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