- : unit = () - : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] fac(0) -> 1 [2] fac(s(x)) -> *(s(x),fac(x)) [3] floop(0,y) -> y [4] floop(s(x),y) -> floop(x, *(s(x),y)) [5] *(x,0) -> 0 [6] *(x,s(y)) -> +( *(x,y),x) [7] +(x,0) -> x [8] +(x,s(y)) -> s(+(x,y)) [9] 1 -> s(0) [10] fac(0) -> s(0) Sub problem: guided: DP termination of: END GUIDED APPLY CRITERIA (Graph splitting) Found 4 components: { --> } { --> } { --> } { --> } APPLY CRITERIA (Subterm criterion) ST: Marked_fac -> 1 APPLY CRITERIA (Subterm criterion) ST: Marked_floop -> 1 APPLY CRITERIA (Subterm criterion) ST: Marked_* -> 2 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: APPLY CRITERIA (Graph splitting) Found 0 components: SOLVED { TRS termination of: [1] fac(0) -> 1 [2] fac(s(x)) -> *(s(x),fac(x)) [3] floop(0,y) -> y [4] floop(s(x),y) -> floop(x, *(s(x),y)) [5] *(x,0) -> 0 [6] *(x,s(y)) -> +( *(x,y),x) [7] +(x,0) -> x [8] +(x,s(y)) -> s(+(x,y)) [9] 1 -> s(0) [10] fac(0) -> s(0) , 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 [ ]} ]} { DP termination of: , CRITERION: ST [ { DP termination of: , CRITERION: SG [ ]} ]} ]} ]} Cime worked for 0.012023 seconds (real time) Cime Exit Status: 0