- : unit = () - : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] g(0,f(x,x)) -> x [2] g(x,s(y)) -> g(f(x,y),0) [3] g(s(x),y) -> g(f(x,y),0) [4] g(f(x,y),0) -> f(g(x,0),g(y,0)) Sub problem: guided: DP termination of: END GUIDED APPLY CRITERIA (Graph splitting) Found 1 components: { --> --> --> --> --> --> --> --> } APPLY CRITERIA (Subterm criterion) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { g(0,f(x,x)) >= x ; g(f(x,y),0) >= f(g(x,0),g(y,0)) ; g(s(x),y) >= g(f(x,y),0) ; g(x,s(y)) >= g(f(x,y),0) ; Marked_g(f(x,y),0) >= Marked_g(x,0) ; Marked_g(f(x,y),0) >= Marked_g(y,0) ; Marked_g(s(x),y) >= Marked_g(f(x,y),0) ; } + Disjunctions:{ { Marked_g(f(x,y),0) > Marked_g(x,0) ; } { Marked_g(f(x,y),0) > Marked_g(y,0) ; } { Marked_g(s(x),y) > Marked_g(f(x,y),0) ; } } === 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: g(0,f(x,x)) >= x constraint: g(f(x,y),0) >= f(g(x,0),g(y,0)) constraint: g(s(x),y) >= g(f(x,y),0) constraint: g(x,s(y)) >= g(f(x,y),0) constraint: Marked_g(f(x,y),0) >= Marked_g(x,0) constraint: Marked_g(f(x,y),0) >= Marked_g(y,0) constraint: Marked_g(s(x),y) >= Marked_g(f(x,y),0) APPLY CRITERIA (Graph splitting) Found 0 components: SOLVED { TRS termination of: [1] g(0,f(x,x)) -> x [2] g(x,s(y)) -> g(f(x,y),0) [3] g(s(x),y) -> g(f(x,y),0) [4] g(f(x,y),0) -> f(g(x,0),g(y,0)) , CRITERION: MDP [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: ORD [ Solution found: polynomial interpretation = [ g ] (X0,X1) = 2*X0 + 2*X1 + 0; [ Marked_g ] (X0,X1) = 2*X0 + 2*X1 + 0; [ f ] (X0,X1) = 1 + 1*X0 + 1*X1 + 0; [ 0 ] () = 0; [ s ] (X0) = 2 + 1*X0 + 0; ]} ]} ]} Cime worked for 0.093495 seconds (real time) Cime Exit Status: 0