- : unit = () - : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] +(+(x,y),z) -> +(x,+(y,z)) [2] +(f(x),f(y)) -> f(+(x,y)) [3] +(f(x),+(f(y),z)) -> +(f(+(x,y)),z) Sub problem: guided: DP termination of: END GUIDED APPLY CRITERIA (Graph splitting) Found 1 components: { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } APPLY CRITERIA (Subterm criterion) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { +(+(x,y),z) >= +(x,+(y,z)) ; +(f(x),+(f(y),z)) >= +(f(+(x,y)),z) ; +(f(x),f(y)) >= f(+(x,y)) ; Marked_+(+(x,y),z) >= Marked_+(x,+(y,z)) ; Marked_+(+(x,y),z) >= Marked_+(y,z) ; Marked_+(f(x),+(f(y),z)) >= Marked_+(f(+(x,y)),z) ; Marked_+(f(x),+(f(y),z)) >= Marked_+(x,y) ; Marked_+(f(x),f(y)) >= Marked_+(x,y) ; } + Disjunctions:{ { Marked_+(+(x,y),z) > Marked_+(x,+(y,z)) ; } { Marked_+(+(x,y),z) > Marked_+(y,z) ; } { Marked_+(f(x),+(f(y),z)) > Marked_+(f(+(x,y)),z) ; } { Marked_+(f(x),+(f(y),z)) > Marked_+(x,y) ; } { Marked_+(f(x),f(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: +(+(x,y),z) >= +(x,+(y,z)) constraint: +(f(x),+(f(y),z)) >= +(f(+(x,y)),z) constraint: +(f(x),f(y)) >= f(+(x,y)) constraint: Marked_+(+(x,y),z) >= Marked_+(x,+(y,z)) constraint: Marked_+(+(x,y),z) >= Marked_+(y,z) constraint: Marked_+(f(x),+(f(y),z)) >= Marked_+(f(+(x,y)),z) constraint: Marked_+(f(x),+(f(y),z)) >= Marked_+(x,y) constraint: Marked_+(f(x),f(y)) >= Marked_+(x,y) APPLY CRITERIA (Graph splitting) Found 1 components: { --> --> --> --> } APPLY CRITERIA (Subterm criterion) ST: Marked_+ -> 1 APPLY CRITERIA (Graph splitting) Found 0 components: SOLVED { TRS termination of: [1] +(+(x,y),z) -> +(x,+(y,z)) [2] +(f(x),f(y)) -> f(+(x,y)) [3] +(f(x),+(f(y),z)) -> +(f(+(x,y)),z) , CRITERION: MDP [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: CG using polynomial interpretation = [ + ] (X0,X1) = 1*X1 + 1*X0; [ Marked_+ ] (X0,X1) = 1*X1 + 1*X0; [ f ] (X0) = 1*X0 + 2; removing [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: ST [ { DP termination of: , CRITERION: SG [ ]} ]} ]} ]} ]} ]} Cime worked for 0.048047 seconds (real time) Cime Exit Status: 0