details

property	value
status	complete
benchmark	thiemann17.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n192.star.cs.uiowa.edu
space	AProVE_07

run statistics

property	value
solver	muterm 6.0.3
configuration	default
runtime (wallclock)	0.601898 seconds
cpu usage	0.602481
user time	0.500755
system time	0.101726
max virtual memory	710628.0
max residence set size	7504.0

stage attributes

key	value
starexec-result	YES

output

YES Problem 1: (VAR v_NonEmpty:S b:S m:S n:S x:S y:S) (RULES empty(cons(n:S,x:S)) -> ffalse empty(nil) -> ttrue head(cons(n:S,x:S)) -> n:S if(ffalse,b:S,x:S) -> if2(b:S,x:S) if(ttrue,b:S,x:S) -> weight_undefined_error if2(ffalse,x:S) -> weight(sum(x:S,cons(0,tail(tail(x:S))))) if2(ttrue,x:S) -> head(x:S) sum(cons(0,x:S),y:S) -> sum(x:S,y:S) sum(cons(s(n:S),x:S),cons(m:S,y:S)) -> sum(cons(n:S,x:S),cons(s(m:S),y:S)) sum(nil,y:S) -> y:S tail(cons(n:S,x:S)) -> x:S tail(nil) -> nil weight(x:S) -> if(empty(x:S),empty(tail(x:S)),x:S) ) Problem 1: Innermost Equivalent Processor: -> Rules: empty(cons(n:S,x:S)) -> ffalse empty(nil) -> ttrue head(cons(n:S,x:S)) -> n:S if(ffalse,b:S,x:S) -> if2(b:S,x:S) if(ttrue,b:S,x:S) -> weight_undefined_error if2(ffalse,x:S) -> weight(sum(x:S,cons(0,tail(tail(x:S))))) if2(ttrue,x:S) -> head(x:S) sum(cons(0,x:S),y:S) -> sum(x:S,y:S) sum(cons(s(n:S),x:S),cons(m:S,y:S)) -> sum(cons(n:S,x:S),cons(s(m:S),y:S)) sum(nil,y:S) -> y:S tail(cons(n:S,x:S)) -> x:S tail(nil) -> nil weight(x:S) -> if(empty(x:S),empty(tail(x:S)),x:S) -> The term rewriting system is non-overlaping or locally confluent overlay system. Therefore, innermost termination implies termination. Problem 1: Dependency Pairs Processor: -> Pairs: IF(ffalse,b:S,x:S) -> IF2(b:S,x:S) IF2(ffalse,x:S) -> SUM(x:S,cons(0,tail(tail(x:S)))) IF2(ffalse,x:S) -> TAIL(tail(x:S)) IF2(ffalse,x:S) -> TAIL(x:S) IF2(ffalse,x:S) -> WEIGHT(sum(x:S,cons(0,tail(tail(x:S))))) IF2(ttrue,x:S) -> HEAD(x:S) SUM(cons(0,x:S),y:S) -> SUM(x:S,y:S) SUM(cons(s(n:S),x:S),cons(m:S,y:S)) -> SUM(cons(n:S,x:S),cons(s(m:S),y:S)) WEIGHT(x:S) -> EMPTY(tail(x:S)) WEIGHT(x:S) -> EMPTY(x:S) WEIGHT(x:S) -> IF(empty(x:S),empty(tail(x:S)),x:S) WEIGHT(x:S) -> TAIL(x:S) -> Rules: empty(cons(n:S,x:S)) -> ffalse empty(nil) -> ttrue head(cons(n:S,x:S)) -> n:S if(ffalse,b:S,x:S) -> if2(b:S,x:S) if(ttrue,b:S,x:S) -> weight_undefined_error if2(ffalse,x:S) -> weight(sum(x:S,cons(0,tail(tail(x:S))))) if2(ttrue,x:S) -> head(x:S) sum(cons(0,x:S),y:S) -> sum(x:S,y:S) sum(cons(s(n:S),x:S),cons(m:S,y:S)) -> sum(cons(n:S,x:S),cons(s(m:S),y:S)) sum(nil,y:S) -> y:S tail(cons(n:S,x:S)) -> x:S tail(nil) -> nil weight(x:S) -> if(empty(x:S),empty(tail(x:S)),x:S) Problem 1: SCC Processor: -> Pairs: IF(ffalse,b:S,x:S) -> IF2(b:S,x:S) IF2(ffalse,x:S) -> SUM(x:S,cons(0,tail(tail(x:S)))) IF2(ffalse,x:S) -> TAIL(tail(x:S)) IF2(ffalse,x:S) -> TAIL(x:S) IF2(ffalse,x:S) -> WEIGHT(sum(x:S,cons(0,tail(tail(x:S))))) IF2(ttrue,x:S) -> HEAD(x:S) SUM(cons(0,x:S),y:S) -> SUM(x:S,y:S) SUM(cons(s(n:S),x:S),cons(m:S,y:S)) -> SUM(cons(n:S,x:S),cons(s(m:S),y:S)) WEIGHT(x:S) -> EMPTY(tail(x:S)) WEIGHT(x:S) -> EMPTY(x:S) WEIGHT(x:S) -> IF(empty(x:S),empty(tail(x:S)),x:S) WEIGHT(x:S) -> TAIL(x:S) -> Rules: empty(cons(n:S,x:S)) -> ffalse empty(nil) -> ttrue head(cons(n:S,x:S)) -> n:S if(ffalse,b:S,x:S) -> if2(b:S,x:S) if(ttrue,b:S,x:S) -> weight_undefined_error if2(ffalse,x:S) -> weight(sum(x:S,cons(0,tail(tail(x:S))))) if2(ttrue,x:S) -> head(x:S) sum(cons(0,x:S),y:S) -> sum(x:S,y:S) sum(cons(s(n:S),x:S),cons(m:S,y:S)) -> sum(cons(n:S,x:S),cons(s(m:S),y:S)) sum(nil,y:S) -> y:S tail(cons(n:S,x:S)) -> x:S popout

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