Term Rewriting System R:
[x]
+(p1, p1) -> p2
+(p1, +(p2, p2)) -> p5
+(p5, p5) -> p10
+(+(x, y), z) -> +(x, +(y, z))
+(p1, +(p1, x)) -> +(p2, x)
+(p1, +(p2, +(p2, x))) -> +(p5, x)
+(p2, p1) -> +(p1, p2)
+(p2, +(p1, x)) -> +(p1, +(p2, x))
+(p2, +(p2, p2)) -> +(p1, p5)
+(p2, +(p2, +(p2, x))) -> +(p1, +(p5, x))
+(p5, p1) -> +(p1, p5)
+(p5, +(p1, x)) -> +(p1, +(p5, x))
+(p5, p2) -> +(p2, p5)
+(p5, +(p2, x)) -> +(p2, +(p5, x))
+(p5, +(p5, x)) -> +(p10, x)
+(p10, p1) -> +(p1, p10)
+(p10, +(p1, x)) -> +(p1, +(p10, x))
+(p10, p2) -> +(p2, p10)
+(p10, +(p2, x)) -> +(p2, +(p10, x))
+(p10, p5) -> +(p5, p10)
+(p10, +(p5, x)) -> +(p5, +(p10, x))

Termination of R to be shown. 



   R
     ↳Dependency Pair Analysis



R contains the following Dependency Pairs:

+'(+(x, y), z) -> +'(x, +(y, z))
+'(+(x, y), z) -> +'(y, z)
+'(p1, +(p1, x)) -> +'(p2, x)
+'(p1, +(p2, +(p2, x))) -> +'(p5, x)
+'(p2, p1) -> +'(p1, p2)
+'(p2, +(p1, x)) -> +'(p1, +(p2, x))
+'(p2, +(p1, x)) -> +'(p2, x)
+'(p2, +(p2, p2)) -> +'(p1, p5)
+'(p2, +(p2, +(p2, x))) -> +'(p1, +(p5, x))
+'(p2, +(p2, +(p2, x))) -> +'(p5, x)
+'(p5, p1) -> +'(p1, p5)
+'(p5, +(p1, x)) -> +'(p1, +(p5, x))
+'(p5, +(p1, x)) -> +'(p5, x)
+'(p5, p2) -> +'(p2, p5)
+'(p5, +(p2, x)) -> +'(p2, +(p5, x))
+'(p5, +(p2, x)) -> +'(p5, x)
+'(p5, +(p5, x)) -> +'(p10, x)
+'(p10, p1) -> +'(p1, p10)
+'(p10, +(p1, x)) -> +'(p1, +(p10, x))
+'(p10, +(p1, x)) -> +'(p10, x)
+'(p10, p2) -> +'(p2, p10)
+'(p10, +(p2, x)) -> +'(p2, +(p10, x))
+'(p10, +(p2, x)) -> +'(p10, x)
+'(p10, p5) -> +'(p5, p10)
+'(p10, +(p5, x)) -> +'(p5, +(p10, x))
+'(p10, +(p5, x)) -> +'(p10, x)

Furthermore, R contains two SCCs. 


   R
     ↳DPs
       →DP Problem 1
         ↳Narrowing Transformation
       →DP Problem 2
         ↳Remaining


Dependency Pairs:

+'(p10, +(p5, x)) -> +'(p10, x)
+'(p10, +(p5, x)) -> +'(p5, +(p10, x))
+'(p10, +(p2, x)) -> +'(p10, x)
+'(p10, +(p2, x)) -> +'(p2, +(p10, x))
+'(p10, +(p1, x)) -> +'(p10, x)
+'(p10, +(p1, x)) -> +'(p1, +(p10, x))
+'(p5, +(p5, x)) -> +'(p10, x)
+'(p5, +(p2, x)) -> +'(p5, x)
+'(p2, +(p2, +(p2, x))) -> +'(p5, x)
+'(p2, +(p2, +(p2, x))) -> +'(p1, +(p5, x))
+'(p2, +(p1, x)) -> +'(p2, x)
+'(p5, +(p2, x)) -> +'(p2, +(p5, x))
+'(p5, +(p1, x)) -> +'(p5, x)
+'(p5, +(p1, x)) -> +'(p1, +(p5, x))
+'(p1, +(p2, +(p2, x))) -> +'(p5, x)
+'(p2, +(p1, x)) -> +'(p1, +(p2, x))
+'(p1, +(p1, x)) -> +'(p2, x)


Rules:


+(p1, p1) -> p2
+(p1, +(p2, p2)) -> p5
+(p5, p5) -> p10
+(+(x, y), z) -> +(x, +(y, z))
+(p1, +(p1, x)) -> +(p2, x)
+(p1, +(p2, +(p2, x))) -> +(p5, x)
+(p2, p1) -> +(p1, p2)
+(p2, +(p1, x)) -> +(p1, +(p2, x))
+(p2, +(p2, p2)) -> +(p1, p5)
+(p2, +(p2, +(p2, x))) -> +(p1, +(p5, x))
+(p5, p1) -> +(p1, p5)
+(p5, +(p1, x)) -> +(p1, +(p5, x))
+(p5, p2) -> +(p2, p5)
+(p5, +(p2, x)) -> +(p2, +(p5, x))
+(p5, +(p5, x)) -> +(p10, x)
+(p10, p1) -> +(p1, p10)
+(p10, +(p1, x)) -> +(p1, +(p10, x))
+(p10, p2) -> +(p2, p10)
+(p10, +(p2, x)) -> +(p2, +(p10, x))
+(p10, p5) -> +(p5, p10)
+(p10, +(p5, x)) -> +(p5, +(p10, x))





On this DP problem, a Narrowing SCC transformation can be performed.
As a result of transforming the rule

+'(p2, +(p2, +(p2, x))) -> +'(p1, +(p5, x))
six new Dependency Pairs are created:

+'(p2, +(p2, +(p2, p5))) -> +'(p1, p10)
+'(p2, +(p2, +(p2, p1))) -> +'(p1, +(p1, p5))
+'(p2, +(p2, +(p2, +(p1, x'')))) -> +'(p1, +(p1, +(p5, x'')))
+'(p2, +(p2, +(p2, p2))) -> +'(p1, +(p2, p5))
+'(p2, +(p2, +(p2, +(p2, x'')))) -> +'(p1, +(p2, +(p5, x'')))
+'(p2, +(p2, +(p2, +(p5, x'')))) -> +'(p1, +(p10, x''))

The transformation is resulting in one new DP problem: 



   R
     ↳DPs
       →DP Problem 1
         ↳Nar
           →DP Problem 3
             ↳Narrowing Transformation
       →DP Problem 2
         ↳Remaining


Dependency Pairs:

+'(p10, +(p5, x)) -> +'(p5, +(p10, x))
+'(p10, +(p2, x)) -> +'(p10, x)
+'(p2, +(p2, +(p2, +(p5, x'')))) -> +'(p1, +(p10, x''))
+'(p2, +(p2, +(p2, +(p2, x'')))) -> +'(p1, +(p2, +(p5, x'')))
+'(p2, +(p2, +(p2, p2))) -> +'(p1, +(p2, p5))
+'(p2, +(p2, +(p2, +(p1, x'')))) -> +'(p1, +(p1, +(p5, x'')))
+'(p2, +(p2, +(p2, p1))) -> +'(p1, +(p1, p5))
+'(p10, +(p2, x)) -> +'(p2, +(p10, x))
+'(p10, +(p1, x)) -> +'(p10, x)
+'(p5, +(p5, x)) -> +'(p10, x)
+'(p5, +(p2, x)) -> +'(p5, x)
+'(p2, +(p2, +(p2, x))) -> +'(p5, x)
+'(p2, +(p1, x)) -> +'(p2, x)
+'(p5, +(p2, x)) -> +'(p2, +(p5, x))
+'(p5, +(p1, x)) -> +'(p5, x)
+'(p5, +(p1, x)) -> +'(p1, +(p5, x))
+'(p1, +(p2, +(p2, x))) -> +'(p5, x)
+'(p2, +(p1, x)) -> +'(p1, +(p2, x))
+'(p1, +(p1, x)) -> +'(p2, x)
+'(p10, +(p1, x)) -> +'(p1, +(p10, x))
+'(p10, +(p5, x)) -> +'(p10, x)


Rules:


+(p1, p1) -> p2
+(p1, +(p2, p2)) -> p5
+(p5, p5) -> p10
+(+(x, y), z) -> +(x, +(y, z))
+(p1, +(p1, x)) -> +(p2, x)
+(p1, +(p2, +(p2, x))) -> +(p5, x)
+(p2, p1) -> +(p1, p2)
+(p2, +(p1, x)) -> +(p1, +(p2, x))
+(p2, +(p2, p2)) -> +(p1, p5)
+(p2, +(p2, +(p2, x))) -> +(p1, +(p5, x))
+(p5, p1) -> +(p1, p5)
+(p5, +(p1, x)) -> +(p1, +(p5, x))
+(p5, p2) -> +(p2, p5)
+(p5, +(p2, x)) -> +(p2, +(p5, x))
+(p5, +(p5, x)) -> +(p10, x)
+(p10, p1) -> +(p1, p10)
+(p10, +(p1, x)) -> +(p1, +(p10, x))
+(p10, p2) -> +(p2, p10)
+(p10, +(p2, x)) -> +(p2, +(p10, x))
+(p10, p5) -> +(p5, p10)
+(p10, +(p5, x)) -> +(p5, +(p10, x))





On this DP problem, a Narrowing SCC transformation can be performed.
As a result of transforming the rule

+'(p5, +(p1, x)) -> +'(p1, +(p5, x))
six new Dependency Pairs are created:

+'(p5, +(p1, p5)) -> +'(p1, p10)
+'(p5, +(p1, p1)) -> +'(p1, +(p1, p5))
+'(p5, +(p1, +(p1, x''))) -> +'(p1, +(p1, +(p5, x'')))
+'(p5, +(p1, p2)) -> +'(p1, +(p2, p5))
+'(p5, +(p1, +(p2, x''))) -> +'(p1, +(p2, +(p5, x'')))
+'(p5, +(p1, +(p5, x''))) -> +'(p1, +(p10, x''))

The transformation is resulting in one new DP problem: 



   R
     ↳DPs
       →DP Problem 1
         ↳Nar
           →DP Problem 3
             ↳Nar
             ...
               →DP Problem 4
                 ↳Narrowing Transformation
       →DP Problem 2
         ↳Remaining


Dependency Pairs:

+'(p10, +(p5, x)) -> +'(p10, x)
+'(p10, +(p2, x)) -> +'(p10, x)
+'(p2, +(p2, +(p2, +(p5, x'')))) -> +'(p1, +(p10, x''))
+'(p2, +(p2, +(p2, +(p2, x'')))) -> +'(p1, +(p2, +(p5, x'')))
+'(p2, +(p2, +(p2, p2))) -> +'(p1, +(p2, p5))
+'(p2, +(p2, +(p2, +(p1, x'')))) -> +'(p1, +(p1, +(p5, x'')))
+'(p2, +(p2, +(p2, p1))) -> +'(p1, +(p1, p5))
+'(p10, +(p2, x)) -> +'(p2, +(p10, x))
+'(p10, +(p1, x)) -> +'(p10, x)
+'(p5, +(p1, +(p5, x''))) -> +'(p1, +(p10, x''))
+'(p5, +(p1, +(p2, x''))) -> +'(p1, +(p2, +(p5, x'')))
+'(p5, +(p1, p2)) -> +'(p1, +(p2, p5))
+'(p5, +(p1, +(p1, x''))) -> +'(p1, +(p1, +(p5, x'')))
+'(p5, +(p1, p1)) -> +'(p1, +(p1, p5))
+'(p1, +(p2, +(p2, x))) -> +'(p5, x)
+'(p10, +(p1, x)) -> +'(p1, +(p10, x))
+'(p5, +(p5, x)) -> +'(p10, x)
+'(p5, +(p2, x)) -> +'(p5, x)
+'(p2, +(p2, +(p2, x))) -> +'(p5, x)
+'(p2, +(p1, x)) -> +'(p2, x)
+'(p1, +(p1, x)) -> +'(p2, x)
+'(p2, +(p1, x)) -> +'(p1, +(p2, x))
+'(p5, +(p2, x)) -> +'(p2, +(p5, x))
+'(p5, +(p1, x)) -> +'(p5, x)
+'(p10, +(p5, x)) -> +'(p5, +(p10, x))


Rules:


+(p1, p1) -> p2
+(p1, +(p2, p2)) -> p5
+(p5, p5) -> p10
+(+(x, y), z) -> +(x, +(y, z))
+(p1, +(p1, x)) -> +(p2, x)
+(p1, +(p2, +(p2, x))) -> +(p5, x)
+(p2, p1) -> +(p1, p2)
+(p2, +(p1, x)) -> +(p1, +(p2, x))
+(p2, +(p2, p2)) -> +(p1, p5)
+(p2, +(p2, +(p2, x))) -> +(p1, +(p5, x))
+(p5, p1) -> +(p1, p5)
+(p5, +(p1, x)) -> +(p1, +(p5, x))
+(p5, p2) -> +(p2, p5)
+(p5, +(p2, x)) -> +(p2, +(p5, x))
+(p5, +(p5, x)) -> +(p10, x)
+(p10, p1) -> +(p1, p10)
+(p10, +(p1, x)) -> +(p1, +(p10, x))
+(p10, p2) -> +(p2, p10)
+(p10, +(p2, x)) -> +(p2, +(p10, x))
+(p10, p5) -> +(p5, p10)
+(p10, +(p5, x)) -> +(p5, +(p10, x))





On this DP problem, a Narrowing SCC transformation can be performed.
As a result of transforming the rule

+'(p5, +(p2, x)) -> +'(p2, +(p5, x))
six new Dependency Pairs are created:

+'(p5, +(p2, p5)) -> +'(p2, p10)
+'(p5, +(p2, p1)) -> +'(p2, +(p1, p5))
+'(p5, +(p2, +(p1, x''))) -> +'(p2, +(p1, +(p5, x'')))
+'(p5, +(p2, p2)) -> +'(p2, +(p2, p5))
+'(p5, +(p2, +(p2, x''))) -> +'(p2, +(p2, +(p5, x'')))
+'(p5, +(p2, +(p5, x''))) -> +'(p2, +(p10, x''))

The transformation is resulting in one new DP problem: 



   R
     ↳DPs
       →DP Problem 1
         ↳Nar
           →DP Problem 3
             ↳Nar
             ...
               →DP Problem 5
                 ↳Narrowing Transformation
       →DP Problem 2
         ↳Remaining


Dependency Pairs:

+'(p10, +(p5, x)) -> +'(p5, +(p10, x))
+'(p10, +(p2, x)) -> +'(p10, x)
+'(p5, +(p2, +(p5, x''))) -> +'(p2, +(p10, x''))
+'(p5, +(p2, +(p2, x''))) -> +'(p2, +(p2, +(p5, x'')))
+'(p5, +(p2, p2)) -> +'(p2, +(p2, p5))
+'(p5, +(p2, +(p1, x''))) -> +'(p2, +(p1, +(p5, x'')))
+'(p2, +(p2, +(p2, +(p5, x'')))) -> +'(p1, +(p10, x''))
+'(p2, +(p2, +(p2, +(p2, x'')))) -> +'(p1, +(p2, +(p5, x'')))
+'(p2, +(p2, +(p2, p2))) -> +'(p1, +(p2, p5))
+'(p2, +(p2, +(p2, +(p1, x'')))) -> +'(p1, +(p1, +(p5, x'')))
+'(p2, +(p2, +(p2, p1))) -> +'(p1, +(p1, p5))
+'(p5, +(p2, p1)) -> +'(p2, +(p1, p5))
+'(p5, +(p1, +(p5, x''))) -> +'(p1, +(p10, x''))
+'(p5, +(p1, +(p2, x''))) -> +'(p1, +(p2, +(p5, x'')))
+'(p5, +(p1, p2)) -> +'(p1, +(p2, p5))
+'(p5, +(p1, +(p1, x''))) -> +'(p1, +(p1, +(p5, x'')))
+'(p5, +(p1, p1)) -> +'(p1, +(p1, p5))
+'(p2, +(p2, +(p2, x))) -> +'(p5, x)
+'(p2, +(p1, x)) -> +'(p2, x)
+'(p10, +(p2, x)) -> +'(p2, +(p10, x))
+'(p10, +(p1, x)) -> +'(p10, x)
+'(p5, +(p5, x)) -> +'(p10, x)
+'(p5, +(p2, x)) -> +'(p5, x)
+'(p5, +(p1, x)) -> +'(p5, x)
+'(p1, +(p2, +(p2, x))) -> +'(p5, x)
+'(p2, +(p1, x)) -> +'(p1, +(p2, x))
+'(p1, +(p1, x)) -> +'(p2, x)
+'(p10, +(p1, x)) -> +'(p1, +(p10, x))
+'(p10, +(p5, x)) -> +'(p10, x)


Rules:


+(p1, p1) -> p2
+(p1, +(p2, p2)) -> p5
+(p5, p5) -> p10
+(+(x, y), z) -> +(x, +(y, z))
+(p1, +(p1, x)) -> +(p2, x)
+(p1, +(p2, +(p2, x))) -> +(p5, x)
+(p2, p1) -> +(p1, p2)
+(p2, +(p1, x)) -> +(p1, +(p2, x))
+(p2, +(p2, p2)) -> +(p1, p5)
+(p2, +(p2, +(p2, x))) -> +(p1, +(p5, x))
+(p5, p1) -> +(p1, p5)
+(p5, +(p1, x)) -> +(p1, +(p5, x))
+(p5, p2) -> +(p2, p5)
+(p5, +(p2, x)) -> +(p2, +(p5, x))
+(p5, +(p5, x)) -> +(p10, x)
+(p10, p1) -> +(p1, p10)
+(p10, +(p1, x)) -> +(p1, +(p10, x))
+(p10, p2) -> +(p2, p10)
+(p10, +(p2, x)) -> +(p2, +(p10, x))
+(p10, p5) -> +(p5, p10)
+(p10, +(p5, x)) -> +(p5, +(p10, x))





On this DP problem, a Narrowing SCC transformation can be performed.
As a result of transforming the rule

+'(p10, +(p1, x)) -> +'(p1, +(p10, x))
six new Dependency Pairs are created:

+'(p10, +(p1, p1)) -> +'(p1, +(p1, p10))
+'(p10, +(p1, +(p1, x''))) -> +'(p1, +(p1, +(p10, x'')))
+'(p10, +(p1, p2)) -> +'(p1, +(p2, p10))
+'(p10, +(p1, +(p2, x''))) -> +'(p1, +(p2, +(p10, x'')))
+'(p10, +(p1, p5)) -> +'(p1, +(p5, p10))
+'(p10, +(p1, +(p5, x''))) -> +'(p1, +(p5, +(p10, x'')))

The transformation is resulting in one new DP problem: 



   R
     ↳DPs
       →DP Problem 1
         ↳Nar
           →DP Problem 3
             ↳Nar
             ...
               →DP Problem 6
                 ↳Narrowing Transformation
       →DP Problem 2
         ↳Remaining


Dependency Pairs:

+'(p10, +(p1, +(p5, x''))) -> +'(p1, +(p5, +(p10, x'')))
+'(p10, +(p1, p5)) -> +'(p1, +(p5, p10))
+'(p10, +(p1, +(p2, x''))) -> +'(p1, +(p2, +(p10, x'')))
+'(p10, +(p1, p2)) -> +'(p1, +(p2, p10))
+'(p10, +(p1, +(p1, x''))) -> +'(p1, +(p1, +(p10, x'')))
+'(p10, +(p1, p1)) -> +'(p1, +(p1, p10))
+'(p10, +(p5, x)) -> +'(p10, x)
+'(p10, +(p2, x)) -> +'(p10, x)
+'(p5, +(p2, +(p5, x''))) -> +'(p2, +(p10, x''))
+'(p5, +(p2, +(p2, x''))) -> +'(p2, +(p2, +(p5, x'')))
+'(p5, +(p2, p2)) -> +'(p2, +(p2, p5))
+'(p5, +(p2, +(p1, x''))) -> +'(p2, +(p1, +(p5, x'')))
+'(p2, +(p2, +(p2, +(p5, x'')))) -> +'(p1, +(p10, x''))
+'(p2, +(p2, +(p2, +(p2, x'')))) -> +'(p1, +(p2, +(p5, x'')))
+'(p2, +(p2, +(p2, p2))) -> +'(p1, +(p2, p5))
+'(p2, +(p2, +(p2, +(p1, x'')))) -> +'(p1, +(p1, +(p5, x'')))
+'(p2, +(p2, +(p2, p1))) -> +'(p1, +(p1, p5))
+'(p5, +(p2, p1)) -> +'(p2, +(p1, p5))
+'(p5, +(p1, +(p5, x''))) -> +'(p1, +(p10, x''))
+'(p5, +(p1, +(p2, x''))) -> +'(p1, +(p2, +(p5, x'')))
+'(p5, +(p1, p2)) -> +'(p1, +(p2, p5))
+'(p5, +(p1, +(p1, x''))) -> +'(p1, +(p1, +(p5, x'')))
+'(p1, +(p2, +(p2, x))) -> +'(p5, x)
+'(p5, +(p1, p1)) -> +'(p1, +(p1, p5))
+'(p2, +(p2, +(p2, x))) -> +'(p5, x)
+'(p2, +(p1, x)) -> +'(p2, x)
+'(p1, +(p1, x)) -> +'(p2, x)
+'(p2, +(p1, x)) -> +'(p1, +(p2, x))
+'(p10, +(p2, x)) -> +'(p2, +(p10, x))
+'(p10, +(p1, x)) -> +'(p10, x)
+'(p5, +(p5, x)) -> +'(p10, x)
+'(p5, +(p2, x)) -> +'(p5, x)
+'(p5, +(p1, x)) -> +'(p5, x)
+'(p10, +(p5, x)) -> +'(p5, +(p10, x))


Rules:


+(p1, p1) -> p2
+(p1, +(p2, p2)) -> p5
+(p5, p5) -> p10
+(+(x, y), z) -> +(x, +(y, z))
+(p1, +(p1, x)) -> +(p2, x)
+(p1, +(p2, +(p2, x))) -> +(p5, x)
+(p2, p1) -> +(p1, p2)
+(p2, +(p1, x)) -> +(p1, +(p2, x))
+(p2, +(p2, p2)) -> +(p1, p5)
+(p2, +(p2, +(p2, x))) -> +(p1, +(p5, x))
+(p5, p1) -> +(p1, p5)
+(p5, +(p1, x)) -> +(p1, +(p5, x))
+(p5, p2) -> +(p2, p5)
+(p5, +(p2, x)) -> +(p2, +(p5, x))
+(p5, +(p5, x)) -> +(p10, x)
+(p10, p1) -> +(p1, p10)
+(p10, +(p1, x)) -> +(p1, +(p10, x))
+(p10, p2) -> +(p2, p10)
+(p10, +(p2, x)) -> +(p2, +(p10, x))
+(p10, p5) -> +(p5, p10)
+(p10, +(p5, x)) -> +(p5, +(p10, x))





On this DP problem, a Narrowing SCC transformation can be performed.
As a result of transforming the rule

+'(p10, +(p2, x)) -> +'(p2, +(p10, x))
six new Dependency Pairs are created:

+'(p10, +(p2, p1)) -> +'(p2, +(p1, p10))
+'(p10, +(p2, +(p1, x''))) -> +'(p2, +(p1, +(p10, x'')))
+'(p10, +(p2, p2)) -> +'(p2, +(p2, p10))
+'(p10, +(p2, +(p2, x''))) -> +'(p2, +(p2, +(p10, x'')))
+'(p10, +(p2, p5)) -> +'(p2, +(p5, p10))
+'(p10, +(p2, +(p5, x''))) -> +'(p2, +(p5, +(p10, x'')))

The transformation is resulting in one new DP problem: 



   R
     ↳DPs
       →DP Problem 1
         ↳Nar
           →DP Problem 3
             ↳Nar
             ...
               →DP Problem 7
                 ↳Narrowing Transformation
       →DP Problem 2
         ↳Remaining


Dependency Pairs:

+'(p10, +(p2, +(p5, x''))) -> +'(p2, +(p5, +(p10, x'')))
+'(p10, +(p2, p5)) -> +'(p2, +(p5, p10))
+'(p10, +(p2, +(p2, x''))) -> +'(p2, +(p2, +(p10, x'')))
+'(p10, +(p2, p2)) -> +'(p2, +(p2, p10))
+'(p10, +(p2, +(p1, x''))) -> +'(p2, +(p1, +(p10, x'')))
+'(p10, +(p2, p1)) -> +'(p2, +(p1, p10))
+'(p10, +(p1, p5)) -> +'(p1, +(p5, p10))
+'(p10, +(p1, +(p2, x''))) -> +'(p1, +(p2, +(p10, x'')))
+'(p10, +(p1, p2)) -> +'(p1, +(p2, p10))
+'(p10, +(p1, +(p1, x''))) -> +'(p1, +(p1, +(p10, x'')))
+'(p10, +(p1, p1)) -> +'(p1, +(p1, p10))
+'(p10, +(p5, x)) -> +'(p10, x)
+'(p5, +(p2, +(p5, x''))) -> +'(p2, +(p10, x''))
+'(p5, +(p2, +(p2, x''))) -> +'(p2, +(p2, +(p5, x'')))
+'(p5, +(p2, p2)) -> +'(p2, +(p2, p5))
+'(p2, +(p2, +(p2, +(p5, x'')))) -> +'(p1, +(p10, x''))
+'(p2, +(p2, +(p2, +(p2, x'')))) -> +'(p1, +(p2, +(p5, x'')))
+'(p2, +(p2, +(p2, p2))) -> +'(p1, +(p2, p5))
+'(p2, +(p2, +(p2, +(p1, x'')))) -> +'(p1, +(p1, +(p5, x'')))
+'(p2, +(p2, +(p2, p1))) -> +'(p1, +(p1, p5))
+'(p5, +(p2, +(p1, x''))) -> +'(p2, +(p1, +(p5, x'')))
+'(p2, +(p2, +(p2, x))) -> +'(p5, x)
+'(p2, +(p1, x)) -> +'(p2, x)
+'(p5, +(p2, p1)) -> +'(p2, +(p1, p5))
+'(p5, +(p1, +(p5, x''))) -> +'(p1, +(p10, x''))
+'(p5, +(p1, +(p2, x''))) -> +'(p1, +(p2, +(p5, x'')))
+'(p5, +(p1, p2)) -> +'(p1, +(p2, p5))
+'(p5, +(p1, +(p1, x''))) -> +'(p1, +(p1, +(p5, x'')))
+'(p5, +(p1, p1)) -> +'(p1, +(p1, p5))
+'(p10, +(p5, x)) -> +'(p5, +(p10, x))
+'(p10, +(p2, x)) -> +'(p10, x)
+'(p10, +(p1, x)) -> +'(p10, x)
+'(p5, +(p5, x)) -> +'(p10, x)
+'(p5, +(p2, x)) -> +'(p5, x)
+'(p5, +(p1, x)) -> +'(p5, x)
+'(p1, +(p2, +(p2, x))) -> +'(p5, x)
+'(p2, +(p1, x)) -> +'(p1, +(p2, x))
+'(p1, +(p1, x)) -> +'(p2, x)
+'(p10, +(p1, +(p5, x''))) -> +'(p1, +(p5, +(p10, x'')))


Rules:


+(p1, p1) -> p2
+(p1, +(p2, p2)) -> p5
+(p5, p5) -> p10
+(+(x, y), z) -> +(x, +(y, z))
+(p1, +(p1, x)) -> +(p2, x)
+(p1, +(p2, +(p2, x))) -> +(p5, x)
+(p2, p1) -> +(p1, p2)
+(p2, +(p1, x)) -> +(p1, +(p2, x))
+(p2, +(p2, p2)) -> +(p1, p5)
+(p2, +(p2, +(p2, x))) -> +(p1, +(p5, x))
+(p5, p1) -> +(p1, p5)
+(p5, +(p1, x)) -> +(p1, +(p5, x))
+(p5, p2) -> +(p2, p5)
+(p5, +(p2, x)) -> +(p2, +(p5, x))
+(p5, +(p5, x)) -> +(p10, x)
+(p10, p1) -> +(p1, p10)
+(p10, +(p1, x)) -> +(p1, +(p10, x))
+(p10, p2) -> +(p2, p10)
+(p10, +(p2, x)) -> +(p2, +(p10, x))
+(p10, p5) -> +(p5, p10)
+(p10, +(p5, x)) -> +(p5, +(p10, x))





On this DP problem, a Narrowing SCC transformation can be performed.
As a result of transforming the rule

+'(p10, +(p5, x)) -> +'(p5, +(p10, x))
six new Dependency Pairs are created:

+'(p10, +(p5, p1)) -> +'(p5, +(p1, p10))
+'(p10, +(p5, +(p1, x''))) -> +'(p5, +(p1, +(p10, x'')))
+'(p10, +(p5, p2)) -> +'(p5, +(p2, p10))
+'(p10, +(p5, +(p2, x''))) -> +'(p5, +(p2, +(p10, x'')))
+'(p10, +(p5, p5)) -> +'(p5, +(p5, p10))
+'(p10, +(p5, +(p5, x''))) -> +'(p5, +(p5, +(p10, x'')))

The transformation is resulting in one new DP problem: 



   R
     ↳DPs
       →DP Problem 1
         ↳Nar
           →DP Problem 3
             ↳Nar
             ...
               →DP Problem 8
                 ↳Narrowing Transformation
       →DP Problem 2
         ↳Remaining


Dependency Pairs:

+'(p10, +(p5, +(p5, x''))) -> +'(p5, +(p5, +(p10, x'')))
+'(p10, +(p5, p5)) -> +'(p5, +(p5, p10))
+'(p10, +(p5, +(p2, x''))) -> +'(p5, +(p2, +(p10, x'')))
+'(p10, +(p5, p2)) -> +'(p5, +(p2, p10))
+'(p10, +(p5, +(p1, x''))) -> +'(p5, +(p1, +(p10, x'')))
+'(p10, +(p5, p1)) -> +'(p5, +(p1, p10))
+'(p10, +(p2, p5)) -> +'(p2, +(p5, p10))
+'(p10, +(p2, +(p2, x''))) -> +'(p2, +(p2, +(p10, x'')))
+'(p10, +(p2, p2)) -> +'(p2, +(p2, p10))
+'(p10, +(p2, +(p1, x''))) -> +'(p2, +(p1, +(p10, x'')))
+'(p10, +(p2, p1)) -> +'(p2, +(p1, p10))
+'(p10, +(p1, +(p5, x''))) -> +'(p1, +(p5, +(p10, x'')))
+'(p10, +(p1, p5)) -> +'(p1, +(p5, p10))
+'(p10, +(p1, +(p2, x''))) -> +'(p1, +(p2, +(p10, x'')))
+'(p10, +(p1, p2)) -> +'(p1, +(p2, p10))
+'(p10, +(p1, +(p1, x''))) -> +'(p1, +(p1, +(p10, x'')))
+'(p5, +(p2, +(p5, x''))) -> +'(p2, +(p10, x''))
+'(p5, +(p2, +(p2, x''))) -> +'(p2, +(p2, +(p5, x'')))
+'(p5, +(p2, p2)) -> +'(p2, +(p2, p5))
+'(p5, +(p2, +(p1, x''))) -> +'(p2, +(p1, +(p5, x'')))
+'(p2, +(p2, +(p2, +(p5, x'')))) -> +'(p1, +(p10, x''))
+'(p2, +(p2, +(p2, +(p2, x'')))) -> +'(p1, +(p2, +(p5, x'')))
+'(p2, +(p2, +(p2, p2))) -> +'(p1, +(p2, p5))
+'(p2, +(p2, +(p2, +(p1, x'')))) -> +'(p1, +(p1, +(p5, x'')))
+'(p2, +(p2, +(p2, p1))) -> +'(p1, +(p1, p5))
+'(p5, +(p2, p1)) -> +'(p2, +(p1, p5))
+'(p5, +(p1, +(p5, x''))) -> +'(p1, +(p10, x''))
+'(p5, +(p1, +(p2, x''))) -> +'(p1, +(p2, +(p5, x'')))
+'(p5, +(p1, p2)) -> +'(p1, +(p2, p5))
+'(p5, +(p1, +(p1, x''))) -> +'(p1, +(p1, +(p5, x'')))
+'(p5, +(p1, p1)) -> +'(p1, +(p1, p5))
+'(p1, +(p2, +(p2, x))) -> +'(p5, x)
+'(p10, +(p1, p1)) -> +'(p1, +(p1, p10))
+'(p10, +(p5, x)) -> +'(p10, x)
+'(p10, +(p2, x)) -> +'(p10, x)
+'(p10, +(p1, x)) -> +'(p10, x)
+'(p5, +(p5, x)) -> +'(p10, x)
+'(p5, +(p2, x)) -> +'(p5, x)
+'(p5, +(p1, x)) -> +'(p5, x)
+'(p2, +(p2, +(p2, x))) -> +'(p5, x)
+'(p2, +(p1, x)) -> +'(p2, x)
+'(p1, +(p1, x)) -> +'(p2, x)
+'(p2, +(p1, x)) -> +'(p1, +(p2, x))
+'(p10, +(p2, +(p5, x''))) -> +'(p2, +(p5, +(p10, x'')))


Rules:


+(p1, p1) -> p2
+(p1, +(p2, p2)) -> p5
+(p5, p5) -> p10
+(+(x, y), z) -> +(x, +(y, z))
+(p1, +(p1, x)) -> +(p2, x)
+(p1, +(p2, +(p2, x))) -> +(p5, x)
+(p2, p1) -> +(p1, p2)
+(p2, +(p1, x)) -> +(p1, +(p2, x))
+(p2, +(p2, p2)) -> +(p1, p5)
+(p2, +(p2, +(p2, x))) -> +(p1, +(p5, x))
+(p5, p1) -> +(p1, p5)
+(p5, +(p1, x)) -> +(p1, +(p5, x))
+(p5, p2) -> +(p2, p5)
+(p5, +(p2, x)) -> +(p2, +(p5, x))
+(p5, +(p5, x)) -> +(p10, x)
+(p10, p1) -> +(p1, p10)
+(p10, +(p1, x)) -> +(p1, +(p10, x))
+(p10, p2) -> +(p2, p10)
+(p10, +(p2, x)) -> +(p2, +(p10, x))
+(p10, p5) -> +(p5, p10)
+(p10, +(p5, x)) -> +(p5, +(p10, x))





On this DP problem, a Narrowing SCC transformation can be performed.
As a result of transforming the rule

+'(p2, +(p2, +(p2, p2))) -> +'(p1, +(p2, p5))
no new Dependency Pairs are created.
The transformation is resulting in one new DP problem: 



   R
     ↳DPs
       →DP Problem 1
         ↳Nar
           →DP Problem 3
             ↳Nar
             ...
               →DP Problem 9
                 ↳Narrowing Transformation
       →DP Problem 2
         ↳Remaining


Dependency Pairs:

+'(p10, +(p5, p5)) -> +'(p5, +(p5, p10))
+'(p10, +(p5, +(p2, x''))) -> +'(p5, +(p2, +(p10, x'')))
+'(p10, +(p5, p2)) -> +'(p5, +(p2, p10))
+'(p10, +(p5, +(p1, x''))) -> +'(p5, +(p1, +(p10, x'')))
+'(p10, +(p5, p1)) -> +'(p5, +(p1, p10))
+'(p10, +(p2, +(p5, x''))) -> +'(p2, +(p5, +(p10, x'')))
+'(p10, +(p2, p5)) -> +'(p2, +(p5, p10))
+'(p10, +(p2, +(p2, x''))) -> +'(p2, +(p2, +(p10, x'')))
+'(p10, +(p2, p2)) -> +'(p2, +(p2, p10))
+'(p10, +(p2, +(p1, x''))) -> +'(p2, +(p1, +(p10, x'')))
+'(p10, +(p2, p1)) -> +'(p2, +(p1, p10))
+'(p10, +(p1, +(p5, x''))) -> +'(p1, +(p5, +(p10, x'')))
+'(p10, +(p1, p5)) -> +'(p1, +(p5, p10))
+'(p10, +(p1, +(p2, x''))) -> +'(p1, +(p2, +(p10, x'')))
+'(p10, +(p1, p2)) -> +'(p1, +(p2, p10))
+'(p10, +(p1, +(p1, x''))) -> +'(p1, +(p1, +(p10, x'')))
+'(p5, +(p2, +(p5, x''))) -> +'(p2, +(p10, x''))
+'(p5, +(p2, +(p2, x''))) -> +'(p2, +(p2, +(p5, x'')))
+'(p5, +(p2, p2)) -> +'(p2, +(p2, p5))
+'(p2, +(p2, +(p2, +(p5, x'')))) -> +'(p1, +(p10, x''))
+'(p2, +(p2, +(p2, +(p2, x'')))) -> +'(p1, +(p2, +(p5, x'')))
+'(p2, +(p2, +(p2, +(p1, x'')))) -> +'(p1, +(p1, +(p5, x'')))
+'(p2, +(p2, +(p2, p1))) -> +'(p1, +(p1, p5))
+'(p5, +(p2, +(p1, x''))) -> +'(p2, +(p1, +(p5, x'')))
+'(p2, +(p2, +(p2, x))) -> +'(p5, x)
+'(p2, +(p1, x)) -> +'(p2, x)
+'(p5, +(p2, p1)) -> +'(p2, +(p1, p5))
+'(p5, +(p1, +(p5, x''))) -> +'(p1, +(p10, x''))
+'(p5, +(p1, +(p2, x''))) -> +'(p1, +(p2, +(p5, x'')))
+'(p5, +(p1, p2)) -> +'(p1, +(p2, p5))
+'(p5, +(p1, +(p1, x''))) -> +'(p1, +(p1, +(p5, x'')))
+'(p5, +(p1, p1)) -> +'(p1, +(p1, p5))
+'(p1, +(p2, +(p2, x))) -> +'(p5, x)
+'(p2, +(p1, x)) -> +'(p1, +(p2, x))
+'(p1, +(p1, x)) -> +'(p2, x)
+'(p10, +(p1, p1)) -> +'(p1, +(p1, p10))
+'(p10, +(p5, x)) -> +'(p10, x)
+'(p10, +(p2, x)) -> +'(p10, x)
+'(p10, +(p1, x)) -> +'(p10, x)
+'(p5, +(p5, x)) -> +'(p10, x)
+'(p5, +(p2, x)) -> +'(p5, x)
+'(p5, +(p1, x)) -> +'(p5, x)
+'(p10, +(p5, +(p5, x''))) -> +'(p5, +(p5, +(p10, x'')))


Rules:


+(p1, p1) -> p2
+(p1, +(p2, p2)) -> p5
+(p5, p5) -> p10
+(+(x, y), z) -> +(x, +(y, z))
+(p1, +(p1, x)) -> +(p2, x)
+(p1, +(p2, +(p2, x))) -> +(p5, x)
+(p2, p1) -> +(p1, p2)
+(p2, +(p1, x)) -> +(p1, +(p2, x))
+(p2, +(p2, p2)) -> +(p1, p5)
+(p2, +(p2, +(p2, x))) -> +(p1, +(p5, x))
+(p5, p1) -> +(p1, p5)
+(p5, +(p1, x)) -> +(p1, +(p5, x))
+(p5, p2) -> +(p2, p5)
+(p5, +(p2, x)) -> +(p2, +(p5, x))
+(p5, +(p5, x)) -> +(p10, x)
+(p10, p1) -> +(p1, p10)
+(p10, +(p1, x)) -> +(p1, +(p10, x))
+(p10, p2) -> +(p2, p10)
+(p10, +(p2, x)) -> +(p2, +(p10, x))
+(p10, p5) -> +(p5, p10)
+(p10, +(p5, x)) -> +(p5, +(p10, x))





On this DP problem, a Narrowing SCC transformation can be performed.
As a result of transforming the rule

+'(p5, +(p1, p2)) -> +'(p1, +(p2, p5))
no new Dependency Pairs are created.
The transformation is resulting in one new DP problem: 



   R
     ↳DPs
       →DP Problem 1
         ↳Nar
           →DP Problem 3
             ↳Nar
             ...
               →DP Problem 10
                 ↳Narrowing Transformation
       →DP Problem 2
         ↳Remaining


Dependency Pairs:

+'(p10, +(p5, +(p5, x''))) -> +'(p5, +(p5, +(p10, x'')))
+'(p10, +(p5, +(p2, x''))) -> +'(p5, +(p2, +(p10, x'')))
+'(p10, +(p5, p2)) -> +'(p5, +(p2, p10))
+'(p10, +(p5, +(p1, x''))) -> +'(p5, +(p1, +(p10, x'')))
+'(p10, +(p5, p1)) -> +'(p5, +(p1, p10))
+'(p10, +(p2, +(p5, x''))) -> +'(p2, +(p5, +(p10, x'')))
+'(p10, +(p2, p5)) -> +'(p2, +(p5, p10))
+'(p10, +(p2, +(p2, x''))) -> +'(p2, +(p2, +(p10, x'')))
+'(p10, +(p2, p2)) -> +'(p2, +(p2, p10))
+'(p10, +(p2, +(p1, x''))) -> +'(p2, +(p1, +(p10, x'')))
+'(p10, +(p2, p1)) -> +'(p2, +(p1, p10))
+'(p10, +(p1, +(p5, x''))) -> +'(p1, +(p5, +(p10, x'')))
+'(p10, +(p1, p5)) -> +'(p1, +(p5, p10))
+'(p10, +(p1, +(p2, x''))) -> +'(p1, +(p2, +(p10, x'')))
+'(p10, +(p1, p2)) -> +'(p1, +(p2, p10))
+'(p10, +(p1, +(p1, x''))) -> +'(p1, +(p1, +(p10, x'')))
+'(p5, +(p2, +(p5, x''))) -> +'(p2, +(p10, x''))
+'(p5, +(p2, +(p2, x''))) -> +'(p2, +(p2, +(p5, x'')))
+'(p5, +(p2, p2)) -> +'(p2, +(p2, p5))
+'(p2, +(p2, +(p2, +(p5, x'')))) -> +'(p1, +(p10, x''))
+'(p2, +(p2, +(p2, +(p2, x'')))) -> +'(p1, +(p2, +(p5, x'')))
+'(p2, +(p2, +(p2, +(p1, x'')))) -> +'(p1, +(p1, +(p5, x'')))
+'(p2, +(p2, +(p2, p1))) -> +'(p1, +(p1, p5))
+'(p5, +(p2, +(p1, x''))) -> +'(p2, +(p1, +(p5, x'')))
+'(p2, +(p2, +(p2, x))) -> +'(p5, x)
+'(p2, +(p1, x)) -> +'(p2, x)
+'(p5, +(p2, p1)) -> +'(p2, +(p1, p5))
+'(p5, +(p1, +(p5, x''))) -> +'(p1, +(p10, x''))
+'(p5, +(p1, +(p2, x''))) -> +'(p1, +(p2, +(p5, x'')))
+'(p5, +(p1, +(p1, x''))) -> +'(p1, +(p1, +(p5, x'')))
+'(p5, +(p1, p1)) -> +'(p1, +(p1, p5))
+'(p1, +(p2, +(p2, x))) -> +'(p5, x)
+'(p2, +(p1, x)) -> +'(p1, +(p2, x))
+'(p1, +(p1, x)) -> +'(p2, x)
+'(p10, +(p1, p1)) -> +'(p1, +(p1, p10))
+'(p10, +(p5, x)) -> +'(p10, x)
+'(p10, +(p2, x)) -> +'(p10, x)
+'(p10, +(p1, x)) -> +'(p10, x)
+'(p5, +(p5, x)) -> +'(p10, x)
+'(p5, +(p2, x)) -> +'(p5, x)
+'(p5, +(p1, x)) -> +'(p5, x)
+'(p10, +(p5, p5)) -> +'(p5, +(p5, p10))


Rules:


+(p1, p1) -> p2
+(p1, +(p2, p2)) -> p5
+(p5, p5) -> p10
+(+(x, y), z) -> +(x, +(y, z))
+(p1, +(p1, x)) -> +(p2, x)
+(p1, +(p2, +(p2, x))) -> +(p5, x)
+(p2, p1) -> +(p1, p2)
+(p2, +(p1, x)) -> +(p1, +(p2, x))
+(p2, +(p2, p2)) -> +(p1, p5)
+(p2, +(p2, +(p2, x))) -> +(p1, +(p5, x))
+(p5, p1) -> +(p1, p5)
+(p5, +(p1, x)) -> +(p1, +(p5, x))
+(p5, p2) -> +(p2, p5)
+(p5, +(p2, x)) -> +(p2, +(p5, x))
+(p5, +(p5, x)) -> +(p10, x)
+(p10, p1) -> +(p1, p10)
+(p10, +(p1, x)) -> +(p1, +(p10, x))
+(p10, p2) -> +(p2, p10)
+(p10, +(p2, x)) -> +(p2, +(p10, x))
+(p10, p5) -> +(p5, p10)
+(p10, +(p5, x)) -> +(p5, +(p10, x))





On this DP problem, a Narrowing SCC transformation can be performed.
As a result of transforming the rule

+'(p5, +(p2, p2)) -> +'(p2, +(p2, p5))
no new Dependency Pairs are created.
The transformation is resulting in one new DP problem: 



   R
     ↳DPs
       →DP Problem 1
         ↳Nar
           →DP Problem 3
             ↳Nar
             ...
               →DP Problem 11
                 ↳Narrowing Transformation
       →DP Problem 2
         ↳Remaining


Dependency Pairs:

+'(p10, +(p5, p5)) -> +'(p5, +(p5, p10))
+'(p10, +(p5, +(p2, x''))) -> +'(p5, +(p2, +(p10, x'')))
+'(p10, +(p5, p2)) -> +'(p5, +(p2, p10))
+'(p10, +(p5, +(p1, x''))) -> +'(p5, +(p1, +(p10, x'')))
+'(p10, +(p5, p1)) -> +'(p5, +(p1, p10))
+'(p10, +(p2, +(p5, x''))) -> +'(p2, +(p5, +(p10, x'')))
+'(p10, +(p2, p5)) -> +'(p2, +(p5, p10))
+'(p10, +(p2, +(p2, x''))) -> +'(p2, +(p2, +(p10, x'')))
+'(p10, +(p2, p2)) -> +'(p2, +(p2, p10))
+'(p10, +(p2, +(p1, x''))) -> +'(p2, +(p1, +(p10, x'')))
+'(p10, +(p2, p1)) -> +'(p2, +(p1, p10))
+'(p10, +(p1, +(p5, x''))) -> +'(p1, +(p5, +(p10, x'')))
+'(p10, +(p1, p5)) -> +'(p1, +(p5, p10))
+'(p10, +(p1, +(p2, x''))) -> +'(p1, +(p2, +(p10, x'')))
+'(p10, +(p1, p2)) -> +'(p1, +(p2, p10))
+'(p10, +(p1, +(p1, x''))) -> +'(p1, +(p1, +(p10, x'')))
+'(p5, +(p2, +(p5, x''))) -> +'(p2, +(p10, x''))
+'(p5, +(p2, +(p2, x''))) -> +'(p2, +(p2, +(p5, x'')))
+'(p2, +(p2, +(p2, +(p5, x'')))) -> +'(p1, +(p10, x''))
+'(p2, +(p2, +(p2, +(p2, x'')))) -> +'(p1, +(p2, +(p5, x'')))
+'(p2, +(p2, +(p2, +(p1, x'')))) -> +'(p1, +(p1, +(p5, x'')))
+'(p2, +(p2, +(p2, p1))) -> +'(p1, +(p1, p5))
+'(p5, +(p2, +(p1, x''))) -> +'(p2, +(p1, +(p5, x'')))
+'(p2, +(p2, +(p2, x))) -> +'(p5, x)
+'(p2, +(p1, x)) -> +'(p2, x)
+'(p5, +(p2, p1)) -> +'(p2, +(p1, p5))
+'(p5, +(p1, +(p5, x''))) -> +'(p1, +(p10, x''))
+'(p5, +(p1, +(p2, x''))) -> +'(p1, +(p2, +(p5, x'')))
+'(p5, +(p1, +(p1, x''))) -> +'(p1, +(p1, +(p5, x'')))
+'(p5, +(p1, p1)) -> +'(p1, +(p1, p5))
+'(p1, +(p2, +(p2, x))) -> +'(p5, x)
+'(p2, +(p1, x)) -> +'(p1, +(p2, x))
+'(p1, +(p1, x)) -> +'(p2, x)
+'(p10, +(p1, p1)) -> +'(p1, +(p1, p10))
+'(p10, +(p5, x)) -> +'(p10, x)
+'(p10, +(p2, x)) -> +'(p10, x)
+'(p10, +(p1, x)) -> +'(p10, x)
+'(p5, +(p5, x)) -> +'(p10, x)
+'(p5, +(p2, x)) -> +'(p5, x)
+'(p5, +(p1, x)) -> +'(p5, x)
+'(p10, +(p5, +(p5, x''))) -> +'(p5, +(p5, +(p10, x'')))


Rules:


+(p1, p1) -> p2
+(p1, +(p2, p2)) -> p5
+(p5, p5) -> p10
+(+(x, y), z) -> +(x, +(y, z))
+(p1, +(p1, x)) -> +(p2, x)
+(p1, +(p2, +(p2, x))) -> +(p5, x)
+(p2, p1) -> +(p1, p2)
+(p2, +(p1, x)) -> +(p1, +(p2, x))
+(p2, +(p2, p2)) -> +(p1, p5)
+(p2, +(p2, +(p2, x))) -> +(p1, +(p5, x))
+(p5, p1) -> +(p1, p5)
+(p5, +(p1, x)) -> +(p1, +(p5, x))
+(p5, p2) -> +(p2, p5)
+(p5, +(p2, x)) -> +(p2, +(p5, x))
+(p5, +(p5, x)) -> +(p10, x)
+(p10, p1) -> +(p1, p10)
+(p10, +(p1, x)) -> +(p1, +(p10, x))
+(p10, p2) -> +(p2, p10)
+(p10, +(p2, x)) -> +(p2, +(p10, x))
+(p10, p5) -> +(p5, p10)
+(p10, +(p5, x)) -> +(p5, +(p10, x))





On this DP problem, a Narrowing SCC transformation can be performed.
As a result of transforming the rule

+'(p10, +(p1, p2)) -> +'(p1, +(p2, p10))
no new Dependency Pairs are created.
The transformation is resulting in one new DP problem: 



   R
     ↳DPs
       →DP Problem 1
         ↳Nar
           →DP Problem 3
             ↳Nar
             ...
               →DP Problem 12
                 ↳Narrowing Transformation
       →DP Problem 2
         ↳Remaining


Dependency Pairs:

+'(p10, +(p5, +(p5, x''))) -> +'(p5, +(p5, +(p10, x'')))
+'(p10, +(p5, +(p2, x''))) -> +'(p5, +(p2, +(p10, x'')))
+'(p10, +(p5, p2)) -> +'(p5, +(p2, p10))
+'(p10, +(p5, +(p1, x''))) -> +'(p5, +(p1, +(p10, x'')))
+'(p10, +(p5, p1)) -> +'(p5, +(p1, p10))
+'(p10, +(p2, +(p5, x''))) -> +'(p2, +(p5, +(p10, x'')))
+'(p10, +(p2, p5)) -> +'(p2, +(p5, p10))
+'(p10, +(p2, +(p2, x''))) -> +'(p2, +(p2, +(p10, x'')))
+'(p10, +(p2, p2)) -> +'(p2, +(p2, p10))
+'(p10, +(p2, +(p1, x''))) -> +'(p2, +(p1, +(p10, x'')))
+'(p10, +(p2, p1)) -> +'(p2, +(p1, p10))
+'(p10, +(p1, +(p5, x''))) -> +'(p1, +(p5, +(p10, x'')))
+'(p10, +(p1, p5)) -> +'(p1, +(p5, p10))
+'(p10, +(p1, +(p2, x''))) -> +'(p1, +(p2, +(p10, x'')))
+'(p10, +(p1, +(p1, x''))) -> +'(p1, +(p1, +(p10, x'')))
+'(p5, +(p2, +(p5, x''))) -> +'(p2, +(p10, x''))
+'(p5, +(p2, +(p2, x''))) -> +'(p2, +(p2, +(p5, x'')))
+'(p2, +(p2, +(p2, +(p5, x'')))) -> +'(p1, +(p10, x''))
+'(p2, +(p2, +(p2, +(p2, x'')))) -> +'(p1, +(p2, +(p5, x'')))
+'(p2, +(p2, +(p2, +(p1, x'')))) -> +'(p1, +(p1, +(p5, x'')))
+'(p2, +(p2, +(p2, p1))) -> +'(p1, +(p1, p5))
+'(p5, +(p2, +(p1, x''))) -> +'(p2, +(p1, +(p5, x'')))
+'(p2, +(p2, +(p2, x))) -> +'(p5, x)
+'(p2, +(p1, x)) -> +'(p2, x)
+'(p5, +(p2, p1)) -> +'(p2, +(p1, p5))
+'(p5, +(p1, +(p5, x''))) -> +'(p1, +(p10, x''))
+'(p5, +(p1, +(p2, x''))) -> +'(p1, +(p2, +(p5, x'')))
+'(p5, +(p1, +(p1, x''))) -> +'(p1, +(p1, +(p5, x'')))
+'(p5, +(p1, p1)) -> +'(p1, +(p1, p5))
+'(p1, +(p2, +(p2, x))) -> +'(p5, x)
+'(p2, +(p1, x)) -> +'(p1, +(p2, x))
+'(p1, +(p1, x)) -> +'(p2, x)
+'(p10, +(p1, p1)) -> +'(p1, +(p1, p10))
+'(p10, +(p5, x)) -> +'(p10, x)
+'(p10, +(p2, x)) -> +'(p10, x)
+'(p10, +(p1, x)) -> +'(p10, x)
+'(p5, +(p5, x)) -> +'(p10, x)
+'(p5, +(p2, x)) -> +'(p5, x)
+'(p5, +(p1, x)) -> +'(p5, x)
+'(p10, +(p5, p5)) -> +'(p5, +(p5, p10))


Rules:


+(p1, p1) -> p2
+(p1, +(p2, p2)) -> p5
+(p5, p5) -> p10
+(+(x, y), z) -> +(x, +(y, z))
+(p1, +(p1, x)) -> +(p2, x)
+(p1, +(p2, +(p2, x))) -> +(p5, x)
+(p2, p1) -> +(p1, p2)
+(p2, +(p1, x)) -> +(p1, +(p2, x))
+(p2, +(p2, p2)) -> +(p1, p5)
+(p2, +(p2, +(p2, x))) -> +(p1, +(p5, x))
+(p5, p1) -> +(p1, p5)
+(p5, +(p1, x)) -> +(p1, +(p5, x))
+(p5, p2) -> +(p2, p5)
+(p5, +(p2, x)) -> +(p2, +(p5, x))
+(p5, +(p5, x)) -> +(p10, x)
+(p10, p1) -> +(p1, p10)
+(p10, +(p1, x)) -> +(p1, +(p10, x))
+(p10, p2) -> +(p2, p10)
+(p10, +(p2, x)) -> +(p2, +(p10, x))
+(p10, p5) -> +(p5, p10)
+(p10, +(p5, x)) -> +(p5, +(p10, x))





On this DP problem, a Narrowing SCC transformation can be performed.
As a result of transforming the rule

+'(p10, +(p1, p5)) -> +'(p1, +(p5, p10))
no new Dependency Pairs are created.
The transformation is resulting in one new DP problem: 



   R
     ↳DPs
       →DP Problem 1
         ↳Nar
           →DP Problem 3
             ↳Nar
             ...
               →DP Problem 13
                 ↳Narrowing Transformation
       →DP Problem 2
         ↳Remaining


Dependency Pairs:

+'(p10, +(p5, p5)) -> +'(p5, +(p5, p10))
+'(p10, +(p5, +(p2, x''))) -> +'(p5, +(p2, +(p10, x'')))
+'(p10, +(p5, p2)) -> +'(p5, +(p2, p10))
+'(p10, +(p5, +(p1, x''))) -> +'(p5, +(p1, +(p10, x'')))
+'(p10, +(p5, p1)) -> +'(p5, +(p1, p10))
+'(p10, +(p2, +(p5, x''))) -> +'(p2, +(p5, +(p10, x'')))
+'(p10, +(p2, p5)) -> +'(p2, +(p5, p10))
+'(p10, +(p2, +(p2, x''))) -> +'(p2, +(p2, +(p10, x'')))
+'(p10, +(p2, p2)) -> +'(p2, +(p2, p10))
+'(p10, +(p2, +(p1, x''))) -> +'(p2, +(p1, +(p10, x'')))
+'(p10, +(p2, p1)) -> +'(p2, +(p1, p10))
+'(p10, +(p1, +(p5, x''))) -> +'(p1, +(p5, +(p10, x'')))
+'(p10, +(p1, +(p2, x''))) -> +'(p1, +(p2, +(p10, x'')))
+'(p10, +(p1, +(p1, x''))) -> +'(p1, +(p1, +(p10, x'')))
+'(p5, +(p2, +(p5, x''))) -> +'(p2, +(p10, x''))
+'(p5, +(p2, +(p2, x''))) -> +'(p2, +(p2, +(p5, x'')))
+'(p2, +(p2, +(p2, +(p5, x'')))) -> +'(p1, +(p10, x''))
+'(p2, +(p2, +(p2, +(p2, x'')))) -> +'(p1, +(p2, +(p5, x'')))
+'(p2, +(p2, +(p2, +(p1, x'')))) -> +'(p1, +(p1, +(p5, x'')))
+'(p2, +(p2, +(p2, p1))) -> +'(p1, +(p1, p5))
+'(p5, +(p2, +(p1, x''))) -> +'(p2, +(p1, +(p5, x'')))
+'(p2, +(p2, +(p2, x))) -> +'(p5, x)
+'(p2, +(p1, x)) -> +'(p2, x)
+'(p5, +(p2, p1)) -> +'(p2, +(p1, p5))
+'(p5, +(p1, +(p5, x''))) -> +'(p1, +(p10, x''))
+'(p5, +(p1, +(p2, x''))) -> +'(p1, +(p2, +(p5, x'')))
+'(p5, +(p1, +(p1, x''))) -> +'(p1, +(p1, +(p5, x'')))
+'(p5, +(p1, p1)) -> +'(p1, +(p1, p5))
+'(p1, +(p2, +(p2, x))) -> +'(p5, x)
+'(p2, +(p1, x)) -> +'(p1, +(p2, x))
+'(p1, +(p1, x)) -> +'(p2, x)
+'(p10, +(p1, p1)) -> +'(p1, +(p1, p10))
+'(p10, +(p5, x)) -> +'(p10, x)
+'(p10, +(p2, x)) -> +'(p10, x)
+'(p10, +(p1, x)) -> +'(p10, x)
+'(p5, +(p5, x)) -> +'(p10, x)
+'(p5, +(p2, x)) -> +'(p5, x)
+'(p5, +(p1, x)) -> +'(p5, x)
+'(p10, +(p5, +(p5, x''))) -> +'(p5, +(p5, +(p10, x'')))


Rules:


+(p1, p1) -> p2
+(p1, +(p2, p2)) -> p5
+(p5, p5) -> p10
+(+(x, y), z) -> +(x, +(y, z))
+(p1, +(p1, x)) -> +(p2, x)
+(p1, +(p2, +(p2, x))) -> +(p5, x)
+(p2, p1) -> +(p1, p2)
+(p2, +(p1, x)) -> +(p1, +(p2, x))
+(p2, +(p2, p2)) -> +(p1, p5)
+(p2, +(p2, +(p2, x))) -> +(p1, +(p5, x))
+(p5, p1) -> +(p1, p5)
+(p5, +(p1, x)) -> +(p1, +(p5, x))
+(p5, p2) -> +(p2, p5)
+(p5, +(p2, x)) -> +(p2, +(p5, x))
+(p5, +(p5, x)) -> +(p10, x)
+(p10, p1) -> +(p1, p10)
+(p10, +(p1, x)) -> +(p1, +(p10, x))
+(p10, p2) -> +(p2, p10)
+(p10, +(p2, x)) -> +(p2, +(p10, x))
+(p10, p5) -> +(p5, p10)
+(p10, +(p5, x)) -> +(p5, +(p10, x))





On this DP problem, a Narrowing SCC transformation can be performed.
As a result of transforming the rule

+'(p10, +(p2, p2)) -> +'(p2, +(p2, p10))
no new Dependency Pairs are created.
The transformation is resulting in one new DP problem: 



   R
     ↳DPs
       →DP Problem 1
         ↳Nar
           →DP Problem 3
             ↳Nar
             ...
               →DP Problem 14
                 ↳Narrowing Transformation
       →DP Problem 2
         ↳Remaining


Dependency Pairs:

+'(p10, +(p5, +(p5, x''))) -> +'(p5, +(p5, +(p10, x'')))
+'(p10, +(p5, +(p2, x''))) -> +'(p5, +(p2, +(p10, x'')))
+'(p10, +(p5, p2)) -> +'(p5, +(p2, p10))
+'(p10, +(p5, +(p1, x''))) -> +'(p5, +(p1, +(p10, x'')))
+'(p10, +(p5, p1)) -> +'(p5, +(p1, p10))
+'(p10, +(p2, +(p5, x''))) -> +'(p2, +(p5, +(p10, x'')))
+'(p10, +(p2, p5)) -> +'(p2, +(p5, p10))
+'(p10, +(p2, +(p2, x''))) -> +'(p2, +(p2, +(p10, x'')))
+'(p10, +(p2, +(p1, x''))) -> +'(p2, +(p1, +(p10, x'')))
+'(p10, +(p2, p1)) -> +'(p2, +(p1, p10))
+'(p10, +(p1, +(p5, x''))) -> +'(p1, +(p5, +(p10, x'')))
+'(p10, +(p1, +(p2, x''))) -> +'(p1, +(p2, +(p10, x'')))
+'(p10, +(p1, +(p1, x''))) -> +'(p1, +(p1, +(p10, x'')))
+'(p5, +(p2, +(p5, x''))) -> +'(p2, +(p10, x''))
+'(p5, +(p2, +(p2, x''))) -> +'(p2, +(p2, +(p5, x'')))
+'(p2, +(p2, +(p2, +(p5, x'')))) -> +'(p1, +(p10, x''))
+'(p2, +(p2, +(p2, +(p2, x'')))) -> +'(p1, +(p2, +(p5, x'')))
+'(p2, +(p2, +(p2, +(p1, x'')))) -> +'(p1, +(p1, +(p5, x'')))
+'(p2, +(p2, +(p2, p1))) -> +'(p1, +(p1, p5))
+'(p5, +(p2, +(p1, x''))) -> +'(p2, +(p1, +(p5, x'')))
+'(p2, +(p2, +(p2, x))) -> +'(p5, x)
+'(p2, +(p1, x)) -> +'(p2, x)
+'(p5, +(p2, p1)) -> +'(p2, +(p1, p5))
+'(p5, +(p1, +(p5, x''))) -> +'(p1, +(p10, x''))
+'(p5, +(p1, +(p2, x''))) -> +'(p1, +(p2, +(p5, x'')))
+'(p5, +(p1, +(p1, x''))) -> +'(p1, +(p1, +(p5, x'')))
+'(p5, +(p1, p1)) -> +'(p1, +(p1, p5))
+'(p1, +(p2, +(p2, x))) -> +'(p5, x)
+'(p2, +(p1, x)) -> +'(p1, +(p2, x))
+'(p1, +(p1, x)) -> +'(p2, x)
+'(p10, +(p1, p1)) -> +'(p1, +(p1, p10))
+'(p10, +(p5, x)) -> +'(p10, x)
+'(p10, +(p2, x)) -> +'(p10, x)
+'(p10, +(p1, x)) -> +'(p10, x)
+'(p5, +(p5, x)) -> +'(p10, x)
+'(p5, +(p2, x)) -> +'(p5, x)
+'(p5, +(p1, x)) -> +'(p5, x)
+'(p10, +(p5, p5)) -> +'(p5, +(p5, p10))


Rules:


+(p1, p1) -> p2
+(p1, +(p2, p2)) -> p5
+(p5, p5) -> p10
+(+(x, y), z) -> +(x, +(y, z))
+(p1, +(p1, x)) -> +(p2, x)
+(p1, +(p2, +(p2, x))) -> +(p5, x)
+(p2, p1) -> +(p1, p2)
+(p2, +(p1, x)) -> +(p1, +(p2, x))
+(p2, +(p2, p2)) -> +(p1, p5)
+(p2, +(p2, +(p2, x))) -> +(p1, +(p5, x))
+(p5, p1) -> +(p1, p5)
+(p5, +(p1, x)) -> +(p1, +(p5, x))
+(p5, p2) -> +(p2, p5)
+(p5, +(p2, x)) -> +(p2, +(p5, x))
+(p5, +(p5, x)) -> +(p10, x)
+(p10, p1) -> +(p1, p10)
+(p10, +(p1, x)) -> +(p1, +(p10, x))
+(p10, p2) -> +(p2, p10)
+(p10, +(p2, x)) -> +(p2, +(p10, x))
+(p10, p5) -> +(p5, p10)
+(p10, +(p5, x)) -> +(p5, +(p10, x))





On this DP problem, a Narrowing SCC transformation can be performed.
As a result of transforming the rule

+'(p10, +(p2, p5)) -> +'(p2, +(p5, p10))
no new Dependency Pairs are created.
The transformation is resulting in one new DP problem: 



   R
     ↳DPs
       →DP Problem 1
         ↳Nar
       →DP Problem 2
         ↳Remaining Obligation(s)




The following remains to be proven:


   R
     ↳DPs
       →DP Problem 1
         ↳Nar
       →DP Problem 2
         ↳Remaining Obligation(s)




The following remains to be proven:

Termination of R could not be shown.
Duration:
0:06 minutes