0.00/0.00	YES
0.00/0.00	
0.00/0.00	
0.00/0.00	Succeeded in reading "/export/starexec/sandbox/benchmark/theBenchmark.trs".
0.00/0.00	    (CONDITIONTYPE ORIENTED)
0.00/0.00	    (VAR y x w z)
0.00/0.00	    (RULES
0.00/0.00	      plus(0,y) -> y
0.00/0.00	      plus(s(x),y) -> s(plus(x,y))
0.00/0.00	      fib(0) -> pair(0,s(0))
0.00/0.00	      fib(s(x)) -> pair(z,w) | fib(x) == pair(y,z), plus(y,z) == w
0.00/0.00	    )
0.00/0.00	    (COMMENT doi:10.4230/LIPIcs.RTA.2015.223 [89] Example 1 submitted by: Thomas Sternagel)
0.00/0.00	
0.00/0.00	No "->="-rules.
0.00/0.00	
0.00/0.00	Decomposed conditions if possible.
0.00/0.00	    (CONDITIONTYPE ORIENTED)
0.00/0.00	    (VAR y x w z)
0.00/0.00	    (RULES
0.00/0.00	      plus(0,y) -> y
0.00/0.00	      plus(s(x),y) -> s(plus(x,y))
0.00/0.00	      fib(0) -> pair(0,s(0))
0.00/0.00	      fib(s(x)) -> pair(z,w) | fib(x) == pair(y,z), plus(y,z) == w
0.00/0.00	    )
0.00/0.00	    (COMMENT doi:10.4230/LIPIcs.RTA.2015.223 [89] Example 1 submitted by: Thomas Sternagel)
0.00/0.00	
0.00/0.00	Removed infeasible rules as much as possible.
0.00/0.00	    (CONDITIONTYPE ORIENTED)
0.00/0.00	    (VAR y x w z)
0.00/0.00	    (RULES
0.00/0.00	      plus(0,y) -> y
0.00/0.00	      plus(s(x),y) -> s(plus(x,y))
0.00/0.00	      fib(0) -> pair(0,s(0))
0.00/0.00	      fib(s(x)) -> pair(z,w) | fib(x) == pair(y,z), plus(y,z) == w
0.00/0.00	    )
0.00/0.00	    (COMMENT doi:10.4230/LIPIcs.RTA.2015.223 [89] Example 1 submitted by: Thomas Sternagel)
0.00/0.00	
0.00/0.00	Try to disprove confluence of the following (C)TRS:
0.00/0.00	    (CONDITIONTYPE ORIENTED)
0.00/0.00	    (VAR y x w z)
0.00/0.00	    (RULES
0.00/0.00	      plus(0,y) -> y
0.00/0.00	      plus(s(x),y) -> s(plus(x,y))
0.00/0.00	      fib(0) -> pair(0,s(0))
0.00/0.00	      fib(s(x)) -> pair(z,w) | fib(x) == pair(y,z), plus(y,z) == w
0.00/0.00	    )
0.00/0.00	    (COMMENT doi:10.4230/LIPIcs.RTA.2015.223 [89] Example 1 submitted by: Thomas Sternagel)
0.00/0.00	
0.00/0.00	Failed either to apply SR and U for normal 1CTRSs to the above CTRS or to prove confluence of any converted TRSs.
0.00/0.00	
0.00/0.00	Try to apply SR and U for 3DCTRSs to the above CTRS.
0.00/0.00	
0.00/0.00	Succeeded in applying U for 3DCTRSs to the above CTRS.
0.00/0.00	U(R) =
0.00/0.00	    (VAR x1 x2 x3 x4)
0.00/0.00	    (RULES
0.00/0.00	      plus(0,x1) -> x1
0.00/0.00	      plus(s(x1),x2) -> s(plus(x1,x2))
0.00/0.00	      fib(0) -> pair(0,s(0))
0.00/0.00	      fib(s(x1)) -> u1(fib(x1),x1)
0.00/0.00	      u1(pair(x2,x3),x1) -> u2(plus(x2,x3),x2,x3,x1)
0.00/0.00	      u2(x4,x2,x3,x1) -> pair(x3,x4)
0.00/0.00	    )
0.00/0.00	
0.00/0.00	U for 3DCTRSs is sound for the above CTRS.
0.00/0.00	
0.00/0.00	U(R) is confluent.
0.00/0.00	
0.00/0.00	YES
0.00/0.00	EOF