- : unit = () - : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] i(0) -> 0 [2] +(0,y) -> y [3] +(x,0) -> x [4] i(i(x)) -> x [5] +(i(x),x) -> 0 [6] +(x,i(x)) -> 0 [7] i(+(x,y)) -> +(i(x),i(y)) [8] +(x,+(y,z)) -> +(+(x,y),z) [9] +(+(x,i(y)),y) -> x [10] +(+(x,y),i(y)) -> x Sub problem: guided: DP termination of: END GUIDED APPLY CRITERIA (Graph splitting) Found 2 components: { --> --> --> --> } { --> --> --> --> } APPLY CRITERIA (Subterm criterion) ST: Marked_i -> 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] i(0) -> 0 [2] +(0,y) -> y [3] +(x,0) -> x [4] i(i(x)) -> x [5] +(i(x),x) -> 0 [6] +(x,i(x)) -> 0 [7] i(+(x,y)) -> +(i(x),i(y)) [8] +(x,+(y,z)) -> +(+(x,y),z) [9] +(+(x,i(y)),y) -> x [10] +(+(x,y),i(y)) -> 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 [ ]} ]} ]} ]} Cime worked for 0.008405 seconds (real time) Cime Exit Status: 0