YES Problem 1: (VAR v_NonEmpty:S x:S y:S) (RULES minus(minus(x:S)) -> x:S minus(f(x:S,y:S)) -> f(minus(y:S),minus(x:S)) minus(h(x:S)) -> h(minus(x:S)) ) Problem 1: Dependency Pairs Processor: -> Pairs: MINUS(f(x:S,y:S)) -> MINUS(x:S) MINUS(f(x:S,y:S)) -> MINUS(y:S) MINUS(h(x:S)) -> MINUS(x:S) -> Rules: minus(minus(x:S)) -> x:S minus(f(x:S,y:S)) -> f(minus(y:S),minus(x:S)) minus(h(x:S)) -> h(minus(x:S)) Problem 1: SCC Processor: -> Pairs: MINUS(f(x:S,y:S)) -> MINUS(x:S) MINUS(f(x:S,y:S)) -> MINUS(y:S) MINUS(h(x:S)) -> MINUS(x:S) -> Rules: minus(minus(x:S)) -> x:S minus(f(x:S,y:S)) -> f(minus(y:S),minus(x:S)) minus(h(x:S)) -> h(minus(x:S)) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: MINUS(f(x:S,y:S)) -> MINUS(x:S) MINUS(f(x:S,y:S)) -> MINUS(y:S) MINUS(h(x:S)) -> MINUS(x:S) ->->-> Rules: minus(minus(x:S)) -> x:S minus(f(x:S,y:S)) -> f(minus(y:S),minus(x:S)) minus(h(x:S)) -> h(minus(x:S)) Problem 1: Subterm Processor: -> Pairs: MINUS(f(x:S,y:S)) -> MINUS(x:S) MINUS(f(x:S,y:S)) -> MINUS(y:S) MINUS(h(x:S)) -> MINUS(x:S) -> Rules: minus(minus(x:S)) -> x:S minus(f(x:S,y:S)) -> f(minus(y:S),minus(x:S)) minus(h(x:S)) -> h(minus(x:S)) ->Projection: pi(MINUS) = 1 Problem 1: SCC Processor: -> Pairs: Empty -> Rules: minus(minus(x:S)) -> x:S minus(f(x:S,y:S)) -> f(minus(y:S),minus(x:S)) minus(h(x:S)) -> h(minus(x:S)) ->Strongly Connected Components: There is no strongly connected component The problem is finite.