- : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] minus(0,y) -> 0 [2] minus(s(x),0) -> s(x) [3] minus(s(x),s(y)) -> minus(x,y) [4] le(0,y) -> true [5] le(s(x),0) -> false [6] le(s(x),s(y)) -> le(x,y) [7] if(true,x,y) -> x [8] if(false,x,y) -> y [9] perfectp(0) -> false [10] perfectp(s(x)) -> f(x,s(0),s(x),s(x)) [11] f(0,y,0,u) -> true [12] f(0,y,s(z),u) -> false [13] f(s(x),0,z,u) -> f(x,u,minus(z,s(x)),u) [14] f(s(x),s(y),z,u) -> if(le(x,y),f(s(x),minus(y,x),z,u),f(x,u,z,u)) Sub problem: guided: DP termination of: END GUIDED APPLY CRITERIA (Graph splitting) Found 3 components: { --> --> --> --> --> --> --> --> --> } { --> } { --> } APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { minus(0,y) >= 0 ; minus(s(x),0) >= s(x) ; minus(s(x),s(y)) >= minus(x,y) ; le(0,y) >= true ; le(s(x),0) >= false ; le(s(x),s(y)) >= le(x,y) ; if(true,x,y) >= x ; if(false,x,y) >= y ; perfectp(0) >= false ; perfectp(s(x)) >= f(x,s(0),s(x),s(x)) ; f(0,y,0,u) >= true ; f(0,y,s(z),u) >= false ; f(s(x),0,z,u) >= f(x,u,minus(z,s(x)),u) ; f(s(x),s(y),z,u) >= if(le(x,y),f(s(x),minus(y,x),z,u),f(x,u,z,u)) ; Marked_f(s(x),0,z,u) >= Marked_f(x,u,minus(z,s(x)),u) ; Marked_f(s(x),s(y),z,u) >= Marked_f(s(x),minus(y,x),z,u) ; Marked_f(s(x),s(y),z,u) >= Marked_f(x,u,z,u) ; } + Disjunctions:{ { Marked_f(s(x),0,z,u) > Marked_f(x,u,minus(z,s(x)),u) ; } { Marked_f(s(x),s(y),z,u) > Marked_f(s(x),minus(y,x),z,u) ; } { Marked_f(s(x),s(y),z,u) > Marked_f(x,u,z,u) ; } } === 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(0,y) >= 0 constraint: minus(s(x),0) >= s(x) constraint: minus(s(x),s(y)) >= minus(x,y) constraint: le(0,y) >= true constraint: le(s(x),0) >= false constraint: le(s(x),s(y)) >= le(x,y) constraint: if(true,x,y) >= x constraint: if(false,x,y) >= y constraint: perfectp(0) >= false constraint: perfectp(s(x)) >= f(x,s(0),s(x),s(x)) constraint: f(0,y,0,u) >= true constraint: f(0,y,s(z),u) >= false constraint: f(s(x),0,z,u) >= f(x,u,minus(z,s(x)),u) constraint: f(s(x),s(y),z,u) >= if(le(x,y),f(s(x),minus(y,x),z,u),f(x,u,z,u)) constraint: Marked_f(s(x),0,z,u) >= Marked_f(x,u,minus(z,s(x)),u) constraint: Marked_f(s(x),s(y),z,u) >= Marked_f(s(x),minus(y,x),z,u) constraint: Marked_f(s(x),s(y),z,u) >= Marked_f(x,u,z,u) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { minus(0,y) >= 0 ; minus(s(x),0) >= s(x) ; minus(s(x),s(y)) >= minus(x,y) ; le(0,y) >= true ; le(s(x),0) >= false ; le(s(x),s(y)) >= le(x,y) ; if(true,x,y) >= x ; if(false,x,y) >= y ; perfectp(0) >= false ; perfectp(s(x)) >= f(x,s(0),s(x),s(x)) ; f(0,y,0,u) >= true ; f(0,y,s(z),u) >= false ; f(s(x),0,z,u) >= f(x,u,minus(z,s(x)),u) ; f(s(x),s(y),z,u) >= if(le(x,y),f(s(x),minus(y,x),z,u),f(x,u,z,u)) ; Marked_le(s(x),s(y)) >= Marked_le(x,y) ; } + Disjunctions:{ { Marked_le(s(x),s(y)) > Marked_le(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(0,y) >= 0 constraint: minus(s(x),0) >= s(x) constraint: minus(s(x),s(y)) >= minus(x,y) constraint: le(0,y) >= true constraint: le(s(x),0) >= false constraint: le(s(x),s(y)) >= le(x,y) constraint: if(true,x,y) >= x constraint: if(false,x,y) >= y constraint: perfectp(0) >= false constraint: perfectp(s(x)) >= f(x,s(0),s(x),s(x)) constraint: f(0,y,0,u) >= true constraint: f(0,y,s(z),u) >= false constraint: f(s(x),0,z,u) >= f(x,u,minus(z,s(x)),u) constraint: f(s(x),s(y),z,u) >= if(le(x,y),f(s(x),minus(y,x),z,u),f(x,u,z,u)) constraint: Marked_le(s(x),s(y)) >= Marked_le(x,y) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { minus(0,y) >= 0 ; minus(s(x),0) >= s(x) ; minus(s(x),s(y)) >= minus(x,y) ; le(0,y) >= true ; le(s(x),0) >= false ; le(s(x),s(y)) >= le(x,y) ; if(true,x,y) >= x ; if(false,x,y) >= y ; perfectp(0) >= false ; perfectp(s(x)) >= f(x,s(0),s(x),s(x)) ; f(0,y,0,u) >= true ; f(0,y,s(z),u) >= false ; f(s(x),0,z,u) >= f(x,u,minus(z,s(x)),u) ; f(s(x),s(y),z,u) >= if(le(x,y),f(s(x),minus(y,x),z,u),f(x,u,z,u)) ; 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(0,y) >= 0 constraint: minus(s(x),0) >= s(x) constraint: minus(s(x),s(y)) >= minus(x,y) constraint: le(0,y) >= true constraint: le(s(x),0) >= false constraint: le(s(x),s(y)) >= le(x,y) constraint: if(true,x,y) >= x constraint: if(false,x,y) >= y constraint: perfectp(0) >= false constraint: perfectp(s(x)) >= f(x,s(0),s(x),s(x)) constraint: f(0,y,0,u) >= true constraint: f(0,y,s(z),u) >= false constraint: f(s(x),0,z,u) >= f(x,u,minus(z,s(x)),u) constraint: f(s(x),s(y),z,u) >= if(le(x,y),f(s(x),minus(y,x),z,u),f(x,u,z,u)) constraint: Marked_minus(s(x),s(y)) >= Marked_minus(x,y) APPLY CRITERIA (Graph splitting) Found 1 components: { --> } APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { minus(0,y) >= 0 ; minus(s(x),0) >= s(x) ; minus(s(x),s(y)) >= minus(x,y) ; le(0,y) >= true ; le(s(x),0) >= false ; le(s(x),s(y)) >= le(x,y) ; if(true,x,y) >= x ; if(false,x,y) >= y ; perfectp(0) >= false ; perfectp(s(x)) >= f(x,s(0),s(x),s(x)) ; f(0,y,0,u) >= true ; f(0,y,s(z),u) >= false ; f(s(x),0,z,u) >= f(x,u,minus(z,s(x)),u) ; f(s(x),s(y),z,u) >= if(le(x,y),f(s(x),minus(y,x),z,u),f(x,u,z,u)) ; Marked_f(s(x),s(y),z,u) >= Marked_f(s(x),minus(y,x),z,u) ; } + Disjunctions:{ { Marked_f(s(x),s(y),z,u) > Marked_f(s(x),minus(y,x),z,u) ; } } === 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(0,y) >= 0 constraint: minus(s(x),0) >= s(x) constraint: minus(s(x),s(y)) >= minus(x,y) constraint: le(0,y) >= true constraint: le(s(x),0) >= false constraint: le(s(x),s(y)) >= le(x,y) constraint: if(true,x,y) >= x constraint: if(false,x,y) >= y constraint: perfectp(0) >= false constraint: perfectp(s(x)) >= f(x,s(0),s(x),s(x)) constraint: f(0,y,0,u) >= true constraint: f(0,y,s(z),u) >= false constraint: f(s(x),0,z,u) >= f(x,u,minus(z,s(x)),u) constraint: f(s(x),s(y),z,u) >= if(le(x,y),f(s(x),minus(y,x),z,u),f(x,u,z,u)) constraint: Marked_f(s(x),s(y),z,u) >= Marked_f(s(x),minus(y,x),z,u) APPLY CRITERIA (Graph splitting) Found 0 components: APPLY CRITERIA (Graph splitting) Found 0 components: APPLY CRITERIA (Graph splitting) Found 0 components: SOLVED { TRS termination of: [1] minus(0,y) -> 0 [2] minus(s(x),0) -> s(x) [3] minus(s(x),s(y)) -> minus(x,y) [4] le(0,y) -> true [5] le(s(x),0) -> false [6] le(s(x),s(y)) -> le(x,y) [7] if(true,x,y) -> x [8] if(false,x,y) -> y [9] perfectp(0) -> false [10] perfectp(s(x)) -> f(x,s(0),s(x),s(x)) [11] f(0,y,0,u) -> true [12] f(0,y,s(z),u) -> false [13] f(s(x),0,z,u) -> f(x,u,minus(z,s(x)),u) [14] f(s(x),s(y),z,u) -> if(le(x,y),f(s(x),minus(y,x),z,u),f(x,u,z,u)) , CRITERION: MDP [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: CG using polynomial interpretation = [ 0 ] () = 0; [ f ] (X0,X1,X2,X3) = 0; [ le ] (X0,X1) = 3*X1; [ s ] (X0) = 2*X0 + 1; [ if ] (X0,X1,X2) = 2*X2 + 2*X1; [ minus ] (X0,X1) = 1*X0 + 1; [ Marked_f ] (X0,X1,X2,X3) = 1*X2 + 2*X0; [ false ] () = 0; [ true ] () = 0; [ perfectp ] (X0) = 0; removing [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: ORD [ Solution found: polynomial interpretation = [ 0 ] () = 0; [ f ] (X0,X1,X2,X3) = 0; [ le ] (X0,X1) = 3*X1 + 0; [ s ] (X0) = 2 + 1*X0 + 0; [ if ] (X0,X1,X2) = 2*X1 + 2*X2 + 0; [ minus ] (X0,X1) = 1*X0 + 0; [ Marked_f ] (X0,X1,X2,X3) = 2*X1 + 0; [ false ] () = 0; [ true ] () = 0; [ perfectp ] (X0) = 0; ]} ]} ]} { DP termination of: , CRITERION: ORD [ Solution found: polynomial interpretation = [ 0 ] () = 0; [ f ] (X0,X1,X2,X3) = 0; [ le ] (X0,X1) = 3*X1 + 0; [ s ] (X0) = 1 + 2*X0 + 0; [ if ] (X0,X1,X2) = 1*X1 + 1*X2 + 0; [ minus ] (X0,X1) = 1*X0 + 0; [ false ] () = 0; [ true ] () = 0; [ Marked_le ] (X0,X1) = 1*X1 + 0; [ perfectp ] (X0) = 0; ]} { DP termination of: , CRITERION: ORD [ Solution found: polynomial interpretation = [ 0 ] () = 0; [ f ] (X0,X1,X2,X3) = 0; [ le ] (X0,X1) = 3*X1 + 0; [ Marked_minus ] (X0,X1) = 1*X1 + 0; [ s ] (X0) = 1 + 2*X0 + 0; [ if ] (X0,X1,X2) = 2*X1 + 1*X2 + 0; [ minus ] (X0,X1) = 1*X0 + 0; [ false ] () = 0; [ true ] () = 0; [ perfectp ] (X0) = 0; ]} ]} ]} Cime worked for 0.297482 seconds (real time) Cime Exit Status: 0