- : unit = () - : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] D(t) -> s(h) [2] D(constant) -> h [3] D(b(x,y)) -> b(D(x),D(y)) [4] D(c(x,y)) -> b(c(y,D(x)),c(x,D(y))) [5] D(m(x,y)) -> m(D(x),D(y)) [6] D(opp(x)) -> opp(D(x)) [7] D(div(x,y)) -> m(div(D(x),y),div(c(x,D(y)),pow(y,2))) [8] D(ln(x)) -> div(D(x),x) [9] D(pow(x,y)) -> b(c(c(y,pow(x,m(y,1))),D(x)),c(c(pow(x,y),ln(x)),D(y))) [10] b(h,x) -> x [11] b(x,h) -> x [12] b(s(x),s(y)) -> s(s(b(x,y))) [13] b(b(x,y),z) -> b(x,b(y,z)) Sub problem: guided: DP termination of: END GUIDED APPLY CRITERIA (Graph splitting) Found 2 components: { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } { --> --> --> --> --> --> --> --> --> } APPLY CRITERIA (Subterm criterion) ST: Marked_D -> 1 APPLY CRITERIA (Subterm criterion) ST: Marked_b -> 1 APPLY CRITERIA (Graph splitting) Found 0 components: APPLY CRITERIA (Graph splitting) Found 0 components: SOLVED { TRS termination of: [1] D(t) -> s(h) [2] D(constant) -> h [3] D(b(x,y)) -> b(D(x),D(y)) [4] D(c(x,y)) -> b(c(y,D(x)),c(x,D(y))) [5] D(m(x,y)) -> m(D(x),D(y)) [6] D(opp(x)) -> opp(D(x)) [7] D(div(x,y)) -> m(div(D(x),y),div(c(x,D(y)),pow(y,2))) [8] D(ln(x)) -> div(D(x),x) [9] D(pow(x,y)) -> b(c(c(y,pow(x,m(y,1))),D(x)),c(c(pow(x,y),ln(x)),D(y))) [10] b(h,x) -> x [11] b(x,h) -> x [12] b(s(x),s(y)) -> s(s(b(x,y))) [13] b(b(x,y),z) -> b(x,b(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 [ ]} ]} ]} ]} Cime worked for 0.020631 seconds (real time) Cime Exit Status: 0