R
↳Dependency Pair Analysis
MEM(x, union(y, z)) -> OR(mem(x, y), mem(x, z))
MEM(x, union(y, z)) -> MEM(x, y)
MEM(x, union(y, z)) -> MEM(x, z)
R
↳DPs
→DP Problem 1
↳Forward Instantiation Transformation
MEM(x, union(y, z)) -> MEM(x, z)
MEM(x, union(y, z)) -> MEM(x, y)
or(true, y) -> true
or(x, true) -> true
or(false, false) -> false
mem(x, nil) -> false
mem(x, set(y)) -> =(x, y)
mem(x, union(y, z)) -> or(mem(x, y), mem(x, z))
innermost
one new Dependency Pair is created:
MEM(x, union(y, z)) -> MEM(x, y)
MEM(x'', union(union(y'', z''), z)) -> MEM(x'', union(y'', z''))
R
↳DPs
→DP Problem 1
↳FwdInst
→DP Problem 2
↳Forward Instantiation Transformation
MEM(x'', union(union(y'', z''), z)) -> MEM(x'', union(y'', z''))
MEM(x, union(y, z)) -> MEM(x, z)
or(true, y) -> true
or(x, true) -> true
or(false, false) -> false
mem(x, nil) -> false
mem(x, set(y)) -> =(x, y)
mem(x, union(y, z)) -> or(mem(x, y), mem(x, z))
innermost
two new Dependency Pairs are created:
MEM(x, union(y, z)) -> MEM(x, z)
MEM(x'', union(y, union(y'', z''))) -> MEM(x'', union(y'', z''))
MEM(x', union(y, union(union(y'''', z''''), z''))) -> MEM(x', union(union(y'''', z''''), z''))
R
↳DPs
→DP Problem 1
↳FwdInst
→DP Problem 2
↳FwdInst
...
→DP Problem 3
↳Forward Instantiation Transformation
MEM(x', union(y, union(union(y'''', z''''), z''))) -> MEM(x', union(union(y'''', z''''), z''))
MEM(x'', union(y, union(y'', z''))) -> MEM(x'', union(y'', z''))
MEM(x'', union(union(y'', z''), z)) -> MEM(x'', union(y'', z''))
or(true, y) -> true
or(x, true) -> true
or(false, false) -> false
mem(x, nil) -> false
mem(x, set(y)) -> =(x, y)
mem(x, union(y, z)) -> or(mem(x, y), mem(x, z))
innermost
three new Dependency Pairs are created:
MEM(x'', union(union(y'', z''), z)) -> MEM(x'', union(y'', z''))
MEM(x'''', union(union(union(y'''', z''''), z''0), z)) -> MEM(x'''', union(union(y'''', z''''), z''0))
MEM(x'''', union(union(y''0, union(y'''', z'''')), z)) -> MEM(x'''', union(y''0, union(y'''', z'''')))
MEM(x'''', union(union(y''', union(union(y'''''', z''''''), z'''')), z)) -> MEM(x'''', union(y''', union(union(y'''''', z''''''), z'''')))
R
↳DPs
→DP Problem 1
↳FwdInst
→DP Problem 2
↳FwdInst
...
→DP Problem 4
↳Forward Instantiation Transformation
MEM(x'''', union(union(y''', union(union(y'''''', z''''''), z'''')), z)) -> MEM(x'''', union(y''', union(union(y'''''', z''''''), z'''')))
MEM(x'''', union(union(y''0, union(y'''', z'''')), z)) -> MEM(x'''', union(y''0, union(y'''', z'''')))
MEM(x'''', union(union(union(y'''', z''''), z''0), z)) -> MEM(x'''', union(union(y'''', z''''), z''0))
MEM(x'', union(y, union(y'', z''))) -> MEM(x'', union(y'', z''))
MEM(x', union(y, union(union(y'''', z''''), z''))) -> MEM(x', union(union(y'''', z''''), z''))
or(true, y) -> true
or(x, true) -> true
or(false, false) -> false
mem(x, nil) -> false
mem(x, set(y)) -> =(x, y)
mem(x, union(y, z)) -> or(mem(x, y), mem(x, z))
innermost
five new Dependency Pairs are created:
MEM(x'', union(y, union(y'', z''))) -> MEM(x'', union(y'', z''))
MEM(x'''', union(y, union(y''0, union(y'''', z'''')))) -> MEM(x'''', union(y''0, union(y'''', z'''')))
MEM(x'''', union(y, union(y''', union(union(y'''''', z''''''), z'''')))) -> MEM(x'''', union(y''', union(union(y'''''', z''''''), z'''')))
MEM(x''', union(y, union(union(union(y'''''', z''''''), z''0''), z'''))) -> MEM(x''', union(union(union(y'''''', z''''''), z''0''), z'''))
MEM(x''', union(y, union(union(y''0'', union(y'''''', z'''''')), z'''))) -> MEM(x''', union(union(y''0'', union(y'''''', z'''''')), z'''))
MEM(x''', union(y, union(union(y''''', union(union(y'''''''', z''''''''), z'''''')), z'''))) -> MEM(x''', union(union(y''''', union(union(y'''''''', z''''''''), z'''''')), z'''))
R
↳DPs
→DP Problem 1
↳FwdInst
→DP Problem 2
↳FwdInst
...
→DP Problem 5
↳Forward Instantiation Transformation
MEM(x''', union(y, union(union(y''''', union(union(y'''''''', z''''''''), z'''''')), z'''))) -> MEM(x''', union(union(y''''', union(union(y'''''''', z''''''''), z'''''')), z'''))
MEM(x''', union(y, union(union(y''0'', union(y'''''', z'''''')), z'''))) -> MEM(x''', union(union(y''0'', union(y'''''', z'''''')), z'''))
MEM(x''', union(y, union(union(union(y'''''', z''''''), z''0''), z'''))) -> MEM(x''', union(union(union(y'''''', z''''''), z''0''), z'''))
MEM(x'''', union(y, union(y''', union(union(y'''''', z''''''), z'''')))) -> MEM(x'''', union(y''', union(union(y'''''', z''''''), z'''')))
MEM(x'''', union(y, union(y''0, union(y'''', z'''')))) -> MEM(x'''', union(y''0, union(y'''', z'''')))
MEM(x'''', union(union(y''0, union(y'''', z'''')), z)) -> MEM(x'''', union(y''0, union(y'''', z'''')))
MEM(x'''', union(union(union(y'''', z''''), z''0), z)) -> MEM(x'''', union(union(y'''', z''''), z''0))
MEM(x', union(y, union(union(y'''', z''''), z''))) -> MEM(x', union(union(y'''', z''''), z''))
MEM(x'''', union(union(y''', union(union(y'''''', z''''''), z'''')), z)) -> MEM(x'''', union(y''', union(union(y'''''', z''''''), z'''')))
or(true, y) -> true
or(x, true) -> true
or(false, false) -> false
mem(x, nil) -> false
mem(x, set(y)) -> =(x, y)
mem(x, union(y, z)) -> or(mem(x, y), mem(x, z))
innermost
nine new Dependency Pairs are created:
MEM(x', union(y, union(union(y'''', z''''), z''))) -> MEM(x', union(union(y'''', z''''), z''))
MEM(x''', union(y, union(union(y''''0, z''''0), union(union(y'''''', z''''''), z'''0)))) -> MEM(x''', union(union(y''''0, z''''0), union(union(y'''''', z''''''), z'''0)))
MEM(x'', union(y, union(union(union(y'''''', z''''''), z''''0), z'''))) -> MEM(x'', union(union(union(y'''''', z''''''), z''''0), z'''))
MEM(x'', union(y, union(union(y''''0, union(y'''''', z'''''')), z'''))) -> MEM(x'', union(union(y''''0, union(y'''''', z'''''')), z'''))
MEM(x'', union(y, union(union(y'''''', union(union(y'''''''', z''''''''), z'''''')), z'''))) -> MEM(x'', union(union(y'''''', union(union(y'''''''', z''''''''), z'''''')), z'''))
MEM(x'', union(y, union(union(y''''0, z''''0), union(y''0'', union(y'''''', z''''''))))) -> MEM(x'', union(union(y''''0, z''''0), union(y''0'', union(y'''''', z''''''))))
MEM(x'', union(y, union(union(y''''0, z''''0), union(y'''''', union(union(y'''''''', z''''''''), z''''''))))) -> MEM(x'', union(union(y''''0, z''''0), union(y'''''', union(union(y'''''''', z''''''''), z''''''))))
MEM(x'', union(y, union(union(y''''', z''''0), union(union(union(y'''''''', z''''''''), z''0''''), z'''''')))) -> MEM(x'', union(union(y''''', z''''0), union(union(union(y'''''''', z''''''''), z''0''''), z'''''')))
MEM(x'', union(y, union(union(y''''', z''''0), union(union(y''0'''', union(y'''''''', z'''''''')), z'''''')))) -> MEM(x'', union(union(y''''', z''''0), union(union(y''0'''', union(y'''''''', z'''''''')), z'''''')))
MEM(x'', union(y, union(union(y''''', z''''0), union(union(y''''''', union(union(y'''''''''', z''''''''''), z'''''''')), z'''''')))) -> MEM(x'', union(union(y''''', z''''0), union(union(y''''''', union(union(y'''''''''', z''''''''''), z'''''''')), z'''''')))
R
↳DPs
→DP Problem 1
↳FwdInst
→DP Problem 2
↳FwdInst
...
→DP Problem 6
↳Argument Filtering and Ordering
MEM(x'', union(y, union(union(y''''', z''''0), union(union(y''''''', union(union(y'''''''''', z''''''''''), z'''''''')), z'''''')))) -> MEM(x'', union(union(y''''', z''''0), union(union(y''''''', union(union(y'''''''''', z''''''''''), z'''''''')), z'''''')))
MEM(x'', union(y, union(union(y''''', z''''0), union(union(y''0'''', union(y'''''''', z'''''''')), z'''''')))) -> MEM(x'', union(union(y''''', z''''0), union(union(y''0'''', union(y'''''''', z'''''''')), z'''''')))
MEM(x'', union(y, union(union(y''''', z''''0), union(union(union(y'''''''', z''''''''), z''0''''), z'''''')))) -> MEM(x'', union(union(y''''', z''''0), union(union(union(y'''''''', z''''''''), z''0''''), z'''''')))
MEM(x'', union(y, union(union(y''''0, z''''0), union(y'''''', union(union(y'''''''', z''''''''), z''''''))))) -> MEM(x'', union(union(y''''0, z''''0), union(y'''''', union(union(y'''''''', z''''''''), z''''''))))
MEM(x'', union(y, union(union(y''''0, z''''0), union(y''0'', union(y'''''', z''''''))))) -> MEM(x'', union(union(y''''0, z''''0), union(y''0'', union(y'''''', z''''''))))
MEM(x'', union(y, union(union(y'''''', union(union(y'''''''', z''''''''), z'''''')), z'''))) -> MEM(x'', union(union(y'''''', union(union(y'''''''', z''''''''), z'''''')), z'''))
MEM(x'', union(y, union(union(y''''0, union(y'''''', z'''''')), z'''))) -> MEM(x'', union(union(y''''0, union(y'''''', z'''''')), z'''))
MEM(x'', union(y, union(union(union(y'''''', z''''''), z''''0), z'''))) -> MEM(x'', union(union(union(y'''''', z''''''), z''''0), z'''))
MEM(x''', union(y, union(union(y''''0, z''''0), union(union(y'''''', z''''''), z'''0)))) -> MEM(x''', union(union(y''''0, z''''0), union(union(y'''''', z''''''), z'''0)))
MEM(x''', union(y, union(union(y''0'', union(y'''''', z'''''')), z'''))) -> MEM(x''', union(union(y''0'', union(y'''''', z'''''')), z'''))
MEM(x''', union(y, union(union(union(y'''''', z''''''), z''0''), z'''))) -> MEM(x''', union(union(union(y'''''', z''''''), z''0''), z'''))
MEM(x'''', union(y, union(y''', union(union(y'''''', z''''''), z'''')))) -> MEM(x'''', union(y''', union(union(y'''''', z''''''), z'''')))
MEM(x'''', union(y, union(y''0, union(y'''', z'''')))) -> MEM(x'''', union(y''0, union(y'''', z'''')))
MEM(x'''', union(union(y''', union(union(y'''''', z''''''), z'''')), z)) -> MEM(x'''', union(y''', union(union(y'''''', z''''''), z'''')))
MEM(x'''', union(union(y''0, union(y'''', z'''')), z)) -> MEM(x'''', union(y''0, union(y'''', z'''')))
MEM(x'''', union(union(union(y'''', z''''), z''0), z)) -> MEM(x'''', union(union(y'''', z''''), z''0))
MEM(x''', union(y, union(union(y''''', union(union(y'''''''', z''''''''), z'''''')), z'''))) -> MEM(x''', union(union(y''''', union(union(y'''''''', z''''''''), z'''''')), z'''))
or(true, y) -> true
or(x, true) -> true
or(false, false) -> false
mem(x, nil) -> false
mem(x, set(y)) -> =(x, y)
mem(x, union(y, z)) -> or(mem(x, y), mem(x, z))
innermost
MEM(x'', union(y, union(union(y''''', z''''0), union(union(y''''''', union(union(y'''''''''', z''''''''''), z'''''''')), z'''''')))) -> MEM(x'', union(union(y''''', z''''0), union(union(y''''''', union(union(y'''''''''', z''''''''''), z'''''''')), z'''''')))
MEM(x'', union(y, union(union(y''''', z''''0), union(union(y''0'''', union(y'''''''', z'''''''')), z'''''')))) -> MEM(x'', union(union(y''''', z''''0), union(union(y''0'''', union(y'''''''', z'''''''')), z'''''')))
MEM(x'', union(y, union(union(y''''', z''''0), union(union(union(y'''''''', z''''''''), z''0''''), z'''''')))) -> MEM(x'', union(union(y''''', z''''0), union(union(union(y'''''''', z''''''''), z''0''''), z'''''')))
MEM(x'', union(y, union(union(y''''0, z''''0), union(y'''''', union(union(y'''''''', z''''''''), z''''''))))) -> MEM(x'', union(union(y''''0, z''''0), union(y'''''', union(union(y'''''''', z''''''''), z''''''))))
MEM(x'', union(y, union(union(y''''0, z''''0), union(y''0'', union(y'''''', z''''''))))) -> MEM(x'', union(union(y''''0, z''''0), union(y''0'', union(y'''''', z''''''))))
MEM(x'', union(y, union(union(y'''''', union(union(y'''''''', z''''''''), z'''''')), z'''))) -> MEM(x'', union(union(y'''''', union(union(y'''''''', z''''''''), z'''''')), z'''))
MEM(x'', union(y, union(union(y''''0, union(y'''''', z'''''')), z'''))) -> MEM(x'', union(union(y''''0, union(y'''''', z'''''')), z'''))
MEM(x'', union(y, union(union(union(y'''''', z''''''), z''''0), z'''))) -> MEM(x'', union(union(union(y'''''', z''''''), z''''0), z'''))
MEM(x''', union(y, union(union(y''''0, z''''0), union(union(y'''''', z''''''), z'''0)))) -> MEM(x''', union(union(y''''0, z''''0), union(union(y'''''', z''''''), z'''0)))
MEM(x''', union(y, union(union(y''0'', union(y'''''', z'''''')), z'''))) -> MEM(x''', union(union(y''0'', union(y'''''', z'''''')), z'''))
MEM(x''', union(y, union(union(union(y'''''', z''''''), z''0''), z'''))) -> MEM(x''', union(union(union(y'''''', z''''''), z''0''), z'''))
MEM(x'''', union(y, union(y''', union(union(y'''''', z''''''), z'''')))) -> MEM(x'''', union(y''', union(union(y'''''', z''''''), z'''')))
MEM(x'''', union(y, union(y''0, union(y'''', z'''')))) -> MEM(x'''', union(y''0, union(y'''', z'''')))
MEM(x'''', union(union(y''', union(union(y'''''', z''''''), z'''')), z)) -> MEM(x'''', union(y''', union(union(y'''''', z''''''), z'''')))
MEM(x'''', union(union(y''0, union(y'''', z'''')), z)) -> MEM(x'''', union(y''0, union(y'''', z'''')))
MEM(x'''', union(union(union(y'''', z''''), z''0), z)) -> MEM(x'''', union(union(y'''', z''''), z''0))
MEM(x''', union(y, union(union(y''''', union(union(y'''''''', z''''''''), z'''''')), z'''))) -> MEM(x''', union(union(y''''', union(union(y'''''''', z''''''''), z'''''')), z'''))
MEM(x1, x2) -> MEM(x1, x2)
union(x1, x2) -> union(x1, x2)
R
↳DPs
→DP Problem 1
↳FwdInst
→DP Problem 2
↳FwdInst
...
→DP Problem 7
↳Dependency Graph
or(true, y) -> true
or(x, true) -> true
or(false, false) -> false
mem(x, nil) -> false
mem(x, set(y)) -> =(x, y)
mem(x, union(y, z)) -> or(mem(x, y), mem(x, z))
innermost