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TRS Equational pair #487092771
details
property
value
status
complete
benchmark
bag-sum-prod-bin.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n141.star.cs.uiowa.edu
space
Mixed_AC
run statistics
property
value
solver
muterm 5.18
configuration
default
runtime (wallclock)
3.43162 seconds
cpu usage
2.94709
user time
2.03639
system time
0.910702
max virtual memory
693148.0
max residence set size
11636.0
stage attributes
key
value
starexec-result
YES
output
YES Problem 1: (VAR b x y) (THEORY (AC * + U)) (RULES *(0(x),y) -> 0(*(x,y)) *(#,x) -> # *(1(x),y) -> +(0(*(x,y)),y) +(0(x),0(y)) -> 0(+(x,y)) +(0(x),1(y)) -> 1(+(x,y)) +(#,x) -> x +(1(x),1(y)) -> 0(+(1(#),+(x,y))) 0(#) -> # U(empty,b) -> b prod(U(x,y)) -> *(prod(x),prod(y)) prod(empty) -> 1(#) prod(singl(x)) -> x sum(U(x,y)) -> +(sum(x),sum(y)) sum(empty) -> 0(#) sum(singl(x)) -> x ) Problem 1: Dependency Pairs Processor: -> FAxioms: *#(*(x3,x4),x5) = *#(x3,*(x4,x5)) *#(x3,x4) = *#(x4,x3) +#(+(x3,x4),x5) = +#(x3,+(x4,x5)) +#(x3,x4) = +#(x4,x3) U#(U(x3,x4),x5) = U#(x3,U(x4,x5)) U#(x3,x4) = U#(x4,x3) -> Pairs: *#(*(0(x),y),x3) -> *#(0(*(x,y)),x3) *#(*(0(x),y),x3) -> *#(x,y) *#(*(0(x),y),x3) -> 0#(*(x,y)) *#(*(#,x),x3) -> *#(#,x3) *#(*(1(x),y),x3) -> *#(+(0(*(x,y)),y),x3) *#(*(1(x),y),x3) -> *#(x,y) *#(*(1(x),y),x3) -> +#(0(*(x,y)),y) *#(*(1(x),y),x3) -> 0#(*(x,y)) *#(0(x),y) -> *#(x,y) *#(0(x),y) -> 0#(*(x,y)) *#(1(x),y) -> *#(x,y) *#(1(x),y) -> +#(0(*(x,y)),y) *#(1(x),y) -> 0#(*(x,y)) +#(+(0(x),0(y)),x3) -> +#(0(+(x,y)),x3) +#(+(0(x),0(y)),x3) -> +#(x,y) +#(+(0(x),0(y)),x3) -> 0#(+(x,y)) +#(+(0(x),1(y)),x3) -> +#(1(+(x,y)),x3) +#(+(0(x),1(y)),x3) -> +#(x,y) +#(+(#,x),x3) -> +#(x,x3) +#(+(1(x),1(y)),x3) -> +#(0(+(1(#),+(x,y))),x3) +#(+(1(x),1(y)),x3) -> +#(1(#),+(x,y)) +#(+(1(x),1(y)),x3) -> +#(x,y) +#(+(1(x),1(y)),x3) -> 0#(+(1(#),+(x,y))) +#(0(x),0(y)) -> +#(x,y) +#(0(x),0(y)) -> 0#(+(x,y)) +#(0(x),1(y)) -> +#(x,y) +#(1(x),1(y)) -> +#(1(#),+(x,y)) +#(1(x),1(y)) -> +#(x,y) +#(1(x),1(y)) -> 0#(+(1(#),+(x,y))) U#(U(empty,b),x3) -> U#(b,x3) PROD(U(x,y)) -> *#(prod(x),prod(y)) PROD(U(x,y)) -> PROD(x) PROD(U(x,y)) -> PROD(y) SUM(U(x,y)) -> +#(sum(x),sum(y)) SUM(U(x,y)) -> SUM(x) SUM(U(x,y)) -> SUM(y) SUM(empty) -> 0#(#) -> EAxioms: *(*(x3,x4),x5) = *(x3,*(x4,x5)) *(x3,x4) = *(x4,x3) +(+(x3,x4),x5) = +(x3,+(x4,x5)) +(x3,x4) = +(x4,x3) U(U(x3,x4),x5) = U(x3,U(x4,x5)) U(x3,x4) = U(x4,x3) -> Rules: *(0(x),y) -> 0(*(x,y)) *(#,x) -> # *(1(x),y) -> +(0(*(x,y)),y) +(0(x),0(y)) -> 0(+(x,y)) +(0(x),1(y)) -> 1(+(x,y)) +(#,x) -> x +(1(x),1(y)) -> 0(+(1(#),+(x,y))) 0(#) -> # U(empty,b) -> b prod(U(x,y)) -> *(prod(x),prod(y)) prod(empty) -> 1(#) prod(singl(x)) -> x sum(U(x,y)) -> +(sum(x),sum(y)) sum(empty) -> 0(#) sum(singl(x)) -> x -> SRules: *#(*(x3,x4),x5) -> *#(x3,x4) *#(x3,*(x4,x5)) -> *#(x4,x5) +#(+(x3,x4),x5) -> +#(x3,x4)
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