/export/starexec/sandbox/solver/bin/starexec_run_default /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES Problem 1: (VAR v_NonEmpty:S x:S y:S) (RULES *(p(x:S),y:S) -> +(*(x:S,y:S),minus(y:S)) *(s(x:S),y:S) -> +(*(x:S,y:S),y:S) *(0,y:S) -> 0 +(p(x:S),y:S) -> p(+(x:S,y:S)) +(s(x:S),y:S) -> s(+(x:S,y:S)) +(0,y:S) -> y:S minus(p(x:S)) -> s(minus(x:S)) minus(s(x:S)) -> p(minus(x:S)) minus(0) -> 0 p(s(x:S)) -> x:S s(p(x:S)) -> x:S ) Problem 1: Dependency Pairs Processor: -> Pairs: *#(p(x:S),y:S) -> *#(x:S,y:S) *#(p(x:S),y:S) -> +#(*(x:S,y:S),minus(y:S)) *#(p(x:S),y:S) -> MINUS(y:S) *#(s(x:S),y:S) -> *#(x:S,y:S) *#(s(x:S),y:S) -> +#(*(x:S,y:S),y:S) +#(p(x:S),y:S) -> +#(x:S,y:S) +#(p(x:S),y:S) -> P(+(x:S,y:S)) +#(s(x:S),y:S) -> +#(x:S,y:S) +#(s(x:S),y:S) -> S(+(x:S,y:S)) MINUS(p(x:S)) -> MINUS(x:S) MINUS(p(x:S)) -> S(minus(x:S)) MINUS(s(x:S)) -> MINUS(x:S) MINUS(s(x:S)) -> P(minus(x:S)) -> Rules: *(p(x:S),y:S) -> +(*(x:S,y:S),minus(y:S)) *(s(x:S),y:S) -> +(*(x:S,y:S),y:S) *(0,y:S) -> 0 +(p(x:S),y:S) -> p(+(x:S,y:S)) +(s(x:S),y:S) -> s(+(x:S,y:S)) +(0,y:S) -> y:S minus(p(x:S)) -> s(minus(x:S)) minus(s(x:S)) -> p(minus(x:S)) minus(0) -> 0 p(s(x:S)) -> x:S s(p(x:S)) -> x:S Problem 1: SCC Processor: -> Pairs: *#(p(x:S),y:S) -> *#(x:S,y:S) *#(p(x:S),y:S) -> +#(*(x:S,y:S),minus(y:S)) *#(p(x:S),y:S) -> MINUS(y:S) *#(s(x:S),y:S) -> *#(x:S,y:S) *#(s(x:S),y:S) -> +#(*(x:S,y:S),y:S) +#(p(x:S),y:S) -> +#(x:S,y:S) +#(p(x:S),y:S) -> P(+(x:S,y:S)) +#(s(x:S),y:S) -> +#(x:S,y:S) +#(s(x:S),y:S) -> S(+(x:S,y:S)) MINUS(p(x:S)) -> MINUS(x:S) MINUS(p(x:S)) -> S(minus(x:S)) MINUS(s(x:S)) -> MINUS(x:S) MINUS(s(x:S)) -> P(minus(x:S)) -> Rules: *(p(x:S),y:S) -> +(*(x:S,y:S),minus(y:S)) *(s(x:S),y:S) -> +(*(x:S,y:S),y:S) *(0,y:S) -> 0 +(p(x:S),y:S) -> p(+(x:S,y:S)) +(s(x:S),y:S) -> s(+(x:S,y:S)) +(0,y:S) -> y:S minus(p(x:S)) -> s(minus(x:S)) minus(s(x:S)) -> p(minus(x:S)) minus(0) -> 0 p(s(x:S)) -> x:S s(p(x:S)) -> x:S ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: MINUS(p(x:S)) -> MINUS(x:S) MINUS(s(x:S)) -> MINUS(x:S) ->->-> Rules: *(p(x:S),y:S) -> +(*(x:S,y:S),minus(y:S)) *(s(x:S),y:S) -> +(*(x:S,y:S),y:S) *(0,y:S) -> 0 +(p(x:S),y:S) -> p(+(x:S,y:S)) +(s(x:S),y:S) -> s(+(x:S,y:S)) +(0,y:S) -> y:S minus(p(x:S)) -> s(minus(x:S)) minus(s(x:S)) -> p(minus(x:S)) minus(0) -> 0 p(s(x:S)) -> x:S s(p(x:S)) -> x:S ->->Cycle: ->->-> Pairs: +#(p(x:S),y:S) -> +#(x:S,y:S) +#(s(x:S),y:S) -> +#(x:S,y:S) ->->-> Rules: *(p(x:S),y:S) -> +(*(x:S,y:S),minus(y:S)) *(s(x:S),y:S) -> +(*(x:S,y:S),y:S) *(0,y:S) -> 0 +(p(x:S),y:S) -> p(+(x:S,y:S)) +(s(x:S),y:S) -> s(+(x:S,y:S)) +(0,y:S) -> y:S minus(p(x:S)) -> s(minus(x:S)) minus(s(x:S)) -> p(minus(x:S)) minus(0) -> 0 p(s(x:S)) -> x:S s(p(x:S)) -> x:S ->->Cycle: ->->-> Pairs: *#(p(x:S),y:S) -> *#(x:S,y:S) *#(s(x:S),y:S) -> *#(x:S,y:S) ->->-> Rules: *(p(x:S),y:S) -> +(*(x:S,y:S),minus(y:S)) *(s(x:S),y:S) -> +(*(x:S,y:S),y:S) *(0,y:S) -> 0 +(p(x:S),y:S) -> p(+(x:S,y:S)) +(s(x:S),y:S) -> s(+(x:S,y:S)) +(0,y:S) -> y:S minus(p(x:S)) -> s(minus(x:S)) minus(s(x:S)) -> p(minus(x:S)) minus(0) -> 0 p(s(x:S)) -> x:S s(p(x:S)) -> x:S The problem is decomposed in 3 subproblems. Problem 1.1: Subterm Processor: -> Pairs: MINUS(p(x:S)) -> MINUS(x:S) MINUS(s(x:S)) -> MINUS(x:S) -> Rules: *(p(x:S),y:S) -> +(*(x:S,y:S),minus(y:S)) *(s(x:S),y:S) -> +(*(x:S,y:S),y:S) *(0,y:S) -> 0 +(p(x:S),y:S) -> p(+(x:S,y:S)) +(s(x:S),y:S) -> s(+(x:S,y:S)) +(0,y:S) -> y:S minus(p(x:S)) -> s(minus(x:S)) minus(s(x:S)) -> p(minus(x:S)) minus(0) -> 0 p(s(x:S)) -> x:S s(p(x:S)) -> x:S ->Projection: pi(MINUS) = 1 Problem 1.1: SCC Processor: -> Pairs: Empty -> Rules: *(p(x:S),y:S) -> +(*(x:S,y:S),minus(y:S)) *(s(x:S),y:S) -> +(*(x:S,y:S),y:S) *(0,y:S) -> 0 +(p(x:S),y:S) -> p(+(x:S,y:S)) +(s(x:S),y:S) -> s(+(x:S,y:S)) +(0,y:S) -> y:S minus(p(x:S)) -> s(minus(x:S)) minus(s(x:S)) -> p(minus(x:S)) minus(0) -> 0 p(s(x:S)) -> x:S s(p(x:S)) -> x:S ->Strongly Connected Components: There is no strongly connected component The problem is finite. Problem 1.2: Subterm Processor: -> Pairs: +#(p(x:S),y:S) -> +#(x:S,y:S) +#(s(x:S),y:S) -> +#(x:S,y:S) -> Rules: *(p(x:S),y:S) -> +(*(x:S,y:S),minus(y:S)) *(s(x:S),y:S) -> +(*(x:S,y:S),y:S) *(0,y:S) -> 0 +(p(x:S),y:S) -> p(+(x:S,y:S)) +(s(x:S),y:S) -> s(+(x:S,y:S)) +(0,y:S) -> y:S minus(p(x:S)) -> s(minus(x:S)) minus(s(x:S)) -> p(minus(x:S)) minus(0) -> 0 p(s(x:S)) -> x:S s(p(x:S)) -> x:S ->Projection: pi(+#) = 1 Problem 1.2: SCC Processor: -> Pairs: Empty -> Rules: *(p(x:S),y:S) -> +(*(x:S,y:S),minus(y:S)) *(s(x:S),y:S) -> +(*(x:S,y:S),y:S) *(0,y:S) -> 0 +(p(x:S),y:S) -> p(+(x:S,y:S)) +(s(x:S),y:S) -> s(+(x:S,y:S)) +(0,y:S) -> y:S minus(p(x:S)) -> s(minus(x:S)) minus(s(x:S)) -> p(minus(x:S)) minus(0) -> 0 p(s(x:S)) -> x:S s(p(x:S)) -> x:S ->Strongly Connected Components: There is no strongly connected component The problem is finite. Problem 1.3: Subterm Processor: -> Pairs: *#(p(x:S),y:S) -> *#(x:S,y:S) *#(s(x:S),y:S) -> *#(x:S,y:S) -> Rules: *(p(x:S),y:S) -> +(*(x:S,y:S),minus(y:S)) *(s(x:S),y:S) -> +(*(x:S,y:S),y:S) *(0,y:S) -> 0 +(p(x:S),y:S) -> p(+(x:S,y:S)) +(s(x:S),y:S) -> s(+(x:S,y:S)) +(0,y:S) -> y:S minus(p(x:S)) -> s(minus(x:S)) minus(s(x:S)) -> p(minus(x:S)) minus(0) -> 0 p(s(x:S)) -> x:S s(p(x:S)) -> x:S ->Projection: pi(*#) = 1 Problem 1.3: SCC Processor: -> Pairs: Empty -> Rules: *(p(x:S),y:S) -> +(*(x:S,y:S),minus(y:S)) *(s(x:S),y:S) -> +(*(x:S,y:S),y:S) *(0,y:S) -> 0 +(p(x:S),y:S) -> p(+(x:S,y:S)) +(s(x:S),y:S) -> s(+(x:S,y:S)) +(0,y:S) -> y:S minus(p(x:S)) -> s(minus(x:S)) minus(s(x:S)) -> p(minus(x:S)) minus(0) -> 0 p(s(x:S)) -> x:S s(p(x:S)) -> x:S ->Strongly Connected Components: There is no strongly connected component The problem is finite.