- : unit = () - : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] +(a,b) -> +(b,a) [2] +(a,+(b,z)) -> +(b,+(a,z)) [3] +(+(x,y),z) -> +(x,+(y,z)) [4] f(a,y) -> a [5] f(b,y) -> b [6] f(+(x,y),z) -> +(f(x,z),f(y,z)) Sub problem: guided: DP termination of: END GUIDED APPLY CRITERIA (Graph splitting) Found 3 components: { --> --> --> --> } { --> --> --> --> } { --> } APPLY CRITERIA (Subterm criterion) ST: Marked_f -> 1 APPLY CRITERIA (Subterm criterion) ST: Marked_+ -> 1 APPLY CRITERIA (Subterm criterion) ST: Marked_+ -> 2 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] +(a,b) -> +(b,a) [2] +(a,+(b,z)) -> +(b,+(a,z)) [3] +(+(x,y),z) -> +(x,+(y,z)) [4] f(a,y) -> a [5] f(b,y) -> b [6] f(+(x,y),z) -> +(f(x,z),f(y,z)) , 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 0.010129 seconds (real time) Cime Exit Status: 0