/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
.(.(x,y),z) -> .(x,.(y,z))
.(i(x),x) -> 1
.(i(y),.(y,z)) -> z
.(1,x) -> x
.(x,i(x)) -> 1
.(x,1) -> x
.(y,.(i(y),z)) -> z
i(.(x,y)) -> .(i(y),i(x))
i(i(x)) -> x
i(1) -> 1
)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 .#(.(x,y),z) -> .#(x,.(y,z))
 .#(.(x,y),z) -> .#(y,z)
 I(.(x,y)) -> .#(i(y),i(x))
 I(.(x,y)) -> I(x)
 I(.(x,y)) -> I(y)
-> Rules:
 .(.(x,y),z) -> .(x,.(y,z))
 .(i(x),x) -> 1
 .(i(y),.(y,z)) -> z
 .(1,x) -> x
 .(x,i(x)) -> 1
 .(x,1) -> x
 .(y,.(i(y),z)) -> z
 i(.(x,y)) -> .(i(y),i(x))
 i(i(x)) -> x
 i(1) -> 1

Problem 1: 

SCC Processor:
-> Pairs:
 .#(.(x,y),z) -> .#(x,.(y,z))
 .#(.(x,y),z) -> .#(y,z)
 I(.(x,y)) -> .#(i(y),i(x))
 I(.(x,y)) -> I(x)
 I(.(x,y)) -> I(y)
-> Rules:
 .(.(x,y),z) -> .(x,.(y,z))
 .(i(x),x) -> 1
 .(i(y),.(y,z)) -> z
 .(1,x) -> x
 .(x,i(x)) -> 1
 .(x,1) -> x
 .(y,.(i(y),z)) -> z
 i(.(x,y)) -> .(i(y),i(x))
 i(i(x)) -> x
 i(1) -> 1
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 .#(.(x,y),z) -> .#(x,.(y,z))
 .#(.(x,y),z) -> .#(y,z)
->->-> Rules:
 .(.(x,y),z) -> .(x,.(y,z))
 .(i(x),x) -> 1
 .(i(y),.(y,z)) -> z
 .(1,x) -> x
 .(x,i(x)) -> 1
 .(x,1) -> x
 .(y,.(i(y),z)) -> z
 i(.(x,y)) -> .(i(y),i(x))
 i(i(x)) -> x
 i(1) -> 1
->->Cycle:
->->-> Pairs:
 I(.(x,y)) -> I(x)
 I(.(x,y)) -> I(y)
->->-> Rules:
 .(.(x,y),z) -> .(x,.(y,z))
 .(i(x),x) -> 1
 .(i(y),.(y,z)) -> z
 .(1,x) -> x
 .(x,i(x)) -> 1
 .(x,1) -> x
 .(y,.(i(y),z)) -> z
 i(.(x,y)) -> .(i(y),i(x))
 i(i(x)) -> x
 i(1) -> 1


The problem is decomposed in 2 subproblems.

Problem 1.1: 

Subterm Processor:
-> Pairs:
 .#(.(x,y),z) -> .#(x,.(y,z))
 .#(.(x,y),z) -> .#(y,z)
-> Rules:
 .(.(x,y),z) -> .(x,.(y,z))
 .(i(x),x) -> 1
 .(i(y),.(y,z)) -> z
 .(1,x) -> x
 .(x,i(x)) -> 1
 .(x,1) -> x
 .(y,.(i(y),z)) -> z
 i(.(x,y)) -> .(i(y),i(x))
 i(i(x)) -> x
 i(1) -> 1
->Projection:
 pi(.#) = 1

Problem 1.1: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 .(.(x,y),z) -> .(x,.(y,z))
 .(i(x),x) -> 1
 .(i(y),.(y,z)) -> z
 .(1,x) -> x
 .(x,i(x)) -> 1
 .(x,1) -> x
 .(y,.(i(y),z)) -> z
 i(.(x,y)) -> .(i(y),i(x))
 i(i(x)) -> x
 i(1) -> 1
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.

Problem 1.2: 

Subterm Processor:
-> Pairs:
 I(.(x,y)) -> I(x)
 I(.(x,y)) -> I(y)
-> Rules:
 .(.(x,y),z) -> .(x,.(y,z))
 .(i(x),x) -> 1
 .(i(y),.(y,z)) -> z
 .(1,x) -> x
 .(x,i(x)) -> 1
 .(x,1) -> x
 .(y,.(i(y),z)) -> z
 i(.(x,y)) -> .(i(y),i(x))
 i(i(x)) -> x
 i(1) -> 1
->Projection:
 pi(I) = 1

Problem 1.2: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 .(.(x,y),z) -> .(x,.(y,z))
 .(i(x),x) -> 1
 .(i(y),.(y,z)) -> z
 .(1,x) -> x
 .(x,i(x)) -> 1
 .(x,1) -> x
 .(y,.(i(y),z)) -> z
 i(.(x,y)) -> .(i(y),i(x))
 i(i(x)) -> x
 i(1) -> 1
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.