f2.2(A,B,C) -> f2.2(-1 + A,D,C) [0 >= 1 + D && A >= 0] f2.2(A,B,C) -> f2.3(-1 + A,D,C) [0 >= 1 + D && A >= 0] f2.2(A,B,C) -> f2.4(-1 + A,D,C) [0 >= 1 + D && A >= 0] f2.3(A,B,C) -> f2.1(A,0,C) [A >= 0] f2.3(A,B,C) -> f2.2(A,0,C) [A >= 0] f2.3(A,B,C) -> f2.3(A,0,C) [A >= 0] f2.4(A,B,C) -> f300.5(A,B,D) [0 >= 1 + A] f300.5(A,B,C) -> exitus616(A,B,C) True f300.5(A,B,C) -> exitus616(A,B,C) True f300.5(A,B,C) -> exitus616(A,B,C) True f300.5(A,B,C) -> exitus616(A,B,C) True f300.5(A,B,C) -> exitus616(A,B,C) True f300.5(A,B,C) -> exitus616(A,B,C) True f300.5(A,B,C) -> exitus616(A,B,C) True Signature: {(exitus616,3);(f2.1,3);(f2.2,3);(f2.3,3);(f2.4,3);(f3.0,3);(f300.5,3)} Rule Graph: [0->{4,5,6,7},1->{8,9,10,11},2->{12,13,14},3->{15},4->{4,5,6,7},5->{8,9,10,11},6->{12,13,14},7->{15},8->{4 ,5,6,7},9->{8,9,10,11},10->{12,13,14},11->{15},12->{4,5,6,7},13->{8,9,10,11},14->{12,13,14},15->{16,17,18,19 ,20,21,22}] + Applied Processor: Decompose Greedy + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22] | `- p:[4,8,5,12,6,10,9,13,14] c: [4,5,6,8,9,10,12,13] | `- p:[14] c: [] MAYBE