23.64/6.98	NO
23.93/7.00	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
23.93/7.00	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
23.93/7.00	
23.93/7.00	
23.93/7.00	Termination w.r.t. Q of the given QTRS could be disproven:
23.93/7.00	
23.93/7.00	(0) QTRS
23.93/7.00	(1) NonTerminationProof [COMPLETE, 2021 ms]
23.93/7.00	(2) NO
23.93/7.00	
23.93/7.00	
23.93/7.00	----------------------------------------
23.93/7.00	
23.93/7.00	(0)
23.93/7.00	Obligation:
23.93/7.00	Q restricted rewrite system:
23.93/7.00	The TRS R consists of the following rules:
23.93/7.00	
23.93/7.00	   a(b(c(x1))) -> c(b(a(x1)))
23.93/7.00	   a(c(x1)) -> a(a(d(a(x1))))
23.93/7.00	   d(a(b(x1))) -> b(a(d(x1)))
23.93/7.00	   d(a(c(x1))) -> b(c(c(x1)))
23.93/7.00	
23.93/7.00	Q is empty.
23.93/7.00	
23.93/7.00	----------------------------------------
23.93/7.00	
23.93/7.00	(1) NonTerminationProof (COMPLETE)
23.93/7.00	We used the non-termination processor [OPPELT08] to show that the SRS problem is infinite.
23.93/7.00	
23.93/7.00	Found the self-embedding DerivationStructure: 
23.93/7.00	"a (a b)^k+1 c c -> a (a b)^k+2 c c"
23.93/7.00	a (a b)^k+1 c c -> a (a b)^k+2 c c
23.93/7.00	by Equivalent"a (a b)^k+1 c c -> a a (b a)^k+1 b c c
23.93/7.00	by Overlap u with r (ol3)"a (a b)^k+1 c -> a a (b a)^k+1 d a
23.93/7.00	by Overlapping Derivationstructures"a (a b)^k+1 c -> a a d (a b)^k+1 a
23.93/7.00	by Equivalent"a (a b)^k+1 c -> a a d a b (a b)^k a
23.93/7.00	by Overlap u with l (ol4)"(a b)^k+1 c -> c b (a b)^k a
23.93/7.00	by Operation rotate"(a b)^k+1 c -> c (b a)^k+1
23.93/7.00	by Operation lift"(a b)^k c -> c (b a)^k
23.93/7.00	by Selfoverlapping OC am1"a b c -> c b a
23.93/7.00	by original rule (OC 1)"""""a c -> a a d a
23.93/7.00	by original rule (OC 1)""""d (a b)^k+1 -> (b a)^k+1 d
23.93/7.00	by Operation lift"d (a b)^k -> (b a)^k d
23.93/7.00	by Selfoverlapping OC am2"d a b -> b a d
23.93/7.00	by original rule (OC 1)"""""d a c -> b c c
23.93/7.00	by original rule (OC 1)""
23.93/7.00	
23.93/7.00	----------------------------------------
23.93/7.00	
23.93/7.00	(2)
23.93/7.00	NO
24.25/7.28	EOF