- : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] -(x,0) -> x [2] -(s(x),s(y)) -> -(x,y) [3] <=(0,y) -> true [4] <=(s(x),0) -> false [5] <=(s(x),s(y)) -> <=(x,y) [6] if(true,x,y) -> x [7] if(false,x,y) -> y [8] perfectp(0) -> false [9] perfectp(s(x)) -> f(x,s(0),s(x),s(x)) [10] f(0,y,0,u) -> true [11] f(0,y,s(z),u) -> false [12] f(s(x),0,z,u) -> f(x,u,-(z,s(x)),u) [13] f(s(x),s(y),z,u) -> if(<=(x,y),f(s(x),-(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: { -(s(x),s(y)) >= -(x,y) ; -(x,0) >= x ; <=(0,y) >= true ; <=(s(x),0) >= false ; <=(s(x),s(y)) >= <=(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,-(z,s(x)),u) ; f(s(x),s(y),z,u) >= if(<=(x,y),f(s(x),-(y,x),z,u),f(x,u,z,u)) ; Marked_f(s(x),0,z,u) >= Marked_f(x,u,-(z,s(x)),u) ; Marked_f(s(x),s(y),z,u) >= Marked_f(s(x),-(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,-(z,s(x)),u) ; } { Marked_f(s(x),s(y),z,u) > Marked_f(s(x),-(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: -(s(x),s(y)) >= -(x,y) constraint: -(x,0) >= x constraint: <=(0,y) >= true constraint: <=(s(x),0) >= false constraint: <=(s(x),s(y)) >= <=(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,-(z,s(x)),u) constraint: f(s(x),s(y),z,u) >= if(<=(x,y),f(s(x),-(y,x),z,u),f(x,u,z,u)) constraint: Marked_f(s(x),0,z,u) >= Marked_f(x,u,-(z,s(x)),u) constraint: Marked_f(s(x),s(y),z,u) >= Marked_f(s(x),-(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: { -(s(x),s(y)) >= -(x,y) ; -(x,0) >= x ; <=(0,y) >= true ; <=(s(x),0) >= false ; <=(s(x),s(y)) >= <=(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,-(z,s(x)),u) ; f(s(x),s(y),z,u) >= if(<=(x,y),f(s(x),-(y,x),z,u),f(x,u,z,u)) ; Marked_<=(s(x),s(y)) >= Marked_<=(x,y) ; } + Disjunctions:{ { Marked_<=(s(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: -(s(x),s(y)) >= -(x,y) constraint: -(x,0) >= x constraint: <=(0,y) >= true constraint: <=(s(x),0) >= false constraint: <=(s(x),s(y)) >= <=(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,-(z,s(x)),u) constraint: f(s(x),s(y),z,u) >= if(<=(x,y),f(s(x),-(y,x),z,u),f(x,u,z,u)) constraint: Marked_<=(s(x),s(y)) >= Marked_<=(x,y) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { -(s(x),s(y)) >= -(x,y) ; -(x,0) >= x ; <=(0,y) >= true ; <=(s(x),0) >= false ; <=(s(x),s(y)) >= <=(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,-(z,s(x)),u) ; f(s(x),s(y),z,u) >= if(<=(x,y),f(s(x),-(y,x),z,u),f(x,u,z,u)) ; Marked_-(s(x),s(y)) >= Marked_-(x,y) ; } + Disjunctions:{ { Marked_-(s(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: -(s(x),s(y)) >= -(x,y) constraint: -(x,0) >= x constraint: <=(0,y) >= true constraint: <=(s(x),0) >= false constraint: <=(s(x),s(y)) >= <=(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,-(z,s(x)),u) constraint: f(s(x),s(y),z,u) >= if(<=(x,y),f(s(x),-(y,x),z,u),f(x,u,z,u)) constraint: Marked_-(s(x),s(y)) >= Marked_-(x,y) APPLY CRITERIA (Graph splitting) Found 1 components: { --> } APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { -(s(x),s(y)) >= -(x,y) ; -(x,0) >= x ; <=(0,y) >= true ; <=(s(x),0) >= false ; <=(s(x),s(y)) >= <=(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,-(z,s(x)),u) ; f(s(x),s(y),z,u) >= if(<=(x,y),f(s(x),-(y,x),z,u),f(x,u,z,u)) ; Marked_f(s(x),s(y),z,u) >= Marked_f(s(x),-(y,x),z,u) ; } + Disjunctions:{ { Marked_f(s(x),s(y),z,u) > Marked_f(s(x),-(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: -(s(x),s(y)) >= -(x,y) constraint: -(x,0) >= x constraint: <=(0,y) >= true constraint: <=(s(x),0) >= false constraint: <=(s(x),s(y)) >= <=(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,-(z,s(x)),u) constraint: f(s(x),s(y),z,u) >= if(<=(x,y),f(s(x),-(y,x),z,u),f(x,u,z,u)) constraint: Marked_f(s(x),s(y),z,u) >= Marked_f(s(x),-(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] -(x,0) -> x [2] -(s(x),s(y)) -> -(x,y) [3] <=(0,y) -> true [4] <=(s(x),0) -> false [5] <=(s(x),s(y)) -> <=(x,y) [6] if(true,x,y) -> x [7] if(false,x,y) -> y [8] perfectp(0) -> false [9] perfectp(s(x)) -> f(x,s(0),s(x),s(x)) [10] f(0,y,0,u) -> true [11] f(0,y,s(z),u) -> false [12] f(s(x),0,z,u) -> f(x,u,-(z,s(x)),u) [13] f(s(x),s(y),z,u) -> if(<=(x,y),f(s(x),-(y,x),z,u),f(x,u,z,u)) , CRITERION: MDP [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: CG using polynomial interpretation = [ - ] (X0,X1) = 3*X0; [ f ] (X0,X1,X2,X3) = 0; [ <= ] (X0,X1) = 1*X1; [ s ] (X0) = 2*X0 + 2; [ if ] (X0,X1,X2) = 1*X2 + 1*X1; [ 0 ] () = 3; [ Marked_f ] (X0,X1,X2,X3) = 3*X0; [ false ] () = 0; [ true ] () = 0; [ perfectp ] (X0) = 0; removing [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: ORD [ Solution found: polynomial interpretation = [ - ] (X0,X1) = 1*X0 + 0; [ f ] (X0,X1,X2,X3) = 0; [ <= ] (X0,X1) = 1*X1 + 0; [ s ] (X0) = 2 + 2*X0 + 0; [ if ] (X0,X1,X2) = 2*X1 + 2*X2 + 0; [ 0 ] () = 3 + 0; [ Marked_f ] (X0,X1,X2,X3) = 3*X1 + 0; [ false ] () = 0; [ true ] () = 0; [ perfectp ] (X0) = 2*X0 + 0; ]} ]} ]} { DP termination of: , CRITERION: ORD [ Solution found: polynomial interpretation = [ - ] (X0,X1) = 3*X0 + 0; [ f ] (X0,X1,X2,X3) = 0; [ <= ] (X0,X1) = 3*X1 + 0; [ s ] (X0) = 1 + 2*X0 + 0; [ if ] (X0,X1,X2) = 2*X1 + 2*X2 + 0; [ 0 ] () = 1 + 0; [ false ] () = 0; [ true ] () = 0; [ Marked_<= ] (X0,X1) = 1*X1 + 0; [ perfectp ] (X0) = 2 + 2*X0 + 0; ]} { DP termination of: , CRITERION: ORD [ Solution found: polynomial interpretation = [ - ] (X0,X1) = 2*X0 + 0; [ f ] (X0,X1,X2,X3) = 0; [ <= ] (X0,X1) = 1*X1 + 0; [ Marked_- ] (X0,X1) = 1*X0 + 0; [ s ] (X0) = 1 + 3*X0 + 0; [ if ] (X0,X1,X2) = 2*X1 + 2*X2 + 0; [ 0 ] () = 3 + 0; [ false ] () = 0; [ true ] () = 0; [ perfectp ] (X0) = 2 + 2*X0 + 0; ]} ]} ]} Cime worked for 0.380655 seconds (real time) Cime Exit Status: 0