/export/starexec/sandbox/solver/bin/starexec_run_default /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files


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YES

Problem 1: 

(VAR x y)
(RULES
+(s(x),y) -> s(+(x,y))
+(x,0) -> x
+(x,s(y)) -> s(+(x,y))
not(false) -> true
not(true) -> false
odd(0) -> false
odd(s(x)) -> not(odd(x))
)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 +#(s(x),y) -> +#(x,y)
 +#(x,s(y)) -> +#(x,y)
 ODD(s(x)) -> NOT(odd(x))
 ODD(s(x)) -> ODD(x)
-> Rules:
 +(s(x),y) -> s(+(x,y))
 +(x,0) -> x
 +(x,s(y)) -> s(+(x,y))
 not(false) -> true
 not(true) -> false
 odd(0) -> false
 odd(s(x)) -> not(odd(x))

Problem 1: 

SCC Processor:
-> Pairs:
 +#(s(x),y) -> +#(x,y)
 +#(x,s(y)) -> +#(x,y)
 ODD(s(x)) -> NOT(odd(x))
 ODD(s(x)) -> ODD(x)
-> Rules:
 +(s(x),y) -> s(+(x,y))
 +(x,0) -> x
 +(x,s(y)) -> s(+(x,y))
 not(false) -> true
 not(true) -> false
 odd(0) -> false
 odd(s(x)) -> not(odd(x))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 ODD(s(x)) -> ODD(x)
->->-> Rules:
 +(s(x),y) -> s(+(x,y))
 +(x,0) -> x
 +(x,s(y)) -> s(+(x,y))
 not(false) -> true
 not(true) -> false
 odd(0) -> false
 odd(s(x)) -> not(odd(x))
->->Cycle:
->->-> Pairs:
 +#(s(x),y) -> +#(x,y)
 +#(x,s(y)) -> +#(x,y)
->->-> Rules:
 +(s(x),y) -> s(+(x,y))
 +(x,0) -> x
 +(x,s(y)) -> s(+(x,y))
 not(false) -> true
 not(true) -> false
 odd(0) -> false
 odd(s(x)) -> not(odd(x))


The problem is decomposed in 2 subproblems.

Problem 1.1: 

Subterm Processor:
-> Pairs:
 ODD(s(x)) -> ODD(x)
-> Rules:
 +(s(x),y) -> s(+(x,y))
 +(x,0) -> x
 +(x,s(y)) -> s(+(x,y))
 not(false) -> true
 not(true) -> false
 odd(0) -> false
 odd(s(x)) -> not(odd(x))
->Projection:
 pi(ODD) = 1

Problem 1.1: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 +(s(x),y) -> s(+(x,y))
 +(x,0) -> x
 +(x,s(y)) -> s(+(x,y))
 not(false) -> true
 not(true) -> false
 odd(0) -> false
 odd(s(x)) -> not(odd(x))
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.

Problem 1.2: 

Subterm Processor:
-> Pairs:
 +#(s(x),y) -> +#(x,y)
 +#(x,s(y)) -> +#(x,y)
-> Rules:
 +(s(x),y) -> s(+(x,y))
 +(x,0) -> x
 +(x,s(y)) -> s(+(x,y))
 not(false) -> true
 not(true) -> false
 odd(0) -> false
 odd(s(x)) -> not(odd(x))
->Projection:
 pi(+#) = 1

Problem 1.2: 

SCC Processor:
-> Pairs:
 +#(x,s(y)) -> +#(x,y)
-> Rules:
 +(s(x),y) -> s(+(x,y))
 +(x,0) -> x
 +(x,s(y)) -> s(+(x,y))
 not(false) -> true
 not(true) -> false
 odd(0) -> false
 odd(s(x)) -> not(odd(x))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 +#(x,s(y)) -> +#(x,y)
->->-> Rules:
 +(s(x),y) -> s(+(x,y))
 +(x,0) -> x
 +(x,s(y)) -> s(+(x,y))
 not(false) -> true
 not(true) -> false
 odd(0) -> false
 odd(s(x)) -> not(odd(x))

Problem 1.2: 

Subterm Processor:
-> Pairs:
 +#(x,s(y)) -> +#(x,y)
-> Rules:
 +(s(x),y) -> s(+(x,y))
 +(x,0) -> x
 +(x,s(y)) -> s(+(x,y))
 not(false) -> true
 not(true) -> false
 odd(0) -> false
 odd(s(x)) -> not(odd(x))
->Projection:
 pi(+#) = 2

Problem 1.2: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 +(s(x),y) -> s(+(x,y))
 +(x,0) -> x
 +(x,s(y)) -> s(+(x,y))
 not(false) -> true
 not(true) -> false
 odd(0) -> false
 odd(s(x)) -> not(odd(x))
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.