- : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] double(0) -> 0 [2] double(s(x)) -> s(s(double(x))) [3] half(0) -> 0 [4] half(s(0)) -> 0 [5] half(s(s(x))) -> s(half(x)) [6] -(x,0) -> x [7] -(s(x),s(y)) -> -(x,y) [8] if(0,y,z) -> y [9] if(s(x),y,z) -> z [10] half(double(x)) -> x 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: { double(0) >= 0 ; double(s(x)) >= s(s(double(x))) ; half(0) >= 0 ; half(double(x)) >= x ; half(s(0)) >= 0 ; half(s(s(x))) >= s(half(x)) ; -(s(x),s(y)) >= -(x,y) ; -(x,0) >= x ; if(0,y,z) >= y ; if(s(x),y,z) >= z ; Marked_double(s(x)) >= Marked_double(x) ; } + Disjunctions:{ { Marked_double(s(x)) > Marked_double(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: double(0) >= 0 constraint: double(s(x)) >= s(s(double(x))) constraint: half(0) >= 0 constraint: half(double(x)) >= x constraint: half(s(0)) >= 0 constraint: half(s(s(x))) >= s(half(x)) constraint: -(s(x),s(y)) >= -(x,y) constraint: -(x,0) >= x constraint: if(0,y,z) >= y constraint: if(s(x),y,z) >= z constraint: Marked_double(s(x)) >= Marked_double(x) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { double(0) >= 0 ; double(s(x)) >= s(s(double(x))) ; half(0) >= 0 ; half(double(x)) >= x ; half(s(0)) >= 0 ; half(s(s(x))) >= s(half(x)) ; -(s(x),s(y)) >= -(x,y) ; -(x,0) >= x ; if(0,y,z) >= y ; if(s(x),y,z) >= z ; Marked_half(s(s(x))) >= Marked_half(x) ; } + Disjunctions:{ { Marked_half(s(s(x))) > Marked_half(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: double(0) >= 0 constraint: double(s(x)) >= s(s(double(x))) constraint: half(0) >= 0 constraint: half(double(x)) >= x constraint: half(s(0)) >= 0 constraint: half(s(s(x))) >= s(half(x)) constraint: -(s(x),s(y)) >= -(x,y) constraint: -(x,0) >= x constraint: if(0,y,z) >= y constraint: if(s(x),y,z) >= z constraint: Marked_half(s(s(x))) >= Marked_half(x) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { double(0) >= 0 ; double(s(x)) >= s(s(double(x))) ; half(0) >= 0 ; half(double(x)) >= x ; half(s(0)) >= 0 ; half(s(s(x))) >= s(half(x)) ; -(s(x),s(y)) >= -(x,y) ; -(x,0) >= x ; if(0,y,z) >= y ; if(s(x),y,z) >= z ; 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: double(0) >= 0 constraint: double(s(x)) >= s(s(double(x))) constraint: half(0) >= 0 constraint: half(double(x)) >= x constraint: half(s(0)) >= 0 constraint: half(s(s(x))) >= s(half(x)) constraint: -(s(x),s(y)) >= -(x,y) constraint: -(x,0) >= x constraint: if(0,y,z) >= y constraint: if(s(x),y,z) >= z constraint: Marked_-(s(x),s(y)) >= Marked_-(x,y) 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] double(0) -> 0 [2] double(s(x)) -> s(s(double(x))) [3] half(0) -> 0 [4] half(s(0)) -> 0 [5] half(s(s(x))) -> s(half(x)) [6] -(x,0) -> x [7] -(s(x),s(y)) -> -(x,y) [8] if(0,y,z) -> y [9] if(s(x),y,z) -> z [10] half(double(x)) -> x , CRITERION: MDP [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: ORD [ Solution found: polynomial interpretation = [ 0 ] () = 0; [ - ] (X0,X1) = 3 + 3*X0 + 3*X1 + 0; [ s ] (X0) = 1 + 1*X0 + 0; [ double ] (X0) = 1 + 2*X0 + 0; [ Marked_double ] (X0) = 3*X0 + 0; [ if ] (X0,X1,X2) = 2 + 3*X0 + 2*X1 + 2*X2 + 0; [ half ] (X0) = 1*X0 + 0; ]} { DP termination of: , CRITERION: ORD [ Solution found: polynomial interpretation = [ 0 ] () = 0; [ - ] (X0,X1) = 2 + 3*X0 + 3*X1 + 0; [ s ] (X0) = 1 + 1*X0 + 0; [ Marked_half ] (X0) = 1*X0 + 0; [ double ] (X0) = 1 + 2*X0 + 0; [ if ] (X0,X1,X2) = 3 + 2*X0 + 3*X1 + 2*X2 + 0; [ half ] (X0) = 1*X0 + 0; ]} { DP termination of: , CRITERION: ORD [ Solution found: polynomial interpretation = [ 0 ] () = 0; [ Marked_- ] (X0,X1) = 1*X0 + 0; [ - ] (X0,X1) = 3 + 3*X0 + 3*X1 + 0; [ s ] (X0) = 1 + 1*X0 + 0; [ double ] (X0) = 1 + 3*X0 + 0; [ if ] (X0,X1,X2) = 2 + 3*X0 + 3*X1 + 3*X2 + 0; [ half ] (X0) = 2 + 1*X0 + 0; ]} ]} ]} Cime worked for 0.088070 seconds (real time) Cime Exit Status: 0