- : unit = () - : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] f(0) -> 0 [2] f(s(0)) -> s(0) [3] f(s(s(x))) -> p(h(g(x))) [4] g(0) -> pair(s(0),s(0)) [5] g(s(x)) -> h(g(x)) [6] h(x) -> pair(+(p(x),q(x)),p(x)) [7] p(pair(x,y)) -> x [8] q(pair(x,y)) -> y [9] +(x,0) -> x [10] +(x,s(y)) -> s(+(x,y)) [11] f(s(s(x))) -> +(p(g(x)),q(g(x))) [12] g(s(x)) -> pair(+(p(g(x)),q(g(x))),p(g(x))) Sub problem: guided: DP termination of: END GUIDED APPLY CRITERIA (Graph splitting) Found 2 components: { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } { --> } APPLY CRITERIA (Subterm criterion) ST: Marked_g -> 1 APPLY CRITERIA (Subterm criterion) ST: Marked_+ -> 2 APPLY CRITERIA (Graph splitting) Found 0 components: APPLY CRITERIA (Graph splitting) Found 0 components: SOLVED { TRS termination of: [1] f(0) -> 0 [2] f(s(0)) -> s(0) [3] f(s(s(x))) -> p(h(g(x))) [4] g(0) -> pair(s(0),s(0)) [5] g(s(x)) -> h(g(x)) [6] h(x) -> pair(+(p(x),q(x)),p(x)) [7] p(pair(x,y)) -> x [8] q(pair(x,y)) -> y [9] +(x,0) -> x [10] +(x,s(y)) -> s(+(x,y)) [11] f(s(s(x))) -> +(p(g(x)),q(g(x))) [12] g(s(x)) -> pair(+(p(g(x)),q(g(x))),p(g(x))) , 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 0.008805 seconds (real time) Cime Exit Status: 0