/export/starexec/sandbox2/solver/bin/starexec_run_default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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YES

Problem 1: 

(VAR x y z)
(RULES
-(s(x),s(y)) -> -(x,y)
-(x,0) -> x
double(0) -> 0
double(s(x)) -> s(s(double(x)))
half(double(x)) -> x
half(0) -> 0
half(s(0)) -> 0
half(s(s(x))) -> s(half(x))
if(0,y,z) -> y
if(s(x),y,z) -> z
)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 -#(s(x),s(y)) -> -#(x,y)
 DOUBLE(s(x)) -> DOUBLE(x)
 HALF(s(s(x))) -> HALF(x)
-> Rules:
 -(s(x),s(y)) -> -(x,y)
 -(x,0) -> x
 double(0) -> 0
 double(s(x)) -> s(s(double(x)))
 half(double(x)) -> x
 half(0) -> 0
 half(s(0)) -> 0
 half(s(s(x))) -> s(half(x))
 if(0,y,z) -> y
 if(s(x),y,z) -> z

Problem 1: 

SCC Processor:
-> Pairs:
 -#(s(x),s(y)) -> -#(x,y)
 DOUBLE(s(x)) -> DOUBLE(x)
 HALF(s(s(x))) -> HALF(x)
-> Rules:
 -(s(x),s(y)) -> -(x,y)
 -(x,0) -> x
 double(0) -> 0
 double(s(x)) -> s(s(double(x)))
 half(double(x)) -> x
 half(0) -> 0
 half(s(0)) -> 0
 half(s(s(x))) -> s(half(x))
 if(0,y,z) -> y
 if(s(x),y,z) -> z
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 HALF(s(s(x))) -> HALF(x)
->->-> Rules:
 -(s(x),s(y)) -> -(x,y)
 -(x,0) -> x
 double(0) -> 0
 double(s(x)) -> s(s(double(x)))
 half(double(x)) -> x
 half(0) -> 0
 half(s(0)) -> 0
 half(s(s(x))) -> s(half(x))
 if(0,y,z) -> y
 if(s(x),y,z) -> z
->->Cycle:
->->-> Pairs:
 DOUBLE(s(x)) -> DOUBLE(x)
->->-> Rules:
 -(s(x),s(y)) -> -(x,y)
 -(x,0) -> x
 double(0) -> 0
 double(s(x)) -> s(s(double(x)))
 half(double(x)) -> x
 half(0) -> 0
 half(s(0)) -> 0
 half(s(s(x))) -> s(half(x))
 if(0,y,z) -> y
 if(s(x),y,z) -> z
->->Cycle:
->->-> Pairs:
 -#(s(x),s(y)) -> -#(x,y)
->->-> Rules:
 -(s(x),s(y)) -> -(x,y)
 -(x,0) -> x
 double(0) -> 0
 double(s(x)) -> s(s(double(x)))
 half(double(x)) -> x
 half(0) -> 0
 half(s(0)) -> 0
 half(s(s(x))) -> s(half(x))
 if(0,y,z) -> y
 if(s(x),y,z) -> z


The problem is decomposed in 3 subproblems.

Problem 1.1: 

Subterm Processor:
-> Pairs:
 HALF(s(s(x))) -> HALF(x)
-> Rules:
 -(s(x),s(y)) -> -(x,y)
 -(x,0) -> x
 double(0) -> 0
 double(s(x)) -> s(s(double(x)))
 half(double(x)) -> x
 half(0) -> 0
 half(s(0)) -> 0
 half(s(s(x))) -> s(half(x))
 if(0,y,z) -> y
 if(s(x),y,z) -> z
->Projection:
 pi(HALF) = 1

Problem 1.1: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 -(s(x),s(y)) -> -(x,y)
 -(x,0) -> x
 double(0) -> 0
 double(s(x)) -> s(s(double(x)))
 half(double(x)) -> x
 half(0) -> 0
 half(s(0)) -> 0
 half(s(s(x))) -> s(half(x))
 if(0,y,z) -> y
 if(s(x),y,z) -> z
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.

Problem 1.2: 

Subterm Processor:
-> Pairs:
 DOUBLE(s(x)) -> DOUBLE(x)
-> Rules:
 -(s(x),s(y)) -> -(x,y)
 -(x,0) -> x
 double(0) -> 0
 double(s(x)) -> s(s(double(x)))
 half(double(x)) -> x
 half(0) -> 0
 half(s(0)) -> 0
 half(s(s(x))) -> s(half(x))
 if(0,y,z) -> y
 if(s(x),y,z) -> z
->Projection:
 pi(DOUBLE) = 1

Problem 1.2: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 -(s(x),s(y)) -> -(x,y)
 -(x,0) -> x
 double(0) -> 0
 double(s(x)) -> s(s(double(x)))
 half(double(x)) -> x
 half(0) -> 0
 half(s(0)) -> 0
 half(s(s(x))) -> s(half(x))
 if(0,y,z) -> y
 if(s(x),y,z) -> z
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.

Problem 1.3: 

Subterm Processor:
-> Pairs:
 -#(s(x),s(y)) -> -#(x,y)
-> Rules:
 -(s(x),s(y)) -> -(x,y)
 -(x,0) -> x
 double(0) -> 0
 double(s(x)) -> s(s(double(x)))
 half(double(x)) -> x
 half(0) -> 0
 half(s(0)) -> 0
 half(s(s(x))) -> s(half(x))
 if(0,y,z) -> y
 if(s(x),y,z) -> z
->Projection:
 pi(-#) = 1

Problem 1.3: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 -(s(x),s(y)) -> -(x,y)
 -(x,0) -> x
 double(0) -> 0
 double(s(x)) -> s(s(double(x)))
 half(double(x)) -> x
 half(0) -> 0
 half(s(0)) -> 0
 half(s(s(x))) -> s(half(x))
 if(0,y,z) -> y
 if(s(x),y,z) -> z
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.