- : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] eq(0,0) -> true [2] eq(0,s(x)) -> false [3] eq(s(x),0) -> false [4] eq(s(x),s(y)) -> eq(x,y) [5] or(true,y) -> true [6] or(false,y) -> y [7] union(empty,h) -> h [8] union(edge(x,y,i),h) -> edge(x,y,union(i,h)) [9] reach(x,y,empty,h) -> false [10] reach(x,y,edge(u,v,i),h) -> if_reach_1(eq(x,u),x,y,edge(u,v,i),h) [11] if_reach_1(true,x,y,edge(u,v,i),h) -> if_reach_2(eq(y,v),x,y,edge(u,v,i),h) [12] if_reach_2(true,x,y,edge(u,v,i),h) -> true [13] if_reach_2(false,x,y,edge(u,v,i),h) -> or(reach(x,y,i,h),reach(v,y,union(i,h),empty)) [14] if_reach_1(false,x,y,edge(u,v,i),h) -> reach(x,y,i,edge(u,v,h)) Sub problem: guided: DP termination of: END GUIDED APPLY CRITERIA (Graph splitting) Found 3 components: { --> --> --> --> --> --> --> } { --> } { --> } APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { eq(0,0) >= true ; eq(0,s(x)) >= false ; eq(s(x),0) >= false ; eq(s(x),s(y)) >= eq(x,y) ; or(true,y) >= true ; or(false,y) >= y ; union(empty,h) >= h ; union(edge(x,y,i),h) >= edge(x,y,union(i,h)) ; reach(x,y,empty,h) >= false ; reach(x,y,edge(u,v,i),h) >= if_reach_1(eq(x,u),x,y,edge(u,v,i),h) ; if_reach_1(true,x,y,edge(u,v,i),h) >= if_reach_2(eq(y,v),x,y,edge(u,v,i),h) ; if_reach_1(false,x,y,edge(u,v,i),h) >= reach(x,y,i,edge(u,v,h)) ; if_reach_2(true,x,y,edge(u,v,i),h) >= true ; if_reach_2(false,x,y,edge(u,v,i),h) >= or(reach(x,y,i,h), reach(v,y,union(i,h),empty)) ; Marked_if_reach_1(true,x,y,edge(u,v,i),h) >= Marked_if_reach_2(eq(y,v), x,y,edge(u,v,i),h) ; Marked_if_reach_1(false,x,y,edge(u,v,i),h) >= Marked_reach(x,y,i,edge(u,v,h)) ; Marked_reach(x,y,edge(u,v,i),h) >= Marked_if_reach_1(eq(x,u),x,y,edge(u,v,i), h) ; Marked_if_reach_2(false,x,y,edge(u,v,i),h) >= Marked_reach(v,y,union(i,h), empty) ; Marked_if_reach_2(false,x,y,edge(u,v,i),h) >= Marked_reach(x,y,i,h) ; } + Disjunctions:{ { Marked_if_reach_1(true,x,y,edge(u,v,i),h) > Marked_if_reach_2(eq(y,v), x,y,edge(u,v,i),h) ; } { Marked_if_reach_1(false,x,y,edge(u,v,i),h) > Marked_reach(x,y,i,edge(u,v,h)) ; } { Marked_reach(x,y,edge(u,v,i),h) > Marked_if_reach_1(eq(x,u),x,y,edge(u,v,i), h) ; } { Marked_if_reach_2(false,x,y,edge(u,v,i),h) > Marked_reach(v,y,union(i,h), empty) ; } { Marked_if_reach_2(false,x,y,edge(u,v,i),h) > Marked_reach(x,y,i,h) ; } } === 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: eq(0,0) >= true constraint: eq(0,s(x)) >= false constraint: eq(s(x),0) >= false constraint: eq(s(x),s(y)) >= eq(x,y) constraint: or(true,y) >= true constraint: or(false,y) >= y constraint: union(empty,h) >= h constraint: union(edge(x,y,i),h) >= edge(x,y,union(i,h)) constraint: reach(x,y,empty,h) >= false constraint: reach(x,y,edge(u,v,i),h) >= if_reach_1(eq(x,u),x,y,edge(u,v,i),h) constraint: if_reach_1(true,x,y,edge(u,v,i),h) >= if_reach_2(eq(y,v), x,y,edge(u,v,i),h) constraint: if_reach_1(false,x,y,edge(u,v,i),h) >= reach(x,y,i,edge(u,v,h)) constraint: if_reach_2(true,x,y,edge(u,v,i),h) >= true constraint: if_reach_2(false,x,y,edge(u,v,i),h) >= or(reach(x,y,i,h), reach(v,y,union(i,h),empty)) constraint: Marked_if_reach_1(true,x,y,edge(u,v,i),h) >= Marked_if_reach_2( eq(y,v),x,y, edge(u,v,i), h) constraint: Marked_if_reach_1(false,x,y,edge(u,v,i),h) >= Marked_reach( x,y,i,edge(u,v,h)) constraint: Marked_reach(x,y,edge(u,v,i),h) >= Marked_if_reach_1(eq(x,u), x,y,edge(u,v,i),h) constraint: Marked_if_reach_2(false,x,y,edge(u,v,i),h) >= Marked_reach( v,y,union(i,h), empty) constraint: Marked_if_reach_2(false,x,y,edge(u,v,i),h) >= Marked_reach(x,y,i,h) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { eq(0,0) >= true ; eq(0,s(x)) >= false ; eq(s(x),0) >= false ; eq(s(x),s(y)) >= eq(x,y) ; or(true,y) >= true ; or(false,y) >= y ; union(empty,h) >= h ; union(edge(x,y,i),h) >= edge(x,y,union(i,h)) ; reach(x,y,empty,h) >= false ; reach(x,y,edge(u,v,i),h) >= if_reach_1(eq(x,u),x,y,edge(u,v,i),h) ; if_reach_1(true,x,y,edge(u,v,i),h) >= if_reach_2(eq(y,v),x,y,edge(u,v,i),h) ; if_reach_1(false,x,y,edge(u,v,i),h) >= reach(x,y,i,edge(u,v,h)) ; if_reach_2(true,x,y,edge(u,v,i),h) >= true ; if_reach_2(false,x,y,edge(u,v,i),h) >= or(reach(x,y,i,h), reach(v,y,union(i,h),empty)) ; Marked_union(edge(x,y,i),h) >= Marked_union(i,h) ; } + Disjunctions:{ { Marked_union(edge(x,y,i),h) > Marked_union(i,h) ; } } === 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: eq(0,0) >= true constraint: eq(0,s(x)) >= false constraint: eq(s(x),0) >= false constraint: eq(s(x),s(y)) >= eq(x,y) constraint: or(true,y) >= true constraint: or(false,y) >= y constraint: union(empty,h) >= h constraint: union(edge(x,y,i),h) >= edge(x,y,union(i,h)) constraint: reach(x,y,empty,h) >= false constraint: reach(x,y,edge(u,v,i),h) >= if_reach_1(eq(x,u),x,y,edge(u,v,i),h) constraint: if_reach_1(true,x,y,edge(u,v,i),h) >= if_reach_2(eq(y,v), x,y,edge(u,v,i),h) constraint: if_reach_1(false,x,y,edge(u,v,i),h) >= reach(x,y,i,edge(u,v,h)) constraint: if_reach_2(true,x,y,edge(u,v,i),h) >= true constraint: if_reach_2(false,x,y,edge(u,v,i),h) >= or(reach(x,y,i,h), reach(v,y,union(i,h),empty)) constraint: Marked_union(edge(x,y,i),h) >= Marked_union(i,h) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { eq(0,0) >= true ; eq(0,s(x)) >= false ; eq(s(x),0) >= false ; eq(s(x),s(y)) >= eq(x,y) ; or(true,y) >= true ; or(false,y) >= y ; union(empty,h) >= h ; union(edge(x,y,i),h) >= edge(x,y,union(i,h)) ; reach(x,y,empty,h) >= false ; reach(x,y,edge(u,v,i),h) >= if_reach_1(eq(x,u),x,y,edge(u,v,i),h) ; if_reach_1(true,x,y,edge(u,v,i),h) >= if_reach_2(eq(y,v),x,y,edge(u,v,i),h) ; if_reach_1(false,x,y,edge(u,v,i),h) >= reach(x,y,i,edge(u,v,h)) ; if_reach_2(true,x,y,edge(u,v,i),h) >= true ; if_reach_2(false,x,y,edge(u,v,i),h) >= or(reach(x,y,i,h), reach(v,y,union(i,h),empty)) ; Marked_eq(s(x),s(y)) >= Marked_eq(x,y) ; } + Disjunctions:{ { Marked_eq(s(x),s(y)) > Marked_eq(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 Sat solver result read === STOPING TIMER real === === STOPING TIMER virtual === constraint: eq(0,0) >= true constraint: eq(0,s(x)) >= false constraint: eq(s(x),0) >= false constraint: eq(s(x),s(y)) >= eq(x,y) constraint: or(true,y) >= true constraint: or(false,y) >= y constraint: union(empty,h) >= h constraint: union(edge(x,y,i),h) >= edge(x,y,union(i,h)) constraint: reach(x,y,empty,h) >= false constraint: reach(x,y,edge(u,v,i),h) >= if_reach_1(eq(x,u),x,y,edge(u,v,i),h) constraint: if_reach_1(true,x,y,edge(u,v,i),h) >= if_reach_2(eq(y,v), x,y,edge(u,v,i),h) constraint: if_reach_1(false,x,y,edge(u,v,i),h) >= reach(x,y,i,edge(u,v,h)) constraint: if_reach_2(true,x,y,edge(u,v,i),h) >= true constraint: if_reach_2(false,x,y,edge(u,v,i),h) >= or(reach(x,y,i,h), reach(v,y,union(i,h),empty)) constraint: Marked_eq(s(x),s(y)) >= Marked_eq(x,y) APPLY CRITERIA (Graph splitting) Found 1 components: { --> --> --> --> --> } APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { eq(0,0) >= true ; eq(0,s(x)) >= false ; eq(s(x),0) >= false ; eq(s(x),s(y)) >= eq(x,y) ; or(true,y) >= true ; or(false,y) >= y ; union(empty,h) >= h ; union(edge(x,y,i),h) >= edge(x,y,union(i,h)) ; reach(x,y,empty,h) >= false ; reach(x,y,edge(u,v,i),h) >= if_reach_1(eq(x,u),x,y,edge(u,v,i),h) ; if_reach_1(true,x,y,edge(u,v,i),h) >= if_reach_2(eq(y,v),x,y,edge(u,v,i),h) ; if_reach_1(false,x,y,edge(u,v,i),h) >= reach(x,y,i,edge(u,v,h)) ; if_reach_2(true,x,y,edge(u,v,i),h) >= true ; if_reach_2(false,x,y,edge(u,v,i),h) >= or(reach(x,y,i,h), reach(v,y,union(i,h),empty)) ; Marked_if_reach_1(true,x,y,edge(u,v,i),h) >= Marked_if_reach_2(eq(y,v), x,y,edge(u,v,i),h) ; Marked_if_reach_1(false,x,y,edge(u,v,i),h) >= Marked_reach(x,y,i,edge(u,v,h)) ; Marked_reach(x,y,edge(u,v,i),h) >= Marked_if_reach_1(eq(x,u),x,y,edge(u,v,i), h) ; Marked_if_reach_2(false,x,y,edge(u,v,i),h) >= Marked_reach(v,y,union(i,h), empty) ; } + Disjunctions:{ { Marked_if_reach_1(true,x,y,edge(u,v,i),h) > Marked_if_reach_2(eq(y,v), x,y,edge(u,v,i),h) ; } { Marked_if_reach_1(false,x,y,edge(u,v,i),h) > Marked_reach(x,y,i,edge(u,v,h)) ; } { Marked_reach(x,y,edge(u,v,i),h) > Marked_if_reach_1(eq(x,u),x,y,edge(u,v,i), h) ; } { Marked_if_reach_2(false,x,y,edge(u,v,i),h) > Marked_reach(v,y,union(i,h), empty) ; } } === 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: eq(0,0) >= true constraint: eq(0,s(x)) >= false constraint: eq(s(x),0) >= false constraint: eq(s(x),s(y)) >= eq(x,y) constraint: or(true,y) >= true constraint: or(false,y) >= y constraint: union(empty,h) >= h constraint: union(edge(x,y,i),h) >= edge(x,y,union(i,h)) constraint: reach(x,y,empty,h) >= false constraint: reach(x,y,edge(u,v,i),h) >= if_reach_1(eq(x,u),x,y,edge(u,v,i),h) constraint: if_reach_1(true,x,y,edge(u,v,i),h) >= if_reach_2(eq(y,v), x,y,edge(u,v,i),h) constraint: if_reach_1(false,x,y,edge(u,v,i),h) >= reach(x,y,i,edge(u,v,h)) constraint: if_reach_2(true,x,y,edge(u,v,i),h) >= true constraint: if_reach_2(false,x,y,edge(u,v,i),h) >= or(reach(x,y,i,h), reach(v,y,union(i,h),empty)) constraint: Marked_if_reach_1(true,x,y,edge(u,v,i),h) >= Marked_if_reach_2( eq(y,v),x,y, edge(u,v,i), h) constraint: Marked_if_reach_1(false,x,y,edge(u,v,i),h) >= Marked_reach( x,y,i,edge(u,v,h)) constraint: Marked_reach(x,y,edge(u,v,i),h) >= Marked_if_reach_1(eq(x,u), x,y,edge(u,v,i),h) constraint: Marked_if_reach_2(false,x,y,edge(u,v,i),h) >= Marked_reach( v,y,union(i,h), empty) APPLY CRITERIA (Graph splitting) Found 1 components: { --> --> } APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { eq(0,0) >= true ; eq(0,s(x)) >= false ; eq(s(x),0) >= false ; eq(s(x),s(y)) >= eq(x,y) ; or(true,y) >= true ; or(false,y) >= y ; union(empty,h) >= h ; union(edge(x,y,i),h) >= edge(x,y,union(i,h)) ; reach(x,y,empty,h) >= false ; reach(x,y,edge(u,v,i),h) >= if_reach_1(eq(x,u),x,y,edge(u,v,i),h) ; if_reach_1(true,x,y,edge(u,v,i),h) >= if_reach_2(eq(y,v),x,y,edge(u,v,i),h) ; if_reach_1(false,x,y,edge(u,v,i),h) >= reach(x,y,i,edge(u,v,h)) ; if_reach_2(true,x,y,edge(u,v,i),h) >= true ; if_reach_2(false,x,y,edge(u,v,i),h) >= or(reach(x,y,i,h), reach(v,y,union(i,h),empty)) ; Marked_if_reach_1(false,x,y,edge(u,v,i),h) >= Marked_reach(x,y,i,edge(u,v,h)) ; Marked_reach(x,y,edge(u,v,i),h) >= Marked_if_reach_1(eq(x,u),x,y,edge(u,v,i), h) ; } + Disjunctions:{ { Marked_if_reach_1(false,x,y,edge(u,v,i),h) > Marked_reach(x,y,i,edge(u,v,h)) ; } { Marked_reach(x,y,edge(u,v,i),h) > Marked_if_reach_1(eq(x,u),x,y,edge(u,v,i), h) ; } } === 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: eq(0,0) >= true constraint: eq(0,s(x)) >= false constraint: eq(s(x),0) >= false constraint: eq(s(x),s(y)) >= eq(x,y) constraint: or(true,y) >= true constraint: or(false,y) >= y constraint: union(empty,h) >= h constraint: union(edge(x,y,i),h) >= edge(x,y,union(i,h)) constraint: reach(x,y,empty,h) >= false constraint: reach(x,y,edge(u,v,i),h) >= if_reach_1(eq(x,u),x,y,edge(u,v,i),h) constraint: if_reach_1(true,x,y,edge(u,v,i),h) >= if_reach_2(eq(y,v), x,y,edge(u,v,i),h) constraint: if_reach_1(false,x,y,edge(u,v,i),h) >= reach(x,y,i,edge(u,v,h)) constraint: if_reach_2(true,x,y,edge(u,v,i),h) >= true constraint: if_reach_2(false,x,y,edge(u,v,i),h) >= or(reach(x,y,i,h), reach(v,y,union(i,h),empty)) constraint: Marked_if_reach_1(false,x,y,edge(u,v,i),h) >= Marked_reach( x,y,i,edge(u,v,h)) constraint: Marked_reach(x,y,edge(u,v,i),h) >= Marked_if_reach_1(eq(x,u), x,y,edge(u,v,i),h) 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] eq(0,0) -> true [2] eq(0,s(x)) -> false [3] eq(s(x),0) -> false [4] eq(s(x),s(y)) -> eq(x,y) [5] or(true,y) -> true [6] or(false,y) -> y [7] union(empty,h) -> h [8] union(edge(x,y,i),h) -> edge(x,y,union(i,h)) [9] reach(x,y,empty,h) -> false [10] reach(x,y,edge(u,v,i),h) -> if_reach_1(eq(x,u),x,y,edge(u,v,i),h) [11] if_reach_1(true,x,y,edge(u,v,i),h) -> if_reach_2(eq(y,v),x,y,edge(u,v,i),h) [12] if_reach_2(true,x,y,edge(u,v,i),h) -> true [13] if_reach_2(false,x,y,edge(u,v,i),h) -> or(reach(x,y,i,h),reach(v,y,union(i,h),empty)) [14] if_reach_1(false,x,y,edge(u,v,i),h) -> reach(x,y,i,edge(u,v,h)) , CRITERION: MDP [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: CG using polynomial interpretation = [ true ] () = 0; [ edge ] (X0,X1,X2) = 1*X2 + 2; [ s ] (X0) = 3*X0; [ Marked_if_reach_1 ] (X0,X1,X2,X3,X4) = 2*X4 + 2*X3 + 3*X2; [ 0 ] () = 0; [ if_reach_1 ] (X0,X1,X2,X3,X4) = 0; [ union ] (X0,X1) = 1*X1 + 1*X0; [ Marked_if_reach_2 ] (X0,X1,X2,X3,X4) = 2*X4 + 2*X3 + 3*X2; [ eq ] (X0,X1) = 0; [ reach ] (X0,X1,X2,X3) = 0; [ or ] (X0,X1) = 2*X1; [ Marked_reach ] (X0,X1,X2,X3) = 2*X3 + 2*X2 + 3*X1; [ false ] () = 0; [ if_reach_2 ] (X0,X1,X2,X3,X4) = 0; [ empty ] () = 2; removing [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: CG using polynomial interpretation = [ true ] () = 0; [ edge ] (X0,X1,X2) = 1*X2 + 1; [ s ] (X0) = 3*X0; [ Marked_if_reach_1 ] (X0,X1,X2,X3,X4) = 2*X4 + 2*X3 + 3*X2 + 2; [ 0 ] () = 0; [ if_reach_1 ] (X0,X1,X2,X3,X4) = 0; [ union ] (X0,X1) = 1*X1 + 1*X0; [ Marked_if_reach_2 ] (X0,X1,X2,X3,X4) = 2*X4 + 2*X3 + 3*X2; [ eq ] (X0,X1) = 0; [ reach ] (X0,X1,X2,X3) = 0; [ or ] (X0,X1) = 2*X1; [ Marked_reach ] (X0,X1,X2,X3) = 2*X3 + 2*X2 + 3*X1 + 2; [ false ] () = 0; [ if_reach_2 ] (X0,X1,X2,X3,X4) = 0; [ empty ] () = 0; removing [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: CG using polynomial interpretation = [ true ] () = 0; [ edge ] (X0,X1,X2) = 1*X2 + 2; [ s ] (X0) = 3*X0; [ Marked_if_reach_1 ] (X0,X1,X2,X3,X4) = 1*X3 + 3*X2 + 3*X1 + 1; [ 0 ] () = 0; [ if_reach_1 ] (X0,X1,X2,X3,X4) = 0; [ union ] (X0,X1) = 2*X1 + 2*X0; [ eq ] (X0,X1) = 0; [ reach ] (X0,X1,X2,X3) = 0; [ or ] (X0,X1) = 2*X1; [ Marked_reach ] (X0,X1,X2,X3) = 1*X2 + 3*X1 + 3*X0 + 3; [ false ] () = 0; [ if_reach_2 ] (X0,X1,X2,X3,X4) = 0; [ empty ] () = 0; removing [ { DP termination of: , CRITERION: SG [ ]} ]} ]} ]} ]} ]} { DP termination of: , CRITERION: ORD [ Solution found: polynomial interpretation = [ true ] () = 0; [ Marked_union ] (X0,X1) = 3*X0 + 0; [ edge ] (X0,X1,X2) = 1 + 1*X2 + 0; [ s ] (X0) = 3*X0 + 0; [ 0 ] () = 0; [ if_reach_1 ] (X0,X1,X2,X3,X4) = 0; [ union ] (X0,X1) = 1*X0 + 2*X1 + 0; [ eq ] (X0,X1) = 0; [ reach ] (X0,X1,X2,X3) = 0; [ or ] (X0,X1) = 2*X1 + 0; [ false ] () = 0; [ if_reach_2 ] (X0,X1,X2,X3,X4) = 0; [ empty ] () = 0; ]} { DP termination of: , CRITERION: ORD [ Solution found: polynomial interpretation = [ true ] () = 0; [ edge ] (X0,X1,X2) = 2 + 0; [ s ] (X0) = 1 + 3*X0 + 0; [ 0 ] () = 0; [ if_reach_1 ] (X0,X1,X2,X3,X4) = 0; [ union ] (X0,X1) = 2*X0 + 1*X1 + 0; [ eq ] (X0,X1) = 0; [ Marked_eq ] (X0,X1) = 1*X0 + 0; [ reach ] (X0,X1,X2,X3) = 0; [ or ] (X0,X1) = 1*X1 + 0; [ false ] () = 0; [ if_reach_2 ] (X0,X1,X2,X3,X4) = 0; [ empty ] () = 0; ]} ]} ]} Cime worked for 0.489260 seconds (real time) Cime Exit Status: 0