- : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] f(0) -> true [2] f(1) -> false [3] f(s(x)) -> f(x) [4] if(true,s(x),s(y)) -> s(x) [5] if(false,s(x),s(y)) -> s(y) [6] g(x,c(y)) -> c(g(x,y)) [7] g(x,c(y)) -> g(x,if(f(x),c(g(s(x),y)),c(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: { f(0) >= true ; f(1) >= false ; f(s(x)) >= f(x) ; if(true,s(x),s(y)) >= s(x) ; if(false,s(x),s(y)) >= s(y) ; g(x,c(y)) >= c(g(x,y)) ; g(x,c(y)) >= g(x,if(f(x),c(g(s(x),y)),c(y))) ; Marked_g(x,c(y)) >= Marked_g(s(x),y) ; Marked_g(x,c(y)) >= Marked_g(x,if(f(x),c(g(s(x),y)),c(y))) ; Marked_g(x,c(y)) >= Marked_g(x,y) ; } + Disjunctions:{ { Marked_g(x,c(y)) > Marked_g(s(x),y) ; } { Marked_g(x,c(y)) > Marked_g(x,if(f(x),c(g(s(x),y)),c(y))) ; } { Marked_g(x,c(y)) > Marked_g(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: f(0) >= true constraint: f(1) >= false constraint: f(s(x)) >= f(x) constraint: if(true,s(x),s(y)) >= s(x) constraint: if(false,s(x),s(y)) >= s(y) constraint: g(x,c(y)) >= c(g(x,y)) constraint: g(x,c(y)) >= g(x,if(f(x),c(g(s(x),y)),c(y))) constraint: Marked_g(x,c(y)) >= Marked_g(s(x),y) constraint: Marked_g(x,c(y)) >= Marked_g(x,if(f(x),c(g(s(x),y)),c(y))) constraint: Marked_g(x,c(y)) >= Marked_g(x,y) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { f(0) >= true ; f(1) >= false ; f(s(x)) >= f(x) ; if(true,s(x),s(y)) >= s(x) ; if(false,s(x),s(y)) >= s(y) ; g(x,c(y)) >= c(g(x,y)) ; g(x,c(y)) >= g(x,if(f(x),c(g(s(x),y)),c(y))) ; Marked_f(s(x)) >= Marked_f(x) ; } + Disjunctions:{ { 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: f(0) >= true constraint: f(1) >= false constraint: f(s(x)) >= f(x) constraint: if(true,s(x),s(y)) >= s(x) constraint: if(false,s(x),s(y)) >= s(y) constraint: g(x,c(y)) >= c(g(x,y)) constraint: g(x,c(y)) >= g(x,if(f(x),c(g(s(x),y)),c(y))) constraint: Marked_f(s(x)) >= Marked_f(x) APPLY CRITERIA (Graph splitting) Found 1 components: { --> } APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { f(0) >= true ; f(1) >= false ; f(s(x)) >= f(x) ; if(true,s(x),s(y)) >= s(x) ; if(false,s(x),s(y)) >= s(y) ; g(x,c(y)) >= c(g(x,y)) ; g(x,c(y)) >= g(x,if(f(x),c(g(s(x),y)),c(y))) ; Marked_g(x,c(y)) >= Marked_g(x,if(f(x),c(g(s(x),y)),c(y))) ; } + Disjunctions:{ { Marked_g(x,c(y)) > Marked_g(x,if(f(x),c(g(s(x),y)),c(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: f(0) >= true constraint: f(1) >= false constraint: f(s(x)) >= f(x) constraint: if(true,s(x),s(y)) >= s(x) constraint: if(false,s(x),s(y)) >= s(y) constraint: g(x,c(y)) >= c(g(x,y)) constraint: g(x,c(y)) >= g(x,if(f(x),c(g(s(x),y)),c(y))) constraint: Marked_g(x,c(y)) >= Marked_g(x,if(f(x),c(g(s(x),y)),c(y))) APPLY CRITERIA (Graph splitting) Found 0 components: APPLY CRITERIA (Graph splitting) Found 0 components: SOLVED { TRS termination of: [1] f(0) -> true [2] f(1) -> false [3] f(s(x)) -> f(x) [4] if(true,s(x),s(y)) -> s(x) [5] if(false,s(x),s(y)) -> s(y) [6] g(x,c(y)) -> c(g(x,y)) [7] g(x,c(y)) -> g(x,if(f(x),c(g(s(x),y)),c(y))) , CRITERION: MDP [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: CG using polynomial interpretation = [ true ] () = 0; [ g ] (X0,X1) = 1*X1; [ 1 ] () = 0; [ 0 ] () = 0; [ if ] (X0,X1,X2) = 2; [ f ] (X0) = 0; [ Marked_g ] (X0,X1) = 2*X1 + 1*X0; [ s ] (X0) = 2; [ false ] () = 0; [ c ] (X0) = 2*X0 + 2; removing [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: ORD [ Solution found: polynomial interpretation = [ true ] () = 0; [ g ] (X0,X1) = 2 + 0; [ 1 ] () = 0; [ 0 ] () = 0; [ if ] (X0,X1,X2) = 1 + 0; [ f ] (X0) = 0; [ Marked_g ] (X0,X1) = 1*X1 + 0; [ s ] (X0) = 0; [ false ] () = 0; [ c ] (X0) = 2 + 0; ]} ]} ]} { DP termination of: , CRITERION: ORD [ Solution found: polynomial interpretation = [ true ] () = 0; [ g ] (X0,X1) = 2 + 0; [ 1 ] () = 0; [ 0 ] () = 0; [ if ] (X0,X1,X2) = 1*X1 + 1*X2 + 0; [ f ] (X0) = 0; [ s ] (X0) = 1 + 1*X0 + 0; [ false ] () = 0; [ Marked_f ] (X0) = 3*X0 + 0; [ c ] (X0) = 0; ]} ]} ]} Cime worked for 0.245766 seconds (real time) Cime Exit Status: 0