MAYBE * Step 1: UnreachableRules MAYBE + Considered Problem: Rules: 0. f12(A,B,C,D,E,F) -> f12(-1 + A,-1 + B,1 + C,G,E,F) [A >= 1 && G >= 1] (?,1) 1. f12(A,B,C,D,E,F) -> f12(-1 + A,B,C,G,E,F) [0 >= G && A >= 1 && A >= 1 + B] (?,1) 2. f22(A,B,C,D,E,F) -> f22(A,B,C,D,E,F) True (?,1) 3. f24(A,B,C,D,E,F) -> f27(A,B,C,D,E,F) True (?,1) 4. f12(A,B,C,D,E,F) -> f22(A,B,C,D,E,F) [0 >= A] (?,1) 5. f0(A,B,C,D,E,F) -> f12(4,G,0,D,G,4) [G >= 1] (1,1) Signature: {(f0,6);(f12,6);(f22,6);(f24,6);(f27,6)} Flow Graph: [0->{0,1,4},1->{0,1,4},2->{2},3->{},4->{2},5->{0,1,4}] + Applied Processor: UnreachableRules + Details: Following transitions are not reachable from the starting states and are revomed: [3] * Step 2: UnsatPaths MAYBE + Considered Problem: Rules: 0. f12(A,B,C,D,E,F) -> f12(-1 + A,-1 + B,1 + C,G,E,F) [A >= 1 && G >= 1] (?,1) 1. f12(A,B,C,D,E,F) -> f12(-1 + A,B,C,G,E,F) [0 >= G && A >= 1 && A >= 1 + B] (?,1) 2. f22(A,B,C,D,E,F) -> f22(A,B,C,D,E,F) True (?,1) 4. f12(A,B,C,D,E,F) -> f22(A,B,C,D,E,F) [0 >= A] (?,1) 5. f0(A,B,C,D,E,F) -> f12(4,G,0,D,G,4) [G >= 1] (1,1) Signature: {(f0,6);(f12,6);(f22,6);(f24,6);(f27,6)} Flow Graph: [0->{0,1,4},1->{0,1,4},2->{2},4->{2},5->{0,1,4}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(5,4)] * Step 3: FromIts MAYBE + Considered Problem: Rules: 0. f12(A,B,C,D,E,F) -> f12(-1 + A,-1 + B,1 + C,G,E,F) [A >= 1 && G >= 1] (?,1) 1. f12(A,B,C,D,E,F) -> f12(-1 + A,B,C,G,E,F) [0 >= G && A >= 1 && A >= 1 + B] (?,1) 2. f22(A,B,C,D,E,F) -> f22(A,B,C,D,E,F) True (?,1) 4. f12(A,B,C,D,E,F) -> f22(A,B,C,D,E,F) [0 >= A] (?,1) 5. f0(A,B,C,D,E,F) -> f12(4,G,0,D,G,4) [G >= 1] (1,1) Signature: {(f0,6);(f12,6);(f22,6);(f24,6);(f27,6)} Flow Graph: [0->{0,1,4},1->{0,1,4},2->{2},4->{2},5->{0,1}] + Applied Processor: FromIts + Details: () * Step 4: Unfold MAYBE + Considered Problem: Rules: f12(A,B,C,D,E,F) -> f12(-1 + A,-1 + B,1 + C,G,E,F) [A >= 1 && G >= 1] f12(A,B,C,D,E,F) -> f12(-1 + A,B,C,G,E,F) [0 >= G && A >= 1 && A >= 1 + B] f22(A,B,C,D,E,F) -> f22(A,B,C,D,E,F) True f12(A,B,C,D,E,F) -> f22(A,B,C,D,E,F) [0 >= A] f0(A,B,C,D,E,F) -> f12(4,G,0,D,G,4) [G >= 1] Signature: {(f0,6);(f12,6);(f22,6);(f24,6);(f27,6)} Rule Graph: [0->{0,1,4},1->{0,1,4},2->{2},4->{2},5->{0,1}] + Applied Processor: Unfold + Details: () * Step 5: AddSinks MAYBE + Considered Problem: Rules: f12.0(A,B,C,D,E,F) -> f12.0(-1 + A,-1 + B,1 + C,G,E,F) [A >= 1 && G >= 1] f12.0(A,B,C,D,E,F) -> f12.1(-1 + A,-1 + B,1 + C,G,E,F) [A >= 1 && G >= 1] f12.0(A,B,C,D,E,F) -> f12.4(-1 + A,-1 + B,1 + C,G,E,F) [A >= 1 && G >= 1] f12.1(A,B,C,D,E,F) -> f12.0(-1 + A,B,C,G,E,F) [0 >= G && A >= 1 && A >= 1 + B] f12.1(A,B,C,D,E,F) -> f12.1(-1 + A,B,C,G,E,F) [0 >= G && A >= 1 && A >= 1 + B] f12.1(A,B,C,D,E,F) -> f12.4(-1 + A,B,C,G,E,F) [0 >= G && A >= 1 && A >= 1 + B] f22.2(A,B,C,D,E,F) -> f22.2(A,B,C,D,E,F) True f12.4(A,B,C,D,E,F) -> f22.2(A,B,C,D,E,F) [0 >= A] f0.5(A,B,C,D,E,F) -> f12.0(4,G,0,D,G,4) [G >= 1] f0.5(A,B,C,D,E,F) -> f12.1(4,G,0,D,G,4) [G >= 1] Signature: {(f0.5,6);(f12.0,6);(f12.1,6);(f12.4,6);(f22.2,6)} Rule Graph: [0->{0,1,2},1->{3,4,5},2->{7},3->{0,1,2},4->{3,4,5},5->{7},6->{6},7->{6},8->{0,1,2},9->{3,4,5}] + Applied Processor: AddSinks + Details: () * Step 6: Failure MAYBE + Considered Problem: Rules: f12.0(A,B,C,D,E,F) -> f12.0(-1 + A,-1 + B,1 + C,G,E,F) [A >= 1 && G >= 1] f12.0(A,B,C,D,E,F) -> f12.1(-1 + A,-1 + B,1 + C,G,E,F) [A >= 1 && G >= 1] f12.0(A,B,C,D,E,F) -> f12.4(-1 + A,-1 + B,1 + C,G,E,F) [A >= 1 && G >= 1] f12.1(A,B,C,D,E,F) -> f12.0(-1 + A,B,C,G,E,F) [0 >= G && A >= 1 && A >= 1 + B] f12.1(A,B,C,D,E,F) -> f12.1(-1 + A,B,C,G,E,F) [0 >= G && A >= 1 && A >= 1 + B] f12.1(A,B,C,D,E,F) -> f12.4(-1 + A,B,C,G,E,F) [0 >= G && A >= 1 && A >= 1 + B] f22.2(A,B,C,D,E,F) -> f22.2(A,B,C,D,E,F) True f12.4(A,B,C,D,E,F) -> f22.2(A,B,C,D,E,F) [0 >= A] f0.5(A,B,C,D,E,F) -> f12.0(4,G,0,D,G,4) [G >= 1] f0.5(A,B,C,D,E,F) -> f12.1(4,G,0,D,G,4) [G >= 1] f22.2(A,B,C,D,E,F) -> exitus616(A,B,C,D,E,F) True f22.2(A,B,C,D,E,F) -> exitus616(A,B,C,D,E,F) True f22.2(A,B,C,D,E,F) -> exitus616(A,B,C,D,E,F) True f22.2(A,B,C,D,E,F) -> exitus616(A,B,C,D,E,F) True Signature: {(exitus616,6);(f0.5,6);(f12.0,6);(f12.1,6);(f12.4,6);(f22.2,6)} Rule Graph: [0->{0,1,2},1->{3,4,5},2->{7},3->{0,1,2},4->{3,4,5},5->{7},6->{6,10,11,12,13},7->{6},8->{0,1,2},9->{3,4 ,5}] + Applied Processor: Decompose Greedy + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12,13] | +- p:[0,3,1,4] c: [0,1,3,4] | `- p:[6] c: [] MAYBE