NO LCTRS Theories Core, Ints Sorts Unit Signature fastfib: Int -> Unit return: Int -> Unit u: (Int, Int, Int, Int, Int) -> Unit v: (Int, Int, Int, Int, Int) -> Unit Rules fastfib(?64) -> u(?64, 1, 0, 0, ?65) u(?66, ?67, ?68, ?69, ?70) -> return(0) [<=(?66, 0)] u(?71, ?72, ?73, ?74, ?75) -> return(1) [and(not(<=(?71, 0)), ?71 = 1)] u(?76, ?77, ?78, ?79, ?80) -> v(?76, ?77, ?78, ?79, 2) [and(not(<=(?76, 0)), not(?76 = 1))] v(?81, ?82, ?83, ?84, ?85) -> v(?81, +(?82, ?83), ?82, +(?82, ?83), +(?85, 1)) [<=(?85, ?81)] v(?86, ?87, ?88, ?89, ?90) -> return(?89) [and(not(<=(?90, ?86)), not(<(?89, 0)))] v(?91, ?92, ?93, ?94, ?95) -> return(-1) [and(not(<=(?95, ?91)), <(?94, 0))] Not confluent by "two different NFs found" with proof: * Critical Pair Inner Rule fastfib(?64') -> u(?64', 1, 0, 0, ?65') Outer Rule fastfib(?64") -> u(?64", 1, 0, 0, ?65") Pair u(?64", 1, 0, 0, ?65') ≈ u(?64", 1, 0, 0, ?65") [=(?65', ?65'), =(?65", ?65")] reaches the non-trivial normal form u(?64", 1, 0, 0, ?65') ≈ u(?64", 1, 0, 0, ?65") [?65' = ?65', ?65" = ?65"] Elapsed Time: 98.76 ms