- : unit = () - : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] le(0,y) -> true [2] le(s(x),0) -> false [3] le(s(x),s(y)) -> le(x,y) [4] minus(0,y) -> 0 [5] minus(s(x),y) -> if_minus(le(s(x),y),s(x),y) [6] if_minus(true,s(x),y) -> 0 [7] if_minus(false,s(x),y) -> s(minus(x,y)) [8] quot(0,s(y)) -> 0 [9] quot(s(x),s(y)) -> s(quot(minus(x,y),s(y))) [10] log(s(0)) -> 0 [11] log(s(s(x))) -> s(log(s(quot(x,s(s(0)))))) Sub problem: guided: DP termination of: END GUIDED APPLY CRITERIA (Graph splitting) Found 4 components: { --> } { --> } { --> --> } { --> } APPLY CRITERIA (Subterm criterion) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { le(0,y) >= true ; le(s(x),0) >= false ; le(s(x),s(y)) >= le(x,y) ; minus(0,y) >= 0 ; minus(s(x),y) >= if_minus(le(s(x),y),s(x),y) ; if_minus(true,s(x),y) >= 0 ; if_minus(false,s(x),y) >= s(minus(x,y)) ; quot(0,s(y)) >= 0 ; quot(s(x),s(y)) >= s(quot(minus(x,y),s(y))) ; log(s(0)) >= 0 ; log(s(s(x))) >= s(log(s(quot(x,s(s(0)))))) ; Marked_log(s(s(x))) >= Marked_log(s(quot(x,s(s(0))))) ; } + Disjunctions:{ { Marked_log(s(s(x))) > Marked_log(s(quot(x,s(s(0))))) ; } } === 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: le(0,y) >= true constraint: le(s(x),0) >= false constraint: le(s(x),s(y)) >= le(x,y) constraint: minus(0,y) >= 0 constraint: minus(s(x),y) >= if_minus(le(s(x),y),s(x),y) constraint: if_minus(true,s(x),y) >= 0 constraint: if_minus(false,s(x),y) >= s(minus(x,y)) constraint: quot(0,s(y)) >= 0 constraint: quot(s(x),s(y)) >= s(quot(minus(x,y),s(y))) constraint: log(s(0)) >= 0 constraint: log(s(s(x))) >= s(log(s(quot(x,s(s(0)))))) constraint: Marked_log(s(s(x))) >= Marked_log(s(quot(x,s(s(0))))) APPLY CRITERIA (Subterm criterion) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { le(0,y) >= true ; le(s(x),0) >= false ; le(s(x),s(y)) >= le(x,y) ; minus(0,y) >= 0 ; minus(s(x),y) >= if_minus(le(s(x),y),s(x),y) ; if_minus(true,s(x),y) >= 0 ; if_minus(false,s(x),y) >= s(minus(x,y)) ; quot(0,s(y)) >= 0 ; quot(s(x),s(y)) >= s(quot(minus(x,y),s(y))) ; log(s(0)) >= 0 ; log(s(s(x))) >= s(log(s(quot(x,s(s(0)))))) ; Marked_quot(s(x),s(y)) >= Marked_quot(minus(x,y),s(y)) ; } + Disjunctions:{ { Marked_quot(s(x),s(y)) > Marked_quot(minus(x,y),s(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: le(0,y) >= true constraint: le(s(x),0) >= false constraint: le(s(x),s(y)) >= le(x,y) constraint: minus(0,y) >= 0 constraint: minus(s(x),y) >= if_minus(le(s(x),y),s(x),y) constraint: if_minus(true,s(x),y) >= 0 constraint: if_minus(false,s(x),y) >= s(minus(x,y)) constraint: quot(0,s(y)) >= 0 constraint: quot(s(x),s(y)) >= s(quot(minus(x,y),s(y))) constraint: log(s(0)) >= 0 constraint: log(s(s(x))) >= s(log(s(quot(x,s(s(0)))))) constraint: Marked_quot(s(x),s(y)) >= Marked_quot(minus(x,y),s(y)) APPLY CRITERIA (Subterm criterion) ST: Marked_if_minus -> 2 Marked_minus -> 1 APPLY CRITERIA (Subterm criterion) ST: Marked_le -> 1 APPLY CRITERIA (Graph splitting) Found 0 components: 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] le(0,y) -> true [2] le(s(x),0) -> false [3] le(s(x),s(y)) -> le(x,y) [4] minus(0,y) -> 0 [5] minus(s(x),y) -> if_minus(le(s(x),y),s(x),y) [6] if_minus(true,s(x),y) -> 0 [7] if_minus(false,s(x),y) -> s(minus(x,y)) [8] quot(0,s(y)) -> 0 [9] quot(s(x),s(y)) -> s(quot(minus(x,y),s(y))) [10] log(s(0)) -> 0 [11] log(s(s(x))) -> s(log(s(quot(x,s(s(0)))))) , CRITERION: MDP [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: ORD [ Solution found: polynomial interpretation = [ true ] () = 0; [ log ] (X0) = 2*X0 + 0; [ s ] (X0) = 2 + 2*X0 + 0; [ 0 ] () = 0; [ if_minus ] (X0,X1,X2) = 1*X1 + 0; [ le ] (X0,X1) = 0; [ Marked_log ] (X0) = 1*X0 + 0; [ minus ] (X0,X1) = 1*X0 + 0; [ false ] () = 0; [ quot ] (X0,X1) = 1*X0 + 0; ]} { DP termination of: , CRITERION: ORD [ Solution found: polynomial interpretation = [ true ] () = 0; [ log ] (X0) = 1*X0 + 0; [ s ] (X0) = 2 + 1*X0 + 0; [ 0 ] () = 0; [ Marked_quot ] (X0,X1) = 3*X0 + 0; [ if_minus ] (X0,X1,X2) = 1*X1 + 0; [ le ] (X0,X1) = 0; [ minus ] (X0,X1) = 1*X0 + 0; [ false ] () = 0; [ quot ] (X0,X1) = 1*X0 + 0; ]} { DP termination of: , CRITERION: ST [ { DP termination of: , CRITERION: SG [ ]} ]} { DP termination of: , CRITERION: ST [ { DP termination of: , CRITERION: SG [ ]} ]} ]} ]} Cime worked for 0.239271 seconds (real time) Cime Exit Status: 0