details

property	value
status	complete
benchmark	15.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n175.star.cs.uiowa.edu
space	Beerendonk_07

run statistics

property	value
solver	muterm 6.0.3
configuration	default
runtime (wallclock)	173.035 seconds
cpu usage	172.098
user time	159.688
system time	12.41
max virtual memory	819264.0
max residence set size	39624.0

stage attributes

key	value
starexec-result	YES

output

YES Problem 1: (VAR v_NonEmpty:S x:S y:S) (RULES add(0,x:S) -> x:S add(s(x:S),y:S) -> s(add(x:S,y:S)) cond1(ttrue,x:S,y:S) -> cond2(gr(x:S,0),x:S,y:S) cond2(ffalse,x:S,y:S) -> cond3(gr(y:S,0),x:S,y:S) cond2(ttrue,x:S,y:S) -> cond1(gr(add(x:S,y:S),0),p(x:S),y:S) cond3(ffalse,x:S,y:S) -> cond1(gr(add(x:S,y:S),0),x:S,y:S) cond3(ttrue,x:S,y:S) -> cond1(gr(add(x:S,y:S),0),x:S,p(y:S)) gr(0,x:S) -> ffalse gr(s(x:S),0) -> ttrue gr(s(x:S),s(y:S)) -> gr(x:S,y:S) p(0) -> 0 p(s(x:S)) -> x:S ) Problem 1: Innermost Equivalent Processor: -> Rules: add(0,x:S) -> x:S add(s(x:S),y:S) -> s(add(x:S,y:S)) cond1(ttrue,x:S,y:S) -> cond2(gr(x:S,0),x:S,y:S) cond2(ffalse,x:S,y:S) -> cond3(gr(y:S,0),x:S,y:S) cond2(ttrue,x:S,y:S) -> cond1(gr(add(x:S,y:S),0),p(x:S),y:S) cond3(ffalse,x:S,y:S) -> cond1(gr(add(x:S,y:S),0),x:S,y:S) cond3(ttrue,x:S,y:S) -> cond1(gr(add(x:S,y:S),0),x:S,p(y:S)) gr(0,x:S) -> ffalse gr(s(x:S),0) -> ttrue gr(s(x:S),s(y:S)) -> gr(x:S,y:S) p(0) -> 0 p(s(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: ADD(s(x:S),y:S) -> ADD(x:S,y:S) COND1(ttrue,x:S,y:S) -> COND2(gr(x:S,0),x:S,y:S) COND1(ttrue,x:S,y:S) -> GR(x:S,0) COND2(ffalse,x:S,y:S) -> COND3(gr(y:S,0),x:S,y:S) COND2(ffalse,x:S,y:S) -> GR(y:S,0) COND2(ttrue,x:S,y:S) -> ADD(x:S,y:S) COND2(ttrue,x:S,y:S) -> COND1(gr(add(x:S,y:S),0),p(x:S),y:S) COND2(ttrue,x:S,y:S) -> GR(add(x:S,y:S),0) COND2(ttrue,x:S,y:S) -> P(x:S) COND3(ffalse,x:S,y:S) -> ADD(x:S,y:S) COND3(ffalse,x:S,y:S) -> COND1(gr(add(x:S,y:S),0),x:S,y:S) COND3(ffalse,x:S,y:S) -> GR(add(x:S,y:S),0) COND3(ttrue,x:S,y:S) -> ADD(x:S,y:S) COND3(ttrue,x:S,y:S) -> COND1(gr(add(x:S,y:S),0),x:S,p(y:S)) COND3(ttrue,x:S,y:S) -> GR(add(x:S,y:S),0) COND3(ttrue,x:S,y:S) -> P(y:S) GR(s(x:S),s(y:S)) -> GR(x:S,y:S) -> Rules: add(0,x:S) -> x:S add(s(x:S),y:S) -> s(add(x:S,y:S)) cond1(ttrue,x:S,y:S) -> cond2(gr(x:S,0),x:S,y:S) cond2(ffalse,x:S,y:S) -> cond3(gr(y:S,0),x:S,y:S) cond2(ttrue,x:S,y:S) -> cond1(gr(add(x:S,y:S),0),p(x:S),y:S) cond3(ffalse,x:S,y:S) -> cond1(gr(add(x:S,y:S),0),x:S,y:S) cond3(ttrue,x:S,y:S) -> cond1(gr(add(x:S,y:S),0),x:S,p(y:S)) gr(0,x:S) -> ffalse gr(s(x:S),0) -> ttrue gr(s(x:S),s(y:S)) -> gr(x:S,y:S) p(0) -> 0 p(s(x:S)) -> x:S Problem 1: SCC Processor: -> Pairs: ADD(s(x:S),y:S) -> ADD(x:S,y:S) COND1(ttrue,x:S,y:S) -> COND2(gr(x:S,0),x:S,y:S) COND1(ttrue,x:S,y:S) -> GR(x:S,0) COND2(ffalse,x:S,y:S) -> COND3(gr(y:S,0),x:S,y:S) COND2(ffalse,x:S,y:S) -> GR(y:S,0) COND2(ttrue,x:S,y:S) -> ADD(x:S,y:S) COND2(ttrue,x:S,y:S) -> COND1(gr(add(x:S,y:S),0),p(x:S),y:S) COND2(ttrue,x:S,y:S) -> GR(add(x:S,y:S),0) COND2(ttrue,x:S,y:S) -> P(x:S) COND3(ffalse,x:S,y:S) -> ADD(x:S,y:S) COND3(ffalse,x:S,y:S) -> COND1(gr(add(x:S,y:S),0),x:S,y:S) COND3(ffalse,x:S,y:S) -> GR(add(x:S,y:S),0) COND3(ttrue,x:S,y:S) -> ADD(x:S,y:S) COND3(ttrue,x:S,y:S) -> COND1(gr(add(x:S,y:S),0),x:S,p(y:S)) COND3(ttrue,x:S,y:S) -> GR(add(x:S,y:S),0) COND3(ttrue,x:S,y:S) -> P(y:S) GR(s(x:S),s(y:S)) -> GR(x:S,y:S) -> Rules: add(0,x:S) -> x:S add(s(x:S),y:S) -> s(add(x:S,y:S)) cond1(ttrue,x:S,y:S) -> cond2(gr(x:S,0),x:S,y:S) cond2(ffalse,x:S,y:S) -> cond3(gr(y:S,0),x:S,y:S) popout

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