- : unit = () - : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] +(x,0) -> x [2] +(0,x) -> x [3] +(s(x),s(y)) -> s(s(+(x,y))) [4] +(+(x,y),z) -> +(x,+(y,z)) [5] *(x,0) -> 0 [6] *(0,x) -> 0 [7] *(s(x),s(y)) -> s(+( *(x,y),+(x,y))) [8] *( *(x,y),z) -> *(x, *(y,z)) [9] sum(nil) -> 0 [10] sum(cons(x,l)) -> +(x,sum(l)) [11] prod(nil) -> s(0) [12] prod(cons(x,l)) -> *(x,prod(l)) Sub problem: guided: DP termination of: END GUIDED APPLY CRITERIA (Graph splitting) Found 4 components: { --> } { --> } { --> --> --> --> --> --> --> --> --> } { --> --> --> --> --> --> --> --> --> } APPLY CRITERIA (Subterm criterion) ST: Marked_sum -> 1 APPLY CRITERIA (Subterm criterion) ST: Marked_prod -> 1 APPLY CRITERIA (Subterm criterion) ST: Marked_* -> 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: APPLY CRITERIA (Graph splitting) Found 0 components: SOLVED { TRS termination of: [1] +(x,0) -> x [2] +(0,x) -> x [3] +(s(x),s(y)) -> s(s(+(x,y))) [4] +(+(x,y),z) -> +(x,+(y,z)) [5] *(x,0) -> 0 [6] *(0,x) -> 0 [7] *(s(x),s(y)) -> s(+( *(x,y),+(x,y))) [8] *( *(x,y),z) -> *(x, *(y,z)) [9] sum(nil) -> 0 [10] sum(cons(x,l)) -> +(x,sum(l)) [11] prod(nil) -> s(0) [12] prod(cons(x,l)) -> *(x,prod(l)) , 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 0.015526 seconds (real time) Cime Exit Status: 0