MAYBE

Problem:
 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))
 isEmpty(empty()) -> true()
 isEmpty(edge(x,y,i)) -> false()
 from(edge(x,y,i)) -> x
 to(edge(x,y,i)) -> y
 rest(edge(x,y,i)) -> i
 rest(empty()) -> empty()
 reach(x,y,i,h) -> if1(eq(x,y),isEmpty(i),eq(x,from(i)),eq(y,to(i)),x,y,i,h)
 if1(true(),b1,b2,b3,x,y,i,h) -> true()
 if1(false(),b1,b2,b3,x,y,i,h) -> if2(b1,b2,b3,x,y,i,h)
 if2(true(),b2,b3,x,y,i,h) -> false()
 if2(false(),b2,b3,x,y,i,h) -> if3(b2,b3,x,y,i,h)
 if3(false(),b3,x,y,i,h) -> reach(x,y,rest(i),edge(from(i),to(i),h))
 if3(true(),b3,x,y,i,h) -> if4(b3,x,y,i,h)
 if4(true(),x,y,i,h) -> true()
 if4(false(),x,y,i,h) -> or(reach(x,y,rest(i),h),reach(to(i),y,union(rest(i),h),empty()))

Proof:
 DP Processor:
  DPs:
   eq#(s(x),s(y)) -> eq#(x,y)
   union#(edge(x,y,i),h) -> union#(i,h)
   reach#(x,y,i,h) -> to#(i)
   reach#(x,y,i,h) -> eq#(y,to(i))
   reach#(x,y,i,h) -> from#(i)
   reach#(x,y,i,h) -> eq#(x,from(i))
   reach#(x,y,i,h) -> isEmpty#(i)
   reach#(x,y,i,h) -> eq#(x,y)
   reach#(x,y,i,h) -> if1#(eq(x,y),isEmpty(i),eq(x,from(i)),eq(y,to(i)),x,y,i,h)
   if1#(false(),b1,b2,b3,x,y,i,h) -> if2#(b1,b2,b3,x,y,i,h)
   if2#(false(),b2,b3,x,y,i,h) -> if3#(b2,b3,x,y,i,h)
   if3#(false(),b3,x,y,i,h) -> to#(i)
   if3#(false(),b3,x,y,i,h) -> from#(i)
   if3#(false(),b3,x,y,i,h) -> rest#(i)
   if3#(false(),b3,x,y,i,h) -> reach#(x,y,rest(i),edge(from(i),to(i),h))
   if3#(true(),b3,x,y,i,h) -> if4#(b3,x,y,i,h)
   if4#(false(),x,y,i,h) -> union#(rest(i),h)
   if4#(false(),x,y,i,h) -> to#(i)
   if4#(false(),x,y,i,h) -> reach#(to(i),y,union(rest(i),h),empty())
   if4#(false(),x,y,i,h) -> rest#(i)
   if4#(false(),x,y,i,h) -> reach#(x,y,rest(i),h)
   if4#(false(),x,y,i,h) -> or#(reach(x,y,rest(i),h),reach(to(i),y,union(rest(i),h),empty()))
  TRS:
   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))
   isEmpty(empty()) -> true()
   isEmpty(edge(x,y,i)) -> false()
   from(edge(x,y,i)) -> x
   to(edge(x,y,i)) -> y
   rest(edge(x,y,i)) -> i
   rest(empty()) -> empty()
   reach(x,y,i,h) -> if1(eq(x,y),isEmpty(i),eq(x,from(i)),eq(y,to(i)),x,y,i,h)
   if1(true(),b1,b2,b3,x,y,i,h) -> true()
   if1(false(),b1,b2,b3,x,y,i,h) -> if2(b1,b2,b3,x,y,i,h)
   if2(true(),b2,b3,x,y,i,h) -> false()
   if2(false(),b2,b3,x,y,i,h) -> if3(b2,b3,x,y,i,h)
   if3(false(),b3,x,y,i,h) -> reach(x,y,rest(i),edge(from(i),to(i),h))
   if3(true(),b3,x,y,i,h) -> if4(b3,x,y,i,h)
   if4(true(),x,y,i,h) -> true()
   if4(false(),x,y,i,h) -> or(reach(x,y,rest(i),h),reach(to(i),y,union(rest(i),h),empty()))
  Open