- : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] f(0,y) -> y [2] f(x,0) -> x [3] f(i(x),y) -> i(x) [4] f(f(x,y),z) -> f(x,f(y,z)) [5] f(g(x,y),z) -> g(f(x,z),f(y,z)) [6] f(1,g(x,y)) -> x [7] f(2,g(x,y)) -> y Sub problem: guided: DP termination of: END GUIDED APPLY CRITERIA (Graph splitting) Found 1 components: { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { f(f(x,y),z) >= f(x,f(y,z)) ; f(0,y) >= y ; f(i(x),y) >= i(x) ; f(g(x,y),z) >= g(f(x,z),f(y,z)) ; f(1,g(x,y)) >= x ; f(2,g(x,y)) >= y ; f(x,0) >= x ; Marked_f(f(x,y),z) >= Marked_f(x,f(y,z)) ; Marked_f(f(x,y),z) >= Marked_f(y,z) ; Marked_f(g(x,y),z) >= Marked_f(x,z) ; Marked_f(g(x,y),z) >= Marked_f(y,z) ; } + Disjunctions:{ { Marked_f(f(x,y),z) > Marked_f(x,f(y,z)) ; } { Marked_f(f(x,y),z) > Marked_f(y,z) ; } { Marked_f(g(x,y),z) > Marked_f(x,z) ; } { Marked_f(g(x,y),z) > Marked_f(y,z) ; } } === 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 === STOPING TIMER real === === STOPING TIMER virtual === No solution found for these parameters. Entering rpo_solver === TIMER virtual : 25.000000 === Search parameters: AFS type: 2 ; time limit: 25.. === STOPING TIMER virtual === === STOPING TIMER virtual === constraint: f(f(x,y),z) >= f(x,f(y,z)) constraint: f(0,y) >= y constraint: f(i(x),y) >= i(x) constraint: f(g(x,y),z) >= g(f(x,z),f(y,z)) constraint: f(1,g(x,y)) >= x constraint: f(2,g(x,y)) >= y constraint: f(x,0) >= x constraint: Marked_f(f(x,y),z) >= Marked_f(x,f(y,z)) constraint: Marked_f(f(x,y),z) >= Marked_f(y,z) constraint: Marked_f(g(x,y),z) >= Marked_f(x,z) constraint: Marked_f(g(x,y),z) >= Marked_f(y,z) APPLY CRITERIA (Graph splitting) Found 0 components: SOLVED { TRS termination of: [1] f(0,y) -> y [2] f(x,0) -> x [3] f(i(x),y) -> i(x) [4] f(f(x,y),z) -> f(x,f(y,z)) [5] f(g(x,y),z) -> g(f(x,z),f(y,z)) [6] f(1,g(x,y)) -> x [7] f(2,g(x,y)) -> y , CRITERION: MDP [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: ORD [ Solution found: RPO with AFS = AFS: and precedence: prec (All symbols are Lex.): { f > g ; f < Marked_f ; g < f ; g < Marked_f ; Marked_f > f ; Marked_f > g ; } ]} ]} ]} Cime worked for 0.028137 seconds (real time) Cime Exit Status: 0