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TRS Equational pair #487092798
details
property
value
status
complete
benchmark
differ.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n150.star.cs.uiowa.edu
space
Mixed_AC
run statistics
property
value
solver
muterm 5.18
configuration
default
runtime (wallclock)
0.760121 seconds
cpu usage
0.649227
user time
0.410106
system time
0.239121
max virtual memory
433812.0
max residence set size
4912.0
stage attributes
key
value
starexec-result
YES
output
YES Problem 1: (VAR f g) (THEORY (AC * +)) (RULES dx(*(f,g)) -> +(*(dx(f),g),*(dx(g),f)) dx(+(f,g)) -> +(dx(f),dx(g)) dx(-(f,g)) -> -(dx(f),dx(g)) dx(/(f,g)) -> -(/(dx(f),g),/(*(dx(g),f),exp(g,2))) dx(0) -> 0 dx(1) -> 0 dx(X) -> 1 dx(a) -> 0 dx(exp(f,g)) -> +(*(dx(f),*(exp(f,-(g,1)),g)),*(dx(g),*(exp(f,g),ln(f)))) dx(ln(f)) -> /(dx(f),f) dx(neg(f)) -> neg(dx(f)) ) Problem 1: Dependency Pairs Processor: -> FAxioms: *#(*(x2,x3),x4) = *#(x2,*(x3,x4)) *#(x2,x3) = *#(x3,x2) +#(+(x2,x3),x4) = +#(x2,+(x3,x4)) +#(x2,x3) = +#(x3,x2) -> Pairs: DX(*(f,g)) -> DX(f) DX(*(f,g)) -> DX(g) DX(+(f,g)) -> DX(f) DX(+(f,g)) -> DX(g) DX(-(f,g)) -> DX(f) DX(-(f,g)) -> DX(g) DX(/(f,g)) -> DX(f) DX(/(f,g)) -> DX(g) DX(exp(f,g)) -> DX(f) DX(exp(f,g)) -> DX(g) DX(ln(f)) -> DX(f) DX(neg(f)) -> DX(f) -> EAxioms: *(*(x2,x3),x4) = *(x2,*(x3,x4)) *(x2,x3) = *(x3,x2) +(+(x2,x3),x4) = +(x2,+(x3,x4)) +(x2,x3) = +(x3,x2) -> Rules: dx(*(f,g)) -> +(*(dx(f),g),*(dx(g),f)) dx(+(f,g)) -> +(dx(f),dx(g)) dx(-(f,g)) -> -(dx(f),dx(g)) dx(/(f,g)) -> -(/(dx(f),g),/(*(dx(g),f),exp(g,2))) dx(0) -> 0 dx(1) -> 0 dx(X) -> 1 dx(a) -> 0 dx(exp(f,g)) -> +(*(dx(f),*(exp(f,-(g,1)),g)),*(dx(g),*(exp(f,g),ln(f)))) dx(ln(f)) -> /(dx(f),f) dx(neg(f)) -> neg(dx(f)) -> SRules: *#(*(x2,x3),x4) -> *#(x2,x3) *#(x2,*(x3,x4)) -> *#(x3,x4) +#(+(x2,x3),x4) -> +#(x2,x3) +#(x2,+(x3,x4)) -> +#(x3,x4) Problem 1: SCC Processor: -> FAxioms: *#(*(x2,x3),x4) = *#(x2,*(x3,x4)) *#(x2,x3) = *#(x3,x2) +#(+(x2,x3),x4) = +#(x2,+(x3,x4)) +#(x2,x3) = +#(x3,x2) -> Pairs: DX(*(f,g)) -> DX(f) DX(*(f,g)) -> DX(g) DX(+(f,g)) -> DX(f) DX(+(f,g)) -> DX(g) DX(-(f,g)) -> DX(f) DX(-(f,g)) -> DX(g) DX(/(f,g)) -> DX(f) DX(/(f,g)) -> DX(g) DX(exp(f,g)) -> DX(f) DX(exp(f,g)) -> DX(g) DX(ln(f)) -> DX(f) DX(neg(f)) -> DX(f) -> EAxioms: *(*(x2,x3),x4) = *(x2,*(x3,x4)) *(x2,x3) = *(x3,x2) +(+(x2,x3),x4) = +(x2,+(x3,x4)) +(x2,x3) = +(x3,x2) -> Rules: dx(*(f,g)) -> +(*(dx(f),g),*(dx(g),f)) dx(+(f,g)) -> +(dx(f),dx(g)) dx(-(f,g)) -> -(dx(f),dx(g)) dx(/(f,g)) -> -(/(dx(f),g),/(*(dx(g),f),exp(g,2))) dx(0) -> 0 dx(1) -> 0 dx(X) -> 1 dx(a) -> 0
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