YES * Step 1: TrivialSCCs YES + Considered Problem: Rules: 0. evalexministart(A,B,C) -> evalexminientryin(A,B,C) True (1,1) 1. evalexminientryin(A,B,C) -> evalexminibb1in(B,A,C) True (?,1) 2. evalexminibb1in(A,B,C) -> evalexminibbin(A,B,C) [100 >= B && A >= C] (?,1) 3. evalexminibb1in(A,B,C) -> evalexminireturnin(A,B,C) [B >= 101] (?,1) 4. evalexminibb1in(A,B,C) -> evalexminireturnin(A,B,C) [C >= 1 + A] (?,1) 5. evalexminibbin(A,B,C) -> evalexminibb1in(-1 + A,C,1 + B) [A + -1*C >= 0 && 100 + -1*B >= 0] (?,1) 6. evalexminireturnin(A,B,C) -> evalexministop(A,B,C) True (?,1) Signature: {(evalexminibb1in,3) ;(evalexminibbin,3) ;(evalexminientryin,3) ;(evalexminireturnin,3) ;(evalexministart,3) ;(evalexministop,3)} Flow Graph: [0->{1},1->{2,3,4},2->{5},3->{6},4->{6},5->{2,3,4},6->{}] + Applied Processor: TrivialSCCs + Details: All trivial SCCs of the transition graph admit timebound 1. * Step 2: Looptree YES + Considered Problem: Rules: 0. evalexministart(A,B,C) -> evalexminientryin(A,B,C) True (1,1) 1. evalexminientryin(A,B,C) -> evalexminibb1in(B,A,C) True (1,1) 2. evalexminibb1in(A,B,C) -> evalexminibbin(A,B,C) [100 >= B && A >= C] (?,1) 3. evalexminibb1in(A,B,C) -> evalexminireturnin(A,B,C) [B >= 101] (1,1) 4. evalexminibb1in(A,B,C) -> evalexminireturnin(A,B,C) [C >= 1 + A] (1,1) 5. evalexminibbin(A,B,C) -> evalexminibb1in(-1 + A,C,1 + B) [A + -1*C >= 0 && 100 + -1*B >= 0] (?,1) 6. evalexminireturnin(A,B,C) -> evalexministop(A,B,C) True (1,1) Signature: {(evalexminibb1in,3) ;(evalexminibbin,3) ;(evalexminientryin,3) ;(evalexminireturnin,3) ;(evalexministart,3) ;(evalexministop,3)} Flow Graph: [0->{1},1->{2,3,4},2->{5},3->{6},4->{6},5->{2,3,4},6->{}] + Applied Processor: Looptree + Details: We construct a looptree: P: [0,1,2,3,4,5,6] | `- p:[2,5] c: [5] YES