- : unit = () - : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] min(X,0) -> X [2] min(s(X),s(Y)) -> min(X,Y) [3] quot(0,s(Y)) -> 0 [4] quot(s(X),s(Y)) -> s(quot(min(X,Y),s(Y))) [5] log(s(0)) -> 0 [6] 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 3 components: { --> } { --> } { --> } APPLY CRITERIA (Subterm criterion) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { min(s(X),s(Y)) >= min(X,Y) ; min(X,0) >= X ; quot(0,s(Y)) >= 0 ; quot(s(X),s(Y)) >= s(quot(min(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: min(s(X),s(Y)) >= min(X,Y) constraint: min(X,0) >= X constraint: quot(0,s(Y)) >= 0 constraint: quot(s(X),s(Y)) >= s(quot(min(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: { min(s(X),s(Y)) >= min(X,Y) ; min(X,0) >= X ; quot(0,s(Y)) >= 0 ; quot(s(X),s(Y)) >= s(quot(min(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(min(X,Y),s(Y)) ; } + Disjunctions:{ { Marked_quot(s(X),s(Y)) > Marked_quot(min(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: min(s(X),s(Y)) >= min(X,Y) constraint: min(X,0) >= X constraint: quot(0,s(Y)) >= 0 constraint: quot(s(X),s(Y)) >= s(quot(min(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(min(X,Y),s(Y)) APPLY CRITERIA (Subterm criterion) ST: Marked_min -> 1 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] min(X,0) -> X [2] min(s(X),s(Y)) -> min(X,Y) [3] quot(0,s(Y)) -> 0 [4] quot(s(X),s(Y)) -> s(quot(min(X,Y),s(Y))) [5] log(s(0)) -> 0 [6] 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 = [ min ] (X0,X1) = 1*X0 + 0; [ log ] (X0) = 1*X0 + 0; [ s ] (X0) = 1 + 1*X0 + 0; [ 0 ] () = 0; [ Marked_log ] (X0) = 1*X0 + 0; [ quot ] (X0,X1) = 1*X0 + 0; ]} { DP termination of: , CRITERION: ORD [ Solution found: polynomial interpretation = [ min ] (X0,X1) = 1*X0 + 0; [ log ] (X0) = 2*X0 + 0; [ s ] (X0) = 2 + 2*X0 + 0; [ Marked_quot ] (X0,X1) = 3*X0 + 0; [ 0 ] () = 0; [ quot ] (X0,X1) = 1*X0 + 0; ]} { DP termination of: , CRITERION: ST [ { DP termination of: , CRITERION: SG [ ]} ]} ]} ]} Cime worked for 0.209827 seconds (real time) Cime Exit Status: 0