- : unit = () - : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] fib(0) -> 0 [2] fib(s(0)) -> s(0) [3] fib(s(s(0))) -> s(0) [4] fib(s(s(x))) -> sp(g(x)) [5] g(0) -> pair(s(0),0) [6] g(s(0)) -> pair(s(0),s(0)) [7] g(s(x)) -> np(g(x)) [8] sp(pair(x,y)) -> +(x,y) [9] np(pair(x,y)) -> pair(+(x,y),x) [10] +(x,0) -> x [11] +(x,s(y)) -> s(+(x,y)) Sub problem: guided: DP termination of: END GUIDED APPLY CRITERIA (Graph splitting) Found 2 components: { --> } { --> } APPLY CRITERIA (Subterm criterion) ST: Marked_g -> 1 APPLY CRITERIA (Subterm criterion) ST: Marked_+ -> 2 APPLY CRITERIA (Graph splitting) Found 0 components: APPLY CRITERIA (Graph splitting) Found 0 components: SOLVED { TRS termination of: [1] fib(0) -> 0 [2] fib(s(0)) -> s(0) [3] fib(s(s(0))) -> s(0) [4] fib(s(s(x))) -> sp(g(x)) [5] g(0) -> pair(s(0),0) [6] g(s(0)) -> pair(s(0),s(0)) [7] g(s(x)) -> np(g(x)) [8] sp(pair(x,y)) -> +(x,y) [9] np(pair(x,y)) -> pair(+(x,y),x) [10] +(x,0) -> x [11] +(x,s(y)) -> s(+(x,y)) , CRITERION: MDP [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: ST [ { DP termination of: , CRITERION: SG [ ]} ]} { DP termination of: , CRITERION: ST [ { DP termination of: , CRITERION: SG [ ]} ]} ]} ]} Cime worked for 0.007974 seconds (real time) Cime Exit Status: 0