- : unit = () - : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] *(x,1) -> x [2] *(1,y) -> y [3] *(i(x),x) -> 1 [4] *(x,i(x)) -> 1 [5] *(x, *(y,z)) -> *( *(x,y),z) [6] i(1) -> 1 [7] *( *(x,y),i(y)) -> x [8] *( *(x,i(y)),y) -> x [9] i(i(x)) -> x [10] i( *(x,y)) -> *(i(y),i(x)) [11] k(x,1) -> 1 [12] k(x,x) -> 1 [13] *(k(x,y),k(y,x)) -> 1 [14] *( *(i(x),k(y,z)),x) -> k( *( *(i(x),y),x), *( *(i(x),z),x)) [15] k( *(x,i(y)), *(y,i(x))) -> 1 Sub problem: guided: DP termination of: END GUIDED APPLY CRITERIA (Graph splitting) Found 2 components: { --> --> --> --> } { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } APPLY CRITERIA (Subterm criterion) ST: Marked_i -> 1 APPLY CRITERIA (Subterm criterion) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { *( *(i(x),k(y,z)),x) >= k( *( *(i(x),y),x), *( *(i(x),z),x)) ; *( *(x,i(y)),y) >= x ; *( *(x,y),i(y)) >= x ; *(1,y) >= y ; *(i(x),x) >= 1 ; *(k(x,y),k(y,x)) >= 1 ; *(x, *(y,z)) >= *( *(x,y),z) ; *(x,1) >= x ; *(x,i(x)) >= 1 ; i( *(x,y)) >= *(i(y),i(x)) ; i(1) >= 1 ; i(i(x)) >= x ; k( *(x,i(y)), *(y,i(x))) >= 1 ; k(x,1) >= 1 ; k(x,x) >= 1 ; Marked_*( *(i(x),k(y,z)),x) >= Marked_*( *(i(x),y),x) ; Marked_*( *(i(x),k(y,z)),x) >= Marked_*( *(i(x),z),x) ; Marked_*( *(i(x),k(y,z)),x) >= Marked_*(i(x),y) ; Marked_*( *(i(x),k(y,z)),x) >= Marked_*(i(x),z) ; Marked_*(x, *(y,z)) >= Marked_*( *(x,y),z) ; Marked_*(x, *(y,z)) >= Marked_*(x,y) ; } + Disjunctions:{ { Marked_*( *(i(x),k(y,z)),x) > Marked_*( *(i(x),y),x) ; } { Marked_*( *(i(x),k(y,z)),x) > Marked_*( *(i(x),z),x) ; } { Marked_*( *(i(x),k(y,z)),x) > Marked_*(i(x),y) ; } { Marked_*( *(i(x),k(y,z)),x) > Marked_*(i(x),z) ; } { Marked_*(x, *(y,z)) > Marked_*( *(x,y),z) ; } { Marked_*(x, *(y,z)) > 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 === 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 === === TIMER virtual : 25.000000 === Search parameters: AFS type: 2 ; time limit: 25.. === STOPING TIMER virtual === === TIMER virtual : 25.000000 === Search parameters: AFS type: 2 ; time limit: 25.. === STOPING TIMER virtual === === TIMER virtual : 25.000000 === Search parameters: AFS type: 2 ; time limit: 25.. === STOPING TIMER virtual === === TIMER virtual : 25.000000 === Search parameters: AFS type: 2 ; time limit: 25.. === STOPING TIMER virtual === === TIMER virtual : 25.000000 === Search parameters: AFS type: 2 ; time limit: 25.. === STOPING TIMER virtual === === TIMER virtual : 15.000000 === Entering poly_solver Starting Sat solver initialization Calling Sat solver... === STOPING TIMER virtual === === TIMER real : 15.000000 === === STOPING TIMER real === Sat solver returned Sat solver result read === STOPING TIMER real === === STOPING TIMER virtual === constraint: *( *(i(x),k(y,z)),x) >= k( *( *(i(x),y),x), *( *(i(x),z),x)) constraint: *( *(x,i(y)),y) >= x constraint: *( *(x,y),i(y)) >= x constraint: *(1,y) >= y constraint: *(i(x),x) >= 1 constraint: *(k(x,y),k(y,x)) >= 1 constraint: *(x, *(y,z)) >= *( *(x,y),z) constraint: *(x,1) >= x constraint: *(x,i(x)) >= 1 constraint: i( *(x,y)) >= *(i(y),i(x)) constraint: i(1) >= 1 constraint: i(i(x)) >= x constraint: k( *(x,i(y)), *(y,i(x))) >= 1 constraint: k(x,1) >= 1 constraint: k(x,x) >= 1 constraint: Marked_*( *(i(x),k(y,z)),x) >= Marked_*( *(i(x),y),x) constraint: Marked_*( *(i(x),k(y,z)),x) >= Marked_*( *(i(x),z),x) constraint: Marked_*( *(i(x),k(y,z)),x) >= Marked_*(i(x),y) constraint: Marked_*( *(i(x),k(y,z)),x) >= Marked_*(i(x),z) constraint: Marked_*(x, *(y,z)) >= Marked_*( *(x,y),z) constraint: Marked_*(x, *(y,z)) >= Marked_*(x,y) APPLY CRITERIA (Graph splitting) Found 0 components: APPLY CRITERIA (Graph splitting) Found 0 components: SOLVED { TRS termination of: [1] *(x,1) -> x [2] *(1,y) -> y [3] *(i(x),x) -> 1 [4] *(x,i(x)) -> 1 [5] *(x, *(y,z)) -> *( *(x,y),z) [6] i(1) -> 1 [7] *( *(x,y),i(y)) -> x [8] *( *(x,i(y)),y) -> x [9] i(i(x)) -> x [10] i( *(x,y)) -> *(i(y),i(x)) [11] k(x,1) -> 1 [12] k(x,x) -> 1 [13] *(k(x,y),k(y,x)) -> 1 [14] *( *(i(x),k(y,z)),x) -> k( *( *(i(x),y),x), *( *(i(x),z),x)) [15] k( *(x,i(y)), *(y,i(x))) -> 1 , CRITERION: MDP [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: ST [ { DP termination of: , CRITERION: SG [ ]} ]} { DP termination of: , CRITERION: ORD [ Solution found: polynomial interpretation = [ * ] (X0,X1) = 2 + 2*X0 + 2*X1 + 1*X1*X0 + 0; [ i ] (X0) = 1*X0 + 0; [ 1 ] () = 0; [ Marked_* ] (X0,X1) = 1*X0 + 2*X1 + 1*X1*X0 + 0; [ k ] (X0,X1) = 2 + 1*X0 + 1*X1 + 0; ]} ]} ]} Cime worked for 0.654302 seconds (real time) Cime Exit Status: 0