Higher_Order_Rewriting_Union_Beta 2019-03-28 22.10 pair #432270295

details

property	value
status	complete
benchmark	lambda2.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n048.star.cs.uiowa.edu
space	Mixed_HO_10

run statistics

property	value
solver	Wanda 2.1c
configuration	default
runtime (wallclock)	2.16271 seconds
cpu usage	4.867
user time	4.58642
system time	0.280583
max virtual memory	6953152.0
max residence set size	184024.0

stage attributes

key	value
starexec-result	NO

output

4.82/2.16	NO
4.82/2.16	We consider the system theBenchmark.
4.82/2.16	
4.82/2.16	  Alphabet:
4.82/2.16	
4.82/2.16	    fapp : [o * o] --> o 
4.82/2.16	    lam : [o] --> o 
4.82/2.16	    subst : [o * o] --> o 
4.82/2.16	    v : [] --> o 
4.82/2.16	
4.82/2.16	  Rules:
4.82/2.16	
4.82/2.16	    fapp(lam(x), y) => subst(x, y) 
4.82/2.16	    subst(v, x) => x 
4.82/2.16	    subst(lam(x), y) => lam(x) 
4.82/2.16	    subst(fapp(x, y), z) => fapp(subst(x, z), subst(y, z)) 
4.82/2.16	
4.82/2.16	This AFS is converted to an AFSM simply by replacing all free variables by meta-variables (with arity 0).
4.82/2.16	
4.82/2.16	This system is non-terminating, as demonstrated by our external first-order non-termination checker:
4.82/2.16	
4.82/2.16	 || The following well-typed term is terminating: subst(fapp(v, v), subst(v, lam(fapp(v, v))))
4.82/2.16	 || 
4.82/2.16	 || proof of resources/system.trs
4.82/2.16	 || # AProVE Commit ID: 500ec9b2e2a919720cb177ef26031cb0220e008e fuhs 20130603
4.82/2.16	 || 
4.82/2.16	 || 
4.82/2.16	 || Termination w.r.t. Q of the given QTRS could be disproven:
4.82/2.16	 || 
4.82/2.16	 || (0) QTRS
4.82/2.16	 || (1) NonTerminationProof [EQUIVALENT, 78 ms]
4.82/2.16	 || (2) NO
4.82/2.16	 || 
4.82/2.16	 || 
4.82/2.16	 || ----------------------------------------
4.82/2.16	 || 
4.82/2.16	 || (0)
4.82/2.16	 || Obligation:
4.82/2.16	 || Q restricted rewrite system:
4.82/2.16	 || The TRS R consists of the following rules:
4.82/2.16	 || 
4.82/2.16	 ||    fapp(lam(%X), %Y) -> subst(%X, %Y)
4.82/2.16	 ||    subst(v, %X) -> %X
4.82/2.16	 ||    subst(lam(%X), %Y) -> lam(%X)
4.82/2.16	 ||    subst(fapp(%X, %Y), %Z) -> fapp(subst(%X, %Z), subst(%Y, %Z))
4.82/2.16	 || 
4.82/2.16	 || Q is empty.
4.82/2.16	 || 
4.82/2.16	 || ----------------------------------------
4.82/2.16	 || 
4.82/2.16	 || (1) NonTerminationProof (EQUIVALENT)
4.82/2.16	 || The following loops were found:
4.82/2.16	 || 
4.82/2.16	 || ---------- Loop: ----------
4.82/2.16	 || 
4.82/2.16	 || subst(fapp(v, v), subst(v, lam(fapp(v, v)))) -> subst(fapp(v, v), lam(fapp(v, v))) with rule subst(v, %X') -> %X' at position [1] and matcher [%X' / lam(fapp(v, v))]
4.82/2.16	 || 
4.82/2.16	 || subst(fapp(v, v), lam(fapp(v, v))) -> fapp(subst(v, lam(fapp(v, v))), subst(v, lam(fapp(v, v)))) with rule subst(fapp(%X, %Y), %Z) -> fapp(subst(%X, %Z), subst(%Y, %Z)) at position [] and matcher [%X / v, %Y / v, %Z / lam(fapp(v, v))]
4.82/2.16	 || 
4.82/2.16	 || fapp(subst(v, lam(fapp(v, v))), subst(v, lam(fapp(v, v)))) -> fapp(lam(fapp(v, v)), subst(v, lam(fapp(v, v)))) with rule subst(v, %X') -> %X' at position [0] and matcher [%X' / lam(fapp(v, v))]
4.82/2.16	 || 
4.82/2.16	 || fapp(lam(fapp(v, v)), subst(v, lam(fapp(v, v)))) -> subst(fapp(v, v), subst(v, lam(fapp(v, v)))) with rule fapp(lam(%X), %Y) -> subst(%X, %Y) at position [] and matcher [%X / fapp(v, v), %Y / subst(v, lam(fapp(v, v)))]
4.82/2.16	 || 
4.82/2.16	 || Now an instance of the first term with Matcher [ ] occurs in the last term at position [].
4.82/2.16	 || 
4.82/2.16	 || Context: []
4.82/2.16	 || 
4.82/2.16	 || 
4.82/2.16	 || ----------------------------------------
4.82/2.16	 || 
4.82/2.16	 || (2)
4.82/2.16	 || NO
4.82/2.16	 || 
4.82/2.16	EOF

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