- : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] D(t) -> s(h) [2] D(constant) -> h [3] D(b(x,y)) -> b(D(x),D(y)) [4] D(c(x,y)) -> b(c(y,D(x)),c(x,D(y))) [5] D(m(x,y)) -> m(D(x),D(y)) [6] D(opp(x)) -> opp(D(x)) [7] D(div(x,y)) -> m(div(D(x),y),div(c(x,D(y)),pow(y,2))) [8] D(ln(x)) -> div(D(x),x) [9] D(pow(x,y)) -> b(c(c(y,pow(x,m(y,1))),D(x)),c(c(pow(x,y),ln(x)),D(y))) [10] b(h,x) -> x [11] b(x,h) -> x [12] b(s(x),s(y)) -> s(s(b(x,y))) [13] b(b(x,y),z) -> b(x,b(y,z)) 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: { D(t) >= s(h) ; D(constant) >= h ; D(b(x,y)) >= b(D(x),D(y)) ; D(c(x,y)) >= b(c(y,D(x)),c(x,D(y))) ; D(m(x,y)) >= m(D(x),D(y)) ; D(opp(x)) >= opp(D(x)) ; D(div(x,y)) >= m(div(D(x),y),div(c(x,D(y)),pow(y,2))) ; D(pow(x,y)) >= b(c(c(y,pow(x,m(y,1))),D(x)),c(c(pow(x,y),ln(x)),D(y))) ; D(ln(x)) >= div(D(x),x) ; b(s(x),s(y)) >= s(s(b(x,y))) ; b(h,x) >= x ; b(b(x,y),z) >= b(x,b(y,z)) ; b(x,h) >= x ; Marked_D(b(x,y)) >= Marked_D(y) ; Marked_D(b(x,y)) >= Marked_D(x) ; Marked_D(c(x,y)) >= Marked_D(y) ; Marked_D(c(x,y)) >= Marked_D(x) ; Marked_D(m(x,y)) >= Marked_D(y) ; Marked_D(m(x,y)) >= Marked_D(x) ; Marked_D(opp(x)) >= Marked_D(x) ; Marked_D(div(x,y)) >= Marked_D(y) ; Marked_D(div(x,y)) >= Marked_D(x) ; Marked_D(pow(x,y)) >= Marked_D(y) ; Marked_D(pow(x,y)) >= Marked_D(x) ; Marked_D(ln(x)) >= Marked_D(x) ; } + Disjunctions:{ { Marked_D(b(x,y)) > Marked_D(y) ; } { Marked_D(b(x,y)) > Marked_D(x) ; } { Marked_D(c(x,y)) > Marked_D(y) ; } { Marked_D(c(x,y)) > Marked_D(x) ; } { Marked_D(m(x,y)) > Marked_D(y) ; } { Marked_D(m(x,y)) > Marked_D(x) ; } { Marked_D(opp(x)) > Marked_D(x) ; } { Marked_D(div(x,y)) > Marked_D(y) ; } { Marked_D(div(x,y)) > Marked_D(x) ; } { Marked_D(pow(x,y)) > Marked_D(y) ; } { Marked_D(pow(x,y)) > Marked_D(x) ; } { Marked_D(ln(x)) > Marked_D(x) ; } } === 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: D(t) >= s(h) constraint: D(constant) >= h constraint: D(b(x,y)) >= b(D(x),D(y)) constraint: D(c(x,y)) >= b(c(y,D(x)),c(x,D(y))) constraint: D(m(x,y)) >= m(D(x),D(y)) constraint: D(opp(x)) >= opp(D(x)) constraint: D(div(x,y)) >= m(div(D(x),y),div(c(x,D(y)),pow(y,2))) constraint: D(pow(x,y)) >= b(c(c(y,pow(x,m(y,1))),D(x)), c(c(pow(x,y),ln(x)),D(y))) constraint: D(ln(x)) >= div(D(x),x) constraint: b(s(x),s(y)) >= s(s(b(x,y))) constraint: b(h,x) >= x constraint: b(b(x,y),z) >= b(x,b(y,z)) constraint: b(x,h) >= x constraint: Marked_D(b(x,y)) >= Marked_D(y) constraint: Marked_D(b(x,y)) >= Marked_D(x) constraint: Marked_D(c(x,y)) >= Marked_D(y) constraint: Marked_D(c(x,y)) >= Marked_D(x) constraint: Marked_D(m(x,y)) >= Marked_D(y) constraint: Marked_D(m(x,y)) >= Marked_D(x) constraint: Marked_D(opp(x)) >= Marked_D(x) constraint: Marked_D(div(x,y)) >= Marked_D(y) constraint: Marked_D(div(x,y)) >= Marked_D(x) constraint: Marked_D(pow(x,y)) >= Marked_D(y) constraint: Marked_D(pow(x,y)) >= Marked_D(x) constraint: Marked_D(ln(x)) >= Marked_D(x) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { D(t) >= s(h) ; D(constant) >= h ; D(b(x,y)) >= b(D(x),D(y)) ; D(c(x,y)) >= b(c(y,D(x)),c(x,D(y))) ; D(m(x,y)) >= m(D(x),D(y)) ; D(opp(x)) >= opp(D(x)) ; D(div(x,y)) >= m(div(D(x),y),div(c(x,D(y)),pow(y,2))) ; D(pow(x,y)) >= b(c(c(y,pow(x,m(y,1))),D(x)),c(c(pow(x,y),ln(x)),D(y))) ; D(ln(x)) >= div(D(x),x) ; b(s(x),s(y)) >= s(s(b(x,y))) ; b(h,x) >= x ; b(b(x,y),z) >= b(x,b(y,z)) ; b(x,h) >= x ; Marked_b(s(x),s(y)) >= Marked_b(x,y) ; Marked_b(b(x,y),z) >= Marked_b(y,z) ; Marked_b(b(x,y),z) >= Marked_b(x,b(y,z)) ; } + Disjunctions:{ { Marked_b(s(x),s(y)) > Marked_b(x,y) ; } { Marked_b(b(x,y),z) > Marked_b(y,z) ; } { Marked_b(b(x,y),z) > Marked_b(x,b(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: D(t) >= s(h) constraint: D(constant) >= h constraint: D(b(x,y)) >= b(D(x),D(y)) constraint: D(c(x,y)) >= b(c(y,D(x)),c(x,D(y))) constraint: D(m(x,y)) >= m(D(x),D(y)) constraint: D(opp(x)) >= opp(D(x)) constraint: D(div(x,y)) >= m(div(D(x),y),div(c(x,D(y)),pow(y,2))) constraint: D(pow(x,y)) >= b(c(c(y,pow(x,m(y,1))),D(x)), c(c(pow(x,y),ln(x)),D(y))) constraint: D(ln(x)) >= div(D(x),x) constraint: b(s(x),s(y)) >= s(s(b(x,y))) constraint: b(h,x) >= x constraint: b(b(x,y),z) >= b(x,b(y,z)) constraint: b(x,h) >= x constraint: Marked_b(s(x),s(y)) >= Marked_b(x,y) constraint: Marked_b(b(x,y),z) >= Marked_b(y,z) constraint: Marked_b(b(x,y),z) >= Marked_b(x,b(y,z)) APPLY CRITERIA (Graph splitting) Found 0 components: APPLY CRITERIA (Graph splitting) Found 0 components: SOLVED { TRS termination of: [1] D(t) -> s(h) [2] D(constant) -> h [3] D(b(x,y)) -> b(D(x),D(y)) [4] D(c(x,y)) -> b(c(y,D(x)),c(x,D(y))) [5] D(m(x,y)) -> m(D(x),D(y)) [6] D(opp(x)) -> opp(D(x)) [7] D(div(x,y)) -> m(div(D(x),y),div(c(x,D(y)),pow(y,2))) [8] D(ln(x)) -> div(D(x),x) [9] D(pow(x,y)) -> b(c(c(y,pow(x,m(y,1))),D(x)),c(c(pow(x,y),ln(x)),D(y))) [10] b(h,x) -> x [11] b(x,h) -> x [12] b(s(x),s(y)) -> s(s(b(x,y))) [13] b(b(x,y),z) -> b(x,b(y,z)) , 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.): { s < D ; s < b ; h < D ; D > s ; D > h ; D > b ; D > c ; D > m ; D > opp ; D > div ; D > pow ; D > 2 ; D > ln ; D > 1 ; b > s ; b < D ; c < D ; m < D ; opp < D ; div < D ; pow < D ; 2 < D ; ln < D ; 1 < D ; } ]} { DP termination of: , CRITERION: ORD [ Solution found: polynomial interpretation = [ s ] (X0) = 1 + 1*X0 + 0; [ opp ] (X0) = 0; [ constant ] () = 0; [ ln ] (X0) = 3 + 1*X0 + 0; [ D ] (X0) = 3 + 3*X0 + 0; [ pow ] (X0,X1) = 0; [ c ] (X0,X1) = 0; [ Marked_b ] (X0,X1) = 2*X0 + 0; [ h ] () = 0; [ div ] (X0,X1) = 3 + 0; [ b ] (X0,X1) = 3 + 2*X0 + 1*X1 + 0; [ 1 ] () = 0; [ t ] () = 0; [ 2 ] () = 0; [ m ] (X0,X1) = 2 + 2*X0 + 0; ]} ]} ]} Cime worked for 0.304975 seconds (real time) Cime Exit Status: 0