- : unit = () - : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] min(x,0) -> 0 [2] min(0,y) -> 0 [3] min(s(x),s(y)) -> s(min(x,y)) [4] max(x,0) -> x [5] max(0,y) -> y [6] max(s(x),s(y)) -> s(max(x,y)) [7] -(x,0) -> x [8] -(s(x),s(y)) -> -(x,y) [9] gcd(s(x),s(y),z) -> gcd(-(max(x,y),min(x,y)),s(min(x,y)),z) [10] gcd(x,s(y),s(z)) -> gcd(x,-(max(y,z),min(y,z)),s(min(y,z))) [11] gcd(s(x),y,s(z)) -> gcd(-(max(x,z),min(x,z)),y,s(min(x,z))) [12] gcd(x,0,0) -> x [13] gcd(0,y,0) -> y [14] gcd(0,0,z) -> z Sub problem: guided: DP termination of: END GUIDED APPLY CRITERIA (Graph splitting) Found 4 components: { --> --> --> --> --> --> --> --> --> } { --> } { --> } { --> } APPLY CRITERIA (Subterm criterion) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { min(0,y) >= 0 ; min(s(x),s(y)) >= s(min(x,y)) ; min(x,0) >= 0 ; max(0,y) >= y ; max(s(x),s(y)) >= s(max(x,y)) ; max(x,0) >= x ; -(s(x),s(y)) >= -(x,y) ; -(x,0) >= x ; gcd(0,0,z) >= z ; gcd(0,y,0) >= y ; gcd(s(x),s(y),z) >= gcd(-(max(x,y),min(x,y)),s(min(x,y)),z) ; gcd(s(x),y,s(z)) >= gcd(-(max(x,z),min(x,z)),y,s(min(x,z))) ; gcd(x,0,0) >= x ; gcd(x,s(y),s(z)) >= gcd(x,-(max(y,z),min(y,z)),s(min(y,z))) ; Marked_gcd(s(x),s(y),z) >= Marked_gcd(-(max(x,y),min(x,y)),s(min(x,y)),z) ; Marked_gcd(s(x),y,s(z)) >= Marked_gcd(-(max(x,z),min(x,z)),y,s(min(x,z))) ; Marked_gcd(x,s(y),s(z)) >= Marked_gcd(x,-(max(y,z),min(y,z)),s(min(y,z))) ; } + Disjunctions:{ { Marked_gcd(s(x),s(y),z) > Marked_gcd(-(max(x,y),min(x,y)),s(min(x,y)),z) ; } { Marked_gcd(s(x),y,s(z)) > Marked_gcd(-(max(x,z),min(x,z)),y,s(min(x,z))) ; } { Marked_gcd(x,s(y),s(z)) > Marked_gcd(x,-(max(y,z),min(y,z)),s(min(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: min(0,y) >= 0 constraint: min(s(x),s(y)) >= s(min(x,y)) constraint: min(x,0) >= 0 constraint: max(0,y) >= y constraint: max(s(x),s(y)) >= s(max(x,y)) constraint: max(x,0) >= x constraint: -(s(x),s(y)) >= -(x,y) constraint: -(x,0) >= x constraint: gcd(0,0,z) >= z constraint: gcd(0,y,0) >= y constraint: gcd(s(x),s(y),z) >= gcd(-(max(x,y),min(x,y)),s(min(x,y)),z) constraint: gcd(s(x),y,s(z)) >= gcd(-(max(x,z),min(x,z)),y,s(min(x,z))) constraint: gcd(x,0,0) >= x constraint: gcd(x,s(y),s(z)) >= gcd(x,-(max(y,z),min(y,z)),s(min(y,z))) constraint: Marked_gcd(s(x),s(y),z) >= Marked_gcd(-(max(x,y),min(x,y)), s(min(x,y)),z) constraint: Marked_gcd(s(x),y,s(z)) >= Marked_gcd(-(max(x,z),min(x,z)), y,s(min(x,z))) constraint: Marked_gcd(x,s(y),s(z)) >= Marked_gcd(x,-(max(y,z),min(y,z)), s(min(y,z))) APPLY CRITERIA (Subterm criterion) ST: Marked_- -> 1 APPLY CRITERIA (Subterm criterion) ST: Marked_max -> 1 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: APPLY CRITERIA (Graph splitting) Found 0 components: SOLVED { TRS termination of: [1] min(x,0) -> 0 [2] min(0,y) -> 0 [3] min(s(x),s(y)) -> s(min(x,y)) [4] max(x,0) -> x [5] max(0,y) -> y [6] max(s(x),s(y)) -> s(max(x,y)) [7] -(x,0) -> x [8] -(s(x),s(y)) -> -(x,y) [9] gcd(s(x),s(y),z) -> gcd(-(max(x,y),min(x,y)),s(min(x,y)),z) [10] gcd(x,s(y),s(z)) -> gcd(x,-(max(y,z),min(y,z)),s(min(y,z))) [11] gcd(s(x),y,s(z)) -> gcd(-(max(x,z),min(x,z)),y,s(min(x,z))) [12] gcd(x,0,0) -> x [13] gcd(0,y,0) -> y [14] gcd(0,0,z) -> z , CRITERION: MDP [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: ORD [ Solution found: polynomial interpretation = [ 0 ] () = 0; [ - ] (X0,X1) = 1*X0 + 0; [ s ] (X0) = 2 + 3*X0 + 0; [ Marked_gcd ] (X0,X1,X2) = 3*X0 + 2*X1 + 1*X2 + 0; [ min ] (X0,X1) = 1*X0 + 0; [ gcd ] (X0,X1,X2) = 3 + 3*X0 + 2*X1 + 1*X2 + 0; [ max ] (X0,X1) = 1*X0 + 1*X1 + 0; ]} { DP termination of: , CRITERION: ST [ { DP termination of: , CRITERION: SG [ ]} ]} { DP termination of: , CRITERION: ST [ { DP termination of: , CRITERION: SG [ ]} ]} { DP termination of: , CRITERION: ST [ { DP termination of: , CRITERION: SG [ ]} ]} ]} ]} Cime worked for 0.149381 seconds (real time) Cime Exit Status: 0