- : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] not(true) -> false [2] not(false) -> true [3] odd(0) -> false [4] odd(s(x)) -> not(odd(x)) [5] +(x,0) -> x [6] +(x,s(y)) -> s(+(x,y)) [7] +(s(x),y) -> s(+(x,y)) 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: { not(false) >= true ; not(true) >= false ; odd(0) >= false ; odd(s(x)) >= not(odd(x)) ; +(s(x),y) >= s(+(x,y)) ; +(x,0) >= x ; +(x,s(y)) >= s(+(x,y)) ; Marked_odd(s(x)) >= Marked_odd(x) ; } + Disjunctions:{ { Marked_odd(s(x)) > Marked_odd(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: not(false) >= true constraint: not(true) >= false constraint: odd(0) >= false constraint: odd(s(x)) >= not(odd(x)) constraint: +(s(x),y) >= s(+(x,y)) constraint: +(x,0) >= x constraint: +(x,s(y)) >= s(+(x,y)) constraint: Marked_odd(s(x)) >= Marked_odd(x) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { not(false) >= true ; not(true) >= false ; odd(0) >= false ; odd(s(x)) >= not(odd(x)) ; +(s(x),y) >= s(+(x,y)) ; +(x,0) >= x ; +(x,s(y)) >= s(+(x,y)) ; Marked_+(s(x),y) >= Marked_+(x,y) ; Marked_+(x,s(y)) >= Marked_+(x,y) ; } + Disjunctions:{ { Marked_+(s(x),y) > Marked_+(x,y) ; } { Marked_+(x,s(y)) > Marked_+(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: not(false) >= true constraint: not(true) >= false constraint: odd(0) >= false constraint: odd(s(x)) >= not(odd(x)) constraint: +(s(x),y) >= s(+(x,y)) constraint: +(x,0) >= x constraint: +(x,s(y)) >= s(+(x,y)) constraint: Marked_+(s(x),y) >= Marked_+(x,y) constraint: Marked_+(x,s(y)) >= Marked_+(x,y) APPLY CRITERIA (Graph splitting) Found 0 components: APPLY CRITERIA (Graph splitting) Found 0 components: SOLVED { TRS termination of: [1] not(true) -> false [2] not(false) -> true [3] odd(0) -> false [4] odd(s(x)) -> not(odd(x)) [5] +(x,0) -> x [6] +(x,s(y)) -> s(+(x,y)) [7] +(s(x),y) -> s(+(x,y)) , CRITERION: MDP [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: ORD [ Solution found: polynomial interpretation = [ false ] () = 0; [ Marked_odd ] (X0) = 3*X0 + 0; [ 0 ] () = 0; [ true ] () = 0; [ + ] (X0,X1) = 2 + 2*X0 + 3*X1 + 0; [ not ] (X0) = 0; [ s ] (X0) = 2 + 1*X0 + 0; [ odd ] (X0) = 2 + 2*X0 + 0; ]} { DP termination of: , CRITERION: ORD [ Solution found: polynomial interpretation = [ false ] () = 0; [ 0 ] () = 0; [ true ] () = 0; [ + ] (X0,X1) = 2*X0 + 2*X1 + 0; [ not ] (X0) = 0; [ s ] (X0) = 1 + 1*X0 + 0; [ odd ] (X0) = 2 + 0; [ Marked_+ ] (X0,X1) = 3*X0 + 3*X1 + 0; ]} ]} ]} Cime worked for 0.036500 seconds (real time) Cime Exit Status: 0