- : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] half(0) -> 0 [2] half(s(s(x))) -> s(half(x)) [3] log(s(0)) -> 0 [4] log(s(s(x))) -> s(log(s(half(x)))) Sub problem: guided: DP termination of: END GUIDED APPLY CRITERIA (Graph splitting) Found 2 components: { --> } { --> } APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { half(0) >= 0 ; half(s(s(x))) >= s(half(x)) ; log(s(0)) >= 0 ; log(s(s(x))) >= s(log(s(half(x)))) ; Marked_log(s(s(x))) >= Marked_log(s(half(x))) ; } + Disjunctions:{ { Marked_log(s(s(x))) > Marked_log(s(half(x))) ; } } === TIMER virtual : 10.000000 === Entering poly_solver Starting Sat solver initialization Calling Sat solver... === STOPING TIMER virtual === === TIMER real : 10.000000 === === STOPING TIMER real === Sat solver returned Sat solver result read === STOPING TIMER real === === STOPING TIMER virtual === constraint: half(0) >= 0 constraint: half(s(s(x))) >= s(half(x)) constraint: log(s(0)) >= 0 constraint: log(s(s(x))) >= s(log(s(half(x)))) constraint: Marked_log(s(s(x))) >= Marked_log(s(half(x))) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { half(0) >= 0 ; half(s(s(x))) >= s(half(x)) ; log(s(0)) >= 0 ; log(s(s(x))) >= s(log(s(half(x)))) ; Marked_half(s(s(x))) >= Marked_half(x) ; } + Disjunctions:{ { Marked_half(s(s(x))) > Marked_half(x) ; } } === TIMER virtual : 10.000000 === Entering poly_solver Starting Sat solver initialization Calling Sat solver... === STOPING TIMER virtual === === TIMER real : 10.000000 === === STOPING TIMER real === Sat solver returned Sat solver result read === STOPING TIMER real === === STOPING TIMER virtual === constraint: half(0) >= 0 constraint: half(s(s(x))) >= s(half(x)) constraint: log(s(0)) >= 0 constraint: log(s(s(x))) >= s(log(s(half(x)))) constraint: Marked_half(s(s(x))) >= Marked_half(x) APPLY CRITERIA (Graph splitting) Found 0 components: APPLY CRITERIA (Graph splitting) Found 0 components: SOLVED { TRS termination of: [1] half(0) -> 0 [2] half(s(s(x))) -> s(half(x)) [3] log(s(0)) -> 0 [4] log(s(s(x))) -> s(log(s(half(x)))) , CRITERION: MDP [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: ORD [ Solution found: polynomial interpretation = [ 0 ] () = 0; [ Marked_log ] (X0) = 3*X0 + 0; [ s ] (X0) = 2 + 2*X0 + 0; [ half ] (X0) = 1*X0 + 0; [ log ] (X0) = 1*X0 + 0; ]} { DP termination of: , CRITERION: ORD [ Solution found: polynomial interpretation = [ 0 ] () = 0; [ s ] (X0) = 1 + 2*X0 + 0; [ half ] (X0) = 1*X0 + 0; [ Marked_half ] (X0) = 1*X0 + 0; [ log ] (X0) = 2*X0 + 0; ]} ]} ]} Cime worked for 0.066887 seconds (real time) Cime Exit Status: 0