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TRS Standard pair #516967776
details
property
value
status
complete
benchmark
#4.35.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n045.star.cs.uiowa.edu
space
Strategy_removed_AG01
run statistics
property
value
solver
muterm 6.0.3
configuration
default
runtime (wallclock)
0.294658899307 seconds
cpu usage
0.214638992
max memory
7434240.0
stage attributes
key
value
output-size
31026
starexec-result
YES
output
/export/starexec/sandbox2/solver/bin/starexec_run_default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES Problem 1: (VAR v_NonEmpty:S k:S l:S l':S s:S s':S t:S t':S x:S x':S y:S z:S) (RULES and(ffalse,y:S) -> ffalse and(ttrue,y:S) -> y:S eq(apply(t:S,s:S),apply(t':S,s':S)) -> and(eq(t:S,t':S),eq(s:S,s':S)) eq(apply(t:S,s:S),lambda(x:S,t:S)) -> ffalse eq(apply(t:S,s:S),var(l:S)) -> ffalse eq(cons(t:S,l:S),cons(t':S,l':S)) -> and(eq(t:S,t':S),eq(l:S,l':S)) eq(cons(t:S,l:S),nil) -> ffalse eq(lambda(x:S,t:S),apply(t:S,s:S)) -> ffalse eq(lambda(x:S,t:S),lambda(x':S,t':S)) -> and(eq(x:S,x':S),eq(t:S,t':S)) eq(lambda(x:S,t:S),var(l:S)) -> ffalse eq(nil,cons(t:S,l:S)) -> ffalse eq(nil,nil) -> ttrue eq(var(l:S),apply(t:S,s:S)) -> ffalse eq(var(l:S),lambda(x:S,t:S)) -> ffalse eq(var(l:S),var(l':S)) -> eq(l:S,l':S) if(ffalse,var(k:S),var(l':S)) -> var(l':S) if(ttrue,var(k:S),var(l':S)) -> var(k:S) ren(var(l:S),var(k:S),var(l':S)) -> if(eq(l:S,l':S),var(k:S),var(l':S)) ren(x:S,y:S,apply(t:S,s:S)) -> apply(ren(x:S,y:S,t:S),ren(x:S,y:S,s:S)) ren(x:S,y:S,lambda(z:S,t:S)) -> lambda(var(cons(x:S,cons(y:S,cons(lambda(z:S,t:S),nil)))),ren(x:S,y:S,ren(z:S,var(cons(x:S,cons(y:S,cons(lambda(z:S,t:S),nil)))),t:S))) ) Problem 1: Innermost Equivalent Processor: -> Rules: and(ffalse,y:S) -> ffalse and(ttrue,y:S) -> y:S eq(apply(t:S,s:S),apply(t':S,s':S)) -> and(eq(t:S,t':S),eq(s:S,s':S)) eq(apply(t:S,s:S),lambda(x:S,t:S)) -> ffalse eq(apply(t:S,s:S),var(l:S)) -> ffalse eq(cons(t:S,l:S),cons(t':S,l':S)) -> and(eq(t:S,t':S),eq(l:S,l':S)) eq(cons(t:S,l:S),nil) -> ffalse eq(lambda(x:S,t:S),apply(t:S,s:S)) -> ffalse eq(lambda(x:S,t:S),lambda(x':S,t':S)) -> and(eq(x:S,x':S),eq(t:S,t':S)) eq(lambda(x:S,t:S),var(l:S)) -> ffalse eq(nil,cons(t:S,l:S)) -> ffalse eq(nil,nil) -> ttrue eq(var(l:S),apply(t:S,s:S)) -> ffalse eq(var(l:S),lambda(x:S,t:S)) -> ffalse eq(var(l:S),var(l':S)) -> eq(l:S,l':S) if(ffalse,var(k:S),var(l':S)) -> var(l':S) if(ttrue,var(k:S),var(l':S)) -> var(k:S) ren(var(l:S),var(k:S),var(l':S)) -> if(eq(l:S,l':S),var(k:S),var(l':S)) ren(x:S,y:S,apply(t:S,s:S)) -> apply(ren(x:S,y:S,t:S),ren(x:S,y:S,s:S)) ren(x:S,y:S,lambda(z:S,t:S)) -> lambda(var(cons(x:S,cons(y:S,cons(lambda(z:S,t:S),nil)))),ren(x:S,y:S,ren(z:S,var(cons(x:S,cons(y:S,cons(lambda(z:S,t:S),nil)))),t:S))) -> The term rewriting system is non-overlaping or locally confluent overlay system. Therefore, innermost termination implies termination. Problem 1: Dependency Pairs Processor: -> Pairs: EQ(apply(t:S,s:S),apply(t':S,s':S)) -> AND(eq(t:S,t':S),eq(s:S,s':S)) EQ(apply(t:S,s:S),apply(t':S,s':S)) -> EQ(s:S,s':S) EQ(apply(t:S,s:S),apply(t':S,s':S)) -> EQ(t:S,t':S) EQ(cons(t:S,l:S),cons(t':S,l':S)) -> AND(eq(t:S,t':S),eq(l:S,l':S)) EQ(cons(t:S,l:S),cons(t':S,l':S)) -> EQ(l:S,l':S) EQ(cons(t:S,l:S),cons(t':S,l':S)) -> EQ(t:S,t':S) EQ(lambda(x:S,t:S),lambda(x':S,t':S)) -> AND(eq(x:S,x':S),eq(t:S,t':S)) EQ(lambda(x:S,t:S),lambda(x':S,t':S)) -> EQ(t:S,t':S) EQ(lambda(x:S,t:S),lambda(x':S,t':S)) -> EQ(x:S,x':S) EQ(var(l:S),var(l':S)) -> EQ(l:S,l':S) REN(var(l:S),var(k:S),var(l':S)) -> EQ(l:S,l':S) REN(var(l:S),var(k:S),var(l':S)) -> IF(eq(l:S,l':S),var(k:S),var(l':S)) REN(x:S,y:S,apply(t:S,s:S)) -> REN(x:S,y:S,s:S) REN(x:S,y:S,apply(t:S,s:S)) -> REN(x:S,y:S,t:S) REN(x:S,y:S,lambda(z:S,t:S)) -> REN(x:S,y:S,ren(z:S,var(cons(x:S,cons(y:S,cons(lambda(z:S,t:S),nil)))),t:S)) REN(x:S,y:S,lambda(z:S,t:S)) -> REN(z:S,var(cons(x:S,cons(y:S,cons(lambda(z:S,t:S),nil)))),t:S) -> Rules: and(ffalse,y:S) -> ffalse and(ttrue,y:S) -> y:S eq(apply(t:S,s:S),apply(t':S,s':S)) -> and(eq(t:S,t':S),eq(s:S,s':S)) eq(apply(t:S,s:S),lambda(x:S,t:S)) -> ffalse eq(apply(t:S,s:S),var(l:S)) -> ffalse eq(cons(t:S,l:S),cons(t':S,l':S)) -> and(eq(t:S,t':S),eq(l:S,l':S)) eq(cons(t:S,l:S),nil) -> ffalse eq(lambda(x:S,t:S),apply(t:S,s:S)) -> ffalse eq(lambda(x:S,t:S),lambda(x':S,t':S)) -> and(eq(x:S,x':S),eq(t:S,t':S)) eq(lambda(x:S,t:S),var(l:S)) -> ffalse eq(nil,cons(t:S,l:S)) -> ffalse eq(nil,nil) -> ttrue eq(var(l:S),apply(t:S,s:S)) -> ffalse eq(var(l:S),lambda(x:S,t:S)) -> ffalse eq(var(l:S),var(l':S)) -> eq(l:S,l':S) if(ffalse,var(k:S),var(l':S)) -> var(l':S) if(ttrue,var(k:S),var(l':S)) -> var(k:S) ren(var(l:S),var(k:S),var(l':S)) -> if(eq(l:S,l':S),var(k:S),var(l':S))
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