details

property	value
status	complete
benchmark	16.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	Beerendonk_07

run statistics

property	value
solver	muterm 6.0.3
configuration	default
runtime (wallclock)	172.478 seconds
cpu usage	171.29
user time	161.094
system time	10.1957
max virtual memory	832000.0
max residence set size	69496.0

stage attributes

key	value
starexec-result	YES

output

YES Problem 1: (VAR v_NonEmpty:S x:S y:S z: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,z:S) -> cond2(gr(x:S,0),x:S,y:S,z:S) cond2(ffalse,x:S,y:S,z:S) -> cond3(gr(y:S,0),x:S,y:S,z:S) cond2(ttrue,x:S,y:S,z:S) -> cond1(gr(add(x:S,y:S),z:S),p(x:S),y:S,z:S) cond3(ffalse,x:S,y:S,z:S) -> cond1(gr(add(x:S,y:S),z:S),x:S,y:S,z:S) cond3(ttrue,x:S,y:S,z:S) -> cond1(gr(add(x:S,y:S),z:S),x:S,p(y:S),z: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,z:S) -> cond2(gr(x:S,0),x:S,y:S,z:S) cond2(ffalse,x:S,y:S,z:S) -> cond3(gr(y:S,0),x:S,y:S,z:S) cond2(ttrue,x:S,y:S,z:S) -> cond1(gr(add(x:S,y:S),z:S),p(x:S),y:S,z:S) cond3(ffalse,x:S,y:S,z:S) -> cond1(gr(add(x:S,y:S),z:S),x:S,y:S,z:S) cond3(ttrue,x:S,y:S,z:S) -> cond1(gr(add(x:S,y:S),z:S),x:S,p(y:S),z: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,z:S) -> COND2(gr(x:S,0),x:S,y:S,z:S) COND1(ttrue,x:S,y:S,z:S) -> GR(x:S,0) COND2(ffalse,x:S,y:S,z:S) -> COND3(gr(y:S,0),x:S,y:S,z:S) COND2(ffalse,x:S,y:S,z:S) -> GR(y:S,0) COND2(ttrue,x:S,y:S,z:S) -> ADD(x:S,y:S) COND2(ttrue,x:S,y:S,z:S) -> COND1(gr(add(x:S,y:S),z:S),p(x:S),y:S,z:S) COND2(ttrue,x:S,y:S,z:S) -> GR(add(x:S,y:S),z:S) COND2(ttrue,x:S,y:S,z:S) -> P(x:S) COND3(ffalse,x:S,y:S,z:S) -> ADD(x:S,y:S) COND3(ffalse,x:S,y:S,z:S) -> COND1(gr(add(x:S,y:S),z:S),x:S,y:S,z:S) COND3(ffalse,x:S,y:S,z:S) -> GR(add(x:S,y:S),z:S) COND3(ttrue,x:S,y:S,z:S) -> ADD(x:S,y:S) COND3(ttrue,x:S,y:S,z:S) -> COND1(gr(add(x:S,y:S),z:S),x:S,p(y:S),z:S) COND3(ttrue,x:S,y:S,z:S) -> GR(add(x:S,y:S),z:S) COND3(ttrue,x:S,y:S,z: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,z:S) -> cond2(gr(x:S,0),x:S,y:S,z:S) cond2(ffalse,x:S,y:S,z:S) -> cond3(gr(y:S,0),x:S,y:S,z:S) cond2(ttrue,x:S,y:S,z:S) -> cond1(gr(add(x:S,y:S),z:S),p(x:S),y:S,z:S) cond3(ffalse,x:S,y:S,z:S) -> cond1(gr(add(x:S,y:S),z:S),x:S,y:S,z:S) cond3(ttrue,x:S,y:S,z:S) -> cond1(gr(add(x:S,y:S),z:S),x:S,p(y:S),z: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,z:S) -> COND2(gr(x:S,0),x:S,y:S,z:S) COND1(ttrue,x:S,y:S,z:S) -> GR(x:S,0) COND2(ffalse,x:S,y:S,z:S) -> COND3(gr(y:S,0),x:S,y:S,z:S) COND2(ffalse,x:S,y:S,z:S) -> GR(y:S,0) COND2(ttrue,x:S,y:S,z:S) -> ADD(x:S,y:S) COND2(ttrue,x:S,y:S,z:S) -> COND1(gr(add(x:S,y:S),z:S),p(x:S),y:S,z:S) COND2(ttrue,x:S,y:S,z:S) -> GR(add(x:S,y:S),z:S) COND2(ttrue,x:S,y:S,z:S) -> P(x:S) COND3(ffalse,x:S,y:S,z:S) -> ADD(x:S,y:S) COND3(ffalse,x:S,y:S,z:S) -> COND1(gr(add(x:S,y:S),z:S),x:S,y:S,z:S) COND3(ffalse,x:S,y:S,z:S) -> GR(add(x:S,y:S),z:S) COND3(ttrue,x:S,y:S,z:S) -> ADD(x:S,y:S) COND3(ttrue,x:S,y:S,z:S) -> COND1(gr(add(x:S,y:S),z:S),x:S,p(y:S),z:S) COND3(ttrue,x:S,y:S,z:S) -> GR(add(x:S,y:S),z:S) COND3(ttrue,x:S,y:S,z: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,z:S) -> cond2(gr(x:S,0),x:S,y:S,z:S) cond2(ffalse,x:S,y:S,z:S) -> cond3(gr(y:S,0),x:S,y:S,z:S) popout

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