MAYBE * Step 1: ArgumentFilter MAYBE + Considered Problem: Rules: 0. f0(A,B,C) -> f15(2,B,C) True (1,1) 1. f15(A,B,C) -> f18(A,A,C) [-2 + A >= 0 && 10 >= A] (?,1) 2. f18(A,B,C) -> f18(A,-1 + B,F) [10 + -1*B >= 0 && A + -1*B >= 0 && 20 + -1*A + -1*B >= 0 && 10 + -1*A >= 0 && -2 + A >= 0 && D >= 1 + E] (?,1) 3. f18(A,B,C) -> f15(1 + A,B,C) [10 + -1*B >= 0 && A + -1*B >= 0 && 20 + -1*A + -1*B >= 0 && 10 + -1*A >= 0 && -2 + A >= 0] (?,1) 4. f15(A,B,C) -> f28(A,B,C) [-2 + A >= 0 && A >= 11] (?,1) Signature: {(f0,3);(f15,3);(f18,3);(f28,3)} Flow Graph: [0->{1,4},1->{2,3},2->{2,3},3->{1,4},4->{}] + Applied Processor: ArgumentFilter [2] + Details: We remove following argument positions: [2]. * Step 2: UnsatPaths MAYBE + Considered Problem: Rules: 0. f0(A,B) -> f15(2,B) True (1,1) 1. f15(A,B) -> f18(A,A) [-2 + A >= 0 && 10 >= A] (?,1) 2. f18(A,B) -> f18(A,-1 + B) [10 + -1*B >= 0 && A + -1*B >= 0 && 20 + -1*A + -1*B >= 0 && 10 + -1*A >= 0 && -2 + A >= 0 && D >= 1 + E] (?,1) 3. f18(A,B) -> f15(1 + A,B) [10 + -1*B >= 0 && A + -1*B >= 0 && 20 + -1*A + -1*B >= 0 && 10 + -1*A >= 0 && -2 + A >= 0] (?,1) 4. f15(A,B) -> f28(A,B) [-2 + A >= 0 && A >= 11] (?,1) Signature: {(f0,3);(f15,3);(f18,3);(f28,3)} Flow Graph: [0->{1,4},1->{2,3},2->{2,3},3->{1,4},4->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(0,4)] * Step 3: FromIts MAYBE + Considered Problem: Rules: 0. f0(A,B) -> f15(2,B) True (1,1) 1. f15(A,B) -> f18(A,A) [-2 + A >= 0 && 10 >= A] (?,1) 2. f18(A,B) -> f18(A,-1 + B) [10 + -1*B >= 0 && A + -1*B >= 0 && 20 + -1*A + -1*B >= 0 && 10 + -1*A >= 0 && -2 + A >= 0 && D >= 1 + E] (?,1) 3. f18(A,B) -> f15(1 + A,B) [10 + -1*B >= 0 && A + -1*B >= 0 && 20 + -1*A + -1*B >= 0 && 10 + -1*A >= 0 && -2 + A >= 0] (?,1) 4. f15(A,B) -> f28(A,B) [-2 + A >= 0 && A >= 11] (?,1) Signature: {(f0,3);(f15,3);(f18,3);(f28,3)} Flow Graph: [0->{1},1->{2,3},2->{2,3},3->{1,4},4->{}] + Applied Processor: FromIts + Details: () * Step 4: AddSinks MAYBE + Considered Problem: Rules: f0(A,B) -> f15(2,B) True f15(A,B) -> f18(A,A) [-2 + A >= 0 && 10 >= A] f18(A,B) -> f18(A,-1 + B) [10 + -1*B >= 0 && A + -1*B >= 0 && 20 + -1*A + -1*B >= 0 && 10 + -1*A >= 0 && -2 + A >= 0 && D >= 1 + E] f18(A,B) -> f15(1 + A,B) [10 + -1*B >= 0 && A + -1*B >= 0 && 20 + -1*A + -1*B >= 0 && 10 + -1*A >= 0 && -2 + A >= 0] f15(A,B) -> f28(A,B) [-2 + A >= 0 && A >= 11] Signature: {(f0,3);(f15,3);(f18,3);(f28,3)} Rule Graph: [0->{1},1->{2,3},2->{2,3},3->{1,4},4->{}] + Applied Processor: AddSinks + Details: () * Step 5: Failure MAYBE + Considered Problem: Rules: f0(A,B) -> f15(2,B) True f15(A,B) -> f18(A,A) [-2 + A >= 0 && 10 >= A] f18(A,B) -> f18(A,-1 + B) [10 + -1*B >= 0 && A + -1*B >= 0 && 20 + -1*A + -1*B >= 0 && 10 + -1*A >= 0 && -2 + A >= 0 && D >= 1 + E] f18(A,B) -> f15(1 + A,B) [10 + -1*B >= 0 && A + -1*B >= 0 && 20 + -1*A + -1*B >= 0 && 10 + -1*A >= 0 && -2 + A >= 0] f15(A,B) -> f28(A,B) [-2 + A >= 0 && A >= 11] f28(A,B) -> exitus616(A,B) True Signature: {(exitus616,2);(f0,3);(f15,3);(f18,3);(f28,3)} Rule Graph: [0->{1},1->{2,3},2->{2,3},3->{1,4},4->{5}] + Applied Processor: Decompose Greedy + Details: We construct a looptree: P: [0,1,2,3,4,5] | `- p:[1,3,2] c: [1,3] | `- p:[2] c: [] MAYBE