- : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] minus(x,0) -> x [2] minus(s(x),s(y)) -> minus(x,y) [3] f(0) -> s(0) [4] f(s(x)) -> minus(s(x),g(f(x))) [5] g(0) -> 0 [6] g(s(x)) -> minus(s(x),f(g(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: { minus(s(x),s(y)) >= minus(x,y) ; minus(x,0) >= x ; f(0) >= s(0) ; f(s(x)) >= minus(s(x),g(f(x))) ; g(0) >= 0 ; g(s(x)) >= minus(s(x),f(g(x))) ; Marked_g(s(x)) >= Marked_g(x) ; Marked_g(s(x)) >= Marked_f(g(x)) ; Marked_f(s(x)) >= Marked_g(f(x)) ; Marked_f(s(x)) >= Marked_f(x) ; } + Disjunctions:{ { Marked_g(s(x)) > Marked_g(x) ; } { Marked_g(s(x)) > Marked_f(g(x)) ; } { Marked_f(s(x)) > Marked_g(f(x)) ; } { Marked_f(s(x)) > Marked_f(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: minus(s(x),s(y)) >= minus(x,y) constraint: minus(x,0) >= x constraint: f(0) >= s(0) constraint: f(s(x)) >= minus(s(x),g(f(x))) constraint: g(0) >= 0 constraint: g(s(x)) >= minus(s(x),f(g(x))) constraint: Marked_g(s(x)) >= Marked_g(x) constraint: Marked_g(s(x)) >= Marked_f(g(x)) constraint: Marked_f(s(x)) >= Marked_g(f(x)) constraint: Marked_f(s(x)) >= Marked_f(x) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { minus(s(x),s(y)) >= minus(x,y) ; minus(x,0) >= x ; f(0) >= s(0) ; f(s(x)) >= minus(s(x),g(f(x))) ; g(0) >= 0 ; g(s(x)) >= minus(s(x),f(g(x))) ; Marked_minus(s(x),s(y)) >= Marked_minus(x,y) ; } + Disjunctions:{ { Marked_minus(s(x),s(y)) > Marked_minus(x,y) ; } } === 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: minus(s(x),s(y)) >= minus(x,y) constraint: minus(x,0) >= x constraint: f(0) >= s(0) constraint: f(s(x)) >= minus(s(x),g(f(x))) constraint: g(0) >= 0 constraint: g(s(x)) >= minus(s(x),f(g(x))) constraint: Marked_minus(s(x),s(y)) >= Marked_minus(x,y) APPLY CRITERIA (Graph splitting) Found 0 components: APPLY CRITERIA (Graph splitting) Found 0 components: SOLVED { TRS termination of: [1] minus(x,0) -> x [2] minus(s(x),s(y)) -> minus(x,y) [3] f(0) -> s(0) [4] f(s(x)) -> minus(s(x),g(f(x))) [5] g(0) -> 0 [6] g(s(x)) -> minus(s(x),f(g(x))) , CRITERION: MDP [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: ORD [ Solution found: polynomial interpretation = [ minus ] (X0,X1) = 1*X0 + 0; [ g ] (X0) = 1*X0 + 0; [ s ] (X0) = 3 + 3*X0 + 0; [ 0 ] () = 0; [ Marked_g ] (X0) = 3 + 1*X0 + 0; [ f ] (X0) = 3 + 3*X0 + 0; [ Marked_f ] (X0) = 3*X0 + 0; ]} { DP termination of: , CRITERION: ORD [ Solution found: polynomial interpretation = [ minus ] (X0,X1) = 1*X0 + 0; [ g ] (X0) = 2*X0 + 0; [ s ] (X0) = 1 + 2*X0 + 0; [ Marked_minus ] (X0,X1) = 1*X0 + 0; [ 0 ] () = 0; [ f ] (X0) = 2 + 2*X0 + 0; ]} ]} ]} Cime worked for 0.064539 seconds (real time) Cime Exit Status: 0