- : unit = () - : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] double(0) -> 0 [2] double(s(x)) -> s(s(double(x))) [3] half(0) -> 0 [4] half(s(0)) -> 0 [5] half(s(s(x))) -> s(half(x)) [6] -(x,0) -> x [7] -(s(x),s(y)) -> -(x,y) [8] if(0,y,z) -> y [9] if(s(x),y,z) -> z [10] half(double(x)) -> x Sub problem: guided: DP termination of: END GUIDED APPLY CRITERIA (Graph splitting) Found 3 components: { --> } { --> } { --> } APPLY CRITERIA (Subterm criterion) ST: Marked_double -> 1 APPLY CRITERIA (Subterm criterion) ST: Marked_half -> 1 APPLY CRITERIA (Subterm criterion) ST: Marked_- -> 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] double(0) -> 0 [2] double(s(x)) -> s(s(double(x))) [3] half(0) -> 0 [4] half(s(0)) -> 0 [5] half(s(s(x))) -> s(half(x)) [6] -(x,0) -> x [7] -(s(x),s(y)) -> -(x,y) [8] if(0,y,z) -> y [9] if(s(x),y,z) -> z [10] half(double(x)) -> 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 0.010226 seconds (real time) Cime Exit Status: 0