- : unit = () - : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] f(j(x,y),y) -> g(f(x,k(y))) [2] f(x,h1(y,z)) -> h2(0,x,h1(y,z)) [3] g(h2(x,y,h1(z,u))) -> h2(s(x),y,h1(z,u)) [4] h2(x,j(y,h1(z,u)),h1(z,u)) -> h2(s(x),y,h1(s(z),u)) [5] i(f(x,h(y))) -> y [6] i(h2(s(x),y,h1(x,z))) -> z [7] k(h(x)) -> h1(0,x) [8] k(h1(x,y)) -> h1(s(x),y) Sub problem: guided: DP termination of: END GUIDED APPLY CRITERIA (Graph splitting) Found 2 components: { --> } { --> } APPLY CRITERIA (Subterm criterion) ST: Marked_f -> 1 APPLY CRITERIA (Subterm criterion) ST: Marked_h2 -> 2 APPLY CRITERIA (Graph splitting) Found 0 components: APPLY CRITERIA (Graph splitting) Found 0 components: SOLVED { TRS termination of: [1] f(j(x,y),y) -> g(f(x,k(y))) [2] f(x,h1(y,z)) -> h2(0,x,h1(y,z)) [3] g(h2(x,y,h1(z,u))) -> h2(s(x),y,h1(z,u)) [4] h2(x,j(y,h1(z,u)),h1(z,u)) -> h2(s(x),y,h1(s(z),u)) [5] i(f(x,h(y))) -> y [6] i(h2(s(x),y,h1(x,z))) -> z [7] k(h(x)) -> h1(0,x) [8] k(h1(x,y)) -> h1(s(x),y) , 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 0.007773 seconds (real time) Cime Exit Status: 0