- : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] fib(0) -> 0 [2] fib(s(0)) -> s(0) [3] fib(s(s(x))) -> +(fib(s(x)),fib(x)) Sub problem: guided: DP termination of: END GUIDED APPLY CRITERIA (Graph splitting) Found 1 components: { --> --> --> --> } APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { fib(0) >= 0 ; fib(s(0)) >= s(0) ; fib(s(s(x))) >= +(fib(s(x)),fib(x)) ; Marked_fib(s(s(x))) >= Marked_fib(s(x)) ; Marked_fib(s(s(x))) >= Marked_fib(x) ; } + Disjunctions:{ { Marked_fib(s(s(x))) > Marked_fib(s(x)) ; } { Marked_fib(s(s(x))) > Marked_fib(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: fib(0) >= 0 constraint: fib(s(0)) >= s(0) constraint: fib(s(s(x))) >= +(fib(s(x)),fib(x)) constraint: Marked_fib(s(s(x))) >= Marked_fib(s(x)) constraint: Marked_fib(s(s(x))) >= Marked_fib(x) APPLY CRITERIA (Graph splitting) Found 0 components: SOLVED { TRS termination of: [1] fib(0) -> 0 [2] fib(s(0)) -> s(0) [3] fib(s(s(x))) -> +(fib(s(x)),fib(x)) , CRITERION: MDP [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: ORD [ Solution found: polynomial interpretation = [ 0 ] () = 3 + 0; [ Marked_fib ] (X0) = 1*X0 + 0; [ s ] (X0) = 2 + 2*X0 + 0; [ fib ] (X0) = 1*X0 + 0; [ + ] (X0,X1) = 2*X1 + 0; ]} ]} ]} Cime worked for 0.030232 seconds (real time) Cime Exit Status: 0