Higher_Order_Rewriting_Union_Beta 2019-03-28 22.10 pair #432270627

details

property	value
status	complete
benchmark	Applicative_AG01_innermost__#4.2.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n132.star.cs.uiowa.edu
space	Uncurried_Applicative_11

run statistics

property	value
solver	Wanda 2.1c
configuration	default
runtime (wallclock)	3.06482 seconds
cpu usage	4.33728
user time	4.04907
system time	0.288203
max virtual memory	7025852.0
max residence set size	148940.0

stage attributes

key	value
starexec-result	NO

output

4.29/3.06	NO
4.29/3.06	We consider the system theBenchmark.
4.29/3.06	
4.29/3.06	  Alphabet:
4.29/3.06	
4.29/3.06	    0 : [] --> b 
4.29/3.06	    cons : [d * e] --> e 
4.29/3.06	    f : [b * b * b] --> a 
4.29/3.06	    false : [] --> c 
4.29/3.06	    filter : [d -> c * e] --> e 
4.29/3.06	    filter2 : [c * d -> c * d * e] --> e 
4.29/3.06	    g : [b] --> b 
4.29/3.06	    map : [d -> d * e] --> e 
4.29/3.06	    nil : [] --> e 
4.29/3.06	    s : [b] --> b 
4.29/3.06	    true : [] --> c 
4.29/3.06	
4.29/3.06	  Rules:
4.29/3.06	
4.29/3.06	    f(g(x), s(0), y) => f(y, y, g(x)) 
4.29/3.06	    g(s(x)) => s(g(x)) 
4.29/3.06	    g(0) => 0 
4.29/3.06	    map(h, nil) => nil 
4.29/3.06	    map(h, cons(x, y)) => cons(h x, map(h, y)) 
4.29/3.06	    filter(h, nil) => nil 
4.29/3.06	    filter(h, cons(x, y)) => filter2(h x, h, x, y) 
4.29/3.06	    filter2(true, h, x, y) => cons(x, filter(h, y)) 
4.29/3.06	    filter2(false, h, x, y) => filter(h, y) 
4.29/3.06	
4.29/3.06	This AFS is converted to an AFSM simply by replacing all free variables by meta-variables (with arity 0).
4.29/3.06	
4.29/3.06	This system is non-terminating, as demonstrated by our external first-order non-termination checker:
4.29/3.06	
4.29/3.06	 || The following well-typed term is terminating: f(g(s(0)), g(s(0)), g(s(0)))
4.29/3.06	 || 
4.29/3.06	 || proof of resources/system.trs
4.29/3.06	 || # AProVE Commit ID: 500ec9b2e2a919720cb177ef26031cb0220e008e fuhs 20130603
4.29/3.06	 || 
4.29/3.06	 || 
4.29/3.06	 || Termination w.r.t. Q of the given QTRS could be disproven:
4.29/3.06	 || 
4.29/3.06	 || (0) QTRS
4.29/3.06	 || (1) NonTerminationProof [EQUIVALENT, 0 ms]
4.29/3.06	 || (2) NO
4.29/3.06	 || 
4.29/3.06	 || 
4.29/3.06	 || ----------------------------------------
4.29/3.06	 || 
4.29/3.06	 || (0)
4.29/3.06	 || Obligation:
4.29/3.06	 || Q restricted rewrite system:
4.29/3.06	 || The TRS R consists of the following rules:
4.29/3.06	 || 
4.29/3.06	 ||    f(g(%X), s(0), %Y) -> f(%Y, %Y, g(%X))
4.29/3.06	 ||    g(s(%X)) -> s(g(%X))
4.29/3.06	 ||    g(0) -> 0
4.29/3.06	 || 
4.29/3.06	 || Q is empty.
4.29/3.06	 || 
4.29/3.06	 || ----------------------------------------
4.29/3.06	 || 
4.29/3.06	 || (1) NonTerminationProof (EQUIVALENT)
4.29/3.06	 || The following loops were found:
4.29/3.06	 || 
4.29/3.06	 || ---------- Loop: ----------
4.29/3.06	 || 
4.29/3.06	 || f(g(s(0)), g(s(0)), g(s(0))) -> f(g(s(0)), s(g(0)), g(s(0))) with rule g(s(%X')) -> s(g(%X')) at position [1] and matcher [%X' / 0]
4.29/3.06	 || 
4.29/3.06	 || f(g(s(0)), s(g(0)), g(s(0))) -> f(g(s(0)), s(0), g(s(0))) with rule g(0) -> 0 at position [1,0] and matcher [ ]
4.29/3.06	 || 
4.29/3.06	 || f(g(s(0)), s(0), g(s(0))) -> f(g(s(0)), g(s(0)), g(s(0))) with rule f(g(%X), s(0), %Y) -> f(%Y, %Y, g(%X)) at position [] and matcher [%X / s(0), %Y / g(s(0))]
4.29/3.06	 || 
4.29/3.06	 || Now an instance of the first term with Matcher [ ] occurs in the last term at position [].
4.29/3.06	 || 
4.29/3.06	 || Context: []
4.29/3.06	 || 
4.29/3.06	 || 
4.29/3.06	 || ----------------------------------------
4.29/3.06	 || 
4.29/3.06	 || (2)
4.29/3.06	 || NO
4.29/3.06	 || 
4.29/3.06	EOF

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