YES * Step 1: TrivialSCCs YES + Considered Problem: Rules: 0. evalndecrstart(A) -> evalndecrentryin(A) True (1,1) 1. evalndecrentryin(A) -> evalndecrbb1in(-1 + A) True (?,1) 2. evalndecrbb1in(A) -> evalndecrbbin(A) [A >= 2] (?,1) 3. evalndecrbb1in(A) -> evalndecrreturnin(A) [1 >= A] (?,1) 4. evalndecrbbin(A) -> evalndecrbb1in(-1 + A) [-2 + A >= 0] (?,1) 5. evalndecrreturnin(A) -> evalndecrstop(A) [1 + -1*A >= 0] (?,1) Signature: {(evalndecrbb1in,1) ;(evalndecrbbin,1) ;(evalndecrentryin,1) ;(evalndecrreturnin,1) ;(evalndecrstart,1) ;(evalndecrstop,1)} Flow Graph: [0->{1},1->{2,3},2->{4},3->{5},4->{2,3},5->{}] + Applied Processor: TrivialSCCs + Details: All trivial SCCs of the transition graph admit timebound 1. * Step 2: Looptree YES + Considered Problem: Rules: 0. evalndecrstart(A) -> evalndecrentryin(A) True (1,1) 1. evalndecrentryin(A) -> evalndecrbb1in(-1 + A) True (1,1) 2. evalndecrbb1in(A) -> evalndecrbbin(A) [A >= 2] (?,1) 3. evalndecrbb1in(A) -> evalndecrreturnin(A) [1 >= A] (1,1) 4. evalndecrbbin(A) -> evalndecrbb1in(-1 + A) [-2 + A >= 0] (?,1) 5. evalndecrreturnin(A) -> evalndecrstop(A) [1 + -1*A >= 0] (1,1) Signature: {(evalndecrbb1in,1) ;(evalndecrbbin,1) ;(evalndecrentryin,1) ;(evalndecrreturnin,1) ;(evalndecrstart,1) ;(evalndecrstop,1)} Flow Graph: [0->{1},1->{2,3},2->{4},3->{5},4->{2,3},5->{}] + Applied Processor: Looptree + Details: We construct a looptree: P: [0,1,2,3,4,5] | `- p:[2,4] c: [4] YES