- : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] .(1,x) -> x [2] .(x,1) -> x [3] .(i(x),x) -> 1 [4] .(x,i(x)) -> 1 [5] i(1) -> 1 [6] i(i(x)) -> x [7] .(i(y),.(y,z)) -> z [8] .(y,.(i(y),z)) -> z [9] .(.(x,y),z) -> .(x,.(y,z)) [10] i(.(x,y)) -> .(i(y),i(x)) Sub problem: guided: DP termination of: END GUIDED APPLY CRITERIA (Graph splitting) Found 2 components: { --> --> --> --> } { --> --> --> --> } APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { .(.(x,y),z) >= .(x,.(y,z)) ; .(1,x) >= x ; .(i(x),x) >= 1 ; .(i(y),.(y,z)) >= z ; .(x,1) >= x ; .(x,i(x)) >= 1 ; .(y,.(i(y),z)) >= z ; i(.(x,y)) >= .(i(y),i(x)) ; i(1) >= 1 ; i(i(x)) >= x ; Marked_i(.(x,y)) >= Marked_i(x) ; Marked_i(.(x,y)) >= Marked_i(y) ; } + Disjunctions:{ { Marked_i(.(x,y)) > Marked_i(x) ; } { Marked_i(.(x,y)) > Marked_i(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: .(1,x) >= x constraint: .(i(x),x) >= 1 constraint: .(i(y),.(y,z)) >= z constraint: .(x,1) >= x constraint: .(x,i(x)) >= 1 constraint: .(y,.(i(y),z)) >= z constraint: i(.(x,y)) >= .(i(y),i(x)) constraint: i(1) >= 1 constraint: i(i(x)) >= x constraint: Marked_i(.(x,y)) >= Marked_i(x) constraint: Marked_i(.(x,y)) >= Marked_i(y) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { .(.(x,y),z) >= .(x,.(y,z)) ; .(1,x) >= x ; .(i(x),x) >= 1 ; .(i(y),.(y,z)) >= z ; .(x,1) >= x ; .(x,i(x)) >= 1 ; .(y,.(i(y),z)) >= z ; i(.(x,y)) >= .(i(y),i(x)) ; i(1) >= 1 ; i(i(x)) >= x ; Marked_.(.(x,y),z) >= Marked_.(x,.(y,z)) ; Marked_.(.(x,y),z) >= Marked_.(y,z) ; } + Disjunctions:{ { Marked_.(.(x,y),z) > Marked_.(x,.(y,z)) ; } { Marked_.(.(x,y),z) > Marked_.(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 Sat solver result read === STOPING TIMER real === === STOPING TIMER virtual === constraint: .(.(x,y),z) >= .(x,.(y,z)) constraint: .(1,x) >= x constraint: .(i(x),x) >= 1 constraint: .(i(y),.(y,z)) >= z constraint: .(x,1) >= x constraint: .(x,i(x)) >= 1 constraint: .(y,.(i(y),z)) >= z constraint: i(.(x,y)) >= .(i(y),i(x)) constraint: i(1) >= 1 constraint: i(i(x)) >= x constraint: Marked_.(.(x,y),z) >= Marked_.(x,.(y,z)) constraint: Marked_.(.(x,y),z) >= Marked_.(y,z) APPLY CRITERIA (Graph splitting) Found 0 components: APPLY CRITERIA (Graph splitting) Found 0 components: SOLVED { TRS termination of: [1] .(1,x) -> x [2] .(x,1) -> x [3] .(i(x),x) -> 1 [4] .(x,i(x)) -> 1 [5] i(1) -> 1 [6] i(i(x)) -> x [7] .(i(y),.(y,z)) -> z [8] .(y,.(i(y),z)) -> z [9] .(.(x,y),z) -> .(x,.(y,z)) [10] i(.(x,y)) -> .(i(y),i(x)) , CRITERION: MDP [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: ORD [ Solution found: polynomial interpretation = [ . ] (X0,X1) = 2 + 1*X0 + 1*X1 + 0; [ i ] (X0) = 2*X0 + 0; [ 1 ] () = 0; [ Marked_i ] (X0) = 3*X0 + 0; ]} { DP termination of: , CRITERION: ORD [ Solution found: polynomial interpretation = [ . ] (X0,X1) = 2 + 1*X0 + 1*X1 + 0; [ Marked_. ] (X0,X1) = 3*X0 + 0; [ i ] (X0) = 2*X0 + 0; [ 1 ] () = 0; ]} ]} ]} Cime worked for 0.052814 seconds (real time) Cime Exit Status: 0