- : unit = () - : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] sqr(0) -> 0 [2] sqr(s(x)) -> +(sqr(x),s(double(x))) [3] double(0) -> 0 [4] double(s(x)) -> s(s(double(x))) [5] +(x,0) -> x [6] +(x,s(y)) -> s(+(x,y)) [7] sqr(s(x)) -> s(+(sqr(x),double(x))) Sub problem: guided: DP termination of: END GUIDED APPLY CRITERIA (Graph splitting) Found 3 components: { --> --> --> --> } { --> } { --> } APPLY CRITERIA (Subterm criterion) ST: Marked_sqr -> 1 APPLY CRITERIA (Subterm criterion) ST: Marked_+ -> 2 APPLY CRITERIA (Subterm criterion) ST: Marked_double -> 1 APPLY CRITERIA (Graph splitting) Found 0 components: APPLY CRITERIA (Graph splitting) Found 0 components: APPLY CRITERIA (Graph splitting) Found 0 components: SOLVED { TRS termination of: [1] sqr(0) -> 0 [2] sqr(s(x)) -> +(sqr(x),s(double(x))) [3] double(0) -> 0 [4] double(s(x)) -> s(s(double(x))) [5] +(x,0) -> x [6] +(x,s(y)) -> s(+(x,y)) [7] sqr(s(x)) -> s(+(sqr(x),double(x))) , 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 [ ]} ]} { DP termination of: , CRITERION: ST [ { DP termination of: , CRITERION: SG [ ]} ]} ]} ]} Cime worked for 0.009164 seconds (real time) Cime Exit Status: 0