details

property	value
status	complete
benchmark	t003.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n073.star.cs.uiowa.edu
space	HirokawaMiddeldorp_04

run statistics

property	value
solver	muterm 6.0.3
configuration	default
runtime (wallclock)	0.0561709 seconds
cpu usage	0.044538
user time	0.023283
system time	0.021255
max virtual memory	113188.0
max residence set size	6200.0

stage attributes

key	value
starexec-result	YES

output

YES Problem 1: (VAR v_NonEmpty:S u:S x:S y:S z:S) (RULES -(s(x:S),s(y:S)) -> -(x:S,y:S) -(x:S,0) -> x:S <=(0,y:S) -> ttrue <=(s(x:S),0) -> ffalse <=(s(x:S),s(y:S)) -> <=(x:S,y:S) f(0,y:S,0,u:S) -> ttrue f(0,y:S,s(z:S),u:S) -> ffalse f(s(x:S),0,z:S,u:S) -> f(x:S,u:S,-(z:S,s(x:S)),u:S) f(s(x:S),s(y:S),z:S,u:S) -> if(<=(x:S,y:S),f(s(x:S),-(y:S,x:S),z:S,u:S),f(x:S,u:S,z:S,u:S)) if(ffalse,x:S,y:S) -> y:S if(ttrue,x:S,y:S) -> x:S perfectp(0) -> ffalse perfectp(s(x:S)) -> f(x:S,s(0),s(x:S),s(x:S)) ) Problem 1: Innermost Equivalent Processor: -> Rules: -(s(x:S),s(y:S)) -> -(x:S,y:S) -(x:S,0) -> x:S <=(0,y:S) -> ttrue <=(s(x:S),0) -> ffalse <=(s(x:S),s(y:S)) -> <=(x:S,y:S) f(0,y:S,0,u:S) -> ttrue f(0,y:S,s(z:S),u:S) -> ffalse f(s(x:S),0,z:S,u:S) -> f(x:S,u:S,-(z:S,s(x:S)),u:S) f(s(x:S),s(y:S),z:S,u:S) -> if(<=(x:S,y:S),f(s(x:S),-(y:S,x:S),z:S,u:S),f(x:S,u:S,z:S,u:S)) if(ffalse,x:S,y:S) -> y:S if(ttrue,x:S,y:S) -> x:S perfectp(0) -> ffalse perfectp(s(x:S)) -> f(x:S,s(0),s(x:S),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: -#(s(x:S),s(y:S)) -> -#(x:S,y:S) <=#(s(x:S),s(y:S)) -> <=#(x:S,y:S) F(s(x:S),0,z:S,u:S) -> -#(z:S,s(x:S)) F(s(x:S),0,z:S,u:S) -> F(x:S,u:S,-(z:S,s(x:S)),u:S) F(s(x:S),s(y:S),z:S,u:S) -> -#(y:S,x:S) F(s(x:S),s(y:S),z:S,u:S) -> <=#(x:S,y:S) F(s(x:S),s(y:S),z:S,u:S) -> F(s(x:S),-(y:S,x:S),z:S,u:S) F(s(x:S),s(y:S),z:S,u:S) -> F(x:S,u:S,z:S,u:S) F(s(x:S),s(y:S),z:S,u:S) -> IF(<=(x:S,y:S),f(s(x:S),-(y:S,x:S),z:S,u:S),f(x:S,u:S,z:S,u:S)) PERFECTP(s(x:S)) -> F(x:S,s(0),s(x:S),s(x:S)) -> Rules: -(s(x:S),s(y:S)) -> -(x:S,y:S) -(x:S,0) -> x:S <=(0,y:S) -> ttrue <=(s(x:S),0) -> ffalse <=(s(x:S),s(y:S)) -> <=(x:S,y:S) f(0,y:S,0,u:S) -> ttrue f(0,y:S,s(z:S),u:S) -> ffalse f(s(x:S),0,z:S,u:S) -> f(x:S,u:S,-(z:S,s(x:S)),u:S) f(s(x:S),s(y:S),z:S,u:S) -> if(<=(x:S,y:S),f(s(x:S),-(y:S,x:S),z:S,u:S),f(x:S,u:S,z:S,u:S)) if(ffalse,x:S,y:S) -> y:S if(ttrue,x:S,y:S) -> x:S perfectp(0) -> ffalse perfectp(s(x:S)) -> f(x:S,s(0),s(x:S),s(x:S)) Problem 1: SCC Processor: -> Pairs: -#(s(x:S),s(y:S)) -> -#(x:S,y:S) <=#(s(x:S),s(y:S)) -> <=#(x:S,y:S) F(s(x:S),0,z:S,u:S) -> -#(z:S,s(x:S)) F(s(x:S),0,z:S,u:S) -> F(x:S,u:S,-(z:S,s(x:S)),u:S) F(s(x:S),s(y:S),z:S,u:S) -> -#(y:S,x:S) F(s(x:S),s(y:S),z:S,u:S) -> <=#(x:S,y:S) F(s(x:S),s(y:S),z:S,u:S) -> F(s(x:S),-(y:S,x:S),z:S,u:S) F(s(x:S),s(y:S),z:S,u:S) -> F(x:S,u:S,z:S,u:S) F(s(x:S),s(y:S),z:S,u:S) -> IF(<=(x:S,y:S),f(s(x:S),-(y:S,x:S),z:S,u:S),f(x:S,u:S,z:S,u:S)) PERFECTP(s(x:S)) -> F(x:S,s(0),s(x:S),s(x:S)) -> Rules: -(s(x:S),s(y:S)) -> -(x:S,y:S) -(x:S,0) -> x:S <=(0,y:S) -> ttrue <=(s(x:S),0) -> ffalse <=(s(x:S),s(y:S)) -> <=(x:S,y:S) f(0,y:S,0,u:S) -> ttrue f(0,y:S,s(z:S),u:S) -> ffalse f(s(x:S),0,z:S,u:S) -> f(x:S,u:S,-(z:S,s(x:S)),u:S) f(s(x:S),s(y:S),z:S,u:S) -> if(<=(x:S,y:S),f(s(x:S),-(y:S,x:S),z:S,u:S),f(x:S,u:S,z:S,u:S)) if(ffalse,x:S,y:S) -> y:S if(ttrue,x:S,y:S) -> x:S perfectp(0) -> ffalse perfectp(s(x:S)) -> f(x:S,s(0),s(x:S),s(x:S)) ->Strongly Connected Components: ->->Cycle: popout

output may be truncated. 'popout' for the full output.

job log

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actions

all output return to TRS Standard